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Modelling the Ultra-Faint Dwarf Galaxies and Tidal Streams of the Milky Way
M. FellhauerUniversidad de Concepcion
in collaboration with
N.W. Evans1, V. Belokurov1, D.B. Zucker1,
M.I. Wilkinson2, G. Gilmore1, M. Irwin1
1Institute of Astronomy; 2Univ. Leicester
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Ladies and gentleman
SDSS Proudly presents:
The ‘Field of Streams’
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The SDSS survey60 million stars are catalogued in SDSS in 5 colours
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All stars of the Milky Way in SDSS:
And then we apply a simple colour-cutAnd are left with only the halo stars…
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“Field of Streams”Belokurov et al. 2006
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A gallery of SDSS dwarfs
D = 220 kpcrh = 550 pcMV = -7.9
D = 60 kpcrh = 220 pcMV = -5.8
D = 150 kpcrh = 140 pcMV = -4.8
D = 44 kpcrh = 70 pcMV = -3.7
CVn I Boo CVn II Com
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Some Implications• Numbers: 10 new MW dwarfs (including UMa I, Leo V &
Boo II) have been found to date, in SDSS data covering ~20% of the sky tens more likely remain undiscovered
• Properties: Ultra-low luminosities (-3.8 ≥ MV ≥ -7.9) and surface brightnesses (µV < 27 mag arcsec-2), odd morphologies are these truly dwarf galaxies or fuzzy star clusters? Are these a distinct class of object?
Hobbit Galaxies?
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MV vs. Log(rh) Mind the Gap?
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But there is even more:
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Leo T: A New Type of Dwarf?
• MV ~ -7.1, • µV~ 26.9 mag
arcsec-2
• (m - M)0 ~ 23.1, ~420 kpc
• Recent < 1 Gyr star formation --blue loop/MS stars
SDSS data
INT DataIrwin et al. 2007
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The Smallest Star-Forming Galaxy?
• Not dead yet: stars formed within past few x 108 yr
• HIPASS: Coincident H I • RV ~ 35 km/s• if @ 450 kpc, ~ 2 105
M in H I (MH I/M ~ 1, cf. Local Group dIrrs)
• Is Leo T the tip of a Local Group “free floating” iceberg? HIPASS
HI
3
°
INT g,rRyan-Weber et al. 2007
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But now to some modelling…
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Ursa Major II and the Orphan Stream
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Complex A
UMa II
Gal
. la
titud
e
Ursa Major II
Gal. longitude
Orphan Stream
MV = -3.8 ± 0.6 mag (approx. 6000 Msun)
~6.7 km/s
Mass estimate: 8 x 104 Msun
Zucker et al. 2006
Belokurov et al. 2007
Muñoz et al. 2007
Martin et al. 2007
Simon & Geha 2007
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Finding an orbit which connects UMa II with the
Orphan Stream
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Galactic Model: analytic potential for the MW
• Logarithmic Halo:– v0 = 186 km/s– Rg = 12 kpc– q = 1
• Miamoto-Nagai Disc:– Md = 1011 Msun
– b = 6.5 kpc, c = 0.26 kpc
• Hernquist Bulge:– Mb = 3.4x1010 Msun
– a = 0.7 kpc
€
h =1
2v0
2 ln(R2 +z2
qΦ2
+ Rg2)
€
d =GMd
R2 + (b+ z2 + c 2 )2
€
b =GMb
r + a
Insert UMa II as a point mass and look for matching orbits
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Possible Orbit:connecting UMa II & Orphan Stream
• UMa II:– RA: 132.8 deg.– DEC: +63.1 deg.
