© ESO, 2013

1. Introduction

The fields of the southern Galactic disk are complicated regions to research. Near the Galactic plane the interstellar medium (ISM) is rich, complex, and dust extinction is extreme and inhomogeneous at small scales. Moreover, the surface density of sources reaches a maximum in the Galactic plane. Fields exhibiting one star brighter than K_s = 18 are catalogued every few square arcsec. Owing to the aforementioned factors, existing optical and low-spatial resolution surveys have thus been inefficient at characterizing populations in the southern Galatic disk. Hence the importance of the VISTA Variables in the Vía Láctea (VVV) survey (Minniti et al. 2010; Saito et al. 2012), which is a near-infrared ESO public survey that is sampling 562 deg² of the Galactic bulge and adjacent regions of the disk. The survey is being carried out via the VISTA telescope, and images are being acquired through 5 broadband filters. The VVV fields examined here overlap with the GLIMPSE survey, which acquired images at 3.6, 4.5, 5.8 and 8 μm. Thus the sources surveyed will have multiband photometry ranging from the near to mid-infrared. The region sampled is of particular interest for ISM studies because the 4th Galactic quadrant hosts the Coal Sack, in tandem with several prominent nebulae and areas exhibiting large star formation rates (SFR). The inner disk region includes large numbers of open clusters (Borissova et al. 2011; Bica et al. 2008; Kharchenko et al. 2005 and references therein) and associations, which allows for detailed stellar population studies. The near-infrared nature of the surveys is particularly pertinent for such analyses since such photometry is less sensitive to dust obscuration than optical observations, thus permitting greater penetration into the disk. The line of sight depth in the 1st and 4th Galactic quadrants is large, and nearby foreground dwarfs stars are mixed with distant red giants along a given line of sight. In addition, the region sampled is pertinent for Galactic structure studies, as there is presently no consensus on the number or delineation of the Galaxy’s major spiral arms (Benjamin et al. 2008; Majaess et al. 2009), and the tail end of the long bar is undercharacterized (Fig. 7 in Majaess 2010).

Fig. 1 Galactic disk fields imaged by the VVV survey. The VVV disk tile names start with d, followed by the numbering as shown in the figure.

Prior to VVV the 2MASS survey (Skrutskie et al. 2006) has been the main near-infrared photometric survey covering much of the Galactic plane, and many models and data in the 2MASS photometric system have appeared in the literature. In comparing with this previous work it is therefore useful, at least until sufficient modeling is available in the VISTA photometric system, to know the 2MASS equivalent magnitudes to the actual VISTA magnitudes. In addition, such transformations allow to combine the information of both surveys to reach a wider magnitude range (e.g. saturated stars in the VVV catalogues can be complemented with the 2MASS magnitudes once they are transformed to the 2MASS system). However we note that, for the greatest accuracy, transformations between different photometric systems should in general be avoided as they will always be dependent on the (usually unknown) spectrum of the objects, but pending availability of more models in the VISTA system we find that it is expedient to estimate what VISTA magnitudes would be in the 2MASS system.

Fig. 2 Transmission curves for the 2MASS and VISTA photometric systems.

Carpenter et al. (2001) produced transformation equations to convert colors and magnitudes from AAO, ARNICA, CIT, DENIS, ESO, LCO, MSSSO, SAAO and UKIRT photometric systems to 2MASS. This paper follows a similar procedure to obtain transformations linking the VVV and 2MASS systems. A well defined set of transformation equations should be valid over a large color baseline (i.e. − 0.5 ≤ (J − K_S) ≤ 4.0) owing to the high (and strongly varying) reddening values, and the presence of (bluer) dwarfs and (redder) giants. In this work we present empirical JHK_s color transformations for 152 tiles completed during year 1 (2010), photometric catalogue version 1.1 (see observation schedule in Minniti et al. 2010), between the VISTA and 2MASS photometric systems. The calibrations were inferred from VVV sources in the southern Galactic disk in the region bounded by − 65.3° ≲ l ≲  − 10.0° and − 2.25° ≲ b ≲  + 2.25°, and apply to all the VVV photometry derived from the Cambridge Astronomical Survey Unit (CASU) catalogues in this area.

Fig. 3 Color−color and color−magnitude diagrams for the tile d003. VVV data (blue dots) have been matched with 2MASS data on the same field (pink dots), where a subsample has been chosen to calculate the coefficients (dark grey). A limiting magnitude (orange dashed line) in each band has been used to avoid saturated VVV stars.

