The Virgo stellar over-density: Mapping the infall of the Sagittarius tidal stream onto the Milky Way disk

0.5 MB·English

by  David Martinez-Delgado

Draftversion February5,2008
PreprinttypesetusingLATEXstyleemulateapjv.10/09/06
THE VIRGO STELLAR OVER-DENSITY: MAPPING THE INFALL OF THE SAGITTARIUS TIDAL STREAM
ONTO THE MILKY WAY DISK
David Mart´ınez-Delgado1,2, Jorge Pen˜arrubia3,4, Mario Juric´5,6, Emilio J. Alfaro2, Zeljko Ivezic´5
Draft versionFebruary 5, 2008
ABSTRACT
The recently discovered Virgo stellar over-density, which expands over 1000deg2 perpendicularly
∼
to the Galactic disk plane (7< Z < 15 kpc, R 7 kpc), is the largest clump of tidal debris ever
∼
detected in the outer halo and is likely related with the accretion of a nearby dwarf galaxy by the
MilkyWay. We carryoutN-body simulationsofthe Sagittariusstreamtoshowthatthis giantstellar
7
over-density is a confirmation of theoretical model predictions for the leading tail of the Sagittarius
0
0 stream to cross the Milky Way plane in the Solar neighborhood. Radial velocity measurements are
2 needed to confirm this association and to further constrain the shape of the Milky Way dark matter
halo through a new generation of theoretical models. If the identification of Virgo over-density and
n
theSagittariusleadingarmiscorrect,wepredicthighlynegativeradialvelocitiesforthestarsofVirgo
a
over-density. The detection of this new portion of the Sagittarius tidal stream would represent an
J
excellent target for the on-going and future kinematic surveys and for dark matter direct detection
1
experiments in the proximity of the Sun.
3
Subject headings: galaxies: individual (Sagittarius) — galaxies:interactions—Galaxy: structure —

2 Galaxy: halo
v
4
0 1. INTRODUCTION dwarf galaxy (Martin et al. 2004; Bellazzini et al. 2004;
1 In the last decade, various large scale CCD surveys Mart´ınez-Delgado et al. 2005), moves on a prograde,
9 (Sloan Digital Sky Survey, 2MASS7, QUEST) have for nearly circular orbit (Pen˜arrubia et al. 2005), according
0 to the recentproper motions measuredby Dinescu et al.
the first time found strong evidence for the presence of
6 (2005). Additionally, Rocha-Pinto et al.(2004) reported
a significant amount of substructure in the halo of the
0 thediscoveryofanewpossibletidalstreamintheTrian-
MilkyWayinformoflongtidalstreamsorstellarclumps
/ gulum/Andromeda constellations, although subsequent
h (Newbergetal. 2002;Majewskietal. 2003). Thesehave
theoretical simulations identified this tidal debris as a
p beeninterpretedastheremnantsoflatestmergersoccur-
- ring as a part ofthe hierarchicalbuild-up of our Galaxy. part of a more distant, metal poor wrap of the Mono-
o ceros tidal stream progenitor (Pen˜arrubia et al. 2005;
In addition, N-body simulations of these merger events
r Mart´ınez-Delgadoet al. 2007, in preparation).
t (Helmi2004;Mart´ınez-Delgadoetal. 2004a;Law,John-
s In addition to these two large tidal streams, the
ston & Majewski 2005; Pen˜arrubia et al. 2006) have
a
analysis of large samples of stellar tracers of halo sub-
: been extensively used to, firstly, associate the tidal de-
v structure(RRLyrae,F-type turnoffstars)haverevealed
bris with their progenitor galaxies, secondly, determine
i the presence of numerous stellar over-densities possibly
X the dynamical history of the progenitor satellites and,
associated with unknown merger events in the outer
thirdly, constrain the distribution of dark matter in the
r halo. In the Virgo constellation, several groups have
a MilkyWay. The ultimate goalofthesestudies is toinfer
reported numerous detections of stellar over-densities
the formation process of the Milky Way from the prop-
using different tracers:
erties of the present fossil records.
(i) The most conspicuous one is a diffuse concentration
Much of the observational and theoretical effort has
of metal poor, old stars situated at 20 kpc from the
focused specially on the two largest tidal streams dis-
∼
Sun in the direction of the Virgo constellation, first
covered so far: the tidal stream of the Sagittarius (Sgr)
detected by means of the identification of its associated
dwarfgalaxy,whichwrapsaroundtheGalaxyinahighly
main-sequence turnoff (MSTO) in a color-magnitude
inclined orbitwith respect to the Milky Way disk (Ibata
diagram (CMD) of a SDSS slice (named S297+63-20.0;
et al. 2001; Mart´ınez-Delgado et al. 2001; Majewski
Newbergetal. 2002). Additionally,Vivas&Zinn(2003)
et al. 2003) and the Monoceros tidal stream (Yanny et
reported a clump of 21 RR Lyrae stars located at
al. 2003; Ibata et al. 2003), a low-latitude tidal stream
∼
20 kpc from the sun in the same region of the sky (see
whoseprogenitor,possiblythecontroversialCanisMajor
also Ivezic et al. 2005 and Vivas & Zinn 2006). This
1InstitutodeAstrof´ısicadeCanarias,LaLaguna, Spain over-density (named the 12h.4 clump) extends over an
2InstitutodeAstrof´ısicadeAndaluc´ıa(CSIC), Granada,Spain areaof the sky of15◦ 1◦ (correspondingto to a spatial
3Max-PlanckInstitutefuerAstronomie,Heidelberg,Germany size of 5.3 kpc 0.3 k×pc at D 20 kpc) and display a
4DepartmentofPhysicsandAstronomy,UniversityofVictoria, × ≃
line-of-sight depth of only 1.5kpc (Vivas 2002), which
VictoriaBC,V8P1A1,Canada ≃
5Department of Astrophysical Sciences, Princeton, NJ 08544 is considerably smaller than that of a similar RR Lyrae
USA over-densitydetected atthe apocenter of the Sgr stream
6InstituteforAdvancedStudy,SchoolofNaturalSciences,Ein- ( 4kpc;Vivas2002). Owingtoitspossibletidalorigin,
