THE NEXT GENERATION VIRGO CLUSTER SURVEY. XIX. TOMOGRAPHY OF MILKY WAY SUBSTRUCTURES IN THE NGVS FOOTPRINT

Large-scale stellar mapping of the Milky Way by panoramic optical and infrared imaging surveys—most notably the Sloan Digital Sky Survey (SDSS) and the Two Micron All Sky Survey (2MASS)—has revealed a rich and complex panoply of faint, remote substructures (e.g., Ibata et al. 2001a, 2001b, 2002; Newberg et al. 2002, 2007; Majewski et al. 2003; Belokurov et al. 2006; Martin et al. 2014). Indeed, the many stellar streams that have now been discovered in the outer Galaxy provide prima facie evidence that the assembly of the halo is an ongoing process. While some of these streams are clearly still attached to their progenitor systems (e.g., the Sagittarius tidal stream), others are seemingly isolated and left adrift away from their ancestral homes (e.g., the Orphan stream; Belokurov et al. 2006; Grillmair 2006). Needless to say, the properties of these stellar streams provide us with invaluable information on both the accretion history of the Milky Way and its gravitational potential.

The archetypal stellar stream—that of the tidally disrupting Sagittarius dwarf galaxy (discovered by Ibata et al. 1994, 1995)—has now been mapped extensively across both the northern and southern hemispheres of the Galaxy (e.g., Mateo et al. 1996, 1998; Totten & Irwin 1998; Majewski et al. 1999, 2003; Ivezić et al. 2000; Yanny et al. 2000, 2009; Dohm-Palmer et al. 2001; Ibata et al. 2001a, 2002; Martínez-Delgado et al. 2001; Vivas et al. 2001; Newberg et al. 2002, 2003; Bellazzini et al. 2003; Belokurov et al. 2006, 2014; Correnti et al. 2010; Niederste-Ostholt et al. 2010; Ruhland et al. 2011; Carlin et al. 2012a; Koposov et al. 2012, 2015; Jerjen et al. 2013; Pila-Díez et al. 2014; Huxor & Grebel 2015; Hyde et al. 2015).

As the quality and quantity of data for the stream have improved, a wide range of models for its formation have been developed and refined (e.g., Velazquez & White 1995; Helmi & White 2001; Ibata et al. 2001b, 2013; Martínez-Delgado et al. 2001; Helmi 2004; Johnston et al. 2005; Law et al. 2005; Fellhauer et al. 2006; Law & Majewski 2010; Peñarrubia et al. 2010; Casey et al. 2012; Deg & Widrow 2013; Gibbons et al. 2014). The latest data now suggest that it is difficult to accommodate both the kinematic and photometric measurements of the leading and trailing arm within one single prolate, spherical, or oblate Milky Way potential (although it is possible if the density profile of the halo is allowed greater freedom; Ibata et al. 2013). From a modeling standpoint, the discovery of an apparent bifurcation in the stream (Belokurov et al. 2006; Koposov et al. 2012; Slater et al. 2013), a recently discovered offset between the trailing arm and the predictions of many models (Belokurov et al. 2014; Koposov et al. 2015), and the possible existence of faint, associated streams (Koposov et al. 2013) have further complicated matters. At the present time, two widely used models for the Sagittarius tidal stream are those of Law & Majewski (2010, hereafter LM10) and Peñarrubia et al. (2010, hereafter Pen10). To lessen the tension between the leading and trailing arm data, these models both use a triaxial—though nearly prolate—halo potential that has the awkward property of not being aligned with the plane of the Milky Way disk. The Pen10 model was specifically focused on modeling the stream bifurcation, which they attribute to a moderate amount of rotation in the stream progenitor. However, no evidence for such rotation has been found in the core of the Sagittarius dwarf galaxy (Peñarrubia et al. 2011).

More recently, Vera-Ciro & Helmi (2013, hereafter VC13) have calculated the orbit of the Sagittarius dwarf galaxy in a Galactic potential that includes both a varying shape with radius—as is seen in cosmological simulations (Vera-Ciro et al. 2011)—and the influence of the Large Magellanic Cloud (LMC). While not a full N-body simulation, a comparison of their test-particle orbit to the latest data showed that this new potential can alleviate some of the earlier tensions. It also showed that the inclusion of the LMC potential can significantly change the orbit of the Sagittarius and its tidal stream. In addition, Gómez et al. (2015) have shown that in such a scenario the Milky Way's response to the orbit of the LMC must also be taken into account. As we shall argue below, new simulations of the Sagittarius stream including all these effects are now needed, while deeper imaging at selected positions along the stream, including direct distance measurements, is needed to constrain the various model parameters.

