Table Of ContentMon.Not.R.Astron.Soc.000,1–8(2009) Printed24January2012 (MNLATEXstylefilev2.2)
A Tale Twice Told: The Luminosity Profiles of the
Sagittarius Tails
M.Niederste-Ostholt1(cid:63), V. Belokurov1, N.W. Evans1
1Institute of Astronomy, Madingley Rd, Cambridge, CB3 0HA
2
1
0
2 May2011
n
a
J ABSTRACT
The Sagittarius dwarf galaxy is the archetype of a tidally disrupting system. Both
1
leading and trailing tails can be observed across at least 180 degrees of the sky and
2
measurements of their luminosity density profiles have recently become available. Us-
] ing numerical simulations, we explore the factors that control the appearance of such
A profiles.
G We use two possible models for the Sgr progenitor. The first is a one-component
Plummer model, which may represent either a dark matter free progenitor, or one in
.
h whichpre-existingdarkmatterhasalreadybeenlargelystripped.Thesecondisatwo-
p component model in which the stars are represented by a Hernquist sphere embedded
-
in a cosmologically modish Navarro-Frenk-White dark halo. Disruption of the models
o
r in the Milky Way galaxy provides us with two tellings of the tale of the formation of
t the Sgr stream. The initial disintegration of the baryons proceeds more slowly for the
s
a two-componentmodelsbecauseoftheprotectivecocoonofdarkmatter.Oncethishas
[ been stripped, though, matters proceed apace. In both cases, the profiles after ∼ 6
pericentric passages provide good matches to the observational data, but the tails are
1
more extended for the two-component models.
v
6 The leading and trailing tails are symmetric at apocentre or pericentre. At other
1 orbital phases, asymmetries are present, as tails are compressed as they approach
5 apocentre and stretched out as they approach pericentre. There may exist density
4 enhancements corresponding to such pile-ups which may be observable in current
. survey data. We re-visit the calculation of Niederste-Ostholt et al. (2010) and slightly
1
0 revise upwards the luminosity of the Sgr progenitor to 9.9−14.4×107L(cid:12) based on
2 insights from the simulations.
1
Key words: galaxies: dwarf galaxies – galaxies: individual (Sagittarius) – galaxies:
:
v simulations
i
X
r
a
1 INTRODUCTION tion,perhapsasmuchasaquarter,oftheentirestellarhalo
of the Milky Way by luminosity (using numbers from Bell
ThispaperprovidestwotellingsofthetaleoftheSagittarius
et al. (2008) or Deason et al. (2011) and Niederste-Ostholt
(Sgr) galaxy.
et al. (2010)).
Eversinceitsdiscovery(Ibataetal.1995),theSgrdwarf
has been recognised as a touchstone of Galactic astronomy. Given its fundamental role, the disruption of the Sgr
It provides an ongoing example of the merging and accre- dwarf and the formation of its tidal tails has been a popu-
tion of galaxies, one of the fundamental processes through lartopicfordetailednumericalinvestigations.Motivatedby
which structure is built in the Universe. It provides one of theproximityoftheremnanttotheGalacticcentre,simula-
thebestmeasuresoftheGalacticpotentialandmass,asits tions as to the effect of Milky Way tides on Sgr began soon
tidal debris can be traced to distances of possibly ∼90 kpc after its discovery (Johnston et al. 1995). The aims of sub-
(Newberg et al. 2003; Belokurov et al. 2006; Koposov et al. sequent simulations are largely threefold. First, some inves-
2011).ThedisruptionofSgrandthespillingofitsstarsand tigators concentrated on understanding the Sgr progenitor
globular clusters into the Galaxy provides a sizeable frac- (e.g. Velazquez & White 1995; Ibata & Lewis 1998; Lokas
etal.2010).TheworkofJiang&Binney(2000)nicelysum-
marizes the degeneracy in the properties of the progenitor,
(cid:63) E-mail:mno,vasily,[email protected] with the then available data being compatible with a very
(cid:13)c 2009RAS
2 M. Niederste-Ostholt et al.
broadrangeofmassesandorbitalhistories.Secondly,there characteristic lengthscale and mass for the baryonic com-
is a body of work that has studied what can be inferred ponent. Their initial mean velocity dispersions are different
about the structure of the Milky Way, particularly its dark (namely ∼15 kms−1 and ∼19 kms−1), but they both have
halo. This though has not led to clear-cut conclusions on mean dispersions consistent with the observations (Ibata
theshapeofthedarkhalowhichhasbeenvariouslyclaimed et al. 1997) at the timestep corresponding to the present-
as spherical, oblate, prolate or triaxial (e.g. Helmi 2004a,b; day epoch (∼10 kms−1 and ∼11 kms−1 respectively).
