Cool DZ white dwarfs I: Identification and spectral analysis

TL;DR

This study identifies and analyzes 231 cool DZ white dwarfs with metal lines from SDSS data, revealing their properties and potential planetary system remnants, with 104 being newly discovered.

Contribution

It provides an improved spectral analysis of DZ white dwarfs using updated models, extending the known sample and characterizing their properties and kinematics.

Findings

Identified 231 cool DZ white dwarfs, including 104 new discoveries.

Derived effective temperatures and metal abundances using improved models.

Detected halo white dwarfs with high tangential velocities.

Abstract

White dwarfs with metal lines in their spectra act as signposts for post-main sequence planetary systems. Searching the Sloan Digital Sky Survey (SDSS) data release 12, we have identified 231 cool (<9000 K) DZ white dwarfs with strong metal absorption, extending the DZ cooling sequence to both higher metal abundances, lower temperatures, and hence longer cooler ages. Of these 231 systems, 104 are previously unknown white dwarfs. Compared with previous work, our spectral fitting uses improved model atmospheres with updated line profiles and line-lists, which we use to derive effective temperatures and abundances for up to 8 elements. We also determine spectroscopic distances to our sample, identifying two halo-members with tangential space-velocities >300 kms-1. The implications of our results on remnant planetary systems are to be discussed in a separate paper.

Figures

Tables

Table 1. Table 1: Coordinates, SDSS spectral identifiers, and photometry for the ultracool white dwarfs we have serendipitously discovered.

SDSS J	Plate-MJD-Fib	$u$ [mag]	$g$ [mag]	$r$ [mag]	$i$ [mag]	$z$ [mag]	Ref.
003908.33$+$303538.9	6526-56543-0006	$21.731\pm 0.260$	$20.397\pm 0.038$	$20.449\pm 0.047$	$20.975\pm 0.096$	$21.159\pm 0.445$
025754.92$+$042807.5	4256-55477-0926	$22.725\pm 0.338$	$21.154\pm 0.040$	$20.650\pm 0.045$	$21.067\pm 0.076$	$21.207\pm 0.263$
100103.42$+$390340.4	1356-53033-0280	$21.303\pm 0.118$	$20.017\pm 0.030$	$19.587\pm 0.021$	$19.956\pm 0.042$	$20.524\pm 0.236$	1
133739.40$+$000142.8	0299-51671-0357	$20.795\pm 0.054$	$19.546\pm 0.022$	$19.138\pm 0.021$	$19.521\pm 0.023$	$20.022\pm 0.088$	2
140237.31$+$080519.1	4863-55688-0792	$21.960\pm 0.195$	$21.419\pm 0.055$	$21.331\pm 0.060$	$21.513\pm 0.131$	$20.966\pm 0.186$
144440.01$+$631924.4	6983-56447-0685	$21.729\pm 0.120$	$20.375\pm 0.031$	$20.223\pm 0.030$	$20.081\pm 0.036$	$20.137\pm 0.130$
170320.12$+$271106.8	5013-55723-0128	$22.500\pm 0.183$	$21.428\pm 0.037$	$20.841\pm 0.032$	$21.164\pm 0.064$	$21.158\pm 0.231$
225817.87$+$012811.1	4290-55527-0290	$21.102\pm 0.096$	$19.828\pm 0.026$	$19.626\pm 0.021$	$20.077\pm 0.032$	$20.528\pm 0.152$
231130.14$+$283444.8	6292-56566-0964	$22.677\pm 0.205$	$21.143\pm 0.029$	$20.958\pm 0.035$	$21.270\pm 0.055$	$21.100\pm 0.179$
234931.16$-$080245.6	7146-56573-0460	$22.432\pm 0.429$	$21.034\pm 0.038$	$20.822\pm 0.050$	$20.972\pm 0.081$	$20.399\pm 0.176$

Table 2. Table 2: Breakdown of methods 1 & 2 for the visually inspected SDSS spectra. For each spectral type, the number / number format indicates the total spectra, and the number of unique systems respectively.

Method	1	2
Main-sequence stars	29545/27660	6645/6253
Carbon stars	148/126	15/12
Quasars	4477/3575	2013/1895
Galaxies	128/123	9/9
WDMS binaries	33/30	0/0
Cool DZ WDs	126/103	291/229
Other WDs	61/59	773/715
Unclassifiable spectra	54/52	808/784
Total	34572/31728	10554/9897

Table 3. Table 5: SDSS PSF photometry for all white dwarfs in our sample. Plate-MJD-fib indicates the SDSS spectrum we used for fitting. N SDSS subscript 𝑁 SDSS N_{\mathrm{SDSS}} is the number of SDSS spectra available per object.

