Transcript Modelling the Ultra-Faint Dwarf Galaxies and Tidal

Modelling the Ultra-Faint
Dwarf Galaxies and Tidal
Streams of the Milky Way
M. Fellhauer
Universidad 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
Ladies and gentleman
SDSS Proudly presents:
The ‘Field of Streams’
The SDSS survey
60 million stars are
catalogued in
SDSS in 5 colours
All stars of the Milky Way in
SDSS:
And then we apply a simple colour-cut
And are left with only the halo stars…
Belokurov et al. 2006
“Field of Streams”
A gallery of SDSS dwarfs
CVn I
Boo
CVn II
Com
D = 220 kpc
rh = 550 pc
MV = -7.9
D = 60 kpc
rh = 220 pc
MV = -5.8
D = 150 kpc
rh = 140 pc
MV = -4.8
D = 44 kpc
rh = 70 pc
MV = -3.7
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?
MV vs. Log(rh)
Mind the Gap?
But there is even more:
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
Irwin et al. 2007
INT Data
SDSS
data
 3°
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
HIPASS
floating” iceberg?
HI
Ryan-Weber et al. 2007
INT g,r
But now to some modelling…
Ursa Major II
and the
Orphan
Stream
Gal. latitude
Orphan Stream
Mass estimate: 8 x 104 Msun
UMa II
Complex A
Gal. longitude
Ursa Major II
Belokurov et
al. 2007
Zucker et al.
2006

Muñoz et al.
2007
MV = -3.8 ± 0.6 mag (approx. 6000 Msun)
~6.7 km/s

Martin et al.
2007
Simon &
Geha 2007
Finding an orbit which
connects UMa II with the
Orphan Stream
Galactic Model: analytic potential for the MW
• Logarithmic Halo:
– v0 = 186 km/s
– Rg = 12 kpc
– q = 1
• Miamoto-Nagai Disc:
2
1 2
z
h  v 0 ln( R 2  2  Rg2 )
2
q
d 
– Md =
sun

– b = 6.5 kpc, c = 0.26 kpc
1011 M
• Hernquist Bulge:
– Mb = 3.4x1010 Msun
– a = 0.7 kpc 
GMd
R 2  (b  z 2  c 2 ) 2
GMb
b 
ra
Insert UMa II as a point mass and look for matching orbits
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
Observational Data (to date)
• UMa II:
Martin et al. 2007
– vhelio = -115 ± 5 km/s
(agrees well enough with our prediction)
– los = 7.4 +4.5-2.8 km/s
• Orphan Stream:
Belokurov et al. 2007
– 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)
Constraining the progenitor
of UMa II and the Orphan Stream
Initial model for UMa II:
use simple Plummer
spheres to constrain
parameter space in
initial mass & scalelength
Constraining the Progenitor:
I. Length of the Tails
Progenitor
must of
beprogenitor mass Simulation
timetime
must
Tails
as function
and simulation
>105 Msun & <107 Msun
be longer than 7.5 Gyr
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
Comparing 2 UMa II models:
One component model Two component model
• Plummer sphere:
– Rpl = 80 pc
– Mpl = 4 x 105 Msun
• 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
Comparison of the 2 models Reproduction of Orphan Stream &
UMa II
Orphan stream
UMa II
1-comp.
2-comp.
1-comp.
2-comp.
Comparing the
before
dissolution
Patchy structure (B) vs. round, bound, A:
sound
&
appearance
& the

is
low
and
v
rad
A massive (D)
kinematics of the
constant
two models:
B: patchy structure,
high
, component
patchy vrad (B)
One
B
with gradient
Before(A), while (B)
Both models show high velocity dispersion
after
dissolution [c]
C:&no
density
enhancement, low ,
C
Mean vrad is patchy with gradient (B) vs. constant within object (D)
gradient in vrad
D
Two component (D)
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:
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
New unpublished data searching
for tidal tails around UMa II
show 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
Bootes
The Boötes
Dwarf Galaxy
Boötes: Observational Facts
• = 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 Munoz et al. 2006
•vrad,sun=+99.9 ± 2.1km/s
•  6.5 ± 2.0 km/s
•[Fe/H] = -2.1
Martin et al. 2007
Belokurov et al. 2006
The Contours or what is real ?
Is there an S-shape in the contours,
i.e. is Boo tidally disturbed ?
Some simple maths…
1
3
rtidal
 M sat 

DGC

 3M MW 
BUT:
 los,0  2.52 
M sat 10 7 M sun 
Rpl kpc 
•rtidal = 250 pc (0.2o)
•DGC = 60 kpc
•MMW(DGC) = 6 x 1011 Msun
 Msat = 70,000 Msun
 agrees with luminous matter
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
• 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 ???
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
Model A (TDG)
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
M/L = 17 (unbound stars)
Model B (mass follows light)
(keeping the same orbit)
Plummer Sphere:
Rpl = 200 pc ; Rcut = 2000 pc
M = 1.6 x 107 Msun
M/L = 620 (DM dominated)
Model C (small DM halo)
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
M/L0 = 550 (<M/L> =1800)
Model D(extended DM halo)
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
M/L0=800 (<M/L>=3400)
Model E (radial orbit e=0.87 (2))
Stars: 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
M/L = 1400
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/Lratio
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.
or (?)
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)
Some advertisement:
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 galaxy
Aim:
• 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
The Sagittarius Tidal Stream
Some words about
Tidal Tails…
How does the ‘Field of Streams’ connect with the tidal tails of
the Sagittarius dwarf galaxy ?
The Bifurcation
(overlap of at least two branches of the tails)
Stream (A) and (B) have
almost the same distance
Stream (C) is located
behind stream (A)
Upper Stream (B)
Lower Stream (A)
“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
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
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
– a=0.7 kpc
=3.4x1010
Msun

2
1 2
z
2
h  v 0 ln( R  2  Rg2 )
2
q
d 
GMd
R 2  (b  z 2  c 2 ) 2
GMb
b 
ra
Galactic Models: 2. - DB
• Dehnen & Binney model (1998)
• 3 discs (ISM, thin, thick) double exponential
• 2 spheroids (bulge, halo) power law
 Rm R
z 
d
d 
exp

 
2zd
 R Rd zd 

m 
 s   0  
r0 
 
 m 
1 
 r0 
2
 m 2  2
z
exp 2 ; m  R 2  2
q
 rt 
‘old’ trailing arm
‘young’ leading arm
‘old’ leading arm
‘’young’ trailing arm
Distances:
Sequence of increasing
initial mass of
Sagittarius
Strength of the Bifurcation
decreases with increasing
mass
MSgr > 7.5 x 108 Msun 
No Bifurcation visible
Increasing the mass matches the measured distances better
So is this just a YASS
(yet another Sagittarius
simulation)
or can we actually learn
something from it ?
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
Miamoto-Nagai + logarith. halo - Dehnen-Binney model
q=0.9
q=0.95
q=1.0
q=1.05
q=1.11
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