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A V and I CCD Mosaic Survey of the

J. T. Kleyna Harvard-Smithsonian Center for Astrophysics

M. J. Geller Harvard-Smithsonian Center for Astrophysics

S. J. Kenyon Harvard-Smithsonian Center for Astrophysics

M. J. Kurtz Harvard-Smithsonian Center for Astrophysics

J. R. Thorstensen Dartmouth College

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Dartmouth Digital Commons Citation Kleyna, J. T.; Geller, M. J.; Kenyon, S. J.; Kurtz, M. J.; and Thorstensen, J. R., "A V and I CCD Mosaic Survey of the Ursa Minor Dwarf Spheroidal Galaxy" (1998). Open Dartmouth: Peer-reviewed articles by Dartmouth faculty. 2117. https://digitalcommons.dartmouth.edu/facoa/2117

This Article is brought to you for free and open access by the Faculty Work at Dartmouth Digital Commons. It has been accepted for inclusion in Open Dartmouth: Peer-reviewed articles by Dartmouth faculty by an authorized administrator of Dartmouth Digital Commons. For more information, please contact [email protected]. THE ASTRONOMICAL JOURNAL, 115:2359È2368, 1998 June ( 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.

A V AND I CCD MOSAIC SURVEY OF THE URSA MINOR DWARF SPHEROIDAL GALAXY J. T.KLEYNA,1 M. J.GELLER,1 S. J.KENYON,1 M. J. KURTZ,1 AND J. R. THORSTENSEN2 Received 1997 October 30; revised 1998 February 17

ABSTRACT We discuss a Johnson-Cousins V - and I-band CCD mosaic survey of the Ursa Minor dwarf spher- oidal galaxy (dSph) to V D 22. We covered UMi with [email protected] ] [email protected] overlapping CCD frames, each frame consisting of two 300 s exposures in each of V and I. We also observed several regions D3¡ from UMi to obtain an estimate of contamination by galaxies and Galactic stars. We report the Ðrst H-R diagram of an entire dSph. Separation of dwarf stars from foreground stars by color allows a robust estimation of the structural parameters of UMi. We examine earlier evidence of two lumps in the UMi stellar distribution. We detect a statistically signiÐcant asymmetry in the stellar distribution of UMi along the major axis. Structure in the stellar distribution of UMi might indicate a tidal origin for UMiÏs high observed mass-to-light ratio. We demonstrate a technique for obtaining the absolute magni- tude of UMi from horizontal-branch star counts compared with M92; this method of luminosity estima- tion is independent of the distance to UMi. We obtainMV \[8.87 ^ pMV, wherepMV \ 0.14 if M92 is a perfect calibrator andpMV [ 0.35 is an upper bound on the error arising from di†erences in stellar populations. Our value forMV is consistent with earlier measurements and has a smaller uncertainty. Key words: galaxies: dwarf È galaxies: individual (Ursa Minor) È galaxies: stellar content È