Johnston et al. 2005; Fellhauer et al. 2006; Law & Majew- The size and mass of Sgr prior to disruption can only
ski 2010). Thirdly, some investigators have been concerned beestimated.However,basedontheluminositydetermined
primarily with the properties of the debris itself, particu- in Niederste-Ostholt et al. (2010), a mass of at least 108
larly as positions, kinematics and metallicities of presumed M for the baryonic component is justifiable. Although we
(cid:12)
streammembershavegraduallybecomeavailablefromwide will consider the effects of the satellite mass and size on
area surveys like 2MASS and SDSS (e.g. Johnston 1998; theshapeoftheluminosityprofiles,ourbenchmarkoneand
Mart´ınez-Delgado et al. 2004; Law et al. 2005; Law & Ma- two-componentmodelshaveabaryonicmassof6.4×108M
(cid:12)
jewski 2010). andacharacteristicradiusr =850pc(c.f.Law&Majewski
c
Recently, Niederste-Ostholt et al. (2010) have used the 2010).
extant2MASSandSDSSsurveydatatoproduceluminosity The evolution of the satellite as it tidally disrupts is
density profiles of both the leading and trailing tails. By followed by looking at snap-shots of the particle distribu-
extrapolating the observed profiles both near the core and tion at various locations along the orbit. The disruption is
along the orbit, the luminosity of the undisrupted system simulated with the particle-mesh code SuperBox (Fellhauer
canbedetermined.Theseprofileshavenotyetbeenexplored etal.2000).Forone-componentmodels,itusesthreenested
bysimulations.Inthiscontribution,weprovidewiththeaid grids of 643 cells each centred on the highest density region
ofN-bodymodelstwore-tellingsofthetaleoftheSgrgalaxy. of the satellite galaxy. The inner high-resolution grid cov-
Weareinterestedinconstrainingthedarkmattercontentof ersthecentralregionofthesatellitewiththegridspanning
the progenitor, as well as understanding what controls the 2×r . The medium resolution grid covers the entire satel-
c
appearance of the tail luminosity profiles. lite (10×r ). The low resolution grid covers 65×R ,
c cutoff
Section 2 is primarily technical and gives details of the where R = 5r is the artificial cut-off radius imposed
cutoff c
set-up of the simulations together with the analyses per- on the initial distribution of the dwarf galaxy. The simula-
formed on the output. Section 3 provides the first telling of tionstepsforwardwithaconstanttime-stepsizeof∆t=1.3
thetalewithsimulationsinwhichthedarkmattershadows Myr,whichleadstoatotalenergyconservationbetterthan
the light in the progenitor. Section 4 provides the second 1% when the satellite is evolved in isolation for ∼ 10 Gyr.
telling of the tale with dark matter dominated progenitors. Forthetwo-componentmodels,therearetwosetsofgrids–
Finally, we draw our conclusions in Section 5. thefirstcoveringthebaryonsandthesecondthedarkmat-
ter particles. The sizes are set up relative to the baryonic
characteristic scale r and the NFW scale radius r in an
c s
analogous way to the one-component models.
2 SET-UP AND ASSUMPTIONS
Theorbithasinitialconditions(x,y,z)=(0,0,55)kpc
An N-body satellite is placed on an orbit in a static Milky and (u,v,w)=(90,0,0) kms−1 which result in a pericentre
Way-likepotentialconsistingofaMiyamoto&Nagai(1975) of ≈ 15 kpc and an apocentre ≈ 55 kpc in line with ob-
disc (M = 7.5×1010M , radial scale length = 3.5 kpc, servations of Sgr (e.g. Ibata & Lewis 1998; Johnston et al.
d (cid:12)
vertical scale length= 0.3 kpc), a Hernquist (1990) bulge 1999a;Ibataetal.2001;Lawetal.2005).Radialandtrans-
(M = 1.3 × 1010M , scale radius = 1.2 kpc), and a verse velocity measurements of the main body of Sgr, as
b (cid:12)
sphericallysymmetriclogarithmichalo(circularvelocity186 well as 2MASS observations of the trailing arm, indicate
kms−1,scalesize12kpc).Similarpotentialshavebeenused that the Sgr dwarf is currently located close to pericentre.
