Turning the Tides on the Ultra-Faint Dwarf Spheroidal Galaxies: Coma Berenices and Ursa Major II
aa r X i v : . [ a s t r o - ph . GA ] O c t Turning the Tides on the Ultra-Faint Dwarf Spheroidal Galaxies:Coma Berenices and Ursa Major II Ricardo R. Mu˜noz , Marla Geha , & Beth Willman ABSTRACT
We present deep CFHT/MegaCam photometry of the ultra-faint Milky Waysatellite galaxies Coma Berenices (ComBer) and Ursa Major II (UMa II). Thesedata extend to r ∼
25, corresponding to three magnitudes below the main se-quence turn-offs in these galaxies. We robustly calculate a total luminosity of M V = − . ± . M V = − . ± . . − . Usinga maximum likelihood analysis, we calculate the half-light radius of ComBer to be r half = 74 ± . ± . ′ ) and its ellipticity ǫ = 0 . ± .
04. In contrast, UMa IIshows signs of on-going disruption. We map its morphology down to µ V = 32 . − and found that UMa II is larger than previously determined, ex-tending at least ∼
700 pc (1 . ◦ on the sky) and it is also quite elongated withan ellipticity of ǫ = 0 . ± .
2. However, our estimate for the half-light radius,123 ± . ± . ′ ) is similar to previous results. We discuss the implicationsof these findings in the context of potential indirect dark matter detections andgalaxy formation. We conclude that while ComBer appears to be a stable dwarfgalaxy, UMa II shows signs of on-going tidal interaction. Subject headings: dark matter – galaxies: dwarf - galaxies: individual (ComaBerenices, Ursa Major II) – Local Group Based on observations obtained at the Canada-France-Hawaii Telescope (CFHT) which is operated bythe National Research Council of Canada, the Institut National des Sciences de l’Univers of the CentreNational de la Recherche Scientifique of France, and the University of Hawaii. Astronomy Department, Yale University, New Haven, CT 06520, USA ([email protected],[email protected]) Haverford College, Department of Astronomy, 370 Lancaster Avenue, Haverford, PA 19041, USA ([email protected])
1. Introduction
For decades, only about a dozen dwarf galaxies were known to orbit the Milky Way.The majority of these systems corresponded to dwarf spheroidal (dSph) galaxies, the leastluminous, but, by number, the dominant galaxy type in the present-day universe. However,over the last five years, and thanks to the advent of the Sloan Digital Sky Survey (SDSS;York et al. 2000) the field of dwarf galaxies in the Milky Way has been revolutionized. Todate, fourteen new systems have been detected as slight overdensities in star count mapsusing the SDSS data (Willman et al. 2005a,b; Belokurov et al. 2006, 2007a, 2008, 2009;Zucker et al. 2006a,b; Sakamoto & Hasegawa 2006; Irwin 2007; Walsh et al. 2009). Theserecent discoveries have revealed a previously unknown population of “ultra-faint” systemswhich have extreme low luminosities, in some cases as low as L V ∼
300 L ⊙ (Martin et al.2008), and in average comparable (or lower) to those of Galactic globular clusters. However,spectroscopic surveys of the majority of these systems reveal kinematics and metallicitiesin line with those of dwarf galaxies (Kleyna et al. 2005; Mu˜noz et al. 2006; Simon & Geha2007; Kirby et al. 2008; Koch et al. 2009; Geha et al. 2009).Dynamical mass estimates of the ultra-faint galaxies based on line-of-sight radial veloci-ties indicate that these galaxies are extremely dark matter dominated, with central mass-to-light ratios (M/L) as high as 1 ,
000 in solar units. These systems are thus good laboratoriesto constrain cosmological models (e.g the ’missing satellites problem’; Kauffmann et al. 1993;Moore 1999; Klypin et al. 1999; Simon & Geha 2007) and to study the properties of darkmatter (Strigari et al. 2008; Kuhlen et al. 2008; Geha et al. 2009). However, these applica-tions hinge critically on the assumption that the masses and density distributions in thesesystems are accurately known. Current mass estimates for the ultra-faint dwarfs are basedon the assumption that the dynamical state of these systems have not been significantlyaffected by Galactic tides, and therefore that they are near dynamical equilibrium.There is circumstantial evidence for past tidal disturbance in a number of these satellitesbased on morphological studies. Coleman et al. (2007) for instance, found the Hercules dSphto be highly elongated, with a major to minor axis ratio of 6:1, larger than for any of the“classical” dSphs, and argued for a tidal origin of this elongation. Belokurov et al. (2007a)reported fairly distorted morphologies for several of the new ultra-faint dwarfs, althoughMartin et al. (2008) showed that results based on low number of star may not be statisticallysignificant because they suffer from shot noise. The strongest evidence for tidal interactionperhaps is for Ursa Major II, which appears to be broken into several clumps, lies close tothe great circle that includes the Orphan Stream (Zucker et al. 2006b; Fellhauer et al. 2007)and shows a velocity gradient along its major axis (Simon & Geha 2007).If dSphs galaxies are currently undergoing tidal stripping, or have in the past, then 3 –kinematical samples are expected to be “contaminated” with unbound or marginally boundstars. This will impact subsequent dynamical modeling, often resulting in overestimatedmass contents (Klimentowski et al. 2007; Lokas 2009). The degree of such contaminationis a function of both the projection of the orbit along the line-of-sight and the strengthof the tidal interaction. Therefore, even though tides do not affect appreciably the innerkinematics of dSphs until the latest stages of tidal disruption (e.g., Oh, Lin, & Aarseth 1995;Johnston et al. 1999; Mu˜noz et al. 2008; Pe˜narrubia et al. 2008), studies aimed at identifyingthe presence of tidal debris can help elucidate the dynamical state of these dwarf galaxies.Obvious tidal features around dSphs would indicate the presence of unbound stars and theireffects on the derived masses would need to be investigated. Alternatively, a lack of cleardetections in the plane of the sky would narrow the possibilities that kinematical samplessuffer from contamination, although