---
author:
- 'N. Lodieu [^1], F. Allard , C. Rodrigo , Y. Pavlenko , A. Burgasser , Y. Lyubchik , B. Kaminsky , D. Homeier'
bibliography:
- '../../AA/mnemonic.bib'
- '../../AA/biblio\_old.bib'
date: 'Received ; accepted '
title: 'Metallicity, temperature, and gravity scales of M subdwarfs'
---

[The aim of the project is to define a metallicity/gravity/temperature scale vs spectral types for metal-poor M dwarfs.]{} [We obtained intermediate-resolution ultraviolet (R$\sim$3300), optical (R$\sim$5400), and near-infrared (R$\sim$3900) spectra of 43 M subdwarfs (sdM), extreme subdwarfs (esdM), and ultra-subdwarfs (usdM) with the X-shooter spectrograph on the European Southern Observatory Very Large Telescope. We compared our atlas of spectra to the latest BT-Settl synthetic spectral energy distribution over a wide range of metallicities, gravities, and effective temperatures to infer the physical properties for the whole M dwarf sequence (M0–M9.5) at sub-solar metallicities and constrain the latest state-of-the-art atmospheric models. ]{} [The BT-Settl models reproduce well the observed spectra across the 450–2500 nm wavelength range except for a few regions. We find that the best fits are obtained for gravities of $\log$(g)=5.0–5.5 for the three metal classes. We infer metallicities of \[Fe/H\]=$-$0.5, $-$1.5, and $-$2.0$\pm$0.5 dex and effective temperatures of 3700–2600K, 3800–2900K, and 3700–2900K for subdwarfs, extreme subdwarfs, and ultra-subdwarfs, respectively. Metal-poor M dwarfs tend to be warmer by about 200$\pm$100K and exhibit higher gravity than their solar-metallicity counterparts. We derive abundances of several elements (Fe, Na, K, Ca, Ti) for our sample but cannot describe their atmospheres with a single metallicity parameter. Our metallicity scale expands the current scales available for midly metal-poor planet-host low-mass stars. Our compendium of moderate-resolution spectra covering the 0.45–2.5 micron range represents an important legacy value for large-scale surveys and space missions to come. ]{}

Introduction {#SpClass_sdM:intro}
============

Mass, gravity, temperature, and metallicity constitute key parameters to understand the formation and evolution of any type of stars. M dwarfs represent the largest community among members of the solar neighbourhood [@henry06; @bochanski10; @kirkpatrick12] and have also become attractive targets to search for Earth-like planets [e.g. @nutzman08; @quirrenbach12a; @sozzetti14]. While the metal content of solar-type stars can be measured with great accuracies [e.g. @adibekyan12a], the metallicity of M dwarfs is more difficult to ascertain due to the significant amount of absorption bands [@kirkpatrick99]. Several groups conducted complementary surveys to assess the metallicity of M dwarfs based on photometry and colours [@bonfils05a; @johnson09a; @schlaufman10a; @neves12; @hejazi15; @dittmann16] and high-resolution spectra or spectral synthesis of multiple systems composed of a solar-type primary and a M dwarf secondary at optical and infrared wavelengths [@woolf05; @woolf06; @bean06a; @woolf09; @rojas_ayala10; @rojas_ayala12; @muirhead12; @terrien12a; @onehag12; @neves13; @neves14; @hejazi15; @newton15a; @lindgren16a]. These surveys usually focus on slightly metal-poor M dwarfs, with metallicities above $-$1.0 dex. An extension to lower metallicities is needed to complement the precise distances that the Gaia satellite [@deBruijne12] will provide for a great number of spectroscopically-confirmed thick disk and halo M dwarfs [@savcheva14] but also understand the role of metallicity on the molecules and dust grains present in the atmosphere of low mass stars.

Subdwarfs are population II dwarfs which appear bluer than solar-metallicity stars due to the dearth of metals in their atmospheres [@baraffe97]. They exhibit thick disk or halo kinematics, including high proper motions or large heliocentric velocities [@gizis97a]. They belong to the first generations of stars and are important tracers of the chemical enrichment history of the Galaxy. The original classification for M subdwarfs (sdM) and extreme subdwarfs (esdM) developed by @gizis97a has been revised and extended by @lepine07c. A new class of subdwarfs, the ultra-subdwarfs (usdM), has been added to the sdM and esdM. The new scheme is based on a parameter, $\zeta_{\rm TiO/CaH}$, which quantifies the weakening of the strength of the TiO band (in the optical) as a function of metallicity. Subdwarfs are easily distinguished from dwarfs with solar abundances because they exhibit stronger metal-hydride absorption bands (FeH, CrH) and metal lines (Ca, Fe) as well as blue infrared colours caused by collision-induced H$_{2}$–H$_{2}$ absorption [@gizis97a; @lepine07c; @lodieu17a]. An independent classification scheme based on metallicity, gravity, and temperature has been proposed for M dwarfs by @jao08 and an extension to the L dwarf regime proposed by @kirkpatrick14 and @zhang17a.

In this paper, we present moderate-resolution 0.45–2.5 $\mu$m spectroscopy of 15 sdM, 16 esdM, and 12 usdM to infer their metallicities and T$_{\rm eff}$ by direct comparison with the latest BT-Settl synthetic models [@allard12]. In Section \[MplusTeff\_sdM:sample\] we present our sample of metal-poor M dwarfs drawn from the literature. In Section \[MplusTeff\_sdM:spec\_obs\] we describe our spectroscopic observations. In Section \[MplusTeff\_sdM:Models\] we introduce the BT-Settl models used to infer the physical parameters of metal-poor M dwarfs. In Section \[MplusTeff\_sdM:Comparison\] we infer the spectral type vs.metallicity/gravity/T$_{\rm eff}$ relation of the three M dwarf metal classes and compare it to independent but complementary studies as well as solar-type M dwarfs. In Section \[MplusTeff\_sdM:discussion\] we discuss our results and the peculiarities of some of the spectra.

Sample selection {#MplusTeff_sdM:sample}
================

To select our sample of subdwarfs, we used the SDSS spectroscopic database which contains a wealth of high-quality spectra covering the 5000–9200Å range at a spectral resolution of $\sim$2000. Hundreds of objects have been classified as sdM, esdM, or usdM following the scheme developed by @lepine07c. This classification is publicly available through the SDSS archive and we have taken advantage of it to retrieve a large sample of low-metallicity M dwarfs.

We selected a sub-sample of low-metallicity stars which represent a sequence going from M0 to M9.5 from optical spectra. The objects were specifically chosen to be the (or among the) brightest of their subclass and be observable either in August or January from the Southern hemisphere to achieve the best signal-to-noise ratio possible over a wide wavelength range. We completed our sample with LHS377 [sdM7; @gizis97a], observed with the same telescope/instrument but at higher spectral resolution [@rajpurohit16a]. Our final sample contains 15 sdM0–sdM9.5, 16 esdM0.0–esdM8.5, and 12 usdM0.0–usdM8.5) with almost one object per spectral sub-type. We are missing the sdM7.5, sdM8, and sdM9 in the subdwarf sequence, the esdM2.5 and esdM8 in the extreme subdwarf sequence, and more usdM (usdM1.5, usdM2, usdM3.0, usdM6.5, usdM7, and usdM8). We note that these targets were included in our original sample but not observed during the ESO service runs. Table \[tab\_MplusTeff\_sdM:log\_obs\_Xshooter\] lists their coordinates, optical SDSS$i$ magnitudes, optical spectral types on the @lepine07c scheme, dates of observations, mean airmass, exposure times in all three arms, and numbers of AB cycles for all 43 subdwarfs.

VLT/X-shooter spectroscopy {#MplusTeff_sdM:spec_obs}
==========================

We carried out spectroscopy from the UV- to the $K$ band with the X-Shooter spectrograph [@dOdorico06; @vernet11] mounted on the Cassegrain focus of the Very Large Telescope (VLT) Unit 2. Observations were conducted in service mode by the European Southern Observatory (ESO) staff over the course of three semesters, between August 2012 and June 2014 (Table \[tab\_MplusTeff\_sdM:log\_obs\_Xshooter\]). The conditions at the time of the observations met the clear sky request, with an airmass less than 1.6, grey conditions, and a seeing better than 1.2 arcsec. We set the individual on-source integration times according to the magnitudes of the targets and used the multiple AB patterns to correct for the sky contribution (mainly) in the near-infrared. All observations were done with the slit oriented at parallactic angle. We list all the M subdwarfs observed with X-shooter in Table \[tab\_MplusTeff\_sdM:log\_obs\_Xshooter\] along with a summary of the logs of the observations.

X-Shooter is a multi wavelength cross–dispersed echelle spectrograph made of three arms covering simultaneously the ultraviolet (UVB; 0.3–0.55 $\mu$m), visible (VIS; 0.55–1.0 $\mu$m), and near–infrared (NIR; 1.0–2.48 $\mu$m) wavelength ranges thanks to the presence of two dichroics splitting the light. The spectrograph is equipped with three detectors: a 4096$\times$2048 E2V CCD44-82, a 4096$\times$2048 MIT/LL CCID20, and a 2096$\times$2096 Hawaii 2RG for the UVB, VIS, and NIR arms, respectively. We set the read-out mode to 400k and low gain without binning. We used the 1.6 arcsec slit in the UVB, 1.5 arcsec in the VIS, and 1.2 arcsec NIR, yielding resolving powers of 3300 (9.9 pixels per full-width-half-maximum), 5400 (9.7 pixels per full-width-half-maximum), and 3900 (5.8 pixels per full-width-half-maximum) in the UVB, VIS, and NIR arms, respectively.

We ran the latest version of the X-shooter pipeline (2.8.0)[^2] on the raw data downloaded from the ESO archive with their associated raw calibration files from our three programmes: 089.C-0140(A), 091.C-0264(A), and 093.C-0610(A). All spectra have their instrumental signature removed, including bias and flat-field. The spectra are wavelength-calibrated, sky-subtracted and finally flux-calibrated. The output products include a 2D spectrum associated with a 1D spectrum. However, the optimal extraction of the 1D spectrum not being yet implemented in the version 2.8.0 of the pipeline, we extracted the UVB, VIS, and NIR spectra with the task under IRAF [@tody86; @tody93]. We note that most of the targets have little flux in the UVB arm, resulting in low signal-to-noise ratio below 550nm and very little flux (or no flux) below 400nm. We corrected the VIS and NIR spectra for telluric bands/lines with the package distributed by ESO [@kausch15; @smette15][^3] mainly because the telluric standards were not necessarily taken at the same airmass as our targets. The regions corrected are: 625–632, 686–696, 716–732, 758–770, 812–834, 893–920, 928–980nm in the VIS arm and 1105–1220, 1253–1280, 1310–1510, 1730–1995, 2000–2035, 2045–2085, 2200–2470nm in the NIR arm.

The final spectral energy distributions (SEDs) of sdM, esdM, and usdM are displayed in figures in Appendix \[MplusTeff\_sdM:appendix\_model\_fits\]. For display purposes, we shifted the observed spectra to the BT-Settl models because of the large velocities of our subdwarfs taking into account that the wavelength scale of models is in vacuum and the observed spectra in the air system (see Section \[MplusTeff\_sdM:Comparison\]). Our sample increases by a factor of five the sample of subdwarfs presented in @rajpurohit16a and extend that recent work to the full sequence of the three metallicity classes of M subdwarfs. We will make publicly available all spectra through the late-type subdwarf archive at http://svo2.cab.inta-csic.es/vocats/ltsa/ [@lodieu17a].