before (seee.g.Johnstonetal.1999b;Lawetal.2005;Fell- The orbital period is approximately 0.7 Gyr. During each
hauer et al. 2006). period, eight snapshots are taken in equally spaced time-
We explore two possibilities for the progenitor Sgr. In steps, chosen so that one snap-shot is at apocentre and one
the first telling of the tale, the satellite is represented by a at pericentre. The orbit lies in the plane perpendicular to
Plummersphereofcharacteristiclengthscaler composedof thegalacticdisk,whichmakesthesubsequentanalysiscon-
c
106 particles.Thissinglecomponentapproachfollowsmany siderably more straightforward. Observations of Sgr debris
previouspapers,includingLaw&Majewski(2010)whoare support the notion that the material torn from the satel-
able to reproduce a wide array of observations. This mass- lite is confined to a plane (Majewski et al. 2003), with an
follows-lightmodelcanbeinterpretedasrepresentingeither orbital pole at ((cid:96),b)=(273.8◦,−13.5◦) i.e. only slightly in-
a situation in which all dark matter has been stripped be- clinedfromtheplaneusedinthisanalysis.Ouraimisnotto
forethebaryonsbeginsignificantdisruption,orinwhichthe reproduceexactlytheorbitoftheSgrgalaxy,buttoobtain
satellite had little dark matter to begin with. In the second systemscloseenoughsoastoexploretheluminosityprofiles
telling, the Sgr galaxy is embedded in a dark matter halo. of the tails.
Specifically, we use a two-component model consisting of Particles are defined as bound, or unbound, depend-
baryons distributed in a Hernquist sphere of lengthscale r ing on whether their kinetic energy exceeds, or not, the
c
embedded in an Navarro-Frenk-White (NFW) dark matter satellite’sinternalpotentialenergydeterminedbySuperBox.
halo with lengthscale r (c.f. Fellhauer et al. 2007). In both Leading and trailing arm particles are then selected based
s
tellings,themodelsarereleasedinthesameMilkyWaypo- on their orbital energies relative to the orbit of the centre
tentialwiththesameinitialconditions.Theyhavethesame of mass. In the inner regions of the satellite, approximately
(cid:13)c 2009RAS,MNRAS000,1–8
A Tale Twice Told: The Luminosity Profiles of the Sagittarius Tails 3
Figure 1.Snapshotsandprofilesofatypicalsimulationlookingface-onintotheorbitalplane.ThesatellitehasaPlummerradius350
pc and mass 108M(cid:12). The plots run forward in time from left to right and top to bottom. The dot shows the Galactic centre, which is
centreoftheCartesianaxes(X,Z)withZ=0definingtheGalacticplane.Theprofilesrepresentthenumberdensityofparticlesalong
the stream with the leading arm in red and the trailing arm in blue. The early evolution of the satellite and its accompanying profiles
areshowninthetoptworows.Theleadingandtrailingtailsbeginformingsymmetricallyandtheprofileslieontopofeachother.The
bottomtworowsshowthelaterevolutionofthesatellite.Asymmetriesbegintooccurasthetailsfillappreciableportionsoftheorbital
path,betweenapocentreandpericentre.Overdensitiesoccurasstarsslowdownnearapocentreandthetailiscompressed,whereaslower
density areas occur the the tail is approaching pericentre and is stretched out. The profiles remain symmetric when Sgr is observed at
either apocentre or pericentre. Asymmetries between the leading and trailing arms appear when Sgr is at intermediate positions along
itsorbit.
one half of the bound particles are assigned to the leading Inaddition,werequirethattheone-componentprogen-
arm and one half to the trailing arm. The profiles are con- itor has lost ∼ 60% of its mass, as suggested in Niederste-
structed in a fashion analogous to that used in Niederste- Ostholt et al. (2010), which allows us to identify the ap-
Ostholt et al. (2010) counting stars from a given arm in propriate pericentric passage (the sixth) to match to the
angularbinscovering1.2◦ onthesky.Thebinsizeischosen present-day data. The timescale over which the disruption
to have sufficient resolution along the tails whilst avoiding isfollowedis4.1Gyrs.Thetwo-componentmodelisallowed
significant bin-to-bin variations. The counts are normalised to evolve through the same number of pericentric passages,
by the length along the stream that is covered by a given andloses∼70%ofitsmassalongtheway.Asitevolvesonto
bin and corrected for the angle that the stream makes with a tighter orbit, the time to the sixth pericentric passage is
the radial direction at that location. slightly shorter at 3.6 Gyrs.