1. INTRODUCTION (1997), in a simulation of dwarfs orbiting inside a realistic halo model, Ðnds that it is possible to produce long-lived The nine dwarf spheroidal (dSph) companions of the unbound remnants with many of the properties of the Galaxy have been the object of intense scrutiny over recent observed dSphÏs. In particular, KroupaÏs remnants have a years. High velocity dispersions, Ðrst indicated by obser- half-light radius of D200 pc, similar to that of UMi and vations of Draco(Aaronson 1983), have been interpreted to Draco; KroupaÏs remnants also have an inferred mean that (1) the dSphÏs have a very high mass-to-light M/L D 10 times solar, arising from a favorable line of sight ratio (M/L D 10 times solar for Ursa Minor and Draco) 2 2 along the orbit. Dispersed remnants may be a viable alter- because of a large dark matter content or (2) they are being native to a large dark matter content. tidally disrupted in the GalaxyÏs gravitational Ðeld. Ursa Minor is one of the more interesting dSphÏs; it has Although many investigators favor the dark matter hypoth- the largest ellipticity (0.55) and, along with Draco, the esis(Pryor 1996; Oh, Lin, & Aarseth 1995; Piatek & Pryor highest observed velocity dispersion. UMi is a candidate for 1995), it remains important to examine alternatives with a disrupted dSph because it is one of the nearest dSphÏs to some care. the Galaxy. Various mechanisms have been proposed for the tidal Several investigators have claimed structure in the stellar disruption of dSphÏs.Kuhn & Miller (1989) suggested that a number density distribution of UMi on a variety of scales. time-dependent Galactic tidal Ðeld could pump energy into Olszewski& Aaronson (1985) found small-scale stellar clus- a dSph by exciting radial oscillations;Sellwood & Pryor ters in a limited-area (D7@ 10@) CCD study of UMi to a (1998), however, Ðnd that these modes are not excited by ] limiting magnitude of V 24.8.Demers et al. (1995) found motion through a logarithmic Galactic potential and prob- \ a small clump of 78 stars in the center of UMi in a study ably do not account for the high apparent M/L of the using two 11@ 10@ frames with a limiting apparent magni- dSphÏs. ] tude of R B 24.Irwin & Hatzidimitriou (1995, hereafter Piatek& Pryor (1995) and Oh et al. (1995) performed IH95), in a study of the whole dwarf from scanned plates, simulations of dSph tidal disruption and found that the saw a double peak in the stellar surface number density. observed velocity dispersion does not rise during dis- In a dynamically stable system with UMiÏs relatively ruption; thus the apparent M/L of a dwarf is not signiÐ- short crossing timescale[p /(2R ) \ 10 yr], structure cantly inÑated by Galactic tides. Ongoing tidal disruption is v 8 should be erased.Kuhn (1993) andcore Kroupa (1997) suggest therefore not an explanation of the high apparent M/L of that the dSphÏs might be long-lived remnants of tidally dis- certain dSphÏs. rupted progenitors. Kuhn (1993) notes that there are orbital Kuhn (1993) argues that dSphÏs with large apparent M/L conÐgurations in which an unbound remnant can survive may be tidally disrupted remnants that remain coherent much longer than the expansion timescale based on the because the stars are on similar orbits; Pryor (1996), remnantÏs internal velocity dispersion would suggest. however, asserts that such disrupted remnants would Numerical simulations of disrupted remnants by Kroupa appearZ10 times larger than observed dSphÏs. Kroupa (1997) suggest that the high observed M/L of some dSphÏs may be explained by an anisotropic velocity distribution ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ combined with a favorable line of sight. SigniÐcantly, the 1 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138. remnants in KroupaÏs (1997) simulations are not regular, 2 Department of Physics and Astronomy, 6127 Wilder Laboratory, but contain lumps and other forms of structure. The limited Dartmouth College, Hanover, NH 03755-3528. number of particles in KroupaÏs simulations could, 2359 2360 KLEYNA ET AL. Vol. 115 however, be an issue in comparing the simulations with observed systems. Here we discuss a V and I CCD survey of UMi, covering an ellipse approximately 60@ ] 30@. Previous surveys of dSphÏs have been limited to large-area coverage with pho- tographic plates (e.g.,Hodge 1964; IH95; Demers, Irwin, & Kunkel1994), or to smaller regions using a CCD (e.g., Olszewski& Aaronson 1985; Smecker-Hane et al. 1994; Mateoet al. 1991). This paper is the Ðrst study that com- bines the broad areal coverage typical of earlier photo- graphic plates with the photometric depth and accuracy of CCD imaging. In° 2, we describe the observations and data reduction; in° 3, we describe functional Ðts to the stellar distribution of UMi. In °° 45,and we discuss the statistical signiÐcance of structure in UMi. In° 6, we estimate the total luminosity of UMi based on horizontal-branch star counts, compared with the globular cluster M92 for calibration. Finally, in ° 7 we use horizontal-branch magnitudes to place a limit on the angle our line of sight makes with the major axis of UMi.

2. OBSERVATIONS FIG. 1.ÈInstrumental (not color-corrected) luminosity function for all We acquired data at the F. L. Whipple Observatory objects in the survey region. The horizontal branch is visible as the small peak at V D 20. (FLWO) 1.2 m telescope during nine nights. The mosaic survey of UMi consists of a total of 27 Ðelds in Johnson- Cousins V and I. Each Ðeld is composed of two 300 s expo- SExtractor performs several types of photometry; we sures in each of the two Ðlters, and for some Ðelds there are used SExtractorÏs MAG–BEST magnitudes, calculated additional 180 s photometric calibration exposures. In addi- using an automatically adjusted aperture. Because SExtrac- tion, we obtained several o†-Ðelds 3¡ from UMi to estimate tor is a relatively new package, we compared MAG–BEST the background stellar population. We often took V and I with IRAF DAOPHOT.APPHOT.PHOT aperture magni- exposures of a particular Ðeld on di†erent nights to take tudes for two overlapping frames, A and B. We deÐne a set advantage of moonless periods for the V observations. The of rms scatters to compare magnitudes for the same objects Ðeld of view [email protected] on a side, and frames are located on a measured using SExtractor and PHOT for frames A and B; uniform grid with an overlap [email protected]. The seeing (stellar for example,p (V A [ V B) is the rms di†erence of the FWHM) varied from1A.4 to 2A.9. SExtractor frame20 AS, magnitudesP, and PHOT frame B magni- We conÐrmed photometric nights by examining the rms tudes for all stars brighter than V \ 20. We Ðnd that (1) scatter of standard stars(Landolt 1992) about a linear Ðt p (V A [ V B) Bp (V A [ V B) B 0.04, so that SExtrac- containing the actual magnitude, an air-mass term, and a tor20 isS, as consistentS, 20 betweenP, P, frames as PHOT, and (2) single V [I color term. Five nights were photometric in V , p (V A [ V A) Bp (V B [ V B) B 0.04, so that SExtrac- with an rms scatter of less than 0.015 mag, and two nights tor20 magnitudesS, P, agree20 withS, PHOTP, magnitudes within a were photometric in I, with rms scatters of 0.02 and 0.01 given frame. We conclude that SExtractor MAG–BEST mag, respectively. On the worst of the nonphotometric magnitudes are as accurate as the standard IRAF aperture nights, we measured an extinction of[0.1 mag. We cali- photometry package.Kleyna et al. (1998) contains the brated out this extinction using overlapping data from detailed tests. photometric nights. Thus, all the data are on a photometric In addition, we convolved frame A with a Gaussian to footing. The uncertainties in the V and I magnitude o†sets double the PSF FWHM. The SExtractor MAG–BEST are formally D0.015 mag. The principal source of system- magnitudes change by an average of 0.016 mag, whereas atic errors in the photometry is night-to-night variation in IRAF PHOT magnitudes change by 0.07 mag. We conclude the color terms: because V and I data were taken on di†er- that SExtractor performs accurate photometry even under ent nights, and because we could not determine the color conditions of varying seeing. In fact, the magnitudes are terms on nonphotometric nights, we resorted to using more robust than those derived from IRAF. average color terms for the entire run. This procedure intro- We determined the global coordinate system (a and d)of duces systematic errors of[0.03 mag. Figure 1 shows the each frame using positions from the US Naval Observatory instrumental V and I histograms for recovered objects, UJ1.0 Catalog(Monet, Canzian, & Henden 1994). We including both stars and galaxies. matched objects by placing them onto a global tangent We used the recently developed SExtractor package projection and identifying objects within1A.5 of each other; (Bertin&Arnouts 1996) forobjectidentiÐcationandphotom- the Ðnal rms deviation in the positions of matched objects is etry. We did not use point-spread function (PSF) Ðtting 0A.3. To determine whether we double-counted slightly mis- photometry, because the PSF varies across the Ðeld of view registered stars, we examined a histogram of pairwise dis- of the FLWO 1.2 m telescope. Also, we did not use the tances between objects; there is no evidence of an excess of star/galaxy discrimination feature of SExtractor, because it small object separations indicating misregistration. breaks down at the faint magnitudes relevant for most of In regions where frames overlap, the matched list of UMiÏs stellar population. Instead, we separated UMi objects contains a signiÐcant bias near the magnitude limit objects from background objects by color. of the survey, because the detection of a faint object is prob- No. 6, 1998 URSA MINOR DWARF SPHEROIDAL 2361