This paper is organized as follows: in Sect. 2 a brief overview is provided of the VVV observations and the CASU pipeline, which produces the photometric catalogues. Section 3 explains the selection procedure for the subsample of VVV-2MASS stars used to derive the photometric transformations. Finally, Sect. 4 contains the discussion of the transformation coefficients obtained, while our conclusions are summarized in Sect. 5.

2. Observations

2.1. VVV Observations

Near-infrared VVV observations were acquired via VISTA (Visible and Infrared Survey Telescope for Astronomy), which is stationed at the Paranal Observatory. VISTA is a 4 m telescope equipped with the VIRCAM instrument (VISTA InfraRed CAMera; Emerson et al. 2006). Each VVV field (called a tile) covers 1.64 deg². There are 152 tiles covering about 250 deg² of the Galactic disk (Fig. 1). The VVV tiles exhibit overlap between consecutive blocks, and for the complete survey the overlap sums to ~42 deg². The equatorial and Galactic coordinates for the center of each tile are listed in Table A.1 of Saito et al. (2012). The VISTA IR mosaic camera has a 1.65 deg diameter field of view, that is sampled with 16 Raytheon 2048 × 2048 arrays (Dalton et al. 2006). The detectors have 0.339′′ pixels which produce a 0.6   deg² field per pointing. Each pointing is called a “pawprint”, with spacings of 42% and 90% between the detectors along the X and Y axes, respectively, where 6 overlapping pawprints are used to build a tile.

The VVV survey includes observations of the complete survey area in the 5 available filters, i.e. Z, Y, J, H, and K_s. As described by Minniti et al. (2010), these multi-band observations were scheduled to be carried out during the first year of the survey (2010), but were partly carried over into 2011 owing to various factors. The principal part of the survey (year 2−5) will be a K_s-band variability study.

2.2. CASU pipeline: photometry

The reduction of IR data is far more complex than reducing optical data. IR detectors are more unstable than optical detectors and sky emission can be several magnitudes brighter than many IR stellar sources (Lewis et al. 2010), and marginally fainter than the saturation limit. In the case of VVV, the limiting magnitude for the aperture photometry of the catalogues appears at K_s = 18 mag in most fields in the disk, with an expected sky brightness at the VISTA site of K_s ≈ 13.0 mag (Cuby et al. 2000). Moreover, IR sky emission varies over short timescales, and changes in spatial scale can be large or small depending on the instrument. Consequently, short exposures are needed, which subsequently increases the amount of information acquired each night. Thus, surveys like VVV require automated pipelines to process the large volumes of nightly data. The VISTA Data Flow System pipeline running at CASU handles the data processing¹.

Fig. 4 Comparison of 2MASS and VVV photometry for stars observed in tile/field d003. In each case an iterative clipping algorithm has been applied to each one of the 20 adaptive bins of the distribution. The selected stars of the clipping algorithm (grey) have been used to calculate the linear fit, and the individual photometric uncertainties of each star were considered.

Zeropoints on the VISTA system are determined using the 2MASS data following a procedure similar to that described for WFCAM1 (Hodgkin et al. 2005). A color selected set of 2MASS stars lying in each pawprint are chosen and their magnitudes on the VISTA photometric system are calculated using the following color equations for data release 1.1 (we adopt K = K_s in the equations for simplicity): $\begin{array}{ccc}{\mathit{J}}_{\mathrm{VVV}}& \mathrm{=}& {\mathit{J}}_{\mathrm{2}\mathrm{MASS}}\mathrm{-}\mathrm{0.077}\mathrm{(}{\mathit{J}}_{\mathrm{2}\mathrm{MASS}}\mathrm{-}{\mathit{H}}_{\mathrm{2}\mathrm{MASS}}\mathrm{)}\mathit{,}\\ {\mathit{H}}_{\mathrm{VVV}}& \mathrm{=}& {\mathit{H}}_{\mathrm{2}\mathrm{MASS}}\mathrm{+}\mathrm{0.032}\mathrm{(}{\mathit{J}}_{\mathrm{2}\mathrm{MASS}}\mathrm{-}{\mathit{H}}_{\mathrm{2}\mathrm{MASS}}\mathrm{)}\mathit{,}\\ {\mathit{K}}_{\mathrm{VVV}}& \mathrm{=}& {\mathit{K}}_{\mathrm{2}\mathrm{MASS}}\mathrm{+}\mathrm{0.010}\mathrm{(}{\mathit{J}}_{\mathrm{2}\mathrm{MASS}}\mathrm{-}{\mathit{K}}_{\mathrm{2}\mathrm{MASS}}\mathrm{)}\mathit{.}\end{array}$An extinction correction, based on Schlegel et al. (1998; henceforth SFD), is applied according to the prescription of Bonifacio et al. (2000). The corrections can be found in the CASU website². The analysis presented here is based on the derived colors and magnitudes established by the CASU pipeline. A detailed account of the CASU pipeline can be found in Irwin et al. (2004), and will not be repeated here.