(cid:13)c 2009RAS,MNRAS000,1–8
4 M. Niederste-Ostholt et al.
(a) (b)
Figure 2. (a): Leading (red) and trailing (blue) arm profiles after 4.15 Gyr for the satellite used by Law & Majewski (2010) with
(M,rc)=6.4×108M(cid:12),850pc.Thesnapshotistakenafterpassingpericentreandthesatellitehaslost∼60%ofitsstars.Theagreement
betweenthesimulatedprofiles(fulllines)andobservations(dashedlines)isgoodthoughthetrailingarmappearsslightlyworsethanthe
leadingarmduetothelog-scale).Theshort-dashdottedlineshowstheextrapolationusedinNiederste-Ostholtetal.(2010).Thelong-
dashdottedlineshowsanextrapolationbasedonthesimulatedprofile,leavingouttheadditionalbumpintheprofile.Niederste-Ostholt
etal.(2010)mayhaveunderestimatedtheamountoflightnotseenintheleadingarmbyasmuchas 80%,thoughthisdoesnotchange
theluminosityrangeproposedfortheprogenitorSgrsincetheextrapolationaccountsforonlyaminorfractionofthetotalluminosity.
(b):Varyingthesizeofprogenitorresultsinapoorermatchwiththeobservations,aschangingthedensityoftheprogenitorinfluences
how quickly stars disperse along the orbit. The left-hand column shows the mass-loss history of a satellite with rc = 950 pc (top) and
800pc(bottom),bothwithmass6.4×108 M(cid:12),comparedtothebenchmarksatellite.Therighthandcolumnshowsthecorresponding
densityprofileswhenthesatellitehaslost60%ofitsmass.Thebenchmarkmodelisinredorblue(leadingortrailing)whilstthelarger
andsmallerscalelengthmodelsareingrey.Therearenoticeabledifferencesinthedensitydistribution.
3 THE FIRST TELLING previous apocentre and are speeding up as they move to-
wardspericentre,andthushavealowerdensity.Thisiscon-
3.1 Luminosity Profiles of the Streams sistentwiththeobservedshapeoftheSgrluminositydensity
profile,wheretheleadingarmhasasignificantlyhigherden-
Figure 1 shows snap-shots from a typical disruption of the
sitythanthetrailingarm(seeFigure10ofNiederste-Ostholt
one-component model, as well as the corresponding density
et al. 2010).
profilealongthestream.Duringtheinitialphaseofthedis-
A progenitor with a different mass or size will, on a
ruption, leading and trailing arms look very similar and
given orbit, disrupt at a different rate and the resulting de-
their density profiles lie very nearly on top of each other.
bris will spread along the orbit with a different speed, de-
As the disruption proceeds and the progenitor and debris
pendingonitstidalradiusatpericentre,whichcontrolsthe
travel around the orbit, the leading and trailing arms de-
scale over which the satellite loses mass (Johnston et al.
velop differently, having different lengths and densities in a
2001). At fixed r (and in an identical host Galactic poten-
given snap shot. c
tial), a more massive progenitor loses mass more slowly, as
The apocentric distances of the leading and trailing
it is more tightly bound. However, the unbound particles
arm debris are approximately 44 kpc and 80 kpc respec-
disperse along the orbit quicker, allowing the tails to grow
tively. These differences can be attributed to the different
longer, due to the larger spread in energies in the unbound
speeds with which unbound particles travel at various loca-
particles.Theslowermass-lossandquickerdispersionresult
tions along the orbit (see e.g. Dehnen et al. 2004; Ku¨pper
in a lower density.
etal.2010)andtheoffsetinenergybetweentheleadingand
trailingarmsrelativetotheorbitofthecentreofmass.Ona If identical one-component satellites are placed on dif-
givenorbit,particlesclosetopericentretravelfastestresult- ferent orbits with the same pericenter, then the debris
ing in lower densities and more stretched out tidal streams. spreads out over larger distances before reaching orbital
By contrast, particles spend more time near apocentre and turning points if the apocentre is larger. So, more eccen-
thetailsappearcompressedandhavehigherdensities.This tric orbits generally have a lower density, since the debris
canbeseen,forexample,inthesnapshotsat3.51Gyrwhich spreads out over a longer orbital path before being com-
are taken when the main body of the progenitor has just pressed at apocentre.
