Carbon-rich (DQ) white dwarfs in the Sloan Digital Sky Survey

TL;DR

This study analyzes a large sample of carbon-rich DQ white dwarfs from SDSS, deriving their atmospheric parameters and exploring their spectral evolution, revealing mass differences related to temperature and carbon dominance.

Contribution

It provides a comprehensive analysis of DQ white dwarfs using SDSS and Gaia data, offering new insights into their atmospheric properties and evolution.

Findings

Hotter DQ white dwarfs (>10000 K) have higher masses (~0.4 Msun)

Cooler DQ white dwarfs (~0.6 Msun) have typical white dwarf masses

A significant fraction of hot DQ stars (>14500 K) have carbon-dominated atmospheres

Abstract

Among the spectroscopically identified white dwarfs, a fraction smaller than 2% have spectra dominated by carbon lines, mainly molecular C2, but also in a smaller group by CI and CII lines. These are together called DQ white dwarfs. We want to derive atmospheric parameters Teff,log g, and carbon abundances for a large sample of these stars and discuss implications for their spectral evolution. Sloan Digital Sky Survey spectra and ugriz photometry were used, together with GAIA Data Release 2 parallaxes and G band photometry. These were fitted to synthetic spectra and theoretical photometry derived from model atmospheres. We found that the DQs hotter than Teff ~10000 K have masses ~0.4 Msun larger than the cooler ones, which have masses typical for the majority of white dwarfs, ~0.6 Msun. A significant fraction of the hotter objects with Teff > 14500 K have atmospheres dominated by carbon.

Tables

Table 1. Table 1: Observed data for the DQ + carbon star sample. p-m-f is the Plate-Epoch (MJD)-Fiber identification of the SDSS spectra, S/N the signal-to-noise ratio. π 𝜋 \pi is the Gaia parallax and G the Gaia magnitude. g is the SDSS g magnitude. The complete table is in the appendix.)

SDSS J	p-m-f	$\pi$ [msec]	g	G	S/N	Type
000011.66$-$085008.3	7167-56604-0752	4.825	19.111	19.056	17.8	DQ
000705.02$+$282104.2	2824-54452-0602	5.420	19.702	19.590	13.6	DQ
001523.91$+$030909.0	4298-55511-0906	5.020	20.028	19.933	8.5	DQ
001908.63$+$184706.0	7592-56947-0123	6.594	19.123	19.160	9.7	wDQ
002531.50$-$110800.9	0653-52145-0086	9.255	17.999	17.949	20.5	DQ
003328.58$+$041834.6	4303-55508-0562	7.497	18.720	18.648	26.2	DQ
…..

Table 2. Table 2: Fit results for the classical DQ with Swan bands. The numbers in parentheses for T eff subscript 𝑇 eff T_{\rm eff} , log ⁡ g 𝑔 \log g , [C/He], and M 𝑀 M / M ⊙ are the internal uncertainties. The complete table is in the appendix.

SDSS J	p-m-f	Teff[K]	log g [cgs]	[C/He]	$M$/M⊙
0000$-$0850	7167-56604-0752	7944 (117)	7.453 (0.164)	$-5.172$ (1.369)	0.311 (0.060)
0007$+$2821	2824-54452-0602	7529 ( 92)	7.931 (0.142)	$-5.427$ (0.584)	0.536 (0.082)
0015$+$0309	4298-55511-0906	7256 (132)	8.004 (0.181)	$-5.678$ (2.117)	0.578 (0.109)
0025$-$1108	0653-52145-0086	8402 ( 82)	7.866 (0.041)	$-4.754$ (0.291)	0.502 (0.023)
0033$+$0418	4303-55508-0562	7700 (108)	7.847 (0.073)	$-5.792$ (0.601)	0.489 (0.040)
…..

Table 3. Table 3: Comparison of average surface gravities for different types of helium-rich cool white dwarfs. Numbers ¡ log ⁡ g 𝑔 \log g ¿ are averages in the T eff subscript 𝑇 eff T_{\rm eff}  interval, slg the 1 ​ σ 1 𝜎 1\sigma width of the distribution, not the uncertainties of the average.

DQ				DZ			DB/DC
$T_{\mathrm{eff}}$	¡$\log g$¿	slg	N	¡$\log g$¿	slg	N	¡$\log g$¿	slg	N
15000-12000			0	8.132	0.168	4	8.016	0.204	15
12000-11000			0	8.015	0.113	13	8.007	0.186	39
11000-10000			0	8.038	0.116	20	7.979	0.190	129
10000- 9000	7.938	0.084	9	8.026	0.106	30	8.027	0.169	153
9000- 8000	7.921	0.124	85	8.049	0.127	44	8.040	0.179	128
8000- 7000	7.941	0.208	81	8.022	0.126	17	8.085	0.183	234
7000- 6000	7.961	0.210	38	7.915	0.151	26	8.039	0.185	249
6000- 5000	7.886	0.326	8	7.717	0.153	12			0
total:	7.935	0.184	221	7.995	0.158	166	8.039	0.185	947

Table 4. Table 4: Fit results for the warm DQ (wDQ). The second number in the columns for T eff subscript 𝑇 eff T_{\rm eff} , log ⁡ g 𝑔 \log g , [C/He], and M 𝑀 M / M ⊙  are the internal uncertainties.

SDSS J	p-m-f	Teff[K]	log g [cgs]	[C/He]	$M$/M⊙
0019$+$1847	7592-56947-0123	10280 (134)	8.546 (0.075)	$-2.840$ (0.025)	0.932 (0.046)
0236$+$2503	2399-53764-0059	14611 (308)	8.777 (0.086)	$-1.823$ (0.057)	1.067 (0.047)
0807$+$1949	4481-55630-0323	14593 (265)	8.847 (0.071)	$1.044$ (0.119)	1.105 (0.038)
0856$+$4513	7327-56715-0052	9353 (203)	8.509 (0.159)	$-3.025$ (0.360)	0.909 (0.099)
0859$+$3257	1272-52989-0309	9798 ( 59)	8.516 (0.011)	$-2.958$ (0.002)	0.914 (0.007)
0919$+$0236	3822-55544-0966	12447 (200)	8.829 (0.069)	$-1.977$ (0.044)	1.095 (0.038)
0936$+$0607	4871-55928-0024	12166 (292)	8.816 (0.088)	$-2.210$ (0.046)	1.088 (0.048)
0958$+$5853	5719-56014-0114	15444 (420)	8.951 (0.054)	$-0.500$ (0.055)	1.161 (0.029)
1049$+$1659	5352-56269-0732	13590 (305)	8.995 (0.091)	$-0.757$ (0.203)	1.186 (0.044)
1058$+$2846	2870-54534-0429	9742 (147)	8.574 (0.074)	$-3.025$ (0.451)	0.949 (0.044)
1100$+$1758	2485-54176-0119	12631 (244)	8.756 (0.080)	$-1.913$ (0.064)	1.055 (0.045)
1140$+$0735	5377-55957-0240	11407 (180)	8.738 (0.000)	$-2.175$ (0.038)	1.044 (0.040)
1140$+$1824	5891-56034-0946	9931 ( 87)	8.431 (0.027)	$-3.000$ (0.014)	0.860 (0.017)
1148$-$0126	0329-52056-0578	9847 ( 86)	8.503 (0.019)	$-3.032$ (0.010)	0.906 (0.012)
1203$+$6450	6975-56720-0446	12977 (133)	8.786 (0.016)	$-1.909$ (0.023)	1.071 (0.009)
1215$+$4700	6640-56385-0532	13940 (302)	8.957 (0.056)	$-2.014$ (0.044)	1.165 (0.027)
1331$+$3727	3984-55333-0118	16741 (334)	9.028 (0.030)	$0.408$ (0.152)	1.165 (0.054)
1332$+$2355	5995-56093-0918	15131 (356)	8.779 (0.099)	$-0.750$ (0.218)	1.068 (0.054)
1339$+$5036	6744-56399-0664	11680 (192)	8.621 (0.063)	$-2.200$ (0.053)	0.978 (0.037)
1341$+$0346	4786-55651-0184	13978 (422)	8.834 (0.177)	$-2.151$ (0.049)	1.098 (0.096)
1434$+$2258	6016-56073-0466	15750 (405)	8.828 (0.084)	$0.725$ (0.727)	1.094 (0.046)
1435$+$5318	1327-52781-0413	15658 (355)	8.900 (0.063)	$-0.747$ (0.273)	1.133 (0.034)
1448$+$0519	4858-55686-0082	15966 (388)	8.943 (0.039)	$0.300$ (0.105)	1.157 (0.022)
1622$+$1849	4060-55359-0346	16693 (479)	9.129 (0.073)	$-0.079$ (0.164)	1.157 (0.012)
1622$+$3004	4953-55749-0483	16131 (267)	8.934 (0.022)	$-0.105$ (0.063)	1.152 (0.012)
1728$+$5558	0358-51818-0296	14772 (193)	8.869 (0.015)	$0.300$ (0.239)	1.117 (0.008)

Table 5. Table 5: Fit results for the hot DQ (hDQ) with T eff subscript 𝑇 eff T_{\rm eff} > > 18000 K. The second number in the columns for T eff subscript 𝑇 eff T_{\rm eff} , log ⁡ g 𝑔 \log g , and M 𝑀 M / M ⊙  are the internal uncertainties. [C/He] = 2 was assumed for these fit (see text).

