Modelling the Ultra-Faint Dwarf Galaxies and Tidal Streams of the Milky Way M. Fellhauer Universidad de Concepcion in collaboration with N.W. Evans 1,

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

Ladies and gentleman

SDSS Proudly presents:

The ‘Field of Streams’

The SDSS survey60 million stars are catalogued in SDSS in 5 colours

All stars of the Milky Way in SDSS:

And then we apply a simple colour-cutAnd are left with only the halo stars…

“Field of Streams”Belokurov et al. 2006

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

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

SDSS data

INT DataIrwin et al. 2007

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

But now to some modelling…

Ursa Major II and the Orphan Stream

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

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:– 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

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:– 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

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

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

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• 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

Orphan stream UMa II

1-comp. 1-comp.2-comp. 2-comp.

Comparison of the 2 models - Reproduction of Orphan Stream &

UMa II

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

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 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

Bootes

The Boötes Dwarf Galaxy

= 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

The Contours or what is real ?

Is there an S-shape in the contours, i.e. is Boo tidally disturbed ?

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 ???

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)

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

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

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

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

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

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

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 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

The Sagittarius Tidal Stream

Some words aboutTidal 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)

Upper Stream (B)

Lower Stream (A)

Stream (A) and (B) havealmost the same distanceStream (C) is locatedbehind 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=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

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

‘young’ leading arm

‘old’ trailing arm

‘old’ leading arm

‘’young’ trailing arm

Distances:

Sequence of increasinginitial mass of Sagittarius

Strength of the Bifurcationdecreases with increasingmass

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

q=0.9

q=0.95

q=1.05

q=1.0

q=1.11

Miamoto-Nagai + logarith. halo - Dehnen-Binney model

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