SDSS J	Plate-MJD-Fib	$N_{\mathrm{SDSS}}$	$u$	$g$	$r$	$i$	$z$
000215.64$+$320914.1	7144-56564-126	2	$21.830\pm 0.120$	$20.530\pm 0.024$	$20.346\pm 0.022$	$20.381\pm 0.034$	$20.329\pm 0.114$
000418.68$+$081929.9	4534-55863-333	1	$24.871\pm 0.704$	$22.133\pm 0.067$	$21.648\pm 0.058$	$21.757\pm 0.092$	$21.701\pm 0.299$
000614.53$+$052039.0	4415-55831-160	1	$22.142\pm 0.261$	$20.507\pm 0.029$	$20.240\pm 0.035$	$20.154\pm 0.046$	$20.282\pm 0.200$
001052.56$-$043014.3	7035-56568-898	1	$21.553\pm 0.137$	$20.317\pm 0.028$	$20.112\pm 0.025$	$20.218\pm 0.040$	$20.285\pm 0.123$
001309.43$+$110949.0	5648-55923-842	1	$23.397\pm 0.488$	$21.612\pm 0.049$	$21.263\pm 0.054$	$21.373\pm 0.095$	$21.537\pm 0.339$
001949.25$+$220926.5	6175-56265-833	1	$21.948\pm 0.217$	$20.394\pm 0.043$	$19.958\pm 0.035$	$20.043\pm 0.041$	$20.140\pm 0.202$
003708.41$-$052532.7	7039-56572-140	2	$22.933\pm 0.388$	$20.087\pm 0.027$	$19.634\pm 0.024$	$19.682\pm 0.024$	$19.784\pm 0.070$
004451.68$+$041819.2	4305-55509-609	1	$19.902\pm 0.042$	$18.773\pm 0.020$	$18.486\pm 0.019$	$18.459\pm 0.022$	$18.564\pm 0.035$
004634.22$+$271737.6	6253-56574-458	1	$21.139\pm 0.109$	$20.372\pm 0.026$	$20.258\pm 0.032$	$20.412\pm 0.051$	$20.780\pm 0.290$
004757.06$+$162836.5	6204-56220-386	1	$25.126\pm 0.786$	$20.865\pm 0.036$	$20.393\pm 0.033$	$20.518\pm 0.041$	$20.380\pm 0.141$
005247.16$+$184649.5	5702-56221-615	1	$25.922\pm 0.716$	$21.571\pm 0.073$	$21.118\pm 0.057$	$21.062\pm 0.069$	$20.745\pm 0.172$
005304.14$+$311555.8	6872-56540-171	1	$22.704\pm 0.512$	$21.298\pm 0.048$	$21.056\pm 0.052$	$21.105\pm 0.080$	$21.141\pm 0.298$
005649.27$+$245335.4	6278-56266-122	1	$24.797\pm 0.853$	$21.536\pm 0.049$	$21.009\pm 0.041$	$20.948\pm 0.059$	$21.431\pm 0.341$
010728.47$+$265019.9	6255-56240-896	1	$23.268\pm 0.643$	$19.359\pm 0.022$	$18.828\pm 0.015$	$18.671\pm 0.018$	$18.783\pm 0.050$
010825.79$-$053755.6	7045-56577-456	2	$22.046\pm 0.215$	$20.392\pm 0.031$	$20.124\pm 0.024$	$20.021\pm 0.048$	$20.363\pm 0.109$
011421.17$+$350547.1	6598-56574-832	1	$23.250\pm 0.578$	$20.958\pm 0.031$	$20.596\pm 0.033$	$20.659\pm 0.051$	$20.387\pm 0.138$
011646.10$+$205001.9	5134-55868-352	1	$19.883\pm 0.033$	$18.209\pm 0.018$	$17.987\pm 0.010$	$18.081\pm 0.014$	$18.187\pm 0.027$
011759.83$+$002138.3	4227-55481-937	2	$20.192\pm 0.047$	$19.316\pm 0.028$	$19.116\pm 0.017$	$19.169\pm 0.022$	$19.368\pm 0.059$
012620.47$+$253433.6	5694-56213-606	1	$22.651\pm 0.531$	$20.639\pm 0.041$	$20.205\pm 0.036$	$20.101\pm 0.040$	$20.308\pm 0.155$
013504.11$+$130240.4	4661-55614-318	2	$20.842\pm 0.073$	$19.311\pm 0.022$	$18.997\pm 0.019$	$18.932\pm 0.019$	$18.985\pm 0.054$
014300.52$+$011356.8	4231-55444-824	4	$20.313\pm 0.053$	$19.410\pm 0.033$	$19.215\pm 0.029$	$19.235\pm 0.021$	$19.403\pm 0.056$
014415.12$+$192021.4	5121-55856-186	1	$24.291\pm 1.603$	$20.690\pm 0.049$	$20.398\pm 0.043$	$20.339\pm 0.063$	$20.364\pm 0.184$
014441.64$+$030536.2	4272-55509-246	1	$22.806\pm 0.304$	$21.302\pm 0.040$	$21.166\pm 0.049$	$21.218\pm 0.074$	$21.379\pm 0.298$
014834.00$-$011235.9	4232-55447-294	2	$21.808\pm 0.118$	$20.752\pm 0.029$	$20.610\pm 0.033$	$20.644\pm 0.043$	$20.683\pm 0.133$
015008.55$+$135433.9	1899-53262-118	1	$21.033\pm 0.079$	$20.152\pm 0.026$	$19.919\pm 0.026$	$19.887\pm 0.030$	$19.849\pm 0.098$
015748.14$+$003315.0	0700-52199-627	1	$21.299\pm 0.074$	$19.591\pm 0.023$	$19.189\pm 0.017$	$19.213\pm 0.020$	$19.359\pm 0.050$
015849.02$-$094225.3	7184-56629-144	1	$21.663\pm 0.169$	$20.408\pm 0.033$	$20.199\pm 0.026$	$20.200\pm 0.038$	$20.472\pm 0.166$
020018.74$+$164631.0	5119-55836-838	1	$22.587\pm 0.259$	$20.891\pm 0.033$	$20.391\pm 0.030$	$20.492\pm 0.047$	$20.489\pm 0.151$
020128.66$+$201521.8	5110-55913-721	1	$21.714\pm 0.236$	$20.392\pm 0.034$	$20.040\pm 0.035$	$20.183\pm 0.069$	$20.325\pm 0.178$
020809.93$-$054258.3	4398-55946-982	1	$23.635\pm 0.773$	$21.179\pm 0.056$	$20.786\pm 0.043$	$20.739\pm 0.051$	$20.836\pm 0.191$
023407.46$-$051028.1	4399-55811-626	1	$22.605\pm 0.301$	$21.103\pm 0.044$	$20.885\pm 0.042$	$20.979\pm 0.066$	$21.010\pm 0.257$
025206.06$-$040130.3	7054-56575-682	1	$21.424\pm 0.117$	$20.280\pm 0.027$	$20.095\pm 0.024$	$20.212\pm 0.035$	$20.423\pm 0.134$
025253.19$+$005439.4	0708-52175-411	1	$20.636\pm 0.055$	$19.863\pm 0.030$	$19.784\pm 0.017$	$19.834\pm 0.025$	$19.950\pm 0.076$
044751.20$+$112403.7	2673-54096-587	1	$21.231\pm 0.088$	$20.364\pm 0.022$	$20.065\pm 0.023$	$19.981\pm 0.028$	$20.124\pm 0.106$
051212.78$-$050503.4		0	$20.722\pm 0.155$	$17.913\pm 0.017$	$17.437\pm 0.017$	$17.424\pm 0.017$	$17.492\pm 0.021$
072144.23$+$392843.3	3655-55240-286	1	$22.767\pm 0.431$	$20.555\pm 0.029$	$20.282\pm 0.039$	$20.383\pm 0.053$	$20.341\pm 0.160$
073549.19$+$205720.9	4480-55591-432	1	$23.084\pm 0.344$	$20.527\pm 0.025$	$19.979\pm 0.020$	$19.922\pm 0.024$	$20.089\pm 0.092$
073635.22$+$411828.1	3664-55245-628	1	$25.470\pm 0.604$	$20.317\pm 0.025$	$19.418\pm 0.026$	$19.272\pm 0.050$	$19.313\pm 0.058$
073953.46$+$311204.2	4448-55538-588	1	$23.832\pm 0.605$	$21.377\pm 0.043$	$20.778\pm 0.037$	$20.652\pm 0.043$	$20.441\pm 0.169$
074153.45$+$314620.4	4443-55539-251	1	$22.581\pm 0.227$	$20.501\pm 0.028$	$20.125\pm 0.022$	$20.120\pm 0.026$	$20.189\pm 0.076$
074414.66$+$464912.5	3665-55247-106	2	$23.021\pm 0.344$	$19.473\pm 0.028$	$18.517\pm 0.012$	$18.316\pm 0.016$	$18.261\pm 0.026$
074444.03$+$440845.6	3671-55483-294	1	$22.612\pm 0.290$	$21.176\pm 0.037$	$21.010\pm 0.052$	$20.978\pm 0.067$	$21.210\pm 0.349$
074450.24$+$270132.6	4462-55600-836	1	$20.980\pm 0.075$	$20.278\pm 0.026$	$20.180\pm 0.030$	$20.410\pm 0.043$	$20.493\pm 0.167$
074456.21$+$164041.8	4492-55565-292	1	$24.635\pm 0.898$	$20.880\pm 0.029$	$20.185\pm 0.022$	$20.027\pm 0.024$	$20.067\pm 0.080$
075853.46$+$101347.4	4510-55559-490	1	$23.820\pm 0.726$	$21.418\pm 0.044$	$20.711\pm 0.032$	$20.751\pm 0.045$	$20.956\pm 0.196$
080003.90$+$224210.1	4471-55617-740	1	$22.321\pm 0.224$	$20.712\pm 0.029$	$20.587\pm 0.040$	$20.561\pm 0.039$	$20.742\pm 0.191$
080626.70$+$305555.7	3755-55504-120	1	$22.001\pm 0.153$	$20.670\pm 0.029$	$20.495\pm 0.027$	$20.598\pm 0.038$	$20.629\pm 0.115$
080643.94$+$405837.7	3803-55513-734	1	$20.563\pm 0.055$	$19.078\pm 0.018$	$18.771\pm 0.015$	$18.773\pm 0.017$	$18.863\pm 0.044$
080740.69$+$493059.7	3684-55246-924	1	$25.311\pm 0.993$	$21.308\pm 0.052$	$20.522\pm 0.036$	$20.330\pm 0.043$	$20.193\pm 0.142$
081606.19$+$233030.1	4468-55894-462	1	$22.021\pm 0.234$	$20.958\pm 0.033$	$20.818\pm 0.035$	$21.073\pm 0.057$	$20.871\pm 0.181$
081828.12$+$124717.2	4504-55571-200	1	$22.060\pm 0.196$	$21.000\pm 0.034$	$20.853\pm 0.039$	$21.021\pm 0.063$	$21.231\pm 0.276$
082303.82$+$054656.1		0	$19.526\pm 0.033$	$17.500\pm 0.014$	$17.155\pm 0.013$	$17.179\pm 0.016$	$17.261\pm 0.022$
083033.65$-$031911.0	2828-54438-401	1	$20.794\pm 0.080$	$19.687\pm 0.016$	$19.491\pm 0.019$	$19.555\pm 0.027$	$19.680\pm 0.112$
083200.38$+$410937.9	3808-55513-148	1	$23.623\pm 0.794$	$21.321\pm 0.050$	$20.631\pm 0.033$	$20.695\pm 0.045$	$20.755\pm 0.138$
083858.56$+$232252.9	3373-54940-462	2	$20.187\pm 0.046$	$19.212\pm 0.020$	$18.860\pm 0.015$	$18.819\pm 0.017$	$18.835\pm 0.036$
084223.14$+$140615.9	2427-53815-040	2	$19.286\pm 0.027$	$18.312\pm 0.022$	$18.166\pm 0.026$	$18.271\pm 0.018$	$18.439\pm 0.028$
084239.85$+$153628.8	5286-56225-336	1	$22.017\pm 0.136$	$20.761\pm 0.037$	$20.479\pm 0.036$	$20.451\pm 0.052$	$20.365\pm 0.131$
084300.22$+$561452.8	5153-56577-159	1	$21.822\pm 0.187$	$20.522\pm 0.037$	$20.306\pm 0.034$	$20.377\pm 0.051$	$20.407\pm 0.186$
085100.23$+$154301.6	5292-55926-402	2	$20.282\pm 0.053$	$19.033\pm 0.014$	$18.726\pm 0.020$	$18.785\pm 0.033$	$18.844\pm 0.052$
085217.60$+$340211.3	4602-55644-366	2	$23.720\pm 0.564$	$21.253\pm 0.041$	$20.438\pm 0.028$	$20.434\pm 0.035$	$20.124\pm 0.090$
090146.86$+$075206.8	4868-55895-702	1	$21.541\pm 0.115$	$20.012\pm 0.020$	$19.800\pm 0.021$	$19.903\pm 0.030$	$20.047\pm 0.126$
090222.98$+$362539.6	4645-55623-596	2	$22.577\pm 0.321$	$20.752\pm 0.032$	$20.462\pm 0.038$	$20.363\pm 0.056$	$20.495\pm 0.222$
090244.75$+$100459.6	5296-55922-260	1	$21.335\pm 0.086$	$20.705\pm 0.026$	$20.620\pm 0.032$	$20.653\pm 0.048$	$20.649\pm 0.153$
090652.19$+$114149.9	5296-55922-944	1	$22.859\pm 0.265$	$20.958\pm 0.032$	$20.795\pm 0.035$	$20.823\pm 0.043$	$20.991\pm 0.160$
090803.35$+$513633.1	5729-56598-406	2	$20.845\pm 0.059$	$19.485\pm 0.021$	$19.255\pm 0.023$	$19.270\pm 0.020$	$19.402\pm 0.061$
090814.52$+$411918.3	4603-55999-334	1	$22.285\pm 0.180$	$21.154\pm 0.032$	$20.919\pm 0.036$	$20.990\pm 0.048$	$21.139\pm 0.205$
091322.38$+$262752.0	5779-56338-164	2	$22.789\pm 0.250$	$20.281\pm 0.038$	$19.786\pm 0.021$	$19.722\pm 0.026$	$19.618\pm 0.056$
091356.05$+$412728.6	4641-55947-678	1	$23.903\pm 0.532$	$21.074\pm 0.031$	$20.628\pm 0.029$	$20.742\pm 0.040$	$20.749\pm 0.132$
091621.36$+$254028.4	2087-53415-166	1	$21.256\pm 0.094$	$18.355\pm 0.014$	$17.473\pm 0.024$	$17.386\pm 0.018$	$17.526\pm 0.021$
092450.03$+$430136.4	4639-55944-860	1	$23.633\pm 0.353$	$21.111\pm 0.033$	$20.888\pm 0.032$	$20.817\pm 0.047$	$20.698\pm 0.143$
092523.09$+$313019.0	1938-53379-608	2	$21.030\pm 0.086$	$18.957\pm 0.021$	$18.606\pm 0.015$	$18.634\pm 0.016$	$18.750\pm 0.041$
092713.34$+$493109.3	5731-56363-684	1	$22.527\pm 0.199$	$21.095\pm 0.035$	$20.744\pm 0.029$	$20.883\pm 0.044$	$20.841\pm 0.152$
092932.49$+$424757.9	4639-55944-034	2	$21.622\pm 0.081$	$20.183\pm 0.031$	$19.914\pm 0.021$	$19.962\pm 0.031$	$20.190\pm 0.100$
093320.01$+$633441.2	7447-56746-366	1	$23.397\pm 0.350$	$21.111\pm 0.035$	$20.817\pm 0.047$	$20.905\pm 0.065$	$20.995\pm 0.280$
093719.14$+$522802.2	2404-53764-197	3	$20.732\pm 0.068$	$19.438\pm 0.023$	$19.168\pm 0.019$	$19.240\pm 0.025$	$19.449\pm 0.078$
093916.03$+$413612.9	4571-55629-621	1	$23.029\pm 0.336$	$20.568\pm 0.026$	$20.183\pm 0.026$	$20.210\pm 0.033$	$20.311\pm 0.120$
093944.58$+$501917.6	0901-52641-584	1	$22.920\pm 0.288$	$19.940\pm 0.018$	$19.484\pm 0.016$	$19.511\pm 0.018$	$19.657\pm 0.062$
094648.94$+$202423.2	5783-56017-824	2	$21.587\pm 0.097$	$20.825\pm 0.029$	$20.629\pm 0.030$	$20.853\pm 0.043$	$20.627\pm 0.140$
094813.73$+$300851.2	5801-56328-728	1	$21.615\pm 0.147$	$20.274\pm 0.031$	$20.034\pm 0.023$	$20.103\pm 0.032$	$20.131\pm 0.094$
095645.14$+$591240.6	0453-51915-621	1	$18.936\pm 0.027$	$18.387\pm 0.020$	$18.409\pm 0.013$	$18.559\pm 0.019$	$18.753\pm 0.037$
100346.66$-$003123.1	3783-55246-902	1	$22.909\pm 0.329$	$20.615\pm 0.030$	$20.059\pm 0.025$	$19.997\pm 0.029$	$20.203\pm 0.111$
100537.43$+$224403.1	6459-56273-144	1	$23.046\pm 0.325$	$21.356\pm 0.045$	$21.117\pm 0.042$	$21.275\pm 1.079$	$21.197\pm 0.215$
100609.15$+$175221.3	5332-55981-544	1	$22.401\pm 0.189$	$20.663\pm 0.041$	$20.179\pm 0.031$	$20.156\pm 0.035$	$20.118\pm 0.106$
101451.15$+$282701.6	6462-56326-444	1	$23.453\pm 0.517$	$21.252\pm 0.042$	$20.701\pm 0.051$	$20.824\pm 0.059$	$21.151\pm 0.282$
101711.53$+$344710.5	4568-55600-124	2	$21.642\pm 0.123$	$20.452\pm 0.027$	$20.247\pm 0.032$	$20.233\pm 0.038$	$20.135\pm 0.115$
101750.24$+$241911.6	6465-56279-332	1	$21.217\pm 0.082$	$19.889\pm 0.026$	$19.768\pm 0.024$	$19.812\pm 0.026$	$19.839\pm 0.086$
101924.73$+$353527.6	4564-55570-466	2	$22.920\pm 0.408$	$21.210\pm 0.040$	$20.889\pm 0.044$	$21.017\pm 0.059$	$21.076\pm 0.215$
101959.51$+$204553.4	5872-56027-268	1	$23.411\pm 0.430$	$21.049\pm 0.037$	$20.583\pm 0.031$	$20.547\pm 0.043$	$20.356\pm 0.102$
102414.83$+$453109.9	6659-56607-412	1	$21.735\pm 0.156$	$20.322\pm 0.034$	$20.038\pm 0.032$	$20.009\pm 0.032$	$20.190\pm 0.108$
102438.05$+$101410.5	1598-53033-081	1	$23.057\pm 0.385$	$20.591\pm 0.029$	$20.031\pm 0.026$	$20.129\pm 0.053$	$20.186\pm 0.129$
103205.15$+$133833.4	5343-55999-834	1	$24.857\pm 0.782$	$21.195\pm 0.038$	$20.784\pm 0.039$	$20.617\pm 0.052$	$21.316\pm 0.349$
103352.89$+$180935.3	2593-54175-225	1	$21.466\pm 0.109$	$19.810\pm 0.018$	$19.447\pm 0.022$	$19.462\pm 0.029$	$19.718\pm 0.104$
103809.19$-$003622.4	0274-51913-265	1	$17.714\pm 0.013$	$17.006\pm 0.020$	$16.942\pm 0.014$	$17.084\pm 0.013$	$17.313\pm 0.016$
103839.00$+$043223.8	4773-55648-618	1	$22.431\pm 0.241$	$20.665\pm 0.031$	$20.303\pm 0.031$	$20.305\pm 0.033$	$20.439\pm 0.140$
104046.48$+$240759.5	3250-54883-505	2	$21.521\pm 0.100$	$19.329\pm 0.018$	$18.829\pm 0.015$	$18.834\pm 0.017$	$18.995\pm 0.042$
104130.65$+$343240.7	4635-55615-408	2	$21.356\pm 0.108$	$20.625\pm 0.036$	$20.590\pm 0.037$	$20.643\pm 0.054$	$20.632\pm 0.206$
104319.84$+$351641.6	2025-53431-328	2	$20.651\pm 0.069$	$18.963\pm 0.017$	$18.648\pm 0.022$	$18.612\pm 0.017$	$18.672\pm 0.035$
104658.12$+$132911.3	5350-56009-118	2	$23.915\pm 0.630$	$20.698\pm 0.026$	$20.069\pm 0.026$	$20.005\pm 0.029$	$19.890\pm 0.082$
105533.73$+$372542.7	4630-55623-900	1	$22.756\pm 0.280$	$20.332\pm 0.031$	$19.751\pm 0.021$	$19.825\pm 0.026$	$19.965\pm 0.083$
105826.60$+$314358.3	6445-56366-988	2	$19.807\pm 0.039$	$19.093\pm 0.023$	$18.949\pm 0.022$	$19.012\pm 0.020$	$19.183\pm 0.058$
110216.09$+$282730.7	6435-56341-510	1	$23.454\pm 0.510$	$21.286\pm 0.047$	$20.868\pm 0.044$	$20.955\pm 0.073$	$20.873\pm 0.210$
110234.21$+$021459.2	3243-54910-298	2	$21.220\pm 0.077$	$19.525\pm 0.024$	$19.196\pm 0.020$	$19.165\pm 0.023$	$19.299\pm 0.063$
110304.15$+$414434.9	4620-55652-506	2	$21.677\pm 0.159$	$19.747\pm 0.022$	$19.397\pm 0.019$	$19.395\pm 0.022$	$19.421\pm 0.057$
110513.62$+$500652.6	6700-56384-146	1	$21.127\pm 0.100$	$20.252\pm 0.028$	$20.190\pm 0.024$	$20.312\pm 0.049$	$20.159\pm 0.140$
110556.17$+$022849.0	4741-55704-652	1	$22.056\pm 0.212$	$20.552\pm 0.034$	$20.174\pm 0.029$	$20.127\pm 0.038$	$19.889\pm 0.139$
110644.27$+$673708.6	7111-56741-676	1	$22.310\pm 0.258$	$20.113\pm 0.026$	$19.673\pm 0.023$	$19.731\pm 0.030$	$19.819\pm 0.098$
111215.05$+$070052.3	1004-52723-111	1	$20.179\pm 0.046$	$19.272\pm 0.018$	$19.243\pm 0.023$	$19.346\pm 0.021$	$19.414\pm 0.060$
111330.26$+$275131.4	6435-56341-036	1	$22.262\pm 0.167$	$20.751\pm 0.030$	$20.415\pm 0.031$	$20.501\pm 0.048$	$20.350\pm 0.144$
113209.59$+$332353.0	4619-55599-069	2	$24.582\pm 0.909$	$21.115\pm 0.044$	$20.756\pm 0.037$	$20.847\pm 0.057$	$21.036\pm 0.227$
113410.85$+$154245.9	5373-56010-938	1	$22.526\pm 0.220$	$21.132\pm 0.034$	$20.978\pm 0.043$	$21.031\pm 0.074$	$20.715\pm 0.212$
114333.46$+$661532.0	7114-56748-973	1	$22.386\pm 0.229$	$20.560\pm 0.027$	$20.013\pm 0.026$	$19.955\pm 0.035$	$20.128\pm 0.121$
114408.04$+$372007.8	4653-55622-700	1	$21.081\pm 0.076$	$20.292\pm 0.025$	$20.194\pm 0.031$	$20.290\pm 0.035$	$20.262\pm 0.133$
114441.92$+$121829.2	1608-53138-515	1	$20.715\pm 0.079$	$18.422\pm 0.017$	$17.849\pm 0.020$	$17.758\pm 0.019$	$17.762\pm 0.024$
114709.09$+$542940.8	6697-56419-035	1	$25.843\pm 0.540$	$21.547\pm 0.053$	$21.030\pm 0.049$	$20.923\pm 0.058$	$20.953\pm 0.257$
114944.94$+$051947.7	4848-55955-088	1	$20.503\pm 0.049$	$19.602\pm 0.024$	$19.480\pm 0.021$	$19.636\pm 0.020$	$19.736\pm 0.073$