passeditsorbitalpericentre(at3.32Gyr).Theleadingarm Figure2acomparestheobservedprofiles(dashedlines)
is approaching the next apocentre and is compressed. The tothesimulatedprofilesproducedbydisruptingoftheLaw
trailing arm particles on the other hand have just left the & Majewski (2010) Plummer sphere. The number of parti-
(cid:13)c 2009RAS,MNRAS000,1–8
A Tale Twice Told: The Luminosity Profiles of the Sagittarius Tails 5
(a) (b)
Figure3.Acomparisonbetweenthedisruptionoftheoneandtwo-componentmodels(a)forthefirst0.8Gyrsand(b)atlatetimes.The
plotsrunforwardintimefromlefttorightandtoptobottom.Inbothpanels,theleft-handcolumnshowstheone-componentPlummer
sphere disrupting in a Milky Way potential. The middle column shows the baryonic component of the two-component model, whilst
the right-hand column shows the evolution of the dark matter component. The extended dark matter begins disrupting immediately.
Compared to the one-component model, the baryons in the two-component model at first disrupt more slowly. This results in lower
density,longertails—compare,forexample,thebaryonicmaterialinthetwocomponentmodelwiththeone-componentmodelat082
Gyr.However,onceasignificantfractionoftheprotectingdarkmatterisremoved,thebaryonicdisruptionaccelerates.
cles is converted to luminosities by assuming M/L = 3.2. tre. There is a pile-up in the trailing arm, stemming from
This implies that the progenitor’s total luminosity is ≈ particles at the previous apocentre.
2×108L , which is at the higher end of the range deter- The time taken to populate the stream (∼4 Gyr) is in
(cid:12)
mined by Niederste-Ostholt et al. (2010). The behaviour of reasonable agreement with other predictions of the age of
the observed leading and trailing arms is well reproduced the debris (Law et al. 2005; Law & Majewski 2010). This
by the simulations. Figure 2b shows, progenitors with the is not surprising, since the satellite and potential are essen-
same total mass, but with different sizes (800 pc < r < tially the same as that of the Law et al. simulations. The
c
950 pc), yield profiles that are different from our best-fit simulationsofLokasetal.(2010)findasignificantlyshorter
model. Consequently, there is significant disagreement with disruptiontimeat1.25Gyr.Thisdifferencelikelyarisesbe-
the observed profiles. causetheyfocusonreproducingthepropertiesofthecoreof
Theleadingandtrailingarmshaveverynearlythesame theprogenitorratherthanthetidalstreams.Astheauthors
number of particles throughout the simulations. According highlight,theshorterinteractiontimescaleisnotnecessarily
toChoietal.(2007),theself-gravityofthedisruptingsatel- inconflictwiththelongerinteractiontimesrequiredtoform
litecanleadtoasymmetriesintheamountofmaterialinthe the tidal tails, but rather suggests that the length of time
leading and trailing arms. However, our Sgr models are at overwhichtheSgrcorehasbeentidallystirredisrelatively
the low-mass end of the satellites considered by Choi et al. short.
(2007) and hence are unlikely to display much asymmetry
betweentheleadingandtrailingarms.Weconcludethatcal-
3.2 The Assumptions of Niederste-Ostholt
culatingthetotalluminosityofSgrprogenitorbasedonmea-
suringtheluminosityofonetailonly(asdoneinNiederste- Niederste-Ostholt et al. (2010) reassembled the stars in the
Ostholt et al. 2010) does not introduce substantial error. Sgrremnantandtidalstreamstoestimatetheluminosityof
The observed asymmetry in density between the lead- theSgrprogenitor.Theyfoundthattheluminosityisinthe
ing and trailing arms can be attributed to the phase of the range(9.6-13.2)×107L(cid:32) orM −15.1to-15.5,makingthe
(cid:12) V
orbit at the time of observation. Shortly after pericentre, Sgr progenitor comparable to, but somewhat less luminous
part of the leading arm is compressed as it approaches the than, the present-day Small Magellanic Cloud.
next orbital apocentre. The trailing arm on the other hand However, Niederste-Ostholt et al. (2010) made several
isstretchedoutasitsparticlesarestillapproachingpericen- assumptions, particularly at locations where stream data
(cid:13)c 2009RAS,MNRAS000,1–8
6 M. Niederste-Ostholt et al.
was sparse or unavailable. These assumptions can now be
tested using the N-body models. They include: (i) the be-
haviouroftheleadingarmnearthecorewhereitisobscured
bytheGalacticdisc;(ii)theextrapolationoftheleadingarm
beyond where it is observed in the SDSS data; and (iii) the
rising density of the trailing arm after an initial drop re-
sulting from the assumed metallicity gradient between the
coreandtails.Inthissection,wecommentoneachofthese
assumptions based on our simulations.