it would not automatically imply that an object has notbeen tidally affected. Tidal features could still exist but be aligned preferentially along theline-of-sight and thus be hard to detect.Ultra-faint dwarf galaxies are useful probes of galaxy formation on the smallest scales(Madau et al. 2008; Ricotti et al. 2008). One of the outstanding questions related to theirdiscovery is whether these galaxies formed intrinsically with such low luminosities, or whetherthey were born as brighter objects and attained their current luminosities through tidalmass loss. Current metallicity measurements (e.g., Kirby et al. 2008) support the formerscenario. They show that the ultra-faint dwarfs are also the most metal poor of the dSphs,following the luminosity-metallicity trend found for the classical dSphs . On the other hand,if tidal features around these objects are firmly detected, it would clearly support the latterhypothesis.Given the importance of the questions at hand, it is essential that we investigate thedynamical state of these satellites. Due to the extreme low luminosity of the ultra-faintdwarfs, and therefore low number of brighter stars available for spectroscopic studies, deepimaging is currently the only way to efficiently detect the presence of faint morphologicalfeatures in the outskirts of these systems. We expect any tidal debris to be of very lowsurface brightness (Bullock & Johnston 2005) so that detecting it via integrated light isvirtually impossible. However, these galaxies are sufficiently nearby to resolve individualstars. Thus, using matched-filter techniques it is possible to detect arbitrarily low surface Simon & Geha (2007), using the same spectroscopic data but a different technique, reported system-atically higher metallicites for the ultra-faint dwarfs than those of Kirby et al. (2008). The discrepancy isexplained by the fact that the former study used the Rutledge et al. (1997) method that relies on the linearrelationship between Ca II triplet equivalent widths and [Fe/H], a technique now known to fail at very lowmetallicities. ∼
35 mag arcsec − , Rockosi et al. 2002; Grillmair 2006).In this article we present the results of a deep, wide-field photometric survey of the ComaBerenices (ComBer) and Ursa Major II (UMa II) dSphs, claimed to be two of the most darkmatter dominated dSphs (Strigari et al. 2008), carried out with the MegaCam imager onthe Canada-France-Hawaii Telescope. In §
2, we present details about the observations anddata reduction, as well as of artificial star tests carried out to determine our completenesslevels and photometric uncertainties. In §
3, we recalculate the structural parameters of thesesystems using a maximum likelihood analysis similar to that of Martin et al. (2008). In § − , whereas UMa II shows asignificantly elongated and distorted shape, likely the result of tidal interaction with theMilky Way. Our discussion and conclusions are presented in § §
6, respectively.
2. Observations and Data Reduction2.1. Observations
Observations of both ComBer and UMa II were made with the MegaCam imager on theCanada-France-Hawaii Telescope (CFHT) in queue mode. MegaCam is a wide-field imagerconsisting of 36 2048 × × field of view witha pixel scale of 0 . ′′ /pixel. UMa II was observed on nights between February and Marchof 2008, whereas ComBer was observed between April and May of 2008.For each dSph, four different, slightly overlapping fields were observed for a total areacoverage of nearly 2 × in the case of ComBer, and 1 . × in the case of UMa II.In each field, the center of the dSph was placed in one of the corners so that, when combined,the galaxy is located at the center of the overlapping regions as shown in Figure 1. For eachof the four fields, we obtained eleven 270s dithered exposures in Sloan g and eleven 468sdithered exposures in Sloan r in mostly dark conditions with typical seeing of 0 . − . ′′ .The dithering pattern was selected from the standard MegaCam operation options in orderto cover both the small and large gaps between chips (the largest vertical gaps in MegaCamare six times wider than the small gaps). 5 – MegaCam data are pre-processed by the CFHT staff using the “Elixir” package (Magnier & Cuillandre2004) prior to delivery. The goal is to provide the user with frames that are corrected forthe instrumental signature across the whole mosaic. This pre-process includes bad pixelcorrection, bias subtraction and flat fielding. A preliminary astrometric and photometricsolution is also included in the pre-processed headers.The World Coordinate System (WCS) information provided with the data is only ap-proximate, and we refine it using the freely available SCAMP package as follows: TerapixSExtrator is run on all chips (SCAMP reads in the output files generated by SExtrator)and output files are written in the FITS-LDAC format. SCAMP is then run on all chips.SCAMP uses the approximate WCS information in the frames’ headers as a starting point,and then computes astrometric solutions using, in our case, the SDSS-Data Release 6 (DR6,York et al. 2000; Adelman-McCarthy et al. 2008) reference catalog which is automaticallydownloaded from the Vizier database. Typically, several hundred stars in common betweeneach of our chips and SDSS are used to compute the astrometry and final solutions. InComBer, fields have typical global astrometric uncertainties of rms ∼ . ′′ , while for fieldsin UMa II they are slightly higher, with rms ∼ . ′′ . The output from SCAMP is a FITSheader file (one per processed frame), which is then used to update the WCS informationfor that given chip. The updated headers are then used to translate x and y positions intofinal equatorial coordinates. Prior to performing point-source photometry on our data, we split each mosaic frameinto its 36 individual chips. To take full advantage of our 11 dithered exposures per field(and per filter), we test two different methods for carrying out the photometry. See http://astromatic.iap.fr/software/scamp/ See http://astromatic.iap.fr/software/sextractor/ LDAC stands for Leiden Data Analysis Center.