115015.73$+$492843.7	6684-56412-006	1	$20.495\pm 0.067$	$19.956\pm 0.027$	$19.887\pm 0.028$	$19.928\pm 0.034$	$19.971\pm 0.105$
115029.52$+$453314.0	6642-56396-549	2	$24.280\pm 0.927$	$21.658\pm 0.057$	$21.066\pm 0.060$	$21.018\pm 0.068$	$20.982\pm 0.199$
115207.15$+$510126.2	6683-56416-348	1	$24.857\pm 0.807$	$21.438\pm 0.046$	$20.845\pm 0.040$	$20.698\pm 0.049$	$20.672\pm 0.165$
115224.51$+$160546.7	5383-56013-772	2	$21.733\pm 0.116$	$20.175\pm 0.025$	$19.952\pm 0.020$	$20.016\pm 0.032$	$20.076\pm 0.090$
115748.34$+$613845.9	7106-56663-173	1	$22.472\pm 0.391$	$21.420\pm 0.059$	$21.266\pm 0.064$	$21.244\pm 0.124$	$21.192\pm 0.415$
115809.38$+$184557.3	5881-56038-014	1	$21.550\pm 0.115$	$20.041\pm 0.025$	$19.883\pm 0.025$	$19.951\pm 0.029$	$20.109\pm 0.093$
115809.88$+$594210.3	7098-56661-152	1	$22.138\pm 0.189$	$20.593\pm 0.024$	$20.304\pm 0.024$	$20.295\pm 0.033$	$20.094\pm 0.110$
115818.76$+$045447.5	4747-55652-590	1	$23.094\pm 0.320$	$20.957\pm 0.035$	$20.255\pm 0.027$	$20.129\pm 0.028$	$20.274\pm 0.091$
115822.31$+$471214.9	6644-56384-812	1	$21.309\pm 0.088$	$20.666\pm 0.033$	$20.624\pm 0.037$	$20.716\pm 0.055$	$20.809\pm 0.219$
115844.35$+$544837.5	6839-56425-090	1	$22.781\pm 0.352$	$21.020\pm 0.042$	$20.774\pm 0.042$	$20.797\pm 0.058$	$20.772\pm 0.237$
120548.97$+$353642.4	4610-55621-722	2	$24.075\pm 1.094$	$20.393\pm 0.034$	$20.095\pm 0.035$	$20.110\pm 0.047$	$20.398\pm 0.141$
121106.42$+$232623.0	5974-56314-668	1	$22.285\pm 0.294$	$20.796\pm 0.034$	$20.524\pm 0.042$	$20.561\pm 0.056$	$20.489\pm 0.136$
121456.39$-$023402.7	0333-52313-399	1	$20.872\pm 0.062$	$18.324\pm 0.017$	$17.749\pm 0.013$	$17.561\pm 0.012$	$17.509\pm 0.021$
121731.31$+$115715.9	5394-56001-974	2	$22.032\pm 0.245$	$20.256\pm 0.036$	$20.066\pm 0.037$	$20.106\pm 0.037$	$20.274\pm 0.120$
121837.12$+$002303.7	2568-54153-352	3	$20.418\pm 0.045$	$19.524\pm 0.017$	$19.350\pm 0.016$	$19.324\pm 0.021$	$19.465\pm 0.059$
122035.75$+$092948.1	5396-55947-158	1	$22.109\pm 0.259$	$20.885\pm 0.038$	$20.644\pm 0.042$	$20.712\pm 0.052$	$20.786\pm 0.184$
122437.07$+$283853.0	5976-56356-818	2	$22.404\pm 0.261$	$19.774\pm 0.020$	$19.224\pm 0.029$	$19.080\pm 0.025$	$19.011\pm 0.047$
122656.39$+$293643.9	2234-53823-273	2	$23.087\pm 0.468$	$20.550\pm 0.029$	$19.737\pm 0.023$	$19.604\pm 0.025$	$19.626\pm 0.089$
122943.92$+$074311.8	5402-55927-698	2	$23.308\pm 0.584$	$20.419\pm 0.036$	$20.072\pm 0.028$	$20.075\pm 0.033$	$20.328\pm 0.146$
123024.03$+$314339.7	6479-56364-318	1	$21.559\pm 0.135$	$20.370\pm 0.025$	$20.182\pm 0.029$	$20.209\pm 0.038$	$20.201\pm 0.121$
123415.21$+$520808.1	0885-52379-269	1	$19.541\pm 0.036$	$18.418\pm 0.027$	$18.298\pm 0.016$	$18.423\pm 0.015$	$18.682\pm 0.032$
123826.92$+$214937.7	5985-56089-738	2	$24.211\pm 0.671$	$20.801\pm 0.043$	$20.316\pm 0.029$	$20.209\pm 0.033$	$20.162\pm 0.090$
124547.10$+$082231.4	5407-55926-966	1	$22.559\pm 0.283$	$20.941\pm 0.035$	$20.524\pm 0.030$	$20.496\pm 0.040$	$20.973\pm 0.231$
124937.50$+$651407.6	6963-56724-634	1	$21.159\pm 0.097$	$20.444\pm 0.028$	$20.392\pm 0.035$	$20.463\pm 0.044$	$21.019\pm 0.269$
125454.93$+$355145.7	3975-55321-364	1	$21.808\pm 0.168$	$20.597\pm 0.025$	$20.450\pm 0.031$	$20.409\pm 0.042$	$20.510\pm 0.134$
125710.13$+$323848.5	6485-56342-980	1	$24.020\pm 0.874$	$21.607\pm 0.054$	$20.962\pm 0.052$	$20.901\pm 0.082$	$20.951\pm 0.234$
125720.87$-$031025.1	3794-55241-204	1	$22.173\pm 0.219$	$20.645\pm 0.037$	$20.281\pm 0.030$	$20.345\pm 0.045$	$20.744\pm 0.224$
125922.03$+$311215.2	1994-53845-010	1	$21.501\pm 0.112$	$19.783\pm 0.021$	$19.444\pm 0.019$	$19.423\pm 0.023$	$19.504\pm 0.058$
125945.32$+$472953.6	6618-56401-742	1	$23.538\pm 0.796$	$20.852\pm 0.051$	$20.578\pm 0.045$	$20.714\pm 0.083$	$20.809\pm 0.318$
130328.06$+$405545.5	4706-55705-506	1	$20.930\pm 0.098$	$19.735\pm 0.039$	$19.539\pm 0.056$	$19.511\pm 0.031$	$19.623\pm 0.093$
130826.36$+$095724.0	5421-55980-840	1	$21.692\pm 0.151$	$21.046\pm 0.039$	$20.994\pm 0.044$	$21.078\pm 0.066$	$21.128\pm 0.268$
130830.03$+$025844.5	4007-55327-584	1	$22.520\pm 0.263$	$20.827\pm 0.034$	$20.502\pm 0.038$	$20.424\pm 0.049$	$20.543\pm 0.172$
131420.49$+$374806.5	3978-55330-030	1	$22.740\pm 0.296$	$20.829\pm 0.035$	$20.477\pm 0.031$	$20.443\pm 0.035$	$20.522\pm 0.109$
131612.86$+$191806.5	5867-56034-712	2	$23.892\pm 0.579$	$21.017\pm 0.038$	$20.546\pm 0.034$	$20.506\pm 0.041$	$20.427\pm 0.112$
131900.18$+$364149.8	3979-55597-929	1	$20.947\pm 0.070$	$20.205\pm 0.029$	$20.153\pm 0.022$	$20.262\pm 0.033$	$20.471\pm 0.152$
132005.53$+$020419.0	4006-55328-686	1	$21.950\pm 0.194$	$21.040\pm 0.044$	$20.899\pm 0.046$	$21.099\pm 0.080$	$21.355\pm 0.389$
132144.04$-$023751.4	4049-55591-276	1	$22.497\pm 0.273$	$20.725\pm 0.033$	$20.126\pm 0.032$	$20.041\pm 0.035$	$19.988\pm 0.117$
132941.79$+$130131.9	5432-56008-689	1	$21.127\pm 0.106$	$19.952\pm 0.028$	$19.829\pm 0.023$	$19.894\pm 0.028$	$20.124\pm 0.098$
133059.26$+$302953.2	2110-53467-148	1	$18.276\pm 0.019$	$16.316\pm 0.022$	$15.888\pm 0.014$	$15.905\pm 0.024$	$16.092\pm 0.029$
133624.26$+$354751.2	2101-53858-254	1	$19.485\pm 0.029$	$17.849\pm 0.020$	$17.642\pm 0.013$	$17.714\pm 0.026$	$17.826\pm 0.018$
133905.97$+$264322.9	6002-56104-590	1	$19.997\pm 0.035$	$18.978\pm 0.021$	$18.775\pm 0.014$	$18.821\pm 0.019$	$18.946\pm 0.037$
134050.31$+$270219.0	6002-56104-622	1	$21.523\pm 0.119$	$20.858\pm 0.031$	$20.811\pm 0.037$	$20.890\pm 0.057$	$20.983\pm 0.218$
134203.60$+$181332.8	5439-56045-828	1	$23.609\pm 0.516$	$21.128\pm 0.036$	$20.609\pm 0.042$	$20.528\pm 0.038$	$20.670\pm 0.135$
134520.99$+$115357.6	1701-53142-440	1	$22.638\pm 0.299$	$19.923\pm 0.018$	$19.387\pm 0.020$	$19.453\pm 0.023$	$19.545\pm 0.058$
134711.47$+$141528.0	5441-56017-258	1	$21.201\pm 0.074$	$19.703\pm 0.014$	$19.497\pm 0.021$	$19.514\pm 0.020$	$19.530\pm 0.062$
135054.01$+$105808.0	5440-55983-996	1	$24.400\pm 0.941$	$20.969\pm 0.044$	$20.374\pm 0.031$	$20.313\pm 0.032$	$20.337\pm 0.110$
135123.86$+$264546.5	6006-56105-212	2	$22.995\pm 0.396$	$20.383\pm 0.023$	$19.874\pm 0.020$	$19.861\pm 0.029$	$19.863\pm 0.111$
135632.62$+$241606.0	2119-53792-216	1	$20.378\pm 0.049$	$19.049\pm 0.016$	$18.731\pm 0.017$	$18.779\pm 0.025$	$18.867\pm 0.039$
135654.01$+$023641.5	4036-55330-762	1	$20.441\pm 0.056$	$19.534\pm 0.016$	$19.504\pm 0.022$	$19.605\pm 0.028$	$19.467\pm 0.088$
140137.31$+$365909.9	1642-53115-198	1	$19.941\pm 0.031$	$18.811\pm 0.018$	$18.534\pm 0.019$	$18.522\pm 0.016$	$18.554\pm 0.034$
140410.72$+$362056.8	2931-54590-302	2	$20.013\pm 0.037$	$18.826\pm 0.033$	$18.455\pm 0.016$	$18.512\pm 0.021$	$18.701\pm 0.034$
140525.20$+$254212.4	6008-56093-808	1	$23.292\pm 0.413$	$20.956\pm 0.034$	$20.719\pm 0.031$	$20.719\pm 0.048$	$20.781\pm 0.188$
140557.09$+$154940.5	2744-54272-586	2	$20.003\pm 0.037$	$18.935\pm 0.020$	$18.779\pm 0.019$	$18.911\pm 0.016$	$19.107\pm 0.037$
141140.27$+$341039.4	3863-55280-502	1	$24.960\pm 0.815$	$20.790\pm 0.030$	$20.084\pm 0.023$	$20.021\pm 0.029$	$19.843\pm 0.106$
141211.53$+$283618.7	6497-56329-380	1	$24.999\pm 0.896$	$21.386\pm 0.051$	$20.590\pm 0.033$	$20.519\pm 0.045$	$20.290\pm 0.127$
142120.11$+$184351.6	5897-56042-460	2	$22.057\pm 0.144$	$20.351\pm 0.028$	$20.083\pm 0.023$	$20.190\pm 0.037$	$20.340\pm 0.111$
142833.77$+$440346.1	2907-54580-126	1	$17.900\pm 0.020$	$17.055\pm 0.016$	$16.878\pm 0.016$	$16.938\pm 0.016$	$17.053\pm 0.022$
142939.38$+$384113.2	4713-56044-876	1	$22.256\pm 0.158$	$20.642\pm 0.028$	$20.399\pm 0.025$	$20.332\pm 0.033$	$20.384\pm 0.100$
143007.15$-$015129.5	0919-52409-358	1	$21.484\pm 0.121$	$19.477\pm 0.022$	$19.033\pm 0.021$	$18.994\pm 0.019$	$19.102\pm 0.057$
144301.55$+$583301.6	6806-56419-314	1	$22.498\pm 0.287$	$21.347\pm 0.041$	$21.262\pm 0.065$	$21.339\pm 0.101$	$22.078\pm 0.727$
144354.13$+$301413.3	3874-55280-732	1	$22.674\pm 0.248$	$21.478\pm 0.047$	$21.273\pm 0.051$	$21.402\pm 0.083$	$21.361\pm 0.248$
144535.03$+$091340.4	5472-55976-842	1	$22.544\pm 0.368$	$21.314\pm 0.047$	$21.033\pm 0.046$	$21.197\pm 0.069$	$21.493\pm 0.356$
144804.49$+$104709.0	5475-56011-394	2	$20.185\pm 0.042$	$18.814\pm 0.016$	$18.651\pm 0.016$	$18.673\pm 0.019$	$18.748\pm 0.033$
150028.02$+$231554.0	6020-56087-828	1	$24.096\pm 0.883$	$21.596\pm 0.051$	$21.381\pm 0.060$	$21.460\pm 0.098$	$21.819\pm 0.564$
150228.70$+$374452.9	5168-56035-732	2	$21.576\pm 0.092$	$19.788\pm 0.018$	$19.455\pm 0.023$	$19.418\pm 0.029$	$19.511\pm 0.047$
150739.03$+$403408.9	6054-56089-176	1	$22.151\pm 0.204$	$21.081\pm 0.043$	$20.941\pm 0.046$	$21.081\pm 0.089$	$21.429\pm 0.393$
151835.63$+$050627.4	1834-54562-231	1	$21.942\pm 0.174$	$19.451\pm 0.019$	$18.861\pm 0.018$	$18.786\pm 0.018$	$18.771\pm 0.040$
152449.58$+$404938.1	2936-54626-537	4	$21.788\pm 0.110$	$20.150\pm 0.024$	$19.760\pm 0.023$	$19.800\pm 0.029$	$19.921\pm 0.095$
153407.58$+$124254.4	4891-55736-812	1	$23.178\pm 0.537$	$21.594\pm 0.059$	$21.151\pm 0.054$	$21.099\pm 0.071$	$20.988\pm 0.262$
153505.75$+$124744.2	2754-54240-570	1	$18.043\pm 0.021$	$15.981\pm 0.020$	$15.498\pm 0.017$	$15.453\pm 0.021$	$15.497\pm 0.014$
153642.53$+$420519.2	6050-56089-620	1	$23.322\pm 0.650$	$20.840\pm 0.043$	$20.303\pm 0.031$	$20.172\pm 0.041$	$20.334\pm 0.159$
153745.52$+$360818.6	4974-56038-738	1	$23.360\pm 0.417$	$21.112\pm 0.032$	$20.674\pm 0.031$	$20.658\pm 0.041$	$20.854\pm 0.140$
154022.79$+$535239.8	6708-56452-298	1	$22.890\pm 0.282$	$21.156\pm 0.035$	$20.952\pm 0.042$	$20.990\pm 0.054$	$21.255\pm 0.239$
154201.75$+$465020.2	6032-56067-716	1	$23.013\pm 0.532$	$20.853\pm 0.045$	$20.424\pm 0.033$	$20.416\pm 0.041$	$20.704\pm 0.188$
154349.79$+$202442.9	3943-55336-100	1	$23.081\pm 0.437$	$21.471\pm 0.043$	$21.089\pm 0.046$	$21.205\pm 0.080$	$21.215\pm 0.336$
154510.31$+$523618.4	6715-56449-768	1	$21.589\pm 0.105$	$20.055\pm 0.028$	$19.697\pm 0.021$	$19.711\pm 0.025$	$19.795\pm 0.068$
154625.33$+$300946.2	4726-55712-632	2	$21.430\pm 0.077$	$19.802\pm 0.022$	$19.530\pm 0.018$	$19.641\pm 0.022$	$19.802\pm 0.064$
154913.45$+$263301.1	3946-55659-698	1	$21.447\pm 0.102$	$20.592\pm 0.031$	$20.548\pm 0.043$	$20.409\pm 0.039$	$20.586\pm 0.194$
154933.23$+$190646.7	3931-55350-572	1	$22.631\pm 0.332$	$21.321\pm 0.045$	$20.949\pm 0.047$	$20.971\pm 0.065$	$20.851\pm 0.262$
155429.00$+$173545.9	2170-53875-154	1	$18.674\pm 0.023$	$17.592\pm 0.016$	$17.418\pm 0.011$	$17.468\pm 0.011$	$17.654\pm 0.023$
160429.80$+$183035.4	3289-54910-379	1	$20.702\pm 0.063$	$19.701\pm 0.020$	$19.552\pm 0.018$	$19.607\pm 0.023$	$19.765\pm 0.087$
161026.10$+$400619.7	6052-56092-036	1	$22.578\pm 0.211$	$21.000\pm 0.029$	$20.749\pm 0.033$	$20.915\pm 0.049$	$21.093\pm 0.237$
161248.17$+$353434.8	4964-55749-238	1	$22.381\pm 0.209$	$21.306\pm 0.042$	$21.305\pm 0.052$	$21.311\pm 0.071$	$21.257\pm 0.972$
161603.00$+$330301.3	4960-55747-224	2	$21.021\pm 0.082$	$19.251\pm 0.020$	$18.976\pm 0.021$	$19.070\pm 0.021$	$19.152\pm 0.047$
162408.57$+$331019.0	4955-55750-650	1	$22.261\pm 0.179$	$21.125\pm 0.035$	$20.963\pm 0.037$	$21.061\pm 0.060$	$20.759\pm 0.147$
162612.73$+$330308.2	4955-55750-774	1	$22.129\pm 0.248$	$20.989\pm 0.038$	$20.786\pm 0.041$	$20.876\pm 0.064$	$20.505\pm 0.151$
162703.34$+$464658.2	6029-56099-975	2	$22.015\pm 0.148$	$20.422\pm 0.023$	$20.129\pm 0.023$	$20.152\pm 0.034$	$20.343\pm 0.109$
163601.33$+$161907.1	4063-55364-316	2	$23.428\pm 0.508$	$20.636\pm 0.028$	$19.535\pm 0.019$	$19.292\pm 0.018$	$19.303\pm 0.049$
164104.94$+$185602.1	4062-55383-728	1	$21.832\pm 0.133$	$20.223\pm 0.021$	$19.848\pm 0.018$	$19.750\pm 0.022$	$19.806\pm 0.069$
164939.22$+$223807.2	4182-55446-900	1	$23.670\pm 0.461$	$21.000\pm 0.029$	$20.349\pm 0.023$	$20.137\pm 0.026$	$20.160\pm 0.085$
165101.72$+$424955.5	6031-56091-046	1	$22.511\pm 0.231$	$19.796\pm 0.018$	$19.196\pm 0.015$	$19.021\pm 0.015$	$19.119\pm 0.048$
170638.11$+$254111.7	5014-55717-420	1	$25.149\pm 1.586$	$20.981\pm 0.040$	$20.912\pm 0.061$	$20.957\pm 0.092$	$20.537\pm 0.237$
210916.51$-$003921.6	0985-52431-104	1	$21.864\pm 0.147$	$20.058\pm 0.019$	$19.763\pm 0.017$	$19.758\pm 0.025$	$19.672\pm 0.066$
211045.34$+$051214.8	4078-55358-358	1	$23.319\pm 0.389$	$21.531\pm 0.044$	$21.147\pm 0.043$	$21.072\pm 0.051$	$21.099\pm 0.212$
212312.20$+$001653.5	4192-55469-974	3	$22.403\pm 0.182$	$20.322\pm 0.021$	$19.902\pm 0.020$	$19.762\pm 0.030$	$19.616\pm 0.075$
215752.30$+$120603.1	5063-55831-628	1	$21.257\pm 0.096$	$19.739\pm 0.021$	$19.406\pm 0.018$	$19.346\pm 0.024$	$19.383\pm 0.049$
222503.70$+$233855.1	6299-56478-666	1	$21.188\pm 0.162$	$19.486\pm 0.023$	$19.269\pm 0.023$	$19.273\pm 0.035$	$19.536\pm 0.124$
223014.70$+$190514.4	5025-55836-498	1	$23.215\pm 0.557$	$20.869\pm 0.038$	$20.256\pm 0.034$	$20.172\pm 0.042$	$20.271\pm 0.153$
223101.11$+$090635.1	5057-56209-944	2	$20.701\pm 0.087$	$19.288\pm 0.016$	$18.937\pm 0.014$	$18.838\pm 0.015$	$18.781\pm 0.043$
223507.65$-$005607.7	4203-55447-092	1	$22.269\pm 0.221$	$20.492\pm 0.031$	$20.209\pm 0.024$	$20.296\pm 0.036$	$20.418\pm 0.145$
223811.10$+$021352.9	4295-55858-413	1	$21.575\pm 0.136$	$20.734\pm 0.033$	$20.544\pm 0.034$	$20.550\pm 0.039$	$20.316\pm 0.120$
223815.97$-$011336.9	4204-55470-321	1	$22.381\pm 0.265$	$20.784\pm 0.040$	$20.587\pm 0.035$	$20.617\pm 0.049$	$20.681\pm 0.172$
225448.83$+$303107.1	6507-56478-276	1	$22.457\pm 0.277$	$19.861\pm 0.020$	$19.326\pm 0.022$	$19.236\pm 0.021$	$19.300\pm 0.059$
230414.48$+$241554.0	6589-56536-655	1	$22.017\pm 0.162$	$19.847\pm 0.021$	$19.172\pm 0.015$	$19.037\pm 0.016$	$18.958\pm 0.045$
231937.39$+$301848.4	6583-56566-754	2	$21.670\pm 0.141$	$20.870\pm 0.029$	$20.811\pm 0.040$	$20.861\pm 0.062$	$20.715\pm 0.185$
232538.93$+$044813.1	4408-55888-256	1	$21.438\pm 0.151$	$19.882\pm 0.025$	$19.578\pm 0.029$	$19.682\pm 0.035$	$19.688\pm 0.114$
232833.31$+$083028.4	6164-56181-140	1	$23.212\pm 0.563$	$21.591\pm 0.053$	$21.010\pm 0.046$	$21.044\pm 0.098$	$21.076\pm 0.299$
233054.31$+$280517.4	6514-56487-489	1	$22.075\pm 0.263$	$20.773\pm 0.032$	$20.556\pm 0.042$	$20.526\pm 0.064$	$20.349\pm 0.188$
233056.81$+$295652.6	6501-56563-406	1	$21.341\pm 0.090$	$19.842\pm 0.020$	$19.644\pm 0.017$	$19.712\pm 0.022$	$19.951\pm 0.097$
233320.38$+$105830.2	6157-56238-852	1	$23.395\pm 0.885$	$21.457\pm 0.041$	$21.179\pm 0.044$	$21.272\pm 0.072$	$21.306\pm 0.269$
234034.61$+$012416.6	4280-55503-444	1	$21.098\pm 0.076$	$19.401\pm 0.024$	$19.079\pm 0.021$	$19.148\pm 0.021$	$19.199\pm 0.045$
234048.74$+$081753.3	2628-54326-108	3	$22.677\pm 1.028$	$20.246\pm 0.021$	$19.806\pm 0.022$	$19.858\pm 0.026$	$19.932\pm 0.074$
234307.67$-$001016.3	4214-55451-438	1	$22.109\pm 0.170$	$20.459\pm 0.029$	$20.073\pm 0.024$	$20.110\pm 0.030$	$20.081\pm 0.104$
235224.26$+$192247.3	6127-56274-424	1	$24.800\pm 1.329$	$21.350\pm 0.046$	$20.912\pm 0.049$	$20.994\pm 0.074$	$21.483\pm 0.917$
235249.13$+$334439.2	7143-56572-070	1	$21.741\pm 0.114$	$20.954\pm 0.027$	$20.746\pm 0.029$	$20.816\pm 0.043$	$20.713\pm 0.172$
235715.03$+$234848.9	6513-56543-314	1	$23.001\pm 0.553$	$21.263\pm 0.051$	$20.906\pm 0.048$	$20.920\pm 0.073$

