Exploring Halo Substructure with Giant Stars: The Velocity Dispersion Profiles of the Ursa Minor and Draco Dwarf Spheroidals At Large Angular Separations

Abstract

We analyze velocity dispersion profiles for the Draco and Ursa Minor (UMi) dwarf spheroidal (dSph) galaxies based on published and new Keck HIRES spectra for stars in the outer UMi field. Washington+DDO51 filter photometric catalogs provide additional leverage on membership of individual stars, and beyond 0.5 King limiting radii (R_lim) identify bona fide dSph members up to 4.5 times more efficiently than simple color-magnitude diagram selections. Previously reported ``cold populations'' R_lim are not obvious in the data and appear only with particular binning; more or less constant and platykurtic dispersion profiles are characteristic of these dSphs to large radii. We report discovery of UMi stars to at least 2.7 R_lim (i.e.,210 arcmin or 4 kpc). Even with conservative assumptions, a UMi mass of M > 4.9 x 10^8 M_(sun) is required to bind these stars, implying an unlikely global mass-to-light ratio of M/L > 900 (M/L)_(sun). We conclude that we have found stars tidally stripped from UMi. Comment: 9 pages, 4 figures. Published in the Astrophysical Journal Letters

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arXiv:astro-ph/0504035v2 17 Nov 2005
Exploring Halo Substructure with Giant Stars: The Velocity
Dispersion Profiles of the Ursa Minor and Draco Dwarf
Spheroidals At Large Angular Separations
Ricardo R. Mu˜ noz1, Peter M. Frinchaboy1, Steven R. Majewski1, Jeffrey R. Kuhn2,
Mei-Yin Chou1, Christopher Palma3, Sangmo Tony Sohn1,4, Richard J. Patterson1&
Michael H. Siegel1,5
ABSTRACT
We analyze velocity dispersion profiles for the Draco and Ursa Minor (UMi)
dwarf spheroidal (dSph) galaxies based on published and new Keck HIRES spec-
tra for stars in the outer UMi field. Washington+DDO51 filter photometric
catalogs provide additional leverage on membership of individual stars, and be-
yond 0.5 King limiting radii (rlim) identify bona fide dSph members up to 4.5
times more efficiently than simple color-magnitude diagram selections. Previ-
ously reported “cold populations” at rlimare not obvious in the data and appear
only with particular binning; more or less constant and platykurtic dispersion
profiles are characteristic of these dSphs to large radii. We report discovery of
UMi stars to at least 2.7rlim(i.e., 210′or 4 kpc). Even with conservative assump-
tions, a UMi mass of M > 4.9×108M⊙is required to bind these stars, implying
an unlikely global mass-to-light ratio of M/L > 900 (M/L)⊙. We conclude that
we have found stars tidally stripped from UMi.
Subject headings:
dwarf spheroidal) – galaxies: kinematics and dynamics – Local Group
galaxies: individual (Ursa Minor dwarf spheroidal, Draco
1Dept.
mc6ss, rjp0i@virginia.edu)
of Astronomy, University of Virginia, Charlottesville, VA 22903-0818 (rrm8f, pmf8b, srm4n,
2Institute for Astronomy, University of Hawaii, Honolulu HI 96822 (kuhn@ifa.hawaii.edu)
3Dept. of Astronomy & Astrophysics, Penn State, University Park, PA 16802 (cpalma@astro.psu.edu)
4Korea Astronomy and Space Science Institute, 61-1 Hwaam-Dong, Yuseong-Gu, Daejeon 305-348 Korea
(tonysohn@kasi.re.kr)
5University of Texas – McDonald Observatory Austin, TX 78712 (siegel@astro.as.utexas.edu)