steinDrive,Princeton,NJ08540 ∼
7 TwoMicronAllSkySurvey they denoted it as the Virgo stellar stream (VSS).
Mart´ınez-Delgado et al. (2004a) suggested that the
2 Mart´ınez-Delgado et al.
VSS might be related to the complex debris structure Sgrgalaxydebris. Inorderto explorea possibleassocia-
of the Sgr stream predicted by the theoretical models in tion of the VSS and VOD with the Sgr tidal stream, we
this region of the sky. However, spectroscopic follow-up shall compare their derived spatial and kinematic prop-
of a sample of these RR Lyrae stars by Duffau et al. erties with those obtained from up-to-date theoretical
(2006) showed a fairly narrow velocity distribution that models.
pointed to a progenitor galaxy less massive than the Our Galaxy model consists of a Miyamoto-Nagai
Sgr dwarf and, therefore, to a hitherto unknown tidally (1975) disk, a Hernquist (1990) bulge and a Navarro,
disrupted dwarf galaxy. Using SDSS photometric data, Frenk&White(1996)darkmatterhalo(hereafter,NFW
these authors estimated that the VSS covers roughly an halo). The gravitational potential of each of those com-
area of 106 deg2 in the sky. ponents in cylindrical coordinates is:
GM
(ii) More recently, Juri´c et al. (2006) detected Φ (r)= d , (1)
d
a remarkable excess of main-sequence stars towards − R2+(a+√z2+b2)2
the direction of Virgo constellation, named the Virgo q
over-density (VOD). These authors construct a three- Φ (r)= GMb, (2)
b
dimensional density distribution of Milky Way stars −r+c
based on the position of 48 million stars obtained by GM q
∼ Φ (r)= h h (3)
the SDSS in order to identify stellar over-densities. The h ln(1+ rvir) rvir 2r ×
VOD density map reveals a giant, diffuse lump of stars rs − rs+rvir s
∞
withoutanyevidenceofadistinctcorethatextendsover m(u) du
2 .
more than 1000 deg2 (see Fig. 1) towards the direc- (cid:20)Z 1+m(u)(1+u) q2 +u − (cid:21)
tion (l,b) =∼(300◦,65◦). This stellar over-density shows 0 h
p
anremarkablyextendedverticalstructureperpendicular There, rvir,rs are the virial and scale radii, respectively,
totheGalacticplane(∆Z 8kpc,withheliocentricdis- Mh = Mh(rvir) and r2 = R2 + z2. The potential of
tancesbetween5-17kpc)th≃atpossiblycrossestheGalac- an axi-symmetric NFW halo was calculated from Chan-
tic plane, extending into the southern Galactic hemi- drasekhar (1960) using elliptic coordinates
sphere (see also Fuchs, Phleps & Meisenheimer 2006).
R2 z2
The density of VOD main-sequence stars peaks at 16 m2(u)= + , (4)
kpcfromtheSun(orRRLyraemagnitudeof 16.7∼),in rs2(1+u) rs2(qh2+u)
∼
good agreement with the RR Lyrae distance determina-
where q is the axis-ratio of iso-density surfaces. In this
h
tion. These authors suggest that the giant stellar over-
contribution, we shall denote oblate and prolate halos as
densitymightberelatedwithahithertounknownmerger
thosewithq <1andq >1,respectively. Forspherical
h h
eventof a nearby,low metallicity dwarfgalaxy.Alterna-
halos Eq. (3) reduces to
tively, Xu, Deng & Hu (2006) suggest that this stellar
lump could be related to a non-axisymmetric Galactic GMh ln(1+r/rs)
Φ = (5)
stellar spheroid (see Sec. 3.1). h −ln(1+ rvir) rvir r ≡
AlthoughVODandVSSarecoincidentinpositionand rs − rs+rvir
ln(1+r/r )
display a huge sky-projected size, the different vertical V2 s .
structuresuggeststhattheyareindependentsystems. In − c r/r
s
absence of radial velocity measurements for the VOD, it
Following Johnston et al. (1999) we fix the disk and
is not possible to address whether they share a common
owriilglinrefoerratroe tchoemmplewtietlhy udniffreerlaentetdn.aFmoersthinistrheiassopna,pwere, b10u1lg0Me p⊙a,raam=et6e.r5skpacs,Mb =d =0.216.0k×pc1a0n11dMc⊙=, 0M.7bk=pc.3.T4h×e
Milky Way halo parameters at z = 0 were taken from
following the nomenclature givento eachover-densityin
Klypin, Zhao & Somerville (2002) being M = 1.0
thTehoerimginaianl paiampeorfs.thispaperistoinvestigatethenature 1012M⊙, rvir = 258kpc, rs = 21.5kpc, whichhleads to×a
concentration at the present epoch of c = r /r = 12.