An important open question that remained in the ob-
served profile of Sgr is the behaviour of the leading arm
in the region where it is obscured by the Milky Way disk.
This is the region at a distance along the stream less than
≈20kpcinFigure2awheretheobservationsoftheleading
arm(reddashedline)end.Fromthesesimulations,itseems
much more likely that the leading arm profile of Sgr dips
down and joins the trailing arm profile near its minimum,
rather than a continuing exponential rise suggested by the
limited observations. This is borne out in other progenitor
models (175 pc < r < 700 pc, 107 < M < 109 M ) and
c (cid:12)
other orbits with pericentre at 15 kpc but apocentric dis-
tances between 35-100 kpc. Based on the drop in density
and the obscuring influence of the Galactic disk, it will be
challenging to detect this portion of the leading arm. Figure 4.Theluminosityprofilesoftheleading(red)andtrail-
In Figure 2a, the leading arm follows an exponential ing (blue) tails for the one-component (solid lines) and two-
component (dashed lines) models after (a) the second pericen-
decay save for another bump in the profile occurring at the
tricpassage,(b)thefourthpericentricpassage,and(c)thesixth
apocentreanorbitaheadofthecurrentlocation.Ifwelook
pericentric passage. It is noticeable that at early times the two-
only at the extrapolated portion of the tail (distance >100
componentmodelissomewhatlessdensethantheone-component
kpc),thenincludingthebumpincreasestheamountoflight
model, but has a much more extended central region and sig-
by 70% over the exponential extrapolation. However, since nificantly longer tidal tails. After four pericentric passages, the
theextrapolatedportionoftheprofilecontainsrelativelylit- densities are already very similar, though the two-component
tlelight,thetotalluminosityinthetailchangesonlyby 5% modelhaslongertails.Finally,aftersixpericentricpassageseven
whenintegratingtheextrapolatedprofileversusintegrating the density in the central region of the two-component satellite
the actual profile, indicating that ignoring the additional matches that of the one-component model closely. Slight differ-
bumphasonlyasmalleffect.Theamountoflightintheex- encesremainalongtheprofileresultingfromthedebrisspreading
fartheralongtheorbit.
trapolated portion of the tail is much more sensitive to the
slopechosen.Theexponentialdeclineoftheleadingarmas-
sumed in the determination of the total luminosity of Sgr
peakindensityofthetrailingarmfollowedbyadropwould
may have been too steep. Employing a shallower extrapo-
support this view.
lation of the leading arm profile increases the total amount
Considering the insights gained from the simulations
of light in the extrapolated portion of the leading arm by
concerningthelightintheleadingarmfartherthan100kpc
as much as ∼ 80%. Including a correction for the bump at
alongthestreamaswellasthebehaviouroftheleadingarm
∼150 kpc along the stream adds another ∼25%.
in the region obscured by the Galactic disk, we can update
Concerning the trailing arm, Majewski et al. (2003) the luminosity range for the Sgr system from 9.6−13.2×
foundtheirdensityprofilebasedon2MASSM-Giantstobe 107L to 9.9−14.4×107L .
(cid:12) (cid:12)
flat. By contrast, Niederste-Ostholt et al. (2010) found the Withintheuncertaintiesinherentinthisapproach,the
trailingarmoftheSgrstreamhasapositiveslopeduetothe luminosity range for Sgr has changed only slightly and
population differences between the satellites core and tails the overwhelming factor controlling the spread remains the
reflectedinthechangingratioofthenumberofMgiantsto luminosity function assumed for Sgr and its debris (see
totalluminosity.Thispopulationdifferenceindicatesapos- Niederste-Ostholt et al. 2010, Figure 4.6).