(a) (b)

FIG. 2.È(V , V [I) CMD of matched objects in (a) the survey region and (b) o†-Ðelds. The giant branch and horizontal branch of UMi are clearly visible in (a). abilistic and an object can be detected several times in an UMi data appear to have a secondary maximum or shoul- overlap region. To eliminate this bias, we divide our survey der along the major axis(Fig. 4b). Furthermore, the stellar region into a grid of 30A ] 30A squares and associate two V number density falls o† more rapidly on the southwest side frames and two I frames with each square. To detect an of UMi than on the northeast side. These features are also object in a particular grid, we must Ðnd it in at least one of visible in the shallow data set(Fig. 4a), and are absent in the these two frames. Thus an object has exactly two chances of ““ outside ÏÏ data set(Fig. 4c), suggesting that they do not detection in each color, even if it lies in a region where many arise from observational biases. The features persist when frames overlap. Failure to adopt this uniform procedure introduces detectable spurious structure by producing an artiÐcial stellar number count enhancement at frame edges and corners. Also, SExtractor does not identify objects within an arcminute of extremely bright, saturated stars; to avoid spatial gaps in the data, we Ðlled in these areas with objects copied from a nearby region of comparable area. Figure 2a shows the (V , V [I) color-magnitude diagram (CMD) of the UMi data, andFigure 2b shows the data for the o†-Ðelds. The horizontal and giant branches are clearly visible in the UMi data. InFigure 3, we divide the UMi data into a region approximately corresponding to the hori- zontal and giant branches of UMi, and a region outside of UMi. We further divide the region inside UMi into (1) shallow and complete data and (2) deep data that extend to the surveyÏs limiting magnitude. The relative number of stars in the shallow set detected in both V frames, compared with the number detected in only one V frame, implies that the shallow data set is over 99% complete. The deep data set, although it contains more stars, may be subject to systematic e†ects arising from variations in observing conditions from night to night. The deep data include 3413 objects, the shallow data include 2265 objects, and the outside (non-UMi) data set contains 3611 objects. Separation of objects by color allows us to remove most background objects and to obtain a cleaner determination of the structural parameters of UMi than FIG. 3.È(V , V [I) CMD of matched objects in the survey region. The previously possible. shallow and deep regions represent the parts of the survey containing the Consistent with the Ðndings ofIH95 and earlier work by majority of the UMi stars, and the ““ outside ÏÏ data consist principally of Olszewski& Aaronson (1985), the isopleths of the deep Galactic foreground stars and galaxies. 2362 KLEYNA ET AL. Vol. 115

(a) (b)

(c)

FIG. 4.ÈStellar isopleths of UMi after Ðltering with a 115A Gaussian kernel: (a) and (b) (shallow and deep data sets, respectively) show evidence of structure in the form of a secondary lump or shoulder; (c) is for the regions of the (V , V [I) CMD presumed to be outside of UMi. Contour intervals are 0.14, 0.21, and 0.057 arcmin~2 for (a)È(c). The absence of any features in (c) suggests that galaxy clusters do not introduce spurious structure, and that separation of UMi objects from background objects using color was very efficient. The origin of the coordinate system is at15h08m35s.8, 67¡24@12A (B1950.0). The polygon encloses the actual survey region, and we padded the region outside the polygon with a uniform distribution of stars at a density equal to the best-Ðt background density.