SDSS J	p-m-f	Teff[K]	log g [cgs]	$M$/M⊙
0106$+$1513	5131-55835-0736	23610 (107)	8.572 (0.125)	0.957 (0.073)
0818$+$0102	2077-53846-0575	24483 ( 97)	8.326 (0.055)	0.807 (0.035)
1104$+$2035	6428-56279-0282	25503 ( 60)	8.661 (0.036)	1.009 (0.020)
1200$+$2252	2643-54208-0469	21880 (172)	8.505 (0.243)	0.915 (0.146)
1426$+$5752	6803-56402-0916	18809 (161)	8.722 (0.120)	1.039 (0.066)
2200$-$0741	0717-52468-0462	23097 ( 88)	8.694 (0.057)	1.026 (0.031)
2348$-$0942	7166-56602-0536	22596 (119)	8.652 (0.160)	1.002 (0.091)

Table 6. Table 6: Selected sample of 304 stars with carbon features

SDSS J	p-m-f	$\pi$ [msec]	g	G	S/N	Type
000011.66$-$085008.3	7167-56604-0752	4.825	19.111	19.056	17.8	DQ
000705.02$+$282104.2	2824-54452-0602	5.420	19.702	19.590	13.6	DQ
001523.91$+$030909.0	4298-55511-0906	5.020	20.028	19.933	8.5	DQ
001908.63$+$184706.0	7592-56947-0123	6.594	19.123	19.160	9.7	wDQ
002531.50$-$110800.9	0653-52145-0086	9.255	17.999	17.949	20.5	DQ
003328.58$+$041834.6	4303-55508-0562	7.497	18.720	18.648	26.2	DQ
004440.31$+$125923.3	6202-56266-0820	5.732	19.923	19.792	11.1	DQ
005505.41$+$085030.6	4544-55855-0064	11.351	18.689	18.392	16.2	DQ
010647.92$+$151327.6	5131-55835-0736	2.826	18.851	19.025	18.0	hDQ
010748.20$+$010240.1	2328-53728-0444	10.714	18.832	18.591	25.0	DQ
011639.84$+$234644.5	5693-56246-0401	11.183	17.769	17.731	34.5	DQ
012723.62$+$004630.0	0399-51817-0099	6.879	18.758	18.728	12.1	DQ
014324.13$+$115455.9	4662-55590-0818	4.797	20.523	20.340	6.6	DQ
015433.57$+$004047.2	0403-51871-0268	8.807	18.677	18.575	13.4	DQ
015441.74$+$140308.0	0430-51877-0558	16.213	17.865	17.666	22.1	DQ
020022.76$+$071459.7	4531-55563-0089	10.203	18.834	18.660	14.3	DQ
020252.80$+$004400.1	7837-56987-0256	9.522	20.203	19.604	12.2	dC
020534.24$+$215600.1	7636-56989-0171	9.522	19.902	19.604	11.7	DQ
022909.51$+$251024.5	2399-53764-0244	7.258	18.870	18.825	18.5	DQ
023633.74$+$250348.9	2399-53764-0059	5.696	18.824	18.945	16.5	wDQ
023945.04$+$002745.0	3745-55234-0924	4.714	19.733	19.631	23.6	DQ
024802.27$+$340802.4	2398-53768-0283	13.035	18.826	18.485	20.2	DQ
025357.12$+$341436.8	2398-53768-0154	3.915	19.781	19.674	9.0	DQ
032054.11$-$071625.4	0460-51924-0236	7.975	19.747	19.384	9.2	DQ
033004.02$+$051450.8	2339-53729-0036	10.226	19.647	19.087	13.5	dC
033218.23$+$003722.5	2069-53376-0148	9.040	18.389	18.333	24.9	DQ
035233.12$+$094641.1	2697-54389-0068	7.721	19.163	18.017	20.5	dC
041601.25$+$071308.9	2826-54389-0369	6.515	19.549	19.377	13.8	DQ
072339.12$+$390839.0	3657-55244-0476	8.476	17.795	17.864	31.0	DQ
073048.27$+$345729.8	2053-53446-0102	0.719	17.715	16.982	28.2	dC
073139.60$+$663618.1	2944-54523-0333	4.707	19.423	19.432	13.0	DQ
073703.83$+$645524.6	2944-54523-0244	5.097	19.619	19.525	11.1	DQ
074008.45$+$181047.2	2915-54497-0274	7.241	19.581	19.433	12.8	DQ
074204.75$+$434835.6	3669-55481-0722	7.164	18.815	18.752	21.1	DQ
074252.35$+$241140.5	4470-55587-0840	5.848	19.066	19.058	16.1	DQ
075000.55$+$232945.8	2916-54507-0474	5.347	20.167	20.084	9.4	DQ
075059.15$+$132855.4	4502-55569-0218	6.156	19.017	18.973	18.3	DQ
075200.65$+$301943.4	3752-55236-0652	5.647	20.171	20.103	9.0	DQ
075230.82$+$444749.9	3671-55483-0028	14.087	16.891	16.893	51.2	DQ
080236.30$+$414741.8	3683-55178-0162	4.257	20.250	20.169	9.2	DQ
080405.76$+$075055.1	2076-53442-0408	4.668	19.711	19.649	11.2	DQ
080455.42$+$171443.5	2081-53357-0171	14.947	19.079	18.521	12.3	DQpec
080558.84$+$072448.5	2076-53442-0505	12.799	19.565	18.984	13.5	DQpec
080708.49$+$194950.0	4481-55630-0323	5.663	18.844	19.032	21.0	wDQ
080843.15$+$464028.7	0438-51884-0063	9.668	20.399	19.558	6.3	DQ
081323.32$+$304744.1	0861-52318-0053	7.248	18.912	18.881	12.6	DQ
081448.31$+$245540.3	4463-55868-0140	16.968	16.921	16.877	14.1	DQ
081839.24$+$010227.5	2077-53846-0575	3.609	17.598	17.869	23.6	hDQ
082219.23$+$202325.8	1927-53321-0125	23.299	16.274	16.129	49.3	DQ
082626.78$+$470911.3	7325-56717-0705	1.221	19.232	17.838	19.9	dC
082710.45$+$210053.0	4483-55587-0850	7.461	19.284	19.127	13.8	DQ
083310.19$+$363846.9	0864-52320-0314	7.038	19.038	18.923	11.0	DQ
083608.56$+$043757.1	3809-55533-0504	5.786	18.842	18.864	19.9	DQ
083618.13$+$243254.6	2330-53738-0627	10.226	19.524	19.087	15.5	DQpec
083637.79$+$481752.5	0550-51959-0433	8.254	18.809	18.683	15.8	DQ
083728.83$+$032129.0	3809-55533-0466	5.787	19.165	19.131	19.6	DQ
083815.75$+$112118.4	5284-55866-0786	7.045	19.263	19.148	15.6	DQ
083921.07$+$084250.3	5284-55866-0206	6.748	20.236	19.945	6.7	DQ
084001.22$+$452933.4	5163-55889-0646	9.516	18.298	18.251	24.3	DQ
084131.55$+$332915.5	0933-52642-0016	18.804	18.457	18.370	14.1	DQ
084531.38$+$614336.4	1875-54453-0184	13.082	17.499	17.458	29.9	DQ
084624.72$+$102406.0	2671-54141-0310	7.721	17.975	18.017	32.3	DQ
085030.31$+$070937.0	5289-55893-0088	4.161	19.341	19.393	17.6	DQ
085506.63$+$063904.7	1189-52668-0535	13.082	17.862	17.740	21.3	DQ
085626.94$+$451337.0	7327-56715-0052	4.804	19.965	20.045	8.3	wDQ
085709.01$+$060357.4	1189-52668-0027	8.116	18.450	18.402	13.7	DQ
085914.63$+$325712.2	1272-52989-0309	43.363	15.086	15.089	69.3	wDQ
090148.21$+$365402.6	8860-57458-0148	6.761	19.000	20.454	21.7	dC
090200.36$+$503723.1	0551-51993-0612	6.086	19.240	19.177	10.2	DQ
090449.73$+$395416.5	1199-52703-0595	6.395	19.560	19.449	7.8	DQ
090514.78$+$090426.5	5299-55927-0646	16.790	16.732	16.694	48.3	DQ
090632.17$+$470235.8	0898-52606-0565	11.654	20.339	19.505	5.1	DQ
091406.56$+$063254.2	1193-52652-0528	1.262	19.504	17.986	13.0	dC
091500.58$+$201903.1	5768-56017-0666	5.167	19.158	19.224	16.9	DQ
091602.83$+$101109.7	5302-55896-0023	25.769	15.806	15.765	53.3	DQ
091922.26$+$023604.4	3822-55544-0966	6.399	18.980	19.077	19.6	wDQ
092011.52$+$530616.9	7289-57039-0974	4.407	19.924	19.875	9.2	DQ
092047.01$+$360352.8	4644-55922-0898	6.487	19.148	19.084	13.6	DQ
092153.48$+$342136.5	5810-56358-0620	5.512	18.599	18.583	23.3	DQ
092613.46$+$472521.1	0900-52637-0041	10.701	18.390	18.267	19.6	DQ
092909.03$+$331011.7	1593-52991-0094	11.009	18.802	18.437	12.8	DQ
093017.14$+$295940.7	2914-54533-0304	6.348	18.792	18.761	25.1	DQ
093448.86$+$115854.3	5313-55973-0175	6.263	18.711	18.710	24.2	DQ
093537.57$+$241708.7	2294-53733-0044	7.897	18.215	18.251	28.1	DQ
093638.04$+$060709.6	4871-55928-0024	6.171	19.135	19.273	12.8	wDQ
093937.62$+$520142.8	5724-56364-0374	13.593	17.162	17.171	37.7	DQ
094004.64$+$021022.6	0477-52026-0493	19.232	17.262	17.129	33.0	DQ
094058.34$+$384350.2	3224-54849-0517	6.891	18.752	18.660	18.5	DQ
094115.18$+$090154.4	1304-52993-0009	11.174	16.763	16.791	37.9	DQ
094138.09$+$441457.7	4695-55957-0208	7.433	18.670	18.632	18.4	DQ
094415.10$+$582749.3	5715-56657-0715	6.433	18.584	18.628	21.8	DQ
094511.56$+$503214.4	7292-56709-0649	4.407	20.216	19.875	13.0	dC
094857.89$+$123243.0	1742-53053-0616	12.428	18.300	18.147	17.8	DQ
095017.10$+$531515.0	0769-52282-0135	36.308	15.176	15.131	43.5	DQ
095137.61$+$624348.7	2403-53795-0577	5.920	18.855	18.833	24.3	DQ