A second prominent substructure in this region of the sky, but one lying at a closer distance, is the Virgo Stellar Stream or Virgo overdensity (hereafter VOD). The VOD is now recognized to span more than 1000 square degrees (Jurić et al. 2008; Jerjen et al. 2013) and contain several dense clumps embedded within it (Vivas et al. 2001; Newberg et al. 2002, 2007; Vivas & Zinn 2003, 2006; Keller et al. 2008, 2009, 2010). In addition to the large-scale excess of halo stars that was originally used to identify the VOD, several distinct, kinematically grouped substructures have now been found in this region (Duffau et al. 2006, 2010, 2014; Newberg et al. 2007; Vivas et al. 2008; Prior et al. 2009; Starkenburg et al. 2009; Brink et al. 2010; Casey et al. 2012). Although most of these kinematical structures show high positive galactocentric velocities, their spread in velocity can be more than 100 km s⁻¹. The nature of these overdensities—and their relationship to the VOD itself and to each other—has yet to be conclusively established. None of them seem obviously associated with the Sagittarius leading arm, the bifurcation feature, or any of the predicted trailing arm features or older wraps in this region. It has been suggested that many, and perhaps all, of these substructures could be explained as the remnants of a now disrupted satellite galaxy (e.g., Carlin et al. 2012b and references therein), with stellar proper-motion measurements for some of the substructures seeming to point to an orbit that has just passed pericenter (Casetti-Dinescu et al. 2006; Carlin et al. 2012b). Whatever the true explanation, it is clear that the sightline toward the constellation of Virgo is a complex and intriguing "crossroad" in the Milky Way—and one for which a consensus has yet to emerge.

By a lucky coincidence, this region of the sky is also home to the rich cluster of galaxies nearest to the Milky Way: the Virgo Cluster, at a distance of 16.5 Mpc (Mei et al. 2007; Blakeslee et al. 2009). The cluster has been the subject of numerous past imaging studies (see, e.g., Binggeli et al. 1985; Richter & Binggeli 1985; Côté et al. 2004 and references therein) and is the target of a new, deep, panoramic, multiband survey with the Canada–France–Hawaii Telescope (CFHT): the Next Generation Virgo Cluster Survey (NGVS; Ferrarese et al. 2012). Although the primary goal of the NGVS is a census and characterization of baryonic substructure within the Virgo Cluster, the survey is also ideally suited for studying the structure of the Milky Way halo along this direction. For instance, in their NGVS study of Virgo's globular cluster populations, Durrell et al. (2014) clearly identified the Sagittarius stellar stream as a prominent foreground feature (see their Figure 5). Our study thus builds on the tradition of using wide-field photometric data sets acquired for background galaxies or clusters to study the intervening halo: those of, e.g., Martin et al. (2014), who mapped the highly structured Galactic foreground within the deep Pan-Andromeda Archaeological Survey (McConnachie et al. 2009), and Pila-Díez et al. (2014), who determined distances along the Sagittarius stream and various other substructures from pencil-beam survey data targeting galaxy clusters.

In this work, we focus on the two main stellar overdensities in, and around, the NGVS region: the Sagittarius stellar stream and the VOD. Using old, metal-poor stars located near the main-sequence turnoff (MSTO) region, we are able to measure accurate distances to these overdensities and explore their three-dimensional structure within the Galaxy. These measurements allow us not only to probe the geometry of these substructures but also to test the predictions of numerical models that hinge on the assumed properties of their progenitors and the Galactic halo potential.

This is the first NGVS paper to focus specifically on the Milky Way foreground star population. Other papers in this series have examined the distribution of globular clusters within the Virgo Cluster (Durrell et al. 2014); the properties of star clusters, ultracompact dwarfs, and galaxies in the cluster core (Zhu et al. 2014; Liu et al. 2015; Zhang et al. 2015); the internal dynamics of low-mass galaxies (Guérou et al. 2015, Toloba et al., in preparation); abundance matching of low-mass galaxies in the cluster core (Grossauer et al. 2015); interactions within possible infalling galaxy groups (Paudel et al. 2013); optical–IR source classification methods (Muñoz et al. 2014); a new member of the inner Oort cloud (Chen et al. 2013); and a catalog of photometric redshifts for background sources (Raichoor et al. 2014).

The paper is organized as follows. We begin with a short introduction to the NGVS in Section 2. In Section 3, we give an overview of the main substructures visible in the very deep NGVS data, including the VOD and the Sagittarius tidal stream. In Section 4, we determine accurate distances to the Sagittarius tidal stream using the NGVS data and compare those distances to the predictions of three leading stream models. We summarize and conclude in Section 5.

The NGVS is a multiband, panoramic imaging survey of the Virgo Cluster carried out with the MegaCam instrument mounted at prime focus on the 3.6 m CFHT. Full details on the survey design, reduction procedures, data products, and science goals have been presented in Ferrarese et al. (2012).

