Faint solar analogs: at the limit of no reddening

TL;DR

This study develops a method to identify faint solar analogs with high precision, accounting for reddening effects, to improve the spectral modeling of Solar System bodies.

Contribution

The paper introduces a spectroscopic methodology for selecting faint solar analogs at the limit of current survey capabilities, including a calibration of atmospheric parameters and reddening effects.

Findings

Identified five solar analogs around V=10.5 mag at 135 pc.

Achieved high precision in atmospheric parameters: 97 K in temperature, 0.06 dex in metallicity.

Found that reddening can significantly affect temperature estimates, with some stars showing E(B-V) ≥ 0.06 mag.

Abstract

The flux distribution of solar analogs is required for calculating the spectral albedo of Solar System bodies such as asteroids and trans-Neptunian objects. Ideally a solar analog should be comparably faint as the target of interest, but only few analogs fainter than V = 9 were identified so far. Only atmospheric parameters equal to solar guarantee a flux distribution equal to solar as well, while only photometric colors equal to solar do not. Reddening is also a factor to consider when selecting faint analog candidates. We implement the methodology for identifying faint analogs at the limit of precision allowed by current spectroscopic surveys. We quantify the precision attainable for the atmospheric parameters effective temperature ($T_{eff}$), metallicity ([Fe/H]), surface gravity (log $g$) when derived from moderate low resolution (R=8000) spectra with S/N $\sim 100$. We calibrated $T_{eff}$ and [Fe/H] as functions of equivalent widths of spectral indices by means of the PCA regression. We derive log $g$, mass, radius, and age from the atmospheric parameters, Gaia parallaxes and evolutionary tracks. We obtained $T_{eff}$/[Fe/H]/log $g$ with precision of 97 K/0.06 dex/0.05 dex. We identify five solar analogs with $V\sim10.5$ (located at $\sim135$ pc): HIP 991, HIP 5811, HIP 69477, HIP 55619 and HIP 61835. Other six stars have $T_{eff}$ close to solar but slightly lower [Fe/H]. Our analogs show no evidence of reddening but for four stars, which present $E(B-V) \geq 0.06$ mag, translating to at least a 200 K decrease in photometric $T_{eff}$.

Tables

Table 1. Table 1: Photometric and astrometric data of the candidates. Stars for which no S/N is given in column 11 were photometrically selected but not spectroscopically observed. The first column lists the Hipparcos number. Columns 2 and 3 display the coordinates, right ascension and declination. Columns 4 and 5 list B − V 𝐵 𝑉 B-V in Johnson and Tycho systems. Columns 6 to 9 list the magnitudes in the indicated photometric bands. V 𝑉 V was extracted from the Hipparcos catalog to which we associated the error of the same band in the Tycho system. Column 10 lists parallaxes from Gaia DR2 (Gaia Collaboration et al. 2018 ) . Column 11 lists the S / N 𝑆 𝑁 S/N of the acquired spectra.

