How spherical is the invisible cow?

1
How spherical is the invisible cow?
Arizona TAP Colloquium October 2007
?

• Jeremy Bailin (McMaster)
• Collaborators Chris Power, Peder Norberg, Josh
  Simon, Dennis Zaritsky, Alberto Bolatto, Brad
  Gibson, Stéphane Herbert-Fort, Geraint Lewis, Tim
  Hendtlass

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Consider A Cow
Sphere is the first approximation we always
make. But we can see that the cow is not really a
sphere its an ellipsoid.
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
3
Consider An Invisible Cow
If we cant see the cow, how can we figure out
its shape?
?
?
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
4
Galactic Dark Matter Halos

• We believe galaxies inhabit halos of dark matter
  (DM) that doesnt interact with (emit/absorb)
  light.
• Evidence Rotation Curves, Stellar Velocity
  Dispersions, Satellite Velocity Dispersions,
  X-ray Gas, Cosmological Structure Formation,
  Gravitational Lensing
• We see the gravitational effects of DM on visible
  matter (stars, gas) but the DM itself is
  invisible.

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
5
Galactic Dark Matter Halos

• Other possibility incorrect theory of gravity
  (eg. MOND)
• Inferred dark matter halo may have different
  properties than those of halo truly made of dark
  matter

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
6
Properties of Dark Matter Halos

• To determine the predictions of dark matter
  theory, we must run expensive cosmological N-body
  simulations.
• Method
• Begin with almost-smooth distribution of dark
  matter particles (with fluctuations from CMB)
• At each timestep, move each particle in
  gravitational field of other particles, within
  expanding spacetime
• See what happens after 13.7 Gyr!

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
7
Cosmological Simulations
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
8
Prediction Halos (Like Cows) Are Flattened
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
9
Prediction Halos are Flattened
Spherical
Extremely Flattened
Baryon cooling results in somewhat more spherical
halos (c/a0.8). (Dubinski 1994 Kazantzidis et
al. 2004 Bailin et al. 2005)
Bailin Steinmetz (2005)
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
10
Inferred Halos in MOND

• If theory of gravity is wrong (eg. MOND), only
  gravitational source is baryonic material.
• In order to fit observational data, monopole
  (spherically-symmetric) term of baryon mass
  distribution must dominate in halo
• Inferred halo is spherical!
• Measurement of flattened halo distinguishes
  between DM and modified gravity.

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
11
How Can We Measure Flattening of Invisible Halos?

• Using its gravitational effect on visible things!
• Some previous methods
• X-ray isophotes (Buote et al. 2002)
• Weak lensing (Hoekstra et al. 2004 Mandelbaum et
  al. 2006)
• Polar ring galaxies (Sackett et al. 1994)
• Flaring of outer gas disk (Olling Merrifield
  2000)

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
12
How Can We Measure Flattening of Invisible Halos?

• Using its gravitational effect on visible things!
• New methods
• Satellite galaxy locations
• Satellite galaxy kinematics
• Elliptical orbits from 2D velocity fields
• Tidal streams

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
13
Introduction to Satellite Galaxies

• Small galaxies in the vicinity of and dynamically
  dominated by larger parent galaxies

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
14
Introduction to Satellite Galaxies

• Small galaxies in the vicinity of and dynamically
  dominated by larger parent galaxies
• Around Milky Way
• LMC, SMC

Roger Smith/NOAO
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
15
Introduction to Satellite Galaxies

• Small galaxies in the vicinity of and dynamically
  dominated by larger parent galaxies
• Around Milky Way
• LMC, SMC
• Sgr dSph

Majewski et al. 2006
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
16
Introduction to Satellite Galaxies

• Small galaxies in the vicinity of and dynamically
  dominated by larger parent galaxies
• Around Milky Way
• LMC, SMC
• Sgr dSph
• Fornax dSph

Phillip Keller
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
17
Introduction to Satellite Galaxies