of the VOD and to analyze whether this stellar lump vir s
According to the results of Pen˜arrubia et al. (2006), the
couldbe relatedtothe Sgrstreamthroughacomparison
evolutionof the host Galaxy potential is not reflected in
between up-to-date theoretical models and the available
the present properties of tidal streams, so that we use a
observational data. The structure, kinematics and pos-
static Milky Way potential for simplicity.
sible origin of the VSS will be analyzed in a companion
The actual disruptionof satellites is modelled by ‘live’
paper.
(i.e. self-consistent, self-gravitating) N-body realiza-
In Sec. 2 the theoretical models of Sgr tidal stream
tions of a King (1960) model, with a dimensionless
are described. In Sec.3 we discuss the possible origins
central potential W = 4, or concentration parameter
of the VOD. In particular, we explore the presence of 0
c log (r /r ) 0.84,wherer andr aretheKingand
tidaldebris fromthe SgrtidalstreaminVirgo by means ≡ 10 t k ≃ k t
tidal radii, respectively. Our satellite models have N =
of update theoretical models and compare its expected
105 particles. The initial and final (i.e present) masses
structural parameter with those derived for Virgo. Fi-
nally, conclusions are given in Sec. 4. are Ms(t0) = 109M⊙ and Ms(tf) = 5×108M⊙, respec-
tively. TheinitialKingandtidalradiusarer (t )=0.58
k 0
2. THEORETICALMODELS kpc and rt(t0)=4.01 kpc.
The equation of motion for each satellite particle is:
The giant stellar over-density detected in the Virgo
constellation is located in a region of the Milky Way d2r
i
where several theoretical models predict the presence of dt2 =−∇(Φs+Φd+Φb+Φh)i (6)
The origin of remnants in Virgo 3
whereΦsistheself-gravitationalpotentialofthesatellite 3. THEORIGINOFTHEVIRGOOVER-DENSITY
galaxy and i=1,...,N. We use superbox (Fellhauer et
InthisSectionweanalysethelikelihoodofvarioussce-
al. 2000)tocalculateΦ ateachtime-stepandsolveEq.6
s narios that may shed light on the nature of the VOD.
through a leap-frog scheme with a constant time-step of
∆t = 0.65 Myr, which is about 1/100th the satellite’s
dynamical time. 3.1. The signature of a tri-axial Galactic stellar halo
Note that the Galactic potential is static and, therefore, An alternative explanation for the presence of the un-
Eq.6doesnotimplementtheresponseoftheMilkyWay expected MS feature in the CMD reported in several
to the presence of Sgr. We also neglect the effects of studies (and so-called the VOD: Newberg et al. 2002;
dynamical friction on the Sgr’s orbit (as suggested by Duffau et al. 2006; Juric et al. 2006; see Sec.1) is to
Law et al. 2005). postulate the existence of a non-axisymmetry Galactic
We have reproduced the N-body models presented in model component, such as a triaxial halo (Newberg &
Lawetal. (2005). Thesemodelsreproducethefollowing Yanny 2005; Xu et al. 2006). We have explored this
observational constraints8: possibility by inspecting a sample of deep CMDs (with
limiting magnitude R 24.5)of Galactic fields taken
lim
1. The heliocentric positionandradialvelocityof the withtheWideFieldCame∼ra(WFC)attheprimefocusof
Sgr dwarf are (D,l,b) = (24kpc,5.6◦, 14.2◦) and IsaacNewton2.5-metertelescope(LaPalma,Spain)dur-
−
vr =171 km/s, respectively. ingdifferentobservingrunsdevotedtothesearchoftidal
debrisassociatedtoknownGalacticsatellitesorglobular
2. The orbital plane of Sgr has an inclination with clusters (Mart´ınez-Delgado et al. 2004b). Table 1 lists
respect to the Milky Way disk of i 76◦. the position of our fields with positive and negative de-
≃ tections of the MS feature in the CMD. These negative
detections can be interpreted as the lack of tidal debris
3. The averaged heliocentric distance for Sgr leading
or that its surface brightness is extremely low to be de-
debris is D 50 kpc. tectedinthe smallfieldofview ofthe WFC (35′ 35′)9.