3. Procedures

3.1. Catalogue construction and 2MASS matching

The VISTA and 2MASS photometric systems do not exactly match, as expected given the observations were carried out at different sites with different telescopes, IR cameras, detectors and filters. Figure 2 shows a comparison of the transmission curves for both photometric systems. As discussed earlier we wish to determine, on a tile by tile basis, the transformations between the VISTA and 2MASS systems for VVV data in the Galactic disk. That is equivalent to changing the CASU calibration for each tile. Nevertheless, the revised transformations should be more robust since red objects will be included in the calibration, whereas the CASU calibration relies principally on blue stars.

The first step in obtaining the transformations was to select a set of VVV and 2MASS observations exhibiting solid photometry. A series of constraints were placed on the 2MASS and VVV photometry to account for undesirable effects arising from crowding and saturation. Extended sources were excluded. The procedure used to obtain a 2MASS-VVV catalogue for each tile can be summarized as follows:

• (a)

  Only sources with VVV K_s photometry defined as “stellar” (sources with a Gaussian sigma parameter between 0.9 and 2.2) were analyzed. This parameter is derived from the three intensity weighted second moments. K_s photometry was chosen since the data extend deeper than J or H for sources in the Galactic plane. Accounting for crowding effects in K_s provides a corresponding solution for the shallower J and H data.

• (b)

  Using the new list of K_s photometry, sources in close proximity to each other are subsequently culled, that is, stars exhibiting $\mathit{r}\mathit{<}\mathrm{2}\stackrel{\mathrm{″}}{.}\mathrm{0}$ (i.e. the 2MASS pixel size) and whose magnitudes display less than a 2 magnitude differential with respect to the brightest star.

• (c)

  The resulting catalogue is then matched with 2MASS, where only stars with photometric quality flag “A” or “B” in a radius of $\mathrm{0}\stackrel{\mathrm{″}}{.}\mathrm{3}$ are selected. For JHK_s data the 2MASS photometric quality flags “A” and “B” correspond to SNR > 10 and SNR > 7, respectively.

• (d)

  The final list is constructed by cross-referencing the VVV K_s and 2MASS JHK_s list, received from the previous step, with the rest of the VVV J and H data matched using a radius of $\mathrm{0}\stackrel{\mathrm{″}}{.}\mathrm{1}$.