Table 4. Table 6: Derived parameters from atmospheric modelling of the SDSS and WHT spectra. Abundances relative to helium are given in dex.

SDSS J	$T_{\mathrm{eff}}$ [K]	Ca	Mg	Fe	Na	Cr	Ti	Ni	H
0002$+$3209	$6410\pm 180$	$-9.05$	$-8.14$	$-7.84$	-	-	-	-	-
0004$+$0819	$5820\pm 380$	$-8.72$	$-7.51$	$-7.51$	$-8.80$	-	-	-	-
0006$+$0520	$6790\pm 170$	$-9.00$	$-8.09$	$-8.39$	-	-	-	-	-
0010$-$0430	$6960\pm 160$	$-8.38$	$-6.92$	$-7.12$	-	-	-	-	-
0013$+$1109	$5830\pm 320$	$-9.11$	$-8.20$	$-8.10$	-	-	-	-	-
0019$+$2209	$5970\pm 150$	$-9.34$	$-8.53$	$-8.58$	$-9.42$	-	-	-	-
0037$-$0525	$5630\pm 120$	$-8.79$	$-7.58$	$-7.68$	$-9.07$	-	-	-	-
0044$+$0418	$6050\pm 70$	$-9.82$	$-8.81$	$-8.71$	-	-	-	-	-
0046$+$2717	$7640\pm 290$	$-7.65$	$-6.19$	$-6.84$	-	$-7.80$	-	-	-
0047$+$1628	$6620\pm 180$	$-7.68$	$-6.77$	$-6.47$	$-8.66$	$-8.53$	-	-	-
0052$+$1846	$5660\pm 290$	$-9.04$	$-7.83$	$-7.53$	-	$-9.59$	-	-	-
0053$+$3115	$6180\pm 320$	$-8.87$	$-8.26$	$-8.66$	-	-	-	-	-
0056$+$2453	$5440\pm 310$	$-9.62$	$-8.61$	$-8.71$	-	-	-	-	-
0107$+$2650	$6190\pm 140$	$-8.44$	$-7.93$	$-7.73$	$-8.22$	-	-	-	-
0108$-$0537	$6010\pm 130$	$-8.79$	$-8.18$	$-8.08$	$-9.27$	-	-	-	-
0114$+$3505	$6370\pm 210$	$-8.51$	$-7.30$	$-7.20$	-	$-9.06$	-	-	-
0116$+$2050	$6207\pm 80$	$-8.81$	$-7.65$	$-7.60$	$-9.29$	-	$-9.74$	$-8.76$	-
0117$+$0021	$6800\pm 80$	$-8.80$	$-7.50$	$-7.60$	-	$-9.48$	-	-	-
0126$+$2534	$5320\pm 120$	$-9.95$	$-8.94$	$-8.64$	-	-	-	-	-
0135$+$1302	$5800\pm 100$	$-9.50$	$-8.70$	$-8.69$	-	-	-	-	-
0143$+$0113	$6700\pm 80$	$-8.50$	$-7.10$	$-7.30$	$-8.68$	-	-	-	$-3.1$
0144$+$1920	$6500\pm 190$	$-8.50$	$-7.34$	$-7.39$	$-8.18$	-	-	-	-
0144$+$0305	$6950\pm 330$	$-8.37$	$-7.21$	$-7.26$	-	-	-	-	-
0148$-$0112	$6830\pm 210$	$-8.82$	$-7.56$	$-7.31$	-	-	-	-	-
0150$+$1354	$6310\pm 160$	$-7.75$	$-6.54$	$-7.24$	$-8.03$	$-10.10$	-	-	$-1.7$
0157$+$0033	$6110\pm 140$	$-8.20$	$-7.39$	$-7.69$	-	-	-	-	-
0158$-$0942	$5940\pm 170$	$-9.52$	$-8.61$	$-8.41$	-	-	-	-	-
0200$+$1646	$5810\pm 180$	$-8.92$	$-7.61$	$-7.91$	$-9.00$	-	-	-	-
0201$+$2015	$6180\pm 140$	$-8.96$	$-7.65$	$-8.25$	-	-	-	-	-
0208$-$0542	$5800\pm 350$	$-8.54$	$-7.53$	$-7.33$	$-8.82$	-	-	-	-
0234$-$0510	$7050\pm 340$	$-8.27$	$-6.91$	$-7.21$	-	-	-	-	-
0252$-$0401	$6950\pm 160$	$-8.57$	$-6.96$	$-7.46$	$-8.25$	$-8.62$	-	-	-
0252$+$0054	$7500\pm 190$	$-8.35$	$-7.24$	$-7.14$	$-7.83$	-	-	-	$\le$$-4.3$
0447$+$1124	$6530\pm 190$	$-8.77$	$-7.26$	$-8.06$	-	-	-	-	$-2.5$
0512$-$0505	$5563\pm 60$	$-8.99$	$-8.05$	$-7.79$	$-9.65$	$-10.09$	-	-	-
0721$+$3928	$6280\pm 150$	$-8.90$	$-7.79$	$-8.09$	-	-	-	-	-
0735$+$2057	$6110\pm 180$	$-7.75$	$-6.74$	$-6.84$	$-8.33$	-	-	-	-
0736$+$4118	$5100\pm 100$	$-8.50$	$-7.69$	$-7.69$	$-9.68$	$-8.95$	-	-	$-3.0$
0739$+$3112	$5080\pm 320$	$-9.50$	$-8.29$	$-8.39$	-	-	-	-	-
0741$+$3146	$5592\pm 140$	$-9.55$	$-8.94$	$-7.50$	-	$-9.60$	$-10.06$	$-9.09$	-
0744$+$4649	$5028\pm 70$	$-8.36$	$-7.99$	$-8.17$	$-9.26$	$-9.69$	$-9.38$	-	-
0744$+$4408	$6370\pm 230$	$-8.75$	$-7.64$	$-7.54$	$-9.23$	-	-	-	-
0744$+$2701	$7890\pm 210$	$-7.68$	$-6.92$	$-6.87$	-	-	-	-	$\le$$-4.3$
0744$+$1640	$4940\pm 190$	$-10.24$	$-8.63$	$-9.33$	-	-	-	-	-
0758$+$1013	$5500\pm 290$	$-8.65$	$-7.54$	$-7.34$	$-8.73$	$-9.20$	-	-	-
0800$+$2242	$6260\pm 260$	$-9.75$	$-8.69$	$-8.69$	-	-	-	-	-
0806$+$3055	$6900\pm 250$	$-7.77$	$-7.01$	$-7.16$	-	$-8.47$	-	-	-
0806$+$4058	$6808\pm 80$	$-8.49$	$-7.38$	$-7.49$	$-8.33$	$-9.11$	-	$-9.00$	-
0807$+$4930	$5100\pm 250$	$-8.39$	$-7.58$	$-7.28$	$-9.27$	$-9.34$	$-9.06$	-	-
0816$+$2330	$7790\pm 300$	$-7.48$	$-6.27$	$-6.37$	-	$-7.68$	$-8.65$	-	$\le$$-4.5$
0818$+$1247	$6810\pm 270$	$-8.58$	$-7.87$	$-7.77$	-	-	-	-	-
0823$+$0546	$6019\pm 60$	$-9.34$	$-8.51$	$-7.36$	-	-	$-9.90$	$-8.59$	-
0830$-$0319	$6400\pm 110$	$-9.10$	$-8.49$	$-8.29$	-	-	-	-	-
0832$+$4109	$6070\pm 190$	$-8.00$	$-7.04$	$-7.04$	$-8.73$	$-8.80$	-	-	-
0838$+$2322	$5670\pm 80$	$-9.80$	$-8.89$	$-9.30$	-	-	-	-	-
0842$+$1406	$7160\pm 90$	$-8.16$	$-7.20$	$-7.30$	-	-	-	-	-
0842$+$1536	$6180\pm 220$	$-9.47$	$-8.46$	$-8.46$	-	-	-	-	-
0843$+$5614	$6600\pm 170$	$-8.65$	$-7.44$	$-7.74$	$-8.23$	-	-	-	-
0851$+$1543	$6300\pm 90$	$-8.50$	$-7.89$	$-8.20$	-	-	-	-	-
0852$+$3402	$5580\pm 180$	$-9.00$	$-8.39$	$-7.79$	$-9.58$	$-9.75$	-	-	-
0901$+$0752	$7100\pm 120$	$-7.12$	$-6.21$	$-6.21$	$-7.70$	$-8.07$	$-8.79$	-	-
0902$+$3625	$6330\pm 210$	$-8.60$	$-7.54$	$-7.64$	$-8.53$	-	-	-	-
0902$+$1004	$7250\pm 250$	$-8.25$	$-7.29$	$-8.19$	-	-	-	-	-
0906$+$1141	$6910\pm 270$	$-7.90$	$-6.64$	$-6.94$	$-8.43$	-	$-8.62$	-	-
0908$+$5136	$6180\pm 90$	$-9.35$	$-8.50$	$-8.24$	-	-	-	-	-
0908$+$4119	$6700\pm 300$	$-8.73$	$-7.07$	$-7.12$	-	-	-	-	-
0913$+$2627	$5210\pm 180$	$-9.75$	$-8.74$	$-8.64$	-	-	-	-	-
0913$+$4127	$5780\pm 290$	$-8.52$	$-7.86$	$-7.16$	-	$-9.42$	$-9.04$	-	-
0916$+$2540	$5378\pm 70$	$-7.48$	$-6.83$	$-7.09$	$-9.32$	$-8.90$	$-8.75$	-	-
0924$+$4301	$5950\pm 240$	$-9.75$	$-8.44$	$-8.54$	-	-	-	-	-
0925$+$3130	$5810\pm 90$	$-9.00$	$-7.79$	$-7.99$	$-9.68$	-	-	-	-
0927$+$4931	$6200\pm 230$	$-8.61$	$-7.20$	$-7.50$	$-9.09$	-	-	-	-
0929$+$4247	$6530\pm 160$	$-8.46$	$-6.85$	$-7.15$	$-8.64$	$-9.01$	-	-	-
0933$+$6334	$6290\pm 370$	$-8.28$	$-7.17$	$-6.77$	-	$-8.83$	-	-	-
0937$+$5228	$6600\pm 100$	$-8.40$	$-7.09$	$-7.50$	$-8.98$	$-9.25$	-	-	-
0939$+$4136	$6310\pm 180$	$-8.30$	$-7.09$	$-6.79$	$-8.58$	$-8.55$	-	-	-
0939$+$5019	$5980\pm 190$	$-8.25$	$-7.04$	$-7.14$	$-9.23$	$-8.70$	-	-	-
0946$+$2024	$7490\pm 390$	$-8.07$	$-6.66$	$-7.06$	-	-	-	-	-
0948$+$3008	$6000\pm 130$	$-9.15$	$-8.04$	$-8.44$	-	-	-	-	-
0956$+$5912	$8800\pm 110$	$-7.15$	$-5.30$	$-6.14$	$-6.60$	$-7.50$	-	-	$-3.6$
1003$-$0031	$5740\pm 140$	$-8.49$	$-7.28$	$-7.28$	$-8.97$	-	-	-	-
1005$+$2244	$6360\pm 320$	$-8.96$	$-8.10$	$-7.40$	-	-	-	-	-
1006$+$1752	$5710\pm 190$	$-9.45$	$-8.94$	$-8.34$	-	-	-	-	-
1014$+$2827	$6250\pm 330$	$-7.68$	$-6.47$	$-6.47$	$-7.86$	$-8.43$	$-9.05$	-	-
1017$+$3447	$6150\pm 190$	$-9.34$	$-8.43$	$-8.33$	-	-	-	-	-
1017$+$2419	$7200\pm 150$	$-8.07$	$-6.86$	$-6.96$	$-8.15$	-	-	-	$\le$$-4.3$
1019$+$3535	$5840\pm 270$	$-8.75$	$-7.64$	$-7.74$	-	-	-	-	-
1019$+$2045	$5300\pm 220$	$-9.36$	$-8.65$	$-8.25$	-	-	-	-	-
1024$+$4531	$5980\pm 160$	$-8.92$	$-8.06$	$-8.11$	-	-	-	-	-
1024$+$1014	$6310\pm 280$	$-7.50$	$-6.54$	$-6.64$	$-8.63$	$-8.40$	$-8.52$	-	-
1032$+$1338	$5490\pm 240$	$-9.33$	$-7.82$	$-8.02$	$-9.01$	-	-	-	-
1033$+$1809	$6070\pm 230$	$-8.55$	$-8.84$	$-8.04$	-	-	-	-	-
1038$-$0036	$7700\pm 60$	$-7.85$	$-6.80$	$-7.40$	$-8.60$	-	$-9.60$	-	$\le$$-4.8$
1038$+$0432	$6510\pm 170$	$-7.50$	$-6.84$	$-6.99$	$-9.13$	$-8.70$	-	-	-
1040$+$2407	$5750\pm 90$	$-8.20$	$-7.29$	$-7.59$	$-8.88$	$-9.35$	$-9.27$	-	-
1041$+$3432	$7500\pm 220$	$-8.20$	$-7.49$	$-7.29$	-	-	-	-	-
1043$+$3516	$6720\pm 120$	$-8.88$	$-8.00$	$-7.20$	-	$-8.92$	$-10.54$	$-8.55$	-
1046$+$1329	$5170\pm 230$	$-9.60$	$-8.39$	$-8.29$	-	-	-	-	-
1055$+$3725	$5600\pm 120$	$-8.24$	$-8.23$	$-7.83$	-	$-9.19$	-	-	-
1058$+$3143	$6850\pm 100$	$-9.02$	$-7.81$	$-8.01$	-	-	-	-	-
1102$+$2827	$6400\pm 380$	$-7.75$	$-6.24$	$-6.44$	$-7.73$	$-8.30$	-	-	-
1102$+$0214	$5730\pm 90$	$-9.75$	$-8.84$	$-8.74$	-	-	-	-	-
1103$+$4144	$5850\pm 100$	$-9.30$	$-7.94$	$-8.04$	$-9.13$	-	-	-	-
1105$+$5006	$7280\pm 190$	$-8.14$	$-6.83$	$-6.93$	-	-	-	-	-
1105$+$0228	$5780\pm 260$	$-9.10$	$-7.84$	$-8.14$	-	-	-	-	-
1106$+$6737	$6400\pm 170$	$-7.88$	$-6.87$	$-7.67$	$-9.36$	-	-	-	-
1112$+$0700	$7560\pm 170$	$-8.53$	$-7.12$	$-7.37$	$-8.76$	-	-	-	$\le$$-4.6$
1113$+$2751	$6180\pm 210$	$-8.42$	$-7.41$	$-7.51$	$-9.20$	-	-	-	-
1132$+$3323	$6250\pm 270$	$-8.23$	$-6.82$	$-7.32$	$-8.71$	$-8.88$	$-8.70$	-	-
1134$+$1542	$6680\pm 250$	$-8.46$	$-7.25$	$-7.35$	$-8.44$	-	-	-	-
1144$+$3720	$7490\pm 190$	$-8.17$	$-6.96$	$-7.16$	$-8.25$	-	-	-	-
1144$+$1218	$5434\pm 100$	$-9.33$	$-8.13$	$-8.37$	-	$-10.22$	-	$-10.13$	$-3.3$
1147$+$5429	$5320\pm 340$	$-9.17$	$-8.16$	$-8.06$	$-9.85$	-	-	-	-
1149$+$0519	$7310\pm 140$	$-8.16$	$-7.30$	$-7.60$	-	-	-	-	$\le$$-4.3$
1150$+$4928	$7210\pm 160$	$-8.76$	$-7.95$	$-7.65$	-	-	-	-	-
1150$+$4533	$5720\pm 320$	$-8.35$	$-7.14$	$-7.14$	$-8.53$	-	-	-	-
1152$+$5101	$5000\pm 240$	$-10.08$	$-8.67$	$-8.97$	-	-	-	-	-
1152$+$1605	$6550\pm 160$	$-8.40$	$-7.19$	$-7.19$	$-8.28$	-	-	-	-
1157$+$6138	$6540\pm 380$	$-9.15$	$-7.44$	$-7.64$	-	-	-	-	-
1158$+$1845	$7250\pm 170$	$-7.75$	$-5.74$	$-6.84$	-	-	-	-	-
1158$+$5942	$6000\pm 170$	$-8.98$	$-8.72$	$-8.02$	-	-	-	-	-
1158$+$0454	$5270\pm 180$	$-8.69$	$-7.68$	$-7.58$	$-8.97$	$-9.34$	$-9.46$	-	-
1158$+$4712	$7650\pm 210$	$-8.06$	$-6.90$	$-6.85$	-	-	-	-	-
1158$+$5448	$6280\pm 340$	$-8.82$	$-7.61$	$-7.61$	-	-	-	-	-
1205$+$3536	$6070\pm 150$	$-8.74$	$-7.43$	$-7.63$	$-8.72$	-	-	-	-
1211$+$2326	$6450\pm 230$	$-8.59$	$-7.28$	$-7.28$	$-8.57$	-	-	-	-
1214$-$0234	$5210\pm 100$	$-9.40$	$-8.19$	$-8.49$	$-8.98$	-	-	-	-
1217$+$1157	$6440\pm 150$	$-8.93$	$-7.52$	$-7.92$	-	-	-	-	-
1218$+$0023	$6100\pm 90$	$-9.61$	$-9.20$	$-8.90$	-	-	-	-	-
1220$+$0929	$6640\pm 150$	$-8.38$	$-7.07$	$-7.37$	$-8.46$	$-8.93$	-	-	-
1224$+$2838	$5210\pm 110$	$-10.00$	$-8.69$	$-8.89$	-	-	-	-	-
1226$+$2936	$4680\pm 240$	$-10.04$	$-8.63$	$-8.93$	-	-	-	-	-
1229$+$0743	$6160\pm 130$	$-8.20$	$-7.29$	$-7.09$	$-8.48$	$-8.85$	$-9.87$	-	-
1230$+$3143	$6510\pm 160$	$-9.12$	$-8.41$	$-8.21$	-	-	-	-	-
1234$+$5208	$7630\pm 100$	$-7.40$	$-6.00$	$-6.39$	$-7.90$	$-7.95$	$-8.87$	-	$\le$$-4.9$
1238$+$2149	$5440\pm 190$	$-9.11$	$-8.10$	$-8.00$	$-8.89$	-	-	-	-
1245$+$0822	$6360\pm 190$	$-8.10$	$-7.34$	$-7.59$	$-8.68$	-	-	-	-
1249$+$6514	$7540\pm 170$	$-8.50$	$-6.89$	$-7.49$	-	-	-	-	-
1254$+$3551	$6620\pm 210$	$-8.96$	$-7.55$	$-7.75$	-	-	-	-	-
1257$+$3238	$5210\pm 340$	$-9.02$	$-7.81$	$-7.61$	$-9.70$	-	-	-	-
1257$-$0310	$6280\pm 230$	$-8.52$	$-7.26$	$-7.31$	-	-	-	-	-
1259$+$3112	$5840\pm 240$	$-9.65$	$-8.74$	$-8.14$	-	-	-	-	-
1259$+$4729	$6260\pm 290$	$-8.80$	$-8.29$	$-7.99$	-	-	-	-	-
1303$+$4055	$6200\pm 120$	$-9.02$	$-7.71$	$-8.11$	-	-	-	-	-
1308$+$0957	$7830\pm 320$	$-8.03$	$-7.52$	$-6.62$	-	-	-	-	$-3.6$
1308$+$0258	$6030\pm 210$	$-9.07$	$-8.16$	$-7.66$	-	-	-	-	-
1314$+$3748	$5940\pm 320$	$-8.48$	$-7.42$	$-7.52$	$-8.71$	-	-	-	-
1316$+$1918	$5350\pm 190$	$-9.90$	$-8.49$	$-8.99$	-	-	-	-	-
1319$+$3641	$7360\pm 190$	$-8.60$	$-7.59$	$-7.49$	-	-	-	-	-
1320$+$0204	$7000\pm 310$	$-8.28$	$-7.37$	$-7.17$	$-7.96$	-	-	-	-
1321$-$0237	$5620\pm 240$	$-8.48$	$-7.47$	$-7.47$	$-8.36$	$-9.33$	-	-	-
1329$+$1301	$6810\pm 150$	$-8.55$	$-7.34$	$-7.44$	$-9.23$	-	-	-	-
1330$+$3029	$6100\pm 60$	$-8.40$	$-7.15$	$-7.30$	$-8.80$	$-9.00$	$-9.70$	$-8.66$	-
1336$+$3547	$6600\pm 70$	$-8.50$	$-7.10$	$-7.39$	$-9.00$	$-9.40$	-	-	-
1339$+$2643	$6300\pm 70$	$-9.13$	$-8.30$	$-8.60$	-	-	-	-	-
1340$+$2702	$7855\pm 260$	$-6.98$	$-5.73$	$-6.27$	$-7.41$	-	-	-	-
1342$+$1813	$5240\pm 220$	$-9.19$	$-8.68$	$-8.58$	-	-	-	-	-
1345$+$1153	$6020\pm 200$	$-8.10$	$-7.49$	$-6.89$	-	$-8.70$	$-9.07$	-	-
1347$+$1415	$6740\pm 120$	$-8.50$	$-7.19$	$-7.29$	-	$-8.75$	-	-	-
1350$+$1058	$5120\pm 170$	$-10.06$	$-8.85$	$-8.75$	-	-	-	-	-
1351$+$2645	$5980\pm 160$	$-8.04$	$-8.33$	$-7.53$	$-9.72$	$-9.19$	$-8.61$	-	-
1356$+$2416	$6030\pm 120$	$-9.20$	$-7.84$	$-8.54$	-	-	-	-	-
1356$+$0236	$8260\pm 180$	$-7.52$	$-6.21$	$-6.41$	$-8.00$	-	-	-	$\le$$-4.2$
1401$+$3659	$6000\pm 110$	$-9.80$	$-8.84$	$-8.94$	-	-	-	-	-
1404$+$3620	$5900\pm 70$	$-9.20$	$-7.90$	$-8.50$	-	-	-	-	-
1405$+$2542	$5880\pm 190$	$-9.50$	$-8.49$	$-8.39$	-	-	-	-	-
1405$+$1549	$7150\pm 110$	$-8.25$	$-7.14$	$-7.14$	$-8.93$	-	-	-	-
1411$+$3410	$5480\pm 210$	$-8.40$	$-7.24$	$-7.39$	$-9.28$	$-9.15$	-	-	-
1412$+$2836	$4990\pm 160$	$-9.40$	$-8.39$	$-7.99$	$-9.58$	-	-	-	-
1421$+$1843	$7300\pm 210$	$-7.35$	$-5.89$	$-6.19$	-	-	-	-	-
1428$+$4403	$6600\pm 60$	$-8.98$	$-8.20$	$-8.40$	-	-	-	-	-
1429$+$3841	$6040\pm 270$	$-9.73$	$-8.72$	$-8.72$	-	-	-	-	-
1430$-$0151	$6150\pm 160$	$-7.55$	$-6.54$	$-6.99$	$-8.13$	$-8.50$	$-8.80$	-	-
1443$+$5833	$7080\pm 340$	$-8.56$	$-7.15$	$-7.25$	-	-	-	-	-
1443$+$3014	$6840\pm 300$	$-8.16$	$-6.90$	$-7.15$	-	-	-	-	-
1445$+$0913	$6580\pm 230$	$-7.98$	$-6.77$	$-6.77$	$-7.81$	$-8.58$	-	-	-
1448$+$1047	$6550\pm 100$	$-8.85$	$-7.77$	$-7.80$	-	-	-	-	-
1500$+$2315	$6530\pm 430$	$-8.40$	$-6.89$	$-7.19$	-	-	-	-	-
1502$+$3744	$5410\pm 100$	$-10.00$	$-8.99$	$-8.99$	-	-	-	-	-
1507$+$4034	$7180\pm 330$	$-8.18$	$-6.57$	$-7.17$	-	-	-	-	-
1518$+$0506	$5020\pm 100$	$-9.65$	$-8.64$	$-8.74$	$-10.03$	-	-	-	-
1524$+$4049	$5900\pm 120$	$-8.90$	$-7.69$	$-7.79$	$-9.18$	$-9.65$	-	-	-
1534$+$1242	$5860\pm 340$	$-8.29$	$-7.78$	$-7.48$	-	-	-	-	-
1535$+$1247	$5773\pm 50$	$-8.61$	$-7.36$	$-7.57$	$-8.72$	$-9.25$	$-9.62$	$-8.90$	$\le$$-3.0$
1536$+$4205	$5800\pm 140$	$-8.70$	$-7.49$	$-7.59$	$-8.78$	$-8.90$	$-8.90$	-	-
1537$+$3608	$5570\pm 270$	$-9.50$	$-8.19$	$-8.49$	-	-	-	-	-
1540$+$5352	$6520\pm 360$	$-8.58$	$-7.07$	$-7.47$	-	-	-	-	-
1542$+$4650	$6060\pm 220$	$-8.15$	$-6.94$	$-7.04$	$-8.18$	$-8.70$	-	-	-
1543$+$2024	$6330\pm 360$	$-8.09$	$-7.33$	$-7.38$	-	-	-	-	-
1545$+$5236	$5840\pm 120$	$-9.19$	$-8.28$	$-8.18$	-	-	-	-	-
1546$+$3009	$6600\pm 120$	$-8.40$	$-7.19$	$-7.19$	$-8.78$	$-8.65$	-	-	-
1549$+$2633	$6290\pm 180$	$-9.66$	$-7.95$	$-8.25$	-	-	-	-	-
1549$+$1906	$6460\pm 290$	$-8.48$	$-7.17$	$-7.22$	$-9.11$	$-8.78$	-	-	-
1554$+$1735	$6630\pm 70$	$-8.60$	$-7.54$	$-7.64$	$-8.90$	-	-	-	-
1604$+$1830	$6400\pm 120$	$-9.48$	$-8.47$	$-8.57$	-	-	-	-	-
1610$+$4006	$6580\pm 280$	$-8.47$	$-7.46$	$-7.11$	-	-	-	-	-
1612$+$3534	$6750\pm 400$	$-8.54$	$-7.43$	$-7.53$	-	-	-	-	-
1616$+$3303	$6400\pm 80$	$-8.25$	$-6.95$	$-7.14$	$-8.93$	$-8.80$	$-9.62$	-	-
1624$+$3310	$6930\pm 340$	$-8.64$	$-7.28$	$-7.53$	-	-	-	-	-
1626$+$3303	$6260\pm 250$	$-8.87$	$-7.41$	$-7.61$	-	-	$-9.04$	-	-
1627$+$4646	$6420\pm 200$	$-8.88$	$-8.07$	$-7.62$	-	$-8.73$	-	-	-
1636$+$1619	$4410\pm 150$	$-9.50$	$-8.29$	$-8.79$	$-10.18$	-	-	-	-
1641$+$1856	$5820\pm 100$	$-10.30$	$-9.49$	$-9.59$	-	-	-	-	-
1649$+$2238	$5332\pm 160$	$-8.62$	$-6.89$	$-7.21$	$-8.29$	$-8.83$	-	-	$-1.8$
1651$+$4249	$5710\pm 200$	$-8.02$	$-6.91$	$-7.31$	$-8.20$	-	-	-	-
1706$+$2541	$6640\pm 260$	$-9.40$	$-8.49$	$-8.89$	-	-	-	-	-
2109$-$0039	$6040\pm 240$	$-8.78$	$-8.42$	$-7.67$	-	-	-	-	-
2110$+$0512	$5680\pm 260$	$-9.21$	$-8.10$	$-8.00$	-	-	-	-	-
2123$+$0016	$5230\pm 140$	$-10.01$	$-8.50$	$-8.50$	$-9.19$	-	-	-	-
2157$+$1206	$6100\pm 100$	$-9.00$	$-7.79$	$-8.09$	$-9.18$	-	-	-	-
2225$+$2338	$7000\pm 130$	$-8.81$	$-7.40$	$-7.80$	-	-	-	-	-
2230$+$1905	$5600\pm 250$	$-8.45$	$-7.14$	$-7.24$	$-8.73$	$-8.90$	-	-	-
2231$+$0906	$5900\pm 90$	$-9.85$	$-9.24$	$-8.84$	-	-	-	-	-
2235$-$0056	$6340\pm 200$	$-8.67$	$-7.66$	$-7.26$	$-8.85$	-	-	-	-
2238$+$0213	$7000\pm 250$	$-8.56$	$-7.55$	$-7.30$	-	-	-	-	-
2238$-$0113	$6800\pm 260$	$-8.89$	$-7.73$	$-7.78$	-	-	-	-	-
2254$+$3031	$5900\pm 90$	$-8.26$	$-6.95$	$-7.25$	$-8.54$	$-9.01$	-	-	-
2304$+$2415	$5060\pm 100$	$-9.54$	$-7.98$	$-8.93$	-	-	-	-	-
2319$+$3018	$7120\pm 200$	$-8.53$	$-7.42$	$-7.37$	$-7.71$	-	-	-	-
2325$+$0448	$6020\pm 100$	$-9.07$	$-8.06$	$-8.06$	$-8.95$	-	-	-	-
2328$+$0830	$5800\pm 330$	$-8.80$	$-7.69$	$-7.59$	-	-	-	-	-
2330$+$2805	$6670\pm 210$	$-8.84$	$-7.73$	$-7.63$	-	-	-	-	-
2330$+$2956	$7000\pm 110$	$-8.24$	$-6.63$	$-7.13$	$-8.02$	-	-	-	-
2333$+$1058	$6220\pm 300$	$-8.79$	$-7.28$	$-7.38$	$-8.67$	-	-	-	-
2340$+$0124	$6200\pm 100$	$-8.50$	$-7.54$	$-7.90$	-	-	-	-	-
2340$+$0817	$5550\pm 120$	$-9.00$	$-7.99$	$-7.69$	-	-	-	-	-
2343$-$0010	$5900\pm 290$	$-9.23$	$-7.82$	$-8.22$	-	-	-	-	-
2352$+$1922	$6170\pm 310$	$-8.34$	$-7.13$	$-7.03$	-	-	-	-	-
2352$+$3344	$7230\pm 220$	$-8.26$	$-6.85$	$-7.05$	$-8.34$	-	-	-	-
2357$+$2348	$6030\pm 240$	$-9.07$	$-7.66$	$-7.76$	-	-	-	-

Table 5. Table 7: The mass fraction of the convection zone, q 𝑞 q , and logarithm of the diffusion timescale in years for each element.