For the first method, we carry out our photometry running first DAOPHOT/Allstaron the individual, non-coadded frames and then running the ALLFRAME package on theresulting files as outlined in Stetson (1994). ALLFRAME performs photometry simultane-ously on all 22 frames for a given field (11 per filter). DAOPHOT/Allstar are required priorto ALLFRAME to determine point spread function (PSF) solutions for each chip as well asto generate starlists for them individually. Optimum starlists to be used as input by ALL-FRAME are obtained by cross matching the DAOPHOT/Allstar results for the individualframes using the DAOMATCH and DAOMASTER packages (Stetson 1993). These packagesalso provide reasonably good estimates of the offsets between dithered individual exposuresnecessary to run ALLFRAME. Final output files from ALLFRAME are then combined intoa single catalog.
In our alternative reduction method, we coadd all 11 exposures per filter for each of the36 individual chips using the SWARP package . SWARP uses the WCS information storedin the frames’ headers to correct for shifts, small rotation between chips and distortions.However, since original WCS information in the headers is only approximate, we refine theastrometry (as described in § § Finally, photometric calibration was carried out by comparison with the SDSS-DataRelease 7 (DR7, Abazajian et al. 2009) catalog. We first match our final photometry withthe SDSS stellar catalog. We typically found several hundred stars in common with SDSS See http://astromatic.iap.fr/software/swarp/ < r < . . < g − r < .
0. The brighter limit is given by the saturation limit of our CFHT data. Wethen fit the equations: g = g instr + g + g ( g − r ) (1) r = r instr + r + r ( g − r ) (2)where g and r are the zero points and g and r are the respective color terms. We do thisfor each chip individually in order to determine whether there are chip-to-chip variations.In all cases, we find that the chip-to-chip differences, for both zero points and color termsare lower than the uncertainties in the derived parameters, and therefore we combine thestars in all 36 chips to derive final zero point and color term values. We do this via a linearleast-squares fit weighting by the respective uncertainties in the photometric magnitudes (asestimated by ALLFRAME) and rejecting 3 σ outliers. We obtain zero point and color termsfor each mosaic field independently (four per dSph, eight total). The resulting constants differby less than 2% in all cases. Uncertainties in the zero points vary from 0 . − .
004 magwhereas uncertainties in the color terms are of the order of ∼ . Final photometric uncertainties and completeness levels are determined via artificialstar tests. We first generate a fake color-magnitude-diagram (CMD) from which we willrandomly select artificial stars. We populate the CMD with stars in the magnitude andcolor ranges of 18 < g/r <
28 and 0 . < ( g − r ) < . < g/r <
28 range than in the brighter half of the CMD. We then select oneof the 11 dithered exposures as our reference frame. In all cases we select the first exposurein the g filter for this purpose. The goal is to inject stars in all 22 frames (per chip) in thesame fake RA and DEC positions in order to mimic real observations. Artificial stars arethen randomly selected from the fake CMD and are injected into the reference frame in auniform grid with a spacing of 40 pixels in both the x and y directions. Using the refinedastrometric solution calculated by SCAMP we convert the x and y positions of the artificialstars into RA and DEC coordinates which are then converted back to x and y positions,but in the reference frame of the other exposures. Care is taken so that all the stars fall 8 –in the common area between the 22 different exposures. In the end, nearly 3 ,
950 stars areintroduced per chip. We repeat this procedure ten times to improve our statistics, each timerandomly offsetting the grid’s zero-point position in x and y . We then carry out photometryon the artificial stars using the ALLFRAME method in the exact same manner as we didfor the science frames.We perform this test on only one chip per mosaic frame due to computational con-straints, for a total of four chips in each dSph. Since each of these fields was observed underslightly different seeing and darkness conditions, their respective magnitude limits are alsoslightly different. Thus, to set conservative overall completeness levels we select the valuesfrom our “shallowest” field in each dSph as our final numbers. We find that this representsa better choice than determining our limits from our combined artificial star’s photometryfor all four chips. In the latter case, the deepest fields dominate the results. The 50% and90% overall completeness levels of our photometry thus correspond to g = 25 . . r = 25 . .
75, respectively, for our ComBer fields, and g = 26 . . r = 25 . .
9, respectively, for UMa II. Figure 2 shows the resulting completeness levels.In order to clean our catalogs of galaxy interlopers and other, non-stellar detections, weapply cuts using DAOPHOT’s sharpness ( sharp ) and χ parameters. To define appropiatecuts, we fit third-degree polynomials to the χ and sharp distributions, as functions of g magnitude, obtained from the artificial star tests. After applying these cuts to both ourphotometric catalog and artificial star photometry our 90% completeness levels drop to g = 24 . r = 24 . g = 24 . r = 24 .