095545.86$+$443640.1	8286-57062-0866	4.034	16.985	20.247	45.6	dC
095837.00$+$585303.0	5719-56014-0114	6.014	18.758	18.958	12.9	wDQ
100523.61$-$011430.7	3769-55240-0546	5.089	19.307	19.305	15.2	DQ
100531.23$+$053809.2	0995-52731-0069	1.862	19.007	17.282	19.3	dC
100958.70$+$010313.2	0502-51957-0216	0.762	18.138	17.201	29.5	dC
101009.56$+$230016.8	6458-56274-0618	7.284	18.422	18.468	22.8	DQ
101219.90$+$004019.7	0502-51957-0095	8.386	17.710	17.762	28.4	DQ
101336.56$+$435054.8	4561-55614-0788	6.939	18.625	18.618	16.8	DQ
101509.60$+$351813.4	4568-55600-0256	5.781	19.001	18.978	16.3	DQ
101750.38$+$373637.5	1427-52996-0216	8.065	18.913	18.853	12.1	DQ
101800.00$+$083820.3	1237-52762-0621	22.825	16.410	16.347	36.6	DQ
102211.67$+$284507.3	2351-53772-0170	7.158	19.127	19.104	12.1	DQ
102635.06$+$272507.3	6463-56340-0894	6.625	18.858	18.832	17.9	DQ
102705.08$+$121836.1	1747-53075-0241	12.428	18.613	18.147	13.7	DQ
102801.75$+$351258.0	1958-53385-0558	13.533	19.389	18.739	10.6	DQ
102836.21$+$253732.8	2349-53734-0535	9.112	19.008	18.783	12.0	DQ
103102.52$+$221714.7	5873-56035-0828	7.359	20.192	20.115	7.3	DQ
103205.85$+$210131.2	5873-56035-0852	5.993	19.124	19.146	15.0	DQ
103210.68$+$451930.0	4691-55651-0758	7.931	18.080	18.114	30.0	DQ
104031.99$+$182206.6	5886-56034-0578	5.079	20.312	20.164	7.0	DQ
104204.26$+$583348.1	7095-56625-0462	7.947	19.084	18.983	10.5	DQ
104505.66$+$213447.2	5874-56039-0954	6.497	19.114	19.043	12.7	DQ
104906.61$+$165923.7	5352-56269-0732	5.759	19.298	19.423	20.4	wDQ
105119.71$+$301946.7	1981-53463-0520	1.924	20.085	18.428	9.1	dC
105248.66$+$591150.6	7095-56625-0848	8.786	18.320	18.275	37.8	DQ
105817.66$+$284609.3	2870-54534-0429	6.480	19.334	19.346	13.1	wDQ
105854.34$+$344018.1	4631-55617-0148	6.035	20.102	19.969	12.1	DQ
110058.04$+$175807.0	2485-54176-0119	7.060	18.589	18.732	13.5	wDQ
110140.41$+$521806.7	6706-56385-0856	5.219	19.220	19.204	14.3	DQ
110406.69$+$203528.6	6428-56279-0282	5.504	17.212	17.496	40.4	hDQ
110831.50$+$134950.5	5360-55983-0034	11.130	18.123	18.041	25.7	DQ
111336.00$+$445505.1	6649-56364-0050	6.681	18.898	18.865	17.4	DQ
111341.33$+$014641.7	0510-52381-0184	22.947	19.205	18.527	10.9	DQpec
112023.61$+$425200.7	1440-53084-0408	9.139	18.616	18.536	12.0	DQ
112324.94$+$352341.5	4618-55600-0334	5.542	19.986	19.791	6.9	DQ
112329.64$+$620714.4	3328-54964-0497	5.959	19.495	19.327	13.6	DQ
112348.02$+$334713.8	4619-55599-0440	7.728	19.044	18.983	13.9	DQ
112604.28$+$441938.6	3215-54861-0257	8.237	19.093	18.978	16.0	DQ
112702.85$+$190912.8	2498-54169-0166	1.249	19.574	18.190	11.9	dC
112731.86$-$021242.2	3233-54891-0206	6.891	17.633	18.660	41.9	dC
112804.62$-$072413.5	2876-54581-0472	2.924	18.867	19.743	35.2	dC
113104.23$+$184558.8	5879-56047-0298	6.496	18.804	18.762	23.2	DQ
113300.58$+$190056.5	5879-56047-0178	5.432	19.127	19.096	19.2	DQ
113534.62$+$572451.7	1310-53033-0485	17.103	16.480	16.371	40.3	DQ
114006.29$+$182401.9	5891-56034-0946	10.553	17.954	17.987	23.7	wDQ
114056.78$+$154014.3	1755-53386-0607	8.632	19.275	19.021	9.9	DQ
114059.88$+$073529.9	5377-55957-0240	6.214	19.166	19.270	14.9	wDQ
114136.53$+$383611.9	1997-53442-0386	12.641	19.920	19.107	7.2	DQpec
114256.66$+$035208.0	4766-55677-0262	5.481	19.261	19.169	15.2	DQ
114851.68$-$012612.8	0329-52056-0578	14.681	17.403	17.406	21.1	wDQ
115149.82$+$452730.3	6642-56396-0596	9.401	17.807	17.833	24.0	DQ
115933.10$+$130031.6	3285-54948-0513	16.104	18.137	17.818	29.5	DQpec
120027.73$+$225212.9	2643-54208-0469	2.320	18.976	19.258	10.8	hDQ
120049.38$+$423726.1	1447-53120-0621	10.826	19.270	18.990	8.8	DQ
120154.70$+$340055.8	2089-53498-0318	24.677	17.754	17.343	33.9	DQ
120331.77$+$645059.6	6975-56720-0446	11.458	17.528	17.656	38.5	wDQ
121149.26$+$044050.8	4749-55633-0722	6.493	19.129	19.058	15.6	DQ
121211.13$+$545221.1	6688-56412-0854	10.581	17.869	17.840	28.5	DQ
121510.66$+$470010.4	6640-56385-0532	6.754	18.764	18.962	13.6	wDQ
122257.72$+$604100.9	6968-56443-0588	5.198	19.187	19.194	15.6	DQ
122545.88$+$470613.0	1451-53117-0035	8.880	19.576	19.147	6.6	DQ
122854.55$+$480620.6	6671-56388-0004	5.839	19.624	19.480	7.1	DQ
123313.48$+$082403.1	1627-53473-0578	12.248	18.666	18.384	14.1	DQpec
123534.88$+$391820.0	3970-55591-0354	12.562	17.113	17.182	35.0	DQ
123752.12$+$415625.8	1454-53090-0146	27.659	17.757	17.150	24.7	DQpec
124034.89$-$014459.7	2922-54612-0392	4.767	19.363	19.352	17.9	DQ
124338.97$+$360729.0	2022-53827-0238	8.559	18.190	18.173	16.2	DQ
124433.81$+$270923.9	2238-54205-0229	6.139	18.340	18.270	16.9	DQ
124701.79$+$411340.8	4703-55617-0438	8.387	18.249	18.246	26.2	DQ
124733.70$+$491524.8	2923-54563-0222	9.114	19.400	19.094	14.6	DQ
124739.05$+$064604.6	1790-53876-0110	19.058	20.041	18.854	4.0	DQpec
124911.75$+$340706.0	3971-55322-0018	13.949	17.087	17.111	39.6	DQ
125017.90$+$252427.6	2661-54505-0444	3.537	18.199	16.501	27.3	dC
125151.56$+$464627.2	1457-53116-0215	9.373	17.818	17.841	20.0	DQ
125245.44$+$194311.2	2615-54483-0381	11.895	17.757	17.713	26.6	DQ
125359.61$+$013925.6	0523-52026-0252	5.624	19.074	19.062	9.7	DQ
125829.51$+$445206.9	1373-53063-0638	2.564	19.986	18.106	8.9	dC
130201.30$+$092351.7	3234-54885-0143	8.800	18.702	18.568	18.6	DQ
130945.51$+$444540.9	6621-56366-0844	9.137	18.970	18.836	17.4	DQpec
131534.80$+$471107.1	6625-56386-0556	11.834	17.760	17.690	29.7	DQ
131640.71$+$081058.7	5423-55958-0996	11.401	18.572	18.392	19.6	DQ
131930.71$+$140136.4	5425-56003-0148	6.901	18.967	18.891	18.3	DQ
131953.49$+$084422.0	5429-55979-0598	9.212	18.060	18.032	28.0	DQ
132232.05$+$373032.9	2102-54115-0356	7.212	18.985	18.932	15.8	DQ
132825.28$+$364016.5	3983-55603-0800	7.931	18.450	18.443	30.2	DQ
132931.08$+$074651.9	1801-54156-0324	14.252	17.223	17.265	31.9	DQ
133127.01$+$670420.0	6825-56717-0629	5.790	18.888	18.898	18.1	DQ
133151.38$+$372754.8	3984-55333-0118	7.466	18.264	18.460	25.6	wDQ
133221.56$+$235502.2	5995-56093-0918	4.409	19.157	19.366	11.4	wDQ
133313.73$+$235722.0	5995-56093-0958	7.596	18.756	18.736	14.6	DQ
133359.86$+$001654.8	0298-51955-0492	24.453	19.420	18.533	11.3	DQpec
133420.09$+$162235.8	5434-56033-0075	8.448	18.135	18.142	24.7	DQ
133641.85$+$192056.2	5862-56045-0694	7.886	19.780	19.537	9.8	DQ
133901.47$+$501434.4	6744-56399-0626	7.592	18.337	18.350	20.6	DQ
133940.50$+$503613.5	6744-56399-0664	5.427	19.114	19.243	11.9	wDQ
134124.28$+$034628.7	4786-55651-0184	4.641	19.329	19.473	13.3	wDQ
134426.47$+$184930.9	2930-54589-0391	8.672	18.071	18.062	40.2	DQ
134707.57$+$381749.7	3852-55243-0630	6.398	19.174	19.160	19.5	DQ
134716.09$+$501942.1	6740-56401-0202	6.487	18.906	18.883	14.9	DQ
134747.94$+$152851.0	5441-56017-0848	6.789	19.133	19.113	15.8	DQ
135057.54$+$050841.0	0855-52375-0474	2.243	17.434	16.064	32.2	dC
135134.35$+$662315.4	6986-56717-0616	9.978	17.703	17.712	31.5	DQ
135201.98$+$221811.4	5869-56064-0716	5.898	19.250	19.188	13.1	DQ
135258.69$+$265853.7	6005-56090-0670	6.494	19.123	19.060	12.3	DQ
135409.79$+$121732.2	5443-56010-0064	4.631	19.486	19.416	12.2	DQ