Once a clean VVV-2MASS catalogue has been created for each VVV tile, the transformation equations were derived. The procedure is similar to that employed by Carpenter (2001). Linear fits for the variables were determined, namely: (K_s)_2MASS-(K_s)_VVV versus (J − K_s)_VVV, (J − H)_2MASS versus (J − H)_VVV, (J − K_s)_2MASS versus (J − K_s)_VVV, and (H − K_s)_2MASS versus (H − K_s)_VVV and coefficients (α_K,β_K), (α_JH,β_JH), (α_JK,β_JK) and (α_HK,β_HK), respectively. Thus, the derived linear fits correspond to the equations: $\begin{array}{ccc}& & {\mathit{K}}_{\mathrm{2}\mathrm{MASS}}\mathrm{-}{\mathit{K}}_{\mathrm{VVV}}\mathrm{=}\mathrm{(}{\mathit{J}}_{\mathrm{VVV}}\mathrm{-}{\mathit{K}}_{\mathrm{VVV}}\mathrm{)}{\mathit{\beta }}_{\mathit{K}}\mathrm{+}{\mathit{\alpha }}_{\mathit{K}}\mathit{,}\\ & & \mathrm{(}{\mathit{J}}_{\mathrm{2}\mathrm{MASS}}\mathrm{-}{\mathit{H}}_{\mathrm{2}\mathrm{MASS}}\mathrm{)}\mathrm{-}\mathrm{(}{\mathit{J}}_{\mathrm{VVV}}\mathrm{-}{\mathit{H}}_{\mathrm{VVV}}\mathrm{)}\mathrm{=}\mathrm{(}{\mathit{J}}_{\mathrm{VVV}}\mathrm{-}{\mathit{H}}_{\mathrm{VVV}}\mathrm{)}{\mathit{\beta }}_{\mathit{JH}}\\ & & \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{+}{\mathit{\alpha }}_{\mathit{JH}}\mathit{,}\\ & & \mathrm{(}{\mathit{J}}_{\mathrm{2}\mathrm{MASS}}\mathrm{-}{\mathit{K}}_{\mathrm{2}\mathrm{MASS}}\mathrm{)}\mathrm{-}\mathrm{(}{\mathit{J}}_{\mathrm{VVV}}\mathrm{-}{\mathit{K}}_{\mathrm{VVV}}\mathrm{)}\mathrm{=}\mathrm{(}{\mathit{J}}_{\mathrm{VVV}}\mathrm{-}{\mathit{K}}_{\mathrm{VVV}}\mathrm{)}{\mathit{\beta }}_{\mathit{JK}}\\ & & \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{+}{\mathit{\alpha }}_{\mathit{JK}}\mathit{,}\\ & & \mathrm{(}{\mathit{H}}_{\mathrm{2}\mathrm{MASS}}\mathrm{-}{\mathit{K}}_{\mathrm{2}\mathrm{MASS}}\mathrm{)}\mathrm{-}\mathrm{(}{\mathit{H}}_{\mathrm{VVV}}\mathrm{-}{\mathit{K}}_{\mathrm{VVV}}\mathrm{)}\mathrm{=}\mathrm{(}{\mathit{H}}_{\mathrm{VVV}}\mathrm{-}{\mathit{K}}_{\mathrm{VVV}}\mathrm{)}{\mathit{\beta }}_{\mathit{HK}}\\ & & \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{+}{\mathit{\alpha }}_{\mathit{HK}}\mathrm{·}\end{array}$An iterative clipping algorithm was applied to reject stars beyond 2.5σ for each adaptive bin (i.e. uniformly populated bins). That allowed us to establish a robust determination of the coefficients for the photometric transformation in each case. A limiting magnitude was applied to each filter during the calculation of the transformations, which ensures that saturated photometry was avoided. The limiting magnitudes used during the procedure were 13.8, 12.8 and 12.8, for J, H and K_s respectively. An example of the color−color and color−magnitude diagrams (CMD) in both photometric systems for tile d003 is shown in Fig. 3, whereas the result of the fitting procedure is shown in Fig. 4.

4. Discussion

Figure 5 displays the color−color diagram of tile d003, where the calculated transformations were applied to the respective VVV colors. The Gaussian fitting applied to the histograms of the JHK_s magnitude residuals, in our transformations for tile d003, exhibits σ ≃ 0.05   mag for stars in the upper 25% of the magnitude range used to calculate the photometric transformations. These residuals are dominated by the 2MASS magnitude dispersion, where 2MASS photometric errors are typically several times higher (~6 on average for this tile) than those in the VVV catalogues.

Table A.1 lists the coefficients obtained for the 152 VVV tiles, while Fig. 6 displays the same coefficients as a function of Galactic longitude and latitude. Similarly, Tables B.1 and B.2 show the derived coefficients per tile for subsamples dominated by main sequence and post main sequence stars respectively. At first glance, the figures suggest a non-random behavior that is presumably related to the structure of the Milky Way. In order to test that hypothesis, we compared how the coefficients varied for low (red, | b| ≲ 1°) and high Galatic latitude fields (green, 2.1° ≳ |b| ≳ 1°). For each subsample we fitted a fourth-order polynomial. A clear distinction between high- and low-latitude fields is observed in the photometric coefficients, with the apparent exception of the β_JK parameter. A similar analysis can be drawn by dividing the sample in low longitude (red, l ≥ 320°) and high longitude fields (green, l < 320°). Where we have fitted a third-order polynomial to fit the subsamples in each case.

The variations of the transformation coefficients across the Galaxy may be caused by multiple effects, as discussed below.

Fig. 5 Color−color diagram for VVV stars transformed to the 2MASS photometric system for tile d003. The transformation equations derived in Fig. 4 have been applied to the VVV colors (grey). The same stars featured in the 2MASS catalogue are overplotted (pink).

