# Introduction

Stars with masses less than 0.6 M$$_\odot$$ are the most numerous in our Galaxy. These are intrinsically cool and faint stars, with complex spectra characterised by molecular absorption of TiO, CaH and VO in the optical, and FeH and H$$_2$$O in the near infrared. Some of them are known to be quite active, with flares larger than the ones produced by the sun. Few of them are the hosts of the closest rocky planets to the Earth, and overall, they should be the most likely hosts of Earth-like planets in the galaxy. The study of M dwarfs has been greatly benefited by surveys covering different regions of the galaxy.

We present colour selected M dwarfs in the b201 tile of the VISTA Variables in the Vía Láctea (VVV) survey. In section 2, we give the description of the survey and of the tile b201. In section 3, we present our M dwarf selection method based on 6 colour selection cuts obtained from SDSS spectroscopically observed M dwarfs. A spectral subtype calibration based on $$(Y-J)$$, $$(Y-K_s)$$, and $$(H-K_s)$$ is given in section 4. In section 5, we show interesting objects blah blah. We discuss our results and conclusions in section 6.

# Data

VISTA Variables in the Vía Láctea (VVV) is a public ESO near-infrared (near-IR) variability survey aimed at scanning the Milky Way Bulge and an adjacent section of the mid-plane. The VVV survey gives near-IR multi-colour information in five passbands: $$Z$$ (0.87 $$\mu m$$), $$Y$$ (1.02 $$\mu m$$), $$J$$ (1.25 $$\mu m$$), $$H$$ (1.64 $$\mu m$$), and $$K_s$$ (2.14 $$\mu m$$) which complements surveys such as 2MASS1, DENIS, GLIMPSE-II, VPHAS+, MACHO, OGLE, EROS, MOA, and GAIA (citation not found: 2012A&A...537A.107S). The survey covers a 562 square degrees area in the Galactic bulge and the southern disk which contains ~$$10^{9}$$ point sources. Each unit of VISTA observations is called a (filled) tile, consisting of six individual (unfilled) pointings (or pawprints) and covers a 1.64 $$deg^{2}$$ field of view. To fill up the VVV area, a total of 348 tiles are used, with 196 tiles covering the bulge (a 14 14 grid) and 152 for the Galactic plane (a 4 38 grid) (citation not found: 2012A&A...544A.147S). We selected one specific tile from the bulge to characterise M-dwarf stars called “b201” which center’s galactic coordinates are $$l$$=350.74816 and $$b$$=-9.68974. This tile is located in the border of the bulge where star density is lower and extinction is small allowing good photometry. Photometric catalogues for the VVV images are provided by the Cambridge Astronomical Survey Unit (CASU2). The catalogues contain the positions, fluxes, and some shape measurements obtained from different apertures, with a flag indicating the most probable morphological classification. In particular, we note that -1 is used to denote the best-quality photometry of stellar objects (citation not found: 2012A&A...544A.147S). Some other flags are -2 (borderline stellar), 0 (noise), (sources containing bad pixels), and -9 (saturated sources).

1. http://apm49.ast.cam.ac.uk/

# Selection Method

In order to identify potential M dwarfs in the VVV tile “b201”, we performed several colour selection cuts using the VVV passbands as described in the subsections below. Before performing those cuts, we did a pre-selection of the objects in the tile “b201” to assure that the objects have the best-quality photometry. The pre-selection consisted on including only objects that had photometry in all five passbands and that were classified as “stellar” in each passband. The total number of 142,321 objects in the tile “b201” satisfied these conditions.

## Color Selection Cuts from SDSS-UKIDSS M dwarfs

The color selection cuts were defined by selecting spectroscopically identified M dwarfs with UKIRT Infrared Deep Sky Survey (UKIDSS) photometry.

We used the Sloan Digital Sky Survey DR7 Spectroscopic M dwarf catalog by West et al. (2011) as the comparative M dwarf sample. The 70,841 M dwarf stars in this catalog had their optical spectra visually inspected and spectral type was assigned by comparing them to spectral templates. Their spectral types range from M0 to M9, with no half subtypes. These catalog also provides values for the CaH2, CaH3 and TiO5 indices, which measure the strength of CaH and TiO molecular features present in the optical spectra of M dwarfs.

We performed a cone search with a radius of 0.5of these SDSS M dwarf stars in the UKIDSS-DR8 survey (Lawrence et al., 2012). The UKIDSS survey is carried out using the Wide Field Camera (WFCAM), with a $$Y$$ (1.0um), $$J$$ (1.2um), $$H$$ (1.6um) and $$K$$ (2.2um) filter set. There were UKIDSS-DR8 matches for almost half of the SDSS M dwarf sample (34,416 matches) . Next, we only kept the UKIDSS counterparts consistent with being a stellar objects (pStar > 0.9), with measured magnitudes in all WFCAM $$YJHK$$ filters, and with CaH and TiO indices compatible with average M dwarf stars. The final SDSS-UKIDSS comparative M dwarf sample consists of 17,774 objects.