135516.57$+$363613.2	3852-55243-0048	11.665	17.684	17.644	37.0	DQ
135628.25$+$000941.2	0301-51942-0231	12.797	18.602	18.346	15.2	DQ
135739.52$+$294921.5	2122-54178-0346	8.398	18.641	18.556	15.1	DQ
135810.42$+$055237.6	4863-55688-0462	5.863	19.047	18.990	14.8	DQ
140625.70$+$020447.0	0532-51993-0475	5.648	18.773	18.670	12.4	DQ
140632.42$+$014838.3	0532-51993-0234	8.856	18.427	18.358	14.0	DQ
140723.00$+$203918.4	5894-56039-0782	6.334	18.653	18.636	17.0	DQ
141648.86$+$301654.0	6497-56329-0888	4.456	20.341	20.293	11.7	DQ
141745.42$+$241222.6	2128-53800-0153	8.342	18.645	18.596	15.4	DQ
142032.63$+$531624.5	7028-56449-0881	6.135	19.371	19.334	11.0	DQ
142413.37$+$083316.5	5462-55978-0432	8.866	17.710	17.751	29.2	DQ
142531.97$+$180115.7	5897-56042-0259	7.575	18.600	18.565	18.8	DQ
142625.72$+$575218.6	6803-56402-0916	3.078	19.148	19.394	12.1	hDQ
142728.30$+$611026.4	0607-52368-0379	23.283	17.154	16.924	35.0	DQ
142812.00$+$443439.8	2932-54595-0125	8.672	19.001	18.062	22.7	dC
143144.83$+$375011.9	1381-53089-0599	6.321	19.337	19.118	10.8	DQ
143227.07$+$475110.7	6752-56366-0851	8.269	18.200	18.175	22.2	DQ
143437.81$+$225859.2	6016-56073-0466	4.836	18.972	19.192	16.6	wDQ
143534.01$+$531815.1	1327-52781-0413	5.005	19.021	19.212	8.4	wDQ
143550.13$+$212014.5	5900-56043-0959	4.999	19.302	19.284	11.4	DQ
144221.53$+$420250.2	6061-56076-0860	5.269	19.092	19.144	16.6	DQ
144537.07$+$185120.4	5903-56064-0342	5.526	19.103	19.082	15.4	DQ
144808.07$+$004755.9	0308-51662-0145	11.170	18.438	18.293	18.0	DQ
144854.80$+$051903.5	4858-55686-0082	8.316	18.007	18.190	26.3	wDQ
144954.84$+$291633.7	3878-55361-0654	6.270	19.215	19.145	14.4	DQ
145005.60$+$102833.8	3388-54947-0393	5.959	17.397	19.327	42.9	dC
145023.96$+$635053.8	2947-54533-0605	4.340	19.664	19.637	8.7	DQ
145725.27$+$210747.4	2150-54510-0288	11.992	19.148	18.741	12.8	DQpec
150126.78$+$210056.9	2150-54510-0135	10.843	18.695	18.239	16.6	DQ
150136.90$+$062720.6	1815-53884-0095	9.279	18.968	18.848	11.3	DQ
150245.71$-$022454.8	0922-52426-0221	1.145	19.187	17.972	12.2	dC
150901.11$+$162012.3	5484-56039-0232	6.238	18.850	18.809	17.8	DQ
151118.19$+$500800.7	1330-52822-0417	6.815	18.986	18.954	9.4	DQ
151417.00$+$142354.1	2766-54242-0126	8.679	19.714	19.343	6.7	DQ
151734.38$+$225619.1	3955-55678-0592	12.614	17.850	17.773	33.1	DQ
151942.63$+$385658.8	4979-56045-0654	5.918	19.045	19.027	16.1	DQ
152030.30$+$270321.5	3851-55302-0214	5.778	19.224	19.120	19.5	DQ
152702.59$+$275213.2	3959-55679-0676	7.521	19.271	19.180	14.9	DQpec
152812.03$+$513444.1	6721-56398-0969	9.630	18.429	18.359	20.1	DQ
152840.05$+$400335.0	2936-54626-0548	7.174	19.042	19.017	19.6	DQ
152854.10$+$044226.6	1835-54563-0179	7.043	19.122	19.012	8.2	DQ
153303.83$+$395818.3	1679-53149-0135	3.342	18.928	19.248	16.8	dC
153447.54$+$414559.4	1679-53149-0616	15.188	17.244	17.167	32.3	DQ
153732.19$+$004343.1	0315-51663-0422	2.618	19.471	17.600	15.1	dC
153746.05$+$133732.9	4890-55741-0439	8.507	18.385	18.323	22.5	DQ
154156.85$+$514421.3	0796-52401-0423	1.140	18.486	17.537	18.5	dC
154234.73$+$254438.7	3947-55332-0760	8.234	19.325	19.133	11.7	DQ
154238.94$+$131455.8	4890-55741-0172	8.556	18.450	18.396	26.9	DQ
154810.66$+$562647.7	0617-52072-0551	6.854	19.028	19.000	10.1	DQ
155155.26$+$082431.8	1727-53859-0442	13.901	18.018	17.872	20.2	DQ
155202.39$+$114829.1	2520-54584-0515	7.142	19.002	18.911	15.0	DQ
155206.42$+$391017.6	5192-56066-0472	8.797	18.696	18.603	13.6	DQ
155413.53$+$033634.5	0595-52023-0373	9.761	18.914	18.686	11.5	DQ
155432.04$+$113616.0	2520-54584-0630	5.714	19.060	19.023	13.6	DQ
160935.76$+$065509.9	1730-53498-0217	11.686	17.737	17.678	23.7	DQ
161018.90$+$303619.1	5009-55707-0838	6.268	19.113	19.059	16.7	DQ
161140.18$+$045127.0	2189-54624-0562	14.823	18.703	18.303	23.0	DQpec
161315.43$+$511608.2	6316-56483-0713	6.201	19.216	19.165	15.5	DQ
161414.12$+$172900.5	2177-54557-0460	18.426	18.671	18.012	21.3	DQpec
161653.36$+$392444.4	1336-52759-0572	10.687	18.325	18.203	17.1	DQ
161847.38$+$061155.2	1732-53501-0218	12.938	18.248	18.255	18.4	DQpec
161853.78$+$504800.8	3288-54908-0467	16.104	17.311	17.818	43.6	dC
161945.61$+$192841.8	4060-55359-0568	9.919	19.425	18.035	17.7	dC
162004.02$+$180912.3	4060-55359-0444	9.919	18.089	18.035	28.7	DQ
162153.79$+$225309.4	4184-55450-0463	8.110	18.521	18.473	21.1	DQ
162205.12$+$184956.7	4060-55359-0346	5.434	19.202	19.383	15.3	wDQ
162236.13$+$300454.5	4953-55749-0483	13.366	16.895	17.095	38.5	wDQ
162635.58$+$154441.6	4056-55357-0734	7.976	19.661	19.440	12.9	DQpec
162721.61$+$304320.2	4953-55749-0732	6.412	18.741	18.742	18.6	DQ
163546.48$+$284335.5	5201-55832-0412	7.425	19.147	19.062	13.2	DQ
163857.96$+$124420.6	4075-55352-0802	9.860	17.788	17.796	45.0	DQ
164143.26$+$483301.8	6318-56186-0724	10.937	18.096	18.036	27.9	DQ
165436.86$+$315754.4	1176-52791-0238	15.781	17.504	17.408	23.3	DQ
165538.46$+$372247.9	5198-55823-0844	6.789	18.491	18.521	20.7	DQ
171221.94$+$340609.9	4994-55739-0426	5.539	19.298	19.271	13.9	DQ
171341.84$+$324007.5	4998-55722-0536	14.362	17.360	17.283	36.8	DQ
172856.22$+$555822.8	0358-51818-0296	21.188	16.024	16.169	48.5	wDQ
180302.57$+$232043.3	2195-54234-0272	15.335	20.478	19.193	9.9	DQpec
183500.21$+$642916.9	2552-54632-0496	18.726	17.594	17.278	38.4	DQpec
204624.45$-$071519.1	0635-52145-0228	6.145	18.916	18.833	11.0	DQ
205316.34$-$070204.3	0636-52176-0267	10.190	19.210	18.818	10.9	DQ
213503.31$+$000318.4	0989-52468-0198	8.283	19.399	19.146	8.5	DQ
214058.23$+$004529.4	4196-55478-0444	6.479	19.369	19.265	17.8	DQ
214247.87$+$090858.8	4093-55475-0084	7.631	19.333	19.210	15.5	DQ
214944.08$+$203921.6	5949-56096-0402	4.727	19.094	19.083	16.9	DQ
215027.79$-$011351.0	4197-55479-0362	11.063	17.465	17.478	45.6	DQ
215652.94$+$055925.1	4096-55501-0804	10.286	18.680	18.556	15.4	DQ
215759.11$+$113729.1	5063-55831-0387	6.581	18.590	18.585	23.3	DQ
220029.09$-$074121.6	0717-52468-0462	5.029	17.781	17.975	21.6	hDQ
220746.17$+$013509.0	4316-55505-0170	8.647	19.467	19.276	12.0	DQ
221245.22$+$061323.4	2323-54380-0113	8.882	19.600	19.397	13.0	DQ
221528.01$+$065220.7	2308-54379-0592	5.313	18.362	18.604	17.8	dC
221850.23$+$212303.7	5946-56101-0356	10.364	17.929	17.902	29.9	DQ
222032.07$+$142032.5	5042-55856-0642	7.431	18.621	18.582	30.5	DQ
222552.64$+$125116.8	5042-55856-0096	6.426	19.774	19.594	18.8	DQ
223224.00$-$074434.3	0721-52228-0533	18.268	18.413	17.912	25.8	DQpec
225459.62$+$002545.3	4206-55471-0156	5.483	19.285	19.225	20.5	DQ
225901.16$+$215843.9	6591-56535-0384	6.805	20.751	20.226	6.3	DQpec
230249.36$+$243027.1	6588-56536-0038	13.792	18.177	17.971	28.9	DQ
231030.24$+$005745.6	4209-55478-0404	6.949	19.153	19.045	18.9	DQ
234130.75$+$151943.5	1894-53240-0463	13.082	18.347	17.458	19.3	dC
234132.83$-$010104.5	0385-51877-0126	8.158	18.309	18.233	20.1	DQ
234843.30$-$094245.4	7166-56602-0536	2.764	19.028	19.263	15.5	hDQ
235443.13$+$362907.2	1880-53262-0153	13.082	17.599	17.458	27.8	dC