∼
×
Fig. 1 shows the position of these negative detection
Items 1. and 2. above show that we have observational
(open circles) over-plotted in the density map of VOD
measurements for five of the six coordinates that deter-
derived by Juri´c et al (2006) from SDSS observations.
mine the Sgr orbit. Law et al. (2005) surveyed the un- Themostinterestingresultis anegativedetection 20◦
known coordinate (namely, the tangential velocity com- ∼
North of the center of our target field (see Table 1) that
ponent,v )sothatthe resultingN-body modelsrepro-
tan clearlyshows a decrease of streamstar counts in a small
duced all the observational constraints listed.
areaof the sky. Althoughour sparsepencil beamsurvey
Among other free parameters, Law et al. (2005) also
cannot constrain the spatial extent of this stellar popu-
explored which halo axis-ratio (q ) would produce the
h lation in the sky, the distribution of negative detections
best-fitting model to the available observational data.
stronglyindicatesthatthisMSpopulationisnotlikelyto
They found that, whereas the geometry and kinematics
beamanifestationofanon-axisymmetricGalacticmodel
of the trailing arm are scarcely sensitive to the adopted
component,butisprobablyassociatedwiththeremnants
q ,radialvelocitymeasurementsoftheleadingarmwere
h of a dwarf galaxy under tidal disruption, in agreement
best matched by prolate (q >1) halo models, in agree-
h with previous studies. Juri´c et al. (2006) have reached
ment with Helmi (2004). However, Johnston, Law and
the same conclusion by analyzing the vertical (Z) distri-
Majewski (2005) showed that Sgr models in prolate ha-
butionofVODdebrisfromtheirsampleofSDSSGstars
los cannot reproduce the observed precession rate in
(0.10<r i<0.15).
the youngest pieces of the Sgr stream. Furthermore, −
they were able to constrain the halo axis-ratio to be
q = 0.83 0.92, excluding models with q > 1 at 3.2. A tidal debris of the Sgr dwarf?
h h
− −
a 3σ level. In view of these results, we have performed 3.2.1. Sky projected density maps
N-body simulations where the halo axis-ratio was fixed
It is well understood both from observations and the-
eithertoq =0.8ortoq =1.4,excludingforthesakeof
h h oreticalmodeling that the Sgrleading armturns around
brevity spherical halos, which neither reproduce the ra-
and falls towards the Galactic plane in the proximity of
dialvelocityvariationalongthestreamnoritsprecession
the Solar neighborhood, yielding a vertical debris struc-
rate.
ture that might cross the Galactic plane and possibly
In a coordinate system where the Sun is located at
extend into the southern Galactic hemisphere (Majew-
(X,Y,Z) = (8,0,0) kpc, with a velocity of (U,V,W) =
ski et al. 2003; Mart´ınez-Delgado et al. 2004a; Law et
( 10, 220,7)km/s(Binney &Merrifield1998),the Sgr
− − al. 2005). This downward flow of the Sgr stars onto the
velocities that best fit the kinematic and spatial distri-
Galactic disk may share similar characteristic to those
butions of stream debris are (237, 35,220) km/s for
− derived for the VOD in the stripe covered by the SDSS.
q = 0.8 (oblate halo) and (244, 39,249) km/s for
h − As a guide for the reader,we illustrate this putative sce-
q =1.4 (prolate halo).
h nario in Fig. 2 together with the identification of the
With those inputs, we have evolved the N-body satel-
different parts of the Sgr tidal streamobtained from our
lite model from 4 Gyr in the past to the present.
theoretical models (see Sec. 5 for a three-dimensional
8 It is also important to remark that we have not input any comparison).
observational data of the VOD inthe fitting of these simulations,
that areonlybased inthefitting ofanindependent setof data of 9Mart´ınez-Delgadoetal. 2004aestimatedthelimitSBdetection
theSgrtidalstream. ofourCMDtechnique isΣ∼32magarcsec−2
4 Mart´ınez-Delgado et al.
ToexaminewhethertheVODisapartoftheSgrtidal The prolate (q =1.4) halo model (bottom panel) pro-
h
structure,we comparethe predictions fromthe theoreti- duces a slightly worse estimate of the location of VOD
calmodelsoutlinedinSec.2totheSDSSdatapresented center and its generalshape. It does predicts a substan-
in Juri´c et al. (2006).When comparing the theoretical tial amount of faint, diffuse debris in the 180 < l < 240
streammodels againstthe SDSS, it is importantto keep region. This is to a degree observed in SDSS data – e.g.
in mind that the observational data may be biased by the density in 180 < l < 210 (see Fig. 1) is apparently
systematic over or underestimates of the distance scale. greater than that in its symmetric counterpart with re-
The stellar distances in SDSS data were derived using spect to the l=0,l=180 direction.
anassumedphotometric paralaxrelationwhose shape is Interestingly, Gondolo et al. (2005) estimated a lo-
well constrained but the zero-point may be offset by as cal stellar density of Sgr leading tail of between 270-740
muchas0.4mag(Juri´cetal. 2006). Thiswouldtranslate stars/kpc3,correspondingtoarangeof2.1to7.4 10−7
into20observedcenterofVODtoanywherefrom8to12 stars/pc3 or -15.4 < ln(δ) < -14.1. This is with×in the
kpc. However, even the worst case scenario would be measured limits of stellar density in the VOD (see Fig.
compatible with the conclusions that we are to present. 23 in Juri´c et al. 2006).
Secondly,theverticalshapeanddensityprofileofVOD We note that the interpretation of the faint density
(Fig. 4, bottom left panel) depend strongly on the de- excess is muddied by the existence of a different narrow
tailsofthe(stillpreliminary)Galacticstellarhalomodel. streamin that region(Juri´c et al. 2006),apparently un-
Thedensitygradientsalongthisverticalstructureshould related to Sgr stream. An alternative scenario is that
thereforebeinterpretedwithcaution,especiallyatlowZ the narrow stream might be the true origin of the den-
(closertothedisk). There,thenumberdensityofGalac- sity excess seen in SDSS data, instead of the Sgr debris.
tic stars dominates over the stars in VOD and even a However, as it will become evident in the next Section,
few percentmismatchinthe Galacticmodelmayleadto thethree-dimensionalstructureoftheVODstronglydis-
an artificial increase (or decrease) of the residual stellar favors this hypothesis.
density ascribed to VOD.