3. Results3.1. Structural Parameters
Our photometric catalogs for both ComBer and UMa II contain an order of magnitudemore stars than the SDSS photometry, and thus provide us with an excellent opportunityto re-estimate the structural properties of these systems. Martin et al. (2008) carried out a 9 –comprehensive analysis of the structural parameters of all the ultra-faints using the originalSDSS photometry. However, in the cases of ComBer and UMa II, owing to their very lowluminosities ( M V ∼ − α , δ ), ellipticity ( ǫ ), positionangle ( θ ), half-light radius ( r half ) and background density (Σ b ). We try three differentdensity profiles, exponential, Plummer (Plummer 1911) and empirical King (King 1962),and obtain structural parameters for all three:Σ exp ( r ) = Σ ,E exp (cid:18) − rr E (cid:19) (3)Σ Plummer ( r ) = Σ , P (cid:18) r r P (cid:19) − (4)Σ King ( r ) = Σ , K (cid:18) r r c (cid:19) − − (cid:18) r t r c (cid:19) − ! (5)where r E and r P are the exponential and Plummer scale lengths and r c and r t correspondto the King core and tidal radii respectively. The exponential scale length is related to thehalf-light radius by the relation r half = 1 . × r E while in the case of the Plummer profile, r P is equivalent to r half .We have followed a procedure similar to the one outlined in Martin et al. (2008) whichrelies on a maximum likelihood (ML) analysis of the data to constrain the structural param-eters. The basic idea of the method is as follows: We assume that the positions of the starsare well represented by a given density profile (one of the three mentioned above) which is,in turn, well described by a set of parameters p , p ,..., p j . We then maximize a function ofthe form: L ( p , p , ..., p j ) = Y i l i ( p , p , ..., p j ) (6)where l i ( p , p , ..., p j ) is the probability of finding the datum i given the set of parameters p , p ,..., p j . In the case of an exponential profile, this function takes the form: In the case of King profiles we calculate their r core and r tidal .
10 – l i ( p , p , ..., p j ) = S exp (cid:18) − r i r E (cid:19) + Σ b (7)where S , r i and r E are expressed in terms of the structural parameters we want to determine.In practice, we look for a global maximum L ( ˆ p , ˆ p , ..., ˆ p j ) by searching the j -dimensionalparameter space. In our case, the parameter space is 6 th -dimensional, with the free param-eters α , δ , ǫ , θ , r half and Σ b . In the case of a King profile, we fix the background densityusing the value obtained for the Plummer profile because of a degeneracy between Σ b andthe King tidal radius. To find a solution, we use the method described in Sand et al. (2009)which relies on the amoeba simplex algorithm (Press 1988) to search the parameter space.This method is somewhat sensitive to the specified region of parameter space to be searched(i.e. the initial guess and allowed range for the parameters) but it runs considerably fasterthan using an iteratively refined grid. In order to derive uncertainties for the structuralparameters, we carry out 10 ,
000 bootstrap (resampling with replacement) realizations ofour data. The distribution of a given parameter is well described by a Gaussian with onlyminor deviations in some cases (King core and tidal radii in particular), and therefore wefit Gaussian functions and report their mean and standard deviation as the mean and 1- σ uncertainty for a given parameter.To facilitate comparison with previous studies, we first compare the results of our algo-rithm when applied to the SDSS data with those derived by Martin et al. (2008). To mimictheir star selection procedure as closely as possible, we select stars within 1 degree from thesatellites’ centers, impose the conditions that r < . g < . L function. However, as shown in the same study, sta-tistical fluctuations due to the low number of stars in these dSphs can dramatically affect themorphology as well as the best-fitting parameters and therefore we regard our uncertaintiesas more realistic.We then apply the ML algorithm to our dataset. We select stars above the 90% com-pleteness levels and within a region around the main sequences of these objects (in orderto improve the signal to noise ratio of dSph versus Milky Way foreground stars). For thispurpose, we use an isochrone for a population 13 Gyr old and [Fe/H]= − .
27 ( Z = 0 . .
075 mag from the isochrone. We varied this distance between0 . .
100 mag and found no significant changes in the final parameters. We note that wedo not match the isochrone to the blue edge of the main sequence as it is customary whenisochrone matching is used to derive star cluster properties, but instead place the isochrone sothat it goes through the middle of the main sequences. For ComBer, our ML method yieldsa r half = 5 . ± . ǫ = 0 . ± .
04 and a position angle θ = − . ± . r half = 14 . ± . ǫ = 0 . ± .
02 and θ = − . ± .
7. The final sets of structural properties for both ComBer and UMa II arepresented in Table 1.This exercise also allows us to compare the results obtained from both our CFHTphotometry and the shallower SDSS data. As it was pointed out by Sand et al. (2009) intheir work on the Hercules dSph, we find relatively good agreement between the resultsobtained with both datasets, but our photometry allows us to place much tighter constrainson the derived structural properties. This is not surprising given that our deeper photometricdatabase is less sensitive to shot-noise effects that plague the shallower SDSS data. Figure5 illustrates this point. In this figure we show the distribution of four structural parametersfor ComBer, α , δ , r half and ǫ for all 10 ,
000 bootstraps and for both datasets where thesmaller uncertainties derived with the CFHT data are evident.In Figures 6 and 7a we show background subtracted density profiles for both satelliteswith the best exponential, Plummer and King models overplotted. These are not fits to thebinned data points, but are models constructed with the best parameters found via the MLmethod. As it can be seen, in the case of ComBer, both the exponential and King profiles areadequate descriptions of the data, with the Plummer profile being perhaps a less adequateone. The case of UMa II is quite different. Neither profile does a good job matching thedata. In fact, as shown in Figure 7b, the data are better matched by a shallower inner powerlaw ( γ = − .
96) and a steeper one in the outer parts ( γ = − .