HIP	$RA$	$DEC$	$\left(B-V\right)$	${\left(B-V\right)}^{Ty}$	$V$	$J$	$H$	$K_s$	parallax (mas)	$S/N$
991	$00:12:18$	$-40:38:44$	$0.600\pm 0.061$	$0.647\pm 0.070$	$10.58\pm 0.047$	$9.476\pm 0.026$	$9.136\pm 0.026$	$9.067\pm 0.024$	$7.0441\pm 0.0326$	108
5811	$01:14:33$	$-49:54:12$	$0.700\pm 0.004$	$0.767\pm 0.090$	$10.62\pm 0.055$	$9.458\pm 0.032$	$9.106\pm 0.033$	$9.077\pm 0.033$	$7.5506\pm 0.0271$	112
6089	$01:18:11$	$-27:36:17$	$0.661\pm 0.015$	$0.647\pm 0.094$	$10.55\pm 0.061$	$9.353\pm 0.030$	$8.990\pm 0.076$	$8.912\pm 0.019$	$8.7481\pm 0.0412$	126
8853	$01:53:51$	$-23:29:52$	$0.530\pm 0.020$	$0.563\pm 0.083$	$10.63\pm 0.058$	$9.672\pm 0.024$	$9.408\pm 0.022$	$9.404\pm 0.023$	$5.2837\pm 0.0386$	90
10663	$02:17:13$	$-24:23:56$	$0.570\pm 0.020$	$0.522\pm 0.100$	$10.62\pm 0.072$	$9.615\pm 0.023$	$9.379\pm 0.022$	$9.289\pm 0.021$	$3.6740\pm 0.0386$	121
13964	$02:59:49$	$-11:20:42$	$0.556\pm 0.015$	$0.548\pm 0.093$	$10.53\pm 0.065$	$9.457\pm 0.023$	$9.058\pm 0.022$	$8.967\pm 0.020$	$9.0105\pm 0.0560$	210
18941	$04:03:36$	$-36:10:40$	$0.590\pm 0.020$	$0.564\pm 0.078$	$10.52\pm 0.055$	$9.376\pm 0.027$	$9.093\pm 0.024$	$9.005\pm 0.021$	$7.0380\pm 0.0221$	114
24742	$05:18:19$	$-48:52:12$	$0.529\pm 0.032$	$0.518\pm 0.091$	$10.67\pm 0.063$	$9.514\pm 0.029$	$9.167\pm 0.022$	$9.095\pm 0.021$	$7.1532\pm 0.0184$	103
29100∗	$06:08:17$	$-30:40:05$	$0.611\pm 0.003$	$0.657\pm 0.081$	$10.56\pm 0.053$	$9.429\pm 0.022$	$9.092\pm 0.022$	$9.054\pm 0.019$	$7.8400\pm 0.2100$	134
31845	$06:39:30$	$-31:25:50$	$0.626\pm 0.015$	$0.777\pm 0.086$	$10.51\pm 0.052$	$9.191\pm 0.023$	$8.832\pm 0.044$	$8.789\pm 0.024$	$9.0866\pm 0.0241$	112
48272	$09:50:29$	$-04:57:37$	$0.536\pm 0.003$	$0.595\pm 0.107$	$10.51\pm 0.072$	$9.387\pm 0.023$	$9.096\pm 0.023$	$8.997\pm 0.020$	$7.3291\pm 0.0359$	92
55619	$11:23:43$	$-25:06:30$	$0.667\pm 0.004$	$0.762\pm 0.092$	$10.55\pm 0.058$	$9.344\pm 0.027$	$8.937\pm 0.026$	$8.884\pm 0.021$	$7.6182\pm 0.0409$	121
56870	$11:39:34$	$-14:04:34$	$0.645\pm 0.003$	$0.872\pm 0.095$	$10.53\pm 0.055$	$9.260\pm 0.024$	$8.931\pm 0.023$	$8.839\pm 0.024$	$9.2905\pm 0.0356$	122
61835	$12:40:17$	$+27:46:34$	$0.588\pm 0.015$	$0.527\pm 0.103$	$10.80\pm 0.073$	$9.719\pm 0.023$	$9.427\pm 0.027$	$9.373\pm 0.022$	$5.5279\pm 0.0527$	143
67692	$13:51:59$	$+26:38:11$	$0.750\pm 0.015$	$0.906\pm 0.102$	$10.94\pm 0.060$	$9.587\pm 0.022$	$9.204\pm 0.019$	$9.139\pm 0.022$	$3.4312\pm 0.0612$	92
69232	$14:10:27$	$-13:56:04$	$0.605\pm 0.025$	$0.647\pm 0.107$	$10.67\pm 0.071$	$9.404\pm 0.023$	$9.055\pm 0.022$	$8.961\pm 0.024$	$7.1930\pm 0.0500$	81
69477	$14:13:25$	$+23:54:03$	$0.562\pm 0.066$	$0.603\pm 0.075$	$10.53\pm 0.052$	$9.307\pm 0.019$	$9.010\pm 0.021$	$8.960\pm 0.024$	$8.2887\pm 0.0321$	114
73234	$14:58:03$	$+09:24:03$	$0.680\pm 0.061$	$0.743\pm 0.077$	$10.59\pm 0.050$	$9.448\pm 0.023$	$9.143\pm 0.023$	$9.078\pm 0.023$	$5.3550\pm 0.0761$	87
75685	$15:27:42$	$-02:45:18$	$0.730\pm 0.015$	$0.872\pm 0.099$	$10.51\pm 0.060$	$9.186\pm 0.024$	$8.870\pm 0.042$	$8.810\pm 0.024$	$6.3801\pm 0.0337$	72
107605	$21:47:41$	$-41:51:17$	$0.640\pm 0.020$	$0.664\pm 0.090$	$10.60\pm 0.060$	$9.498\pm 0.022$	$9.243\pm 0.027$	$9.180\pm 0.021$	$6.4888\pm 0.0456$	170
111826	$22:39:01$	$+32:18:03$	$0.762\pm 0.065$	$0.850\pm 0.086$	$10.53\pm 0.053$	$9.216\pm 0.027$	$8.817\pm 0.026$	$8.796\pm 8.786$	$8.4807\pm 0.0326$	125
13052	$02:47:45$	$+80:15:54$	0.784 $\pm$ 0.062	0.899 $\pm$ 0.080	10.53 $\pm$ 0.047	9.155 $\pm$ 0.022	8.811 $\pm$ 0.029	8.711 $\pm$ 0.025	11.1187 $\pm$ 0.0436	—
16294	$03:30:03$	$+51:30:43$	0.520 $\pm$ 0.020	0.729 $\pm$ 0.086	10.56 $\pm$ 0.054	9.337 $\pm$ 0.020	9.119 $\pm$ 0.026	9.053 $\pm$ 0.020	5.4415 $\pm$ 0.0526	—
17514	$03:45:00$	$-38:51:33$	0.598 $\pm$ 0.015	0.782 $\pm$ 0.010	10.64 $\pm$ 0.063	9.447 $\pm$ 0.021	9.111 $\pm$ 0.024	9.017 $\pm$ 0.023	7.6114 $\pm$ 0.0324	—
46072	$09:23:41$	$+65:48:31$	0.675 $\pm$ 0.044	0.737 $\pm$ 0.055	10.53 $\pm$ 0.035	9.329 $\pm$ 0.020	9.062 $\pm$ 0.017	8.979 $\pm$ 0.016	7.0718 $\pm$ 0.0272	—
53442	$10:55:58$	$+29:19:13$	0.552 $\pm$ 0.067	0.592 $\pm$ 0.076	10.51 $\pm$ 0.051	9.362 $\pm$ 0.021	9.041 $\pm$ 0.016	8.955 $\pm$ 0.018	7.5127 $\pm$ 0.0845	—
53990	$11:02:39$	$-32:44:17$	0.550 $\pm$ 0.020	0.732 $\pm$ 0.090	10.67 $\pm$ 0.057	9.553 $\pm$ 0.024	9.336 $\pm$ 0.024	9.229 $\pm$ 0.021	5.3337 $\pm$ 0.0431	—
55229	$11:18:36$	$+50:44:55$	0.688 $\pm$ 0.062	0.753 $\pm$ 0.078	10.76 $\pm$ 0.048	9.580 $\pm$ 0.022	9.269 $\pm$ 0.028	9.235 $\pm$ 0.023	4.4272 $\pm$ 0.0394	—
55809	$11:26:11$	$+53:32:39$	0.654 $\pm$ 0.049	0.729 $\pm$ 0.065	10.50 $\pm$ 0.042	9.257 $\pm$ 0.019	9.001 $\pm$ 0.031	8.852 $\pm$ 0.022	5.3923 $\pm$ 0.0330	—
59223	$12:08:47$	$+30:56:33$	0.542 $\pm$ 0.065	0.580 $\pm$ 0.074	10.51 $\pm$ 0.051	9.464 $\pm$ 0.022	9.220 $\pm$ 0.021	9.162 $\pm$ 0.017	6.2389 $\pm$ 0.0398	—
59369	$12:10:49$	$+32:44:54$	0.573 $\pm$ 0.067	0.615 $\pm$ 0.076	10.58 $\pm$ 0.051	9.523 $\pm$ 0.027	9.174 $\pm$ 0.028	9.191 $\pm$ 0.019	5.5150 $\pm$ 0.0364	—
60523	$12:24:25$	$+53:26:54$	0.680 $\pm$ 0.055	0.743 $\pm$ 0.069	10.77 $\pm$ 0.043	9.650 $\pm$ 0.027	9.356 $\pm$ 0.026	9.261 $\pm$ 0.018	6.3396 $\pm$ 0.0294	—
61957	$12:41:51$	$+26:49:47$	0.585 $\pm$ 0.015	0.511 $\pm$ 0.075	10.54 $\pm$ 0.052	9.540 $\pm$ 0.023	9.264 $\pm$ 0.021	9.220 $\pm$ 0.020	4.4171 $\pm$ 0.1482	—
63588	$13:01:51$	$+27:20:15$	0.594 $\pm$ 0.015	0.802 $\pm$ 0.112	10.70 $\pm$ 0.069	9.525 $\pm$ 0.026	9.271 $\pm$ 0.034	9.131 $\pm$ 0.020	6.0707 $\pm$ 0.0460	—
67215	$13:46:26$	$+82:31:46$	0.695 $\pm$ 0.065	0.783 $\pm$ 0.086	10.52 $\pm$ 0.054	9.474 $\pm$ 0.020	9.222 $\pm$ 0.017	9.157 $\pm$ 0.017	6.2334 $\pm$ 0.0259	—
69554	$14:14:14$	$+38:19:58$	0.723 $\pm$ 0.066	0.819 $\pm$ 0.087	10.79 $\pm$ 0.053	9.568 $\pm$ 0.020	9.256 $\pm$ 0.016	9.209 $\pm$ 0.016	7.2600 $\pm$ 0.0256	—
73854	$15:05:37$	$+45:23:49$	0.724 $\pm$ 0.064	0.800 $\pm$ 0.083	10.53 $\pm$ 0.052	9.435 $\pm$ 0.021	9.164 $\pm$ 0.019	9.098 $\pm$ 0.020	7.3037 $\pm$ 0.0241	—
74061	$15:08:09$	$+39:58:12$	0.633 $\pm$ 0.064	0.700 $\pm$ 0.085	10.58 $\pm$ 0.055	9.462 $\pm$ 0.021	9.098 $\pm$ 0.021	9.008 $\pm$ 0.014	5.3679 $\pm$ 0.0723	—
76272	$15:34:45$	$+62:16:44$	0.592 $\pm$ 0.065	0.637 $\pm$ 0.075	10.52 $\pm$ 0.051	9.684 $\pm$ 0.021	9.315 $\pm$ 0.017	9.216 $\pm$ 0.020	6.2103 $\pm$ 0.0269	—
102416	$20:45:13$	$+60:19:35$	0.642 $\pm$ 0.064	0.712 $\pm$ 0.085	10.52 $\pm$ 0.055	9.341 $\pm$ 0.023	9.027 $\pm$ 0.031	8.970 $\pm$ 0.019	7.8116 $\pm$ 0.0293	—
110560	$22:23:49$	$+24:23:34$	0.573 $\pm$ 0.016	0.773 $\pm$ 0.097	10.64 $\pm$ 0.059	9.440$\pm$ 0.022	9.172 $\pm$ 0.021	9.106 $\pm$ 0.018	5.0932 $\pm$ 0.0383	—
*The parallax of this candidate was extracted from the Gaia DR1 catalog (Gaia Collaboration et al. 2016a, b).

Table 2. Table 2: Fundamental parameters of the observed faint solar analog candidates. The first column lists the Hipparcos number. The three faint solar analogs with atmospheric parameters compatible with those of the Sun within 1 σ 𝜎 \sigma errors are highlighted in large bold numbers, and the other three within 2 σ 𝜎 \sigma errors in small bold numbers. The brackets indicate stars with suspected significant reddening values: the latter are listed in Table  3 . Column 2 gives the best T eff subscript 𝑇 eff T_{\mathrm{eff}}  obtained by the weighted average of the values in columns 3 and 4. Column 3 displays T eff P ​ C ​ A superscript subscript 𝑇 eff 𝑃 𝐶 𝐴 T_{\mathrm{eff}}^{PCA}  corrected by the equation given in Sect.  5.3 . Column 4 displays T eff phot superscript subscript 𝑇 eff phot T_{\text{eff}}^{\text{phot}}  from the photometric calibrations of Casagrande et al. ( 2010 ) and the colors in Table  1 Columns 5 to the last are self-explanatory. Three candidates listed in table 1 but for which we could not derive atmospheric parameters from PCA because their values lie outside the valid range of our calibrations are not listed here: they are HIP 13964, HIP 24742 and HIP 69232.