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1. Introduction
Dwarf spheroidal (dSph) galaxies are thought to be strongly dark matter (DM) dom-
inated, with global mass-to-light ([M/L]tot) ratios ranging from a few to hundreds in solar
units. Spectroscopic databases are now available for some dSphs to their King limiting radii,
rlim(Kleyna et al. 2004; Wilkinson et al. 2004, hereafter W04), and beyond (Tolstoy et al.
2004; Westfall et al. 2005; R. Mu˜ noz et al., in preparation, hereafter M05), enabling in-
vestigation of the dSph kinematics and inferred mass distribution to large radii. Yet, very
low stellar densities, still formidably challenge efficient spectroscopic study of dSphs at large
angular separations. The photometric filtering techniques that are the basis of this series of
papers successfully overcome this problem and can substantially increase the radial extent
of dSph dynamical surveys.
Derived radial velocity (RV) dispersion (σv) profiles for dSphs tend to remain rather flat
to well past the core radius. Kleyna et al. (2002) attempted to fit the flat Draco (Dra) dSph
profile using two-parameter spherical models (Wilkinson et al. 2002) that yield increasing
M/L with radius and a net (M/L)tot of 440 ± 240.
anisotropy parameter model to the σv profiles of the Fornax and Dra dSphs, derived ∼
109M⊙ masses for these two systems. Cosmology-dependent studies (Stoehr et al. 2002;
Hayashi et al. 2003) based on ΛCDM models interpret the flat σv profiles as consistent
with massive DM halos surrounding luminous cores. This interpretation helps alleviate the
“missing satellites” problem (Kauffmann et al. 1993; Klypin et al. 1999; Moore et al. 1999)
endemic to these cosmologies. MW tidal effects on dSphs have also been considered (e.g.,
Hodge & Michie 1969; Kuhn & Miller 1989; Kuhn 1993; Kroupa 1997; G´ omez-Flechoso et al.
1999; Fleck & Kuhn 2003; M05) with predictions of potentially significant unbound stellar
populations producing flat/rising dSph σvprofiles.
? Lokas (2002), applying a constant
W04 and Kleyna et al. (2004) recently reported flat or slightly rising σvprofiles that
suddenly decline near the rlimof the Dra, Ursa Minor (UMi) and Sextans dSphs. Such widely
separated cold populations in dSphs are of interest because they have been interpreted as
signs of mild tidal disruption, but more importantly, because they severely mitigate against
the idea of extended, heated populations around dSphs (W04). How far dSphs really extend
as well as the bound versus unbound nature of putative “extratidal” components remains
unanswered. Spectroscopic observation of dSph-associated stars beyond rlimis thus impor-
tant to confirm the reality of the extended populations and to ascertain their dynamical
state.
In this Letter the W04 RVs up to rlimfor Dra and UMi are combined with new RVs
for UMi stars to several rlimto reassess the σvprofiles of these dSphs. Washington+DDO51
filter photometry aids our discrimination of dSph giant star members. We show that: (1)