40) reminiscent of the densityprofile derived by Grillmair (2009) for the Bo¨otes III stellar overdensity or the inner powerlaw shown by the tidally stripped Palomar 5 (Pal 5) globular cluster (Odenkirchen et al.2003). This result is consistent with a scenario wherein UMa II has been significantly tidallystripped, as suggested by Zucker et al. (2006b). We will explore this possibility in moredepth in §
4. 12 –
We estimate the absolute total magnitudes of ComBer and UMa II following a proceduresimilar to that outlined by Walsh et al. (2008). This method relies solely on the number ofstars belonging to the galaxy, and not on their individual magnitudes. As pointed out byMartin et al. (2008), Walsh et al. (2008) and Sand et al. (2009), the extreme low luminosityof the ultra-faint galaxies and therefore the low number of stars they contain, make tradi-tional methods, like the addition of fluxes from individual stars, too sensitive to the inclusion(or exclusion) of potential members (outliers). Adding or subtracting a few red-giant-branchstars (with absolute magnitudes as bright as M V = − . ∼ − . Z = 0 . − . − .
5. In addition, we usetheoretical luminosity functions computed using two different initial mass functions (IMF):a Salpeter (1955) with cutoff at 0 .
01 M ⊙ and a Chabrier (2001) log-normal.The theoretical luminosity function gives us the relative number of stars in magnitudebins, which can be integrated to obtain the total flux down to a given magnitude limit. Oneof the parameters we determine using the ML algorithm is the background surface densityΣ b which is related the number of stars N ∗ that belong to the galaxies by: N ∗ = N total − A Σ b (8)where N total is the total number of stars used to derive the structural parameters and A represents the total area of our fields. We use this N ∗ to normalize the theoretical luminosityfunction. By integrating the luminosity function and correcting by this normalization factorwe obtain the actual flux corresponding to our galaxies down to the respective magnitudelimits. To account for the light contributed by stars fainter than this limit, we add theremaining normalized integrated flux.As mentioned above, this method differs from traditional ones, and our derived lumi-nosities are conceptually different from those derived for brighter galaxies. In our method, 13 –two different galaxies comprised of the same population and with exactly the same numberof stars will always have the same luminosity. However, in practice this will most likelynot be the case as one might expect galaxies with similar populations to show an intrinsicspread in luminosities even if they have the same number of stars. To account properly forthis we estimate uncertainties in our derived absolute magnitudes by carrying out a boot-strap analysis. The procedure is as follows: We treat the theoretical luminosity functionused to calculate the luminosities as a cumulative probability function (down to our 90%completeness levels) of the number of stars expected as a function of magnitude. We thenrandomly draw a number N ∗ of stars from the luminosity function and add their fluxes. Wedo this 10,000 times. Using this method, for the case of a Salpeter IMF we find, for ComBer, M V = − . ± . V − r = 0 .
16 from Girardi et al. 2004). For UMa II we obtain M V = − . ± .
5. For the second choice of IMF we obtain M V = − . ± . M V = − . ± . §
4. Morphology
A main goal of this study is to re-assess to what extent Galactic tides may be affectingthe structure of ComBer and UMa II. Ever since the early numerical simulations of disruptedsatellites by Piatek & Pryor (1995) and Oh, Lin, & Aarseth (1995), the observed elongationof dSph galaxies have been associated with the degree of their tidal interaction with theMilky Way . In § ǫ = 0 .
36) roughly alongthe direction of the Galactic center (shown by the solid line in Figure 8). UMa II, on theother hand, is much more elongated, with ǫ = 0 . (UMa II has galacticcoordinates of [l,b]=[152.5, 37.5]). While alignment with the Galactic center is expected inintrinsically elongated satellites, it is not a sufficient condition to infer active tidal strippingin the case of ComBer. Tides can still affect a system without necessarily stripping stars off The same studies, and more recently Mu˜noz et al. (2008) have pointed out that this is not usuallythe case. Intrinsically spherical satellites are tidally elongated only when the satellite has become nearlyunbound. This does not preclude UMa II from being elongated along the direction of the Galactic center, but suchelongation would be mostly along the line-of-sight and therefore very difficult to detect.