In brief, the survey covers an area of 104 deg² inscribed within the virial radii of Virgo's two main subclusters: the A subcluster to the north, centered on Virgo's cD M87, and the B subcluster to the south, centered on Virgo's optically brightest galaxy, M49. Observations were carried out in four optical bands—u*, g, i, and z—in the MegaCam filter system¹² to 10σ point-source depths of u* = 24.8, g = 25.9, i = 25.1, and z = 23.3 AB mag. The survey has subarcsecond seeing in all bands, with a median seeing of 054 in the i band. The survey also includes partial coverage of the NGVS footprint in the r band (see, e.g., Raichoor et al. 2014).

In Figure 1, we show the location of the NGVS footprint within the large-scale Milky Way stellar halo in the northern hemisphere, as seen by SDSS. In this figure, SDSS DR7 was used to create a density map of MSTO stars selected by the following color criteria:

$$\begin{eqnarray}&&0.2\lt ({g}_{{\rm{SDSS}}}-{r}_{{\rm{SDSS}}})\lt 0.3\\ &&({u}_{{\rm{SDSS}}}-{g}_{{\rm{SDSS}}})\gt 0.4.\end{eqnarray} \tag{ 1 }$$

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A magnitude cut of 20.4 < g_SDSS < 21.4 was also applied in order to select SDSS stars having approximate distances of 15 kpc ≲ d_⊙ ≲ 35 kpc. In this distance range, the two overdensities that we focus on in this paper—namely, the VOD and the brighter branch of the Sagittarius tidal stream bifurcation—are unmistakable. The Sagittarius tidal tail is running diagonally from (α, δ) ∼ (120°, 20°) to (200°, 10°). The fainter bifurcation feature is seen above the main stream. By contrast, the VOD appears as an immense overdensity that peaks at (α, δ) ∼ (190°–5°). Although its center lies well south of our fields, the VOD also extends northward into the NGVS footprint. Note that the NGVS also includes four outlying background fields (see the four squares in Figure 1 and Ferrarese et al. 2012) located ∼16° from the center of the footprint. Among the four NGVS background fields, two lie well off the main portion of the Sagittarius tidal stream, but two others fall squarely along the stream. As we show below, these two fields turn out to provide important constraints on the overall geometry of the stream.

Our analysis of these substructures obviously requires a catalog of stellar sources selected from the NGVS. Within the NGVS footprint, a catalog optimized for compact and unresolved sources was created as described in Liu et al. (2015) and summarized below. Note that the NGVS has implemented several data-processing pipelines, each optimized for a specific goal; for the purpose of this work, a source catalog was generated using NGVS stacks processed through the MegaPipe (Gwyn 2008) pipeline, which adopts a global estimation of the sky background. For compact and unresolved sources, these stacks provide the highest photometric accuracy (see Ferrarese et al. 2012 for details). Photometry was then performed using SExtractor (Bertin & Arnouts 1996) in dual-image mode with the g band—the deepest of the NGVS bands—as the detection image. Aperture magnitudes were measured in apertures of diameter 3, 4, 5, 6, 7, 8, 16, and 32 pixels (each pixel corresponding to 0187) and then corrected to an infinite aperture. This last step was performed by applying an aperture correction measured by matching the MegaCam 16-pixel aperture magnitudes to SDSS PSF magnitudes (transposed to the MegaCam photometric system as given in Equation (4) of Ferrarese et al. 2012) for a number of bright but unsaturated stars. All other aperture magnitudes (within 3, 4, 5, 6, 7, and 8 pixels) were then corrected to a 16-pixel aperture. Because of PSF variations from field to field, aperture corrections were calculated separately for each field and, of course, for each filter.

Point sources were then selected as having $-0.1\leqslant ({m}_{4}-{m}_{8})\leqslant +0.15$ mag, where m₄ and m₈ are the corrected aperture magnitudes measured within 4 and 8 pixels, respectively. The smaller of these two apertures is well matched to the average seeing of the MegaCam images given the pixel scale. The PSF is sufficiently uniform over the images that all point sources cluster tightly in (m₄ − m₈) (the same is generally true for the difference in any two aperture magnitudes). Although point-source selections were carried out separately in each of the u*, g, and i bandpasses, the overall results are not affected by the choice of bandpass (or a combination of them). Therefore, for the remainder of this work, we use the catalog of stellar sources derived in the g band. As a final step in the catalog preparation, the photometry for each object was dereddened following Schlegel et al. (1998). Note that the reddening along this line of sight is quite low (see, e.g., Boissier et al. 2015), with M87, which marks the center of the Virgo Cluster, having $E(B-V)=0.022$ mag.