In Fig. 3 we plot two equal-area projections of stream 3.2.2. Three-dimensional spatial structure
particles from the models with oblate qh = 0.8 and pro- We compare now the three-dimensional structure of
late qh = 1.4 halos (top and bottom, respectively). In the VOD to the structure obtained from the theoreti-
theseplots,theNorthGalacticpoleisinthecenter,con- cal models of the Sgr stream in that region of the sky.
centriccirclesarelinesofconstantGalacticlatitudeband We examine various cross-sections (horizontal and per-
theradiallinesdenotelocationsofconstantGalacticlon- pendicular to the Galactic plane) of the VOD and the
gitude l. The Galactic center is to the left. We restrict equivalent cross-sections of the Sgr stream model.
the theoretical sample to the distance range of Juri´c et InFig.4weplotthemeasuredstellardensity(left)and
al. (2006) data by including only particles at b > 0 and thatobtainedfromthe Sgrstreammodels for twodiffer-
5kpc < d < 15kpc. To estimate the two-dimensional entvaluesofhaloflattening,q =0.8(middle)andq =1.4
h h
projected density distribution, we convolve the particles (right). The density shown on the top left panel is that
with a 2D Gaussian σ = 2.9deg kernel. The resulting shown in Fig. 8 (middle-left panel) of Juri´c et al (2006).
density is shown as varying shades of gray (black and Beforediscussingitsimplications,wewillverybrieflyde-
whiteregionsdenotingthehighestlowestdensity,respec- scribe the method used here (for a more detailed discus-
tively) and can be directly compared with the observed sion we refer the reader to Juri´c et. al 2006): The SDSS
morphology of the VOD displayed in Fig 1 (that was has observed 4.2 million G stars (0.1 < r i < 0.15)
made with the same scale). withinthesur∼veyarea. Toconvertthe SDSS−starcounts
These maps show a conspicuous, diffuse lump of Sgr to spatialnumber density, we estimated the distances to
stream stars that extends over a few hundreds of square individual stars using the photometric parallax relation
degrees, whose shape and extent resembles those of the of Juri´c et al. (Eq. 1). From the estimated absolute and
stellar over-density displayed in Fig. 1. The position of measuredapparentmagnitudes,andfromastrometry,we
the over-density center (defined as the location of max- calculatethethree-dimensional(X,Y,Z),positionsofall
imum density) in the sky depends on the shape of the stars in the SDSS stellar sample. We then bin them to
halo, and is consistent with simulations of Law et al. dx = 500pc pixels in the coordinate system as defined
(2005), Fig. 13. The oblate model (qh=0.8) produces a aboveto obtaina three-dimensionalstar-countmap. Fi-
better agreement with the SDSS data, with the over- nally, by dividing the map by the volume that was ob-
density being centered at (l,b)=(277,63). This corre- served within each voxel, we obtain a three dimensional
spondstoasmalloffset, 11deg,withrespecttotheob- map of number density within the Milky Way.
∼
servedposition of the VOD ((l,b)=(300,65))as reported ThedensityshownintheleftpanelofFig. 4isaplanar
by Juri´c et al. (2006). Taking into account the uncer- cross-section of the 3D map along a plane parallel with
tainties in the Sgr stream modeling (see Sec. 2) and in the Galactic plane, and at Z =10kpc above it. The col-
the SDSS data as noted above, the agreement in posi- ors encode the stellar number density (stars pc−3) on a
tion is remarkable. This result also provides a natural natural log scale, ranging from exp( 15.46) = 1.910−7
explanationfor the huge apparentextensionofthis tidal (blue) to exp( 14.03) = 8.310−7 sta−rs pc−3 (red). The
remnant, since we are observing through a stellar tidal black regions a−re places where SDSS has not observed.
stream that approaches the Sun in an almost radial di- The yellow dot marks the position of the Sun in X-Y
rection in a localized area of the sky.10 plane (X = 8kpc, Y = 0kpc) The circles visualize the
presumed axial symmetry of the Galaxy. If the Galactic
10 An analogy can be found when a meteoroid stream crosses number density distribution was axially symmetric, the
theEarth;seeNakamuraetal. 2000.
color contours in the observed regions would trace such
The origin of remnants in Virgo 5
circles around the Galactic center, and the density dis- to the best fitGalactic halomodel ofJuri´cetal. (2006).