14 –of that system (C. Simpson & K. Johnston, in preparation).The quality of our photometric data, which reach at least three magnitudes below themain sequence turn-off in both galaxies, allows us to address the tidal stripping questionmore directly by studying the morphology of these satellites, this time much more reliablythan in previous studies. To look for potential tidal features, we create smoothed isodensitycontour maps. The photometric catalogs used to create these maps are the same as those weused to derive structural parameters, and include all star-like objects (i.e., after sharp and χ cuts) down to our 90% completeness levels that live in a region around the main sequenceas defined in § ′′ × ′′ bins which are subsequently spatially smoothed with an exponential filter of scale 2 ′ . Otherreasonable bin sizes and exponential scales were tried as well, with no significant change inthe overall results. Figure 8 shows the resulting map for ComBer. This object shows fairly regular con-tours similar to those found using SDSS photometry (Belokurov et al. 2007a) but at a muchhigher statistical significance. We do not detect signs of potential tidal debris down to the3 σ isodensity contour level (the lowest one shown in Fig. 11) which corresponds to a surfacebrightness of ∼ . − . The lack of significant elongation, clumpiness or irreg-ularities in the morphology of ComBer indicate that it is unlikely that it is currently beingsignificantly affected by tides. This, coupled with the kinematics of ComBer measured bySimon & Geha (2007) and the corresponding mass derivation, supports the interpretationthat ComBer is in fact a stable dwarf galaxy. Even if ComBer is being tidally perturbedat levels below our detection limits, such low-level effects are not likely to alter its innerkinematics appreciably (e.g., Read et al. 2006; Mu˜noz et al. 2008; Pe˜narrubia et al. 2008).We note that our countour maps do not show the actual smoothed surface brightnesscontours, but instead show “significance contours”, i.e, for each dwarf, we calculate the meansurface density and its standard deviation in areas away from the region dominated by thegalaxy (background density), and plot the background-subtracted local density divided bythe standard deviation. If the values of pixels in our surface density map are well described bya Gaussian distribution, then the standard deviation used here would measure precisely howsignificant our features are in terms of σ values. However, the distribution of pixels will, mostlikely, not be well described by a Gaussian, and therefore we need an experiment to determinethe true significance of features in our data. To do this we first randomize the position ofthe stars, but leave the photometry untouched. We then select stars photometrically and 15 –generate smoothed density maps in the same way as we do for the actual data. Whenwe perform this test, we find that 3 σ overdensities randomly scattered across the field arenot uncommon, but higher significance features are very rare. We therefore conclude thatisolated 3 σ features detected in our real maps are very likely random noise and do not reflectpotential tidal features.To assess both the robustness of the overall shape of ComBer and the significance ofapparent substructure in its outer density contours, specifically a hint of elongation in thenortheast-southwest direction, we carry out a different test. In this case, we bootstrap ourphotometric samples (as opposed to randomly assign positions to the stars) and redo themaps. Figure 9 shows eight different bootstrap realizations of the data. It can be inferredfrom the figure that hints of substructure in the outer parts of ComBer are not statisticallysignificant, but the overall shape and structure of this system are well established with ourdata. This is not surprising, given the improvement in the number of stars that belong tothe satellite achieved with our photometry.We conclude that ComBer is unlikely to be significantly affected by Galactic tides andtherefore it represents a solid case of a stable dwarf galaxy whose characteristic size is smallerthan ∼
120 pc.
In contrast to the regular morphology of ComBer, UMa II looks entirely different. Figure10 shows its isodensity contour map, where the 3 σ contours are equivalent to 32 . − . Our photometry confirms previous findings that UMa II is highly elongated and itshows that UMa II is larger than previously reported, extending at least three times beyondits measured half-light radius, or nearly 700 pc ( ∼ . ◦ ) on the sky. More striking perhaps,is the fact that contours of UMa II looks more like a boxy-like system than an elliptical one.Only the very inner parts of UMa II resemble a spheroidal object.In Figure 10 we also show the best-fit orbit derived for UMa II by Fellhauer et al. (2007),based on the assumption that it is the progenitor of the “Orphan Stream” (Zucker et al.2006b; Belokurov et al. 2007b). This shows that the observed east-west elongation of UMa IIdoes not match the predicted direction from the model, although this is not enough to ruleout a connection between the two systems.To assess the statistical significance of our results we carry out the same tests we de-scribed in section § σ features are likely background noise but higher significance ones are real.Likewise, making contour maps after bootstrapping the data shows that the overall shape ofUMa II is fairly well established and is insensitive to resampling. We illustrate this in Figure11 where we show isodensity contours for eight different bootstrap realizations of our UMa IIdata.Zucker et al. (2006b) found tentative evidence that UMa II might be broken into severalclumps (see their Figure 1). Our contour map for this object does not show statisticallysignificant substructure. However, we are able to reproduce this results if we make contourmaps use only stars brighter than g = 23. We regard the presence of substructure in theinner parts of UMa II as statistical fluctuations in its density due to low number of stars.Another of the ultra-faints that looks similarly elongated as UMa II is the Hercules dSph.A recent study of this object by Sand et al. (2009), who use deep photometry obtained withthe Large-Binocular-Telescope (LBT), show that Hercules has an ellipticity ǫ = 0 .
67 andextends at least 500 pc ( ∼ ′ on the sky). We measured an ellipticity ǫ = 0 .
5. Discussion