Figure 2 shows the (Hess) color–magnitude diagram (CMD) of all NGVS stellar (point-like) sources identified in this way. The average photometric error in i and (g − i) as a function of i-band magnitude is shown on the left-hand side of the figure. This figure illustrates the location of Milky Way stars along this line of sight, which is dominated by faint MS halo stars, plus some very red disk dwarfs in the solar neighborhood. At the faintest magnitudes, one sees residual contamination from compact, background galaxies. At brighter magnitudes, still another source of contamination is discernible: globular clusters belonging to the Virgo Cluster that appear as nearly point-like at this distance (Jordán et al. 2005; Durrell et al. 2014). We will discuss our treatment of these various contaminants below.

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3.1. Selecting a Tracer Population

In this work, we use main-sequence (MS) stars located near the MSTO as our stellar tracers. MSTO stars are not as accurate distance indicators as some other stellar tracers (e.g., blue horizontal branch [BHB] stars), but they are more numerous than other stellar types and, as such, are attractive targets for mapping large-scale structure.

To map halo features using MS stars, we begin by constructing a polygon in the CMD centered on the MS of a particular theoretical isochrone (an "MS box") in order to select stars located near the turnoff region. Each box is centered on an isochrone that we henceforth adopt as the fiducial for this analysis: a PARSEC isochrone having an age of 9 Gyr and a metallicity of [M/H] = −0.695 dex (Bressan et al. 2012), which has MSTO i-band absolute magnitude = 3.8. These values have been chosen to match the Sagittarius stream properties in this region of the sky (Chou et al. 2007). In the left panel of Figure 2, the PARSEC isochrone is overplotted on top of the most visible turnoff feature that we see within the NGVS CMD: that of the Sagittarius stream. Grafted onto this isochrone, our MS boxes are wide enough to accommodate MS stars having a dispersion in metallicity and age centered on these mean values.

The MS boxes have been limited in (g − i) color space by requiring

$$\begin{eqnarray}&&0.20\lt (g-i)\lt 0.55.\end{eqnarray} \tag{ 2 }$$

Here the blue boundary corresponds to the MSTO color and the red boundary has been chosen to minimize contamination by Virgo globular clusters (whose position in the CMD is indicated in the right panel of Figure 2; see also Figure 1 of Durrell et al. 2014). By moving this selection box vertically in the CMD, we can identify MS stars at a range of heliocentric distances. When doing so, the vertical widths of the boxes are scaled smoothly as a function of magnitude to ensure that the physical depth of each sample of stars selected within the boxes is 5 kpc. Examples of MS boxes at three different distances are shown in the right panel of Figure 2.

For stars selected inside any of the MS boxes, we impose a second constraint: a color selection of

$$\begin{eqnarray}&&0.58\lt ({u}^{*}-g)\lt 0.90\end{eqnarray} \tag{ 3 }$$

that eliminates disk white dwarfs from our sample of MSTO halo stars. In Figure 3, this additional color selection is shown in the (u* − g)–(g − i) color–color diagram. The location of white dwarf stars and background galaxies is shown, demonstrating that, although the white dwarfs and MS stars have similar (g − i) colors, they are cleanly separated using the (u* − g) index. Especially at fainter magnitudes, we find that up to ∼20% of our MS samples would actually be (disk) white dwarf candidates if this extra color selection criterion were ignored. Such a contamination rate would heavily skew the distance estimates for these stars, as demonstrated in Figure 4. In this figure, we calculate MSTO distances to stars in the TRILEGAL model mock catalog (Girardi et al. 2005, 2012), from which we took a selection of stars comparable in galactic latitude and magnitude range to our NGVS sample. The distance is calculated from the difference between the apparent magnitude of MSTO stars in the model (selected by 0.1 < (g − i) < 0.35) and an absolute magnitude of i = 4, in accordance with the approximate MSTO absolute magnitude of halo stars with age ∼11 Gyr and [Fe/H] ∼ −1.0. In order to derive the needed accurate distances to individual stars—rather than a characterization of the distance distribution of the population—we focus for the purpose of this test solely on the MSTO stars and thus use a (g − i) range smaller than that used for the MS boxes. The two panels show the derived and model input distances both with and without an extra (u* − g) cut applied to the model stars. Clearly, for deep photometric studies of halo star populations, the addition of a second color index that includes a blue bandpass is absolutely essential.

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Background galaxies in our sample of MSTO halo stars are also reduced by the combined color cuts, but extend into the MSTO region shown in Figure 3 with increasing number at fainter magnitudes. Significant contamination from these misidentified background galaxies occurs at i ∼ 23.5 (see Figure 2); therefore, we adopt this as the depth limit to our analysis.