tributionwouldrespectthesymmetrywithrespecttore- In the case of q =0.8 halo, the Sgr leading armis nearly
h
flectionalongtheX axis(ρ(X,Y,Z)=ρ( X,Y,Z)). As perpendicular to the Galactic plane, with a slight down-
−
seen in the left panel, the density distribution is neither warddensity gradient, in agreementwith the findings of
circularnorsymmetric,andexhibitsastrongdensityen- Juri´cet al. (2006). Its locationagreesto within ∆R 1
∼
hancement centered approximately at X =6,Y =4kpc, kpc of the observed position of Virgo over-density. In
the VOD (Juri´c et al. 2006). contrast,althoughthe prolatemodels(q =1.4)correctly
h
We test under which conditions the VOD might be reproducetheGalactocentricdistanceoftheover-density
plausibly identified with the leading arm of the Sgr (R 6 7kpc), they fail in order to reproduce the ob-
∼ −
tidal stream by over-plotting the equivalent X-Y slices served morphology. These models show a strong den-
at Z = 10kpc of simulated Sgr debris over the contours sity maximum at (R,Z) (7,8)kpc (incompatible with
≃
of the SDSS observed area (the gray area in middle and the density map) and pieces of debris scattered out to
leftpanels). Thefiguresinthemiddleandleftpanelsare R 12.5kpc (not detected by SDSS). In this working
∼
constructed in a manner similar to the method used for scenario, the VOD morphology strongly disfavours pro-
SDSS data outlined above. However, we note that the late halo models.
particle counts have been averaged in the 9 kpc < Z < Theconclusionsobtainedfromthesecross-sectionscan
11 kpc slice. The difference in thickness, compared to be summarized in the different spatial perspectives dis-
dx=500pcthicknessusedforSDSSdensityestimationis playedinFigure511,whichclearlyshowsthecoincidence
toaccountfortheeffectofradialsmearingintroducedby in position of the VOD and the location of the Sgr lead-
the intrinsic σ 0.3mag dispersion of the photomet- ing tail. Note that this part of the stream distributes
Mr ∼
ric parallax relation. This effect increases the effective nearlyperpendicularly to the Galactic disk in this direc-
radial SDSS voxel scale (for a more detailed discussion, tion of the sky. The panels of Fig. 5 show two different
see Juri´c et al. 2006). We estimate the density of Sgr 3-dimensional projections (top and bottom row) of our
debris by convolving the simulation particles in the ob- Sgr model computed for oblate q = 0.8 (left column)
h
served volume with a σ =0.5 kpc Gaussian kernel, thus and prolate q = 1.4 halos (right column). They visual-
h
obtainingthefinaldistributionshowninthepanels. The ize the simulated Sgr dwarf and its tidally stripped tails
color scheme is that used in the right panel, with equal- in rainbow color map, with the color encoding the col-
density contours added. We also plot, as small yellow umn density of simulation particles (red being the high-
crosses,theindividualsimulationparticlesthatfalloffof est,bluethelowest),whichareover-plottedinthepanels
the lowest equal-density contour. as black dots. Note that the core of Sgr dwarf corre-
As it was the case in Fig. 3, the oblate q =0.8 model spondstothedarkestregionowingtothehighdensityof
h
agrees well with the data within the observational and N-body particles that are still gravitationally bound to
theoretical uncertainties. It successfully reproduces the the dwarf’s remnants. The coordinate system origin is
diffuseshapeoftheover-densityandthelocationofover- locatedattheGalacticcenterwiththeredaxis(X)point-
density maximum. The location of the maximum for ing towardsthe Sun (yellowcircle)and the blue axis (Z)
q = 0.8 model locates within 1.5 to 2kpc of the ob- pointing towardsthe North Galactic pole. The regionin
h
served R 6.5 7kpc maximum of VOD, and the dif- which Juri´c et al. (2006) detect the VOD is marked by
∼ −
fuse morphology of the q = 0.8 model appears to show thewhitewire-framebox,whereasthelocationofVSSas
h
aconsiderablybettermatchto theobservedmorphology reported by Duffau et al. (2006; see Sec. 1) is shown by
than that of the q = 1.4 model. Some debris from the the blue wire frame. This coincidence points to a plau-
h
q = 1.4 model (right panels) can be also found at the sible identification of VOD with the leading arm of the
h
location of the VOD. However, this model predicts the Sgrtidalstreamor,attheveryleast,tolikelysignificant
existence of other over-densities where none have been pollution of VOD as seen in the SDSS density maps by
detected and the morphology at the VOD location is ir- the Sgr tidal debris.
reconcilable with that inferred from the SDSS data. Taken together, the analysis of figures 1, 3, 4 and 5
We now examine the vertical distribution of matter in clearly suggests that the Virgo over-density may corre-
the VODandcompare it with the models ofSgr stream. spond to the detection of the Sgr stream’s leading arm
The bottompanelsofFig.4comparethe observedverti- falling onto the Milky Way plane. Furthermore, the ob-
calstellarnumberdensitydistributionintheGalaxy,cut servedmorphologyisbestdescribedbymodelsassuming
alonganarrowφ=30degplanethatpassesthroughthe an oblate Milky Way halo. With these results at hand,
centerofthe Galaxyandthe centerofthe VOD(the red it appears fairly unlikely that the VOD is a tidal stream
dashedboxontopmiddleandleftpanelsofFig.4). The unrelated to the Sgr dwarf and yet it has the predicted
horizontal coordinate is the distance from the Galactic location and morphology of the Sgr leading arm.
center,R,alongthe φ=30◦ direction, while the vertical
coordinate is the height above the Galactic plane. As 3.2.3. Radial velocity of the Virgo over-density
in the case of the top left panel, the bottom left panel
At present there is no kinematic information available
showstheover-densityasmeasuredfromSDSSdata(and
on the stars of Virgo over-density. Radial velocities are
is equivalent to the top right panel of Fig. 22 in Juri´c et
necessary in order to establish unambiguously whether
al.2006),while the two panels to the rightshow the sim-
the Virgo over-density is associated to the Sgr stream.