[@c @c c c c c c c@]{} R.A (J2000) & dec (J2000) & $i'$ & SpT & Date & Airm & ExpT & Cycles hh:mm:ss.ss & dd:mm:ss.s & mag & & & & sec/sec/sec & 23:46:59.87 & $-$00:59:43.9 & 15.166 & sdM0.0 & 13Aug2012 & 1.30 & 90/66/66 & 2AB 21:22:02.76 & $+$00:44:56.8 & 14.996 & sdM0.5 & 21May2012 & 1.13 & 90/66/66 & 2AB 00:48:00.05 & $+$00:28:49.4 & 15.260 & sdM1.0 & 13Aug2012 & 1.22 & 90/66/66 & 2AB 00:51:25.68 & $-$00:37:16.9 & 16.666 & sdM1.5 & 18Aug2012 & 1.10 & 216/216/240 & 2AB 23:57:32.54 & $-$01:10:36.3 & 15.692 & sdM2.0 & 17Aug2012 & 1.32 & 90/66/66 & 2AB 01:17:46.53 & $-$00:01:05.3 & 16.196 & sdM2.5 & 13Aug2012 & 1.36 & 90/66/66 & 2AB 03:24:49.81 & $-$00:15:05.0 & 14.942 & sdM3.0 & 15Aug2012 & 1.14 & 90/66/66 & 2AB 02:12:08.59 & $+$00:37:01.5 & 14.918 & sdM3.5 & 19Aug2012 & 1.11 & 90/66/66 & 2AB 03:46:01.58 & $+$00:55:11.6 & 15.872 & sdM4.0 & 19Aug2012 & 1.14 & 90/66/66 & 2AB 22:57:48.05 & $+$14:29:39.9 & 18.336 & sdM4.5 & 07Jul2013 & 1.39 & 276/292/300 & 5AB 00:48:36.45 & $+$00:09:31.7 & 17.175 & sdM5.0 & 10Jan2012 & 1.32 & 90/66/66 & AB 23:53:36.94 & $+$00:47:34.1 & 18.025 & sdM5.5 & 14Jul2013 & 1.26 & 276/292/300 & 5AB 00:25:52.59 & $+$01:09:24.9 & 17.797 & sdM6.0 & 19Aug2012 & 1.18 & 266/266/290 & 5AB 16:10:28.99 & $-$00:40:53.0 & 15.903 & sdM6.5 & 10Jun2012 & 1.11 & 90/66/66 & 2AB 02:05:33.75 & $+$12:38:24.0 & 18.107 & sdM8.0 & 11Aug2012 & 1.30 & 266/266/290 & 5AB 10:13:07.35 & $-$13:56:20.4 & 16.010 & sdM9.5 & 09May2013 & 1.34 & 126/142/150 & 1AB 01:37:55.30 & $-$09:39:41.9 & 17.488 & esdM0.0 & 08Sep2013 & 1.45 & 276/292/300 & 5AB 23:25:41.30 & $+$00:04:19.6 & 16.203 & esdM0.5 & 18Aug2012 & 1.13 & 90/66/66 & 2AB 00:38:02.86 & $+$00:50:14.2 & 17.520 & esdM1.0 & 14Jul2013 & 1.20 & 276/292/300 & 5AB 23:40:39.45 & $-$00:51:18.4 & 16.263 & esdM1.5 & 12Aug2012 & 1.49 & 90/66/66 & 2AB 12:55:29.19 & $-$03:30:55.8 & 17.536 & esdM2.0 & 11Jul2013 & 1.18 & 276/292/300 & 5AB 12:53:53.35 & $+$12:12:48.7 & 16.531 & esdM3.0 & 11Jul2013 & 1.30 & 126/142/150 & 3AB 14:52:04.63 & $+$10:18:26.3 & 17.892 & esdM3.5 & 30Jun2014 & 1.22 & 276/292/300 & 5AB 00:40:18.18 & $-$10:41:55.9 & 17.405 & esdM4.0 & 18Aug2012 & 1.04 & 276/292/300 & 5AB 01:09:54.11 & $-$10:12:12.6 & 14.766 & esdM4.5 & 04Aug2013 & 1.05 & 126/142/150 & 1AB 13:31:51.15 & $-$00:09:19.0 & 18.180 & esdM5.0 & 15Jun2013 & 1.16 & 276/292/300 & 5AB 09:03:07.95 & $+$08:42:43.2 & 15.988 & esdM5.5 & 18Apr2014 & 1.20 & 126/142/150 & 1AB 15:36:47.08 & $+$02:55:01.5 & 19.071 & esdM6.0 & 12Aug2012 & 1.14 & 276/276/300 & 6AB 01:33:46.24 & $+$13:28:22.4 & 17.830 & esdM6.5 & 04Aug2013 & 1.37 & 276/292/300 & 5AB 02:35:57.61 & $+$01:08:00.5 & 19.190 & esdM7.0 & 09Sep2013 & 1.11 & 456/472/480 & 4AB 05:58:58.91 & $-$29:03:26.7 & 16.320 & esdM7.5 & 27Aug2012 & 1.34 & 216/216/240 & 2AB 04:52:09.94 & $-$22:45:08.4 & 17.220 & esdM8.5 & 17Aug2012 & 1.13 & 216/216/240 & 2AB 03:27:28.10 & $-$00:50:01.4 & 17.462 & usdM0.0 & 16Spe2012 & 1.09 & 266/266/290 & 5AB 15:34:04.63 & $+$09:36:22.5 & 17.984 & usdM0.5 & 09Aug2013 & 1.22 & 266/266/290 & 5AB 15:12:18.36 & $+$09:30:40.7 & 17.890 & usdM1.0 & 23Jul2013 & 1.23 & 276/292/300 & 5AB 20:59:20.57 & $+$00:00:33.4 & 17.853 & usdM2.5 & 11Aug2012 & 1.12 & 266/266/290 & 5AB 10:41:07.20 & $+$06:33:04.7 & 18.062 & usdM3.0 & 31May2013 & 1.27 & 246/262/270 & 5AB 15:35:40.74 & $+$08:21:43.3 & 18.008 & usdM4.0 & 10Aug2013 & 1.21 & 276/292/300 & 5AB 14:17:48.62 & $+$07:11:05.4 & 17.658 & usdM4.5 & 12Jul2013 & 1.18 & 276/292/300 & 5AB 12:04:26.91 & $+$13:29:23.3 & 16.549 & usdM5.0 & 12Jun2012 & 1.33 & 216/216/240 & 2AB 16:27:54.22 & $+$00:37:14.0 & 18.384 & usdM5.5 & 17Aug2012 & 1.15 & 266/266/290 & 5AB 16:41:23.73 & $+$24:49:42.4 & 17.233 & usdM6.0 & 15Jul2013 & 1.58 & 126/142/150 & 3AB 08:22:33.69 & $+$17:00:19.9 & 17.300 & usdM7.5 & 03Apr2013 & 1.39 & 126/142/150 & 3AB 12:27:05.06 & $-$04:47:20.7 & 16.630 & usdM8.5 & 11Jul2013 & 1.35 & 126/142/150 & 3AB \[tab\_MplusTeff\_sdM:log\_obs\_Xshooter\]

BT-Settl synthetic spectra {#MplusTeff_sdM:Models}
==========================

To infer the range of physical parameters (gravities i.e. $\log$(g), metallicities \[M/H\], and T$_{\rm eff}$) for our sequence of subdwarfs, we employed the BT-Settl models [@allard03a; @allard07a; @allard10a; @allard11; @allard12] available for retrieval at France Allard’s webpage[^4]. The BT-Settl models account for TiO [@plez98; @plez08] and H$_{2}$O ([@barber06a] among other opacities using the @caffau11a abundance values and mixing information for the CO$^{5}$BOLD code [@steiner07; @freytag10a]. These models are valid for a wide range of T$_{\rm eff}$ (400–8000K), gravities ($\log$(g)=2.5–6.0 dex), and metallicities (from $-$5.0 to solar). The synthetic SEDs span the wavelength range from 10Å up to 1000$\mu$m. The stellar metallicity is defined by the total iron content of a star because iron is the easiest species to measure spectroscopically. The abundance ratio \[Fe/H\] is defined as the logarithm of the ratio of a star’s iron abundance compared to that of the Sun, where $-$1.0 dex means that a star has one-tenth of the solar metallicity. The determination of the metallicity is only valid if the abundance of all elements follow the abundance of iron. However, this statement might not be totally true in the case of halo dwarfs that suffered different nucleosynthesis events.

We downloaded the spectra from the CIFIST2011 grid[^5] and considered the ranges that encompass the spectral types of the three metallicity classes: T$_{\rm eff}$=4000–2500K, gravity ($\log$g=4.5–5.5 dex), and metallicity \[M/H\] (from $-$2.5 dex to solar). These models assumes solar abundance values (Z=0.0153, Z/X=0.0209) from @caffau11a with alpha enhancement taken into account as follows: \[alpha/H\]=$+$0.2 relative to solar for \[M/H\]=$-$0.5 dex and \[alpha/H\]=$+$0.4 for lower metallicities. For direct comparison, we limited the wavelength range to 450–2500 nm and smoothed the synthetic SEDs with the Interactive Data Language (IDL) function[^6] to the spectral resolution of our X-shooter spectra.

Throughout the paper, we use the term metallicity \[Fe/H\] which is given by the BT-Settl models. We do not infer abundances or metallicities of single element but the global values given by the synthetic spectra. The former can differ from the latter as shown for a metal-poor low-mass binary [@pavlenko15]. The study of abundances of individual elements in subdwarfs is beyond the scope of this paper but will be investigated in a future publication.

Comparison: observations vs. models {#MplusTeff_sdM:Comparison}
===================================

We fitted the observed spectra with the BT-Settl SEDs with a chi-square ($\chi^2$) minimisation procedure described in Sect. \[MplusTeff\_sdM:Comparison\_chi2\]. We derived the temperature (Sect. \[MplusTeff\_sdM:Comparison\_Teff\]) and metallicity (Sect. \[MplusTeff\_sdM:Comparison\_MH\]) scales from the best model fits.

Chi-square fitting {#MplusTeff_sdM:Comparison_chi2}
------------------

We performed a $\chi^2$ fit to compare the observed spectra with those in the BT-Settl theoretical library. We considered the following ranges in temperature, gravity, and metallicity: 4000–2500K, $\log$g=4.5–6.0 dex, and \[M/H\] between $-$3.0 and 0.0 dex, as expected for old low-mass M-type dwarfs. The steps are 100K and 0.5 dex in temperatures and gravity $+$ metallicity, respectively. We ignored regions of the observed spectra strongly affected by telluric bands, in particular the 530–570 nm, 928–1010 nm, 1110–1150 nm, 1340–1460 nm, 1790–1970 nm wavelength ranges.

We shifted our observed spectra to the wavelength of the models. We calculated the heliocentric radial velocities for our sample of metal-poor M dwarfs using a set of about 15 lines (potassium, sodium, iron, and calcium) in the 610–840 nm wavelength range, the exact number depending on the quality of the spectrum and strength of the line (Table \[tab\_MplusTeff\_sdM:table\_param\]). We measured consistent shifts between these five strong lines for all sources, with dispersions of the order of a few km/s. We assume that the true error bars are set by the resolution of our X-shooter spectra (3900–6700), corresponding to radial velocity uncertainties of approximately 15–25 km/s.

Then, we minimized the $\chi^2$ value for each observed and theoretical spectrum, as:

$$\label{eq:chi2}
\chi^2 = \frac{1}{N} \sum_i\left\{ \frac{ ({\rm F}_{\rm obs,i} - A \ {\rm F}_{\rm mod,i})^2}{(\Delta{\rm F}_{\rm obs,i})^2}\right\}$$

The scale factor $A$ is calculated to minimize $\chi^2$ for each case as:

$$\label{eq:chi2b}
A = \frac{ \sum_i({\rm F}_{\rm obs,i} {\rm F}_{\rm mod,i}/ \Delta{\rm F}_{\rm obs,i}^2)}{\sum_i({\rm F}_{\rm mod,i}^2/\Delta{\rm F}_{\rm obs,i}^2)}$$

In both expressions the sum is performed over the full wavelength range. ${\rm F}_{\rm obs,i}$ and $\Delta{\rm F}_{\rm obs,i}$ are the observed values of the flux and its associated errors, respectively. ${\rm F}_{\rm mod,i}$ are the corresponding values of the theoretical spectrum.

To avoid the fact that points with small observational errors have an excessive weight in the fitting process, we calculated the average of the error values in each spectrum as:

$$\label{eq:chi2c}
|\Delta{\rm F}_{\rm obs}| = \frac{1}{N} \sum_i\Delta{\rm F}_{\rm obs,i}$$

Then, we fixed the error to be half the average for those points with smaller errors during the fitting process.

Overall, we find that the BT-Settl reproduce well the SEDs of metal-poor M dwarfs and in particular the main molecular bands. However, we noticed that some of the main atomic lines are not well reproduced: ((Figs. \[fig\_MplusTeff\_sdM:full\_XSH\_model\_lines\_sdM\], \[fig\_MplusTeff\_esdM:full\_XSH\_model\_lines\_esdM\], \[fig\_MplusTeff\_usdM:full\_XSH\_model\_lines\_usdM\]). The lines of the sodium doublet at $\sim$820 nm predicted by the BT-Settl models appear too broad for spectral types later than approx M5. The calcium lines seem too narrow for ultra-subdwarfs but look correctly reproduced for subdwarfs and extreme subdwarfs. This mis-match between observations and models yields over or under estimates of the abundances of these elements. The disappearance of these elements in other molecules (e.g. CaOH) could also explain the observed discrepancy. We note that the potassium doublet at around 760/790nm is well reproduced by the models, except for the latest spectral types ($\geq$M7) and the coolest sources (Figs. \[fig\_MplusTeff\_sdM:full\_XSH\_model\_lines\_sdM\], \[fig\_MplusTeff\_esdM:full\_XSH\_model\_lines\_esdM\], \[fig\_MplusTeff\_usdM:full\_XSH\_model\_lines\_usdM\]).

As a consequence, we opted for four fitting procedures, described below, to gauge the uncertainties on the physical parameters derived from the synthetic spectra. We describe them below:

1.  “FF” corresponds to the fit of the full SED of each subtype and metal class from 450 to 2500 nm (Figs. \[fig\_MplusTeff\_sdM:full\_XSH\_model\_FF\_sdM\]–\[fig\_MplusTeff\_sdM:full\_XSH\_model\_FF\_usdM\]).

2.  “LL” corresponds the fitting procedure of a few lines in the optical spectra (K and Na). The model spectra shown correspond to the physical parameters derived from the line fits (Figs. \[fig\_MplusTeff\_sdM:full\_XSH\_model\_LL\_sdM\]–\[fig\_MplusTeff\_sdM:full\_XSH\_model\_LL\_usdM\]).

3.  “FL”: in this case we fix the temperature derived from the full fit and adjust gravity and metallicity to converge towards the best fit of the aforementioned lines (Figs. \[fig\_MplusTeff\_sdM:full\_XSH\_model\_FL\_sdM\]–\[fig\_MplusTeff\_sdM:full\_XSH\_model\_FL\_usdM\]).