The effectiveness of this approach in eliminating contamination from background sources, including globular clusters in the Virgo Cluster, is illustrated in Figure 5. In the left panel of this figure, we show the location of Virgo galaxies within the NGVS footprint, with symbol sizes scaled according to galaxy B-band luminosity. The supergiant elliptical galaxies M49 and M87 are denoted by the red crosses in each panel of this figure. The middle panel shows a density map of the NGVS point sources brighter than i = 23.5 mag, a selection that eliminates most of the contamination from background galaxies. However, it is clear that significant contamination from misidentified Virgo globular clusters remains, manifesting as strong density peaks at the location of M49, M87, and many other Virgo galaxies. In the right panel of Figure 5, we show a map of MS stars selected using a selection both on i-band magnitude and on location in the (u* − g)–(g − i) color–color diagram. Clearly, the contamination from globular clusters has now been largely eliminated by the color–color selection and no longer affects our view of the intervening halo.

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In the remainder of the paper, we adopt the MS star selection process described above, which allows the halo to be traced out to distances of d_⊙ ∼ 90 kpc. Because NGVS is several magnitudes deeper than SDSS—the 95% completeness limit of SDSS is reached at i = 21.3 (Abazajian et al. 2009)—it allows us to probe a lot deeper into the outer halo. MS mapping based on SDSS photometry alone has mainly focussed on distances <20 kpc (e.g., Jurić et al. 2008).

3.2. Blue Horizontal Branch Stars as Tracers

3.3. Halo Tomography

In Figure 6, we use our selection criteria for MS boxes placed at different distances to perform tomography of the Milky Way halo. Density maps for stars within each distance slice are shown in 3' by 3' cells, smoothed with a Gaussian filter of FWHM = 12'. The nine panels in Figure 6 show MS stars centered on our fiducial isochrone at mean heliocentric distances of d_⊙ = 5, 10, 15, 20, 25, 30, 40, 50, and 60 kpc. These distances are labeled in each panel, along with the mean MSTO magnitude in each bin.

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Already at distances of 5–12 kpc, an overdensity begins to appear in the southern half of the survey footprint, at a location and distance consistent with the VOD (see Section 1). At distances of 25–40 kpc, the Sagittarius tidal stream is clearly seen slicing across the NGVS footprint. At farther distances (up to 50 kpc), the Sagittarius tidal stream still appears at a low level. Although a certain distance spread within the stream is seen, as well as expected (see also Sections 4.2.2 and 4.4), the tails of this distribution can be mostly ascribed to remnant contamination from white dwarf populations and photometric uncertainties. At intermediate distances, we see a rather lumpy stellar distribution that could be due to a mixture of stars belonging to these two substructures. We do not clearly detect the bifurcation feature that runs parallel to the Sagittarius stream at slightly higher declinations (e.g., Belokurov et al. 2006; Koposov et al. 2012; Slater et al. 2013; de Boer et al. 2015). This is because, at the highest declinations probed by the NGVS, the secondary stream is too faint and no clear background region is available within the NGVS footprint for it to stand out against.

The VOD, which has previously been observed at distances ranging from 5 to 30 kpc, is known to spread over thousands of square degrees (Jurić et al. 2008; Jerjen et al. 2013). The VOD stellar density reaches its maximum at lower declinations than are accessible by the NGVS, and, indeed, most previous studies have targeted areas of declinations lower than those examined here. We note that several formation models for the Sagittarius stream suggest that some trailing arm debris and/or older wraps could be present within the NGVS footprint at smaller distances than the leading arm. Based on photometry alone (i.e., without any radial velocity or proper-motion information), it is difficult to conclusively rule out the possibility that some of the substructure we attribute to the VOD may instead be associated with the Sagittarius tidal debris. However, according to current models, any secondary streams are not expected to be as strong as the prominent overdensity we see in our data. For instance, in the LM10 model, no debris features in the NGVS fields are predicted at ∼12–18 kpc, which is where we see our peak density. Henceforth, we will therefore refer to the southerly feature detected between 5 and 25 kpc as the VOD and consider it separately from the Sagittarius stream.

We see the VOD first appear at d_⊙ ∼ 8 kpc and disappear completely by d_⊙ ∼ 25 kpc. In this distance range many smaller "hotspot" regions can be observed within the broader overdensity feature itself. Spatially, the VOD is separated from the Sagittarius tidal stream in distance as well as location on the sky. In the density maps shown in Figure 6, the stream appears clearly in the mid-upper region of the footprint, whereas the VOD is strongest at the very bottom of the survey, at decl. ≲8°. A sharp cutoff is used to indicate the strongest part of the VOD in panel (b) of Figure 6, though it appears across the entire region with density decreasing toward the top right (see panels (b) and (c)).

As shown in, e.g., Helmi et al. (2011), galactic substructures tend to be distributed very anisotropically on the sky in halo simulations carried out within a ΛCDM framework. One should therefore be careful about naively linking two overdensities on the sky to a common physical origin. Indeed, it may be prudent to look more deeply into regions that are already known to show an abundance of substructures. Although this is exactly what we have done in our analysis, it is worth noting that we find no convincing evidence for new overdensities lying behind the Sagittarius leading arm.