SDSS J	$\log \left(q\right)$	Ca	Mg	Fe	Na	Cr	Ti	Ni
0002$+$3209	$-5.34$	$6.18$	$6.62$	$6.17$	$6.57$	$6.15$	$6.13$	$6.21$
0004$+$0819	$-5.51$	$6.05$	$6.51$	$6.05$	$6.46$	$6.03$	$6.01$	$6.09$
0006$+$0520	$-5.27$	$6.20$	$6.65$	$6.21$	$6.60$	$6.19$	$6.16$	$6.25$
0010$-$0430	$-5.32$	$6.15$	$6.58$	$6.16$	$6.53$	$6.13$	$6.11$	$6.19$
0013$+$1109	$-5.44$	$6.16$	$6.58$	$6.11$	$6.53$	$6.09$	$6.07$	$6.15$
0019$+$2209	$-5.38$	$6.25$	$6.63$	$6.16$	$6.58$	$6.14$	$6.12$	$6.19$
0037$-$0525	$-5.54$	$6.05$	$6.51$	$6.04$	$6.46$	$6.02$	$6.00$	$6.08$
0044$+$0418	$-5.30$	$6.39$	$6.71$	$6.23$	$6.66$	$6.20$	$6.18$	$6.26$
0046$+$2717	$-5.32$	$6.11$	$6.54$	$6.14$	$6.49$	$6.11$	$6.09$	$6.17$
0047$+$1628	$-5.51$	$6.01$	$6.43$	$6.02$	$6.39$	$6.00$	$5.97$	$6.06$
0052$+$1846	$-5.49$	$6.13$	$6.56$	$6.08$	$6.51$	$6.06$	$6.04$	$6.12$
0053$+$3115	$-5.41$	$6.12$	$6.58$	$6.12$	$6.53$	$6.10$	$6.08$	$6.16$
0056$+$2453	$-5.41$	$6.33$	$6.65$	$6.15$	$6.60$	$6.13$	$6.11$	$6.19$
0107$+$2650	$-5.48$	$6.06$	$6.51$	$6.06$	$6.46$	$6.04$	$6.02$	$6.10$
0108$-$0537	$-5.46$	$6.09$	$6.54$	$6.09$	$6.49$	$6.06$	$6.04$	$6.12$
0114$+$3505	$-5.43$	$6.09$	$6.54$	$6.10$	$6.49$	$6.08$	$6.05$	$6.13$
0116$+$2050	$-5.42$	$6.11$	$6.57$	$6.12$	$6.52$	$6.09$	$6.07$	$6.15$
0117$+$0021	$-5.30$	$6.18$	$6.63$	$6.19$	$6.58$	$6.17$	$6.14$	$6.22$
0126$+$2534	$-5.37$	$6.44$	$6.70$	$6.19$	$6.65$	$6.17$	$6.17$	$6.22$
0135$+$1302	$-5.38$	$6.30$	$6.65$	$6.16$	$6.60$	$6.14$	$6.12$	$6.20$
0143$+$0113	$-5.36$	$6.13$	$6.57$	$6.14$	$6.53$	$6.12$	$6.09$	$6.18$
0144$+$1920	$-5.40$	$6.11$	$6.55$	$6.12$	$6.50$	$6.09$	$6.07$	$6.15$
0144$+$0305	$-5.33$	$6.14$	$6.58$	$6.16$	$6.53$	$6.13$	$6.11$	$6.19$
0148$-$0112	$-5.29$	$6.19$	$6.63$	$6.19$	$6.58$	$6.17$	$6.15$	$6.23$
0150$+$1354	$-5.56$	$5.97$	$6.41$	$5.99$	$6.36$	$5.97$	$5.94$	$6.02$
0157$+$0033	$-5.54$	$6.01$	$6.45$	$6.02$	$6.41$	$6.00$	$5.97$	$6.05$
0158$-$0942	$-5.35$	$6.32$	$6.66$	$6.18$	$6.61$	$6.16$	$6.14$	$6.21$
0200$+$1646	$-5.48$	$6.09$	$6.55$	$6.08$	$6.50$	$6.06$	$6.04$	$6.12$
0201$+$2015	$-5.40$	$6.13$	$6.59$	$6.13$	$6.54$	$6.11$	$6.09$	$6.17$
0208$-$0542	$-5.55$	$6.02$	$6.48$	$6.02$	$6.43$	$6.00$	$5.98$	$6.06$
0234$-$0510	$-5.32$	$6.14$	$6.58$	$6.16$	$6.53$	$6.13$	$6.11$	$6.19$
0252$-$0401	$-5.30$	$6.17$	$6.60$	$6.18$	$6.56$	$6.16$	$6.13$	$6.21$
0252$+$0054	$-5.23$	$6.19$	$6.62$	$6.21$	$6.58$	$6.19$	$6.16$	$6.25$
0447$+$1124	$-5.35$	$6.15$	$6.59$	$6.15$	$6.55$	$6.13$	$6.11$	$6.19$
0512$-$0505	$-5.51$	$6.11$	$6.54$	$6.07$	$6.49$	$6.04$	$6.02$	$6.10$
0721$+$3928	$-5.39$	$6.13$	$6.59$	$6.14$	$6.54$	$6.12$	$6.09$	$6.17$
0735$+$2057	$-5.61$	$5.95$	$6.38$	$5.96$	$6.34$	$5.93$	$5.91$	$5.99$
0736$+$4118	$-5.68$	$5.95$	$6.42$	$5.95$	$6.37$	$5.92$	$5.90$	$5.98$
0739$+$3112	$-5.48$	$6.29$	$6.62$	$6.11$	$6.56$	$6.09$	$6.07$	$6.14$
0741$+$3146	$-5.40$	$6.31$	$6.65$	$6.15$	$6.59$	$6.13$	$6.11$	$6.19$
0744$+$4649	$-5.72$	$5.92$	$6.39$	$5.92$	$6.34$	$5.89$	$5.87$	$5.95$
0744$+$4408	$-5.39$	$6.12$	$6.57$	$6.13$	$6.53$	$6.11$	$6.08$	$6.16$
0744$+$2701	$-5.28$	$6.14$	$6.56$	$6.16$	$6.51$	$6.14$	$6.11$	$6.20$
0744$+$1640	$-5.38$	$6.55$	$6.73$	$6.19$	$6.67$	$6.18$	$6.23$	$6.23$
0758$+$1013	$-5.59$	$6.01$	$6.48$	$6.01$	$6.43$	$5.99$	$5.96$	$6.04$
0800$+$2242	$-5.27$	$6.38$	$6.71$	$6.24$	$6.66$	$6.21$	$6.19$	$6.27$
0806$+$3055	$-5.43$	$6.06$	$6.49$	$6.08$	$6.44$	$6.05$	$6.03$	$6.11$
0806$+$4058	$-5.34$	$6.14$	$6.58$	$6.15$	$6.53$	$6.13$	$6.11$	$6.19$
0807$+$4930	$-5.70$	$5.93$	$6.40$	$5.93$	$6.35$	$5.91$	$5.89$	$5.96$
0816$+$2330	$-5.33$	$6.10$	$6.52$	$6.13$	$6.47$	$6.10$	$6.07$	$6.16$
0818$+$1247	$-5.32$	$6.15$	$6.60$	$6.17$	$6.55$	$6.14$	$6.12$	$6.20$
0823$+$0546	$-5.37$	$6.26$	$6.64$	$6.16$	$6.59$	$6.14$	$6.12$	$6.20$
0830$-$0319	$-5.33$	$6.19$	$6.63$	$6.18$	$6.58$	$6.15$	$6.13$	$6.21$
0832$+$4109	$-5.58$	$5.98$	$6.42$	$5.99$	$6.37$	$5.96$	$5.94$	$6.02$
0838$+$2322	$-5.35$	$6.38$	$6.69$	$6.19$	$6.64$	$6.17$	$6.16$	$6.23$
0842$+$1406	$-5.32$	$6.14$	$6.57$	$6.16$	$6.53$	$6.13$	$6.11$	$6.19$
0842$+$1536	$-5.32$	$6.30$	$6.67$	$6.20$	$6.61$	$6.17$	$6.15$	$6.23$
0843$+$5614	$-5.36$	$6.14$	$6.59$	$6.15$	$6.54$	$6.12$	$6.10$	$6.18$
0851$+$1543	$-5.45$	$6.08$	$6.53$	$6.09$	$6.48$	$6.06$	$6.04$	$6.12$
0852$+$3402	$-5.51$	$6.11$	$6.54$	$6.07$	$6.49$	$6.05$	$6.03$	$6.10$
0901$+$0752	$-5.51$	$5.98$	$6.40$	$6.00$	$6.35$	$5.98$	$5.95$	$6.04$
0902$+$3625	$-5.42$	$6.10$	$6.55$	$6.10$	$6.50$	$6.08$	$6.06$	$6.14$
0902$+$1004	$-5.29$	$6.16$	$6.59$	$6.18$	$6.55$	$6.15$	$6.13$	$6.21$
0906$+$1141	$-5.41$	$6.08$	$6.51$	$6.09$	$6.46$	$6.07$	$6.04$	$6.13$
0908$+$5136	$-5.34$	$6.26$	$6.65$	$6.18$	$6.60$	$6.16$	$6.14$	$6.22$
0908$+$4119	$-5.33$	$6.16$	$6.61$	$6.17$	$6.56$	$6.15$	$6.12$	$6.20$
0913$+$2627	$-5.42$	$6.37$	$6.67$	$6.16$	$6.61$	$6.14$	$6.12$	$6.19$
0913$+$4127	$-5.56$	$6.02$	$6.47$	$6.02$	$6.42$	$6.00$	$5.97$	$6.05$
0916$+$2540	$-5.82$	$5.81$	$6.25$	$5.82$	$6.21$	$5.80$	$5.77$	$5.85$
0924$+$4301	$-5.32$	$6.37$	$6.70$	$6.21$	$6.64$	$6.19$	$6.17$	$6.24$
0925$+$3130	$-5.47$	$6.11$	$6.56$	$6.09$	$6.51$	$6.07$	$6.05$	$6.13$
0927$+$4931	$-5.45$	$6.08$	$6.53$	$6.09$	$6.49$	$6.07$	$6.04$	$6.12$
0929$+$4247	$-5.40$	$6.11$	$6.55$	$6.12$	$6.50$	$6.09$	$6.07$	$6.15$
0933$+$6334	$-5.48$	$6.05$	$6.49$	$6.06$	$6.44$	$6.03$	$6.01$	$6.09$
0937$+$5228	$-5.39$	$6.11$	$6.55$	$6.12$	$6.50$	$6.09$	$6.07$	$6.15$
0939$+$4136	$-5.48$	$6.05$	$6.50$	$6.06$	$6.45$	$6.04$	$6.02$	$6.10$
0939$+$5019	$-5.56$	$6.00$	$6.45$	$6.01$	$6.40$	$5.99$	$5.96$	$6.04$
0946$+$2024	$-5.27$	$6.16$	$6.59$	$6.18$	$6.54$	$6.15$	$6.13$	$6.21$
0948$+$3008	$-5.40$	$6.18$	$6.60$	$6.14$	$6.55$	$6.11$	$6.09$	$6.17$
0956$+$5912	$-5.30$	$6.11$	$6.51$	$6.14$	$6.47$	$6.11$	$6.08$	$6.18$
1003$-$0031	$-5.57$	$6.01$	$6.46$	$6.01$	$6.41$	$5.99$	$5.96$	$6.04$
1005$+$2244	$-5.36$	$6.15$	$6.61$	$6.15$	$6.56$	$6.13$	$6.11$	$6.19$
1006$+$1752	$-5.40$	$6.28$	$6.64$	$6.15$	$6.58$	$6.13$	$6.11$	$6.18$
1014$+$2827	$-5.59$	$5.96$	$6.39$	$5.97$	$6.34$	$5.95$	$5.92$	$6.01$
1017$+$3447	$-5.35$	$6.26$	$6.65$	$6.18$	$6.59$	$6.16$	$6.13$	$6.21$
1017$+$2419	$-5.32$	$6.13$	$6.56$	$6.15$	$6.52$	$6.13$	$6.10$	$6.19$
1019$+$3535	$-5.51$	$6.06$	$6.52$	$6.06$	$6.47$	$6.04$	$6.02$	$6.09$
1019$+$2045	$-5.48$	$6.25$	$6.60$	$6.10$	$6.55$	$6.08$	$6.06$	$6.14$
1024$+$4531	$-5.45$	$6.10$	$6.56$	$6.10$	$6.51$	$6.08$	$6.06$	$6.14$
1024$+$1014	$-5.61$	$5.94$	$6.37$	$5.96$	$6.32$	$5.93$	$5.91$	$5.99$
1032$+$1338	$-5.46$	$6.24$	$6.60$	$6.11$	$6.55$	$6.09$	$6.07$	$6.15$
1033$+$1809	$-5.49$	$6.06$	$6.51$	$6.06$	$6.46$	$6.04$	$6.02$	$6.10$
1038$-$0036	$-5.28$	$6.15$	$6.57$	$6.17$	$6.52$	$6.14$	$6.12$	$6.21$
1038$+$0432	$-5.56$	$5.97$	$6.39$	$5.98$	$6.35$	$5.96$	$5.93$	$6.02$
1040$+$2407	$-5.62$	$5.96$	$6.41$	$5.97$	$6.36$	$5.95$	$5.92$	$6.00$
1041$+$3432	$-5.25$	$6.18$	$6.61$	$6.20$	$6.56$	$6.17$	$6.14$	$6.23$
1043$+$3516	$-5.30$	$6.18$	$6.63$	$6.19$	$6.58$	$6.17$	$6.14$	$6.22$
1046$+$1329	$-5.45$	$6.32$	$6.64$	$6.13$	$6.59$	$6.11$	$6.09$	$6.16$
1055$+$3725	$-5.65$	$5.95$	$6.41$	$5.96$	$6.36$	$5.93$	$5.91$	$5.99$
1058$+$3143	$-5.26$	$6.21$	$6.66$	$6.22$	$6.61$	$6.20$	$6.17$	$6.25$
1102$+$2827	$-5.54$	$5.99$	$6.42$	$6.00$	$6.37$	$5.98$	$5.95$	$6.04$
1102$+$0214	$-5.35$	$6.37$	$6.69$	$6.19$	$6.63$	$6.17$	$6.15$	$6.23$
1103$+$4144	$-5.41$	$6.24$	$6.62$	$6.14$	$6.57$	$6.12$	$6.10$	$6.18$
1105$+$5006	$-5.30$	$6.15$	$6.58$	$6.17$	$6.53$	$6.14$	$6.12$	$6.20$
1105$+$0228	$-5.46$	$6.15$	$6.58$	$6.11$	$6.53$	$6.08$	$6.06$	$6.14$
1106$+$6737	$-5.52$	$6.01$	$6.44$	$6.02$	$6.40$	$6.00$	$5.97$	$6.06$
1112$+$0700	$-5.20$	$6.22$	$6.65$	$6.24$	$6.60$	$6.21$	$6.19$	$6.27$
1113$+$2751	$-5.49$	$6.05$	$6.50$	$6.06$	$6.45$	$6.04$	$6.01$	$6.09$
1132$+$3323	$-5.50$	$6.03$	$6.48$	$6.04$	$6.43$	$6.02$	$6.00$	$6.08$
1134$+$1542	$-5.37$	$6.12$	$6.57$	$6.14$	$6.52$	$6.11$	$6.09$	$6.17$
1144$+$3720	$-5.26$	$6.17$	$6.60$	$6.19$	$6.55$	$6.17$	$6.14$	$6.23$
1144$+$1218	$-5.47$	$6.24$	$6.60$	$6.11$	$6.55$	$6.09$	$6.07$	$6.14$
1147$+$5429	$-5.52$	$6.18$	$6.57$	$6.07$	$6.51$	$6.05$	$6.03$	$6.11$
1149$+$0519	$-5.29$	$6.15$	$6.58$	$6.17$	$6.54$	$6.15$	$6.12$	$6.21$
1150$+$4928	$-5.23$	$6.22$	$6.66$	$6.23$	$6.61$	$6.21$	$6.18$	$6.26$
1150$+$4533	$-5.60$	$5.98$	$6.44$	$5.99$	$6.39$	$5.96$	$5.94$	$6.02$
1152$+$5101	$-5.40$	$6.49$	$6.71$	$6.18$	$6.65$	$6.16$	$6.19$	$6.22$
1152$+$1605	$-5.40$	$6.10$	$6.54$	$6.11$	$6.50$	$6.09$	$6.06$	$6.15$
1157$+$6138	$-5.30$	$6.21$	$6.65$	$6.20$	$6.60$	$6.17$	$6.15$	$6.23$
1158$+$1845	$-5.36$	$6.09$	$6.52$	$6.12$	$6.47$	$6.09$	$6.06$	$6.15$
1158$+$5942	$-5.43$	$6.12$	$6.57$	$6.11$	$6.52$	$6.09$	$6.07$	$6.15$
1158$+$0454	$-5.62$	$6.01$	$6.47$	$5.99$	$6.42$	$5.97$	$5.95$	$6.03$
1158$+$4712	$-5.25$	$6.17$	$6.60$	$6.19$	$6.55$	$6.17$	$6.14$	$6.23$
1158$+$5448	$-5.40$	$6.12$	$6.58$	$6.13$	$6.53$	$6.10$	$6.08$	$6.16$
1205$+$3536	$-5.46$	$6.08$	$6.54$	$6.09$	$6.49$	$6.07$	$6.04$	$6.12$
1211$+$2326	$-5.40$	$6.11$	$6.56$	$6.12$	$6.51$	$6.10$	$6.07$	$6.16$
1214$-$0234	$-5.49$	$6.26$	$6.61$	$6.10$	$6.55$	$6.08$	$6.06$	$6.14$
1217$+$1157	$-5.35$	$6.16$	$6.61$	$6.16$	$6.56$	$6.14$	$6.11$	$6.19$
1218$+$0023	$-5.32$	$6.34$	$6.68$	$6.21$	$6.63$	$6.18$	$6.16$	$6.24$
1220$+$0929	$-5.39$	$6.11$	$6.55$	$6.12$	$6.50$	$6.10$	$6.07$	$6.16$
1224$+$2838	$-5.38$	$6.46$	$6.71$	$6.19$	$6.65$	$6.17$	$6.18$	$6.22$
1226$+$2936	$-5.44$	$6.49$	$6.70$	$6.16$	$6.64$	$6.14$	$6.18$	$6.19$
1229$+$0743	$-5.53$	$6.02$	$6.46$	$6.03$	$6.41$	$6.00$	$5.98$	$6.06$
1230$+$3143	$-5.31$	$6.20$	$6.64$	$6.19$	$6.59$	$6.17$	$6.15$	$6.23$
1234$+$5208	$-5.37$	$6.08$	$6.49$	$6.10$	$6.45$	$6.08$	$6.05$	$6.14$
1238$+$2149	$-5.51$	$6.16$	$6.56$	$6.07$	$6.51$	$6.05$	$6.03$	$6.11$
1245$+$0822	$-5.50$	$6.03$	$6.47$	$6.04$	$6.43$	$6.02$	$6.00$	$6.08$
1249$+$6514	$-5.21$	$6.21$	$6.65$	$6.23$	$6.60$	$6.21$	$6.18$	$6.27$
1254$+$3551	$-5.31$	$6.18$	$6.63$	$6.19$	$6.58$	$6.16$	$6.14$	$6.22$
1257$+$3238	$-5.56$	$6.13$	$6.53$	$6.04$	$6.48$	$6.02$	$6.00$	$6.07$
1257$-$0310	$-5.45$	$6.08$	$6.53$	$6.09$	$6.48$	$6.06$	$6.04$	$6.12$
1259$+$3112	$-5.35$	$6.34$	$6.67$	$6.19$	$6.62$	$6.17$	$6.15$	$6.22$
1259$+$4729	$-5.41$	$6.12$	$6.57$	$6.12$	$6.52$	$6.10$	$6.08$	$6.16$
1303$+$4055	$-5.39$	$6.15$	$6.60$	$6.14$	$6.55$	$6.12$	$6.10$	$6.18$
1308$+$0957	$-5.23$	$6.18$	$6.61$	$6.21$	$6.56$	$6.18$	$6.15$	$6.24$
1308$+$0258	$-5.41$	$6.15$	$6.59$	$6.13$	$6.54$	$6.11$	$6.08$	$6.16$
1314$+$3748	$-5.53$	$6.03$	$6.48$	$6.03$	$6.43$	$6.01$	$5.99$	$6.07$
1316$+$1918	$-5.38$	$6.42$	$6.70$	$6.18$	$6.64$	$6.16$	$6.16$	$6.22$
1319$+$3641	$-5.22$	$6.21$	$6.65$	$6.23$	$6.60$	$6.20$	$6.18$	$6.26$
1320$+$0204	$-5.33$	$6.14$	$6.57$	$6.15$	$6.53$	$6.13$	$6.10$	$6.19$
1321$-$0237	$-5.60$	$5.99$	$6.45$	$5.99$	$6.40$	$5.97$	$5.95$	$6.03$
1329$+$1301	$-5.33$	$6.15$	$6.59$	$6.16$	$6.54$	$6.14$	$6.11$	$6.20$
1330$+$3029	$-5.51$	$6.04$	$6.49$	$6.05$	$6.44$	$6.02$	$6.00$	$6.08$
1336$+$3547	$-5.38$	$6.12$	$6.56$	$6.13$	$6.52$	$6.11$	$6.08$	$6.17$
1339$+$2643	$-5.35$	$6.18$	$6.63$	$6.17$	$6.58$	$6.15$	$6.12$	$6.20$
1340$+$2702	$-5.43$	$6.03$	$6.44$	$6.06$	$6.39$	$6.03$	$6.00$	$6.09$
1342$+$1813	$-5.52$	$6.19$	$6.57$	$6.07$	$6.51$	$6.05$	$6.03$	$6.11$
1345$+$1153	$-5.58$	$5.98$	$6.43$	$5.99$	$6.38$	$5.97$	$5.95$	$6.03$
1347$+$1415	$-5.35$	$6.14$	$6.58$	$6.15$	$6.53$	$6.12$	$6.10$	$6.18$
1350$+$1058	$-5.38$	$6.48$	$6.71$	$6.19$	$6.66$	$6.17$	$6.19$	$6.22$
1351$+$2645	$-5.59$	$5.97$	$6.41$	$5.98$	$6.37$	$5.96$	$5.93$	$6.01$
1356$+$2416	$-5.39$	$6.20$	$6.61$	$6.15$	$6.56$	$6.13$	$6.10$	$6.18$
1356$+$0236	$-5.27$	$6.14$	$6.55$	$6.17$	$6.50$	$6.14$	$6.11$	$6.20$
1401$+$3659	$-5.31$	$6.38$	$6.70$	$6.22$	$6.65$	$6.20$	$6.18$	$6.25$
1404$+$3620	$-5.41$	$6.20$	$6.61$	$6.13$	$6.55$	$6.11$	$6.09$	$6.17$
1405$+$2542	$-5.37$	$6.31$	$6.65$	$6.17$	$6.60$	$6.15$	$6.13$	$6.21$
1405$+$1549	$-5.30$	$6.15$	$6.58$	$6.17$	$6.54$	$6.14$	$6.12$	$6.20$
1411$+$3410	$-5.64$	$5.96$	$6.43$	$5.97$	$6.38$	$5.94$	$5.92$	$6.00$
1412$+$2836	$-5.52$	$6.26$	$6.60$	$6.09$	$6.54$	$6.07$	$6.05$	$6.12$
1421$+$1843	$-5.43$	$6.04$	$6.46$	$6.06$	$6.41$	$6.04$	$6.01$	$6.10$
1428$+$4403	$-5.31$	$6.18$	$6.63$	$6.18$	$6.58$	$6.16$	$6.14$	$6.22$
1429$+$3841	$-5.31$	$6.37$	$6.70$	$6.21$	$6.64$	$6.19$	$6.17$	$6.25$
1430$-$0151	$-5.64$	$5.92$	$6.35$	$5.94$	$6.31$	$5.91$	$5.89$	$5.97$
1443$+$5833	$-5.28$	$6.18$	$6.62$	$6.19$	$6.57$	$6.17$	$6.14$	$6.23$
1443$+$3014	$-5.38$	$6.10$	$6.54$	$6.12$	$6.49$	$6.09$	$6.07$	$6.15$
1445$+$0913	$-5.46$	$6.05$	$6.48$	$6.06$	$6.43$	$6.04$	$6.01$	$6.09$
1448$+$1047	$-5.34$	$6.16$	$6.61$	$6.16$	$6.56$	$6.14$	$6.12$	$6.20$
1500$+$2315	$-5.41$	$6.10$	$6.54$	$6.11$	$6.49$	$6.08$	$6.06$	$6.14$
1502$+$3744	$-5.36$	$6.45$	$6.71$	$6.20$	$6.66$	$6.18$	$6.18$	$6.24$
1507$+$4034	$-5.31$	$6.15$	$6.58$	$6.16$	$6.53$	$6.14$	$6.11$	$6.20$
1518$+$0506	$-5.47$	$6.34$	$6.64$	$6.13$	$6.59$	$6.11$	$6.09$	$6.16$
1524$+$4049	$-5.47$	$6.09$	$6.55$	$6.09$	$6.50$	$6.07$	$6.05$	$6.12$
1534$+$1242	$-5.58$	$5.99$	$6.44$	$6.00$	$6.39$	$5.97$	$5.95$	$6.03$
1535$+$1247	$-5.54$	$6.03$	$6.49$	$6.03$	$6.44$	$6.01$	$5.99$	$6.07$
1536$+$4205	$-5.52$	$6.05$	$6.51$	$6.05$	$6.46$	$6.03$	$6.00$	$6.08$
1537$+$3608	$-5.42$	$6.30$	$6.64$	$6.15$	$6.58$	$6.12$	$6.11$	$6.18$
1540$+$5352	$-5.38$	$6.12$	$6.57$	$6.13$	$6.52$	$6.11$	$6.08$	$6.16$
1542$+$4650	$-5.56$	$6.00$	$6.44$	$6.01$	$6.39$	$5.98$	$5.96$	$6.04$
1543$+$2024	$-5.50$	$6.03$	$6.47$	$6.04$	$6.42$	$6.01$	$5.99$	$6.07$
1545$+$5236	$-5.43$	$6.19$	$6.60$	$6.13$	$6.55$	$6.10$	$6.08$	$6.16$
1546$+$3009	$-5.39$	$6.11$	$6.55$	$6.12$	$6.50$	$6.09$	$6.07$	$6.15$
1549$+$2633	$-5.28$	$6.35$	$6.70$	$6.23$	$6.65$	$6.21$	$6.19$	$6.26$
1549$+$1906	$-5.41$	$6.10$	$6.54$	$6.11$	$6.50$	$6.08$	$6.06$	$6.14$
1554$+$1735	$-5.36$	$6.14$	$6.58$	$6.15$	$6.53$	$6.12$	$6.10$	$6.18$
1604$+$1830	$-5.28$	$6.31$	$6.68$	$6.22$	$6.63$	$6.20$	$6.18$	$6.25$
1610$+$4006	$-5.39$	$6.11$	$6.56$	$6.12$	$6.51$	$6.10$	$6.08$	$6.16$
1612$+$3534	$-5.34$	$6.14$	$6.58$	$6.15$	$6.54$	$6.13$	$6.11$	$6.19$
1616$+$3303	$-5.46$	$6.06$	$6.50$	$6.07$	$6.46$	$6.05$	$6.02$	$6.11$
1624$+$3310	$-5.29$	$6.17$	$6.61$	$6.18$	$6.57$	$6.16$	$6.14$	$6.22$
1626$+$3303	$-5.40$	$6.13$	$6.58$	$6.13$	$6.53$	$6.11$	$6.09$	$6.17$
1627$+$4646	$-5.36$	$6.15$	$6.60$	$6.15$	$6.55$	$6.13$	$6.11$	$6.19$
1636$+$1619	$-5.56$	$6.32$	$6.61$	$6.07$	$6.56$	$6.05$	$6.05$	$6.10$
1641$+$1856	$-5.27$	$6.52$	$6.76$	$6.26$	$6.71$	$6.24$	$6.24$	$6.29$
1649$+$2238	$-5.62$	$5.99$	$6.46$	$5.99$	$6.41$	$5.97$	$5.94$	$6.02$
1651$+$4249	$-5.66$	$5.93$	$6.37$	$5.94$	$6.33$	$5.91$	$5.89$	$5.97$
1706$+$2541	$-5.25$	$6.27$	$6.69$	$6.23$	$6.64$	$6.21$	$6.19$	$6.27$
2109$-$0039	$-5.46$	$6.09$	$6.54$	$6.09$	$6.49$	$6.07$	$6.04$	$6.12$
2110$+$0512	$-5.45$	$6.20$	$6.59$	$6.11$	$6.54$	$6.09$	$6.07$	$6.15$
2123$+$0016	$-5.38$	$6.46$	$6.71$	$6.19$	$6.65$	$6.17$	$6.18$	$6.22$
2157$+$1206	$-5.41$	$6.13$	$6.59$	$6.13$	$6.54$	$6.11$	$6.08$	$6.16$
2225$+$2338	$-5.26$	$6.20$	$6.64$	$6.21$	$6.59$	$6.19$	$6.16$	$6.25$
2230$+$1905	$-5.61$	$5.99$	$6.45$	$5.99$	$6.40$	$5.96$	$5.94$	$6.02$
2231$+$0906	$-5.31$	$6.39$	$6.71$	$6.22$	$6.65$	$6.20$	$6.18$	$6.25$
2235$-$0056	$-5.41$	$6.11$	$6.56$	$6.12$	$6.51$	$6.09$	$6.07$	$6.15$
2238$+$0213	$-5.29$	$6.17$	$6.61$	$6.18$	$6.56$	$6.16$	$6.13$	$6.22$
2238$-$0113	$-5.28$	$6.19$	$6.64$	$6.20$	$6.59$	$6.18$	$6.15$	$6.23$
2254$+$3031	$-5.58$	$5.99$	$6.44$	$6.00$	$6.39$	$5.97$	$5.95$	$6.03$
2304$+$2415	$-5.48$	$6.30$	$6.63$	$6.11$	$6.57$	$6.09$	$6.07$	$6.15$
2319$+$3018	$-5.27$	$6.18$	$6.62$	$6.20$	$6.57$	$6.17$	$6.15$	$6.23$
2325$+$0448	$-5.41$	$6.15$	$6.59$	$6.13$	$6.54$	$6.11$	$6.08$	$6.16$
2328$+$0830	$-5.50$	$6.07$	$6.52$	$6.06$	$6.47$	$6.04$	$6.02$	$6.10$
2330$+$2805	$-5.32$	$6.17$	$6.62$	$6.18$	$6.57$	$6.15$	$6.13$	$6.21$
2330$+$2956	$-5.33$	$6.13$	$6.57$	$6.15$	$6.52$	$6.12$	$6.10$	$6.18$
2333$+$1058	$-5.42$	$6.11$	$6.57$	$6.12$	$6.52$	$6.09$	$6.07$	$6.15$
2340$+$0124	$-5.47$	$6.07$	$6.52$	$6.07$	$6.47$	$6.05$	$6.03$	$6.11$
2340$+$0817	$-5.51$	$6.11$	$6.54$	$6.07$	$6.49$	$6.04$	$6.02$	$6.10$
2343$-$0010	$-5.41$	$6.21$	$6.61$	$6.14$	$6.56$	$6.12$	$6.09$	$6.17$
2352$+$1922	$-5.50$	$6.04$	$6.49$	$6.05$	$6.44$	$6.02$	$6.00$	$6.08$
2352$+$3344	$-5.29$	$6.16$	$6.59$	$6.18$	$6.55$	$6.15$	$6.13$	$6.21$
2357$+$2348	$-5.41$	$6.15$	$6.59$	$6.13$	$6.54$	$6.11$	$6.08$