HIP	best $T_{\mathrm{eff}}$	$T_{\mathrm{eff}}^{PCA}$ $\pm 97$	$T_{\text{eff}}^{\text{phot}}$	[Fe/H] $\pm 0.06$	log g	Mass	Radius	Age
	(K)	(K)	(K)	(dex)	(dex)	(M☉)	(R☉)	(Gyr)
991	$5829\pm 85$	5750	$5875\pm 74$	$-0.05$	$4.38\pm 0.06$	$0.99\pm 0.05$	$1.07\pm 0.05$	$6.2\pm 2.7$
5811	$5653\pm 67$	5600	$5696\pm 88$	$+0.02$	$4.39\pm 0.05$	$0.96\pm 0.05$	$1.04\pm 0.04$	$7.9\pm 2.6$
6089	$5684\pm 20$	5669	$5698\pm 95$	$-0.23$	$4.46\pm 0.04$	$0.90\pm 0.04$	$0.93\pm 0.03$	$6.9\pm 1.5$
8853	$6160\pm 50$	6121	$6192\pm 87$	$-0.17$	$4.32\pm 0.04$	$1.09\pm 0.05$	$1.20\pm 0.04$	$4.10\pm 1.0$
10663	$6125\pm 26$	6140	$6102\pm 120$	$-0.07$	$4.05\pm 0.03$	$1.24\pm 0.05$	$1.74\pm 0.04$	$4.4\pm 0.6$
18941	$5955\pm 90$	6015	$5887\pm 103$	$-0.29$	$4.39\pm 0.07$	$0.96\pm 0.06$	$1.04\pm 0.04$	$6.4\pm 2.9$
$[$29100$]$	$T_{\mathrm{eff}}^{PCA}$	6022	$5824\pm 46$	$-0.33$	$4.49\pm 0.05$	$0.95\pm 0.05$	$0.92\pm 0.04$	$3.3\pm 2.3$
31845	$5705\pm 132$	5785	$5596\pm 113$	$-0.29$	$4.47\pm 0.06$	$0.89\pm 0.05$	$0.91\pm 0.04$	$7.2\pm 4.2$
48272	$5941\pm 14$	5930	$5950\pm 92$	$-0.36$	$4.40\pm 0.04$	$0.93\pm 0.05$	$1.01\pm 0.04$	$6.8\pm 0.9$
55619	$5686\pm 69$	5758	$5653\pm 65$	$-0.02$	$4.37\pm 0.05$	$0.96\pm 0.05$	$1.06\pm 0.04$	$8.0\pm 2.6$
56870	$5687\pm 108$	5753	$5599\pm 112$	$-0.28$	$4.49\pm 0.05$	$0.89\pm 0.05$	$0.89\pm 0.04$	$6.4\pm 4.0$
61835	$5895\pm 88$	5848	$5979\pm 132$	$-0.07$	$4.30\pm 0.05$	$1.02\pm 0.04$	$1.19\pm 0.05$	$7.1\pm 2.4$
67692*	—	—	$5427\pm 37$	$-0.04$	$3.83\pm 0.04$	$1.23\pm 0.04$	$2.25\pm 0.06$	$5.2\pm 0.4$
69477	$5744\pm 49$	5726	$5812\pm 193$	$+0.02$	$4.46\pm 0.05$	$0.99\pm 0.05$	$0.98\pm 0.04$	$4.1\pm 2.7$
$[$73234$]$	$T_{\mathrm{eff}}^{PCA}$	5979	$5775\pm 101$	$-0.17$	$4.28\pm 0.13$	$1.04\pm 0.06$	$1.22\pm 0.16$	$5.8\pm 2.0$
$[$75685$]$	$T_{\mathrm{eff}}^{PCA}$	6163	$5515\pm 44$	$-0.02$	$4.40\pm 0.04$	$1.10\pm 0.04$	$1.10\pm 0.04$	$2.1\pm 1.5$
107605	$5835\pm 45$	5809	$5874\pm 120$	$-0.20$	$4.30\pm 0.03$	$0.95\pm 0.04$	$1.14\pm 0.04$	$0.95\pm 1.8$
$[$111826$]$	$T_{\mathrm{eff}}^{PCA}$	5655	$5474\pm 47$	$+0.09$	$4.45\pm 0.06$	$0.98\pm 0.05$	$0.98\pm 0.04$	$5.0\pm 3.1$
*$T_{\text{eff}}^{\text{phot}}$ and $T_{\mathrm{eff}}$ from H$\alpha$ agree for this candidate. These values are out of the PCA applicability range, and $T_{\mathrm{eff}}^{PCA}$  was found to be significantly
hotter than $T_{\text{eff}}^{\text{phot}}$and $T_{\mathrm{eff}}$ from H$\alpha$. No reddening was estimated for this candidate and we consider its atmospheric parameters as unreliable.

Table 3. Table 3: Color excess values E ​ ( B − V ) 𝐸 𝐵 𝑉 E(B-V) of candidates with significant T eff phot superscript subscript 𝑇 eff phot T_{\text{eff}}^{\text{phot}}  underestimations, compared with predictions from the SFD, SFD-B, and A&L models plus our own estimate in column 4. The last column gives the T eff phot superscript subscript 𝑇 eff phot T_{\text{eff}}^{\text{phot}}  underestimation with respect to T eff P ​ C ​ A superscript subscript 𝑇 eff 𝑃 𝐶 𝐴 T_{\mathrm{eff}}^{PCA}  implicated by the values in column 4.

HIP	SFD	SFD-B	A&L	this work	$\Delta$$T_{\mathrm{eff}}$ (K)
29100	0.0426	0.0136	0.0104	$0.058\pm 0.042$	198
73234	0.0244	0.0244	0.0206	$0.062\pm 0.061$	204
75685	0.1647	0.0963	0.0221	$0.203\pm 0.043$	648
111826	0.0290	0.0290	0.0104	$0.063\pm 0.051$	182

Table 4. Table 4: Atmospheric parameters of the calibration stars. The first column lists the HD number, except for the last star. Columns 2, 3, and 4 are the atmospheric parameters, followed by column 5, with the literature source coded by number: 1 Ghezzi et al. ( 2010a , b ) , 2 Porto de Mello et al. ( 2014 ) , 3 da Silva et al. ( 2012 ) , 4 da Silva et al. ( 2011 ) , 5 da Silva & Porto de Mello ( 2000 ) , 6 Bensby et al. ( 2003 ) , 7 Luck & Heiter ( 2006 ) , 8 Lyra & Porto de Mello ( 2005 ) . The last column gives the S / N 𝑆 𝑁 S/N — both values are presented in case of two observations for one star.

HD	$T_{\mathrm{eff}}$ (K)	[Fe/H]	$\log g$	Author	$S/N$
1461	5717	0.17	4.33	1	155
1581	5908	$-0.20$	4.26	1	166
2151	5866	$-0.11$	4.00	1	324
4391	5829	$-0.08$	4.45	8	201
7570	6196	0.24	4.41	1	297
8291	5835	0.03	4.30	2	141
9562	5794	0.16	3.95	1	217
9986	5820	0.09	4.48	2	297
10647	6155	$-0.06$	4.44	1	223
10700	5321	$-0.56$	4.46	1	471
12264	5810	0.06	4.54	2	194
16417	5788	0.14	4.05	1	272
17051	6239	0.16	4.55	1	269
19994	6081	0.08	4.07	1	192
20010	6280	$-0.02$	4.26	7	368
20029	6184	0.07	4.31	1	224, 170
20630	5723	0.09	4.36	1	274
30495	5740	0.09	4.36	5	237
30562	5986	0.27	4.30	5	424
34721	5957	$-0.10$	4.21	5	177, 252
36553	6022	0.27	3.73	5	498
39091	6037	0.08	4.42	1	207
39587	6029	$-0.01$	4.62	1	426
43587	5950	0.01	4.36	5	109
43947	5889	$-0.27$	4.32	1	117
52298	6253	$-0.31$	4.41	1	204
65907	6027	$-0.31$	4.57	1	320
98649	5775	$-0.02$	4.44	2	151
105901	5845	$-0.01$	4.54	2	117
112164	6014	0.32	4.05	3	131, 228
115382	5775	$-0.08$	4.40	2	106
117939	5608	$-0.26$	4.19	1	230
118598	5755	0.02	4.44	2	169
131117	5904	0.10	3.96	1	135, 184
134060	5904	0.10	4.25	1	149
138573	5750	0.00	4.41	2	294
146233	5795	$-0.03$	4.42	2	313, 310
147584	6090	$-0.06$	4.45	6	332
150248	5687	$-0.11$	4.30	1	486, 134
156274	5242	$-0.37$	4.40	1	163
157089	5785	$-0.47$	4.09	1	182
159656	5845	0.09	4.32	2	357
160691	5695	0.23	4.02	1	263
162396	6026	$-0.37$	4.08	1	39
164595	5790	$-0.04$	4.44	2	147
172051	5502	$-0.16$	4.43	5	496
182572	5569	0.40	4.10	4	449
187237	5850	0.16	4.48	2	284
189567	5656	$-0.26$	4.20	1	431
190248	5691	0.39	4.26	1	273
193307	6018	$-0.34$	4.18	1	341
196378	5996	$-0.44$	3.92	1	409
196755	5639	0.04	3.70	1	243
199288	5724	$-0.60$	4.55	1	227
199960	5940	0.27	4.26	7	326
203608	6022	$-0.67$	4.31	1	214
205420	6255	0.00	3.89	1	450, 171
206395	6305	0.23	4.38	1	256, 269
206860	6106	$-0.04$	4.68	4	247
207043	5775	0.07	4.55	2	276
210918	5721	$-0.09$	4.27	1	161
211415	5753	$-0.25$	4.27	5	202
212330	5670	$-0.02$	3.91	1	279, 232
215648	6178	$-0.027$	3.97	1	451, 301
216436	5755	0.04	3.94	2	70
221287	6241	$-0.02$	4.37	1	236
221343	5755	0.04	4.05	2	177
222368	6200	$-0.02$	4.13	1	810
BD+15 3364	5785	0.07	4.44	2	175