To convert the WFCAM $$YJHK$$ magnitudes of the SDSS-UKIDSS M dwarf sample to VISTA $$YJHK_s$$ magnitudes, we used the conversions provided by the CASU 1, derived from regions observed with both VISTA and WFCAM.

The mean and standard deviation for all of the colors from VISTA $$YJHK_s$$ photometry per M spectral subtype, as well as the number of stars considered their computation, are shown in Table \ref{spec_color}.

Sp.T. $$\overline{Y-J}$$ $$\sigma(Y-J)$$ $$\overline{Y-H}$$ $$\sigma(Y-H)$$ $$\overline{Y-K_s}$$ $$\sigma(Y-K_s)$$ $$\overline{J-H}$$ $$\sigma(J-H)$$ $$\overline{J-K_s}$$ $$\sigma(J-K_s)$$ $$\overline{H-K_s}$$ $$\sigma(H-K_s)$$ $$\#$$ stars
M0 0.428 0.092 1.039 0.087 1.163 0.063 0.611 0.116 0.734 0.092 0.124 0.079 1946
M1 0.449 0.077 1.047 0.061 1.200 0.064 0.598 0.086 0.751 0.081 0.153 0.046 2520
M2 0.467 0.061 1.042 0.073 1.219 0.058 0.575 0.088 0.752 0.071 0.177 0.058 3043
M3 0.487 0.081 1.043 0.062 1.241 0.064 0.556 0.089 0.754 0.083 0.198 0.038 3293
M4 0.515 0.083 1.057 0.090 1.278 0.068 0.542 0.110 0.762 0.085 0.220 0.075 2872
M5 0.555 0.096 1.092 0.069 1.34 0 0.082 0.538 0.103 0.786 0.099 0.248 0.044 1264
M6 0.619 0.082 1.150 0.067 1.442 0.076 0.531 0.087 0.823 0.084 0.292 0.033 1224
M7 0.664 0.117 1.198 0.126 1.513 0.136 0.533 0.064 0.849 0.068 0.315 0.037 1141
M8 0.758 0.070 1.304 0.102 1.662 0.122 0.546 0.052 0.904 0.067 0.358 0.033 320
M9 0.850 0.079 1.429 0.114 1.830 0.139 0.579 0.054 0.980 0.071 0.401 0.038 151

\label{spec_color}

We have defined our limits in each magnitude difference as the mean value of spectral type M0 minus its standard deviation for the lower cut, and the mean value of spectral type M9 plus its standard deviation for the higher cut. The resulting limits are:

0.336 < $$(Y-J)_{VISTA}$$< 0.929

0.952 < $$(Y-H)_{VISTA}$$< 1.544

1.100 < $$(Y-K_s)_{VISTA}$$ < 1.969

0.432 < $$(J-H)_{VISTA}$$< 0.727

0.642 < $$(J-K_s)_{VISTA}$$ < 1.051

0.045 < $$(H-K_s)_{VISTA}$$ < 0.438

From our preselection of 142,321 objects, only 23,345 objects have colours that are consistent with M dwarf stars, according to the color-cuts shown above. A 40$$\%$$ of these objects have magnitudes 12$$<$$K$$_s$$$$<$$16, and therefore have reliable magnitudes for variability and are the best M dwarf candidates to detect any possible transits (9,232 objects).

## Spectral Types and Distances for VVV M dwarfs

By inspecting the mean colors per spectral type in Table \ref{spec_color}, it is noticeable that spectral type is a monotonically increasing function for the following colors: $$Y-J$$, $$Y-K_s$$, and $$H-Ks$$. We conducted multivariate regressions on the $$Y-J$$, $$Y-K_s$$, and $$H-Ks$$ colors, for the 17,774 stars in the SDSS-UKIDSS comparative M dwarf sample to identify the best-fit relationship to predict each star’s spectral type. The resulting subtype calibration is

M subtype & = 5.394 (Y-J) + 4.370 (Y-J)^2
& + 24.325 (Y-K_s) - 7.614 (Y-K_s)^2
& + 7.063 (H-K_s) -20.779
RMSE_V & = 1.109

with $$RMSE_V$$ being the root-mean-square error of validation, a sensible estimate of average prediction error (see APPENDIX in Rojas-Ayala et al., 2012). Spectral types for all the M dwarf candidates are given in Table XX.

We looked for the location of M dwarfs at different distances in the Colour-Magnitude Diagram (CMD) using the nearby M dwarfs with $$M_{K_s}$$ and spectral type estimates in Rojas-Ayala et al. (2012). Using colour transformations from WFCAM to the VISTA system, we estimated the aparent $$K_s$$ magnitudes at different distances per spectral type (Table \ref{absolutemag}). The locations of the M dwarf sequence at 60pc, 300pc and 1000pc coincide with the location of the colour-based selection of M dwarfs describe above, as shown in the CMD of Figure XX. Based on t