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UMi members exist well past rlim(§3). (2) The σv’s of Dra and UMi remain more or less
constant to past rlim(§5). (3) A cold population at rlimfor one of the dSphs is found only
under certain binning schemes, and furthermore, depends on how one defines outliers (§5).
(4) The Washington+DDO51 method is at least 5 times more efficient at finding bona fide
dSph members than color magnitude diagram (CMD)-selection schemes (§4).
2. Photometric and Spectroscopic Data
Previous contributions in this series (Majewski et al. 2000a; Majewski et al. 2000b;
Palma et al. 2003, hereafter P03; Westfall et al. 2005) show that Washington+DDO51
photometry effectively identifies rare dSph giant star members against the high Milky Way
foreground in the low density wings of dSphs (see §4). We use a similar methodology here,
where giant star candidates are first selected within the two-color diagram (2CD) boundary
shown in Fig. 1. The UMi photometry is from P03 supplemented with similar Mosaic camera
data along the northeast UMi major axis taken with the Mayall 4-meter telescope on UT
2002 May 4-6. The Dra photometry was obtained with the MiniMosaic (MiniMo) camera
and WIYN telescope on UT 2004 March 12-13 and 2005 April 16-19. MiniMo’s field of view
is not optimal for large area photometric surveys; these data were taken as a backup project
when the instrument for our primary observing program failed. As a consequence we only
partially surveyed Dra, covering a total area of ∼ 0.84 deg2. Median photometric errors for
this dataset are (σM,σT2,σDDO51) = (0.014, 0.014, 0.018) at M = 21.0
We have been unable to obtain spectroscopic follow-up of Dra giant candidates identified
with our photometry. However, M. Wilkinson graciously provided the W04 RV database for
416 and 266 observed stars in the directions of the Dra and UMi dSphs, respectively. Typical
RV errors for these data are 2.4 (Dra) and 2.9kms−1(UMi). We cross-identify by celestial
coordinates 254 UMi field stars (95%) but only 212 Dra field stars (51%) between the W04
and our databases.
To these data we add Keck HIRES (Vogt et al. 1994) spectra for 52 UMi field stars
obtained UT 2002 May 21-22 and UT 2004 May 12-13 (data available from authors). We
deliberately targeted UMi giant candidates at large radii. The spectra were reduced with
standard IRAF echelle reduction methodology with RVs determined using the fxcor package
on the Mg triplet (5130 − 5210˚ A) order. Our quoted RV errors are determined as in Vogt
et al. (1995) with a median of 4.3kms−1, calibrated by 19 multiple measures of six different
UMi stars. For nine stars in common with Armandroff, Olszewski, & Pryor (1995) we obtain
a mean RV difference of 0.3kms−1with dispersion of only 2.9kms−1. The union of our data
with that of W04 yields 309 unique RVs for the UMi field.

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3.Revisiting dSph Membership
The Washington+DDO51 database can be used not only to select dSph giant star
candidates before spectroscopy (as done here for UMi) but for after-the-fact assessment of
likely membership of stars in existing RV catalogues. Figure 1 shows our CMD and 2CD
for UMi and Dra. Filled/open circles designate RV stars more/less likely to be giants based
on positions in the 2CD (with “giants” adopted as stars bounded by the thin line). A few
stars just outside our giant selection criteria that have an RV consistent with that of the
dSph have been considered giants as well. The “likely giant stars” tend to lie closer to the
red/asymptotic giant branches of the dSphs than the “less likely giants” (Fig. 1).
Figure 2 shows RVs for all stars versus elliptical radius, re, normalized to rlim= 77.′9 for
UMi (P03) and 40.′1 for Dra (Odenkirchen et al. 2001). An “elliptical radius” corresponds
to the semi-major radius of the ellipse centered on the dSph that intersects the position of
the star and has the measured ellipticity of the dSph (0.54 for UMi and 0.29 for Dra; from
above references). We adopt elliptical rather than circular radii to follow the distribution of
stars, although a dSph’s gravitational potential and tidal boundary do not necessarily mimic
its observed shape (we revisit circular radii in §5).
The W04 3σ rejection criterion to discriminate likely dSph members (dashed lines in
Fig. 2) corresponds to ±39kms−1around < RV >= −290.8kms−1for Dra and ±36kms−1
around < RV >= −245.2kms−1for UMi. By these criteria (Fig. 2) only six of our pho-
tometric Dra giant candidates lie outside this velocity range, proving the reliability of our
photometric discrimination technique. Among stars classified as giants by our photometric
technique, two (solid squares in Fig. 2) lie just outside the RV range at −246.1 ± 4.6kms−1
and −332.03 ± 4.8kms−1(uncertainties within 1σ of the “Dra member” RV limit). While
for ∼ 200 Dra members one expects only ∼ 0.5 outliers at > 3σ for a Gaussian distribution,
the kurtosis excesses (γ2) of both the Dra and UMi RV distributions flatten from near Gaus-
sian (γ2= 0) to γ2= −0.8 and −0.9, respectively, at re> 0.4rlim, so that more apparent
“outliers” might be expected. Based on these two arguments and the “giant star” colors of
these two stars we consider them to be very likely Dra members.
In UMi, a larger number of giant candidates than in Dra live clearly outside the RV
criteria (Fig. 2). Because even the faintest stars with RVs have quite small photometric un-
certainties (P03), it is not likely that these “false positives” are due to photometric error, but
rather represent field halo giants or metal-poor dwarf stars with weak Mgb+MgH absorption.
Among the “non-UMi” giant candidates there appears to be RV clumpiness, with 9/9/7 stars
having σv= 9.2±2.3/9.6±2.6/16.6±4.6kms−1around < RV >= 6.4/−54.8/−163.8kms−1,
respectively. These RV clumps of giant candidates have σv’s of order those observed in UMi
and Dra, as well as in the Sagittarius (Sgr) tidal tails (Majewski et al. 2004) and are rem-