Table 6. Table 8: Distances d 𝑑 d , proper-motions μ 𝜇 \mu , transverse motions v ⟂ subscript 𝑣 perpendicular-to v_{\perp} , and white dwarf cooling ages for our DZ sample.

SDSS J	$d$ [pc]	$\mu$ [mas yr-1]	$v_{⟂}$ [km s-1]	Age [Gyr]		SDSS J	$d$ [pc]	$\mu$ [mas yr-1]	$v_{⟂}$ [km s-1]	Age [Gyr]
0002$+$3209	$210\pm 28$	$38.4\pm 5.3$	$38.5\pm 7.6$	${2.6}_{-0.6}^{+0.8}$		0004$+$0819	$336\pm 46$	-	-	${3.7}_{-1.2}^{+1.6}$
0006$+$0520	$216\pm 28$	-	-	${2.1}_{-0.5}^{+0.6}$		0010$-$0430	$221\pm 30$	$66.7\pm 4.2$	$70\pm 11$	${2.0}_{-0.4}^{+0.5}$
0013$+$1109	$277\pm 36$	-	-	${3.7}_{-1.1}^{+1.4}$		0019$+$2209	$155\pm 20$	$45.4\pm 3.3$	$33.4\pm 5.0$	${3.3}_{-0.9}^{+1.0}$
0037$-$0525	$125\pm 16$	$12.5\pm 3.5$	$7.4\pm 2.3$	${4.2}_{-1.1}^{+1.0}$		0044$+$0418	$79\pm 10$	$63.1\pm 6.6$	$23.8\pm 4.0$	${3.2}_{-0.8}^{+0.9}$
0046$+$2717	$272\pm 37$	$28.7\pm 4.6$	$37.2\pm 7.8$	${1.5}_{-0.3}^{+0.4}$		0047$+$1628	$246\pm 32$	-	-	${2.3}_{-0.5}^{+0.7}$
0052$+$1846	$250\pm 33$	-	-	${4.2}_{-1.3}^{+1.4}$		0053$+$3115	$276\pm 37$	-	-	${2.9}_{-0.8}^{+1.1}$
0056$+$2453	$214\pm 28$	-	-	${4.9}_{-1.5}^{+1.2}$		0107$+$2650	$101\pm 13$	$262.5\pm 3.1$	$126\pm 17$	${2.9}_{-0.8}^{+0.8}$
0108$-$0537	$173\pm 23$	$26.7\pm 3.4$	$22.1\pm 4.0$	${3.2}_{-0.9}^{+0.9}$		0114$+$3505	$243\pm 32$	-	-	${2.6}_{-0.7}^{+0.8}$
0116$+$2050	$68.3\pm 8.9$	$118.4\pm 2.8$	$38.5\pm 5.1$	${2.9}_{-0.8}^{+0.8}$		0117$+$0021	$132\pm 18$	$501.8\pm 7.4$	$316\pm 42$	${2.1}_{-0.5}^{+0.5}$
0126$+$2534	$140\pm 18$	$122.4\pm 4.7$	$81\pm 11$	${5.5}_{-1.3}^{+0.6}$		0135$+$1302	$94\pm 12$	$105.5\pm 3.6$	$47.4\pm 6.2$	${3.7}_{-1.0}^{+1.0}$
0143$+$0113	$137\pm 18$	$74.4\pm 3.8$	$48.6\pm 6.9$	${2.2}_{-0.5}^{+0.6}$		0144$+$1920	$225\pm 30$	$31.9\pm 4.5$	$34.2\pm 6.7$	${2.5}_{-0.6}^{+0.8}$
0144$+$0305	$356\pm 48$	-	-	${2.0}_{-0.5}^{+0.7}$		0148$-$0112	$266\pm 36$	$13.4\pm 4.8$	$17.0\pm 6.5$	${2.1}_{-0.5}^{+0.6}$
0150$+$1354	$167\pm 22$	$96.8\pm 3.8$	$77\pm 11$	${2.7}_{-0.7}^{+0.8}$		0157$+$0033	$120\pm 16$	$31.5\pm 6.7$	$18.0\pm 4.5$	${3.1}_{-0.8}^{+0.9}$
0158$-$0942	$171\pm 22$	$86.3\pm 5.0$	$70\pm 10$	${3.4}_{-0.9}^{+1.0}$		0200$+$1646	$186\pm 24$	$52.0\pm 4.6$	$46.0\pm 7.3$	${3.7}_{-1.0}^{+1.1}$
0201$+$2015	$174\pm 23$	-	-	${2.9}_{-0.8}^{+0.9}$		0208$-$0542	$227\pm 30$	-	-	${3.8}_{-1.2}^{+1.5}$
0234$-$0510	$321\pm 44$	-	-	${1.9}_{-0.5}^{+0.6}$		0252$-$0401	$215\pm 29$	$66.7\pm 4.2$	$68\pm 10$	${2.0}_{-0.4}^{+0.5}$
0252$+$0054	$206\pm 28$	$57.4\pm 4.7$	$56.5\pm 8.9$	${1.6}_{-0.3}^{+0.3}$		0447$+$1124	$188\pm 25$	$32.7\pm 5.0$	$29.3\pm 5.9$	${2.4}_{-0.6}^{+0.7}$
0512$-$0505	$55.5\pm 6.9$	$85.2\pm 3.1$	$22.5\pm 2.9$	${4.5}_{-1.1}^{+0.8}$		0721$+$3928	$199\pm 26$	-	-	${2.8}_{-0.7}^{+0.8}$
0735$+$2057	$176\pm 23$	$38.2\pm 5.5$	$32.1\pm 6.2$	${3.1}_{-0.8}^{+0.9}$		0736$+$4118	$93\pm 12$	$141.7\pm 3.1$	$62.5\pm 7.9$	${6.1}_{-1.1}^{+0.5}$
0739$+$3112	$169\pm 21$	-	-	${6.1}_{-1.6}^{+1.0}$		0741$+$3146	$153\pm 19$	-	-	${4.4}_{-1.1}^{+1.0}$
0744$+$4649	$59.7\pm 7.3$	$69.4\pm 3.3$	$19.7\pm 2.6$	${6.4}_{-1.1}^{+0.4}$		0744$+$4408	$289\pm 39$	$72.1\pm 4.9$	$99\pm 15$	${2.6}_{-0.7}^{+0.9}$
0744$+$2701	$272\pm 37$	$23.9\pm 4.0$	$31.0\pm 6.8$	${1.4}_{-0.3}^{+0.3}$		0744$+$1640	$118\pm 15$	-	-	${6.6}_{-1.2}^{+0.5}$
0758$+$1013	$197\pm 26$	-	-	${4.7}_{-1.4}^{+1.2}$		0800$+$2242	$220\pm 30$	-	-	${2.8}_{-0.8}^{+1.0}$
0806$+$3055	$266\pm 36$	-	-	${2.0}_{-0.5}^{+0.6}$		0806$+$4058	$114\pm 16$	$111\pm 11$	$60\pm 10$	${2.1}_{-0.5}^{+0.5}$
0807$+$4930	$156\pm 20$	-	-	${6.1}_{-1.4}^{+0.8}$		0816$+$2330	$369\pm 51$	-	-	${1.4}_{-0.3}^{+0.4}$
0818$+$1247	$294\pm 41$	-	-	${2.1}_{-0.5}^{+0.7}$		0823$+$0546	$52.2\pm 6.7$	$251.9\pm 2.7$	$62.6\pm 8.1$	${3.2}_{-0.9}^{+0.9}$
0830$-$0319	$140\pm 19$	$51.9\pm 3.4$	$34.6\pm 5.2$	${2.6}_{-0.7}^{+0.7}$		0832$+$4109	$234\pm 31$	$55.0\pm 5.4$	$61\pm 10$	${3.1}_{-0.9}^{+1.0}$
0838$+$2322	$84\pm 10$	$41.9\pm 3.3$	$16.8\pm 2.5$	${4.1}_{-1.0}^{+0.9}$		0842$+$1406	$93\pm 12$	$79.3\pm 4.8$	$35.3\pm 5.2$	${1.8}_{-0.4}^{+0.4}$
0842$+$1536	$209\pm 28$	$36.3\pm 3.6$	$36.0\pm 6.0$	${2.9}_{-0.8}^{+1.0}$		0843$+$5614	$218\pm 30$	$20.9\pm 4.1$	$21.7\pm 5.2$	${2.3}_{-0.5}^{+0.7}$
0851$+$1543	$99\pm 13$	$76.4\pm 3.0$	$36.0\pm 5.0$	${2.8}_{-0.7}^{+0.7}$		0852$+$3402	$176\pm 22$	-	-	${4.4}_{-1.2}^{+1.1}$
0901$+$0752	$209\pm 28$	$44.7\pm 3.9$	$44.4\pm 7.0$	${1.9}_{-0.4}^{+0.4}$		0902$+$3625	$222\pm 29$	-	-	${2.7}_{-0.7}^{+0.9}$
0902$+$1004	$290\pm 40$	-	-	${1.8}_{-0.4}^{+0.5}$		0906$+$1141	$306\pm 41$	-	-	${2.0}_{-0.5}^{+0.6}$
0908$+$5136	$119\pm 15$	$43.8\pm 3.7$	$24.8\pm 3.9$	${3.0}_{-0.8}^{+0.8}$		0908$+$4119	$303\pm 42$	-	-	${2.2}_{-0.5}^{+0.8}$
0913$+$2627	$111\pm 14$	$72.1\pm 4.8$	$38.1\pm 5.4$	${5.8}_{-1.3}^{+0.7}$		0913$+$4127	$212\pm 28$	-	-	${3.8}_{-1.1}^{+1.3}$
0916$+$2540	$43.4\pm 5.4$	$237.8\pm 2.8$	$49.1\pm 6.2$	${5.3}_{-1.2}^{+0.6}$		0924$+$4301	$236\pm 31$	$52.0\pm 4.8$	$58.3\pm 9.3$	${3.4}_{-1.0}^{+1.1}$
0925$+$3130	$81\pm 10$	$137.0\pm 3.3$	$53.1\pm 6.9$	${3.7}_{-0.9}^{+1.0}$		0927$+$4931	$248\pm 33$	$65.6\pm 5.5$	$78\pm 12$	${2.9}_{-0.8}^{+1.0}$
0929$+$4247	$185\pm 25$	$15.0\pm 3.7$	$13.2\pm 3.7$	${2.4}_{-0.6}^{+0.7}$		0933$+$6334	$269\pm 36$	-	-	${2.8}_{-0.8}^{+1.2}$
0937$+$5228	$132\pm 18$	$69.0\pm 3.6$	$43.2\pm 6.2$	${2.3}_{-0.5}^{+0.6}$		0939$+$4136	$202\pm 27$	$43.7\pm 5.4$	$42.0\pm 7.7$	${2.7}_{-0.7}^{+0.8}$
0939$+$5019	$134\pm 17$	$81.6\pm 5.5$	$52.1\pm 7.6$	${3.3}_{-0.9}^{+1.0}$		0946$+$2024	$311\pm 43$	-	-	${1.6}_{-0.4}^{+0.5}$
0948$+$3008	$164\pm 21$	$70.0\pm 3.6$	$54.5\pm 7.4$	${3.3}_{-0.9}^{+0.9}$		0956$+$5912	$139\pm 19$	$125.8\pm 3.0$	$83\pm 12$	${1.0}_{-0.2}^{+0.1}$
1003$-$0031	$161\pm 20$	$40.7\pm 5.8$	$31.2\pm 5.9$	${3.9}_{-1.0}^{+1.0}$		1005$+$2244	$301\pm 41$	$50\pm 14$	$72\pm 22$	${2.6}_{-0.7}^{+1.0}$
1006$+$1752	$159\pm 20$	-	-	${4.0}_{-1.1}^{+1.1}$		1014$+$2827	$257\pm 35$	-	-	${2.8}_{-0.8}^{+1.1}$
1017$+$3447	$186\pm 25$	$115.9\pm 3.6$	$103\pm 14$	${3.0}_{-0.8}^{+0.9}$		1017$+$2419	$199\pm 27$	$77.4\pm 3.6$	$73\pm 11$	${1.8}_{-0.4}^{+0.4}$
1019$+$3535	$239\pm 31$	-	-	${3.7}_{-1.1}^{+1.3}$		1019$+$2045	$169\pm 22$	$84.5\pm 5.4$	$68.0\pm 9.7$	${5.5}_{-1.5}^{+0.9}$
1024$+$4531	$166\pm 21$	$15.7\pm 5.4$	$12.3\pm 4.5$	${3.3}_{-0.9}^{+1.0}$		1024$+$1014	$194\pm 26$	$51.3\pm 4.8$	$47.4\pm 7.6$	${2.7}_{-0.7}^{+1.0}$
1032$+$1338	$198\pm 25$	-	-	${4.8}_{-1.4}^{+1.1}$		1033$+$1809	$131\pm 17$	$225\pm 99$	$140\pm 66$	${3.1}_{-0.9}^{+1.1}$
1038$-$0036	$58.9\pm 7.8$	$99.1\pm 2.9$	$27.8\pm 3.8$	${1.5}_{-0.3}^{+0.2}$		1038$+$0432	$228\pm 30$	-	-	${2.4}_{-0.6}^{+0.7}$
1040$+$2407	$91\pm 12$	$166.6\pm 3.4$	$72.5\pm 9.4$	${3.9}_{-1.0}^{+0.9}$		1041$+$3432	$299\pm 41$	-	-	${1.6}_{-0.3}^{+0.4}$
1043$+$3516	$105\pm 14$	$148.9\pm 3.2$	$75\pm 10$	${2.2}_{-0.5}^{+0.6}$		1046$+$1329	$126\pm 16$	-	-	${5.9}_{-1.4}^{+0.9}$
1055$+$3725	$134\pm 17$	$105.7\pm 5.1$	$67.5\pm 9.4$	${4.4}_{-1.1}^{+1.0}$		1058$+$3143	$122\pm 16$	$38.8\pm 4.5$	$22.5\pm 4.0$	${2.1}_{-0.5}^{+0.5}$
1102$+$2827	$288\pm 39$	-	-	${2.6}_{-0.7}^{+1.1}$		1102$+$0214	$101\pm 13$	$96.5\pm 3.6$	$46.3\pm 6.2$	${3.9}_{-1.0}^{+0.9}$
1103$+$4144	$117\pm 15$	$53.0\pm 3.8$	$29.6\pm 4.3$	${3.6}_{-0.9}^{+0.9}$		1105$+$5006	$245\pm 33$	$35.8\pm 4.0$	$41.8\pm 7.4$	${1.7}_{-0.4}^{+0.4}$
1105$+$0228	$166\pm 21$	-	-	${3.8}_{-1.1}^{+1.3}$		1106$+$6737	$161\pm 22$	$62.1\pm 3.9$	$47.8\pm 7.1$	${2.6}_{-0.7}^{+0.8}$
1112$+$0700	$163\pm 22$	$67.7\pm 3.9$	$52.4\pm 7.7$	${1.5}_{-0.3}^{+0.3}$		1113$+$2751	$213\pm 28$	$22.4\pm 4.6$	$22.7\pm 5.5$	${2.9}_{-0.8}^{+0.9}$
1132$+$3323	$257\pm 35$	-	-	${2.8}_{-0.8}^{+1.0}$		1134$+$1542	$309\pm 41$	-	-	${2.2}_{-0.5}^{+0.8}$
1144$+$3720	$252\pm 34$	$16.5\pm 4.7$	$19.8\pm 6.2$	${1.6}_{-0.3}^{+0.4}$		1144$+$1218	$50.2\pm 6.2$	$617.1\pm 5.8$	$147\pm 18$	${5.0}_{-1.2}^{+0.7}$
1147$+$5429	$212\pm 28$	$96.5\pm 5.2$	$97\pm 14$	${5.4}_{-1.7}^{+1.2}$		1149$+$0519	$174\pm 23$	$40.1\pm 3.5$	$33.3\pm 5.3$	${1.7}_{-0.4}^{+0.4}$
1150$+$4928	$202\pm 27$	$62.2\pm 3.9$	$59.7\pm 8.8$	${1.8}_{-0.4}^{+0.4}$		1150$+$4533	$253\pm 33$	-	-	${4.0}_{-1.2}^{+1.5}$