Our understanding of the ultra-faint Milky Way satellites hinge on having reliable mor-phologies and robust structural parameters. Tidal disruption can result in disturbed mor-phologies and tidal features which can be very low surface brightness, yet have a profoundaffect on the interpretation of a given object. Deep photometry is the only means to assessthe presence or absence of faint tidal structure. In the absence of complete disruption, welldetermined sizes and luminosities are critical in calculating the total mass of a system. Ourmain goal in this paper is to search for signs of tidal features and determine structural pa-rameters around the Milky Way satellites ComBer and UMa II. Our r − and g -band CFHTphotometry reaches three magnitudes below the main sequence turn-off in these systems,corresponding to stars which are two to three magnitudes fainter than currently accessibleto spectroscopic studies.We achieve similar surface brightness limits for both ComBer and UMa II ( ∼ . − ), yet find very different morphologies for these two ultra-faint satellites. As seen inFigures 8 and 9, ComBer is remarkably regular and devoid of potential tidal features, in starkcontrast to the elongated and irregular structure seen in UMa II. Since low number of starscan produce spurious features and/or shapes that can later be interpreted as signs of tidal 17 –stripping (Martin et al. 2008), we have outlined in § σ contours in these figures lack statisticalsignificance, all higher σ contours are robust to resampling and should be regarded as a solidresult.ComBer is remarkably regular and devoid of morphological features potentially dueto tidal debris down to a surface brightness level of 32 . − . We have found aslight elongation in the direction toward the Galactic center but no discernible irregulari-ties are visible. We cannot of course completely rule out the presence of unbound debrisat fainter surface brightnesses, but, if present, it should reflect only mild, low-level tidaleffects. Similarly, we cannot rule out the presence of tidal tails along the line-of-sight. Inthe kinematic survey of ComBer, Simon & Geha (2007) report a velocity dispersion for thisobject of 4 . ± . − with only one possible interloper star beyond 3 σ of the velocitydistribution. This suggests against the presence of tidal debris along the line of sight. In theabsence of evidence to the contrary, we conclude that ComBer is in dynamical equilibrium,and therefore current mass determinations should be robust.Simon & Geha (2007) also report that radial velocity members of ComBer near themain sequence turn-off lie in a broader color region than the other ultra-faint dwarfs intheir sample, which they attribute to the effects of multiple stellar populations of differentages and metallicities. We have investigated this and find that this spread is a reflection oflarger photometric errors in the shallower SDSS data. We will further investigate the stellarpopulations of the two objects presented here in a separate paper.In contrast to ComBer, UMa II shows signs of disequilibrium. The contours of UMa IIare elongated, irregular and extend for at least 1 . ◦ , three times its r half . Only the very innercore of UMa II looks somewhat spheroidal. Unlike the case of most other dSphs, UMa II’sstellar density distribution is not well matched by any of the commonly used density profiles(King, Plummer or exponential), and instead it is better matched by two power laws. Severalstudies (e.g., Johnston et al. 1999; Mu˜noz et al. 2008; Pe˜narrubia et al. 2009) show that adwarf satellite initially in a Plummer or King configuration develops a power law componentin the outer parts as tidal debris is stripped by the Milky Way. However, they also showthat the inner parts of the satellite retain a core-like density until the very latest stagesof tidal disruption. The lack of a proper core in the stellar density profile of UMa II maybe a indication that this system is in fact in the throes of destruction. Another way toassess qualitatively to what extent UMa II may have been tidally affected, is by comparingthe “break” in its density profile to those of other well-studied disrupting objects such as By “break” we mean the inflection point where the inner density profile transitions into a power law due
18 –Pal 5 or the Sagittarius (Sgr) dSph. These objects show a clear “break” in their densitydistributions around the region where tidal debris is being stripped. In the case of Pal 5 thishappens at a surface density relative to the central one of Σ N, / Σ break ∼
100 whereas forSgr this value is closer to 200. If for UMa II we take the point where the inner power lawchanges slope as the “break” point, we obtain Σ N, / Σ break ∼
25, higher than for Pal 5 andSgr. In addition, this break in UMa II occurs relatively closer to the center than in these twosystems, at a break radius r b ≈ × r half compared to r b ≈ × r half for the latter. All theseobservations further support a tidal scenario for UMa II.Simon & Geha (2007) detect a velocity gradient along the major axis of UMa II, mea-suring an 8 . ± . − velocity difference between in eastern and western halves of thisobject– in the same direction as the elongation seen in our deep photometry. They also pointout that the UMa II’s velocity dispersion of 6 . ± . − is an outlier in the observedtrend of lower velocity dispersion with decreasing luminosity followed by other Galactic dwarfgalaxies (see their Figure 10a). Given UMa II’s absolute magnitude of M V = − .
93, a valueof 3–4 km s − would be more in line with the observed trend. One possibility to explain thisobservation is that the velocity dispersion of UMa II has been inflated by Galactic tides. Wenote however that these observations are limited to a small region inside r half of the system.Despite the observational evidence discussed above in favor of the tidal stripping of UMa II,our current data set does not allow us to conclude that this object is completely unbound orout of dynamical equilibrium. Kinematical data in outer regions are required to determinemore precisely the nature of UMa II and to further explore its possible association with theOrphan Stream.In the context of the galaxy versus cluster issue raised by Gilmore et al. (2007, 2008),our findings (or lack thereof) imply that ComBer is solidly situated in the gap (in M V ver-sus r half space) between star clusters and dwarf galaxies, and likely cannot be explainedaway as an evaporating cluster or dissolving dwarf galaxy. Metallicity measurements sup-port this scenario. While our photometric work presented here show that the stellar con-tent of ComBer (and UMa II) is consistent with being dominated by a very metal poorpopulation of [Fe/H] ∼ − . ∼ − . ∼ − .
9, which is more metal poor than any of the Galactic to the presence of tidal debris.
19 –globular clusters. In addition, both studies show a metallicity spread of 0.6 dex in this dSph,typical of a dwarf galaxies. The same argument can be invoked to argue that UMa II is adisrupting dwarf galaxy as opposed to a dissolving star cluster.