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iniscent of foreground halo substructure discovered in our similar survey of Carina (M05);
our giant star identification method may be finding other halo substructure in the UMi field.
Nevertheless, the majority of stars we photometrically classify as giants do lie inside the
W04 “UMi” RV range (see §4). A remaining photometric giant candidate (triangle) lies
just outside the UMi RV limits but well inside the giant region in the 2CD and along the
RGB locus for UMi; we strongly suspect this star is a UMi member and include it in our σv
analysis (§5). In the end, 182 UMi and 210 Dra stars are included in our σvprofiles (§5).
4. Photometric efficiency
Particularly at large angular radii, the sky density of dSph stars with brightnesses
amenable to current spectroscopic capability (i.e., red giants) is swamped by foreground
stars. To improve overall efficiency of target selection, various groups (e.g., W04) select dSph
targets by position on/near the dSph’s giant branch in the CMD. This typically decreases
foreground contamination by an order of magnitude but “false positive” sources still well
outnumber dSph stars outside rlim(Majewski et al. 2005; Westfall et al. 2005). However, our
Washington+DDO51 photometric technique improves sample reliability by an additional
order of magnitude over, for example, the W04 CMD selection.
Over all angular separations (to re= 7.7rlimin the case of UMi) our technique yields a
dSph member identification efficiency of 87% for UMi and 97% for Dra. Our “false positive”
identifications all lie beyond 0.5rlim(we ignore the possibility that their RV clumping is due
to wrapped UMi tidal debris arms, as observed in the Sgr system; Majewski et al. 2003).
W04’s overall success rate for their CMD-selected candidates, to only re∼ 0.8rlimfor UMi
and re∼ 1.8rlimfor Dra, is 62% and 50%, respectively. Considering targets with re/rlim> 0.5,
the W04 efficiency drops to 38% (28/73) and 19% (45/239) respectively, whereas our selection
method at similar radii still nets an overall efficiency of 77% (23/30) and 85% (23/27) for UMi
and Dra. This 2 to 4.5 times greater member selection efficiency optimizes the exploration
of low density dSphs galaxies with valuable 6 to 10-m class telescope time.
5. Velocity Dispersion Profiles and Interpretation
Our σv profiles are computed using equal sample-size binning, but similar results are
found with equal, linear bin sizes (though some bins are poorly populated in this scheme).
The method of Armandroff & Da Costa (1986) is used to calculate σv, because a Maximum
Likelihood method like that used by W04 assumes a Gaussian velocity distribution at all