In this section, we use our halo star density maps to examine the three-dimensional structure of the Sagittarius tidal stream, specifically its distance gradient along the line of sight.

4.1. CMD Analysis of the Sagittarius Tidal Stream

The Sagittarius stream first appears in Figure 6 at a distance of d_⊙ ∼ 20 kpc and reaches its greatest prominence in panel (f), at a distance of ∼30 kpc. The stream is clearly visible as a broad swath extending from higher to lower decl. as R.A. increases.

Examination of panels (f)–(g) of Figure 6 shows hints of a significant distance gradient in the Sagittarius stream across the NGVS field, with the largest R.A. region being systematically farther away than the other extreme. We explore this further in Figure 7, where we show the CMDs of halo MS stars selected within the red and blue boxes drawn in panel (vi) of Figure 6. The two NGVS background fields at δ ≥ 20°, which do not intersect any obvious substructures in this distance range (see Figure 1), were used to create a reference CMD that was subtracted from the CMDs of the tidal stream regions. These background-subtracted CMDs are shown in the left and middle panels of Figure 7. Our fiducial isochrone is shown as the dashed green curve in each panel, shifted to a common distance modulus of (m − M) = 17.8 mag (d_⊙ ≈ 36.3 kpc).

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A differential CMD for the Sagittarius stream is shown in the right panel of Figure 7, in which the CMD in the middle panel (composed of stars within the blue spatial box in panel (f) of Figure 6) was subtracted from the CMD in the left panel (composed of stars in the red spatial box in panel (f) of Figure 6). The results of this subtraction in the right panel of Figure 7 are color-coded according to the differential over- or underabundance of the number of stars in the red or blue spatial box, respectively. This differential analysis illustrates that the mean distance to the stream changes with position on the sky. This is most clearly seen to the left and right of the MS of the overplotted fiducial isochrone. Whereas left of the isochrone MS the pixels are mostly blue (corresponding to a relative overabundance of stars in the blue spatial box at larger distance), they are mostly red on the right side, in line with a relative overabundance of stars in the red spatial box at closer distances. By fitting an isochrone to both spatial fields separately, we find that the vertical shift between the two best fits corresponds to a distance difference of ∼13 kpc.

4.2. Main-sequence Turnoff Star Analysis

4.2.1. Refining Our CMD Analysis

The deep photometry and excellent image quality available in the NGVS allow us to identify MS halo stars in this region of the sky—with minimal contamination—to larger distances than has been possible in the past (e.g., Jurić et al. 2008; Sesar et al. 2011). Additionally, this excellent data set enables the measurement of distances to a higher level of precision than we have demonstrated thus far using broad MS boxes. We therefore present a more refined approach in this section.

We begin by fine-tuning the box dimensions so that their width at each luminosity is proportional to the uncertainty of the photometric measurements (resulting in a trapezoid-like shape in the CMD; see the left and middle panels of Figure 7). This allows us to compensate naturally for the larger photometric uncertainties of fainter stars when assessing their likelihood as Sagittarius stream members. The aim of this exercise is to maximize our selection of Sagittarius stream stars, so we use again our fiducial isochrone as the ridge line of this MS box. Subsequently, we step this spatial box down the CMD to represent populations at increasing distance, and at each step we apply the weighting scheme to effectively cross-correlate the observed stellar density on the CMD with that of the model isochrone. At each step of the MS box, as the region shifts down the CMD, the highest weights are assigned to stars lying along the ridge line of the MS region (i.e., those most likely to be at the exact distance of the MS region). The assigned weights decrease for stars that are more displaced from the ridge line according to a Gaussian function whereby the width is set such that the edges correspond to a 3σ level, following Equation (3) of Pila-Díez et al. (2014). When implementing this algorithm, we apply the same selections on (g − i) and (u* − g) color described in Section 3 (i.e., Equations (2) and (3)). At each position of the MS box, the integral of the weighted stars inside the box represents the MS star density.

4.2.2. Sagittarius Stream Distances

In the above approach, a peak in the MS star density profile corresponds to an overdensity at the distance modulus applied to the fiducial isochrone. To measure distances at various positions along the stream, we divide the NGVS footprint into 2 deg² cells and apply the algorithm to each cell separately. Figure 8 illustrates this process, emphasizing the distance gradient along the stream within the NGVS footprint. In the left panel, two cells at either end of the stream have been highlighted. In the right panel, we show the corresponding MS star density distributions for these regions. The two peaks are separated in mean distance by 6 kpc. This is slightly smaller compared to the distance separation inferred from the CMD analysis described in Section 4.1, but note that the spatial boxes are different as well.