1152$+$5101	$165\pm 21$	-	-	${6.4}_{-1.3}^{+0.7}$		1152$+$1605	$188\pm 26$	$48.7\pm 3.9$	$43.5\pm 6.9$	${2.4}_{-0.6}^{+0.7}$
1157$+$6138	$335\pm 46$	-	-	${2.4}_{-0.6}^{+1.0}$		1158$+$1845	$212\pm 28$	$68.5\pm 3.4$	$69.1\pm 9.7$	${1.8}_{-0.4}^{+0.4}$
1158$+$5942	$186\pm 24$	$16.3\pm 5.2$	$14.5\pm 5.0$	${3.3}_{-0.9}^{+1.0}$		1158$+$0454	$146\pm 19$	$26.1\pm 5.0$	$18.2\pm 4.2$	${5.6}_{-1.3}^{+0.8}$
1158$+$4712	$319\pm 44$	$60.1\pm 5.5$	$91\pm 15$	${1.5}_{-0.3}^{+0.3}$		1158$+$5448	$254\pm 35$	-	-	${2.8}_{-0.8}^{+1.1}$
1205$+$3536	$176\pm 23$	-	-	${3.1}_{-0.8}^{+0.9}$		1211$+$2326	$238\pm 32$	$106.6\pm 4.8$	$121\pm 17$	${2.5}_{-0.6}^{+0.8}$
1214$-$0234	$43.2\pm 5.3$	$550\pm 19$	$113\pm 14$	${5.8}_{-1.2}^{+0.5}$		1217$+$1157	$188\pm 25$	$36.4\pm 5.2$	$32.6\pm 6.3$	${2.5}_{-0.6}^{+0.7}$
1218$+$0023	$119\pm 16$	$59.8\pm 4.0$	$33.9\pm 5.0$	${3.1}_{-0.8}^{+0.8}$		1220$+$0929	$263\pm 35$	$18.9\pm 4.9$	$23.6\pm 7.0$	${2.3}_{-0.5}^{+0.7}$
1224$+$2838	$85\pm 11$	$99.9\pm 3.5$	$40.5\pm 5.2$	${5.8}_{-1.2}^{+0.6}$		1226$+$2936	$85\pm 11$	$205.2\pm 5.1$	$83\pm 11$	${7.1}_{-1.1}^{+0.5}$
1229$+$0743	$183\pm 24$	$18.9\pm 4.9$	$16.5\pm 4.8$	${3.0}_{-0.8}^{+0.8}$		1230$+$3143	$198\pm 27$	$39.8\pm 4.7$	$37.5\pm 6.8$	${2.4}_{-0.6}^{+0.7}$
1234$+$5208	$112\pm 15$	$94.1\pm 3.2$	$50.3\pm 7.1$	${1.5}_{-0.3}^{+0.3}$		1238$+$2149	$157\pm 20$	$74.9\pm 4.9$	$55.9\pm 7.9$	${5.0}_{-1.3}^{+0.9}$
1245$+$0822	$236\pm 31$	-	-	${2.7}_{-0.7}^{+0.8}$		1249$+$6514	$275\pm 37$	$81.0\pm 7.8$	$106\pm 18$	${1.6}_{-0.3}^{+0.3}$
1254$+$3551	$234\pm 32$	$107.6\pm 7.4$	$120\pm 18$	${2.3}_{-0.5}^{+0.7}$		1257$+$3238	$198\pm 26$	$51.9\pm 4.8$	$49.0\pm 7.9$	${5.7}_{-1.7}^{+1.1}$
1257$-$0310	$206\pm 28$	-	-	${2.8}_{-0.7}^{+0.9}$		1259$+$3112	$118\pm 15$	$75.6\pm 3.8$	$42.5\pm 5.9$	${3.7}_{-1.0}^{+1.2}$
1259$+$4729	$228\pm 31$	$66.7\pm 5.5$	$72\pm 12$	${2.8}_{-0.8}^{+1.0}$		1303$+$4055	$139\pm 18$	$27.7\pm 3.4$	$18.3\pm 3.4$	${2.9}_{-0.8}^{+0.8}$
1308$+$0957	$386\pm 54$	-	-	${1.4}_{-0.3}^{+0.4}$		1308$+$0258	$208\pm 27$	-	-	${3.2}_{-0.9}^{+1.0}$
1314$+$3748	$205\pm 28$	$54.3\pm 4.9$	$52.9\pm 8.6$	${3.4}_{-1.0}^{+1.3}$		1316$+$1918	$166\pm 21$	$48.3\pm 3.5$	$38.0\pm 5.5$	${5.3}_{-1.4}^{+0.8}$
1319$+$3641	$236\pm 32$	$22.4\pm 4.8$	$25.1\pm 6.4$	${1.7}_{-0.4}^{+0.4}$		1320$+$0204	$317\pm 44$	$18.0\pm 6.0$	$27.1\pm 9.8$	${1.9}_{-0.5}^{+0.6}$
1321$-$0237	$156\pm 20$	-	-	${4.3}_{-1.3}^{+1.2}$		1329$+$1301	$186\pm 25$	$167.0\pm 7.6$	$148\pm 21$	${2.1}_{-0.5}^{+0.6}$
1330$+$3029	$26.1\pm 3.4$	$487.0\pm 2.4$	$60.6\pm 7.8$	${3.1}_{-0.8}^{+0.8}$		1336$+$3547	$65.6\pm 8.9$	$126.5\pm 2.6$	$39.5\pm 5.4$	${2.3}_{-0.6}^{+0.6}$
1339$+$2643	$98\pm 13$	$64.3\pm 3.0$	$30.1\pm 4.3$	${2.8}_{-0.7}^{+0.7}$		1340$+$2702	$373\pm 51$	$7.8\pm 3.8$	$13.8\pm 7.1$	${1.4}_{-0.3}^{+0.3}$
1342$+$1813	$168\pm 21$	$74.3\pm 5.1$	$59.5\pm 8.6$	${5.7}_{-1.4}^{+0.9}$		1345$+$1153	$131\pm 17$	$139.9\pm 3.8$	$87\pm 11$	${3.2}_{-0.9}^{+1.0}$
1347$+$1415	$158\pm 21$	$14.0\pm 3.5$	$10.5\pm 3.0$	${2.2}_{-0.5}^{+0.6}$		1350$+$1058	$139\pm 17$	$69.7\pm 5.0$	$46.1\pm 6.5$	${6.0}_{-1.2}^{+0.7}$
1351$+$2645	$161\pm 20$	$55.4\pm 4.4$	$42.5\pm 6.4$	${3.3}_{-0.9}^{+1.0}$		1356$+$2416	$90\pm 12$	$112.2\pm 3.2$	$48.3\pm 6.3$	${3.2}_{-0.9}^{+0.9}$
1356$+$0236	$214\pm 30$	$24.9\pm 5.2$	$25.4\pm 6.5$	${1.2}_{-0.2}^{+0.2}$		1401$+$3659	$80\pm 10$	$59.8\pm 2.9$	$22.7\pm 3.1$	${3.3}_{-0.9}^{+0.9}$
1404$+$3620	$77.0\pm 9.8$	$176.2\pm 3.0$	$64.6\pm 8.3$	${3.5}_{-0.9}^{+0.9}$		1405$+$2542	$214\pm 28$	$21.1\pm 4.9$	$21.6\pm 5.8$	${3.5}_{-1.0}^{+1.1}$
1405$+$1549	$124\pm 17$	$112.8\pm 3.1$	$66.4\pm 9.1$	${1.8}_{-0.4}^{+0.4}$		1411$+$3410	$149\pm 19$	$70.3\pm 4.8$	$49.9\pm 7.1$	${4.8}_{-1.3}^{+1.0}$
1412$+$2836	$148\pm 19$	$103.0\pm 3.6$	$72.8\pm 9.5$	${6.5}_{-1.1}^{+0.5}$		1421$+$1843	$245\pm 34$	$36.4\pm 3.8$	$42.5\pm 7.3$	${1.7}_{-0.4}^{+0.4}$
1428$+$4403	$44.1\pm 6.0$	$278.8\pm 2.5$	$58.5\pm 8.0$	${2.3}_{-0.6}^{+0.6}$		1429$+$3841	$192\pm 25$	$34.7\pm 3.7$	$31.7\pm 5.3$	${3.2}_{-0.9}^{+1.1}$
1430$-$0151	$115\pm 15$	$60.4\pm 3.7$	$33.1\pm 4.8$	${3.0}_{-0.8}^{+0.9}$		1443$+$5833	$380\pm 53$	$209.9\pm 4.2$	$380\pm 53$	${1.9}_{-0.4}^{+0.6}$
1443$+$3014	$370\pm 51$	-	-	${2.1}_{-0.5}^{+0.7}$		1445$+$0913	$317\pm 43$	-	-	${2.3}_{-0.6}^{+0.8}$
1448$+$1047	$100\pm 13$	$63.9\pm 3.2$	$30.6\pm 4.3$	${2.4}_{-0.6}^{+0.6}$		1500$+$2315	$363\pm 52$	-	-	${2.4}_{-0.7}^{+1.1}$
1502$+$3744	$102\pm 13$	$104.0\pm 3.8$	$50.3\pm 6.6$	${5.1}_{-1.2}^{+0.7}$		1507$+$4034	$338\pm 46$	-	-	${1.8}_{-0.4}^{+0.6}$
1518$+$0506	$67.4\pm 8.4$	$39.7\pm 3.8$	$12.7\pm 2.0$	${6.4}_{-1.1}^{+0.5}$		1524$+$4049	$143\pm 19$	$26.2\pm 3.9$	$17.8\pm 3.6$	${3.5}_{-0.9}^{+1.0}$
1534$+$1242	$276\pm 37$	-	-	${3.6}_{-1.1}^{+1.4}$		1535$+$1247	$19.4\pm 2.4$	$247.8\pm 2.3$	$22.9\pm 2.9$	${3.8}_{-0.9}^{+0.9}$
1536$+$4205	$181\pm 23$	$41.4\pm 5.6$	$35.7\pm 6.7$	${3.7}_{-1.0}^{+1.0}$		1537$+$3608	$193\pm 24$	-	-	${4.5}_{-1.3}^{+1.3}$
1540$+$5352	$294\pm 40$	-	-	${2.4}_{-0.6}^{+1.0}$		1542$+$4650	$209\pm 27$	$50.5\pm 5.5$	$50.3\pm 8.5$	${3.2}_{-0.9}^{+1.0}$
1543$+$2024	$306\pm 42$	-	-	${2.7}_{-0.8}^{+1.1}$		1545$+$5236	$134\pm 18$	$47.2\pm 5.9$	$30.2\pm 5.4$	${3.6}_{-1.0}^{+1.0}$
1546$+$3009	$157\pm 21$	$18.4\pm 3.4$	$13.7\pm 3.1$	${2.3}_{-0.6}^{+0.6}$		1549$+$2633	$222\pm 30$	$51.3\pm 3.6$	$54.1\pm 8.2$	${2.8}_{-0.7}^{+0.8}$
1549$+$1906	$292\pm 39$	$42.2\pm 4.9$	$59\pm 10$	${2.5}_{-0.6}^{+0.9}$		1554$+$1735	$58.6\pm 7.7$	$147.5\pm 2.5$	$41.2\pm 5.4$	${2.3}_{-0.5}^{+0.6}$
1604$+$1830	$142\pm 19$	$55.1\pm 3.1$	$37.4\pm 5.4$	${2.6}_{-0.7}^{+0.7}$		1610$+$4006	$274\pm 38$	-	-	${2.3}_{-0.6}^{+0.8}$
1612$+$3534	$362\pm 52$	$39.6\pm 5.5$	$68\pm 14$	${2.2}_{-0.6}^{+0.9}$		1616$+$3303	$117\pm 15$	$52.0\pm 3.5$	$29.1\pm 4.3$	${2.6}_{-0.7}^{+0.7}$
1624$+$3310	$319\pm 44$	-	-	${2.0}_{-0.5}^{+0.7}$		1626$+$3303	$256\pm 34$	$17.9\pm 5.2$	$21.8\pm 7.0$	${2.8}_{-0.8}^{+1.0}$
1627$+$4646	$193\pm 26$	$19.0\pm 4.0$	$17.5\pm 4.4$	${2.6}_{-0.7}^{+0.8}$		1636$+$1619	$66.9\pm 8.0$	$87.0\pm 4.1$	$27.7\pm 3.6$	${7.7}_{-0.9}^{+0.3}$
1641$+$1856	$137\pm 17$	$53.9\pm 3.4$	$35.1\pm 5.0$	${3.7}_{-1.0}^{+1.0}$		1649$+$2238	$147\pm 18$	$31.8\pm 4.0$	$22.2\pm 4.0$	${5.4}_{-1.4}^{+0.7}$
1651$+$4249	$106\pm 14$	$80\pm 16$	$41\pm 10$	${4.0}_{-1.1}^{+1.2}$		1706$+$2541	$281\pm 38$	$13.7\pm 5.2$	$18.4\pm 7.6$	${2.3}_{-0.5}^{+0.8}$
2109$-$0039	$149\pm 19$	$42.8\pm 5.0$	$30.5\pm 5.4$	${3.2}_{-0.9}^{+1.1}$		2110$+$0512	$252\pm 33$	-	-	${4.1}_{-1.2}^{+1.3}$
2123$+$0016	$116\pm 14$	$109.5\pm 4.8$	$60.4\pm 8.0$	${5.7}_{-1.3}^{+0.7}$		2157$+$1206	$127\pm 17$	$38.9\pm 3.6$	$23.5\pm 3.8$	${3.1}_{-0.8}^{+0.8}$
2225$+$2338	$147\pm 20$	$43.2\pm 7.0$	$30.2\pm 6.3$	${2.0}_{-0.4}^{+0.4}$		2230$+$1905	$168\pm 22$	$17.3\pm 3.1$	$13.8\pm 3.1$	${4.4}_{-1.3}^{+1.3}$
2231$+$0906	$93\pm 12$	$218.4\pm 3.0$	$97\pm 13$	${3.5}_{-0.9}^{+0.9}$		2235$-$0056	$200\pm 27$	-	-	${2.7}_{-0.7}^{+0.8}$
2238$+$0213	$267\pm 36$	-	-	${1.9}_{-0.5}^{+0.6}$		2238$-$0113	$258\pm 35$	-	-	${2.1}_{-0.5}^{+0.7}$
2254$+$3031	$120\pm 15$	$49.4\pm 3.1$	$28.3\pm 4.0$	${3.5}_{-0.9}^{+0.9}$		2304$+$2415	$79.1\pm 9.8$	$115.2\pm 3.6$	$43.4\pm 5.5$	${6.3}_{-1.1}^{+0.5}$
2319$+$3018	$306\pm 41$	-	-	${1.9}_{-0.4}^{+0.4}$		2325$+$0448	$134\pm 17$	$40.3\pm 3.2$	$25.8\pm 3.9$	${3.2}_{-0.9}^{+0.9}$
2328$+$0830	$251\pm 34$	-	-	${3.8}_{-1.2}^{+1.4}$		2330$+$2805	$249\pm 33$	$44.9\pm 4.5$	$53.3\pm 8.9$	${2.2}_{-0.5}^{+0.7}$
2330$+$2956	$180\pm 24$	$36.2\pm 3.6$	$31.0\pm 5.1$	${2.0}_{-0.4}^{+0.4}$		2333$+$1058	$302\pm 40$	-	-	${2.9}_{-0.8}^{+1.1}$
2340$+$0124	$114\pm 15$	$115.1\pm 3.0$	$62.7\pm 8.4$	${2.9}_{-0.8}^{+0.8}$		2340$+$0817	$132\pm 16$	$138.1\pm 3.6$	$86\pm 11$	${4.5}_{-1.1}^{+1.0}$
2343$-$0010	$163\pm 22$	$59.1\pm 5.2$	$45.9\pm 7.2$	${3.5}_{-1.0}^{+1.3}$		2352$+$1922	$272\pm 37$	-	-	${3.0}_{-0.9}^{+1.1}$
2352$+$3344	$312\pm 42$	$20.6\pm 3.8$	$30.6\pm 7.0$	${1.8}_{-0.4}^{+0.4}$		2357$+$2348	$251\pm 33$	-	-	${3.2}_{-0.9}^{+1.1}$