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radii, which is not observed for either dSph, and is also not expected in a disrupted system
(M05). To assess the influence of bin size and geometry Figure 3 shows the UMi dispersion
profile versus elliptical (panel a) and circular radii (panel b) with 17, 12 and 7 members
per bin (and the outermost bins accumulating any odd, extra star). As expected, profile
variability is less pronounced as the number of stars per bin increases. The general UMi
trend is an initial decline in σv followed by a gentle rise and then a slightly decreasing
profile. The sudden decline to a “cold point” reported by W04 appears only in the highest
resolution binning that is most susceptible to statistical fluctuations. While larger samples
of stars in the outer regions of dSphs would be helpful, UMi seems to share the trend of
more or less flat dispersion profiles observed in the outskirts of other dSphs (Mateo 1997,
Westfall et al. 2005, M05).
The Dra profiles (Fig. 4) use 21, 16 and 8 stars per bin, with solid circles for the 208
star samples. Open symbols show the outer profiles when the stars marked as squares in
Figure 2 are included. Except for a single bin in the lower profile of panel (b), the same
general σv behavior is seen at large radii as in UMi: a flat (or maybe slowly decreasing)
profile (depending on the binning) is observed past rlim. In fact, a non-binning test, like the
“one-by-one” test used by Kleyna et al. (2004) for Sextans, does not show a cold population
in the outermost dispersion points for either dSph. Moreover, a χ2fit of the σvdistribution
to a constant value for both UMi and Dra shows that there is no evidence that the outermost
stars have a σvthat is statistically different from those of stars at smaller projected radii.
Tidal disruption can create an unbound stellar population near a dSph. This seems
to be a natural explanation for producing both the observed extended stellar distributions
and flat/slowly declining velocity dispersion profiles at large radii in dSphs (Kuhn & Miller
1989; Kroupa 1997; Mayer et al. 2002, Fleck & Kuhn 2003; M05). While the flat σvprofiles
observed in UMi and Dra have also been modeled by an ad hoc extended DM halo (Kleyna
et al. 2002), two additional piece of evidence support a tidal disruption scenario. First, the
observed platykurtic velocity distributions at large radii in both UMi and Dra more closely
match the flattened RV distributions of unbound dSph stars at large radii in detailed N-body
tidal disruption simulations (e.g. M05).
Second, our new Keck RVs have verified the most widely separated member stars for
any dSph other than the tidally disrupting Sgr galaxy. Our most separated UMi-field star
having a UMi RV is at a linear distance of 238′(4.8 kpc) and near the minor axis; this star’s
elliptical radius of re= 6.6rlimimplies a major axis radius of 10.4 kpc if the UMi ellipticity
is maintained at all radii. Assuming a spherical potential for UMi, the required mass to keep
this star bound to the dSph is M > 3MMW(r/RGC)3, or 7.6×108M⊙for a Milky Way mass
within the UMi distance (RGC = 69 kpc) of MMW = 7.6 × 1011M⊙(Burkert 1997); this