Fig. 6 Coefficients of the VVV-2MASS transformations as a function of Galactic longitude and latitude for 152 VVV tiles in the Galactic disk. Top and second row, we divided the sample into low (red; | b| ≲ 1°) and high latitude fields (green; 2.1° ≳ |b| ≳ 1°). A fourth order polynomial was fitted in each case. Third and bottom row, photometric coefficients divided into low longitude (red; l ≳ 320°), and high longitude fields (green; l ≲ 320°).

4.1. Extinction on the disk for the VISTA fields

Extinction in the Galactic plane can be extreme and uneven at small scales. As mentioned, an extinction correction was employed in the VISTA pipeline based in part on the SFD map. The problems of SFD in regions of high extinction are well documented. Arce & Goodman (1999) evaluated the reliability of the SFD maps in the Taurus Dark Cloud complex, using 4 separate methods. Their results demonstrate a consistent overestimation by a factor of 1.3 to 1.5 in regions of smooth extinction and A_V > 0.5 mag. By contrast, reddening values were underestimated in regions with steep extinction gradients. Subsequent studies have shown similar results in globular clusters (see Majewski et al. 2011 and references therein), whereby reddening values were overestimated by factors of 1.2 to 1.5. Moreover, the comparison between Majewski et al. (2011) extinction map, based on 2MASS (NIR)/Spitzer-IRAC observations, and the SFD map revealed clear discrepancies. Majewski et al. (2011) attributed the offset to the fact that long wavelength (100 μ) infrared dust emission is not a viable tracer of dust extinction (SFD maps). A similar result was found recently using VVV data. Gonzalez et al. (2012) compared their bulge extinction map with the SFD map, and a significant difference appeared for | b| < 6°. In addition to the limitations of the applied SFD maps, offsets in the photometric transformations are expected owing to the different filters employed by 2MASS and VVV. Thus the transformations may be affected by reddening and spectral type. Figure 7 illustrates that effect via a comparison of Padova isochrones (Girardi et al. 2000, 2002) on the 2MASS and VISTA photometric systems. In that example an old disk population (~10 Gyr; Carraro et al. 1999) affected by high extinction (A_V ~ 10) displays divergent colors.

Fig. 7 Comparison of isochrones in the 2MASS (black) and VISTA (grey) photometric systems for a 10 Gyr population (Z = 0.019) observed through two extinction values (Av = 0 and Av = 10).

Figure 8 and Table 1 show the photometric coefficients for 152 tiles as a function of the reddening used in the zeropoint correction for each tile, and their respective correlation results (r_S is the Spearman’s rank order correlation coefficient). The calculated correlations are significant in most of the coefficients, only β_JK and α_JK show little dependence on E(B − V). Thus these results confirm our original assessment regarding the influence of extinction (see also Fig. 6). Since 2MASS and VVV colors and magnitudes must coincide for A0V spectral type and E(B − V) = 0, as Fig. 7 shows, our photometric transformations should follow consistent relations when extrapolated to zero reddening. As expected, the linear fits for the α coefficients tend to zero for E(B − V) = 0, an effect that seems to grow stronger with the correlation r_S. Similarly, and in spite of the dispersion observed, these plots show a rough agreement with the inverse transformations that can be derived from the CASU equations (without their extinction corrections) in Sect. 2.2; which produce β_JK = 0.075 and β_JH = 0.109 for E(B − V) = 0, as can be seen in Fig. 8. All this confirms the reliability of the photometric transformations obtained.

4.2. Mapping the Galactic disk with VVV

Figure 9 hosts the color−magnitude and color−color diagram for all fields in the VVV catalogue with VVV-2MASS color transformations. The diagram features 88 million stars obtained from our combined JHK_s catalogues of the Galactic disk. The combined CMD reveals the saturated population around K_s ~ 10   mag. However, our tests with individual tile-catalogues implied that saturation was typically near K_s ~ 13   mag (Fig. 4).

The combined color−color diagram can be used to calculate the infrared color excess ratio (Indebetouw et al. 2005). The measured color excess ratio in our diagram is E(J − H)/E(H − K) = 2.13 ± 0.04, which was inferred from the VVV data converted to the 2MASS system with 1.5 ≥ (H − K_s) ≥ 0.5. The corresponding value in the original VISTA system is E(J − H)/E(H − K) = 2.02 ± 0.04. These reddening laws are in general agreement with previously reported values for numerous lines of sight toward the inner Galaxy (Straižys & Laugalys 2008; Majaess et al. 2011).