we use only the objects SExtractor identiÐes as stars. Thus, background is approximately 4 times lower because of our these features do not result from misidentiÐed clumps of selection by color (0.31 arcmin~2 vs. 1.16 arcmin~2), which galaxies. eliminates much of the possible contamination by clusters of galaxies. 3. FITTING THE STELLAR DISTRIBUTION OF URSA MINOR To Ðt the surface number density distribution, we choose a power law with a core (PLC) of the form Once we eliminate nonmembers of UMi by selecting on color, we use the remaining objects to determine the struc- M(l [ 1) & (r) \ ] & , (1) tural parameters of UMi. Unlike plate-based previous work PLC na2(1 [ v)[1 ] Q2(r; h, a, v, r )]l b (e.g.,IH95), our photometry is sufficiently good to allow 0 separation of dSph population by color. We thus obtain a where M is the total number of stars,&b is the background more robust and less background-contaminated character- density, l[1, and Q2 is a quadratic form in the Cartesian ization of the shape of UMiÏs stellar distribution. For coordinates r \ (x, y) such that Q2(r; h, a, v,r ) \ 1 deÐnes example, our shallow data reach the same central surface an ellipse centered onr \ (a , d ) with semimajor0 axis a, 0 0 0 density (D4 arcmin~2)asIH95Ïs (D4.2 arcmin~2), but our semiminor axis a(1 [ v), and position angle h. The value of No. 6, 1998 URSA MINOR DWARF SPHEROIDAL 2363

Q containing half of the total stars is Q \ (21@(l~1) [ 1)1@2, and the half-mass radius may be deÐned1@2 as r \ a(1 [ v)1@2Q . The l \ 2 case corresponds to a projected1@2 Plummer proÐle,1@2 and for l ] O,& (r) approaches a Gaussian in Q. PLC We also Ðt an ellipticized single-component King model (King 1962) of the form G C r2 D~1@2H2 k (1]Q2)~1@2[ 1] t ]& , a2(1[v) b & (r)\ K if Q2 ¹ rt2/[a2(1 [ v)] , g& , otherwise , (2) b where k is a normalization constant. This model has been widely used to Ðt dSphÏs(IH95 and references therein), and it yields a good Ðt to eight of the known dSphÏs, albeit with an excess of stars outside the King tidal radius rt. To Ðt a surface number density model &(r) to a set of observed star positionsri, we employ a maximum likeli- hood method. First, we normalize &(r) to yield&3 (r), which has a unit area integral over the survey region; then we maximize the sumL \ ;i ln &3 (ri) over the space of param- eters describing the model. Table 1 lists the best-Ðt values and errors for both FIG. 5.ÈFits of the stellar distribution of UMi to a power-law model models; we obtain the parameter uncertainties in Table 1 by with a core (PLC) and to a King model, for the deep and the shallow data. creating artiÐcial data using the best-Ðt parameters for the The two models are virtually indistinguishable, although the PLC model real data and then measuring the scatter of the parameters yields a slightly better Ðt for both data sets. recovered from these artiÐcial data.Figure 5 overlays the best Ðts on the observed distribution of stars for the shallow these models. In particular, the extratidal stars previously and the deep data. suggested by King model Ðts to UMi and other dSphÏs may, Though the PLC model produces a slightly better formal as pointed out by previous authors(IH95), be a measure of Ðt, the two Ðtting functions are essentially indistinguishable. the inappropriateness of the King model near its edges The di†erence between the best-Ðt L for the two models is rather than an indication of ongoing tidal disruption. far less than the scatter in L computed from the artiÐcial IH95, in their King model Ðt to UMi, computed best-Ðt data. These data cannot distinguish between the two core and tidal radiirc \ [email protected] ^ [email protected] andrt \ [email protected] ^ 3.6.@ Our models. value ofrc (Table 1) agrees well with that of IH95, but our When we Ðt the data using a PLC model with the con- value ofrt is smaller by D30%. The Ðt by IH95 extends straint l \ 1orl\20, the Ðt is considerably worse than farther out than ours; their ““ extratidal ÏÏ stars may inÑate rt either the unconstrained PLC model or the King model. when included in the Ðt. The relatively good Ðt of the PLC and King models may be To test whether the disagreement between our value of rt a general feature of models with two radial parameters (a and that ofIH95 results from their extratidal stars, we pad and l for the PLC model,rc andrt for the King model) and our data with a similarly elevated background. We note probably cannot be attributed to any physical suitability of that the extratidal stars of IH95 are equal to 5%È10% of TABLE 1 FIT PARAMETERS FOR URSA MINOR