Table 7. Table 7: Fit results for the classical DQ with Swan bands. The numbers in parentheses for T eff subscript 𝑇 eff T_{\rm eff} , log ⁡ g 𝑔 \log g , [C/He], and M 𝑀 M / M ⊙  are the internal uncertainties.

SDSS J	p-m-f	Teff[K]	log g [cgs]	[C/He]	$M$/M⊙
0000$-$0850	7167-56604-0752	7944 (117)	7.453 (0.164)	$-5.172$ (1.369)	0.311 (0.060)
0007$+$2821	2824-54452-0602	7529 ( 92)	7.931 (0.142)	$-5.427$ (0.584)	0.536 (0.082)
0015$+$0309	4298-55511-0906	7256 (132)	8.004 (0.181)	$-5.678$ (2.117)	0.578 (0.109)
0025$-$1108	0653-52145-0086	8402 ( 82)	7.866 (0.041)	$-4.754$ (0.291)	0.502 (0.023)
0033$+$0418	4303-55508-0562	7700 (108)	7.847 (0.073)	$-5.792$ (0.601)	0.489 (0.040)
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1424$+$0833	5462-55978-0432	9329 (110)	7.891 (0.041)	$-4.430$ (0.437)	0.516 (0.023)
1425$+$1801	5897-56042-0259	7993 (116)	7.894 (0.067)	$-5.146$ (1.308)	0.516 (0.038)
1427$+$6110	0607-52368-0379	6313 ( 39)	7.894 (0.018)	$-6.666$ (0.249)	0.513 (0.010)
1431$+$3750	1381-53089-0599	6313 ( 78)	7.358 (0.104)	$-6.727$ (0.674)	0.270 (0.036)
1432$+$4751	6752-56366-0851	8563 ( 92)	7.908 (0.037)	$-4.934$ (0.618)	0.525 (0.021)
1435$+$2120	5900-56043-0959	8780 (157)	7.947 (0.132)	$-4.581$ (2.941)	0.548 (0.077)
1442$+$4202	6061-56076-0860	8812 (129)	7.964 (0.104)	$-4.713$ (0.975)	0.558 (0.062)
1445$+$1851	5903-56064-0342	8195 (113)	7.802 (0.108)	$-5.120$ (1.992)	0.467 (0.057)
1448$+$0047	0308-51662-0145	7075 ( 63)	8.011 (0.041)	$-6.127$ (1.491)	0.582 (0.025)
1449$+$2916	3878-55361-0654	7966 ( 97)	8.011 (0.094)	$-5.190$ (1.462)	0.585 (0.057)
1450$+$6350	2947-54533-0605	8060 (137)	7.799 (0.188)	$-4.928$ (0.838)	0.465 (0.098)
1501$+$0627	1815-53884-0095	7216 ( 74)	8.167 (0.064)	$-5.755$ (0.836)	0.681 (0.042)
1501$+$2100	2150-54510-0135	5728 ( 27)	7.228 (0.046)	$-6.140$ (0.094)	0.223 (0.014)
1509$+$1620	5484-56039-0232	8398 (113)	7.871 (0.131)	$-5.132$ (2.098)	0.504 (0.072)
1511$+$5008	1330-52822-0417	7836 ( 98)	7.973 (0.056)	$-5.466$ (1.095)	0.561 (0.034)
1514$+$1423	2766-54242-0126	7094 ( 40)	8.296 (0.054)	$-3.998$ (0.330)	0.767 (0.036)
1517$+$2256	3955-55678-0592	7530 ( 61)	7.983 (0.025)	$-5.752$ (0.277)	0.567 (0.015)
1519$+$3856	4979-56045-0654	8293 (111)	7.926 (0.067)	$-4.974$ (0.680)	0.535 (0.038)
1520$+$2703	3851-55302-0214	7849 (113)	7.808 (0.100)	$-5.368$ (0.408)	0.469 (0.052)
1528$+$0442	1835-54563-0179	7485 ( 83)	7.925 (0.110)	$-5.685$ (3.812)	0.532 (0.063)
1528$+$4003	2936-54626-0548	7734 (108)	8.061 (0.056)	$-5.478$ (0.554)	0.615 (0.035)
1528$+$5134	6721-56398-0969	7626 ( 66)	8.020 (0.030)	$-5.356$ (0.268)	0.589 (0.019)
1534$+$4145	1679-53149-0616	7745 ( 76)	7.907 (0.026)	$-5.794$ (0.572)	0.523 (0.015)
1537$+$1337	4890-55741-0439	8017 ( 83)	7.896 (0.055)	$-5.348$ (0.548)	0.517 (0.031)
1542$+$1314	4890-55741-0172	8150 ( 83)	7.994 (0.047)	$-5.153$ (1.412)	0.575 (0.029)
1542$+$2544	3947-55332-0760	6691 ( 64)	7.990 (0.059)	$-6.292$ (0.392)	0.570 (0.036)
1548$+$5626	0617-52072-0551	8013 (108)	8.066 (0.054)	$-5.274$ (1.012)	0.619 (0.034)
1551$+$0824	1727-53859-0442	6741 ( 58)	7.932 (0.029)	$-6.146$ (0.979)	0.535 (0.017)
1552$+$1148	2520-54584-0515	7870 (110)	8.009 (0.076)	$-5.216$ (0.751)	0.583 (0.046)
1552$+$3910	5192-56066-0472	7614 ( 81)	8.055 (0.040)	$-5.524$ (2.216)	0.611 (0.025)
1554$+$0336	0595-52023-0373	6716 ( 75)	7.893 (0.053)	$-6.411$ (0.674)	0.513 (0.030)
1554$+$1136	2520-54584-0630	8382 (107)	7.865 (0.087)	$-4.750$ (0.388)	0.501 (0.048)
1609$+$0655	1730-53498-0217	8012 ( 98)	7.934 (0.036)	$-5.438$ (0.713)	0.539 (0.021)
1610$+$3036	5009-55707-0838	8133 ( 96)	7.986 (0.063)	$-4.925$ (0.455)	0.570 (0.038)
1613$+$5116	6316-56483-0713	7990 (120)	8.011 (0.072)	$-5.077$ (2.317)	0.585 (0.044)
1616$+$3924	1336-52759-0572	7257 ( 60)	7.955 (0.028)	$-5.787$ (0.384)	0.549 (0.016)
1620$+$1809	4060-55359-0444	7859 ( 68)	7.889 (0.034)	$-5.433$ (0.307)	0.513 (0.019)
1621$+$2253	4184-55450-0463	8147 ( 97)	7.957 (0.045)	$-5.259$ (0.479)	0.553 (0.026)
1627$+$3043	4953-55749-0732	8406 ( 88)	7.870 (0.058)	$-5.130$ (2.155)	0.504 (0.032)
1635$+$2843	5201-55832-0412	7890 (105)	8.188 (0.061)	$-5.244$ (1.038)	0.697 (0.040)
1638$+$1244	4075-55352-0802	8669 ( 79)	7.933 (0.032)	$-4.805$ (0.337)	0.540 (0.019)
1641$+$4833	6318-56186-0724	7735 ( 75)	8.021 (0.028)	$-5.476$ (0.389)	0.590 (0.017)
1654$+$3157	1176-52791-0238	7389 ( 63)	8.033 (0.022)	$-5.479$ (0.264)	0.597 (0.014)
1655$+$3722	5198-55823-0844	8881 ( 83)	7.928 (0.045)	$-4.436$ (0.533)	0.537 (0.026)
1712$+$3406	4994-55739-0426	8145 (106)	7.954 (0.084)	$-5.148$ (2.366)	0.551 (0.049)
1713$+$3240	4998-55722-0536	8070 ( 55)	7.999 (0.018)	$-4.970$ (0.191)	0.578 (0.011)
2046$-$0715	0635-52145-0228	8147 ( 98)	7.769 (0.075)	$-5.226$ (2.019)	0.449 (0.038)
2053$-$0702	0636-52176-0267	6726 ( 38)	8.075 (0.049)	$-4.648$ (0.175)	0.622 (0.031)
2135$+$0003	0989-52468-0198	6379 ( 56)	7.865 (0.202)	$-6.746$ (0.935)	0.497 (0.112)
2140$+$0045	4196-55478-0444	7605 (100)	8.039 (0.102)	$-5.495$ (0.412)	0.601 (0.063)
2142$+$0908	4093-55475-0084	7328 (102)	8.147 (0.173)	$-5.618$ (0.595)	0.669 (0.112)
2149$+$2039	5949-56096-0402	8873 (118)	7.684 (0.185)	$-4.182$ (0.150)	0.409 (0.086)
2150$-$0113	4197-55479-0362	9046 (103)	7.962 (0.038)	$-4.542$ (0.727)	0.557 (0.023)
2156$+$0559	4096-55501-0804	6973 ( 87)	8.035 (0.047)	$-6.249$ (1.361)	0.597 (0.029)
2157$+$1137	5063-55831-0387	8711 (101)	7.839 (0.079)	$-4.632$ (1.019)	0.487 (0.043)
2207$+$0135	4316-55505-0170	6432 ( 73)	8.067 (0.073)	$-6.698$ (1.009)	0.617 (0.045)
2212$+$0613	2323-54380-0113	6730 ( 84)	8.280 (0.104)	$-6.174$ (1.164)	0.756 (0.069)
2218$+$2123	5946-56101-0356	8255 ( 62)	7.983 (0.029)	$-4.951$ (0.358)	0.569 (0.018)
2220$+$1420	5042-55856-0642	8670 (122)	8.050 (0.070)	$-4.750$ (0.569)	0.610 (0.043)
2225$+$1251	5042-55856-0096	6498 (130)	7.851 (0.216)	$-6.519$ (1.670)	0.489 (0.118)
2254$+$0025	4206-55471-0156	8295 (130)	7.867 (0.142)	$-4.967$ (0.458)	0.502 (0.079)
2302$+$2430	6588-56536-0038	6863 ( 53)	8.017 (0.026)	$-6.357$ (0.264)	0.586 (0.016)
2310$+$0057	4209-55478-0404	7881 ( 67)	8.017 (0.102)	$-3.971$ (0.064)	0.588 (0.062)
2341$-$0101	0385-51877-0126	8568 (117)	7.924 (0.059)	$-4.897$ (0.614)	0.535 (0.034)