4.  “LF”: we fix the gravity and metallicity from the fits of the line and adjust the effective temperature fitting the full SED of each subtype and subclass. (Figs. \[fig\_MplusTeff\_sdM:full\_XSH\_model\_LF\_sdM\]–\[fig\_MplusTeff\_sdM:full\_XSH\_model\_LF\_usdM\]).

In general, we find that the “FF” fitting procedure reproduces best all observed spectra. Therefore, we conclude that the physical parameters derived from this option are the most probable.

We list the model-dependent physical parameters in Table \[tab\_MplusTeff\_sdM:table\_param\] and display the best fits provided by the synthetic SEDs (red lines) to observed X-shooter spectra (black lines) for each metal class in Appendix \[MplusTeff\_sdM:appendix\_model\_fits\].

We have also looked at the physical parameters derived from the model fit to the optical region of the X-shooter spectra (600–1000nm) from which the spectral classification of subdwarfs is based [@gizis97a; @lepine07c]. We find that on average the optical spectra give equal or cooler effective temperatures, lower gravites, and/or lower metallicities (Table \[tab\_MplusTeff\_sdM:table\_best\_fits\_VV\] in Appendix \[MplusTeff\_sdM:appendix\_model\_fits\]).

[@c @c @c c c c c c c c c c c c c c c@]{} & & & & SpT & RV & $\log$g & T$_{\rm eff}$ & \[Fe/H\] & Mass & RV & $\log$g & T$_{\rm eff}$ & \[Fe/H\] & Mass & RV & $\log$g & T$_{\rm eff}$ & \[Fe/H\] & Mass & km// & dex & K & dex & M$_{\odot}$ & km/s & dex & K & dex & M$_{\odot}$ & km/s & dex & K & dex & M$_{\odot}$ M0.0 & $+$122.6 & 4.5 & 3600 & $-$1.5 & 0.133 & $-$9.2 & 5.0 & 3800 & $-$1.0 & 0.275 & $+$122.6 & 4.5 & 3500 & $-$2.0 & 0.106 M0.5 & $-$45.1 & 5.0 & 3700 & $-$1.0 & 0.216 & $-$97.3 & 5.0 & 3700 & $-$1.5 & 0.153 & $-$117.1 & 5.5 & 3700 & $-$2.5 & 0.125 M1.0 & $-$33.7 & 5.0 & 3700 & $-$0.5 & 0.352 & $-$259.7 & 5.5 & 3800 & $-$0.5 & 0.421 & $-$15.9 & 5.5 & 3700 & $-$1.0 & 0.216 M1.5 & $-$78.7 & 4.5 & 3600 & $-$0.0 & 0.600 & $-$46.7 & 5.0 & 3600 & $-$1.0 & 0.178 & — & — & — & — & — M2.0 & $-$133.8 & 5.5 & 3600 & $-$0.5 & 0.272 & $+$40.6 & 5.5 & 3600 & $-$1.0 & 0.178 & — & — & — & — & — M2.5 & $-$39.7 & 5.5 & 3600 & $-$0.5 & 0.272 & — & — & — & — & — & $-$138.8 & 5.5 & 3600 & $-$1.5 & 0.133 M3.0 & $-$52.6 & 5.0 & 3500 & $-$0.0 & 0.450 & $+$35.3 & 5.5 & 3500 & $-$1.5 & 0.120 & $+$178.0 & 6.0 & 3800 & $-$0.5 & 0.421 M3.5 & $-$21.7 & 5.0 & 3400 & $-$0.5 & 0.177 & $-$52.5 & 5.5 & 3500 & $-$1.5 & 0.120 & — & — & — & — & — M4.0 & $-$67.2 & 5.0 & 3400 & $-$1.0 & 0.129 & $-$81.3 & 5.5 & 3400 & $-$1.5 & 0.110 & $-$19.8 & 4.5 & 3200 & $-$1.5 & 0.098 M4.5 & $-$470.7 & 5.5 & 3300 & $-$1.0 & 0.117 & $-$60.7 & 5.5 & 3400 & $-$1.0 & 0.129 & $-$102.5 & 5.5 & 3400 & $-$2.0 & 0.100 M5.0 & $-$31.6 & 5.0 & 3200 & $-$0.0 & 0.150 & $+$21.7 & 4.5 & 3200 & $-$1.5 & 0.098 & $+$180.0 & 5.5 & 3500 & $-$2.5 & 0.106 M5.5 & $-$12.5 & 5.5 & 3200 & $-$1.0 & 0.107 & $+$318.1 & 5.5 & 3300 & $-$2.0 & 0.098 & $-$25.1 & 4.5 & 3300 & $-$2.0 & 0.098 M6.0 & $-$87.8 & 5.5 & 3200 & $-$1.0 & 0.107 & $-$38.5 & 5.5 & 3300 & $-$2.0 & 0.098 & $+$104.8 & 5.5 & 3300 & $-$2.0 & 0.098 M6.5 & $-$57.2 & 5.5 & 2900 & $-$0.0 & 0.063 & $-$3.7 & 5.5 & 3300 & $-$2.0 & 0.098 & — & — & — & — & — M7.0 & — & 5.0 & 3000 & $-$1.0$^{a}$ & 0.096 & $-$167.1 & 5.5 & 3200 & $-$0.0 & 0.096 & — & — & — & — & — M7.5 & — & — & — & — & — & $+$191.1 & 5.0 & 3000 & $-$2.0 & 0.090 & $+$122.1 & 5.5 & 3100 & $-$2.5 & 0.092 M8.0 & $-$208.9 & 5.5 & 2900 & $-$2.0 & 0.089 & — & — & — & — & — & — & — & — & — & — M8.5 & — & — & — & — & — & $+$72.7 & 5.5 & 3000 & $-$2.0 & 0.090 & $+$85.0 & 5.5 & 3100 & $-$2.5 & 0.092 M9.5 & $+$64.7 & 5.0 & 2800 & $-$2.0 & 0.088 & — & — & — & — & — & — & — & — & — & — \[tab\_MplusTeff\_sdM:table\_param\]

Temperature scale {#MplusTeff_sdM:Comparison_Teff}
-----------------

We derived comparable T$_{\rm eff}$ intervals for all three metallicity classes (Table \[tab\_MplusTeff\_sdM:table\_param\]) fitting the full SEDs (Tables \[tab\_MplusTeff\_sdM:table\_best\_fits\_FF\] and \[tab\_MplusTeff\_sdM:table\_best\_fits\_FL\]). The T$_{\rm eff}$ range from $\sim$3800K for the earlier M subdwarfs down to $\sim$2600K for the latest spectral types. We can hardly distinguish the three classes in the T$_{\rm eff}$ vs. spectral type diagram shown in Fig. \[fig\_MplusTeff\_sdM:plot\_SpT\_Teff\] within the error bars of 100K set by the steps available in the models. We overplotted the temperature scale of field M dwarfs (solid black line in Fig. \[fig\_MplusTeff\_sdM:plot\_SpT\_Teff\])from the latest relation of @rajpurohit13, whose trend is comparable to earlier studies within error bars [@bessell91; @leggett96; @leggett00a; @testi09a]. Dwarfs with spectral types earlier than M2 are indistinguishable in the temperature parameter space. Overall, the temperatures of metal-poor M dwarfs are similar to those of solar-type M dwarfs with an offset of 200$\pm$100K towards warmer temperatures. They follow a linear trend with some spectral types being off by 100K or 200K, which may be due to the error on the spectral classification or binarity which is mainly based on a spectral index measuring the strength of the CaH and TiO bands in the optical [@lepine07c].

We note that the temperature scale of the line fitting option tends to infer lower effective temperatures by at least 100K with a similar interval for temperatures hotter than 3400K, producing ranges of 3700–2700K. The agreement is better at lower temperatures and within the uncertainty of 100K (Tables \[tab\_MplusTeff\_sdM:table\_best\_fits\_LL\] and \[tab\_MplusTeff\_sdM:table\_best\_fits\_LF\]). We also find that the fit to the optical region only yields typically lower effective temperature by 100K to 200K (Table \[tab\_MplusTeff\_sdM:table\_best\_fits\_VV\] in Appendix \[MplusTeff\_sdM:appendix\_model\_fits\]).

![T$_{\rm eff}$ as a function of spectral type for solar-metallicity M dwarfs (black diamonds with line), sdM (red dots), esdM (green triangles) and usdM (blue squares). Error bars on spectral types and model parameters are marked for sdM only for clarity purposes. Error bars on spectral type and temperatures are $\pm$0.25 and $\pm$100K, respectively. The point for the sdM7 subdwarf corresponds to LHS377 from @rajpurohit16a. []{data-label="fig_MplusTeff_sdM:plot_SpT_Teff"}](plot_subdwarfs_SpT_Teff.png){width="\linewidth"}

Gravity scale {#MplusTeff_sdM:Comparison_grav}
-------------

Subdwarfs are old low-mass stars that belong to the thick diskor halo of our Galaxy. On average, they are much older than their solar-metallicity counterparts. @monteiro06a identified several white dwarf-subdwarf systems in the thick disk and derived ages of 6–9 Gyr for two of them with M subdwarf companions. From the comparison with FGK stellar templates selected as benchmarks for the Gaia mission [@jofre14a], @scholz15b inferred a possible age of 12 Gyr for an ancient metal-poor ($-$2.0$\pm$0.2 dex) F-type star member of the Galactic halo due to its large tangential velocity. On average, we expect our sample to be older than 5 Gyr.

From the fit of the BT-Settl models to the full VIS$+$NIR spectral energy distribution of our M subdwarfs, we infer gravities of 4.5–5.5 dex for all metal classes, except for one object with $\log$(g)=6.0 dex (usdM3.0, see discussion section). However, we observe a possible trend of increasing mean gravity with lower metallicity, going from 5.0 dex for sdM to 5.5 dex for esdM and usdM (Fig. \[fig\_MplusTeff\_sdM:plot\_SpT\_logg\]). We note that the range of gravities of the CIFIST models is limited to 6.0 dex, higher gravities are desirable to corroborate this statement. We also note that the fit to the optical region only yields typically lower gravities by 0.5 to 1.0 dex (Table \[tab\_MplusTeff\_sdM:table\_best\_fits\_VV\] in Appendix \[MplusTeff\_sdM:appendix\_model\_fits\]).

If we average the gravities for the metallicities derived from the model fit independently from the metal class (i.e. sdM, esdM, usdM), we observe that targets with metallicities of $-$0.5 dex have on average lower gravities ($\sim$4.9 dex) than more metal-poor objects where mean gravities lie between 5.2 and 5.3 dex. The difference in gravity between field M dwarfs and M subdwarfs is below our error bar of 0.5 dex, while the difference between metallicities is five times smaller than our error bars.

![Gravity as a function of spectral type for sdM (red dots), esdM (green triangles) and usdM (blue squares). Error bars on spectral type and gravity are $\pm$0.5 and $\pm$0.5 dex, respectively. The point for the sdM7 subdwarf corresponds to LHS377 from @rajpurohit16a. []{data-label="fig_MplusTeff_sdM:plot_SpT_logg"}](plot_subdwarfs_SpT_logg.png){width="\linewidth"}

![Metallicity as a function of spectral type for sdM (red dots), esdM (green triangles) and usdM (blue squares). Error bars on spectral type and metallicity are $\pm$0.5 and $\pm$0.5 dex, respectively. []{data-label="fig_MplusTeff_sdM:plot_SpT_FeH"}](plot_subdwarfs_SpT_FeH.png){width="\linewidth"}

Metallicity scale {#MplusTeff_sdM:Comparison_MH}
-----------------

Our work is extending the current metallicity scale of M dwarfs to metallicities below $-$0.5 dex with an accuracy on the calibration of the order of 0.25–0.5 dex. The classification is available in the optical for subdwarfs [@gizis97a; @lepine07c; @jao08; @savcheva14; @kesseli17a] but this is the first time this is attempted for a large sample of M0–M9 dwarfs [see also @rajpurohit16a]. The determination of the metallicity scale of subdwarfs is key for several reasons. First, the range of metallicities for M subdwarfs is poorly constrained up to now for these objects that represent the first generation of stars and are key sources to study the chemical evolution of our Galaxy. On the other hand, M dwarfs are becoming popular to search for low-mass planets by the radial velocity and transit techniques, leading independent groups to look at their metallicity. Nonetheless, all the studies referenced in the introduction focussed on M dwarfs with metallicity slightly below solar with calibrations accurate to $<$0.15 dex either photometrically [@bonfils05a; @johnson09a; @schlaufman10a; @neves12; @hejazi15; @dittmann16] or spectroscopically [@woolf05; @woolf06; @bean06a; @woolf09; @rojas_ayala10; @rojas_ayala12; @muirhead12; @terrien12a; @onehag12; @neves13; @neves14; @hejazi15; @newton15a; @lindgren16a].

The number of M dwarf hosts below 0.5 M$_{\odot}$ and metallicities lower than $-$0.5 dex is extremely small ($\leq$0.2%) compared to the 3396 confirmed planets[^7]. Only three metal-poor M dwarfs have one or several planets: Kapteyn [sdM1.0; Fe/H=$-$0.86 dex; @anglada_escude14; @robertson15a], GJ667 [K3V$+$K5V; Fe/H=$-$0.55 dex; @feroz14; @anglada_escude13a; @delfosse13], and Kepler1124 [Fe/H=$-$0.59 dex; @morton16a]. Another four Kepler M stars with masses in the range 0.5–0.6 M$_{\odot}$ and metallicities between $-$0.5 and $-$1.0 harbour planets.