Fig. 8 Coefficients of the VVV-2MASS transformations as a function of the reddening used to correct the zeropoint for 152 VVV fields in the Galactic disk. We included in each plot a linear fit with an iterative clipping algorithm similar to that used to calculate the photometric transformations. Grey points are those rejected during the clipping procedure. Moreover, the Spearman’s rank order correlation coefficient rS has been calculated in each case.

Fig. 9 Binned color−magnitude and color−color diagrams for all sources defined as stellar in the VVV catalogues (86 millions), which constitutes 152 tiles of the Galactic disk. Magnitudes have been transformed to the 2MASS photometric system in each tile using the respective coefficients. The CMD has been calculated at a resolution of 500 × 1600 bins, which corresponds to a binsize of 0.005 mags/bin. Similarly, our color−color diagram for the tiles of the Galactic disk was constructed at a resolution of 400 × 800 bins and the same binsize of the binned CMD. The latter includes an unreddened 0.05 Gyr isochrone (grey solid line) in the 2MASS system for reference.

Fig. 10 Map featuring the number of sources or the disk tiles (152 fields) in VVV with a 0.005° × 0.005° bin/pixel size. Top, map for all the sources in our combined JHKs catalogues, 136 million sources. Second row, map for all the stellar sources, 88 million stars. Third row, map for stellar sources for the objects lying in a stripe in the color−color diagram defined by (H − K) × 1.97 + 0.54 ≥ (J − H) ≥ (H − K) × 1.97 + 0.24 and (H − K) ≥ 0.4; this selection should be dominated by disk red giants with high extinction. Bottom, same as before, but for (H − K) ≤ 0.4; the population selected in this starcount map should be dominated by red-giants and some main sequence stars with low extinction.

Figure 10 shows the source-count maps for all tiles processed for this work. Duplications in the overlapping regions between tiles have been avoided in the starcount maps, as in the CMD and color−color diagrams, by constructing simultaneously the three corresponding binned plots (CMD, color−color diagram and starcount map). Once a pixel has been used in the starcount map, only counts from the same tile will be accepted in the three binned plots. The first of these count maps in Fig. 10 includes all 136 × 10⁶ detected sources in the 152 tiles, regardless of their classification. The second map consists only of stellar sources (88 × 10⁶ objects). There exist differences in the general number of counts per tile which we attribute to variations in the observation conditions between the tiles, in addition to patchy disk obscuration. Similarly, a marginal vertical stripe pattern is observed in many tiles. That pattern is a known background variation related to the construction of the tiles from the 6 pawprint images. As expected, when compared with the map including just stellar sources (second row), the general map including all the sources (top) displays more detailed structure in regions where diffuse sources are expected. Finally, for the last two starcount maps, we selected two subsamples of all the stellar sources by defining the following region in the color−color diagram: $\begin{array}{ccc}\mathrm{(}\mathit{H}\mathrm{-}\mathit{K}\mathrm{)}\mathrm{\times }\mathrm{1.97}\mathrm{+}\mathrm{0.54}\mathrm{\ge }\mathrm{(}\mathit{J}\mathrm{-}\mathit{H}\mathrm{)}\mathrm{\ge }\mathrm{(}\mathit{H}\mathrm{-}\mathit{K}\mathrm{)}\mathrm{\times }\mathrm{1.97}\mathrm{+}\mathrm{0.24}\mathit{,}& & \end{array}$and dividing the stars in that strip at (H − K) = 0.4. Stars featuring (H − K) ≥ 0.4 should be dominated by disk giants with moderate to high extinction, while stars exhibiting (H − K) < 0.4 are dominated by nearby disk giants and dwarfs with low extinction. The resolution and extent of these maps allow for a detailed study of Galactic structure which will be the subject of a future work.

5. Conclusions

We have derived empirical transformations from VVV to 2MASS for 152 fields of the VVV survey of the Galactic disk. The transformations in each case have been derived using an iterative clipping algorithm, which improves the robustness of the coefficients. The coefficients reflect the inverse of the relations used in calibrating onto the VISTA photometric system, and as expected we have found statistically significant correlations between the transformation coefficients and the Galactic extinction used in the disk. Our results also suggest some scatter in the transformations which in the case of high extinction fields seem to be related with the inadequacy of the SFD maps used in the zeropoint calibration and require further analysis. Our photometric transformations allow to avoid some of the described uncertainties when working with the VVV catalogues as well as to complement with 2MASS observations when working with saturated objects in the VVV catalogues.