Full text

*Aims. *We want to derive atmospheric parameters $T_{\rm eff}$, $\log g$, and carbon abundances for a large sample of these stars and discuss implications for their spectral evolution.

*Methods. *Sloan Digital Sky Survey spectra and $ugriz$ photometry were used, together with Gaia Data Release 2 parallaxes and $G$ band photometry. These were fitted to synthetic spectra and theoretical photometry derived from model atmospheres.

Results. We found that the DQs hotter than $T_{\rm eff}$ $\approx$10000 K have masses $\approx$0.4  M⊙ larger than the classical DQ, which have masses typical for the majority of white dwarfs ($\approx$0.6 M*⊙*). We found some evidence that the peculiar DQ below 10000 K also have significantly larger masses and may thus be the descendants of the hot and warm DQs above 10000 K. A significant fraction of the hotter objects with $T_{\rm eff}$ $>14500$ K have atmospheres dominated by carbon.

1 Introduction

White dwarfs of spectral type DQ are a subclass of hydrogen-poor objects, i.e. hydrogen is not the dominant element as in the vast majority of white dwarfs. Historically the first objects known (henceforth simply called DQ) are characterized by Swan bands of the C2 molecule in the optical region. Later objects with strong C i resonance lines in the UV were added to this class (Sion et al., 1983), even if they don’t show any features in the optical range. Systematic analyses of larger samples are Dufour et al. (2005) and Koester & Knist (2006). Contrary to the numerous metal-polluted hydrogen- and helium-rich white dwarfs, where the metals are believed to be accreted from the debris of disintegrating members of a former planetary system, the carbon in the DQ (at least those below 10000 K) is a result of dredge-up by an extending convection zone in the upper helium layer (Koester et al., 1982; Pelletier et al., 1986).

With the discovery of thousands of new white dwarfs thanks to the Sloan Digital Sky Survey (SDSS, York et al., 2000; Abolfathi et al., 2018) a number of hotter objects with carbon features were found (Liebert et al., 2003; Dufour et al., 2008). The latter analysis surprisingly concluded that the group of hot objects showing mostly C ii in the range of effective temperatures from 18000 to 24000 K was in fact dominated by carbon in their atmospheres, with only occasional traces of hydrogen, helium, or oxygen. Several members of this group show magnetic fields, light variations, and unusually high masses. In spite of many suggestions the evolutionary status of these objects is not fully understood (Fortier & Dufour, 2015).

Between the classical DQ and the new “hot DQ” (hDQ here) class several objects with spectra dominated by C i lines in the optical range are now termed “warm DQ” (wDQ here) (Dufour et al., 2013; Fortier & Dufour, 2015). These objects are believed to be helium-dominated, but with large carbon contributions of $\log$(N(C)/N(He)) (abbreviated as [C/He] henceforth) $\approx-3$ to $-2$.

Several authors have found that the carbon abundances, when shown as a function of $T_{\rm eff}$, have a clear tendency from higher to lower values with decreasing temperature, and that a separate second sequence exist with higher abundances (see e.g. Kepler et al., 2016). The upper sequence was also suggested to have higher masses, although the data were very limited.

The surface gravities and masses are very difficult to determine spectroscopically and only few were known until recently. The situation was much improved when the Gaia Data Release 2 (DR2) parallaxes for many of these objects were published (Gaia Collaboration et al., 2018). Atmospheric parameters for a large sample of white dwarfs with Gaia parallaxes and SDSS spectra, which also included many DQ white dwarfs, was studied by Gentile Fusillo et al. (2019). The first application of such a sample, which additionally obtained abundances, was Coutu et al. (2018), which very clearly shows two separate sequences in the mass distribution as well as the abundance vs. $T_{\rm eff}$ distribution. All objects up to the highest $T_{\rm eff}$ of $\approx$15000 K in their results have helium dominated atmospheres with [C/He] $<-1.5$. The hottest object is SDSSJ1448+0519 (we use this shorthand notation, the complete official SDSS name can be found in Table 1, if necessary via the p-m-f designation of the spectra), identified with the parameters $T_{\rm eff}$ = 15473 K, $\log g$ = 8.94, [C/He] = $-1.70$. This object is also in our sample (described in section 2). We calculated a model with these parameters. The model shows strong He lines at 4472, 5877, and 6679 Å (all these regions are not included in the figure on the poster), which are completely absent in the observed spectrum. With our analysis we find instead that this object has a carbon-dominated atmosphere with an upper limit on the helium abundance of [He/C] ¡ $-0.30$. This raises the question of the nature of the transition between hot and normal DQ, roughly in the temperature range 10000-18000 K. Since the helium lines become invisible below 12000 K, or even higher in low S/N spectra, this is a difficult question, which is the major topic of this study. In addition we will present some results for a fairly large sample of classical cool DQ and a few hot DQ, which generally agree with previous findings.