SHALLOW DATA DEEP DATA

PARAMETER Most Likely Value 1 p Errors 2 p Errors Most Likely Value 1 p Errors 2 p Errors PLC model: M ...... 1464 `119 `253 2273 `168 `370 ~89 ~184 ~157 ~256 h (deg) ...... 49.4 `1.6 `2.9 51.0 `1.7 `3.1 ~1.4 ~3.1 ~1.3 ~2.9 a (B1950.0) ...... 1508 27.5 ^22a `40a 15 08 23.0 ^17a `32a 0 ~41 ~34 d (B1950.0) ...... ]67 25 12 ^20a `38a ]67 24 30 ^17a `33a 0 ~41 ~34 a (arcmin) ...... 26.9 `8.8 `58.4 22.4 `5.4 `11.1 v ...... 0.554 `~4.80.023 `~8.00.043 0.519 ^~2.80.020 ^~5.60.040 l ...... 3.53 ~0.019`1.85 ~0.044`22.60 2.80 `0.97 `2.38 r (arcmin) ...... 10.09 ~0.84`0.67 ~1.37`1.44 10.62 ~0.46`0.73 ~0.84`1.46 50 `~0.48 `~0.82 `~0.59 `~0.94 &b (arcmin~2)...... 0.305 0.024 0.049 0.461 0.032 0.064 King model: ~0.027 ~0.046 ~0.031 ~0.056 ` ` ` rc (arcmin)b ...... 15.2 2.3 7.0 13.6 ^1.5 3.1 r (arcmin) ...... 34.0 ~2.1`2.9 ~3.7`6.5 39.1 `4.3 ~2.2`9.4 t ~2.4 ~4.9 ~3.2 ~5.6 NOTES.ÈMaximum likelihood Ðt parameters for Ursa Minor, for deep and shallow data sets. Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds. a Arcseconds. b Where rc \ a(1 [ v)1@2. 2364 KLEYNA ET AL. Vol. 115 their background density. Hence we pad the region outside our data with a 50@ ] 50@ box of background stars, with a density 10% higher than our o†-Ðeld background. When we Ðt a King model to this padded data, our value of rt increases to that found by IH95. An important concern is that our limited o†-Ðeld cover- age may a†ect our ability to estimate the background and may make our other Ðt parameters less reliable. However, we note the following: (1) Our Monte Carlo estimates of the errors on the Ðt parameters include uncertainties in the background. (2) Although we know the background to within 0.03 arcmin~2, versus 0.01 arcmin~2 forIH95, the JN variations in the higher background of IH95, taken across the face of UMi, eliminate this disadvantage. Taking both the uncertainty and Poisson noise in the background into account, IH95 expect about 900 ^ 31 background stars within the core radius of UMi; we expect 240 ^ 28. (3) Our background estimates using two o†-Ðelds on opposite sides of UMi match at the 0.44 p level, suggesting that systematic variations in the background are not a problem. Finally, the value of the Ðt parameters is insensitive to the FIG. 6.ÈIsopleths for artiÐcial data created using the best-Ðt PLC method we use to determine the background; the result is model for the shallow data, containing the same number of objects as the the same for a background based entirely on the o†-Ðelds, artiÐcial data set. These data, although drawn from a smooth distribution or based on both the o†-Ðelds and the central survey region. with a single peak, appear as bimodal as the shallow data set (Fig. 4a). 4. METHOD FOR TESTING THE SIGNIFICANCE OF THE SECONDARY PEAK of the second-highest peak in each set, and determine the strength of the correlation of the locations of these second- Several authors, beginning withOlszewski & Aaronson ary peaks among the divisions. We then compare the sta- (1985), have reported structure in the stellar distribution of tistic with Monte Carlo data drawn from a best-Ðt smooth UMi.Demers et al. (1995) reported a concentration of stars distribution(° 3) to test whether the actual distribution is at the center of UMi, but their survey covered only the lumpier than the artiÐcial data. central region of the dwarf. The photographic plate study of The exact procedure is as follows: IH95 covers all of UMi to a depth roughly comparable to our shallow data; their Figure 1h shows a secondary peak 1. For each ofNs random shuffles of a set of stars S, comparable to ourFigure 4a. However, this peak does not divide the shuffled data intoNg subgroupssij, where i \ 1, show up in our deeperFigure 4b; there is only an extended ..., Ns indexes the shuffle and j \ 1, ..., Ng indexes the shoulder in the stellar distribution. Possibly, the secondary subsets within a shuffle. maximum seen by IH95 and in our shallow data is a 2. For eachsij, generate a smooth distribution by apply- Poisson noise artifact present among the brightest stars of ing a Gaussian Ðlter to the stellar distribution along a 50A UMi. In fact, when we construct artiÐcial data sets using the grid. On each grid, letrij denote the position of the second- parameters of our Ðts to UMi, these sets often contain fea- highest local maximum grid point. tures very similar to the secondary peak in the shallow UMi 3. For each shuffle i, sum over the secondary peaks to data.Figure 6, for example, shows an artiÐcial realization of calculate the statistic our shallow data, created using our best-Ðt PLC param- a \[; ln (o r [ r o2]1) . (3) eters. Although these data were drawn from a smooth dis- i ij ij{ j{;j tribution, they appear as lumpy as the shallow UMi data set We obtain the form of this statistic by noting that the prob- (Fig. 4a). ability that two points in a two-dimensional uniform dis- Conventional statistical tests for structure in clusters of tribution fall within a distance of r of each other is r ; objects (seePinkney et al. 1996 for a comparison) are P 2 thus, equation (3) is a crude likelihood equation, with a 0 unsuitable for our study of UMi. For instance, the Lee i \ when the secondary maxima are perfectly correlated in the statistic(Fitchett & Webster 1987) depends on using second N subsamples. The purpose of the 1 inside the parentheses moments of projected line densities to Ðnd a dispersion- g is to keep the statistic bounded if two maxima should fall on minimizing division of the data; the second moment, the same grid point. however, diverges in the presence of a uniform background 4. Usea6 ; a /N as the measure of the strength of a and, even in the absence of a background, is divergent for \ i i g secondary peak of the original set S. A value of a that is many distributions of astrophysical interest. The path close to zero indicates that the distribution contains a linkage criterion employed byDemers et al. (1995) to Ðnd strong secondary peak, because the original peak in S per- lumps in four dSphÏs is applicable over regions small sists among the subsamples s . enough that the stellar number density is approximately ij constant; this method is also unsuitable for detecting the We take this approach because, although it is difficult to relatively large scale structure that may be present in UMi. characterize the signiÐcance of a peak in a smoothed, spa- We have devised a simple statistic, therefore, to quantify tially nonuniform distribution of stars, it is obvious that what the human eye perceives as large-scale lumpiness: we spurious peaks caused by random noise have a height that divide the data into several equal-size sets, Ðnd the location scales as the square root of the total number of stars. If the No. 6, 1998 URSA MINOR DWARF SPHEROIDAL 2365 original distribution, S, contains a 2 p spurious peak and we [100A and are smoothed out entirely at a smoothing scale divide S into four resamplingssj, then eachsj has one- Z200A; hence we limit our search for signiÐcant lumpiness fourth of the original peak, which will be at a 1 p signiÐ- to four Ðlter values between these extremes. In the shallow cance withinsj. The remnant of the original peak will thus data, we do not detect a signiÐcant secondary maximum in compete with additional 1 p peaks introduced by the the stellar surface number density; in the deep data, we resampling process, and the original peak in S will be obtain a signiÐcant detection only at a 115A smoothing judged insigniÐcant. If the original peak in S were more scale, and the detection is only at the p \ 0.05 level. The low signiÐcant (e.g., 4 p), then the spurious peaks introduced by signiÐcance of the statistic, further weakened by the Ðlter- the resampling would not drown out the remnants of the scale tuning required to obtain a detection, makes the original peak in thesj as often. A signiÐcant detection attempt to detect a secondary peak in UMi inconclusive. would result because the remnant peaks in thesj would be Figure 7 shows the positions of the primary and second- correlated. ary peaks for each resamplingsij of the deep data set. It is Essentially, each resamplingsj introduces additional apparent that the location of the secondary peak disagrees random noise and spurious peaks on top of any peaks in the with the secondary peak in ourFigure 4a and in Figure 1h original distribution S. A value ofa6 close to zero indicates ofIH95. It does, however, correspond to the shoulder on that an original peak in S dominates the random peaks the northeast side of the major axis inFigure 4b. A plot of introduced in the resampling process. lump positions for the shallow data, analogous to Figure 7, We obtain the signiÐcance ofa6 by applying our technique shows that the second peak of the resamplingssij is not to random data drawn from a PLC distribution. We ask concentrated in one place. We conclude that the secondary whether thea6 of the observed data set is signiÐcantly larger peak we see in Figure 4a is an artifact of small number than that for the simulated data. We obtain the PLC statistics. The shoulder in Figure 4b, however, is probably a parameters used to construct the null hypothesis by Ðrst real feature of the data. BecauseOlszewski & Aaronson generating distributions based on the best-Ðt parameters for (1985), using deeper data covering 6@ ] 10@, claim evidence the real data; we then recover the parameters using the of a secondary peak, the possibility of a bimodal distribu- maximum likelihood approach in° 3. This two-stage tion cannot be dismissed without deeper data covering the approach incorporates the errors in the best-Ðt parameters entire dwarf. into the Ðnal measure of signiÐcance and tends to decrease ASYMMETRY the signiÐcance of thea6 in the real data. 5. In tests using artiÐcial data, thea6 -statistic is sensitive The surface number density contour diagram of UMi enough to detect a D75-star 140A Gaussian lump in a data (Fig. 4) is apparently asymmetric; the isopleths are more set with the same number of stars as our shallow data. closely spaced on the southwest side of the major axis than Other tests, including the Lee statistic(Fitchett & Webster on the northeast side. We know of no mechanism for sus- 1987), do not recover such lumps. Like many tests, our taining such an asymmetry in an equilibrium dynamical method has the disadvantage of requiring a parametric Ðt system. to construct the null hypothesis; it has the further disadvan- To rule out the possibility that the stellar distribution is tage of being dependent on a smoothing scale. actually symmetric, and that the observed asymmetry arises The observed features in the isopleths of UMi are domi- from Poisson noise, we construct a simple asymmetry sta- nated by random noise at a Gaussian smoothing scale of tistic, b (Fig. 8). First, we Ðlter the distribution along the