Equations

$$\begin{array}[]{lp{0.5\linewidth}}<\sigma(B-V)>&= 0.07\\ <\sigma(B-V)^{Ty}>&= 0.12\\ <\sigma(M_{V})>&= 0.80\\ <\sigma(M_{V})^{Ty}>&= 0.80\\ \end{array}$$

$$\begin{array}[]{lp{0.5\linewidth}}<\sigma(B-V)>&= 0.067\\ <\sigma(B-V)^{Ty}>&= 0.112\\ <\sigma(M_{V})>&= 0.609\\ <\sigma(M_{V})^{Ty}>&= 0.682\\ \end{array}$$

$$\begin{array}{rl}EW\text{leavevmode}(\text{mA˚})& =c_0+c_1\text{[Fe/H]}+c_2{T}_{\text{eff}}+c_3\log g\text{leavevmode}+\\ & +c_4\text{[Fe/H]}{T}_{\text{eff}}+c_5\text{[Fe/H]}\log g+c_6{T}_{\text{eff}}\log g\text{leavevmode}+\\ & +c_7(\text{[Fe/H]}{)}^2+c_8(T_{\text{eff}}{)}^2+c_9(\log g{)}^2\end{array}$$

$$Variable=\frac{Variable-⟨Variable⟩}{\sigma (Variable)},$$

$$\begin{array}{rl}{T}_{\text{eff}}& =5913(\pm 12)+18(\pm 3)PC1-124(\pm 9)PC2\\ & -7(\pm 3)(PC1\times PC2)\end{array}$$

$$\begin{array}{rl}[\text{Fe/H}]& =-0.01(\pm 0.01)-0.039(\pm 0.0)PC1\\ & -0.042(\pm 0.0)PC2\end{array}$$

$$\begin{array}{rl}\log g& =4.30(\pm 0.03)-0.0(\pm 0.01)PC1+0.06(\pm 0.02)PC2\\ & -0.01(\pm 0.01)(PC1\times PC2)\end{array}$$

Full text

*Aims. *We aim at implementing the methodology for identifying faint analogs at the limit of precision allowed by current spectroscopic surveys. We quantify the precision attainable for the atmospheric parameters effective temperature ($T_{\mathrm{eff}}$), metallicity ([Fe/H]), surface gravity (log g) when derived from moderate low resolution ($R=8000$) spectra with $S/N\sim 100$. We estimate the significance of reddening at 100-300 pc from the Sun.

*Methods. *We used the less precise photometry in the Hipparcos catalog to select potential analogs with $V\sim 10.5$ (located at $\sim 135$ pc). We calibrated $T_{\mathrm{eff}}$ and [Fe/H] as functions of equivalent widths of spectral indices by means of the Principal Component Analysis (PCA) regression. We derive log g, mass, radius, and age from the atmospheric parameters, Gaia parallaxes and evolutionary tracks. We evaluated the presence of reddening for the candidates by underestimations of photometric $T_{\mathrm{eff}}$ with respect to those derived by spectral indices. These determinations are validated with extinction maps.

*Results. *We obtained atmospheric parameters $T_{\mathrm{eff}}$/[Fe/H]/log g with precision of 97 K/0.06 dex/0.05 dex. From 21 candidates analysed, we identify five solar analogs: HIP 991, HIP 5811, and HIP 69477 have solar parameters within 1$\sigma$ errors, and HIP 55619 and HIP 61835 within 2$\sigma$ errors. Other six stars have $T_{\mathrm{eff}}$ close to solar but slightly lower [Fe/H]. Our analogs show no evidence of reddening but for four stars, which present $E(B-V)\geq 0.06$ mag, translating to at least a 200 K decrease in photometric $T_{\mathrm{eff}}$.

1 Introduction

The Sun remains the primary and most fundamental reference object in stellar astrophysics, being the golden standard for a variety of physical and chemical properties and still the sole star for which we access both extensively and accurately important fundamental parameters (Porto de Mello et al. 2014; Ramírez et al. 2009; Meléndez et al. 2006; Cayrel de Strobel 1996). On the one hand, the search for stars identical to the Sun in their physical properties, the so called solar twins, did provide an interesting contextualization of the properties of the “Sun as a star”. For example, concerning its age, chromospheric activity, and detailed chemical abundance (Meléndez et al. 2014; Li et al. 2012; Do Nascimento et al. 2009; Porto de Mello & da Silva 1997) among other quantities. On the other hand, a very relevant motivation to find and characterize stars that reproduce the solar spectrophotometric properties, something that solar twins are naturally expected to do, is the need to know reliable reference stars, observable at night under the same conditions as other targets of interest (Soubiran & Triaud 2004; Porto de Mello et al. 2014). Hence the need to look for solar analogs, stars that closely reproduce the solar flux distribution, and may thus act as solar surrogates in the night sky.

According to the traditional definition of Cayrel de Strobel (1996), solar analogs are solar-type stars with atmospheric parameters effective temperature ($T_{\mathrm{eff}}$), metallicity ([Fe/H]111[A/B] = $\log{\left(\frac{N(\text{A})}{N(\text{B})}\right)_{\text{Star}}}-\log{\left(\frac{N(\text{A})}{N(\text{B})}\right)_{\text{Sun}}}$, where $N$ denotes the number abundance of a given element.), and surface gravity (log g) similar to those of the Sun within specified uncertainty criteria, and therefore they present a solar flux distribution. Stars with photometric colors equal to solar are sometimes called solar analogs in the literature, but we remark that the use of this working definition should be taken with care because solar photometric colors, only, hardly imply a solar flux distribution. This is the reason why their atmospheric parameters must be proven to be solar by spectroscopic techniques. Solar analogs may serve as calibrating objects when the solar flux distribution needs to be observed at night, that is, as “solar proxies” or “solar surrogates”. Ideally they should be known to magnitudes comparably faint to the targets of interest in order to record the instrumental signature in the spectra of both the target and the proxy. Furthermore, the availability of a list of solar analogs well spread in the sky allows the users to choose a solar proxy close to the target, to be observed with a similar airmass to record the same telluric features as in the target’s spectrum. A proper solar proxy then guarantees the complete removal of the solar signature, of the instrumental signature, and of the telluric features, which is essential for recovering accurately the body’s albedo, whose shape and inclination are used for taxonomy (e.g., Chapman et al. 1975; Tholen & Barucci 1989). Since Solar System bodies such as trans-Neptunian objects with $V\sim 15$, or fainter, are routinely observed nowadays, it is reasonable to require solar proxies with, for example $V=$ 13-14. Such proxies are at least 10 times brighter than common targets but should still allow convenient corrections.

Porto de Mello et al. (2014) recently provided a sizable list of solar analogs, characterized both photometrically and spectroscopically, and well distributed in the night sky, widely extending both in quality and quantity the initial work of Hardorp (1982), who provided a first impetus on the search for solar analogs. Surprisingly, Hardorp’s lists are still being referred to nowadays. However, the lists of Porto de Mello et al. reach no fainter than $V\sim 9$, not much better than Hardorp’s, only sampling stars within 50 pc of the Sun. This magnitude range is too bright for telescopes of the 8-10m class. An example that illustrates the need for fainter solar analogs is the use of the stars BD+00 3383 ($V=10.50$) and HD 11532 ($V=9.71$). They both showed acceptable performances as solar proxies although no detailed spectroscopy was applied to them for determining their atmospheric parameters. They were used for recovering albedos from the infrared to the visible (e.g., Merlin et al. 2017; Dumas et al. 2011; Alvarez-Candal et al. 2008), and the UV (e.g., Snodgrass et al. 2017). For a solar-type star, the flux variation as a function of the atmospheric parameters from the infrared to the visible keeps nearly a constant shape, but this no longer applies from $\lambda$5000 downwards to the UV, a region much more sensitive to $T_{\mathrm{eff}}$, [Fe/H], and log *g * shifts, in this order. For example, Fig 1 in Fernley et al. (1996) shows that a variation of $-200$ K from the solar $T_{\mathrm{eff}}$ increases the flux by $\sim 15$% at 4000 Å with respect to that at 5000 Å. In cases like this, solar analogs with atmospheric parameters precisely close to solar are advisable in order to assert minimum influence on the intrinsic shape of the target’s albedo.