In addition, we presented a stellar CMD and a color−color diagram for 134 × 10⁶ sources in the Galactic plane. The stellar CMD is dominated by main sequence stars in the disk, whose breadth is widened by differential extinction. The sequence tied

to more distant red giants is also seen. In addition, the derived infrared color excess ratio is in agreement with previously reported values. Finally, we present density maps of main sequence stars and red giants. These are useful for identifying overdensities such as star clusters and Galactic spiral arms, as well as the less-populated regions that may correspond to dense clouds.

Acknowledgments

M.S. acknowledges support by Fondecyt project No. 3110188 and Comité Mixto ESO- Chile. We gratefully acknowledge use of data from the ESO Public Survey programme ID 179.B-2002 taken with the VISTA telescope, data products from the Cambridge Astronomical Survey Unit, and funding from the FONDAP Center for Astrophysics 15010003, the BASAL CATA Center for Astrophysics and Associated Technologies PFB-06, the MILENIO Milky Way Millennium Nucleus from the Ministry of Economys ICM grant P07-021-F. R.K.S. and D.M. acknowledge financial support from CONICYT through Gemini Project No. 32080016 and by Proyecto FONDECYT Regular No. 1090213. Support for R.K.S. is provided by the Ministry for the Economy, Development, and Tourism’s Programa Iniciativa Científica Milenio through grant P07-021-F, awarded to The Milky Way Millennium Nucleus. J.B. is supported by FONDECYT No. 1120601. R.K. acknowledges support from Proyecto FONDECYT Regular No. 1130140 and Centro de Astrofísica de Valparaíso. A.R.L. thanks partial financial support from DIULS project CDI12141. RB thanks financial support from FONDECYT Regular No. 1120668. This material is based upon work supported in part by the National Science Foundation under Grant No. 1066293 and the hospitality of the Aspen Center for Physics.

References

Appendix A: Coefficients of the photometric transformations

Appendix B: Coefficients of the photometric transformations separated by populations

In addition to the transformations presented in the previous section, we have produced similar coefficients discriminating the different stellar populations with a simple procedure. Figure B.1 illustrates the technique: for each field we calculated a color histogram for a range of colors, where a double Gaussian fit is used to estimate the minimum between the main sequence and post-main sequence star distributions. This minimum is then used as limit to separate both populations in the CMD. Tables B.1 and B.2 show the derived coefficients of the photometric transformations for main sequence, and post main sequence stars respectively, which have been calculated using the same procedure applied to the complete sample.

Fig. B.1 Example of the procedure applied to separate the stellar populations in each tile. Left, CMD for the VVV tile d003, the subsample of stars between the black dashed lines has been chosen to calculate an histogram of the color equation (J − K)ROT = (J − K + 1.0)    ×    0.985 − (10.0 − K)    ×    0.174. Right, respective histogram for the stars selected in the CMD, a double Gaussian fitting (solid purple line) is used estimate the minimum between the main sequence and post main sequence distributions (red dashed line), which is used to separate the populations.

Appendix C: Variation of the photometric coefficients per tile

Thus far we presented photometric transformations calculated for each tile. Here we explore the variation of the transformation coefficients across single tiles. We divided a complete tile in 64 (8 × 8) parts. Each of these 64 sub-fields (1597 × 1957 pixels) was used to calculate the transformation coefficients with the same procedure applied to complete tiles. We chose two tiles with different reddenings, namely tiles d003 and d050 (with modified SFD reddenings E(B − V) ≃ 1.18 and E(B − V) ≃ 3.29, respectively). The average and dispersion, which for both fields are shown in Table C.1, were weighted by the number of stars per sub-tile. Figure C.1 shows the map of the coefficients for tile d003. In general, there is general agreement between the average of the coefficients and those calculated for the complete field (Table A.1). In some cases the variations are beyond the error bars, which may be attributed to population and extinction variations, or small statistics (~300 stars) per sub-field. Furthermore, the observed weighted dispersion displays similar values for most of the coefficients ~0.02 mag, with the exception of β_HK, which exhibits a dispersion three times larger (~0.06 mag). Again, the observed dispersion in β_HK (Fig. 8) appears sensitive to extinction.

Fig. C.1 Variations of the coefficients for the photometric transformations across a single tile, tile d003. The complete tile has been divided in 64 parts (8 × 8). (Top), number of stars per sub-field. (Second row to bottom), map of coefficients of the photometric transformations and their respective errors.