– Dsun: 30 ± 5 kpc
• Prediction for this orbit:– vhelio: -100 km/s
: -0.33 mas/yr
: -0.51 mas/yr
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Observational Data (to date)
• UMa II:– vhelio = -115 ± 5 km/s
(agrees well enough with our prediction)
los = 7.4 +4.5-2.8 km/s
• Orphan Stream:– Position known over 40 deg.– Distances between 20 (low DEC) and 32
kpc (high DEC)
– vhelio = -35 km/s (low DEC); +105 km/s (high DEC)
Martin et al. 2007
Belokurov et al. 2007
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Constraining the progenitorof UMa II and the Orphan Stream
Initial model for UMa II:
use simple Plummer spheres to constrain parameter space in initial mass & scale-length
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Constraining the Progenitor: I. Length of the Tails
Tails as function of progenitor mass and simulation timeProgenitor must be>105 Msun & <107 Msun
Simulation time must be longer than 7.5 Gyr
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Constraining the Progenitor:II. Morphology of UMa II
• Progenitors with more than 105 Msun
must be almost destroyed to account for the patchy structure, the low mass of the remnant and the high velocity dispersion of UMa II
• Progenitors with more than 106 Msun do not get sufficiently disrupted to account for the substructure
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Comparing 2 UMa II models:
One component model• Plummer sphere:
– Rpl = 80 pc
– Mpl = 4 x 105 Msun
Two component model• Hernquist sphere:
– Rh = 200 pc
– Mh = 5 x 105 Msun
• NFW halo:
– RNFW = 200 pc
– MNFW = 5 x 106 Msun
inserted at the position of UMa II 10 Gyr ago
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Orphan stream UMa II
1-comp. 1-comp.2-comp. 2-comp.
Comparison of the 2 models - Reproduction of Orphan Stream &
UMa II
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Comparing the appearance & the kinematics of the two models:
One component (B)
Before(A), while (B)& after dissolution [c]
Two component (D)
A
B
C
D
Patchy structure (B) vs. round, bound, sound & massive (D)
Both models show high velocity dispersion
Mean vrad is patchy with gradient (B) vs. constant within object (D)
A: before dissolution is low and vrad constant
B: patchy structure, high , patchy vrad
with gradient
C: no density enhancement, low ,gradient in vrad
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Conclusions:
• It is possible that UMa II is the progenitor of the Orphan Stream
• If UMa II is a massive star cluster or a dark matter dominated dwarf galaxy ?Decide for yourself…
or wait for better data.
But then we have some predictions:
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If better data will be available:• Predictions from our models:
– At the Orphan Stream: if the progenitor was more massive than 106 Msolar than we should see the wrap around of the leading arm at the same position but at different distances & velocities
– At UMa II: if the satellite is DM dominated the contours should become smoother; if UMa II is the progenitor of the Orphan Stream the satellite is not well embedded in its DM halo anymore (otherwise there would be no tidal tails)
– A disrupting star cluster will show a patchy structure in the mean line-of-sight velocities with a gradient through the object; a DM dominated bound satellite will have a constant vrad within the object
Latest News:
Simon & Geha (2007):
Seem to confirm gradient in radial velocity
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New unpublished data searching for tidal tails around UMa IIshow no sign of tidal tails -
Solution:a) Connection between UMa II
and the Orphan Stream does not exist
b) Tails are still to faint to detect
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Bootes
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The Boötes Dwarf Galaxy
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= 14h 00m 06s , = +14o 30’ 00”
•m-M = 18.9 mag Dsun = 62 ± 3 kpc
•MV = -5.8 mag (M/L=2) M ≈ 37,000 Msun
0 = 28 mag/arcsec2
•Rpl = 13’ (230 pc)
•vrad,sun=+95.6 ± 3.4km/s 6.6 ± 2.3km/s•[Fe/H] = -2.5
•vrad,sun=+99.9 ± 2.1km/s 6.5 ± 2.0 km/s
•[Fe/H] = -2.1
Boötes: Observational Facts
Belokurov et al. 2006
Munoz et al. 2006
Martin et al. 2007
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The Contours or what is real ?