In the present work we implement methods to identify faint solar analogs. The definition of “faint” is subjective because it has to conform to the requirements of the users, or to the faintest analogs identified so far. For example, stars that were considered faint in the Hipparcos catalog are definitely not so for present Gaia standards; 20 years of technological advances allow much deeper sky prospecting. Since we hunt solar analogs, the definition of faint we adopt conforms to the apparent magnitude of the stars whose photometric, astrometric, and spectroscopic available data have the minimum quality to determine their atmospheric parameters with reasonable precision and present techniques: 100 K/0.05 dex/0.05 dex in $T_{\mathrm{eff}}$/[Fe/H]/log g. We employ as our initial screening photometric data from Hipparcos, obviously not current, though they were so at the time our survey started. Much more precise photometric and astrometric data were made available by Gaia (Gaia Collaboration et al. 2016a). However, the stars with the less precise photometry in Hipparcos, close to this catalog’s completeness limit, those with $V\sim 10.5$, are still competitive as reasonably faint solar analogs. The methods here implemented can be readily applied to spectra with similar characteristics acquired by telescopes of 8-10m, corresponding to stars of $V=16$-18.

Interstellar extinction arises as an additional problem for the selection of candidates as they become increasingly fainter and farther away. Solar analogs are most probably located in the Galactic thin disk because the metallicity distribution of this population is essentially solar (e.g., Adibekyan et al. 2013). The scale height of the thin disk is estimated at $\sim 300$ pc (Jurić et al. 2008, and references therein), thus at longer distances, a more productive search would be performed by pointing to the Galactic plane than to the poles. At the same time, pointing to the plane implies candidates with more attenuated magnitudes and more reddened colors, thus precise corrections for Galactic layers must be applied. Such solar analogs will probably not satisfy the need for solar surrogates, either photometrically or spectroscopically, from the blue limit of the $H$ band to shorter wavelengths because extinction increases fast from there (e.g., Gordon et al. 2003, Fig. 10).

Some faint solar analogs and twins were already identified, for example Inti 1 with $V=12.86$ (Galarza et al. 2016), KIC 10971974 with $V=11.05$ (Beck et al. 2017), and those in the M67 cluster with $V\sim 14.60$ (Pasquini et al. 2008; Önehag et al. 2011). Here we provide a short list of solar analogs as products of testing our methods. They should be subsequently submitted to more precise spectroscopic analyses to better determine their fundamental parameters derive other quantities as rotation, detailed chemical composition, magnetic activity, and asteroseismological properties.

This paper is organized as follows: In Sect. 2 we describe the selection criterion of the candidates. In Sect. 3 we describe the data reduction. Sect. 4 describes the Principal Component Analisis (PCA) regression applied to spectral indices. Sect. 5 presents the fundamental parameters derived for the candidates. In Sect. 6 we determine the influence of reddening on photometric colors. In Sect. 7 we summarize the information obtained for the best solar analogs identified, and finally in Sect. 8, we synthesize our conclusions.

2 Selecting the sample of faint analog candidates

This survey was launched by the time the Hipparcos catalog (Perryman et al. 1997) was the reference for the most precise parallaxes, colors, and magnitudes for solar-type stars, and the procedure we employed consider this fact.

We start our search by selecting candidates by colors (proxies of $T_{\mathrm{eff}}$ and [Fe/H]) and absolute magnitudes (proxy of log g), the observable quantities that allow a gross selection. The colors of widespread use, and having available several $T_{\mathrm{eff}}$ calibrations, are $B-V$ and ($B-V$)Ty from the Johnson and Tycho (Hoeg et al. 1997) systems. The initial procedure follows closely the one in Porto de Mello et al. (2014): “boxes” were prospected around the solar colors and absolute magnitudes ($B-V$)${}_{\odot}=0.654$, ($B-V$)${}_{\odot}^{\rm Ty}=0.733$, M${}_{\mathrm{V}_{\odot}}=4.82$, M${}_{\rm V_{\odot}}^{\rm Ty}=4.88$. Hipparcos is complete up to $V\sim 9$, but still lists fainter stars in decreasing degrees of completeness down to $V\sim 11$. We chose Hipparcos for the sample selection because it has more precise parallaxes than Tycho, which permits a more reliable selection based in magnitudes, although Tycho goes deeper, being complete down to $V^{Ty}=10$, and still 90% complete down to $V^{Ty}\sim 10.5$.

The final list of candidates to be analyzed spectroscopically should have a size compatible with the accomplishment of this project in the Observatório Pico dos Dias (OPD) operated by Laboratório Nacional de Astrofisica (LNA/CNPq) within a period of a few years. These practical order considerations constrain the candidate list to, at most, some tens of objects. We emphasize, however, that while we used Hipparcos for the sample selection, the determination of log g, mass, radius, age, and reddening were updated with the parallaxes of Gaia DR2 (Gaia Collaboration et al. 2016a, 2018).

We started with some coarse tests to gauge the size of the sample. Solar-type stars with $V$ between 10.5 and 11.2 were considered, the faint limit of Hipparcos. The dimensions of the boxes around the solar colors and absolute magnitudes were set by the mean of the 1$\sigma$ errors of all stars contained within the box, self-consistently. We worked simultaneously with boxes around the Johnson and Tycho solar colors and absolute magnitudes, and we kept stars within 2$\sigma$ of the boxes’ centers. The average uncertainties of color and absolute magnitude for the stars contained in the box, respectively, are very similar to the uncertainty values used to define the boxes in the first place, representative uncertainties being:

[TABLE]

These tests constrained samples with around 300 stars, which we decreased by considering only those objects, within these initial 2$\sigma$ boxes defined by average errors, for which the individual uncertainty implied in a 2$\sigma$ agreement with the solar values defining the centers of the boxes. This second sample totalled 203 stars, average errors being:

[TABLE]

Finally, we fine tuned this subsample by retaining only those objects for which the individual errors were no larger than the average errors defined for each box, thus a 1$\sigma$ criterion, applying the cuts stepwise in the M${}_{\rm V_{\odot}}$, M${}_{\rm V_{\odot}}^{\rm Ty}$, ($B-V$)${}_{\odot}^{\rm Ty}$ and ($B-V$)⊙ dimensions, in this order. We have purposefully disregarded reddening in the selection process in order to gauge its influence in the method of selection.

The selected candidate sample contains 41 stars, and it is listed in Table 1. It displays the stellar photometric and astrometric measurements as shown in the catalogs Hipparcos, Two Micron All Sky Survey (Cutri et al. 2003), and Gaia DR2. The table is divided in two parts, the first one lists the observed stars, that we refer henceforth simply as “candidates”, for which the $S/N$ is noted. We also show in Fig. 1 the spatial distribution of the candidates in galactic coordinates. No candidates are located towards the galactic plane, thus their reddening is expected to be low, with some exceptions as found in Sect. 6.

3 Observations and data reduction

Spectroscopic observations were performed with the long-slit coudé spectrograph, coupled to the 1.60m telescope of OPD in six missions from 1998 to 2013. The spectra cover a range of 500 Å centered in $\lambda$6563 (H$\alpha$), and have a nominal resolution of $R=\lambda/\Delta\lambda\sim$ 8000. The signal-to-noise ratio ($S/N$) of the spectra spans between 70 and 220 for the candidates, and between 70 and 810 for the calibration stars, see Tables 1 and 4, respectively.

The data reduction was carried out by the standard procedure using IRAF222Image Reduction and Analysis Facility (IRAF) is distributed by the National Optical Astronomical Observatories (NOAO), which is operated by the Association of Universities for Research in Astronomy (AURA), Inc., under contract to the National Science Foundation (NSF)., i.e. for one-dimensional spectra extraction, bias and flat-field corrections were performed prior to background and scattered light subtraction. The pixel-to-wavelength calibration was obtained by comparing the spectra of stars with a Thorium-Argon lamp spectra acquired in the same night of the observations. Doppler corrections were applied for all spectra and continuum normalizations were performed by fitting low-order polynomials to the highest flux regions following a systematic procedure.

4 Calibration of spectral indices

In order to determine the atmospheric parameters of the candidates, we built a calibration by means of the Principal Component Analysis (PCA) applied to the equivalent width (EW) of the spectral indices. At $R=8000$, individual metallic lines are not resolved, thus, the determination of atmospheric parameters using spectroscopic techniques such as the excitation and ionization equilibrium of Fe lines, and Balmer-lines fitting is not possible. Alternatively, spectral indices have been validated as competitive in this task using intermediate quality spectra (e.g. Ghezzi et al. 2014).