We present VLT/X-shooter spectra at a resolution of 5400 and 3900 in the VIS and NIR arms, respectively. We estimate metallicity that rely on models and synthetic spectra whose steps are 0.5 dex, which we set as our error bars. Overall, we find that the overall SEDs of subdwarfs, extreme subdwarfs, and ultra-subdwarfs are best reproduced by metallicities between solar and $-$1.0 dex, $-$1.0 and $-$2.0 dex, and $-$1.0 and $-$2.5 dex, respectively (Fig. \[fig\_MplusTeff\_sdM:plot\_SpT\_FeH\]). We note that a few sdM have solar metallicities, including the sdM6.5 (1610$-$0040), a known astrometric binary [@koren16] with a mix of spectral features typical of both L subdwarfs and solar-type M dwarfs [@lepine03b; @reiners06a; @cushing06]. We also emphasise that the two coolest subdwarfs (sdM8 and sdM9.5) in our sample have on average lower metallicities than subdwarfs earlier than sdM7, suggesting saturation of the metallicity index [@lepine07c] used in the classification of subdwarf [@zhang17a]. We conclude that there is a trend towards lower mean metallicity from subdwarfs ($-$0.5$\pm$0.5 dex) to extreme subdwarfs ($-$1.5$\pm$0.5 dex), and ultra-subdwarfs ($-$2.0$\pm$0.5 dex), consistent with the original definition of these three metal classes. However, we observe variations from one object to the other, preventing assigning a given M/H for each metal class. We note that the metallicity scale of the line fitting option differs significantly from the fit of the SEDs, producing lower metallicities by at least 1.0 dex. (Tables \[tab\_MplusTeff\_sdM:table\_best\_fits\_LL\] and \[tab\_MplusTeff\_sdM:table\_best\_fits\_LF\]). We find the same trend if we consider only the optical range (600–1000 nm) for our fitting procedure.

We compared our global results to the recent analysis of @rajpurohit16a also based on VLT/X-shooter spectra but for a much smaller sample of subdwarfs: six sdM (five sdM0.5–M3 and one sdM7), two esdM (esdM2 and esdM4), and a usdM4.5. In their Table 2, they list two possible fits, which usually differ by either 100K or 0.5 dex in gravity or metallicity. Our physical parameters agree with their results within 1–2$\sigma$ of the steps of the synthetic SEDs (Table \[tab\_MplusTeff\_sdM:table\_param\]). The difference can be explained by the uncertainties on the spectral types, typically 0.5 sub-type. We conclude that both T$_{\rm eff}$ vs. spectral type relations are consistent within current error bars on observational and theoretical sides. Moreover, as stated in @rajpurohit16a, these results are fully consistent with the physical parameters derived from higher resolution optical spectroscopy [@rajpurohit14].

We can also compare our work to the physical parameters of the metal-poor binary G224-58AB composed of a esdK5 and a esdM5.5. @pavlenko15 derived the temperature and gravity for the secondary (T$_{\rm eff}$=3200$\pm$100 K, $\log$g=5.0$\pm$0.5), and inferred the metallicity from the primary (\[Fe/H\]=$-$1.92 dex). Their parameters are in good agreement with our values for the esdM5.5 (SDSSJ09030795$+$0842432) in our sample: T$_{\rm eff}$=3300$\pm$100K, $\log$g=5.5$\pm$0.5 dex, and \[Fe/H\]=$-$1.5$\pm$0.5 dex (Table \[tab\_MplusTeff\_sdM:table\_param\]). Their abundance analysis suggests that many elements (e.g. calcium; \[Ca/H\]=$-$1.39$\pm$0.03) are over-abundant compared to iron. We do also find that, although the BT-Settl SEDs reproduce well the molecular bands of the observed spectra, they fail to fit the atomic lines of many elements like Fe, K, Na, and Ca. In other words, the atomic lines from the BT-Settl models are too broad and over-estimate the abundances of single elements (see Sect. \[MplusTeff\_sdM:Comparison\_Abund\]). The disappearance of these elements in other molecules (e.g. CaOH) could also explain the observed discrepancy.

Masses {#MplusTeff_sdM:Comparison_Mass}
------

We inferred model-dependent masses for our sample of subdwarfs from their temperatures looking at the predictions of the NextGen models [@baraffe97], assuming ages of 10 Gyr for these old objects. Although this approach is not correct due to the different inputs physics in the NextGen and BT-Settl grids [computation available on France Allard’s webpage; @baraffe15], it provides estimates on the masses of these low-metallicity M dwarfs. We derived masses below 0.35 M$_{\odot}$ for the most massive M subdwarfs down to $\sim$0.087 M$_{\odot}$ for the coolest objects in our sample, i.e. close to the stellar/substellar boundary with uncertainties of the order of 10% (Table \[tab\_MplusTeff\_sdM:table\_param\]). We note that the gravities quoted by the @baraffe97 models are in the range $\log$(g)=5.0–5.5 dex, consistent with the aforementioned gravities derived from the synthetic SEDs within the error bars of 0.5 dex.

                Wavelength range                    Elements       \# lines
  --------------------------------------------- ---------------- ------------
                   5750–5995Å                    Na, Ti, Ca, Fe   2, 1, 1, 1
                   7640–7730Å                          K              2
                   8080–8350Å                        Na, Fe          3, 1
                   8300–8850Å                      Ca, Ti, Fe      3, 10, 7
   \[MplusTeff\_sdM:elements\_for\_abundance\]                   

  : Spectral regions, elements, and their numbers of lines considered to derive abundances of our sample of subdwarfs

[@l @c @c @c @c @c @c@]{} SpT & Model & Na & K & Ca & Ti & Fe sdM0.5 & 3700-4.5-1.0 & 0.3$_{-0.2}^{+0.3}$ & 0.7$_{-0.3}^{+0.4}$ & 1.2$_{-0.0}^{+0.0}$ & 0.9$_{-0.1}^{+0.1}$ & 0.9$_{-0.0}^{+0.1}$ sdM1.0 & 3700-5.0-0.5 & 0.2$_{-0.2}^{+0.2}$ & 0.3$_{-0.3}^{+0.3}$ & 0.5$_{-0.2}^{+0.1}$ & 0.4$_{-0.1}^{+0.1}$ & 0.4$_{-0.1}^{+0.1}$ sdM1.5$^{*}$ & 3400-4.5-1.5 & 0.4$_{-0.1}^{+0.1}$ & 0.6$_{-0.2}^{+0.2}$ & 1.0$_{-0.0}^{+0.0}$ & 0.5$_{-0.1}^{+0.1}$ & 0.5$_{-0.1}^{+0.1}$ sdM2.0$^{*}$ & 3500-4.5-1.0 & 0.7$_{-0.2}^{+0.2}$ & 1.0$_{-0.3}^{+0.3}$ & 0.9$_{-0.0}^{+0.0}$ & 0.5$_{-0.1}^{+0.1}$ & 0.5$_{-0.1}^{+0.1}$ sdM2.5$^{*}$ & 3500-4.5-1.0 & 0.6$_{-0.2}^{+0.2}$ & 0.9$_{-0.3}^{+0.3}$ & 0.7$_{-0.0}^{+0.0}$ & 0.6$_{-0.1}^{+0.1}$ & 0.5$_{-0.1}^{+0.1}$ sdM3.0 & 3500-5.0-0.0 & $-$0.2$_{-0.1}^{+0.1}$ & 0.6$_{-0.2}^{+0.2}$ & 0.2$_{-0.0}^{+0.0}$ & 0.0$_{-0.1}^{+0.1}$ & 0.1$_{-0.0}^{+0.0}$ sdM3.5 & 3400-5.0-0.5 & 0.2$_{-0.2}^{+0.2}$ & 0.3$_{-0.3}^{+0.2}$ & 0.3$_{-0.0}^{+0.1}$ & 0.3$_{-0.2}^{+0.2}$ & 0.1$_{-0.1}^{+0.1}$ sdM4.0 & 3400-5.5-0.5 & $-$0.1$_{-0.2}^{+0.3}$ & 0.2$_{-0.3}^{+0.3}$ & 0.8$_{-0.0}^{+0.0}$ & 0.4$_{-0.1}^{+0.2}$ & 0.2$_{-0.1}^{+0.1}$ sdM4.5 & 3100-4.5-1.5 & 0.5$_{-0.2}^{+0.2}$ & 0.6$_{-0.3}^{+0.3}$ & 0.6$_{-0.0}^{+0.0}$ & 0.9$_{-0.3}^{+0.3}$ & 0.4$_{-0.1}^{+0.1}$ sdM5.0$^{*}$ & 3200-5.5-0.0 & 0.5$_{-0.2}^{+0.2}$ & 0.3$_{-0.3}^{+0.4}$ & 0.0$_{-0.0}^{+0.0}$ & 0.3$_{-0.2}^{+0.3}$ & 0.1$_{-0.1}^{+0.2}$ sdM5.5 & 3200-5.5-1.0 & 0.0$_{-0.2}^{+0.2}$ & 0.1$_{-0.3}^{+0.3}$ & 0.4$_{-0.0}^{+0.2}$ & 0.6$_{-0.2}^{+0.2}$ & 0.1$_{-0.1}^{+0.1}$ sdM6.0 & 3000-4.5-1.5 & 0.6$_{-0.2}^{+0.2}$ & 0.3$_{-0.3}^{+0.4}$ & 1.4$_{-0.0}^{+0.0}$ & 0.7$_{-0.2}^{+0.3}$ & 0.4$_{-0.1}^{+0.2}$ sdM6.5$^{*}$ & 2900-5.5-0.0 & 0.2$_{-0.4}^{+0.5}$ & 0.4$_{-0.5}^{+0.6}$ & 0.0$_{-0.0}^{+0.0}$ & 0.0$_{-0.2}^{+0.3}$ & 0.0$_{-0.1}^{+0.2}$ sdM8.0 & 2800-5.0-2.5 & 0.4$_{-0.2}^{+0.2}$ & 0.3$_{-0.2}^{+0.2}$ & 0.7$_{-0.0}^{+0.0}$ & 0.6$_{-0.2}^{+0.2}$ & 0.0$_{-0.1}^{+0.1}$ sdM9.5 & 2600-4.5-2.5 & 0.6$_{-0.2}^{+0.2}$ & 0.4$_{-0.2}^{+0.2}$ & 0.5$_{-0.0}^{+0.0}$ & 0.8$_{-0.2}^{+0.2}$ & 0.5$_{-0.1}^{+0.1}$ esdM0.0 & 3600-4.5-1.5 & 0.2$_{-0.2}^{+0.2}$ & 0.4$_{-0.2}^{+0.3}$ & 0.6$_{-0.0}^{+0.0}$ & 0.6$_{-0.1}^{+0.2}$ & 0.3$_{-0.0}^{+0.1}$ esdM0.5 & 3600-4.5-1.5 & 0.2$_{-0.2}^{+0.2}$ & 0.6$_{-0.2}^{+0.3}$ & 0.5$_{-0.0}^{+0.0}$ & 0.6$_{-0.1}^{+0.2}$ & 0.3$_{-0.0}^{+0.1}$ esdM1.0 & 3600-4.5-1.5 & 0.3$_{-0.2}^{+0.2}$ & 0.6$_{-0.2}^{+0.3}$ & 0.6$_{-0.0}^{+0.0}$ & 0.7$_{-0.1}^{+0.2}$ & 0.1$_{-0.0}^{+0.1}$ esdM1.5 & 3400-4.5-1.5 & 0.2$_{-0.2}^{+0.2}$ & 0.4$_{-0.2}^{+0.3}$ & 0.7$_{-0.0}^{+0.0}$ & 0.7$_{-0.1}^{+0.2}$ & 0.4$_{-0.0}^{+0.1}$ esdM2.0 & 3400-4.5-1.5 & 0.3$_{-0.2}^{+0.2}$ & 0.5$_{-0.2}^{+0.3}$ & 0.8$_{-0.0}^{+0.0}$ & 0.9$_{-0.1}^{+0.2}$ & 0.5$_{-0.0}^{+0.1}$ esdM3.0 & 3400-5.0-1.5 & 0.2$_{-0.2}^{+0.2}$ & 0.5$_{-0.2}^{+0.2}$ & 0.7$_{-0.0}^{+0.0}$ & 0.9$_{-0.2}^{+0.2}$ & 0.4$_{-0.1}^{+0.1}$ esdM3.5 & 3400-5.0-1.5 & 0.0$_{-0.2}^{+0.2}$ & 0.4$_{-0.2}^{+0.2}$ & 0.4$_{-0.0}^{+0.0}$ & 0.7$_{-0.2}^{+0.2}$ & 0.2$_{-0.1}^{+0.1}$ esdM4.0 & 3200-4.5-2.0 & 0.5$_{-0.2}^{+0.2}$ & 0.7$_{-0.2}^{+0.2}$ & 0.4$_{-0.0}^{+0.0}$ & 0.9$_{-0.2}^{+0.2}$ & 0.4$_{-0.1}^{+0.1}$ esdM4.5 & 3200-4.5-1.5 & 0.6$_{-0.2}^{+0.2}$ & 0.4$_{-0.2}^{+0.2}$ & 0.9$_{-0.0}^{+0.0}$ & 0.8$_{-0.2}^{+0.2}$ & 0.4$_{-0.1}^{+0.1}$ esdM5.0 & 3200-4.5-1.5 & 0.4$_{-0.2}^{+0.2}$ & 0.7$_{-0.2}^{+0.3}$ & 0.7$_{-0.0}^{+0.0}$ & 0.9$_{-0.2}^{+0.2}$ & 0.5$_{-0.1}^{+0.1}$ esdM5.5 & 3100-4.5-2.0 & 0.6$_{-0.2}^{+0.2}$ & 0.8$_{-0.2}^{+0.2}$ & 0.8$_{-0.0}^{+0.0}$ & 1.2$_{-0.3}^{+0.3}$ & 0.7$_{-0.1}^{+0.2}$ esdM6.0 & 3200-5.0-2.0 & 0.1$_{-0.2}^{+0.2}$ & 0.6$_{-0.2}^{+0.2}$ & 0.4$_{-0.0}^{+0.0}$ & 0.8$_{-0.2}^{+0.2}$ & 0.4$_{-0.1}^{+0.1}$ esdM6.5 & 3100-4.5-2.0 & 0.3$_{-0.3}^{+0.3}$ & 0.7$_{-0.2}^{+0.2}$ & 0.7$_{-0.0}^{+0.0}$ & 1.0$_{-0.3}^{+0.3}$ & 0.4$_{-0.1}^{+0.1}$ esdM7.5 & 3000-5.0-2.0 & 0.2$_{-0.2}^{+0.2}$ & 0.6$_{-0.2}^{+0.2}$ & 0.7$_{-0.0}^{+0.0}$ & 0.8$_{-0.2}^{+0.2}$ & 0.3$_{-0.1}^{+0.1}$ esdM8.5 & 2800-4.5-2.5 & 0.4$_{-0.2}^{+0.2}$ & 0.6$_{-0.2}^{+0.2}$ & 0.6$_{-0.0}^{+0.0}$ & 0.8$_{-0.2}^{+0.3}$ & 0.1$_{-0.1}^{+0.1}$ usdM0.0 & 3500-4.5-2.5 & 0.5$_{-0.3}^{+0.4}$ & 1.2$_{-0.4}^{+0.5}$ & 1.2$_{-0.0}^{+0.0}$ & 0.6$_{-0.2}^{+0.3}$ & 0.2$_{-0.2}^{+0.2}$ usdM0.5$^{*}$ & 3600-5.0-2.5 & $-$0.4$_{-0.2}^{+0.3}$ & 0.6$_{-0.4}^{+0.4}$ & 0.4$_{-0.0}^{+0.0}$ & 0.5$_{-0.2}^{+0.2}$ & 0.1$_{-0.1}^{+0.1}$ usdM1.0 & 3600-5.0-1.5 & $-$0.2$_{-0.2}^{+0.3}$ & 0.6$_{-0.4}^{+0.4}$ & 0.5$_{-0.0}^{+0.0}$ & 0.3$_{-0.2}^{+0.2}$ & 0.2$_{-0.1}^{+0.1}$ usdM2.5 & 3400-4.5-2.0 & 0.1$_{-0.2}^{+0.2}$ & 0.8$_{-0.4}^{+0.4}$ & 1.0$_{-0.0}^{+0.0}$ & 0.7$_{-0.2}^{+0.2}$ & 0.8$_{-0.1}^{+0.1}$ usdM3.0 & 3400-4.5-2.0 & $-$0.2$_{-0.2}^{+0.2}$ & 1.2$_{-0.4}^{+0.4}$ & 0.9$_{-0.0}^{+0.0}$ & 0.5$_{-0.2}^{+0.4}$ & 0.3$_{-0.1}^{+0.1}$ usdM4.0$^{*}$ & 3500-5.5-2.0 & 0.1$_{-0.2}^{+0.3}$ & 0.8$_{-0.3}^{+0.4}$ & 0.9$_{-0.0}^{+0.0}$ & 0.8$_{-0.2}^{+0.2}$ & 0.5$_{-0.1}^{+0.1}$ usdM4.5 & 3300-5.0-2.0 & $-$0.1$_{-0.2}^{+0.3}$ & 0.6$_{-0.3}^{+0.3}$ & 0.5$_{-0.0}^{+0.0}$ & 0.5$_{-0.2}^{+0.2}$ & 0.3$_{-0.1}^{+0.1}$ usdM5.0 & 3400-5.5-2.5 & $-$0.4$_{-0.2}^{+0.2}$ & 0.6$_{-0.3}^{+0.3}$ & 0.6$_{-0.0}^{+0.0}$ & 0.5$_{-0.2}^{+0.2}$ & 0.3$_{-0.1}^{+0.1}$ usdM6.0 & 3200-5.0-2.0 & 0.1$_{-0.1}^{+0.2}$ & 1.0$_{-0.3}^{+0.3}$ & 0.4$_{-0.0}^{+0.0}$ & 0.6$_{-0.1}^{+0.1}$ & 0.3$_{-0.1}^{+0.1}$ usdM7.5 & 3000-5.0-2.5 & $-$0.1$_{-0.2}^{+0.2}$ & 1.0$_{-0.3}^{+0.3}$ & 0.4$_{-0.1}^{+0.1}$ & 0.6$_{-0.1}^{+0.1}$ & 0.2$_{-0.1}^{+0.2}$ usdM8.5 & 3000-5.5-2.5 & $-$0.2$_{-0.2}^{+0.2}$ & 0.8$_{-0.3}^{+0.3}$ & 0.3$_{-0.1}^{+0.1}$ & 0.4$_{-0.2}^{+0.2}$ & 0.0$_{-0.1}^{+0.2}$ \[MplusTeff\_sdM:results\_abundance\]