(a) (b)

FIG. 7.ÈLocations of highest and second-highest peaks in the deep data set. Each point comes from a single resamplingsij (° 4). The location of the secondary maximum is closer to the center of UMi than in previous studies(IH95), and the signiÐcance of the detection of the second peak is only 2 p. 2366 KLEYNA ET AL. Vol. 115

worst-case 0.1 mag di†erence in limiting depth, consistent with the maximum night-to-night excursions of the photo- metric solutions, and if we approximate the V luminosity function ofFigure 1 as the power law N(m) P 100.3m, then we underestimate the surface number density on the southwest side of the major axis by a relative factor of 1.08 compared with the northeast side. The inclusion of this re- scaling factor decreases the signiÐcance of the asymmetry of the deep data to the p \ 0.02 level and makes the value of b for the deep data equal to that for the shallow data. However, the di†erence between the mean extinction for the southwest and northeast sides of the major axis is actually only 0.01 mag; hence, the signiÐcance of the asymmetry is greater in the deeper data. As another test of asymmetry, we project stars in a 10@- wide band around the major axis onto the major axis and perform a Kolmogorov-Smirnov (K-S) comparison between the northeast and southwest sides of the projected distribution; the point on the line where the distribution is split is selected to minimize the signiÐcance of the asym- metry. This K-S test shows that the shallow (deep) data are asymmetric at the p \ 0.2 (p \ 0.01) signiÐcance level.