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There are several sources of uncertainty intrinsic to this method. The first is the choice of theoretical isochrone used for the ridge line of the MS region (which we have chosen specifically to match what is known about Sagittarius stream stars in this region of the sky; see, e.g., Chou et al. 2007). Other sources of error include sampling errors caused by the limited number of stars available in a given box, photometric errors on the individual stellar magnitudes and colors, and contamination by foreground and/or background sources.

We have accounted for photometric uncertainties in our distance measurements by implementing a "bootstrapping" method. Random 90% completeness stellar subsets were selected, and the cross-correlation algorithm was run on each of them to investigate the robustness of the original distance estimate. This procedure has been repeated 250 times for each region. The red and blue histograms shown in the right panel of Figure 8 are the 90% completeness peak distance distributions for the same two example regions used to create the corresponding MS density distributions. The percentiles of the 90% completeness histograms are taken as the uncertainties on our distance measurements throughout this work.

In cases where the bootstrapping method yielded more than one distinct peak in MS star density distribution, the individual peaks were treated as separate overdensities—each with its own distance estimate and accompanying error distribution. This approach acknowledges the possibility that any given line of sight might cut through multiple overdense regions, rather than forcing the method to find only a single peak or, worse, defining a final distance as the mean of two distinct peaks. However, we do define a threshold above which a distance peak is considered to be a real feature. In what follows, we consider only those overdensities that were identified by the bootstrapping method as a main feature in more than 40% of the cases. Because they should provide a useful test of future simulations, we have summarized our findings in Table 1. From left to right, the columns of this table record the cell R.A. and decl., measured distance modulus, upper and lower 1σ errors, and adopted weights. These weights correspond to the fraction of times the overdensity peak at this distance is recovered in our bootstrapping tests.

Table 1.  Sagittarius Stream Distances Derived from the NGVS

αcenter	δcenter	(m − M)	+σ	–σ	Weight (/100)
(deg)	(deg)	(mag)	(mag)	(mag)
183.0	10.0	17.56	0.27	0.09	100
183.0	11.0	17.53	0.16	0.16	62
183.0	12.0	17.60	0.45	0.05	100
183.0	13.0	17.14	0.15	0.01	46
183.0	13.0	17.53	0.29	0.02	54
183.0	14.0	17.50	0.06	0.01	69
185.0	9.0	17.42	0.13	0.05	58
185.0	9.0	17.88	0.00	0.09	42
185.0	10.0	17.75	0.17	0.06	90
185.0	11.0	17.50	0.01	0.03	41
185.0	11.0	17.85	0.07	0.02	59
185.0	12.0	17.33	0.18	0.18	48
185.0	12.0	18.03	0.02	0.11	52
185.0	13.0	17.65	0.00	0.05	64
185.0	14.0	17.73	0.15	0.03	93
185.0	15.0	17.65	0.09	0.14	100
187.0	9.0	17.93	0.07	0.01	67
187.0	10.0	18.03	0.02	0.07	81
187.0	11.0	17.93	0.07	0.11	87
187.0	12.0	18.00	0.05	0.09	64
187.0	13.0	17.48	0.17	0.01	74
187.0	14.0	17.67	0.02	0.16	64
187.0	15.0	17.70	0.01	0.19	79
187.0	16.0	17.15	0.05	0.09	56
187.0	16.0	17.44	0.34	0.02	44
187.0	17.0	17.62	0.11	0.07	92
189.0	7.0	17.95	0.05	0.04	78
189.0	8.0	17.47	0.00	0.23	45
189.0	9.0	17.69	0.14	0.36	100
189.0	10.0	17.78	0.27	0.14	100
189.0	11.0	17.71	0.03	0.02	88
189.0	12.0	17.81	0.15	0.07	99
189.0	13.0	17.62	0.29	0.02	68
189.0	14.0	17.19	0.09	0.00	42
189.0	14.0	17.75	0.01	0.01	58
191.0	8.0	17.60	0.14	0.09	100
191.0	9.0	17.80	0.08	0.24	99
191.0	10.0	17.55	0.05	0.04	85
191.0	11.0	17.75	0.12	0.01	73
191.0	12.0	17.83	0.08	0.05	80
191.0	13.0	17.87	0.05	0.18	93
191.0	14.0	17.81	0.15	0.02	86
193.0	11.0	17.74	0.09	0.18	84
193.0	12.0	17.89	0.07	0.06	96
171.8a	20.8	17.24	0.14	0.14	100
203.4a	6.8	18.14	0.18	0.09	100

Note.

^aNGVS background fields.