Equations

$$A=\frac{{\sum }_i{f}_i{t}_i/{\sigma }_i^2}{{\sum }_j{t}_j^2/{\sigma }_j^2},$$

$$\int V(x)\sin (2\pi x)\mathrm{d}x,$$

$${\sigma }_T^2={\left(50\mathrm{K}\right)}^2+{\left(\frac{T_{\mathrm{eff}}}{5\mathrm{SN}}\right)}^2.$$

Full text

††pubyear: 2017††pagerange: Cool DZ white dwarfs I: Identification and spectral analysis–LABEL:lastpage

1 Introduction

White dwarfs are often found to have traces of metals polluting their otherwise pristine atmospheres of hydrogen or helium (van Maanen, 1917; Weidemann, 1960; Hintzen & Tapia, 1975; Shipman et al., 1977; Aannestad & Sion, 1985; Zuckerman & Reid, 1998; Koester & Kepler, 2015). These are classified as spectral types DAZ, DBZ, and DZ, depending on whether hydrogen, helium, or no lines are present in the spectrum in addition to those from metals (Sion et al., 1983). Due to gravitational settling, metals are expected to sink below the observable photosphere on time scales many orders of magnitude shorter than the white dwarf cooling age (Koester, 2009). Therefore the observed atmospheric contamination by metals at 25–50 percent (Zuckerman et al., 2003; Koester et al., 2014) of white dwarfs requires recent or ongoing accretion of metal-rich material (Vauclair et al., 1979).

In the last two decades it has become clear that these accreted metals originate from rocky debris that has survived the post-main sequence evolution of its host star (Graham et al., 1990; Jura, 2003; Farihi et al., 2010). This astonishing realisation has led to white dwarfs becoming the primary tool for directly probing the bulk compositions of rocky planetary material (Zuckerman et al., 2007; Gänsicke et al., 2012).

The first indicator pointing towards a planetary origin for metal-pollution came from the detection of white dwarfs with infra-red excesses (Zuckerman & Becklin, 1987; Becklin et al., 2005; Kilic et al., 2005). The infra-red flux is interpreted to come from circumstellar dust discs that have thermally reprocessed the light incident from the close-by white dwarf (Graham et al., 1990). Gaseous components to these discs have also been identified at a handful of young metal-polluted white dwarfs (e.g. Gänsicke et al., 2006; Dufour et al., 2012; Melis et al., 2012; Farihi et al., 2012; Wilson et al., 2014; Guo et al., 2015), typically through double peaked emission lines of Ca ii and Fe ii.

The now established scenario is that perturbations to the trajectories of small planetary objects such as asteroids can occasionally push them onto grazing orbits with the degenerate star (Debes & Sigurdsson, 2002). Mass-loss during evolution off of the main-sequence results in reduced dynamical stability at the white dwarf stage, increasing the probability of this scenario occurring (Veras & Gänsicke, 2015). Once within the white dwarf’s Roche radius, the planetesimal is tidally disrupted which circularises into a debris disc, and finally is accreted onto the surface of the star (Jura, 2003; Veras et al., 2014a). A recent review of remnant planetary systems by Veras (2016) can be consulted for more details.

While this picture of evolved planetary systems has adequately explained observations for more than a decade, the most unambiguous evidence surfaced only recently, with deep transits (up to 40 percent) in the K2 lightcurve of WD1145$+$017, leading to the discovery of a disintegrating planetesimal orbiting near the Roche radius of this star ($P_{\mathrm{orb}}\simeq 4.5$ hr) (Vanderburg et al., 2015; Gänsicke et al., 2016; Alonso et al., 2016; Rappaport et al., 2016). WD1145$+$017 also exhibits an infra-red excess, broad absorption features from transiting circumstellar gas (Xu et al., 2016), and an atmosphere enriched with metals. WD1145$+$017 therefore provides the firmest link between metals in the atmospheres of white dwarfs and rocky planetary material. Unfortunately the prospect of detecting a statistically large sample of WD1145$+$017-like systems in the near future is low considering the chance alignment required, and the potentially short timescales for which transits are visible. For the foreseeable future, the study of white dwarfs with metal-line spectra remains the primary tool in understanding the variety of remnant planetary systems.

Over the last 15 years, the Sloan Digital Sky Survey (SDSS) has been an invaluable source of white dwarf discoveries, providing spectroscopy for $>40\,000$ stellar remnants of all spectral types and spanning all temperature regimes (Kleinman et al., 2004; Eisenstein et al., 2006; Kleinman et al., 2013; Kepler et al., 2015, 2016). More than one thousand of these white dwarfs also possess metal-lines.

In this work we consider only DZ white dwarfs, which have spectra with only metal lines present. The absence of hydrogen/helium lines simply reflects their relatively low effective temperatures ($T_{\mathrm{eff}}$) as they have cooled for at least $\simeq 0.5$ Gyr since leaving the tip of the AGB. Below $\simeq 12\,000$ K helium atoms are almost entirely in the ground state, while optical transitions of helium all occur between excited states. Therefore white dwarfs with pure helium atmospheres, have featureless spectra below $\simeq 12\,000$ K. Below $\simeq 5000$ K the Balmer lines also disappear for white dwarfs with hydrogen dominated atmospheres. Because of the wider temperature range that helium lines are absent, but also because of the much lower opacity of helium compared with hydrogen (leading to stronger metal lines for given abundances), most of the known DZ stars have atmospheres dominated by helium. This includes the first known metal-polluted white dwarf, vMa2 (van Maanen, 1917), which is both the prototype DZ, and the first acquired evidence for an extrasolar planetary system (Zuckerman, 2015; Farihi, 2016), although another 90 years were needed for a correct interpretation (Jura, 2003).

Prior atmospheric analyses of DZ white dwarfs by Bergeron et al. (2001) and Dufour et al. (2007), found a wide range in the level of observed metal pollution across the $T_{\mathrm{eff}}$ range of their samples (see Figure 9 of Dufour et al., 2007). However below $\simeq 7000$ K only one object, G165-7 (SDSS J1330$+$3029 later in this work), was found with \mbox{\log[\mathrm{Ca/He}]}>-9 dex. The authors noted that this could be explained as a selection bias. The majority of the DZs analysed by Dufour et al. (2007) came from the SDSS white dwarf catalogue of Eisenstein et al. (2006), which was subject to a colour-cut excluding objects with ($u-g$) sufficiently red to overlap the main-sequence. This colour-cut would also preclude the identification of SDSS objects spectrally similar to G165-7 ($u-g=1.96\pm 0.03$ mag), which was instead included by Dufour et al. (2007) as one of twelve additional systems from Bergeron et al. (1997) and Bergeron et al. (2001).

The suspicion of selection effects by Dufour et al. (2007) was soon proved correct by Koester et al. (2011) (hereafter KGGD11) who searched specifically for DZs with strong metal-pollution and low $T_{\mathrm{eff}}$ similar to G165-7. KGGD11 noted that such white dwarfs would follow cooling tracks extending below the main-sequence in ($u-g)$ vs. $(g-r)$ (see Figure 1), exhibiting colours not possible for other types of stars due to extremely strong H/K line absorption in the SDSS $u$-band. In total KGGD11, identified 26 cool DZs (\mbox{T_{\mathrm{eff}}}<9000 K) with spectra strongly line-blanketed by metals, occupying a previously sparse corner of the $T_{\mathrm{eff}}$ vs. $\log[\mathrm{Ca/He}]$ plane.

In this study, we extend the work of KGGD11 to SDSS DR12, finding 231 cool DZ white dwarfs with strong metal lines. These stars provide not only detailed information on ancient exoplanetary chemistry, but also serve as laboratories for state of the art atomic physics under the extreme conditions found in white dwarf atmospheres.

As our analysis of DZ white dwarfs covers a broad range of astrophysical phenomena, we present our results in three distinct papers. Here (Paper I), we discuss the identification of our DZ sample, our latest model atmospheres, and the fitting of these models to the observed spectra. Additionally we examine the properties of our new sample combined with the complementary work of Dufour et al. (2007) and Koester & Kepler (2015). In paper II, we discuss the bulk compositions of the accreted planetesimals which we obtained from our spectral fits, as well as our sample in the wider context of ancient exoplanetary systems. Finally, we find that more than 10 percent of our DZ sample exhibit Zeeman-splitting from strong ($>0.5$ MG) magnetic fields which we discuss in paper III.

2 White dwarf identification

2.1 Spectroscopic search

We adopted two distinct methods to identify DZ white dwarfs from the SDSS DR12 spectra. The first (method 1) makes use of various data cuts (colour, proper-motion, etc.) to filter the number of objects requiring visual inspection. Following the release of SDSS DR12, we employed a new identification scheme (method 2) where we fit all SDSS spectra with DZ templates. This method was found to be superior to method 1 as it required fewer spectra to be visually inspected, and allowed a larger range of colour space to be explored. We still describe the first method briefly as the initial results it provided were used to calibrate the template fitting approach.

2.1.1 Method 1

The first method is essentially an extension of the work by KGGD11 to subsequent SDSS data releases. We restricted our search for further cool DZs firstly to SDSS point-sources, and then performing a colour-colour cut in ($u-g)$ vs. $(g-r)$ (dashed region in Figure 1), similar to that used by KGGD11. This region avoids the main sequence and contains the 17 coolest and most metal polluted DZs found by KGGD11. While this area of colour-space was chosen to avoid other types of stellar objects, it is instead home to quasars with Ly-$\alpha$ breaks occurring in the $u$-band, which were intensely targeted for spectroscopy in SDSS-III (Ross et al., 2012). While this targeting strategy leads to cool DZ stars being serendipitously observed, these quasars required filtering from our colour selection.

We removed quasars using a combination of proper-motion and spectroscopic redshifts: We required a $>3\sigma$ detection of proper-motions, where SDSS proper-motion errors are typically 2–6 mas yr*-1*. The total proper-motion is chi-distributed with two degrees-of-freedom, whereas the 1-$\sigma$ errors correspond to single components, therefore $\simeq 1$ percent of the $\simeq$477 000 quasar spectra111 See http://www.sdss.org/dr12/scope/ for a breakdown of all SDSS DR12 spectroscopy. will have measured proper-motions in excess of our $3\sigma$-cut. Using only proper-motion to filter quasars was insufficient as these are not always available for faint, $g>20$ objects, due to lack of cross-detections in USNO-B. Additionally a few high proper-motion systems ($>100$ mas yr*-1*) have such large displacement between SDSS and USNO-B photometry that cross-matching fails. For instance, SDSS J1144$+$1218 (KGGD11) has no available SDSS proper-motion, but is found in PPMXL with a celestial motion of $617\pm 6$ mas yr*-1*(see appendix Table LABEL:tab:dist).

We supplemented our proper-motion cut with a cut on redshift, $z$, to remove additional quasars, and avoid missing DZs with no SDSS proper-motion – systems only needed to pass one of the two tests to make it to the next stage. For the redshift cut we imposed $z-3\sigma_{z}<0.01$, removing both quasar and galaxy spectra from our sample. The relative rarity of cool DZ spectra in SDSS can lead to incorrect spectral classification and subsequently an incorrect redshift estimate from the SDSS pipeline. Therefore we allowed objects with the zwarning flag not equal to zero to “automatically pass” our redshift test (zero indicates a $z$ value that is deemed to be correct). However of the 17 KGGD11 DZs within our colour-cut, five were found with $1.38<z<1.41$ and zwarning $=0$, indicating that DZ stars can be misclassified as quasars with no warning flags raised in this narrow redshift range. Therefore an exception to our redshift cut was made for the few SDSS spectra with $1.3<z<1.5$.

Our combined proper-motion/redshift cut successfully removed most QSOs and galaxies, thus reducing the size of the sample of purely colour-selected spectra by $33$ percent to around 100 000. At this stage, all 17 DZs from KGGD11 were still contained within the selection.

As this sample was still rather large for visual inspection, we sought to remove additional contaminants. Most of the remaining spectra were of K/M dwarfs at the border of our colour-cut. We performed template fitting for spectral subclasses K1–M9 to remove these cool main sequence stars. For M dwarfs we used the templates from Rebassa-Mansergas et al. (2007). For subclasses K1, K3, K5 and K7 we created templates by combining multiple (at least 20 per subclass) high signal-to-noise (S/N) SDSS spectra which we identified in the CasJobs database (Li & Thakar, 2008) using the class and subclass attributes.

We fitted each of the 100 000 spectra against all stellar templates, obtaining a reduced chi-squared ($\chi^{2}_{\mathrm{red}}$) for each fit. The template with lowest $\chi^{2}_{\mathrm{red}}$ for a given spectrum was recorded as the best-fitting template. The median S/N was also recorded for each SDSS spectrum.

The resulting distribution in the S/N vs. $\chi^{2}_{\mathrm{red}}$ plane (Figure 2) is bimodal at high-signal to noise indicating probable main sequence stars in the lower cluster, and objects spectrally different to the K/M star templates in the upper branch. The bulk of spectra are found at low signal-to-noise/low $\chi^{2}_{\mathrm{red}}$, and so are of too poor quality for meaningful analysis. The KGGD11 DZs were used to define a cut-off for the remaining spectra as indicated by the red line. This has the effect of removing the high S/N and low $\chi^{2}_{\mathrm{red}}$ (main sequence) objects, as well as very low S/N spectra.

The $\chi^{2}_{\mathrm{red}}$-S/N cut reduced the sample size down to $\simeq 35\,000$ spectra which we visually inspected for DZ white dwarfs. In total we identified 126 spectra corresponding to 103 unique DZ stars. Some objects had additional spectra which were not identified via method 1 (e.g. because of low S/N), but were found upon searching for spectra with the same SDSS ObjID. This brought the total number of DZ spectra to 138 for the 103 systems.

2.1.2 Method 2

While we successfully identified more than 100 cool, metal-rich DZs with method 1, its scope was severely limited by our initial colour-cut. Of the 26 DZ white dwarfs in the KGGD11 sample, 9 were excluded by this cut (Figure 1), suggesting that many more DZs may have colours overlapping the main-sequence in ($u-g)$ vs. $(g-r)$. Additionally, the $u$-band errors for DZs in SDSS are sometimes $>1.0$ mag, and so while the true $u-g$ value should place a system below the main sequence in Figure 1, the measured colour could instead escape our colour cut. Furthermore, the possibility remained that systems could fail both our proper-motion and redshift tests, or also fall under our $\chi^{2}_{\mathrm{red}}$-cut in Figure 2.

Method 2 essentially uses only the SDSS spectra for identification, and so allows us to identify objects that would otherwise be photometrically degenerate with main sequence stars. To provide zeroth-order estimates of atmospheric parameters for our spectral fitting (described later in Section 5), we generated a grid of DZ models of varying $T_{\mathrm{eff}}$ and $\log[\mathrm{Ca/He}]$. The grid spanned $4400\,\text{K}\leq T_{\mathrm{eff}}\leq 14\,000$ K in steps of 200 K and $-10.5\leq\log[\mathrm{Ca/He}]\leq-7$ in steps of 0.25 dex (735 DZ model spectra). For all models in the grid the surface gravity, $\log g$, is fixed to the canonical value of 8. Other elements were fixed to bulk Earth abundances (McDonough, 2000) relative to Ca. We found our model grid could also be used as templates to identify DZ white dwarfs through fitting to the SDSS spectra.

We supplemented our DZ grid with a list of the highest quality SDSS spectra with average S/N $>100$ These consisted entirely of main sequence stars of spectral-types B through K, and amounted to 768 spectra bringing the total number of templates to 1503.

With these template spectra at hand we fitted each template against all 2.4M SDSS spectra with mean S/N $>3$ – this S/N cut removes not only the poorest quality spectra, but also quasars where the bulk of the signal is contained within a few narrow emission lines. For each fit the template spectra were linearly interpolated onto the same wavelength grid as the SDSS spectrum under consideration – the high S/N requirement of the non-DZ templates meant the effects of interpolating noise were kept to a minimum. Secondly, a reduced $\chi^{2}$ was calculated between the SDSS spectrum and interpolated template with only a scaling factor as a free parameter. Ignoring the small flux errors on the non-DZ templates, the optimum scaling factor, $A$, has the simple analytic form

[TABLE]

where the $f_{i}$ and $\sigma_{i}$ are the fluxes and errors on the SDSS spectra and the $t_{i}$ are the unscaled fluxes on the interpolated templates. For each SDSS spectrum, the template with the lowest $\chi^{2}_{\mathrm{red}}$ was considered to be the best fit.

SDSS spectra which best fit a non-DZ template were immediately discarded, reducing the 2.4M spectra to $\simeq 244\,000$. All SDSS DZ spectra identified via method 1 still remained after this cut. Next we applied a single colour cut of $u-g>0.50$, essentially enforcing that white dwarfs in our sample contain significant absorption in the blue end of their spectra. This has the effect of removing DZ stars with \mbox{T_{\mathrm{eff}}}>9000 K for the most metal rich objects and T_{\mathrm{eff}}$$>6500 K for the lowest metallicities in our grid. Hotter objects are not the focus of this work.

Although only $\simeq 10$ percent of objects best-fit a DZ template, the best fit does not imply a good fit. Thus we next cut on $\chi^{2}_{\mathrm{red}}$vs. S/N, similarly to method 1 (Figure 2). The cut is a parabola in $\log(\chi^{2}_{\mathrm{red}})$ vs. $\log(S/N)$, whose scale we chose to keep all objects identified through method 1. This is shown in Figure 3.

At S/N > 7, the distribution in Figure 3 becomes trimodal in $\chi^{2}_{\mathrm{red}}$ with only the upper cluster filtered by our cut. We found the majority of points in the intermediate distribution had best fitting templates with the lowest two values of $\log[\mathrm{Ca/He}]$ ($-10.5$ and $-10.25$ dex) in our model grid. This is because those templates are relatively featureless and so had a tendency to match other types of main-sequence stars. Therefore we chose to remove all spectra matching the low Ca-abundance templates, leaving only $\simeq 10\,600$ spectra for visual inspection222 While this final cut inevitably biases us towards high-metallicity systems, objects with \mbox{\log[\mathrm{Ca/He}]}<-10 do not permit meaningful chemical analyses of the accreted material, with Ca as potentially the only detected element..