2 Observations and choice of sample

The original sample in our study (572 stars) included all stars classified as DQ from the 34973 white dwarfs in Kleinman et al. (2013); Kepler et al. (2015, 2016, 2019), even if the classification was uncertain. Therefore the DQs represent at most 1.6% of the classified white dwarfs from SDSS, and 9% of the non-DAs.

From these we selected the spectra with highest S/N obtained by SDSS up to DR14 for stars having Gaia DR2 parallaxes, necessary to estimate the $T_{\rm eff}$, $\log g$, and mass. We further eliminated some wrong or uncertain type identifications, and objects with low signal-to-noise ratio (S/N) or very weak features. We did not aim at complete samples, but for a sample with accurate parameter determinations. Most spectra have S/N $>10$, but we included some with lower values if the features were strong and easily recognized. Also eliminated were objects with Gaia parallax uncertainties larger than $25\%$. We were then left with 304 stars, all showing clear carbon features of Swan bands of the C2 molecules, or lines from C i and/or C ii. These stars are listed in Table 1, together with some of the observed data.

When we started the analysis, 29 objects indicated very low surface gravities, at the lowest gravities of our model grids, but still without a reasonable fit. Visual inspection revealed very narrow bands and lines, in particular H$\alpha$. These objects are very similar to those described in Whitehouse et al. (2018), and we classify them as dwarf carbon stars (dC); they will not be discussed further in this study. Another 21 objects show Swan bands, but of a peculiar, rounded shape and usually blue-shifted. This shift is not really understood yet, but the discussions center on pressure shifts of the Swan bands in high density helium Hall & Maxwell (2008); Kowalski (2010). Since our models do not include this effect, we cannot determine accurate parameters for these peculiar DQ (DQpec), but will discuss their relevance for the spectral evolution of the DQ in Sect. 6. This leaves 254 objects for the analysis. Fig. 2 shows examples for all types discussed here: DQ, warm DQ, hot DQ, peculiar DQ, and dwarf carbon stars dC.

3 Theoretical models

We calculated theoretical atmosphere models using basically the methods described in Koester (2010). However, the code was completely rewritten, using the more modern FORTRAN95 language, which supports a much stronger modularization of the programs. We updated the equation of state (EOS) to use many more molecules, and include non-ideal effects for neutral and charged interactions consistently in EOS and secondary quantities as adiabatic derivatives, heat capacity, and the adiabatic gradient. The absorption coefficients include more negative ions than in previous versions of the code, and many photoionization cross sections.

For the current DQ models 12 molecular species of H and C were included, with 300 C2 bands, 211 cross sections from C i to C iv, and 713 spectral lines. We calculated two grids, the cool one with 5000 K $\leq$ $T_{\rm eff}$ $\leq$ 15000 K, step 250 K, 7.0 $\leq$ $\log g$ $\leq$ 9.5  dex, step 0.25, $-9.5$ $\leq$[C/He] $\leq-2.0$, step 0.5, altogether 7216 models. The second, hot grid had 9000 K$\leq$ $T_{\rm eff}$ $\leq$ 20000 K, step 250 K, and 20000 K $\leq$ $T_{\rm eff}$ $\leq$ 30000 K, step 1000 K, 7.0 $\leq$ $\log g$ $\leq$ 9.5 dex, step 0.25, $-4.0\leq$ [C/He] $\leq$ +4.0, step 0.5, resulting in 10285 models. The total model grids thus comprise 17501 models.

From the synthetic spectra we calculated theoretical photometry for the SDSS $ugriz$ filters and the Gaia $G$ filter by convolving with the filter bandpasses and applying appropriate zeropoints. We also converted these theoretical magnitudes to absolute magnitudes by using the Montreal mass-radius-relation111http://www.astro.umontreal.ca/~bergeron/CoolingModels, except for $\log g$ $>9.00$, where we used the zero-temperature relation for carbon from Hamada & Salpeter (1961). Since all objects in our sample have Gaia parallaxes, we can transform the distance in a distance modulus $m-M=5\log(\mathrm{distance/pc})-5$. The advantage is that the distance is expressed on a magnitude scale and can be used in the fitting in the same way as the other 6 magnitudes ($ugrizG$).

4 Analysis of photometric and spectroscopic data

The new parallaxes provide a very strong constraint on the radius or in our fitting method on the distance modulus $m-M$. With observed magnitude $m$ and $M$ from our theoretical grid this is an equally strong constraint of the surface gravity $\log g$. As this depends only on the average level of the observed photometry and not on the shape of the energy distribution, this is a much more robust determination than the usual spectroscopic method using spectral line profiles.

Our tests indicated that the most successful procedure is an iteration between spectroscopic and photometric fitting. For the cool and warm DQ ($T_{\rm eff}$ ¡ 18000 K) we used the photometry with fixed [C/He] to obtain $T_{\rm eff}$ and $\log g$; the spectroscopic fitting is used with fixed $T_{\rm eff}$ and $\log g$ and determines a new value for [C/He]. The iteration stops when the latter value does not change within the uncertainty. As a final consistency check we have done a last spectroscopy fitting with $\log g$ and [C/He] fixed, but $T_{\rm eff}$ freely variable. If this spectroscopic $T_{\rm eff}$ agreed with the photometric one, the procedure was stopped.

For the hot DQ (hDQ) we used the photometry only for $\log g$ and spectroscopy for $T_{\rm eff}$ and [C/He]. This worked better in the hotter temperature range, since the dependence of the photometry on temperature gets smaller in the optical Raleigh-Jeans range. The absence of He lines in the hot DQ indicates a [C/He] ¿ 1. Since the spectra do not change significantly with even higher ratios, we use a fixed [C/He]= 2 to obtain $T_{\rm eff}$ from spectroscopy and $\log g$ from photometry.

When using photometry for more distant objects, the interstellar reddening is always a concern. Fortunately for our objects the maximum reddening through the galactic disk, obtained from the SDSS database is always small, mostly in the range 0.04 $\leq$ E(B-V) $\leq$ 0.05, because the SDSS observations are by design mostly in a direction perpendicular to the plane of the Galaxy. We have taken a fraction of this value depending on the estimated distance, calculated as in Gentile Fusillo et al. (2019).

5 Results

The objects showing Swan bands were fitted with the low temperature grid, the others with the hot grid.

5.1 The classical DQ

Table 2 presents the results for the atmospheric parameters of the 221 DQ white dwarfs in the final sample. The range of temperatures and abundances agrees with previous studies of large samples like Dufour et al. (2005) and Koester & Knist (2006). With the exception of a figure in Coutu et al. (2018) this is, however, the first time that large numbers of surface gravities (or masses) are presented for these objects. There is one cool DQ identified in Coutu et al. (2018) which is also in our sample: SDSSJ1355+3636, with $T_{\rm eff}$ = 8040 K, $\log g$ = 7.91, [C/He] = $-5.04$. While the atmospheric parameters agree quite well with our solution in Table 2, the [C/He] ratio we obtain is $\approx 0.7$ dex higher.

The gravities of the cool DQ are comparable to those of other cool helium-dominated objects, as is demonstrated in Table 3. The DZ, DB, and DC objects were drawn from the samples in Kleinman et al. (2013); Kepler et al. (2015, 2016, 2019), but the parameters were redetermined for this study. A significant fraction of DB white dwarfs is known to contain traces of hydrogen (spectral type DBA), and Bergeron et al. (2019) have argued that using pure helium atmospheres for cool DC can lead to artificially higher masses. We have used different grids with [H/He] between $-3.0$ and $-6.0$ for the fitting. The results in the table were obtained with $-4.0$, which we have preferred because the resulting average masses are almost constant from 15000 K down to 6000 K. The DZ were fitted with [H/He]=$-4.5$, but in this case the effect of the hydrogen is not important, since the free electrons come from the metals.

The average masses between the three types of helium-rich objects are slightly different, with the DQ having the smallest masses and DZ and DC about 0.06 resp. 0.10 dex larger. Considering the extreme physical conditions in cool helium-rich atmospheres, the uncertainties of the amount of hydrogen present, and the uncertain reddening, we will not speculate on possible reasons for this difference but refer further discussion to future work.

5.2 The warm DQ (wDQ)

These objects are characterized by C i lines and occasionally at the cool end with weak C2 bands. Unfortunately there appear to be severe problems with the atomic data of these lines. Our main source was the Vienna Atomic Line Database (VALD, Kupka et al., 1999, 2000; Piskunov et al., 1995) 222http://vald.astro.univie.ac.at/~vald3/php/vald.php. Spectral fits with theoretical models agree reasonably in the red part of the spectrum $\lambda>4600$ Å. In the blue part, however, many lines are predicted much stronger than they appear in the observed spectrum. In the National Institute for Standards and Technology (NIST, Kramida et al., 2018) database333 https://www.nist.gov/pml/atomic-spectra-database are only two lines in this range with $\log\ gf$ values published, none with class A quality. The sources are Haris & Kramida (2017) and Luo & Pradhan (1989). In a literature search we found only very few data, but some indication that the VALD data can be quite wrong. Victor & Escalante (1988) give $\log\ gf$ values of $-2.143$ for the 4270.221 Å line, whereas the VALD value is $-1.637$, and NIST has $-1.5$. For the 4892.019 Å line the same source has $-3.602$, compared to $-1.541$ in VALD. We have replaced those and a few other lines from the same source, and arbitrarily scaled the values for several strong lines in the blue region to be compatible with the fit to the red part. This can be considered as an empirical $gf$ determination; the argument for this procedure is to make the theoretical photometry more reliable. For the spectral fitting we used only the region longward of 4600 Å.