• Small galaxies in the vicinity of and dynamically
  dominated by larger parent galaxies
• Around Milky Way
• LMC, SMC
• Sgr dSph
• Fornax dSph
• Scl, Car, UMi, UMa I II, Boo I II

Belokurov et al. 2006
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
18
Introduction to Satellite Galaxies

• Small galaxies in the vicinity of and dynamically
  dominated by larger parent galaxies
• Around M31
• M32
• NGC205

Robert Gendler
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
19
Introduction to Satellite Galaxies

• Small galaxies in the vicinity of and dynamically
  dominated by larger parent galaxies
• Around M31
• M32
• NGC205
• And I - XVI (minus IV, VIII?)

And VI Armandroff et al. 1998
And XVI Ibata et al. 2007
And II Da Costa et al. 2000
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
20
Halos Contain Substructure
Subhalos
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
21
Method 1 Locations of Satellites

• Subhalos in cosmological halos are more common
  along halo major axis (Knebe et al. 2004 Zentner
  et al. 2005)
• If satellites are associated with subhalos and if
  there are no dynamical biases, then so do
  satellites!
• We can study anisotropic distribution of
  satellite galaxies to detect halo flattening!
• Complications
• anisotropic infall from filaments
• visible satellites may be biased subset of
  subhalos
• dynamical timescales may be different for
  satellites on different orbits

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
22
Locations of Satellites

• Previous conflicting results
• Holmberg, Zaritsky et al., Milky Way, M31
  Satellites of spirals lie perpendicular to disk
• Studies using 2dFGRS, SDSS Satellites of
  ellipticals lie along elliptical major axis,
  satellites of spirals are isotropic
• Conundrum largest samples give one answer, but
  best samples give another!
• Small number statistics or systematic error?

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
23
Selecting Satellites of Isolated Galaxies

• Our goal Use mock catalogues from cosmological
  simulations to evaluate how well previous studies
  have selected true satellites of isolated
  galaxies
• Conclusion Almost all previous studies have been
  dominated by galaxy groups, where primary does
  not dominate the environment, instead of
  satellites of isolated dominant primary galaxies
• Exceptions Zaritsky et al., Milky Way, M31 -
  these are the ones that show polar distribution
  of satellites!
• With our criteria, we expect 10 contamination.
  Most previous studies had gt50.

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
24
Angular Distribution of Satellite Galaxies in SDSS
All primaries
Early-type primaries
Late-type primaries
Cumulative Fraction
N
90o
Disk Angle
Disk Angle
0o
Bailin et al., submitted
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
25
Angular Distribution of Satellite Galaxies

• Satellites of isolated spirals lie near minor
  axis, of isolated ellipticals lie near major
  axis!
• Previous conflicting results due to looking at
  galaxy group members vs. true satellites,
  confusion between ellipticals and spirals.
• Indication of halo shape? Maybe! But hard to
  disentangle from complications (ie. dynamical
  selection effects), especially around disk
  galaxies.
• Possible solution use kinematics of satellites,
  which are dominated by shape of potential

Satellite Galaxies Where are they located?
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
26
Method 2 Kinematics of Satellite Galaxies

• Satellite velocity dispersions have been used to
  measure extent, radial profile of halos (eg.
  Zaritsky et al. 1993 Klypin Prada 2007)
• In non-spherical halo, velocities along major
  axis are higher than along minor axis at a given
  radius
• Compare velocities of satellites along visible
  major, minor axes to detect halo shape!
• Avoids complications associated with satellite
  locations
• Requires more satellites than available in SDSS!
• Future work Add 6dF satellites.

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
27
Kinematics of Satellite Galaxies

• Satellites of disk galaxies tend to orbit
  prograde to disk
• Also a sharp mildly retrograde peak!
• Interpretation?