![image](plot_abundances_subdwarfs_Yakiv_Fe_Ti_scatter.png){width="0.48\linewidth"} ![image](plot_abundances_subdwarfs_Yakiv_Fe_Ca_scatter.png){width="0.48\linewidth"} ![image](plot_abundances_subdwarfs_Yakiv_Fe_K_scatter.png){width="0.48\linewidth"} ![image](plot_abundances_subdwarfs_Yakiv_Fe_Na_scatter.png){width="0.48\linewidth"} ![image](plot_abundances_subdwarfs_Yakiv_Na_K_scatter.png){width="0.48\linewidth"}

Abundances {#MplusTeff_sdM:Comparison_Abund}
----------

We decided to work with the temperatures, gravities, and metallicities derived from the best fits to the optical regions only (Table \[tab\_MplusTeff\_sdM:table\_best\_fits\_VV\] in Appendix \[MplusTeff\_sdM:appendix\_model\_fits\]) to derive the abundances of several elements (Table \[MplusTeff\_sdM:elements\_for\_abundance\]). The relatively low resolution and reduced signal-to-noise of the observed spectra limit the accuracy of our results. Moreover, we work here with metal-deficient stars, in which spectra are not critically affected by blending effects. We carried out the minimisation procedure using the PHOENIX model atmospheres to compute synthetical spectra with the WITA program [@pavlenko97a]. In these computations, we accounted for the main molecular opacity sources, as described in @pavlenko15 and @pavlenko14. We employed the atomic line information from the the VALD2 and VALD3 databases [@kupka99; @ryabchikova11]. We selected a few spectral ranges with well defined atomic lines and fitted them in framework of the LTE approach to determine abundances of several elements listed in Table \[MplusTeff\_sdM:elements\_for\_abundance\].

To determine the abundances, we compared the residuals of the fluxes and reduced to the local continuum or pseudo-continuum of the observed spectra. We determined these continua/pseudo-continua for all spectral ranges given in Table \[MplusTeff\_sdM:elements\_for\_abundance\]. We carried out the computations for 20 points abundance grid with a step 0.1 dex around the mean abundance for each metal and spectral subclass. The abundances correspond to over-abundances if they are positive, fixing the iron abundances to the metallicity derived from the model fit of the optical region, assuming a solar abundance of iron of $-$4.55 dex [@asplund09].

When several lines are present in a given spectral range, we averaged the values of each abundance. We give the uncertainties on the abundances rounded to the nearest integer for a range of $\pm$100K in effective temperature, which represents the error on our model fits (and the step of the models). We note that the sodium, potassium, and neutral calcium lines are the most sensitive to small changes in effective temperature due to the low ionisation potentials. We estimate the formal accuracy of the abundance determination to be $\pm$0.1 dex due to several uncertainties in the procedure, such as low signal-to-noise ratio and the determination of the levels of the continuum and pseudo-continuum. We list the final abundances of five elements (Na, K, Ca, Ti, and Fe) with their uncertainties in Table \[MplusTeff\_sdM:results\_abundance\]. Some of the stars, marked with an asterisk, have low signal-noise spectra so the abundances should be interpreted with caution.

We should note that any significant changes in the abundance of alkali metals affect the fluxes of the continuum, hence, the strength of the lines. Alkali metals (Na, K, Ca, Mg) are known donors of free electrons in atmospheres of late-type stars. In our case, we re-computed the continuum fluxes for all the abundances, so, in a first approach, we accounted for the effect of opacity changes. However, these changes of abundances may affect the temperature structure of the model atmosphere, changes not accounted for because we employed model atmospheres with a fixed temperature structure.

Our abundance analysis was performed for the model parameters obtained from the fits to observed SEDs (Section \[MplusTeff\_sdM:Models\]). Furthermore, resolution of the fitted spectra was not high enough to get high quality results. On the second hand, we work here with metal-deficient stars, in which spectra are not critically affected by blending effects. We determined a few spectral ranges with well defined atomic lines and fitted them in framework of the LTE approach. Despite all factors constraining the accuracy of our analysis we get a few confident enough results:

-   we see a shift of Ti abundance distribution toward larger metallicities with respect to Fe for the lowest metallicities (top left panel of Fig. \[fig\_MplusTeff\_sdM:hists\_abundances\]).

-   we observe a Ca over-abundance in the atmospheres of all subdwarfs (top right panel of Fig. \[fig\_MplusTeff\_sdM:hists\_abundances\]). This result agrees with the known enhancement of $\alpha$ elements in the atmospheres of halo dwarfs [e.g. @francois86a; @nissen94a; @gratton94a; @fuhrmann95a].

-   we find that K tends to be over-abundant at higher metallicities, opposite effect to Na (middle panels of Fig. \[fig\_MplusTeff\_sdM:hists\_abundances\]). This difference increases with lower metallicity and is most notable for ultra-subdwarfs. Perhaps, these elements have different chemical histories. The difference is well seen in the comparison plot of the distribution of both species where the three metal classes are fairly well separated (bottom panel of Fig. \[fig\_MplusTeff\_sdM:hists\_abundances\].

-   we cannot describe the abundances in the atmospheres of our targets with one parameter metallicity (Table \[MplusTeff\_sdM:results\_abundance\] and Fig. \[fig\_MplusTeff\_sdM:hists\_abundances\]).

Discussion {#MplusTeff_sdM:discussion}
==========

We observe that on average the optical range of the subdwarf spectra yields cooler temperatures, lower gravities, and metallicities. Hence, the availability of the near-infrared slope is quite important to determine the physical parameters of the three metal classes and break down the temperature/metallicity degeneracy present in the analysis of the sole visible range. The temperature sequence is well determined for all metal class, with the earliest spectral types being the warmest cases. The metallicity is on average lower for the ultra-subdwarfs, with all three metal class being more metal poor than solar as expected. Those results are, however, global with the physical parameters sensitive to steps of the models in temperature, gravity, and metallicity. Smaller changes in those parameters are most likely limited by the quality (signal-to-noise ratio) and resolution of the X-shooter spectra.

We checked the few cases where our best fits suggest solar metallicity. There are four sdM in this case (including the sdM6.5 specifically treated below) and only one esdM (esdM7.0) also discussed below. For the sdM1.5 we find that the best “FF” fits indicate solar metallicity while the other procedures suggest $-$0.5 dex. The inspection of the width of the lines (K, Na, Ca) is inconclusive to decide on one or the other metallicity (Fig. \[fig\_MplusTeff\_sdM:full\_XSH\_model\_lines\_sdM\]). For the sdM3.0, all four fits are identical and suggest solar metallicity while the third best fit of the “FF” procedure yields $-$0.5 dex. The case of sdM5.0 indicates solar metallicity too but all other fits suggest $-$0.5 dex, confirmed by the width of the sodium and potassium lines, which advocate metallicity lower than solar with a temperature 3200K. In the case of these three subdwarfs, we conclude that they might be peculiar somehow and require further investigation with better quality data.

We also reviewed the four extreme subdwarfs (esdM1.0, esdM1.5, esdM2.0, and esdM4.5) with differences of 200K or more in temperature and $\geq$ 1.0 dex in metallicity comparing the four fitting procedure described in Section \[MplusTeff\_sdM:Comparison\_chi2\]. We note that the three best fits of the “FF” procedure yield results within the step of the models. Therefore, we inspected the sodium, potassium, and calcium lines where we noticed that the best model fits occurred for the lowest metallicity values in all cases (Fig. \[fig\_MplusTeff\_esdM:full\_XSH\_model\_lines\_esdM\]).

Finally, we observe four notable outliers discussed below after checking the best fits derived from the different procedures. We emphasise that we obtained one single spectrum per target.