FIG. 8.ÈAsymmetry statistic, where h is the maximum background- 6. LUMINOSITY ESTIMATE FOR URSA MINOR subtracted stellar surface number density along a line down the major axis; d andd (withd º d ) are the distances at which the density falls to h/2, Much of the difficulty in deriving the mass-to-light ratio and1 the2 asymmetry1 statistic2 is given byb \ d /d [ 1. The density curve of UMi arises from the large uncertainty in the luminosity. shown is for the deep data set, with a 150A Gaussian1 2 Ðlter; for this curve, It is difficult to estimate UMiÏs total luminosity by inte- b \ 0.7. Distance increases from northeast to southwest. grating the observed luminosity function directly, because (1) our catalog of UMiÏs population is contaminated with a large number of galaxies and Galactic stars, (2) our small major axis with a two-dimensional Gaussian. Next, we let number of o†-Ðelds makes it difficult to remove this con- d andd be the distances where the Ðltered distribution tamination, and (3) our survey does not reach the main- falls1 to half2 its maximum value, requiring that d º d . sequence turno†. Finally, we deÐne the asymmetry asb \ d /d [ 1. To1 test2 However,Olszewski & Aaronson (1985) found that the the signiÐcance of the observed b, we calculate1 2 b for 1000 age and metallicity of UMiÏs stellar population are very simulated distributions using the best-Ðt PLC models (a similar to those of the globular cluster M92. Therefore, if we similar procedure to the signiÐcance computation for the take the claim of Olszewski & Aaronson (1985) at face a6 -statistic). Table 2 shows b for the deep and shallow data value, we can estimate the luminosity of UMi by assuming for two Gaussian Ðlter widths. We also compare the value that the fraction of the total luminosity contributed by the of b for the shallow data set with the b for simulated deep blue horizontal branch (HB) is the same for UMi and M92. data sets to allow for systematic e†ects. Except for the Then we can measure the luminosity of UMi by rescaling shallow data with a 150A Ðlter, the actual data are asym- the luminosity of M92 by the relative HB star counts. Our estimate ofM , the absolute V magnitude of UMi, is metric at a greater than 2 p (p \ 0.05) signiÐcance level, with V,UMi the 250A deep data signiÐcant at the D3 p (p D 0.003) level. completely independent of the distance to UMi. The deep data are consistently more asymmetric than the The total number of HB stars in our survey region is shallow data. An observational bias, such as a brighter 368 ^ 36; the uncertainty is only 10% because there is little detection threshold on the southwest (steeper) side of the contamination in the region of the color-magnitude major axis, would produce this di†erence. If we assume a diagram corresponding to the HB. Using data provided by M. Bolte (1997, private communication), we count 300 ^ 17 stars in the HB of M92, implying that L /L \ 1.33 TABLE 2 ^ 0.13, or M [ M \[0.31 ^ 0.10. UMi M92 UMi M92 ASYMMETRY STATISTIC b The apparent luminosity of M92 is V \ 6.39 ^ ([0.05), with a V -band extinction of 0.065 mag(Webbink 1985). The Filter Width (p) distance modulus of M92 is less certain, however. Reid Data Set (arcsec) b SigniÐcance (1997), using Hipparcos-recalibrated subdwarf Ðtting, Shallow ...... 150 1.50 0.18 obtains(m [ M) \ 14.93 ^ 0.1. Storm, Carney, & Shallow ...... 250 1.36 0.06 Latham(1994), usingM92 the completely independent Baade- Deep ...... 150 1.76 0.035 Wesselink method, obtained (m [ M) \ 14.60 ^ 0.26. Deep ...... 250 1.46 [0.001 M92 Mixed ...... 250 1.36 0.01 These results are consistent at the 0.24 signiÐcance level; we combine them to obtain(m [ M) \ 14.89 ^ 0.09. Fur- NOTES.ÈAsymmetry statistic b and signiÐcance for deep thermore,Caloi, DÏAntona, & MazzitelliM92 (1997) compute and shallow data at two Gaussian Ðlter widths. ““ Mixed ÏÏ (m [ M) \ 14.72 using HB modeling; they did not data compare the value b \ 1.36 obtained for the shallow M92 data set with the b obtained for artiÐcial data with the same report an error. If we estimate their uncertainty as 0.2 mag, number of stars as the deep data set. the results of Caloi et al. (1997) are consistent with the other No. 6, 1998 URSA MINOR DWARF SPHEROIDAL 2367 distance moduli at the 0.43 signiÐcance level, changing our that the results for V and I agree in sign and size; thus, a value for(m [ M) by only 0.03 mag. favorable projection angle cannot be ruled out. Combining theM92 apparent luminosity of M92 with its distance modulus, we obtain an absolute luminosity 8. CONCLUSION MV \[8.57 ^ 0.09; this value is almost 0.4 mag brighter,M92 than the commonly tabulated value, but it is con- Olszewski& Aaronson (1985), Demers et al. (1995), and sistent withReidÏs (1997) Ðnding that the distance to M92 IH95 have reported structure in the Ursa Minor dSph on various scales. The presence of structure is important has historically been underestimated. Combining MV ,M92 because it suggests that tidal disruption may play a role in with the relative HB star counts yields MV \[8.87 ^ 0.14. This value is consistent with previous,UMi estimates the large apparent M/L of UMi and other dSphÏs. ([8.7, Webbink 1985;[8.9, Caldwell et al. 1992; We have examined the evidence for structure by per- forming a large-scale V - and I-band CCD survey of UMi [8.5 ^ 0.5,IH95). Our error onMV assumes that M92 is a perfect calibrator, and that the only,UMi important contri- and constructing the Ðrst CCD H-R diagram of a complete bution to the uncertainty is from the distance modulus of dSph. Because we have good-quality two-color photometry, M92. we are able to remove much of the foreground star and We can also apply the HB star count method to estimate background galaxy contamination from our catalog of the known luminosity of M5 from the data ofSandquist et UMi stars, giving a more robust estimate of UMiÏs struc- al.