4.1 Calibration stars

We observed a sample of 69 solar-type stars for calibrating spectral indices. They are called hereafter “calibration stars” and are listed in Table 4. Their atmospheric parameters were extracted from the literature and the sources are provided in the table. Most of the sample (39 stars) is found in Ghezzi et al. (2010a, b), where $T_{\mathrm{eff}}$ determinations are based on excitation & ionization equilibrium of Fe lines. The rest of the stars belong to catalogs where $T_{\mathrm{eff}}$ was also derived by the same technique, excepting 16 stars for which parameters were extracted from Porto de Mello et al. (2014), where $T_{\mathrm{eff}}$ is the average of photometric calibrations and H$\alpha$ line-profile fitting. The mean quoted precision of this sample is $\sim 40$ K, and 0.02 dex, 0.10 dex in $T_{\mathrm{eff}}$, [Fe/H], and log g. 10 stars were observed twice with the purpose of estimating uncertainties of the indices measurements: HD 146233, HD 150248, HD 112164, HD 131117, HD 34721, HD 20029, HD 206395, HD 212330, HD205420 and HD 215648.

The distribution of the calibration stars in the parameter space is shown in Fig. 2. They are more densely packed around the solar parameters $T_{\mathrm{eff}}$ = 5772 K (Prša et al. 2016; Heiter et al. 2015), [Fe/H] = 0 dex, and $\log{g}=4.44$ dex to calibrate as best as possible the solar analogs area. Notice that the area for $T_{\mathrm{eff}}$ ¡ 5600 K is practically empty. This feature highlights the applicability limitation of our method, especially towards cooler and metal-poor stars. Therefore we choose to adopt the applicability range of our calibrations as follows: $5600\leq$ $T_{\mathrm{eff}}$ $\leq$ 6300 K, $-0.3\leq$ [Fe/H] $\leq 0.4$ dex, log g $\geq 4.1$ dex.

4.2 Identification of indices

Following (Ghezzi et al. 2014) we only selected indices dominated by iron peak elements, from both neutral and ionized species – with a contribution of more than 90%– (Fe I, Fe II, Ti II, V I, Cr I, Cr II, Mn I, Co I, Ni I). These indices are shown to best correlate with atmospheric parameters. The inspection was carried out along the available spectral range avoiding the H$\alpha$ profile.

Line identification was performed by comparing simultaneously the Kitt Peak National Observatory solar atlas (KPNO, Kurucz 2005)333http://kurucz.harbard.edu/sun.html with spectra of the Sun (reflected off Ganymede), HD 19637, and HD 182572; as shown in Fig. 3. The comparison between KPNO and Ganymede helps to visually identify metallic lines into the indices, whose contributions were estimated by their EWs as listed in the catalog of Moore et al. (1966). The element species were also checked using the VALD3 database (Ryabchikova et al. 2015). The spectrum of HD 19637 (hot and metal-poor star) was used for dismissing the weakest indices, while the spectrum of HD 182572 (cool and metal-rich star) was used to better define the wavelength limits of the indices. We selected 42 well defined indices that were submitted to the sensitivity test described below.

4.3 Calibration by PCA

Correlations of the EWs of the indices with the atmospheric parameters $T_{\mathrm{eff}}$, [Fe/H], and log g are approximated by a Taylor polynomial expansion of second order, as given in Eq. 1.

[TABLE]

Following the same procedures of Ghezzi et al. (2014), we select 24 indices with the best sensitivity to $T_{\mathrm{eff}}$ and [Fe/H] (class 1 and 2, according to their definition), to which we then applied the PCA regression.

The PCA extracts important information of correlated data sets, in which the direction of the greater variability of the correlations is searched. It finds a new basis in which the data sets exhibit their greatest variance, providing groups of non-correlated orthogonal components (Principal Components, PC’s) based on linear combinations of the original input variables (the spectral indices EWs in our case). This approach enables the extraction of the most relevant combinations of the original input variables and, thus, they can be used for efficient discrimination of objects of different nature that present similar observables (e.g. Blanco-Cuaresma et al. 2015; Hunt et al. 2012), and can be also calibrated against physically motivated variables, such as $T_{\mathrm{eff}}$, [Fe/H], and log g, as done by Muñoz Bermejo et al. (2013), and as we do in the present work.

The variables were standardized to take into account their different scales as follows:

[TABLE]

where $\langle Variable\rangle$ and $\sigma(Variable)$ are, respectively, its average and standard deviation. We explored the correlations between the PC’s and the atmospheric parameters of our calibration sample finding that the first (PC1) and the second (PC2) principal components are better related to all three parameters, i.e. they correspond to 90% of the total cumulative variance of the data. The other, higher order, principal components do not show significant correlation with the atmospheric parameters and thus were discarded. We used the best regressive model to build a calibration for each one of the atmospheric parameters. Eqs. 3, 4, and 5, show the atmospheric parameters as functions of PC1 and PC2:

[TABLE]

[TABLE]

[TABLE]

The internal uncertainties of these analyses are 93 K, 0.06 dex, and 0.16 dex, for each atmospheric parameter, $T_{\mathrm{eff}}$, [Fe/H] and log g, respectively.

5 Fundamental parameters of the candidates

5.1 Spectroscopic effective temperature and metallicity

We call hereafter spectroscopic parameters those derived from the PCA calibration of spectral indices, and we simbolize them hereafter by $T_{\mathrm{eff}}^{PCA}$, [Fe/H]PCA, and log gPCA. The adopted values and uncertainties of stellar atmospheric parameters were estimated from $10^{5}$ Monte Carlo (MC) simulations, assuming that the EW’s errors follow Gaussian distributions. The fractional EW errors estimated from the subsample of stars with two observations are found to be $\sim 4$% (the stars are indicated in Table 4). The outcome of MC simulations are EW distributions that were propagated by Eq. 3, 4, and 5 to finally obtain a distribution of atmospheric parameters from which the most probable values and their errors were associated to the medians and standard deviations.

We applied this procedure to the calibration sample in order to check the consistency between the PCA-based parameters and those of the literature, the results are shown in Fig. 4. The agreement is satisfactory only for $T_{\mathrm{eff}}$ and [Fe/H]. Accordingly, log g values derived by spectral indices are dismissed, and we determine them by evolutionary tracks in Sect. 5.5. The plots confirm that the stars with parameters out of the applicability range are biased (red squares) to hotter and more metal-rich diagnostics, in general. The plots also show that the spectroscopic PCA parameters of the only calibration star with a spectrum of $S/N<100$ (a value representative of the candidate star sample) agree with the literature values. Literature $T_{\mathrm{eff}}$’s of the outlier HD 206860 (red triangle) were reviewed; the initially adopted $T_{\mathrm{eff}}$ was found to be too hot, being actually the hottest one in the published range.

The atmospheric parameters of the candidates derived by the procedures described above are presented in Table 1. We keep henceforth the notation $T_{\mathrm{eff}}^{PCA}$ for temperatures derived by spectral indices, and the values presented in the table were corrected by the equation given in Sect. 5.3. Only parameters within the range of applicability pointed out in Sect. 4.1 are provided.

5.2 IRFM-photometric effective temperature

We derived another set of temperatures using the metallicity-dependent color calibrations of Casagrande et al. (2010) based on the InfraRed Flux Method (IRFM Blackwell & Shallis 1977; Blackwell et al. 1979, 1980), we symbolize it henceforth as $T_{\text{eff}}^{\text{phot}}$. Casagrande et al. corrected the systematics of previous IRFM implementations, their temperature scale was found to be in precise agreement with $T_{\mathrm{eff}}$ derived from interferometric measurements for the metallicity range in this work (Casagrande et al. 2014; Giribaldi et al. 2019). Thus, we consider the $T_{\text{eff}}^{\text{phot}}$ as the standard scale.

We derived $T_{\text{eff}}^{\text{phot}}$ by computing the weighted mean of the temperatures obtained with the $(B-V)$, $(B-V)^{Ty}$, $(V-J)$, $(V-H)$ and $(V-K_{s})$ colors, and [Fe/H]. The total uncertainty \sigma$$T_{\text{eff}}^{\text{phot}} was computed expanding the errors of colors, [Fe/H], and the internal uncertainty of the color calibration given by the authors.

5.3 Consistency between spectroscopic and IRFM-photometric effective temperatures

The accuracy of effective temperature measurements and the consistency between temperature scales is a recurrent topic in stellar astrophysics, and its importance increased with the discovery of exoplanets and the arrival of precise data from large surveys. Spectroscopic and photometric scales show discrepancies for parameters far from solar, see for example comparisons in Casagrande et al. (2010), Heiter et al. (2015), and references in Table 4.