Is there an S-shape in the contours, i.e. is Boo tidally disturbed ?
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Some simple maths…
rtidal =Msat
3MMW
⎛
⎝⎜⎞
⎠⎟
13
DGC
•rtidal = 250 pc (0.2o)•DGC = 60 kpc•MMW(DGC) = 6 x 1011 Msun
Msat = 70,000 Msun agrees with luminous matter
los,0 = 2.52 ×M sat 107M sun⎡⎣ ⎤⎦Rpl kpc[ ]
km / s•Rpl = 200 pc
los,0 = 0.5 km/s ???
• los,0 = 7 km/s, Msat = 70,000 Msun Rpl = 20 pc Boo too bright in the centre (20 mag/arcsec2) NO
BUT:
• los,0 = 7 km/s, Rpl = 200 pc Msat = 1.5 x 107 Msun
Boo heavily dark matter dominated, rtidal = 1.2 kpc (1o)
or Boo is elongated along the line of sight ???
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Finding an Orbit
• We assume the orbital path from the on-set of the possible tails: Rperi Rapo e
(1) -0.53 -0.62 1.8 66.2 0.95
(2) -0.54 -0.70 4.7 66.2 0.87
(3) -0.58 -0.90 14.8 67.2 0.64
(4) -0.63 -1.20 36.9 76.6 0.35
(5) -0.66 -1.40 48.8 104.3 0.36
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Model A (TDG)
M/L = 17 (unbound stars)
Assuming a non-extreme orbit (e=0.35, Rperi=37kpc, Rapo=77kpc)
Plummer Sphere:
Rpl = 202 pc ; Rcut = 500 pc
M = 8.0 x 105 Msun
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Model B (mass follows light)M/L = 620 (DM dominated) (keeping the same orbit)
Plummer Sphere:
Rpl = 200 pc ; Rcut = 2000 pc
M = 1.6 x 107 Msun
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Model C (small DM halo)M/L0 = 550 (<M/L> =1800)
Stars: Hernquist Sphere
Rsc = 300 pc ; Rcut = 300 pc
M = 3.0 x 104 Msun
DM: NFW-Profile
Rsc = 300 pc ; Rcut = 1200 pc
M = 4.5 x 107 Msun
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Model D(extended DM halo)M/L0=800 (<M/L>=3400)Stars: Hernquist Sphere
Rsc = 250 pc ; Rcut = 500 pc
M = 4.0 x 104 Msun
DM: NFW-Profile
Rsc = 1000 pc ; Rcut = 2500 pc
M = 3.0 x 108 Msun
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Model E (radial orbit e=0.87 (2))M/L = 1400Stars: Hernquist Sphere
Rsc = 250 pc ; Rcut = 400 pc
M = 5.0 x 104 Msun
DM: NFW-Profile
Rsc = 250 pc ; Rcut = 1000 pc
M = 1.25 x 108 Msun
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We also run models on orbit (3) which is similar to orbits of sub-haloes in cosmological simulations:
• Initial models have to be more massive to get a similar remnant• Final models have a higher central M/L-ratio and a lower average M/L-ratio
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Conclusions• Tidally disrupted models could be ruled
out by means of numerical simulations and later by improved contours.
• The S-shape of Boo (tidal distortion) might not be real or is due to rotation.
• The velocity dispersion is now robust, so Boo is an intrinsically flattened system which is heavily DM dominated.
• OR: Low-number sampling of stars mimics elongation and fuzzy structure.
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or (?)
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Model A projected along the tails:
gauss = 0.8 km/s (red) all distances = 5.7 km/s (black) d<500pc = 5.0 km/s (green)
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Some advertisement:
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Formation of Dwarf Galaxies:(PhD project of P. Assmann (Concepcion))
• Consider star formation in a DM halo• Stars form in star clusters, which suffer from gas-
expulsion• Star clusters inside the DM halo merge and form a
dwarf galaxyAim:• Constrain the parameter space of successful
progenitors (halo shapes, SFEs, profile of star cluster distribution)
• Look for fossil records of the formation in velocity space
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The Sagittarius Tidal Stream
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Some words aboutTidal Tails…
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How does the ‘Field of Streams’ connect with the tidal tails of the Sagittarius dwarf galaxy ?