-   [*[sdM0.0]{}*]{} is not included in our abundance analysis because the sodium and potassium lines are clearly resolved in our X-shooter spectrum. We confirm this target as a spectroscopic binary, which will be discussed in a separate paper. Any fit to spectral lines and abundance analysis on the spectrum taken at this specific epoch is therefore flawed.

-   [*[sdM6.5]{}*]{} (1610$-$0040) is a known astrometric binary [@koren16] with a mix of spectral features typical of both L subdwarfs and solar-type M dwarfs [@lepine03b; @reiners06a; @cushing06]. We derive a temperature of 2900K with a gravity of 5.5 dex and solar metallicity with a reasonable “FF” model fit (Fig. \[fig\_MplusTeff\_sdM:full\_XSH\_model\_FF\_sdM\]).

-   [*[esdM7.0]{}*]{} show solar metallicity in the case of the full fitting procedure but lower metallicities with the other three cases. We inspected the sodium, potassium, and calcium lines of this object and conclude that the lines are broader than model predictions at solar metallicity, favouring the metal poor solution. (Fig. \[fig\_MplusTeff\_esdM:full\_XSH\_model\_lines\_esdM\]). We note that this object has a low quality spectrum too.

-   [*[usdM3.0]{}*]{} exhibits a large difference when inspecting the best three chi$^{2}$ fits using the “FF” procedure, with variations of up to 200K in temperature and 2.0 dex in metallicity. These differences are larger than any other object in our sample. We inspected the width and depth of the main sodium and potassium lines and find that they appear shallower with a potential double peak, which may indicate binarity (Fig. \[fig\_MplusTeff\_usdM:full\_XSH\_model\_lines\_usdM\]). However, we obtained one single spectrum for this source so we cannot exclude other phenomenon like rotation, flare activity or spots that can affect our results. A few additional spectra with a minimum spectral resolution of 10000 are required to confirm this possibility, which would explain the large variations in the determination of the physical parameters.

Conclusions {#MplusTeff_sdM:conclusions}
===========

Our atlas of VLT/X-shooter 0.45–2.5 $\mu$m moderate-resolution spectra represents an important database to classify metal-poor subdwarfs and has a legacy value for future large-scale surveys [WEAVE, 4MOST, LSST; @dalton12; @dalton14; @deJong14a; @ivezic08a] and space missions to come such as the James Webb Space Telescope [@gardner09] and Euclid [@mellier16a]. We derived radial velocities for all subdwarfs from the shift of the strongest optical lines. We inferred physical parameters (metallicities, temperatures, and gravities) for 43 metal-poor M dwarf by comparing their spectral energy distributions over the 450–2500nm range to the latest BT-Settl synthetic spectra. The main results of our analysis are:

-   the best gravity range for M subdwarfs is $\log$(g)=5.0–5.5 dex.

-   the metallicities inferred from the BT-Settl models for subdwarfs, extreme subdwarfs, and ultra-subdwarfs are $-$0.5, $-$1.5, and $-$2.0 dex with errors of 0.5 dex, respectively.

-   the ranges in T$_{\rm eff}$ for subdwarfs, extreme subdwarfs, and ultra-subdwarfs are comparable and lie in the intervals 3700–2600K, 3800–2900K, and 3700–2900K with uncertainties of 100K, respectively.

-   the Ca and Ti elements show an over-abundance while Na behaves in an opposite manner when compared to the iron abundance.

Improvements in the determination of the physical parameters and abundances of metal-poor low-mass dwarfs require refined and uniform/complete model atmosphere grids to improve the fits. More advanced procedures are needed to improve the quality of the fits to observed SEDs treating atomic lines in a self-consistent approach, with model atmospheres and spectra are computed for one set of input parameters. Models should take into account the enhancement of C/O and improve the modelling of single lines updating abundances of the various elements present in cool atmospheres. To truly determine the physical parameters of M subdwarfs and test evolutionary models at low metallicity, the discovery of metal-poor low-mass transiting eclipsing binaries is key.

NL was funded by the Ramón y Cajal fellowship number 08-303-01-02, and supported by the grants numbers AYA2010-19136 and AYA2015-69350-C3-2-P from Spanish Ministry of Economy and Competitiveness (MINECO). We thank Victor Béjar, Yakiv Pavlenko, and ZengHua Zhang for constructive comments on this work. The research leading to these results has received funding from the French Programme National de Physique Stellaire and the Programme National de Plan- etologie of CNRS (INSU). FA thanks financial support from the Fundación Jesús Serra for a 2 month stay (Jan–Feb 2015) as a visiting professor at the Instituto de Astrofísica de Canarias (IAC) in Tenerife.

This work is based on observations collected with X-shooter on the VLT at the European Southern Observatory, Chile, under programmes 089.C-0140(A), 091.C-0264(A), 092.D-0600(A), and 093.C-0610(A).

This research has made use of the Simbad and Vizier databases, operated at the Centre de Données Astronomiques de Strasbourg (CDS), and of NASA’s Astrophysics Data System Bibliographic Services (ADS).

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss.org. SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU) / University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatory of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional / MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.

Model fit to VLT/X-shooter spectra {#MplusTeff_sdM:appendix_model_fits}
==================================

![image](sdM_allfits_FF.png){width="\linewidth"}

![image](esdM_allfits_FF.png){width="\linewidth"}

![image](usdM_allfits_FF.png){width="\linewidth"}

![image](sdM_allfits_LL.png){width="\linewidth"}

![image](esdM_allfits_LL.png){width="\linewidth"}

![image](usdM_allfits_LL.png){width="\linewidth"}

![image](sdM_allfits_FL.png){width="\linewidth"}

![image](esdM_allfits_FL.png){width="\linewidth"}

![image](usdM_allfits_FL.png){width="\linewidth"}

![image](sdM_allfits_LF.png){width="\linewidth"}

![image](esdM_allfits_LF.png){width="\linewidth"}

![image](usdM_allfits_LF.png){width="\linewidth"}

![image](sdM_lines2.png){width="0.90\linewidth"}

![image](esdM_lines2.png){width="0.90\linewidth"}

![image](usdM_lines2.png){width="\linewidth"}

Tables with physical parameters of subdwarfs {#MplusTeff_sdM:appendix_tables}
============================================

[c c c c c c c c]{} SpT & Range & T$_{\rm eff}$ & $\log$g & M/H & chi$^{2}$ & Factor & Model\
sdM0.0 & FF & 3600 & 4.5 & -2.0 & 1.336 & 2.263e-22 & lte036.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat sdM0.5 & FF & 3700 & 5.0 & -1.0 & 72.07 & 1.782e-21 & lte037.0-5.0-1.0a+0.4.BT-Settl.spec.7.dat sdM1.0 & FF & 3700 & 5.0 & -0.5 & 67.22 & 1.609e-21 & lte037.0-5.0-0.5a+0.2.BT-Settl.spec.7.dat sdM1.5 & FF & 3600 & 4.5 & -0.0 & 66.4 & 3.168e-22 & lte036.0-4.5-0.0a+0.0.BT-Settl.spec.7.dat sdM2.0 & FF & 3600 & 5.5 & -0.5 & 46.01 & 9.281e-22 & lte036.0-5.5-0.5a+0.2.BT-Settl.spec.7.dat sdM2.5 & FF & 3600 & 5.5 & -0.5 & 35.09 & 7.689e-22 & lte036.0-5.5-0.5a+0.2.BT-Settl.spec.7.dat sdM3.0 & FF & 3500 & 5.0 & -0.0 & 88.51 & 2.208e-21 & lte035.0-5.0-0.0a+0.0.BT-Settl.spec.7.dat sdM3.5 & FF & 3400 & 5.0 & -0.5 & 161.6 & 3.916e-21 & lte034.0-5.0-0.5a+0.2.BT-Settl.spec.7.dat sdM4.0 & FF & 3400 & 5.0 & -1.0 & 58.22 & 1.54e-21 & lte034.0-5.0-1.0a+0.4.BT-Settl.spec.7.dat sdM4.5 & FF & 3300 & 5.5 & -1.0 & 59.07 & 2.072e-22 & lte033.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat sdM5.0 & FF & 3200 & 5.0 & -0.0 & 62.52 & 5.826e-22 & lte032.0-5.0-0.0a+0.0.BT-Settl.spec.7.dat sdM5.5 & FF & 3200 & 5.5 & -1.0 & 60.94 & 2.764e-22 & lte032.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat sdM6.0 & FF & 3200 & 5.5 & -1.0 & 52.62 & 3.327e-22 & lte032.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat sdM6.5 & FF & 2900 & 5.5 & -0.0 & 828.4 & 4.589e-21 & lte029.0-5.5-0.0a+0.0.BT-Settl.spec.7.dat sdM8.0 & FF & 2900 & 5.5 & -2.0 & 49.54 & 3.094e-22 & lte029.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat sdM9.5 & FF & 2800 & 5.0 & -2.0 & 26.84 & 1.071e-21 & lte028.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM0.0 & FF & 3800 & 5.0 & -1.0 & 46.36 & 1.789e-22 & lte038.0-5.0-1.0a+0.4.BT-Settl.spec.7.dat esdM0.5 & FF & 3700 & 5.0 & -1.5 & 28.12 & 4.847e-22 & lte037.0-5.0-1.5a+0.4.BT-Settl.spec.7.dat esdM1.0 & FF & 3800 & 5.5 & -0.5 & 50.66 & 1.683e-22 & lte038.0-5.5-0.5a+0.2.BT-Settl.spec.7.dat esdM1.5 & FF & 3600 & 5.0 & -1.0 & 24.61 & 6.996e-22 & lte036.0-5.0-1.0a+0.4.BT-Settl.spec.7.dat esdM2.0 & FF & 3600 & 5.5 & -1.0 & 54.63 & 2.229e-22 & lte036.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat esdM3.0 & FF & 3500 & 5.5 & -1.5 & 82.5 & 6.294e-22 & lte035.0-5.5-1.5a+0.4.BT-Settl.spec.7.dat esdM3.5 & FF & 3500 & 5.5 & -1.5 & 38 & 1.883e-22 & lte035.0-5.5-1.5a+0.4.BT-Settl.spec.7.dat esdM4.0 & FF & 3400 & 5.5 & -1.5 & 53.24 & 2.04e-22 & lte034.0-5.5-1.5a+0.4.BT-Settl.spec.7.dat esdM4.5 & FF & 3400 & 5.5 & -1.0 & 260.6 & 3.594e-21 & lte034.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat esdM5.0 & FF & 3200 & 4.5 & -1.5 & 39.72 & 1.952e-22 & lte032.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat esdM5.5 & FF & 3300 & 5.5 & -2.0 & 87.47 & 1.533e-21 & lte033.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat esdM6.0 & FF & 3300 & 5.5 & -2.0 & 27.35 & 8.065e-23 & lte033.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat esdM6.5 & FF & 3300 & 5.5 & -2.0 & 84.99 & 2.61e-22 & lte033.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat esdM7.0 & FF & 3200 & 5.5 & -0.0 & 8.431 & 8.349e-23 & lte032.0-5.5-0.0a+0.0.BT-Settl.spec.7.dat esdM7.5 & FF & 3000 & 5.0 & -2.0 & 75.73 & 8.239e-22 & lte030.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM8.5 & FF & 3000 & 5.5 & -2.0 & 46.61 & 3.916e-22 & lte030.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM0.0 & FF & 3500 & 4.5 & -2.0 & 81.52 & 2.637e-22 & lte035.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat usdM0.5 & FF & 3700 & 5.5 & -2.5 & 35.49 & 8.444e-23 & lte037.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat usdM1.0 & FF & 3700 & 5.5 & -1.0 & 34.9 & 1.245e-22 & lte037.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat usdM2.5 & FF & 3600 & 5.5 & -1.5 & 40.94 & 1.724e-22 & lte036.0-5.5-1.5a+0.4.BT-Settl.spec.7.dat usdM3.0 & FF & 3800 & 6.0 & -0.5 & 40.92 & 9.605e-23 & lte038.0-6.0-0.5a+0.2.BT-Settl.spec.7.dat usdM4.0 & FF & 3200 & 4.5 & -1.5 & 8.887 & 2.545e-22 & lte032.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat usdM4.5 & FF & 3400 & 5.5 & -2.0 & 79.52 & 2.428e-22 & lte034.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM5.0 & FF & 3500 & 5.5 & -2.5 & 128.5 & 5.667e-22 & lte035.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat usdM5.5 & FF & 3300 & 4.5 & -2.0 & 12.52 & 5.669e-23 & lte033.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat usdM6.0 & FF & 3300 & 5.5 & -2.0 & 40.62 & 4.176e-22 & lte033.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM7.5 & FF & 3100 & 5.5 & -2.5 & 25.7 & 3.749e-22 & lte031.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat usdM8.5 & FF & 3100 & 5.5 & -2.5 & 49.69 & 4.503e-22 & lte031.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat \[tab\_MplusTeff\_sdM:table\_best\_fits\_FF\]