Precise radius measurements from interferometry allow to derive $T_{\mathrm{eff}}$ semidirectly for nearby stars, thus they can be used to test the accuracy of model-dependent techniques, for example by using the Gaia Benchmark Stars (Heiter et al. 2015). This task was performed by Giribaldi et al. (2019) for a parameter space similar to that analyzed in this work. They found that the IRFM $T_{\mathrm{eff}}$ scale implemented by Casagrande et al. (2010) agree with the interferometric one, as already reported by Casagrande et al. (2014). On the other hand, they found that spectroscopic $T_{\mathrm{eff}}$ scales based in LTE + 1D model atmospheres present a bias as a function of [Fe/H], producing $T_{\mathrm{eff}}$ underestimations/overestimations for metal-poor/metal-rich stars, regardless of line lists and particular implementations of the technique.

Giribaldi et al. showed a trend of the spectroscopic $T_{\mathrm{eff}}$ scale of Ghezzi et al. (2010a, b) (our calibrations are based mainly on it) with respect to $T_{\mathrm{eff}}$ based on interferometry as a function of [Fe/H], and provided corrections for it, that is, to empyrically convert this scale to the interferometric one (or to the IRFM one, which is equivalent). In Fig. 5, we show the comparison between $T_{\text{eff}}^{\text{phot}}$ and the temperatures from the literature ($T_{\mathrm{eff}}^{lit}$), which are essentially spectroscopic, for the calibration stars. We observe a similar trend to that shown by Giribaldi et al. (Fig. 10 in the paper), and find that the equations given by the authors above444Reduced into one equation here: $T_{\text{eff}}^{\text{phot}}$ = ($T_{\mathrm{eff}}^{lit}$ $+\leavevmode\nobreak\ 410$)$/1.08-153$[Fe/H] + 22; where $T_{\mathrm{eff}}^{lit}$ represents the temperatures from the literature listed in Table 4. subtract the trend. This equation is applied to $T_{\mathrm{eff}}^{PCA}$ of the candidates, so the values listed in Table 2 are corrected values. These empirical corrections may be not elegant, but they are useful to assert accurate $T_{\mathrm{eff}}$ for non-solar [Fe/H]. They removed, for example, $\sim 50$ K excess for the hot more metal-rich candidates HIP 10663 and HIP 75685, but they do not affect $T_{\mathrm{eff}}$ of solar analogs. $T_{\text{eff}}^{\text{phot}}$ and $T_{\mathrm{eff}}^{PCA}$ (corrected by the equation given above) of the candidates are compared in Fig. 6, where $T_{\mathrm{eff}}^{PCA}$ is used as the absolute scale in the abscissa due to its insensitivity to reddening. No trends are observed in the comparisons against $T_{\mathrm{eff}}$ and [Fe/H], and the offset between both scales is practically null (we considered only the stars without any evidence of reddening to compute this difference, see Sec. 6 for details). This asserts the consistency of the corrected spectroscopic and photometric scales. Stars with significant temperature differences are highlighted by filled symbols in Fig. 6. Their associated reddening values are discussed in Sect. 6.

5.4 Effective temperature from H$\alpha$ profiles

Once the consistency between spectroscopic and photometric scales is realized by applying corrections to $T_{\mathrm{eff}}^{PCA}$, significantly cooler $T_{\text{eff}}^{\text{phot}}$ suggest the presence of reddening. Here we verify by means of H$\alpha$ profiles whether significant temperature differences are indeed due to reddening effects on $T_{\text{eff}}^{\text{phot}}$. Although the limited resolution of our spectra does not allow a precise application of the H$\alpha$ profile fitting and prevents the precise determination of $T_{\mathrm{eff}}$, temperature differences higher than $\sim 200$ K are discernible.

$T_{\mathrm{eff}}$ from H$\alpha$ is not affected by reddening and its determination practically does not depend on other parameters at solar metallicity (e.g. Fuhrmann et al. 1993; Barklem et al. 2002). Its main source of error is the normalization, which is a complex task in high resolution spectra, due to the short wavelength ranges that the profile leaves available into a spectral order for interpolating a polynomial that can reliably approximate the spectrograph response. However, our moderate resolution spectra are more than 3 times wider than the profile region, hence our normalization recovers the profile shape reasonably well. In Fig. 8 we compare the observed profiles of HIP 67692 and HIP 75685 with synthetic profiles, from the grid of Barklem et al. (2002), corresponding to temperatures similar to their $T_{\mathrm{eff}}^{PCA}$ and $T_{\text{eff}}^{\text{phot}}$. This grid is found to be $-28$ K accurate for the metallicty of these stars (Giribaldi et al. 2019). We also plot observed profiles of other candidates with $T_{\mathrm{eff}}^{PCA}$values very similar to these two stars. The top plot in the figure shows that the profile of HIP 67692 is more compatible with its $T_{\text{eff}}^{\text{phot}}$, while the bottom plot favors $T_{\mathrm{eff}}^{PCA}$ for HIP 75685, whose profile is slightly deeper than that of HIP 10663 with $T_{\mathrm{eff}}^{PCA}$ $\sim$ 6150 K. Accordingly, T_{\mathrm{eff}}^{PCA}$$\sim 5400 K for HIP 67692 is not listed in Table 2, since this value lies out of the valid range of our indices calibration.

5.5 Surface gravity, mass, and age

From the Gaia parallaxes (Gaia Collaboration et al. 2018), plus the best $T_{\mathrm{eff}}$, and [Fe/H] values shown in Tables 1 and 2, we calculated stellar luminosities using bolometric corrections from Andrae et al. (2018) and extinction values from our reddening estimates in Table 3. Surface gravity, mass, and age were obtained from theoretical evolutionary tracks of Kim et al. (2002) and Yi et al. (2003) following the procedure described in Grieves et al. (2018).

6 Reddening

The hunt for solar analogs begins, necessarily, by selecting candidates with solar photometric colors, as they are the most direct observational parameters able to quantify similarities between stars. Once photometric mimics to solar produced by the degeneracy of the atmospheric parameters (principally $T_{\mathrm{eff}}$–[Fe/H]) are identified and discarded, solar-like colors should lead to stars with the same atmospheric parameters as the Sun. However, in the presence of interstellar extinction a star which presents observed reddened colors equal to solar will have different combinations of atmospheric parameters tending to be hotter than the Sun. For hunters of solar analogs and twins at large distances, this implies that reddening corrections must be considered. For users of solar proxies, it also means that regardless of whether the intrinsic atmospheric parameters of a star are solar, the observed colors will always be reddened, i.e. $B-V_{\star}$ ¿ $B-V_{\sun}$. Therefore, a faint star with apparent solar colors will have a flux distribution different from solar, and when used to remove the solar spectral signature from the spectrum of the target, it will introduce systematic trends in its spectral albedo.

We estimate reddening values for the candidates for which $T_{\text{eff}}^{\text{phot}}$ are smaller than $T_{\mathrm{eff}}^{PCA}$. These are are shown as filled triangles in Fig. 6. The color excess $E(B-V)=(B-V)_{reddened}-(B-V)_{intrinsic}$ is then computed by the difference between the color required to obtain the average $T_{\text{eff}}^{\text{phot}}$ and that required to obtain $T_{\mathrm{eff}}^{PCA}$ by using the calibrations of Casagrande et al. (2010). Since $T_{\text{eff}}^{\text{phot}}$ was determined by the weighted average of several colors, $(B-V)_{reddened}$ are not exactly the same as those in Table 1. Table 3 shows $E(B-V)$ estimated by this method: they can be considered as lower limit estimates of the actual reddening in $B-V$, since this actual reddening is somewhat diluted by the process of determining the average $T_{\text{eff}}^{\text{phot}}$ also employing colors which are less affected by reddening than $B-V$.

6.1 Extinction models

We compare here our $E(B-V)$ estimates with those predicted by two extinction maps. Reddening estimations by other methods such as Ca II H & K lines, Na I D lines (e.g. Alves-Brito et al. 2010; Curtis 2017), and diffuse interstellar bands (Law et al. 2017) were not possible due to the limitations established by the resolution and wavelength coverage of our spectra. The description of dust distribution in our Galaxy has progressed a lot over the last two decades for both 2D and 3D maps and models (Robin et al. 2015; Sale 2015). Schlegel et al. (1998) (hereafter SFD) published 2D maps based on the FIR emission detected by COBE/DIRBE satellite. This model was reviewed by Beers et al. (2002) in order to correct overestimations of the total reddening in internal regions of the Galaxy (hereafter SFD-B).

Amôres & Lépine (2005, hereafter A&L) presented two models for interstellar extinction in the Galaxy that take into account the gas distribution for HI and HII. In the first model, the Galaxy is axisymmetric (ALA) and extinction increases linearly as function of distance. In the second model (ALS), the spiral structure is considered and the extinction increases by steps each time a spiral arm is crossed. They compared their models for a wide range of distances and directions by using some catalogues, such as Neckel & Klare (1980), Savage et al. (1985), and Guarinos (1992). The last catalogue has the majority of their stars located at distances up to 500 pc.