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The Bifurcation (overlap of at least two branches of the tails)
Upper Stream (B)
Lower Stream (A)
Stream (A) and (B) havealmost the same distanceStream (C) is locatedbehind stream (A)
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“Houston - we have a Problem”:
• How can the two streams be so close in position and distance– Is there no peri-centre shift ?– Is there almost no shift of the plane of the orbit ?– Is it caused by two objects orbiting each other ?
• No, see LMC & SMC
– Did Sagittarius collide with another object ?• Maybe, but that’s not causing a bifurcated stream
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Model for Sagittarius:
• Plummer sphere with 1M particles– Rpl = 0.35 - 0.5 kpc ; Rcut = 1.75 - 3.0 kpc– Mpl = 108 - 109 Msun
• Position today = 18h 55m.1 ; = -30o 29’– Dsun = 25 kpc ; vrad = 137 km/s
• Proper motions– HST, Schmidt plates, Law et al. fit & variations
• Orbit followed from -10 Gyr until today
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Galactic Models: 1. - ML• Logarithmic Halo:
– V0=186 km/s– Rg =12 kpc
• Miamoto-Nagai Disc:– Md=1011Msun
– b=6.5 kpc, c=0.26 kpc
• Hernquist Bulge:– Mb=3.4x1010 Msun
– a=0.7 kpc
€
h =1
2v0
2 ln(R2 +z2
qΦ2
+ Rg2)
€
d =GMd
R2 + (b+ z2 + c 2 )2
€
b =GMb
r + a
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Galactic Models: 2. - DB
• Dehnen & Binney model (1998)• 3 discs (ISM, thin, thick) double exponential• 2 spheroids (bulge, halo) power law
€
ρd =Σd2zd
exp −RmR
−R
Rd−z
zd
⎛
⎝ ⎜
⎞
⎠ ⎟
ρ s = ρ 0
m
r0
⎛
⎝ ⎜
⎞
⎠ ⎟
−γ
1+m
r0
⎛
⎝ ⎜
⎞
⎠ ⎟
γ −β
exp −m2
rt2
⎛
⎝ ⎜
⎞
⎠ ⎟;m
2 = R2 +z2
q2
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‘young’ leading arm
‘old’ trailing arm
‘old’ leading arm
‘’young’ trailing arm
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Distances:
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Sequence of increasinginitial mass of Sagittarius
Strength of the Bifurcationdecreases with increasingmass
MSgr > 7.5 x 108 Msun
No Bifurcation visible
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Increasing the mass matches the measured distances better
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So is this just a YASS(yet another Sagittarius
simulation)or can we actually learn
something from it ?
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What’s your result ?
• You should have spotted 7 simulations which show a bifurcation and maybe a few very weak ones.
• All simulations with bifurcation have
0.95 ≤ q ≤ 1.05
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q=0.9
q=0.95
q=1.05
q=1.0
q=1.11
Miamoto-Nagai + logarith. halo - Dehnen-Binney model
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Conclusions
• Bifurcation only appears in spherical or almost spherical halos
Q kpc ≈ 0.95 - 0.97• Higher masses blur out the bifurcation but
decrease the distance error
MSgr ≤ 7.5x108 Msun
• HST proper motion does not reproduce the bifurcation in any Galactic model
• Bifurcation only appears in spherical or almost spherical halos
Q kpc ≈ 0.95 - 0.97• Higher masses blur out the bifurcation but
decrease the distance error
MSgr ≤ 7.5x108 Msun
• HST proper motion does not reproduce the bifurcation in any Galactic model