[c c c c c c c c]{} SpT & Range & T$_{\rm eff}$ & $\log$g & M/H & chi$^{2}$ & Factor & Model\
sdM0.0 & LL & 3600 & 5.5 & -2.5 & 1.274 & 2.182e-22 & lte036.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat sdM0.5 & LL & 3500 & 4.5 & -1.5 & 65.2 & 2.303e-21 & lte035.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat sdM1.0 & LL & 3600 & 5.0 & -0.5 & 44.52 & 1.843e-21 & lte036.0-5.0-0.5a+0.2.BT-Settl.spec.7.dat sdM1.5 & LL & 3600 & 5.0 & -0.5 & 53.5 & 2.944e-22 & lte036.0-5.0-0.5a+0.2.BT-Settl.spec.7.dat sdM2.0 & LL & 3300 & 4.5 & -1.5 & 54.06 & 1.418e-21 & lte033.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat sdM2.5 & LL & 3400 & 5.0 & -1.0 & 33.27 & 1.013e-21 & lte034.0-5.0-1.0a+0.4.BT-Settl.spec.7.dat sdM3.0 & LL & 3500 & 5.0 & -0.0 & 86.06 & 2.228e-21 & lte035.0-5.0-0.0a+0.0.BT-Settl.spec.7.dat sdM3.5 & LL & 3300 & 5.0 & -1.0 & 100 & 4.559e-21 & lte033.0-5.0-1.0a+0.4.BT-Settl.spec.7.dat sdM4.0 & LL & 3300 & 5.0 & -1.0 & 43 & 1.854e-21 & lte033.0-5.0-1.0a+0.4.BT-Settl.spec.7.dat sdM4.5 & LL & 3200 & 5.0 & -1.5 & 64.01 & 2.467e-22 & lte032.0-5.0-1.5a+0.4.BT-Settl.spec.7.dat sdM5.0 & LL & 3200 & 5.5 & -0.5 & 64.17 & 5.346e-22 & lte032.0-5.5-0.5a+0.2.BT-Settl.spec.7.dat sdM5.5 & LL & 3100 & 5.0 & -1.5 & 62.38 & 3.231e-22 & lte031.0-5.0-1.5a+0.4.BT-Settl.spec.7.dat sdM6.0 & LL & 3000 & 4.5 & -1.5 & 68.92 & 4.55e-22 & lte030.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat sdM6.5 & LL & 2600 & 4.5 & -2.5 & 360.4 & 4.65e-21 & lte026.0-4.5-2.5a+0.4.BT-Settl.spec.7.dat sdM8.0 & LL & 2800 & 5.0 & -2.5 & 68.93 & 3.399e-22 & lte028.0-5.0-2.5a+0.4.BT-Settl.spec.7.dat sdM9.5 & LL & 2700 & 5.0 & -2.5 & 33.25 & 1.083e-21 & lte027.0-5.0-2.5a+0.4.BT-Settl.spec.7.dat esdM0.0 & LL & 3800 & 5.0 & -1.0 & 52.51 & 1.807e-22 & lte038.0-5.0-1.0a+0.4.BT-Settl.spec.7.dat esdM0.5 & LL & 3600 & 5.0 & -2.0 & 36.42 & 5.423e-22 & lte036.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM1.0 & LL & 3500 & 4.5 & -2.0 & 43.43 & 2.508e-22 & lte035.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM1.5 & LL & 3400 & 4.5 & -2.0 & 32.73 & 9.175e-22 & lte034.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM2.0 & LL & 3300 & 4.5 & -2.0 & 41.6 & 3.457e-22 & lte033.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM3.0 & LL & 3400 & 5.0 & -1.5 & 54.27 & 7.476e-22 & lte034.0-5.0-1.5a+0.4.BT-Settl.spec.7.dat esdM3.5 & LL & 3400 & 5.0 & -2.0 & 30.57 & 2.211e-22 & lte034.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM4.0 & LL & 3300 & 5.0 & -1.5 & 60.87 & 2.371e-22 & lte033.0-5.0-1.5a+0.4.BT-Settl.spec.7.dat esdM4.5 & LL & 3100 & 4.5 & -2.0 & 188.1 & 5.634e-21 & lte031.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM5.0 & LL & 3100 & 4.5 & -2.0 & 36.16 & 2.286e-22 & lte031.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM5.5 & LL & 3200 & 5.0 & -2.0 & 65.67 & 1.831e-21 & lte032.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM6.0 & LL & 3100 & 4.5 & -2.0 & 29.34 & 1.116e-22 & lte031.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM6.5 & LL & 3200 & 5.0 & -2.0 & 62.31 & 3.104e-22 & lte032.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM7.0 & LL & 3000 & 4.5 & -2.0 & 2.347 & 9.268e-23 & lte030.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM7.5 & LL & 3000 & 5.0 & -2.0 & 93.43 & 8.48e-22 & lte030.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM8.5 & LL & 2900 & 5.0 & -2.5 & 54.67 & 4.499e-22 & lte029.0-5.0-2.5a+0.4.BT-Settl.spec.7.dat usdM0.0 & LL & 3600 & 5.5 & -2.5 & 52.74 & 2.186e-22 & lte036.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat usdM0.5 & LL & 3700 & 5.5 & -2.0 & 52.29 & 8.588e-23 & lte037.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM1.0 & LL & 3600 & 5.0 & -2.0 & 38.42 & 1.449e-22 & lte036.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM2.5 & LL & 3500 & 5.0 & -2.0 & 35.32 & 1.999e-22 & lte035.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM3.0 & LL & 3600 & 5.5 & -2.0 & 38.99 & 1.27e-22 & lte036.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM4.0 & LL & 3400 & 5.0 & -2.0 & 0.7288 & 1.663e-22 & lte034.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM4.5 & LL & 3300 & 5.0 & -2.0 & 81.28 & 2.949e-22 & lte033.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM5.0 & LL & 3500 & 5.5 & -2.0 & 91.84 & 5.981e-22 & lte035.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM5.5 & LL & 3500 & 5.5 & -2.0 & 11.58 & 3.992e-23 & lte035.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM6.0 & LL & 3200 & 5.0 & -2.0 & 44.5 & 5.027e-22 & lte032.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM7.5 & LL & 3000 & 5.0 & -2.0 & 39.86 & 4.725e-22 & lte030.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM8.5 & LL & 3000 & 5.5 & -2.5 & 60.58 & 5.247e-22 & lte030.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat \[tab\_MplusTeff\_sdM:table\_best\_fits\_LL\]

[c c c c c c c c]{} SpT & Range & T$_{\rm eff}$ & $\log$g & M/H & chi$^{2}$ & Factor & Model\
sdM0.0 & FL & 3600 & 5.5 & -2.5 & 1.274 & 2.182e-22 & lte036.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat sdM0.5 & FL & 3700 & 5.0 & -0.5 & 67.14 & 1.791e-21 & lte037.0-5.0-0.5a+0.2.BT-Settl.spec.7.dat sdM1.0 & FL & 3700 & 5.0 & -0.5 & 45.51 & 1.627e-21 & lte037.0-5.0-0.5a+0.2.BT-Settl.spec.7.dat sdM1.5 & FL & 3600 & 5.0 & -0.5 & 53.5 & 2.944e-22 & lte036.0-5.0-0.5a+0.2.BT-Settl.spec.7.dat sdM2.0 & FL & 3600 & 5.0 & -0.0 & 60.82 & 9.902e-22 & lte036.0-5.0-0.0a+0.0.BT-Settl.spec.7.dat sdM2.5 & FL & 3600 & 5.0 & -0.0 & 35.7 & 8.194e-22 & lte036.0-5.0-0.0a+0.0.BT-Settl.spec.7.dat sdM3.0 & FL & 3500 & 5.0 & -0.0 & 86.06 & 2.228e-21 & lte035.0-5.0-0.0a+0.0.BT-Settl.spec.7.dat sdM3.5 & FL & 3400 & 5.0 & -0.0 & 102.6 & 4.24e-21 & lte034.0-5.0-0.0a+0.0.BT-Settl.spec.7.dat sdM4.0 & FL & 3400 & 5.0 & -0.5 & 49.18 & 1.64e-21 & lte034.0-5.0-0.5a+0.2.BT-Settl.spec.7.dat sdM4.5 & FL & 3300 & 5.5 & -1.0 & 65.18 & 2.143e-22 & lte033.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat sdM5.0 & FL & 3200 & 5.5 & -0.5 & 64.17 & 5.346e-22 & lte032.0-5.5-0.5a+0.2.BT-Settl.spec.7.dat sdM5.5 & FL & 3200 & 5.5 & -1.0 & 64.82 & 2.837e-22 & lte032.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat sdM6.0 & FL & 3200 & 5.5 & -1.0 & 71.23 & 3.416e-22 & lte032.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat sdM6.5 & FL & 2900 & 5.5 & -1.0 & 457.5 & 3.619e-21 & lte029.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat sdM8.0 & FL & 2900 & 5.5 & -2.0 & 70.63 & 3.246e-22 & lte029.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat sdM9.5 & FL & 2800 & 5.5 & -2.0 & 36.7 & 1.048e-21 & lte028.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat esdM0.0 & FL & 3800 & 5.0 & -1.0 & 52.51 & 1.807e-22 & lte038.0-5.0-1.0a+0.4.BT-Settl.spec.7.dat esdM0.5 & FL & 3700 & 5.5 & -2.0 & 36.68 & 4.752e-22 & lte037.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat esdM1.0 & FL & 3800 & 5.5 & -1.0 & 51.58 & 1.689e-22 & lte038.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat esdM1.5 & FL & 3600 & 5.5 & -1.0 & 35.37 & 6.833e-22 & lte036.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat esdM2.0 & FL & 3600 & 5.5 & -1.0 & 48.16 & 2.251e-22 & lte036.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat esdM3.0 & FL & 3500 & 5.5 & -1.5 & 61.37 & 6.495e-22 & lte035.0-5.5-1.5a+0.4.BT-Settl.spec.7.dat esdM3.5 & FL & 3500 & 5.5 & -2.0 & 34.19 & 1.914e-22 & lte035.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat esdM4.0 & FL & 3400 & 5.5 & -1.0 & 67.85 & 2.034e-22 & lte034.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat esdM4.5 & FL & 3400 & 5.5 & -1.0 & 211.3 & 3.624e-21 & lte034.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat esdM5.0 & FL & 3200 & 5.0 & -1.5 & 40.53 & 1.967e-22 & lte032.0-5.0-1.5a+0.4.BT-Settl.spec.7.dat esdM5.5 & FL & 3300 & 5.5 & -1.5 & 74.79 & 1.598e-21 & lte033.0-5.5-1.5a+0.4.BT-Settl.spec.7.dat esdM6.0 & FL & 3300 & 5.5 & -2.5 & 31.14 & 8.05e-23 & lte033.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat esdM6.5 & FL & 3300 & 5.5 & -1.5 & 72.68 & 2.71e-22 & lte033.0-5.5-1.5a+0.4.BT-Settl.spec.7.dat esdM7.0 & FL & 3200 & 5.5 & -2.5 & 2.51 & 6.41e-23 & lte032.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat esdM7.5 & FL & 3000 & 5.0 & -2.0 & 93.43 & 8.48e-22 & lte030.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM8.5 & FL & 3000 & 5.5 & -2.0 & 54.82 & 4.189e-22 & lte030.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM0.0 & FL & 3500 & 4.5 & -2.0 & 54.08 & 2.592e-22 & lte035.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat usdM0.5 & FL & 3700 & 5.5 & -2.0 & 52.29 & 8.588e-23 & lte037.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM1.0 & FL & 3700 & 5.5 & -2.0 & 38.67 & 1.27e-22 & lte037.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM2.5 & FL & 3600 & 5.5 & -2.0 & 35.69 & 1.745e-22 & lte036.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM3.0 & FL & 3800 & 5.5 & -0.5 & 46.05 & 1.005e-22 & lte038.0-5.5-0.5a+0.2.BT-Settl.spec.7.dat usdM4.0 & FL & 3200 & 4.5 & -2.0 & 0.772 & 2.22e-22 & lte032.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat usdM4.5 & FL & 3400 & 5.5 & -2.0 & 85.36 & 2.539e-22 & lte034.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM5.0 & FL & 3500 & 5.5 & -2.0 & 91.84 & 5.981e-22 & lte035.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM5.5 & FL & 3300 & 5.0 & -2.0 & 11.84 & 5.247e-23 & lte033.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM6.0 & FL & 3300 & 5.5 & -2.0 & 47.7 & 4.314e-22 & lte033.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM7.5 & FL & 3100 & 5.5 & -2.0 & 40.37 & 4.046e-22 & lte031.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM8.5 & FL & 3100 & 5.5 & -2.0 & 72.9 & 4.879e-22 & lte031.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat \[tab\_MplusTeff\_sdM:table\_best\_fits\_FL\]