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4.3. Comparison with Other Measurements

A comparison of the distances derived in this work with those from the literature is shown in Figure 9. For convenience, the distances have been plotted against the Sagittarius stream coordinate, Λ_⊙, which is a coordinate system defined along the Sagittarius stream (for details, see Majewski et al. 2003).¹³ Since only one of the Sagittarius stream coordinates is given in this figure on the x-axis, a naive plotting of literature results will give a large range caused by targets that are associated with leading or trailing arm debris, respectively (as well as older wraps). Here we show only stars associated with leading arm debris by the various authors, as this is the component of the Sagittarius stream that we see in the NGVS footprint. There is generally good agreement among the different studies, especially when one considers that different tracers have been used in the various studies, each with their own typical distance uncertainties. Moreover, Majewski et al. (2004) and Shi et al. (2012) use individual stars as tracers, whereas our measurements, as well as the points shown for Pila-Díez et al. (2014) and Belokurov et al. (2014), measure distances to a population of tracer stars, which explains the reduced dispersion in the latter measurements. The larger dispersion in Majewski et al. (2004) relative to the work of Shi et al. (2012) can further be explained by the fact that Shi et al. (2012) measured only distances to stars that were spatially overlapping with the LM10 model of the Sagittarius stream, whereas no such restriction was used in the earlier work of Majewski et al. (2004).

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Our observed distances to the stream are shown as the colored triangles in Figure 9, as well as in each panel of Figure 10. The symbol sizes of each distance measurement have been scaled by the area under the corresponding peak in the bootstrapping method histogram. To supplement measurements within the main body of the NGVS footprint, we also include the two NGVS background fields situated along the Sagittarius stream (see Figure 1). These are shown as black triangles offset by ∼15° from the other NGVS data points.

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4.4. Comparison with Numerical Models

We have used deep, multiband (u*giz) imaging from the NGVS to perform tomography of the Galactic halo in a ∼100 deg² region in the direction of the Virgo Cluster. This region of the sky is known to contain two of the most prominent structures in the halo of the Milky Way: the VOD and the Sagittarius stellar stream. Compared to the SDSS, our NGVS photometry both is significantly deeper (by ≈3.2 mag for point sources) and has greatly improved image quality (054 versus 13). We describe an algorithm to select candidate MSTO stars using a combination of source concentration, i-band magnitude, and (g − i) and (u* − g) colors. Using this technique, we are able to identify MSTO halo stars out to distances of d_⊙ ∼ 90 kpc, with negligible contamination from background sources such as faint, compact galaxies and globular clusters in the Virgo Cluster.

We have carried out tomography of the halo using an MSTO star filtering approach. The VOD appears in our data at distances between 5 and 28 kpc and is notoriously clumpy in nature. It is most prominent at low declinations, but extends nearly to the highest declinations reached in the survey. By contrast, the Sagittarius stream slices directly through the NGVS footprint at distances between 25 and 40 kpc. Carefully dividing the stream into 2 deg² cells, we measure the distance gradient along the leading arm and compare to the predictions of several numerical models. Our distances are in somewhat better agreement with the model of Peñarrubia et al. (2010) than that of Law & Majewski (2010). Good agreement is also found with the results of Vera-Ciro & Helmi (2013), who provide a test-particle orbit of the Sagittarius galaxy in a Milky Way potential that is of changing shape with radius and includes the influence of the LMC. We find no evidence for new halo substructures beyond a distance of d_⊙ ∼ 40 kpc.

Future papers in this series will explore the stellar kinematics in the NGVS and surrounding regions, as well as the properties of white dwarfs inside the NGVS footprint. For the time being, our tomographic analysis demonstrates how deep, multiband imaging at carefully chosen locations can be used to probe efficiently the three-dimensional geometry of halo streams. The time is thus ripe for a newer generation of stream simulations that can be used to better constrain the accretion history of the Milky Way and its gravitational potential.

We would like to thank the anonymous referee for insightful comments that helped to improve this paper. E.S. acknowledges partial funding from the Canadian Institute for Advanced Research (CIFAR) Global Scholars Academy. The authors thank Carlos Vera-Ciro for very helpful discussions and for sharing the compilation data from Vera-Ciro & Helmi (2013). E.S. and J.F.N. thank the organizers of the KITP program Galactic Archaeology and Precision Stellar Astrophysics for a stimulating workshop where part of this work has been completed. As such, this research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. C.L. acknowledges support from the National Natural Science Foundation of China (NSFC, Grant Nos. 11203017 and 11125313). This work is supported in part by the French Agence Nationale de la Recherche (ANR) Grant Programme Blanc VIRAGE (ANR10-BLANC-0506-01) and by the Canadian Advanced Network for Astronomical Research (CANFAR), which has been made possible by funding from CANARIE under the Network-Enabled Platforms program. This research used the facilities of the Canadian Astronomy Data Center operated by the National Research Council of Canada with the support of the Canadian Space Agency. The NGVS team owes a debt of gratitude to the director and the staff of the Canada–France–Hawaii Telescope (CFHT), whose dedication, ingenuity, and expertise have helped make the survey a reality.

Facilities: CFHT (MegaCam).