A&L, Arce & Goodman (1999), among other works find that Schlegel et al. (1998) overestimates extinction for $E(B-V)\sim 0.15$ mag. Some simplifications done in the map such as resolution and the unique value used for dust temperature are provided as explanations for it. The overestimations are expected to mainly affect the Galactic plane and towards molecular clouds, however it is not explored from which distance they start to be relevant.

Our choice was to use the ALA model of A&L and the SFD-B model to test their consistency with our estimates from T_{\mathrm{eff}}^{PCA}$$- $T_{\text{eff}}^{\text{phot}}$ at $\sim 170$ pc, their $E(B-V)$ are listed in Table 3. Fig. 7 shows $E(B-V)$ from A&L and SFD-B for all candidates plotted against T_{\mathrm{eff}}^{PCA}$$- $T_{\text{eff}}^{\text{phot}}$ from derredened colors (red triangles), and also from non-derredened colors (blue bars) for the reader to check the corresponding temperature corrections. $E(B-V)$, $E(B-V)^{Ty}$, $E(V-J)$, $E(V-H)$, and $E(V-K)$ were considered to obtain derredened $T_{\text{eff}}^{\text{phot}}$; same values were used for Johnson and Thycho, while 2MASS reddenings were converted from Johnson by the relations given by Zagury & Turner (2012) for $R_{V}=3.14$. The errors of derredened $T_{\text{eff}}^{\text{phot}}$ were estimated expanding those of $E(B-V)$ given by the models, colors, parallax, [Fe/H], and photometric calibrations. These errors turned to be practically the same as those from non-derredened $T_{\text{eff}}^{\text{phot}}$ because the error budget is dominated by parallax errors, which are negligible for the Gaia data in our distance range.

Both models remove (or at least minimize) the differences of the labeled stars, except for HIP 75685. For this case, SFD-B predicts a substantially higher $E(B-V)$ than A&L, but still lower than our estimate $E(B-V)$ $\sim$ 0.20 mag. This value agrees with that of SFD, which is the total reddening predicted by the model for the line of sight, although it is in the range where the model predictions are known to present problems ($E(B-V)>0.15$ mag) as pointed out above. Given the reasonable agreement between these independent estimates of reddening, we consider the case for these three objects as substantial, particularly for HIP 75685.

7 Best faint solar analogs

The results of the previous sections point towards the identification of a sample of faint solar analogs of $V\sim 10.5$ which reproduce well the atmospheric parameters of the Sun and should be good matches for its spectrophotometric flux distribution for a wide range of wavelengths. Three stars have atmospheric parameters agreeing with solar within 1$\sigma$ of their formal errors: HIP 991, HIP 5811 and HIP 69477. Other two candidates agree in the same sense but within 2$\sigma$ of their errors: HIP 55619 and HIP 61835. Their ages are found to be comparable or larger than the Sun’s, and moreover their H$\alpha$ line cores do not show any discernible fill-in from a high level of chromospheric activity, which should be apparent even in moderately low resolution spectra (Lyra & Porto de Mello 2005). All evidence point to their being middle-aged, inactive solar analogs. Their estimated masses and radii also closely match the solar ones within formal uncertainties, but HIP 61835 which has a slightly larger radius. They are reasonably well distributed across the sky but slightly biased towards southern declinations due to the reach of our observations.

Six additional objects have $T_{\mathrm{eff}}$ matching the solar one but appear as slightly metal$-$poor, in the $-$0.30 $<$ [Fe/H] $<$ $-$0.20 range. They are probably poorer solar matches for shorter wavelengths but should reproduce the Sun increasingly better towards redder spectral ranges and are probably very good in the infrared (Porto de Mello et al. 2014). These are HIP 6089, HIP 18941, HIP 31845, HIP 48272, HIP 56870 and HIP 107605. Consistently with their more diverse atmospheric parameters, their masses and radii do not match the Sun’s as closely as the best analogs, but all of them (excepting HIP 107605) appear to be old stars and thus free from a high degree of chromospheric activity, and are also reasonably well scattered in the sky. These latter stars may be considered by potential users to be reasonable matches to the Sun as a function of the desired precision and accuracy for the target observations. All of the aforementioned eleven faint solar analogs are free from any evidence of reddening according to our analysis. We could not find any sign of binarity in the spectra of the candidates analysed, and better quality observations should be used to eliminate this possibility.

8 Conclusions

Motivated by the demand for faint spectrophotometric solar analogs, we implemented the methodologies to derive atmospheric parameters with optimized precision from moderately low resolution and S/N spectra. We selected a sample of candidates with $V\sim 10.5$ in the Hipparcos catalog by matching the solar MV and $B-V$ values in the Johnson and Tycho systems, subsequently we submitted a subsample of them to spectroscopic analysis. The method for deriving atmospheric parameters consist on a system of 24 spectral indices, whose sensitivity to $T_{\mathrm{eff}}$ and [Fe/H] were mathematically modeled by the PCA regression. The models were based on published spectroscopic $T_{\mathrm{eff}}$’s (based on the excitation and ionization equilibrium of Fe lines in LTE + 1D model atmospheres), thus $T_{\mathrm{eff}}$ derived by the spectral indices may be also deemed spectroscopic. Considering the discrepancies between $T_{\mathrm{eff}}$ scales from different techniques at parameters far from solar, we assured the consistency of the spectroscopic $T_{\mathrm{eff}}$ with the photometric $T_{\mathrm{eff}}$ (Casagrande et al. 2010) – which is consistent with the interferometric $T_{\mathrm{eff}}$ of the Gaia Benchmark Stars (Heiter et al. 2015) – using the relations given by Giribaldi et al. (2019). The corrected spectroscopic $T_{\mathrm{eff}}$ are shown to match the photometric ones. Excepting for the stars showing evidence of reddening, finally adopted $T_{\mathrm{eff}}$ were derived by averaging the photometric and spectroscopic determinations. The finally derived spectroscopic $T_{\mathrm{eff}}$ and [Fe/H] have internal precision, respectively, of 97 K and 0.06 dex. The PCA index system is very successful in recovering atmospheric parameters with good precision, even for low S/N spectra, and may be used to study fainter stars in large databases; the accuracy of the such parameters entirely relies on the accuracy of the calibrating sample.

Surface gravities, masses, radii and ages were derived from the finally adopted atmospheric parameters and Gaia parallaxes by means of theoretical evolutionary tracks and isochrones (Kim et al. 2002; Yi et al. 2003). We identified 11 solar analogs to different degrees of resemblance to the Sun: their individual suitability as solar surrogates is judged in Sect.7. Fundamental parameters for them and other candidate stars that did not fully meet the requirements as solar analogs are displayed in Table 2; their photometric and astrometric parameters are listed in Table 1.

Initial candidates lie between 90 pc and 290 pc, and we estimated reddening for them independently from published extinction models, by comparing photometric $T_{\mathrm{eff}}$ with corrected spectroscopic $T_{\mathrm{eff}}$, since corrected spectroscopic $T_{\mathrm{eff}}$ are shown to be consistent with photometric ones. We find evidence of significant reddening for four candidates which present significant cooler photometric $T_{\mathrm{eff}}$. A common reddening value at these distances resulted in $E(B-V)$ $\sim 0.06$ mag, which translates to a $\sim 200$ K decrease in photometric $T_{\mathrm{eff}}$. Our estimates are validated by predictions from the SFD-B and A&L extinction models, except for one star HD 75685, which appears to lie in a very dense region.

The identified analogs have no evidence of reddening, and may be used photometrically and spectroscopically for subtracting the solar signature with good precision from observations of Solar System bodies. In the visible and infrared regions they should present very good matching to the Sun, even in the UV up to 4000 Å. Our reddening analysis shows that solar analog candidates will be progressively more affected by reddening. These stars will present spectra and colors that appear to belong to cooler stars as they become fainter (or more affected by reddening), as seems to be the case of HIP 75685. As future generations of larger telescopes increase the demand for faint stars matching the solar spectra, this will become a relevant issue to be addressed for the very faint solar analogs: photometrically selected solar analogs will not match the actual spectroscopic properties of the Sun.

Acknowledgements.

REG acknowledges scholarships from CAPES and ESO, GFPM acknowledges grant 474972/2009-7 from CNPq/Brazil, DLS acknowledges a scholarship from CAPES and FAPESP 2016/20667-8, and MLUM acknowledges scholarships from FAPERJ and CAPES. We thank the staff of the OPD/LNA for considerable support in the many observing runs carried out during this project. We also thank the anonymous referee for helpful and constructive criticism to this work. Use was made of the Simbad database, operated at the CDS, Strasbourg, France, and of NASA’s Astrophysics Data System Bibliographic Services. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This work presents results from the European Space Agency (ESA) space mission Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia MultiLateral Agreement (MLA). The Gaia mission website is https://www.cosmos.esa.int/gaia. The Gaia archive website is https://archives.esac.esa.int/gaia.

Appendix A