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translates to (M/L)tot> 1,400 (M/L)⊙when we adopt L = 5.4 × 105L⊙(P03). However,
if the tidal boundary of UMi is more elongated, a larger M/L is implied; at the limit where
the tidal boudary is elongated according to its central ellipticity, this star, were it placed at
its corresponding major axis radius (i.e., r = reor 10.4 kpc), implies an astounding UMi
(M/L)tot> 14,400 (M/L)⊙for UMi.
It might be argued that the latter star is a field halo interloper, since its RV is only ∼ 60
km s−1(to the retrograde side) of that expected for a non-rotating halo (assuming a 232 km
s−1solar rotation about the Galactic center) and within the σvof a hot MW halo (∼ 100 km
s−1; e.g., Sirko et al. 2004). Higher S/N spectroscopy to test this star’s chemical properties
would be useful. However, under the above MW dynamics, the second most separated “RV
member” — at 210′(4 kpc), or re= 2.7rlimalong the UMi major axis — is retrograde by
∼ 105 km−1. A UMi-bound star at this projected radius implies a UMi mass > 4.9 × 108
M⊙or (M/L)tot> 900 (M/L)⊙.
One could use a Milky Way model, like the Besancon model (http : //bison.obs −
besancon.fr/modele/) to estimate the expected Milky Way background; this model predicts
∼ 3.2 MW halo giants in the range of RV, color and magnitude of the present 9.7 deg2UMi
survey area outside rlim, under the assumption that we have observed all possible targets
in the field, whereas we have only observed 37% (implying about 1 interloper in our > rlim
RV sample). However, the Besancon model uses smooth population density laws to describe
mean densities and does not account for second order substructure perturbations. In the case
that our color-color-magnitude-RV sampling of parameter space happens to be dominated
by a substructure “void”, the Besancon model background should be an overestimate. Were
our sampling instead overpopulated by substructure, the model would underestimate the
background. But the presence of the substructure should be obvious by coherence in our
parameter space, while, for there to be interlopers within our UMi sample, these stars would
have to both lie at roughly the UMi distance (to share position in the CMD and 2CD) and
have about the UMi RV — a situation we consider improbable. Moreover, the Besancon
model in fact overpredicts by 2.3× the number of Milky Way stars we see outside the UMi
RV-member range; accounting for this factor, in the limit of a smooth halo, implies only 0.5
Milky Way contaminants within the UMi RV sample. In the end, we regard as unlikely that
both of the outermost UMi RV members are contaminants.
If either of these outer dSph stars are bound, UMi has the largest M/L of any galaxy
by yet another order of magnitude or two than previously suggested. The corresponding
physical dimensions of UMi would rival the King profile extent of the Sgr density distribution,
of which a significant fraction, however, has been shown must be unbound (Majewski et al.
2003). From the extreme physical dimensions implied it is difficult to avoid the conclusion

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that true extratidal stars have now been identified for the UMi system — results consistent
with suggestions of tidal disruption of this dSph by photometric analyses as early as that
of Hodge (1964) and more recently by Mart´inez-Delgado et al. (2001), P03, and G´ omez-
Flechoso & Mart´inez-Delgado (2003). The existence of shared photometric and RV trends
between UMi and Dra to at least rlimpoints to a possible tidal disruption scenario for Dra
as well (e.g., Smith, Kuhn, & Hawley 1997).
We gratefully acknowledge support by NSF grant AST-0307851, NASA/JPL contract
1228235, the David and Lucile Packard Foundation, Frank Levinson through the Celerity
Foundation, the Virginia Space Grant Consortium, and the IfA/UH. We thank the referee,
N. Wyn Evans for helpful suggestions to improve the paper.
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Fig.
Solid/open circles show stars with available RV data selected/not selected photometrically
to be Dra giants based on panel (b). (b) (M − T2,M − DDO51,)odiagram for the same
data as panel (a). (c) and (d): CMD and 2CD for the UMi dSph from P03. For clarity, only
stars within one rlimhave been plotted. Symbols in (c) and (d) have similar meaning as for
panels (a) and (b) but for the UMi field.
1.— (a) Color-magnitude diagram (CMD) for the Dra dSph photometric catalog.

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0 0.51 1.520 0.51 1.5
Fig. 2.— RV versus elliptical radius (normalized to rlim) for the Dra (a) and UMi (b)
dSphs. Symbols are as in Fig. 1. Dashed lines delineate the 3σ RV range adopted as dSph
membership criteria by W04. Arrows indicate the RVs of stars outside the plotted area
(normalized radii indicated for these stars next to their arrows). Dotted lines show RV
expected for zero Galactic rotation velocity, assuming a 232 km s−1solar rotation velocity
about the MW.

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Fig. 3.— RV dispersion profiles for the UMi dSph. The panels use (top to bottom) 17, 12
and 7 stars per bin. Solid symbols show σv’s calculated from the 182 star sample. Panels
show profiles versus (a) elliptical and (b) circular radii.

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Fig. 4.— Same as Fig. 3 for the Dra dSph. From upper to lower panel, 21, 16 and 8 stars
are used per bin. Open symbols show the profile when the stars shown by squares in Fig. 2
are included.