ulated density of the Sgr tidal stream as obtained from
Theoretical models predict that, independently of the
our simulations (Sec. 2) using an oblate (q =0.8) and a
h
prolate (q =1.4) halo. The color scheme is the same as
h 11 This figure is a snapshot of a set of movies included as sup-
for the top panels, except that in the case of the bottom
plementarymaterialintheelectronicversionofthispaperandalso
left panel we show the fractional residuals with respect availableathttp://www.astro.princeton.edu/∼mjuric/sgr-virgo/
6 Mart´ınez-Delgado et al.
halo shape, the leading arm of the Sgr stream is present oreticalpredictions from the present Sgr stream models.
in this area of the sky and moves on average with nega- According to these models, the Virgo over-density cor-
tive radial velocities as it falls onto the Milky Way disk. responds to Sgr leading arm falling onto the Milky Way
However,theexactmagnitudeofthemeanradialvelocity disk. InagreementwithotherportionsoftheSgrstream,
isavitaldiscriminatorforthehaloshape,asprolateand thespatialdistributionoftheVODisbestreproducedby
oblate halos leadto fairly distinct trends of V along the models with oblate halos q < 1. However, we must re-
r h
leadingarm(Mart´ınez-Delgadoetal. 2004a;Helmi2004, mark that a unambiguous associationbetween the VOD
Law et al. 2005). We must remark that at presentthere and the Sgr stream cannot be established in absence of
is no information on the kinematics of the Sgr leading stellar kinematics.
arm in this area of the sky, since this part of the stream If the Virgo over-density proves to belong to the Sgr
was not coveredby the spectroscopic survey of M-giants streamitmightrepresentthekeypiecetosolvethepara-
carried out by Majewski et al. (2004). dox described above, as we have for the first time the
There have been radial velocity measurements of RR opportunity to measure the radialvelocity of millions of
Lyrae stars in the Virgo constellation that have shown stream stars just in the region where observations and
the presence of a spatial over-density (called the 12h.4 theoretical models do not match.
clump, see Sec. 1) located at D 20 kpc. Duffau et Additionally, the detection of a new portion of the
≃
al. (2006)find ameanradialvelocityinthe galacticrest stream’s leading arm provides strong constraints on fu-
frame of (V ) 99.8 km/s (see Table 1) with a fairly ture theoreticalmodels and willhelp to addresswhether
r gsr
lowvelocitydispe≃rsion(σ=17.3kms−1),unexpectedfor the Sgr stream passes through the solar neighbourhood
the smooth population of RR Lyrae in the Milky Way, asitcrossestheMilkyWayplane(aspredictedbyKundu
that suggests a possible tidal stream detection. Accord- et al. 2002, Majewski et al. 2003; Mart´ınez-Delgado et
ingtothetheoreticalmodelsofthe Sgrstream,the posi- al. 2004). In that case, the Sgr stream would repre-
tivevalueof(V ) excludesamembershipofthesestars sent an important target for the on-going RAVE sur-
r gsr
to the leading arm. However, it is unclear whether the vey (Steinmetz et al. 2006), whose goal is to measure
12h.4 clump is not associated to the Sgr stream at all, the radial velocity of around 106 stars in both hemi-
since the oblate halo models (q =0.8 in this work)also spheres. Thankstothelargesampleofradialvelocities,if
h
predictthe presenceofthe trailingarmstarsinthatvol- the Milky Way crossingoccurs at a heliocentric distance
ume of the Milky Way (see Fig. 5, where the blue box D < 3 kpc, its presence will be detected in form of an
represents the 12h.4 clump position) with an averaged excess of stars with vr < 0 in the Northern hemisphere
radialvelocityof(Vr)gsr=90km/s,fairlysimilartothat (b ≥ 0) and with vr > 0 for b < 0 with respect to the
reported by Duffau et al. (2006) ((V ) =+83 or +100 backgroundpopulation of Milky Way stars (Pen˜arrubia,
r gsr
km/s,depending oftheirsampleselection). Therefore,if Navarro & Helmi, in preparation). The presence of a
the 12h.4 clumpprovesto belongto the Sgrtrailing arm tidal stream in the solar neighbourhood also represents
anexcellenttargetforWeaklyInteractingMassiveParti-
it would favor the models with q <1.
h
cles (WIMPs) direct detection experiments, since a sub-
4. DISCUSSION structure of dark matter in the proximity of the Sun
Theoretical models of the Sgr stream are not able to wouldyielda“cold”flowofWIMPsthoughtthedetector
reproduce all the observational constraints. All models of either of these dark matter experiments (see Savage,
agree that the geometry of the tidal stream (i.e its 3D Freese and Gondolo 2006 and Gondolo et al. 2005 for
spatialdistribution) clearlyrules outhalo models with a details). This wouldmake the solar vicinity an excellent
prolate shape (Mart´ınez-Delgado et al. 2004a, Johnston labforprobing the physicalpropertiesandnature of the
et al. 2005, Law et al. 2005) and that Milky Way halos dark matter.