6. Conclusions
We have carried out a deep, wide-field photometric survey of the Coma Berenices andUrsa Major II dwarf spheroidal galaxies using the MegaCam Imager on CFHT, reachingdown to r ∼
25 mag, more than three magnitudes below the main sequence turn-offs ofthese Galactic satellites. This increases roughly by an order of magnitude, with respect tothe original SDSS photometry, the number of stars that belong to the respective galaxies andthat are available determination of their structural properties and for morphological studies.Our results can be summarized as follows:1. We used a maximum likelihood analysis similar to the one used by Martin et al.(2008) and Sand et al. (2009) to calculate structural parameters for three different densityprofiles: King, Plummer and exponential. We find characteristic sizes of r half = 74 ± . ± . ′ ) and 123 ± . ± . ′ ) for ComBer and UMa II respectively (from the expo-nential profile). Our results provide much tighter constraints on these structural parametersthan possible with previous datasets, but are consistent with earlier determinations usingSDSS photometry.2. We have re-calculated the total luminosities for both systems and find, for ComBer M V = − . ± . M V = − . ± . . − .Additionally, its number density profile is reasonably well matched by a choice of eitherKing, Plummer or exponential profile. We thus conclude that ComBer is likely a stabledwarf galaxy which would make it one of the most dark matter dominated of the dSphsystems.4. We have also studied the morphology of UMa II and find that, unlike ComBer, itshows signs of being significantly disrupted. UMa II is larger than previously determined,extending at least ∼
700 pc (1 . ◦ on the sky) and it is also quite elongated. Its density 20 –profile and overall shape resemble a structure possibly in the latest stages of tidal destruction.Furthermore, its number density profile is not well matched by neither of the three profiles wetried and it is much better described by two power laws, further supporting a tidal scenario.5. The overall 2D surface density distributions of both systems are not affected byshot-noise and are therefore robust. We find no evidence for isolated tidal debris beyond themain bodies of ComBer and UMa II to our surface brightness limits of 32 . . − , respectively.Deep, wide-field imaging of the recently discovered ultra-faint galaxies currently lagsbehind spectroscopic observations of these objects. We show in this paper that high quality,deep photometry is an equally important tool in studying the dynamical state of the ultra-faint dwarfs. These data can also be used to constrain the star formation histories of ComBerand UMa II which we will explore in a future contribution.We acknowledge David Sand, Josh Simon and Gail Gutowski for useful discussionsand Peter Stetson for graciously providing copies of DAOPHOT and ALLFRAME. M.Gand B.W. acknowledge support from the National Science Foundation under award numberAST-0908752. REFERENCES
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24 –Table 1. Structural Parameters for both ComBer and UMa IIParameter Mean Uncertainty Mean UncertaintyComa Berenices Ursa Major II α ,exp (h m s) 12:26:59.00 ± ′′ ± ′′ δ ,exp (d m s) +23:54:27.2 ± ′′ +63:07:59.2 ± ′′ r h,exp (arcmin) 5.8 ± . ± . r h,exp (pc) 74 ± ± r h, P (arcmin) 5.9 ± . ± . r h, P (pc) 76 ± ± ǫ exp ± .
04 0.50 ± . θ exp (degrees) − ± . − ± . N ∗ ,exp ±
22 1335 ± r c (arcmin) 4.2 ± . ± . r c (pc) 54 ± ± r t (arcmin) 27.9 ± . ± . r t (pc) 355 ±
43 560 ± M V a (Salpeter) − . ± . − . ± . M V a (Chabrier) − . ± . − . ± . a Using a distance of 44 and 30 kpc for ComBer and UMa II respectively, fromMartin et al. (2008) 25 –Fig. 1.— Schematic view of our photometric coverage for ComBer. We observed four differentfields with MegaCam covering roughly 2 × centered on the dSph galaxy. Here, theellipse represents the half-light radius derived by Martin et al. (2008). A similar observingpattern was used for UMa II but for a total area of 1 . × . 26 –Fig. 2.— Completeness levels as a function of magnitude for our shallowest field in ComBer(upper panel) and in UMa II (lower panel). Solid and dotted lines represent the completenesslevels as a function of g and r magnitude respectively. The dashed lines mark the 90%completeness levels, corresponding to g = 25 . r = 24 .
75 in the case of ComBer and g = 25 . r = 24 . r < ′ ) of ComBer. The dashedlines mark the 90% completeness level after χ and sharp cuts have been applied to removenon-stellar objects. As it can be seen, our CFHT photometry reaches at least three magni-tudes below the main sequence-turn-off of ComBer. We have complemented our photometrywith SDSS data for g >
20. The error bars to the left were determined from the artificialstar tests and represent the standard deviation of a Gaussian function fitted to the error dis-tribution as a function of magnitude. A theoretical isochrone for a 13 Gyr old, [Fe/H]=-2.27population is shown with a solid red line (from Girardi et al. 2004). 28 –Fig. 4.— Similar to Figure 3 but for UMa II. 29 –Fig. 5.— Comparison between structural parameters for ComBer derived by applying ourML method to both the CFHT and SDSS photometry. Solid histograms represent all 10 , Upper panel : similar to Figure 6, but for UMa II. Note that neither profile representsa good fit to the observed data points.
Lower panel: background subtracted number densityprofile of UMa II where the data points have been fitted with two power laws. These linesrepresent a much better visual fit to the data points than the density profiles used to deriveUMa II’ structural parameters. 32 –Fig. 8.— Isodensity contour map for ComBer. The contours represent 3, 6, 10, 15, 20, 35,55 and 75 σ above the mean density measured away from the main body of ComBer. Thesolid line shows the direction toward the Galactic center. The smoothing scale length of 2 ′ is also indicated in the figure. 33 –Fig. 9.— Isodensity contour maps for eight random bootstrap realizations of our photometricdata for ComBer. The upper left panel (thicker axis) shows the contours for the actual data.As in Figure 8, we show 3, 6, 10, 15, 20, 35, 55 and 75 σ above the mean density. Whilethe lowest 3 σ contours are not statistically significant, all more significant contours are wellstablished with these data. 34 –Fig. 10.— Isodensity contour map for UMa II. The contours in this case represent 3, 6, 10,16, 26, 38, 55 and 70 σ above the density measured in regions away from UMa II. The solidline marks the direction of the orbit derived by Fellhauer et al. (2007) assuming that UMa IIis associated with the Orphan Stream. As in Figure 8, the smoothing scale length is shownfor reference. 35 –Fig. 11.— Similar to Figure 9 but for UMa II. The contours shown are similar to Figure 10,i. e., 3, 6, 10, 16, 26, 38, 55 and 70 σσ