sible metallicity or age gradient between different regions
of the undisrupted dwarf. The existence of such a gradient
is already observed by Chou et al. (2007) who find a mean
4 THE SECOND TELLING
metallicitydifferenceof∼0.6dexin[Fe/H]betweenthecore
andthestream.Thefactthatthesimulationsreproducethis Dwarf galaxies show ample evidence of being dark matter
behavior suggests that the proposed population gradient is dominated. So far our models have ignored the possibility
infactanacceptableapproximation.However,wealsoneed thatthestarsvisible fromtheSgrgalaxywereinitiallyem-
toconsiderthatthedensityofthetrailingarmisincreasing bedded in a dark matter halo. This motivates our second
when moving away from the core due to the pile-up of par- telling of the tale of the Sgr galaxy.
ticles at the previous apocentre in the orbit, towards which Using the code employed in Fellhauer et al. (2007), we
the end of the trailing arm is reaching. The discovery of a generateatwo-componentgalaxyconsistingofbaryonsdis-
(cid:13)c 2009RAS,MNRAS000,1–8
A Tale Twice Told: The Luminosity Profiles of the Sagittarius Tails 7
tributed in a Hernquist sphere embedded in an NFW dark componentmodelthantheone-component,(thoughneither
matter halo. The two-component model is released in the model is as flatted as the actual Sgr remnant). The ratio of
Milky Way potential with the same initial conditions as initialtofinalbaryonicmasswithina5kpcapertureis0.43
the one-component model and luminosity profiles for the fortheone-componentcaseand0.29forthetwocomponent.
baryons are produced in the same fashion. This shows that more of the baryonic material is removed
Specifically, the stellar distribution is represented by a fromtheimmediatevicinityoftheSgrremnantinthelatter
Hernquist sphere of 106 particles. It has a mass of 6.4× case.
108M(cid:12) and a scale radius of 850 pc, thus closely matching
thePlummermodelemployedabove.TheNFWhaloisrep-
resented by 5×105 particles with a scale radius of 3.5 kpc 5 DISCUSSION AND CONCLUSIONS
and a virial radius of 52.5 kpc. This concentration (c≈15)
We have used the particle mesh-code SuperBox to disrupt
results in the baryonic component having a starting mean
velocity dispersion of ∼ 19 kms−1. This is larger than the modelsoftheSagittariussatelliteinaMilkyWaypotential.
Asprogenitors,weconstructedNbodyrepresentationswith
initial velocity dispersion of the one-component model. As
similar baryonic components, but with very different dark
the disruption takes place,the mean velocity dispersion de-
matter content. The one-component models mimic a situa-
clines to a value that lies within the observational bounds
tion in which any dark matter has been stripped from the
at the present epoch.
dwarfgalaxypriortothedisruptionofthebaryoniccompo-
Figure 3 shows the tidal evolution of the two model
nent,orinwhichthesatellitehadverylittledarkmatterin
satellites considered in this paper. The left-hand column
the beginning. The two-component models have a baryonic
shows the one-component Plummer model for comparison
componentembeddedwithinacosmologically-inspireddark
purposes.Themiddleandright-handcolumnsshowtheevo-
halo. Their disruption in the Milky Way potential provides
lutionofthetwo-componentmodel’sbaryonicanddarkmat-
two tellings of the tale of the formation of the Sgr galaxy
ter distributions respectively. Notice that the dark-matter
and its tidal streams.
NFW halo begins to disrupt immediately. The presence of
The stellar components are structurally indistinguish-
dark matter increases the baryons’ tidal radius. On the one
ableatoutset,havingsimilarcharacteristiclengthscalesand
hand, this initially inhibits the disruption of the baryonic
masses.Theyhavedifferentinitialmeanvelocitydispersions,
component, when compared to the evolution of the Plum-
but this ensures that the remnant’s final velocity disper-
mer model. However, the increased tidal radius translates
sion lies within the present-day observational constraints.
intoanincreasedenergyspreadinthedebris.Thisresultsin
Wehaveprovidedthefirstcomparisonsbetween simulation
thickertailsandstarsdispersingfasteralongtheorbitpop-
dataandtheobservedluminositydensityprofilesofthelead-
ulating the tails out to longer distances. The dark matter
ing and trailing Sgr tails constructed by Niederste-Ostholt
halo quickly becomes significantly disrupted (after ca. two
et al. (2010).