As we determine $T_{\rm eff}$ and $\log g$ through the photometry, the results do not depend much on the [C/He] ratio. On the other hand, keeping $T_{\rm eff}$ and $\log g$ fixed when analyzing the spectra, the only remaining variable is the abundance ratio. The carbon is diluted in the helium, weakening the lines and leading to the abundance determination. As long as [C/He] $\leq-1.0$ this works well. However, at higher ratios the influence of helium weakens and the errors get much larger, up to 0.73 dex. In two cases (SDSSJ1448+0519, SDSSJ1728+5558) this lead to best fit models, which predicted strong He lines, that are not observed. We have determined individual lower limits of [C/He] and continued the iteration for $T_{\rm eff}$ and $\log g$ with these limits fixed. These objects are indicated with asterisks in Fig. 3

The results of this analysis are shown in Table 4 and Fig. 3. Apart from SDSSJ1448+0519 shown in Fig. 1, there is one other warm DQ in our sample also identified in Coutu et al. (2018), SDSSJ1215+4700 with $T_{\rm eff}$ = 12349 K, $\log g$ = 8.80, [C/He] = $-2.27$. Our temperature is 1600 K higher, the other parameters agree reasonably well.

Many of the wDQ show Balmer lines of hydrogen. We therefore had calculated the grid with trace hydrogen of [H/He] = $-4.5$, a typical value for DBs. Some objects, however, show even much stronger H$\alpha$ than in the best fitting model, one of the strongest being SDSSJ1622+3004. We determined the H abundance as [H/He ] = $-2.00$ and verified that this did not change the model spectrum except close to the Balmer lines. The fit results for the wDQ are therefore not affected. In a subsequent paper we will study the extent of the convection zones beyond the bottom of the atmospheres (all models in our grids are convective down to the bottom of the model) with envelope models. We will then also determine accurate hydrogen abundances to determine the total masses of H and He in the convection zone. This could help to understand the origin and evolution of DQ stars.

5.3 Hot DQ (hDQ)

We have arbitrarily identified the objects with $T_{\rm eff}$ $>18000$ K as hot DQs, since there is a continuous transition in the strength of C ii lines (e.g. 4621, 5146, 5891, 5893, 6153, 6463, 6579, 6584 Å) compared to C i lines. The complete absence of He lines in all hDQ translates in lower limits of [C/He] = 1.0 to 2.0, depending on the S/N of the spectrum. Since the fit results do not change with further increase of this ratio we have used a fixed value of [C/He] = 2.0 for the fit.

6 Discussion and conclusions

Detailed results of the analysis are presented in Tables 2, 4, and 5, but the main result is seen in Fig. 3. In the bottom panel, showing the abundances as function of temperature, the classical DQs form a very well defined dominant sequence from 9000 K, [C/He]=$-4.5$ down to 5000 K, [C/He]=$-7.0$. This agrees with previous findings in the literature, e.g. Pelletier et al. (1986); Dufour et al. (2005); Koester & Knist (2006). A number of objects are located in a range about 1.0-1.5 dex in abundance above this sequence, and there may be another sequence at the upper limit of this range, although the evidence is not too strong. Going to higher $T_{\rm eff}$, the upper sequence continues with the warm DQs up to 17000 K, [C/He] around 0.0. This is surprising since the warm DQs have been considered as helium-dominated like the classical DQ (e.g. Coutu et al., 2018). Among the hottest group is SDSSJ1448+0519 mentioned in the introduction and shown in Fig. 1, which clearly cannot have as much helium as found in Coutu et al. (2018). This group seems to be a transition to the hot DQ, which are clearly carbon dominated, although the helium content cannot be determined from the available spectra; the squares in the figure are approximate lower limits for carbon.

Taking this bottom panel at face value, this would argue for a continuous transition of very carbon-rich spectra to ever lower C abundances with decreasing temperature. It is tempting to identify this with some convection zones changing in depth with changes of $T_{\rm eff}$  but there are contradictions to our current understanding of He layer convection, which shows a maximum depth around 10000 K (Fontaine & Brassard, 2005).

Even more puzzling is the top panel of Fig. 3. While the cool DQ seem to have normal surface gravities around 8.0 and thus normal masses, this is clearly not true for warm and hot DQ. The current assumption was that the warm DQ have about the same masses as the cool ones, but we find instead a sequence increasing from $\log g$ $\geq$ 8.5 to 9.1 with $T_{\rm eff}$ from 10000 to 18000 K, whereas the hot DQ have only $\log g$ $\approx$ 8.5-8.7. The high $\log g$ values for the range 13000-17000 K are the most puzzling result of our study. Considering the problems with the atomic data for C i discussed above, one might question the validity of our analysis. As a test we have used the spectra also for the temperature determination and the photometry only for the surface gravity, as in the hot DQ. There are small differences in the parameters obtained, but the general picture with the high $\log g$ around 15000 K remains.

We note that the $\log g$ determination via photometry and parallax is very robust: assuming that the correct temperature for a 15000 K determination were 13000 K, i.e. an error of 2000 K, the surface gravity would only go down from 9.0 to 8.83, still significantly higher than at higher and lower $T_{\rm eff}$. One might argue that the mass-radius relation used – for He atmosphere white dwarfs – is not appropriate, when [C/He] $\approx$0.0. However, at 15000 K, $\log g$ = 9.0 the radius changes very little between helium atmosphere (0.00571 R*⊙), hydrogen atmosphere (0.00573 R⊙), or even the zero-temperature Hamada-Salpeter radius (0.00570 R⊙* for carbon, Hamada & Salpeter (1961))

The problems with the C i atomic data, some differences between our results and Coutu et al. (2018) and the unexpected surface gravities for the warm DQ indicate that improvements to the model calculations may still be necessary. In spite of these remaining uncertainties it is clear that there are two separate groups of carbon white dwarfs. The classical DQ can be understood as dredge-up of the helium convection zone from the tail of the C/He transition layer (Koester et al., 1982; Pelletier et al., 1986); the decrease of the carbon abundance with decreasing temperature is a result of the depth of the convection zone decreasing again below the maximum near 10000 K, as predicted by model calculations (Fontaine & Brassard, 2005). If the high masses of warm and hot DQ (which together may form the second group) are confirmed, they cannot be the progenitors of the cool DQs. There are only two cool DQ with $\log g$ $>$ 8.50. This number seems too small because of the slowing down of the evolution at low temperatures; a final conclusion, however, would need a population synthesis taking into account the accurate evolution including crystallization and Debye cooling, as well as the observational detection biases in the SDSS.

Because our models do not adequately describe the spectra of the peculiar DQ, we cannot determine reliable temperatures for them. The presence of strong Swan bands indicates a range from 10000-5000 K. We have therefore used a fixed temperature of 7500 K, [C/He] = $-5.00$ and used the photometry to estimate the surface gravities. If the real $T_{\rm eff}$ is higher, the real $\log g$ will be higher than our result, and vice versa for lower real $T_{\rm eff}$. This indicates that the average result could be a reasonable indicator of the typical gravities of the DQpec. This average for the 21 DQpec in the sample is 8.625, with a distribution width of 0.298. This value is shown as a large circle in Fig.3, confirming the possible identification of the DQpec as descendants of the hot and warm classes. The position close to the two cool DQ with higher gravity suggests that the two objects may in fact belong to the DQpec class.

The high gravity also supports the idea that the unusual shape and shift of the molecular Swan bands is indeed due to the high He densities in these massive white dwarfs (Kowalski, 2010). We do not yet know the C/He ratio for these stars, but a comparison of band strengths with those in normal DQs indicates helium-dominated atmospheres with slightly larger [C/He] values as in the DQ.

Another open question is how the hot DBs with small traces of carbon visible only in the ultraviolet (Fontaine & Brassard, 2005; Koester et al., 2014) are related to the two groups. Except for one object in the latter study accretion as origin of the carbon is considered highly unlikely, either because no other metals are observed, or because the inferred C/Si ratio in the accreted matter is extremely large. This is quite different from what is observed in accreting DAZ and DBZ in the same temperature range (Koester et al., 2014), leaving dredge-up of the carbon as plausible explanation. Since they do not share the very high masses with the hot DQ they could be related to the classical cool DQ.

In a subsequent paper we will study the evolution of the convection zones in mixed H/He/C envelopes and the total amount of hydrogen and helium present in them. Hopefully that can shed some light on the origin and evolution of these puzzling stars.

Acknowledgements.

We thank Patrick Dufour and Simon Coutu for sharing with us a poster presented at the EUROWD-21 workshop in Austin 2018. We have used their results in the belief that they are public. Only very recently we realized that this paper is not available in the public archive of the conference. We acknowledge that Coutu et al. (2018) was the first paper to determine carbon abundances for DQ using Gaia data. Our current study was motivated by their results. This work was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES)

• Finance Code 001, Conselho Nacional de Desenvolvimento Científico e Tecnológico - Brasil (CNPq), and Fundação de Amparo à Pesquisa do Rio Grande do Sul (FAPERGS) - Brasil. This research has made use of NASA’s Astrophysics Data System Bibliographic Services, SIMBAD database, operated at CDS, Strasbourg, France, the NIST and VALD atomic databases, and public data from the Sloan Digital Sky Survey and the Gaia Mission.

Appendix A Full tables of objects and results

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