(1996) based on M92. The result di†ers from the tural parameters. observed absolute magnitude of M5 by 0.35 mag. This dis- The isopleth plot of our shallow data(Fig. 4a) shows the agreement implies that di†erences in stellar populations secondary peak in the surface stellar number density report- between M5 and M92 lead to an additional D0.32 mag ed earlier byIH95, but it vanishes in our deeper data set. error term, after removing the contribution from error in Using a resampling technique, we demonstrate that the sec- the distance moduli. Because the metallicity of M5 is higher ondary peak is statistically insigniÐcant in the shallow data. than that of M92 and UMi([Fe/H] B [1.3 vs. In the deeper data set, the shoulder in the isopleth map (Fig. [Fe/H] B [2.1), the 0.32 mag errorM5 is probably an 4b) corresponds to a secondary peak that is signiÐcant at upper limit.M92,UMi the [2 p level. Several asymmetry statistics show that the shallow data Our measurement ofMV does not account for varia- tions in stellar populations,,UMi because we compare UMi only are asymmetric along the major axis at the [2 p level and with M92. For example, the horizontal branch of UMi the deep data are asymmetric at the 3 p level. Because of the spans a range in V magnitude about 0.2 mag smaller than steep power-law shape of the luminosity function (Fig. 1), the range of the horizontal branch of M92, an e†ect that however, the deep data are subject to unknown systematic Olszewski& Aaronson (1985) probably did not notice biases, which might reduce the asymmetry in the deep data because of their small survey area. A comparison of several to the 2 p level. low-luminosity globular clusters would lead to a better esti- We also use the H-R diagram to obtain an improved mate of the error. estimate of UMiÏs luminosity. Under the assumption that Upon rescaling the mass-to-light ratio from Table 10 of UMi and the globular cluster M92 have similar stellar populations, we used the ratio of the number of HB stars in IH95, our value ofMV reduces the mass-to-light ratio of UMi from(M/L ) \,UMi90 ^ 43 to 70`30 times solar, where UMi and M92 to compute UMiÏs luminosity. Our value of UMi ~20 the error is based on the conservative 0.35 mag error esti- MV \[8.87 ^ pMV (0.14 \pMV\0.35) agrees with bright- er previous estimates and implies a mass-to-light ratio of mate on MV . ,UMi (M/L ) \ 70`30 times solar. Our method of measuring 7. PROJECTION EFFECTS the luminosityUMi ~20 of UMi is applicable to other dSphÏs and has One ofKroupaÏs (1997) two disrupted remnant simula- the advantage that it is independent of the dSph distance tions has a large apparent M/L through a favorable (17¡.5) modulus. line-of-sight alignment of the model dwarfÏs orbit. In this Finally, we use the variation of the mean HB magnitude model, an observer interprets projected tidal streaming as a across UMi to place a limit on the angle our line of sight large velocity dispersion. To test whether the long axis of makes with UMiÏs major axis. Our data are consistent both UMi is being viewed in projection, we divide UMiÏs HB with an angle of 90¡ (no projection of the major axis) and into two sets along the major axis; the Ðrst set consists of all with an angle of17¡.5; the latter projection angle was the stars at least 10@ to the northeast of the center, and the source of a large apparent M/L in one of the models of second set consists of all stars at least 10@ to the southwest. Kroupa (1997). If we are viewing the major axis in projection, we expect a A CCD survey with a wide-Ðeld camera to a limiting di†erence in the mean magnitudes of the two sets. magnitude ofV Z 24 would easily reach the main-sequence Taking the distance to UMi,D \ 65 kpc, and the turno†, providing a much large population of stars to study. UMi Because we Ðnd statistically signiÐcant signs of structure in major-axis core radius,rc B 200 pc, we expect a magnitude data withV [ 23, deeper data would yield an unambiguous di†erence of *M B 5 log[1 ] 2rc/(D tan 17¡.5)] B 0.04. For our southwest and northeast HBUMi star sets, we obtain measure of the structure of the dwarf. mean magnitude di†erences SV T [ SV T \ 0.025 ^ 0.021 andSIT [ SIT \ 0.036 ^SW0.035. TheNE uncer- We thank Michael Bolte for allowing us to use his globu- tainties in these valuesSW comeNE principally from the intrinsic lar cluster data and Chris Kochanek for helpful discussions. spread of the horizontal branch. We also thank the MDM Observatory sta†, and the sta† of The di†erences in magnitude we observe are consistent at Fred Lawrence Whipple Observatory, for their assistance in the 1 p level both with projection angles ranging from 90¡ obtaining observations. This research was supported by the (no projection) to less than17¡.5. It is suggestive, however, Smithsonian Institution. 2368 KLEYNA ET AL.

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