orbits) resulting in an accelerated rate of disruption of the
Our main conclusions are
baryonic component. This effect is increased by a slight or-
bitaldecayexperiencedbythetwo-componentsatelliteonce [1] The profiles of the tails can provide a strong constraint
the dark-matter disrupts (the pericentre shrinks from ≈15 on the dark matter content of the Sgr system, though this
kpc to ≈11 kpc). requires deeper data than is currently available. The two-
Theleadingandtrailingtailprofileshapesatthesnap- component model has longer tails than the one-component
shots taken after then second, fourth, and sixth pericen- model.Thisisbecausethetidalradiusandthestartingmean
tric passage are shown in Figure 4. The sixth passage cor- velocity dispersion of the baryonic component in the two-
responds to the one chosen above as a comparison to the componentmodelarelargerthanthatoftheone-component
observations with Sagittarius. In this case, the final pro- model. Stars diffuse slightly more quickly along the tails,
files of the two-component model look similar to those of whichasaconsequencearelongerandlessdense.Thelength
the one-component model, albeit longer. Since the agree- of the tails is an important discriminant. If we do observe
ment between the profiles is good near the satellite core, very long tails for Sgr, then a one component model would
the two-component and one-component models are almost need to be more massive to populate them to those dis-
indistinguishable based on the currently observed data. tances.Eventhoughthereissomefreedomtovarythe(stel-
Nonetheless,deeperdatacoulddistinguishbetweenthe lar)masstolightratiobyafactorof∼2fromourassumed
profiles.Thebaryonicmaterialinthetwo-componentmodel value of 3.2, we have verified by simulations that this does
startsoffwithahighermeanvelocitydispersionthantheone not permit the present data on the tail length and profiles
component-model (∼ 19 kms−1 as opposed to 15 kms−1), to be matched.
though both remnants have essentially the same mean ve-
[2] One-component models successfully reproduce the den-
locity dispersion at the end. This however means that the
sity of the tails with only a baryonic component. Two-
starsinthetailsproducedbythetwo-componentmodelare
component models produce similar results within 180◦ of
moving on average somewhat faster and so the tails grow
the remnant. Although the addition of a dark matter halo
longer over the disruption timescale. At the present orbital
does initial protect the baryons from disruption, once the
phase, this is especially the case for the trailing arm. One
dark matter halo has been removed, the profiles develop in
possiblediscriminantbetweenthemodelsmightbetosearch
asimilarfashion.Withthepresentdata,itisnotpossibleto
for this extended trailing tail using giant stars or blue hori-
distinguish between one and two-component models based
zontal branch stars.
on fitting the profiles.
There are also differences in the properties of the rem-
nant, which is more compact and rounder in the two- [3] The simulations support the idea that the amount of
(cid:13)c 2009RAS,MNRAS000,1–8
8 M. Niederste-Ostholt et al.
light in the leading and trailing arms is nearly identical. Chou M.-Y., Majewski S. R., Cunha K., et al., 2007, The
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tween the leading and trailing arms observed in Sgr is the Deason A. J., Belokurov V., Evans N. W., 2011, MNRAS,
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the next orbital apocentre. The trailing arm on the other 2004, The Astronomical Journal, 127, 2753
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FellhauerM.,KroupaP.,BaumgardtH.,etal.,2000,New
[4] The simulations have strengthened a number of the as-
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sumptions made by Niederste-Ostholt et al. (2010) in de-
HelmiA.,2004a,MonthlyNoticesoftheRoyalAstronom-
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ical Society, 351, 2, 643
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Helmi A., 2004b, The Astrophysical Journal, 610, L97
gion where it is obscured by the Galactic disk, dips down
Hernquist L., 1990, Astrophysical Journal, 356, 359
to become symmetric with the trailing arm. Furthermore,
IbataR.,LewisG.F.,IrwinM.,TottenE.,QuinnT.,2001,
the extrapolation of the leading arm’s profile proposed in
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ACKNOWLEDGMENTS
Law D. R., Majewski S. R., 2010, ApJ, 714, 229
Wethankthereferee,DavidLaw,foracarefulreadingofthe Lokas E. L., Kazantzidis S., Majewski S. R., Law D. R.,
paperandvaluablecomments.MNOthankstheGatesCam- Mayer L., Frinchaboy P. M., 2010, arXiv, astro-ph.CO
bridge Trust, the Isaac Newton Studentship fund and the Majewski S. R., Skrutskie M. F., Weinberg M. D., Os-
Science and Technology Facilities Council (STFC), whilst theimerJ.C.,2003,TheAstrophysicalJournal,599,1082
VB acknowledges financial support from the Royal Society. Mart´ınez-DelgadoD.,Go´mez-FlechosoM.A´.,AparicioA.,
Carrera R., 2004, The Astrophysical Journal, 601, 242
Miyamoto M., Nagai R., 1975, PASJ, 27, 533
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