[c c c c c c c c]{} SpT & Range & T$_{\rm eff}$ & $\log$g & M/H & chi$^{2}$ & Factor & Model\
sdM0.0 & LF & 3700 & 5.5 & -2.5 & 3.692 & 2.021e-22 & lte037.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat sdM0.5 & LF & 3600 & 4.5 & -1.5 & 87.73 & 1.999e-21 & lte036.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat sdM1.0 & LF & 3700 & 5.0 & -0.5 & 67.22 & 1.609e-21 & lte037.0-5.0-0.5a+0.2.BT-Settl.spec.7.dat sdM1.5 & LF & 3500 & 5.0 & -0.5 & 93.49 & 3.502e-22 & lte035.0-5.0-0.5a+0.2.BT-Settl.spec.7.dat sdM2.0 & LF & 3500 & 4.5 & -1.5 & 60.84 & 1.051e-21 & lte035.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat sdM2.5 & LF & 3600 & 5.0 & -1.0 & 37.11 & 7.791e-22 & lte036.0-5.0-1.0a+0.4.BT-Settl.spec.7.dat sdM3.0 & LF & 3500 & 5.0 & -0.0 & 88.51 & 2.208e-21 & lte035.0-5.0-0.0a+0.0.BT-Settl.spec.7.dat sdM3.5 & LF & 3400 & 5.0 & -1.0 & 169.9 & 3.924e-21 & lte034.0-5.0-1.0a+0.4.BT-Settl.spec.7.dat sdM4.0 & LF & 3400 & 5.0 & -1.0 & 58.22 & 1.54e-21 & lte034.0-5.0-1.0a+0.4.BT-Settl.spec.7.dat sdM4.5 & LF & 3300 & 5.0 & -1.5 & 66.55 & 2.115e-22 & lte033.0-5.0-1.5a+0.4.BT-Settl.spec.7.dat sdM5.0 & LF & 3100 & 5.5 & -0.5 & 98.69 & 6.395e-22 & lte031.0-5.5-0.5a+0.2.BT-Settl.spec.7.dat sdM5.5 & LF & 3100 & 5.0 & -1.5 & 66.45 & 3.139e-22 & lte031.0-5.0-1.5a+0.4.BT-Settl.spec.7.dat sdM6.0 & LF & 3100 & 4.5 & -1.5 & 66.98 & 3.779e-22 & lte031.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat sdM6.5 & LF & 2800 & 4.5 & -2.5 & 8854 & 5.129e-21 & lte028.0-4.5-2.5a+0.4.BT-Settl.spec.7.dat sdM8.0 & LF & 3000 & 5.0 & -2.5 & 83.22 & 2.962e-22 & lte030.0-5.0-2.5a+0.4.BT-Settl.spec.7.dat sdM9.5 & LF & 3000 & 5.0 & -2.5 & 63.45 & 8.95e-22 & lte030.0-5.0-2.5a+0.4.BT-Settl.spec.7.dat esdM0.0 & LF & 3800 & 5.0 & -1.0 & 46.36 & 1.789e-22 & lte038.0-5.0-1.0a+0.4.BT-Settl.spec.7.dat esdM0.5 & LF & 3700 & 5.0 & -2.0 & 29.55 & 4.919e-22 & lte037.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM1.0 & LF & 3600 & 4.5 & -2.0 & 72.12 & 2.124e-22 & lte036.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM1.5 & LF & 3500 & 4.5 & -2.0 & 29.95 & 7.937e-22 & lte035.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM2.0 & LF & 3500 & 4.5 & -2.0 & 91.63 & 2.571e-22 & lte035.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM3.0 & LF & 3500 & 5.0 & -1.5 & 97.21 & 6.376e-22 & lte035.0-5.0-1.5a+0.4.BT-Settl.spec.7.dat esdM3.5 & LF & 3400 & 5.0 & -2.0 & 44.81 & 2.134e-22 & lte034.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM4.0 & LF & 3400 & 5.0 & -1.5 & 55 & 2.057e-22 & lte034.0-5.0-1.5a+0.4.BT-Settl.spec.7.dat esdM4.5 & LF & 3200 & 4.5 & -2.0 & 439 & 4.69e-21 & lte032.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM5.0 & LF & 3200 & 4.5 & -2.0 & 43.03 & 1.99e-22 & lte032.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM5.5 & LF & 3200 & 5.0 & -2.0 & 92.35 & 1.738e-21 & lte032.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM6.0 & LF & 3200 & 4.5 & -2.0 & 30.38 & 9.303e-23 & lte032.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM6.5 & LF & 3200 & 5.0 & -2.0 & 88.16 & 2.966e-22 & lte032.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM7.0 & LF & 3000 & 4.5 & -2.0 & 10.14 & 1.032e-22 & lte030.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM7.5 & LF & 3000 & 5.0 & -2.0 & 75.73 & 8.239e-22 & lte030.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM8.5 & LF & 3000 & 5.0 & -2.5 & 50.75 & 4.173e-22 & lte030.0-5.0-2.5a+0.4.BT-Settl.spec.7.dat usdM0.0 & LF & 3600 & 5.5 & -2.5 & 232.8 & 2.315e-22 & lte036.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat usdM0.5 & LF & 3800 & 5.5 & -2.0 & 36.52 & 7.582e-23 & lte038.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM1.0 & LF & 3600 & 5.0 & -2.0 & 39.32 & 1.403e-22 & lte036.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM2.5 & LF & 3500 & 5.0 & -2.0 & 45.49 & 1.938e-22 & lte035.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM3.0 & LF & 3600 & 5.5 & -2.0 & 43.27 & 1.199e-22 & lte036.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM4.0 & LF & 3300 & 5.0 & -2.0 & 10.1 & 2.222e-22 & lte033.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM4.5 & LF & 3400 & 5.0 & -2.0 & 103 & 2.461e-22 & lte034.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM5.0 & LF & 3500 & 5.5 & -2.0 & 206.1 & 5.591e-22 & lte035.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM5.5 & LF & 3400 & 5.5 & -2.0 & 13.36 & 4.883e-23 & lte034.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM6.0 & LF & 3300 & 5.0 & -2.0 & 49.56 & 4.229e-22 & lte033.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM7.5 & LF & 3100 & 5.0 & -2.0 & 62.7 & 3.727e-22 & lte031.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM8.5 & LF & 3100 & 5.5 & -2.5 & 49.69 & 4.503e-22 & lte031.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat \[tab\_MplusTeff\_sdM:table\_best\_fits\_LF\]

[c c c c c c c c]{} SpT & Range & T$_{\rm eff}$ & $\log$g & M/H & chi$^{2}$ & Factor & Model\
sdM0.0 & VV & 3500 & 4.5 & -2.5 & 1.506 & 2.581e-22 & lte035.0-4.5-2.5a+0.4.BT-Settl.spec.7.dat sdM0.5 & VV & 3700 & 4.5 & -1.0 & 72.9 & 1.816e-21 & lte037.0-4.5-1.0a+0.4.BT-Settl.spec.7.dat sdM1.0 & VV & 3700 & 5.0 & -0.5 & 66.12 & 1.636e-21 & lte037.0-5.0-0.5a+0.2.BT-Settl.spec.7.dat sdM1.5 & VV & 3400 & 4.5 & -1.5 & 48.5 & 3.784e-22 & lte034.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat sdM2.0 & VV & 3500 & 4.5 & -1.0 & 48.26 & 1.082e-21 & lte035.0-4.5-1.0a+0.4.BT-Settl.spec.7.dat sdM2.5 & VV & 3500 & 4.5 & -1.0 & 35.1 & 9.046e-22 & lte035.0-4.5-1.0a+0.4.BT-Settl.spec.7.dat sdM3.0 & VV & 3500 & 5.0 & -0.0 & 89.26 & 2.224e-21 & lte035.0-5.0-0.0a+0.0.BT-Settl.spec.7.dat sdM3.5 & VV & 3400 & 5.0 & -0.5 & 153.6 & 4.033e-21 & lte034.0-5.0-0.5a+0.2.BT-Settl.spec.7.dat sdM4.0 & VV & 3400 & 5.5 & -0.5 & 47.24 & 1.627e-21 & lte034.0-5.5-0.5a+0.2.BT-Settl.spec.7.dat sdM4.5 & VV & 3100 & 4.5 & -1.5 & 64.16 & 2.845e-22 & lte031.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat sdM5.0 & VV & 3200 & 5.5 & -0.0 & 57.52 & 5.62e-22 & lte032.0-5.5-0.0a+0.0.BT-Settl.spec.7.dat sdM5.5 & VV & 3200 & 5.5 & -1.0 & 69.85 & 2.79e-22 & lte032.0-5.5-1.0a+0.4.BT-Settl.spec.7.dat sdM6.0 & VV & 3000 & 4.5 & -1.5 & 60.23 & 4.532e-22 & lte030.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat sdM6.5 & VV & 2900 & 5.5 & -0.0 & 367.4 & 4.09e-21 & lte029.0-5.5-0.0a+0.0.BT-Settl.spec.7.dat sdM8.0 & VV & 2800 & 5.0 & -2.5 & 55.29 & 3.348e-22 & lte028.0-5.0-2.5a+0.4.BT-Settl.spec.7.dat sdM9.5 & VV & 2600 & 4.5 & -2.5 & 28.39 & 1.454e-21 & lte026.0-4.5-2.5a+0.4.BT-Settl.spec.7.dat esdM0.0 & VV & 3600 & 4.5 & -1.5 & 51.33 & 2.339e-22 & lte036.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat esdM0.5 & VV & 3600 & 4.5 & -1.5 & 33.95 & 5.464e-22 & lte036.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat esdM1.0 & VV & 3600 & 4.5 & -1.5 & 54.39 & 2.181e-22 & lte036.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat esdM1.5 & VV & 3400 & 4.5 & -1.5 & 31.73 & 9.081e-22 & lte034.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat esdM2.0 & VV & 3400 & 4.5 & -1.5 & 65.67 & 2.973e-22 & lte034.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat esdM3.0 & VV & 3400 & 5.0 & -1.5 & 81.18 & 7.466e-22 & lte034.0-5.0-1.5a+0.4.BT-Settl.spec.7.dat esdM3.5 & VV & 3400 & 5.0 & -1.5 & 43.41 & 2.206e-22 & lte034.0-5.0-1.5a+0.4.BT-Settl.spec.7.dat esdM4.0 & VV & 3200 & 4.5 & -2.0 & 61.63 & 2.746e-22 & lte032.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM4.5 & VV & 3200 & 4.5 & -1.5 & 326.9 & 4.852e-21 & lte032.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat esdM5.0 & VV & 3200 & 4.5 & -1.5 & 45.1 & 1.963e-22 & lte032.0-4.5-1.5a+0.4.BT-Settl.spec.7.dat esdM5.5 & VV & 3100 & 4.5 & -2.0 & 88.56 & 2.14e-21 & lte031.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM6.0 & VV & 3200 & 5.0 & -2.0 & 29.11 & 9.46e-23 & lte032.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM6.5 & VV & 3100 & 4.5 & -2.0 & 86.41 & 3.646e-22 & lte031.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM7.0 & VV & 3000 & 4.5 & -2.0 & 5.132 & 9.173e-23 & lte030.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat esdM7.5 & VV & 3000 & 5.0 & -2.0 & 89.47 & 8.325e-22 & lte030.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat esdM8.5 & VV & 2800 & 4.5 & -2.5 & 52.36 & 5.534e-22 & lte028.0-4.5-2.5a+0.4.BT-Settl.spec.7.dat usdM0.0 & VV & 3500 & 4.5 & -2.5 & 51.01 & 2.583e-22 & lte035.0-4.5-2.5a+0.4.BT-Settl.spec.7.dat usdM0.5 & VV & 3600 & 5.0 & -2.5 & 42.57 & 9.734e-23 & lte036.0-5.0-2.5a+0.4.BT-Settl.spec.7.dat usdM1.0 & VV & 3600 & 5.0 & -1.5 & 40.24 & 1.445e-22 & lte036.0-5.0-1.5a+0.4.BT-Settl.spec.7.dat usdM2.5 & VV & 3400 & 4.5 & -2.0 & 50.77 & 2.315e-22 & lte034.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat usdM3.0 & VV & 3400 & 4.5 & -2.0 & 40.27 & 1.684e-22 & lte034.0-4.5-2.0a+0.4.BT-Settl.spec.7.dat usdM4.0 & VV & 3500 & 5.5 & -2.0 & 2.578 & 1.425e-22 & lte035.0-5.5-2.0a+0.4.BT-Settl.spec.7.dat usdM4.5 & VV & 3300 & 5.0 & -2.0 & 83.97 & 2.923e-22 & lte033.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM5.0 & VV & 3400 & 5.5 & -2.5 & 131.2 & 6.592e-22 & lte034.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat usdM5.5 & VV & 3800 & 6.0 & -0.5 & 16.71 & 2.727e-23 & lte038.0-6.0-0.5a+0.2.BT-Settl.spec.7.dat usdM6.0 & VV & 3200 & 5.0 & -2.0 & 44.45 & 4.976e-22 & lte032.0-5.0-2.0a+0.4.BT-Settl.spec.7.dat usdM7.5 & VV & 3000 & 5.0 & -2.5 & 28.43 & 4.579e-22 & lte030.0-5.0-2.5a+0.4.BT-Settl.spec.7.dat usdM8.5 & VV & 3000 & 5.5 & -2.5 & 51.61 & 5.169e-22 & lte030.0-5.5-2.5a+0.4.BT-Settl.spec.7.dat \[tab\_MplusTeff\_sdM:table\_best\_fits\_VV\]

[^1]: Based on observations collected at the European Southern Observatory, Chile, under programmes 089.C-0140(A), 091.C-0264(A), 092.D-0600(A), and 093.C-0610(A)

[^2]: http://www.eso.org/sci/software/pipelines/

[^3]: http://www.eso.org/sci/software/pipelines/skytools/molecfit

[^4]: http://perso.ens-lyon.fr/france.allard/

[^5]: phoenix.ens-lyon.fr/Grids/BT-Settl/CIFIST2011/SPECTRA/

[^6]: http://astro.uni-tuebingen.de/software/idl/aitlib/misc/gaussfold.html

[^7]: last update on 10 October 2016 at exoplanetarchive.ipac.caltech.edu