Appendix D: Transformation coefficients divided by latitude and longitude

All Tables

All Figures

	Fig. 1 Galactic disk fields imaged by the VVV survey. The VVV disk tile names start with d, followed by the numbering as shown in the figure.
In the text

	Fig. 2 Transmission curves for the 2MASS and VISTA photometric systems.
In the text

	Fig. 3 Color−color and color−magnitude diagrams for the tile d003. VVV data (blue dots) have been matched with 2MASS data on the same field (pink dots), where a subsample has been chosen to calculate the coefficients (dark grey). A limiting magnitude (orange dashed line) in each band has been used to avoid saturated VVV stars.
In the text

	Fig. 4 Comparison of 2MASS and VVV photometry for stars observed in tile/field d003. In each case an iterative clipping algorithm has been applied to each one of the 20 adaptive bins of the distribution. The selected stars of the clipping algorithm (grey) have been used to calculate the linear fit, and the individual photometric uncertainties of each star were considered.
In the text

	Fig. 5 Color−color diagram for VVV stars transformed to the 2MASS photometric system for tile d003. The transformation equations derived in Fig. 4 have been applied to the VVV colors (grey). The same stars featured in the 2MASS catalogue are overplotted (pink).
In the text

Fig. 6 Coefficients of the VVV-2MASS transformations as a function of Galactic longitude and latitude for 152 VVV tiles in the Galactic disk. Top and second row, we divided the sample into low (red; | b| ≲ 1°) and high latitude fields (green; 2.1° ≳ |b| ≳ 1°). A fourth order polynomial was fitted in each case. Third and bottom row, photometric coefficients divided into low longitude (red; l ≳ 320°), and high longitude fields (green; l ≲ 320°).

In the text

	Fig. 7 Comparison of isochrones in the 2MASS (black) and VISTA (grey) photometric systems for a 10 Gyr population (Z = 0.019) observed through two extinction values (Av = 0 and Av = 10).
In the text

Fig. 8 Coefficients of the VVV-2MASS transformations as a function of the reddening used to correct the zeropoint for 152 VVV fields in the Galactic disk. We included in each plot a linear fit with an iterative clipping algorithm similar to that used to calculate the photometric transformations. Grey points are those rejected during the clipping procedure. Moreover, the Spearman’s rank order correlation coefficient rS has been calculated in each case.

In the text

Fig. 9 Binned color−magnitude and color−color diagrams for all sources defined as stellar in the VVV catalogues (86 millions), which constitutes 152 tiles of the Galactic disk. Magnitudes have been transformed to the 2MASS photometric system in each tile using the respective coefficients. The CMD has been calculated at a resolution of 500 × 1600 bins, which corresponds to a binsize of 0.005 mags/bin. Similarly, our color−color diagram for the tiles of the Galactic disk was constructed at a resolution of 400 × 800 bins and the same binsize of the binned CMD. The latter includes an unreddened 0.05 Gyr isochrone (grey solid line) in the 2MASS system for reference.

In the text

Fig. 10 Map featuring the number of sources or the disk tiles (152 fields) in VVV with a 0.005° × 0.005° bin/pixel size. Top, map for all the sources in our combined JHKs catalogues, 136 million sources. Second row, map for all the stellar sources, 88 million stars. Third row, map for stellar sources for the objects lying in a stripe in the color−color diagram defined by (H − K) × 1.97 + 0.54 ≥ (J − H) ≥ (H − K) × 1.97 + 0.24 and (H − K) ≥ 0.4; this selection should be dominated by disk red giants with high extinction. Bottom, same as before, but for (H − K) ≤ 0.4; the population selected in this starcount map should be dominated by red-giants and some main sequence stars with low extinction.

In the text

Fig. B.1 Example of the procedure applied to separate the stellar populations in each tile. Left, CMD for the VVV tile d003, the subsample of stars between the black dashed lines has been chosen to calculate an histogram of the color equation (J − K)ROT = (J − K + 1.0)    ×    0.985 − (10.0 − K)    ×    0.174. Right, respective histogram for the stars selected in the CMD, a double Gaussian fitting (solid purple line) is used estimate the minimum between the main sequence and post main sequence distributions (red dashed line), which is used to separate the populations.

In the text

	Fig. C.1 Variations of the coefficients for the photometric transformations across a single tile, tile d003. The complete tile has been divided in 64 parts (8 × 8). (Top), number of stars per sub-field. (Second row to bottom), map of coefficients of the photometric transformations and their respective errors.
In the text