with q < 1 are preferred at a 3σ level. Paradoxically,
h
the models that best explainthe streamstructure failto
reproducetheradialvelocitytrendalongtheleadingarm
WethankstoBrianYannyandKathyVivasformaking
unless prolate halo models (q > 1) are invoked (Helmi
h availabletoussomeresultsontheVirgotidalstreamdur-
2004). Apparently, the present status of the Sgr stream
ing the preparationof this paper. We also thanks to the
modeling is that of a fish biting its tail.
anonymous referee for useful comments that helped to
It is not clear how to reconcile observations and the-
improvethismanuscript. DMDacknowledgesfundingby
ory. Possible explanations for this mismatch are: (i) the
the Spanish Ministry of Education and Science (Ramon
Milky Way models are over-simplistic (although similar
y Cajal contract and research project AYA 2001-3939-
models successfully reproduce other tidal streams such
C03-01). JP thanks Julio Navarro for financial support.
asMonoceros,Pen˜arrubiaetal2005,andtheMagellanic
Funding for the SDSS and SDSS-II has been pro-
stream, Ruzicka, Palous& Theis 2006,both streams be-
vided by the Alfred P. Sloan Foundation, the Partic-
ing best reproduced by models with oblate halos) or (ii)
ipating Institutions, the National Science Foundation,
the presence of possible systematic errors on the data of
the U.S. Department of Energy, the National Aeronau-
the Sgr tidal stream used in the computation of these
tics and Space Administration, the Japanese Monbuka-
simulations (as suggested by Chou et al. 2006).
gakusho,theMaxPlanckSociety,andtheHigherEduca-
In this contribution, we have investigated the origin
tion Funding Council for England. The SDSS Web Site
of the Virgo over-densitydiscoveredfrom the analysis of
is http://www.sdss.org/.
the SDSS data. The VOD is the largest clump of tidal
The SDSS is managed by the Astrophysical Research
debris ever detected in the outer halo of the Milky Way.
Consortium for the Participating Institutions. The Par-
We find that the position, apparent angular size, stellar
ticipatingInstitutionsaretheAmericanMuseumofNat-
density and three dimensional geometry match the the-
The origin of remnants in Virgo 7
ural History, Astrophysical Institute Potsdam, Univer- ences(LAMOST), LosAlamos NationalLaboratory,the
sity of Basel, Cambridge University, Case Western Re- Max-Planck-Institute for Astronomy (MPIA), the Max-
serve University, University of Chicago, Drexel Univer- Planck-Institute for Astrophysics (MPA), New Mexico
sity, Fermilab, the Institute for Advanced Study, the State University, Ohio State University, University of
Japan Participation Group, Johns Hopkins University, Pittsburgh, University of Portsmouth, Princeton Uni-
the Joint Institute for Nuclear Astrophysics, the Kavli versity, the United States Naval Observatory, and the
Institute for Particle Astrophysics and Cosmology, the University of Washington.
Korean Scientist Group, the Chinese Academy of Sci-
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8 Mart´ınez-Delgado et al.
Fig. 1.— Density maps from SDSS of the North Galactic hemisphere. Position of our positive (solid triangles) and negative
(open circles) detection of the Virgo stellar over-density given in Table 1, overplotted on a Lambert projection of the density
map of Virgo given in Juri´c et al. (2005). This map was generated by selecting MS stars with b < 0deg, 0.2 < g−r < 0.3
and 20<r<21. Concentric circles correspond to constant galactic latitude (the North Galactic pole is in the center; and the
outermost circle correspond to b=0deg. The high density patch at l=45, b > 30 is the Milky Way disk protruding into the
survey region.
TABLE 1
Positive andnegativedetections ofVirgofromcolour-magnitudediagrams
RA(J2000) Dec(J2000) l b Detection
12:24:00.00 -1:00:00.0 288.62 61.11 Positive
12:24:00.00 -0:30:00.0 288.39 61.59 Positive
10:20:00.00 40:00:00.0 180.71 56.24 Negative
13:48:16.00 52:08:32.0 103.69 62.81 Negative
15:37:49.00 69:17:31.0 104.68 41.44 Negative
12:40:00.00 18:20:00.0 285.67 80.82 Negative
13:56:21.00 -27:10:04.0 320.28 33.51 Negative
13:07:53.00 29:21:00.0 65.42 85.75 Negative
10:49:22.00 51:03:04.0 158.57 56.78 Negative
14:07:37.00 11:50:28.0 356.10 66.48 Negative
16:11:05.00 14:57:29.0 28.76 42.18 Negative
14:44:27.00 -1:00:00.0 351.54 50.88 Negative
The origin of remnants in Virgo 9
Fig. 2.— Galactic X-Z projection of our N-body simulation of the Sgr tidal stream in a Milky Way dark matter halo with
qh =0.8. Forsimplicity,onlyparticlesunboundlessthan2.5Gyragohavebeenplotted. ItdisplaystheSgrleadingarmfalling
onto the Galactic disk, crossing the proximity of the Sun (yellow circle). The particles with a position consistent with that of
theVOD are marked with red colour.
10 Mart´ınez-Delgadoet al.
Fig. 3.—Density maps of the Sgr leading tail stars with heliocentric distance d<15kpc from our N-bodysimulation of theSgr
tidal stream in a Milky Way dark matter halo with qh =0.8 (top panel) andqh =1.4 (bottom panel).