Herbert-Fort et al., submitted
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
28
Method 3 2D Velocity Fields

• Disk galaxies contain stars and gas on (nearly)
  closed orbits. In spherical potential, these are
  circular.
• If potential in plane of disk is elliptical,
  closed orbits are also elliptical.
• Measure ellipticity of orbits to infer
  ellipticity of potential.
• 2D Velocity Fields from Integral Field Units or
  radio (HI, CO) data cubes (eg. Simon et al. 2005)
• Projected shape distributions (eg. Ryden 2006)
• May also help resolve cusp-core discrepancy
  (Hayashi et al. 2007)

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
29
Disk Self-Gravity

• Disk is deformed by elliptical potential, becomes
  elliptical.
• Elliptical disk contributes to (dilutes)
  ellipticity of potential.
• Must self-consistently solve for ellipticity of
  potential and shape of disk!
• Previous attempts (Jog 2000) did not take radial
  variation of ellipticity into account. We do!

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
30
Disk Self-Gravity

• Must iteratively solve

Bailin et al. (2007)
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
31
Effect of Disk Self-Gravity
Bailin et al. (2007)
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
32
Disk Ellipticity in Triaxial Halo
b/a0.7
b/a0.8
b/a0.9
Bailin et al. (2007)
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
33
Detection of Disk Ellipticity

• In progress Test observational techniques of
  measuring halo profile, ellipticity
• Generate mock 2D velocity field from halo of a
  given shape.
• Analyze mock observations using same method as
  real observations.
• How well do inferred halo profile, ellipticity
  compare to input parameters?
• Tentatively looks like ellipticity is recovered
  well, but cusps can be hidden for certain
  configurations.

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
34
Method 4 Tidal Streams

• If we could watch one star orbit around a galaxy
  for several Gyr, we could infer the shape of the
  potential.
• Next best thing tidal streams of disrupting
  satellite galaxies contain lots of stars at
  different phases of similar orbits!

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
35
Tidal Streams

• Compare velocity, position of Sgr tidal stream
  stars to models in halos with different
  flattenings, see which one reproduces
  observations.
• Conflicting answers!
• Flattened, like disk (Martinez-Delgado et al.
  2004 Johnston et al. 2005)
• Spherical (Ibata et al. 2001 Fellhauer et al.
  2006)
• Elongated perpendicular to disk (Helmi 2004)
• Depends on which part of the stream is used! (Law
  et al. 2005)

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
36
Self-Consistent Models of Tidal Streams

• Because of current mass of Sgr, previous studies
  assumed MW does not react to its presence. But
  Sgr was more massive before disruption, so this
  is probably not a good assumption.
• Our goal model the MW-Sgr stream
  self-consistently, constrain halo shape and
  orbital history of Sgr.

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
37
Self-Consistent Models of Satellite Disruption
How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
38
Self-Consistent Models of Tidal Streams

• Self-consistent treatment of both Milky Way and
  Sagittarius makes a dramatic difference!
• Much more difficult to derive initial conditions
  that place Sgr at present position and velocity
  after 5 Gyr of evolution, requires algorithims
  that explore parameter space very efficiently.
• Still in progress!

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
39
Conclusions

• Prediction Dark matter halos are elliptical
  (c/a0.65 to 0.8 depending on effects of
  baryons), whereas modified gravity predicts that
  inferred halos are spherical.
• Satellite galaxies of disks are distributed
  perpendicular to disk, of ellipticals are
  distributed along major axis. May be indication
  of halo shape.
• We will be able to test this using the kinematics
  of satellite galaxies along major vs. minor axis
  once we increase our sample by combining SDSS
  with 6dF.

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
40
Conclusions

• Elliptical halo potential causes disk ellipticity
  that is measurable in 2D velocity fields. But
  must take disk self-gravity into account to
  interpret correctly!
• May help resolve cusp-core debate.
• Sgr stream can be used to measure shape of our
  halo, but requires simulating live Milky Way.
  The first such simulations are in progress.
• The flattening of dark matter halos is a testable
  prediction of the dark matter paradigm.

How Spherical Is The Invisible Cow?
Jeremy Bailin,
Arizona TAP Colloquium, Oct 2007
41
Extra Slides
42
Disk/Halo Alignment in Simulations
Bailin et al. 2005