The Formation of Disk Galaxies

1
The Formation of Disk Galaxies

• Ariyeh Maller
• UMASS
• Avishai Dekel
• University of Jerusalem
• Maller and Dekel 2003 MNRAS, 335, 487
• Maller, Dekel and Somerville 2002 MNRAS, 329, 423

2
Outline

• The Standard Theory
• Initially baryons trace dark matter.
• Detailed conservation of angular momentum.
• Problems with the Standard Theory
• The angular momentum catastrophe.
• The distribution of specific angular momentum.
• Bulge formation from low angular momentum
  material.
• New ideas
• A hierarchical model of the build up of angular
  momentum.
• Spin segregation from feedback.

3
Some Notation

• Angular Momentum
• Specific Angular Momentum
• Spin parameter

4
The Standard Model of Disk Formation

• Detailed Conservation of Angular Momentum
• (Mestel 1963)
• Baryons initially trace dark matter
• (Fall and Estafiou 1980)
• Adiabatic Contraction
• (Barnes and White 1984, Bluementhal et al 1986)
• Realistic Halo Profile
• (Dalconton et al 1996, Mo et al 1997)
• Bulge formation from disk instabilities
• (Dalconton et al 1996, Mo et al 1997, van der
  Bosch 1998)
• Supernova feedback
• (van der Bosch et al 2000, 2002)

5
Problems with the Standard Model

• The angular momentum catastrophe
• Hydrodynamical simulations show that the
  angular
• momentum of the baryons is not conserved
  during collapse
• (Navarro and Benz 1991, Steinmetz and Navarro
  1998, 2000,
• Sommer-Larson et al 2000)
• The j-profile mismatch
• The distribution of specific angular momentum
  in N-body simulations does not agree with
  observations
• (Bullock et al 1999, van der Bosch et al 2000)
• Other problems
• The spread in disk sizes seems to be narrower
• then the spread in ? values. (Lacey and de Jong
  2000)
• Major mergers should lead to spheroids, but they
  also
• have the highest ? values. (Gardner 2000,
  Wechsler 2000)

6
The angular momentum catastrophe

• In hydrodynamical
• simulations baryons
• have 10 of the
• angular momentum
• of observed disks.
• This has been associated
• with the problem of
• over-cooling also
• seen in hydrodynamical
• simulations

Navarro and Steinmetz 2000
7
Problems with the Standard Model

• The angular momentum catastrophe
• Hydrodynamical simulations show that the
  angular
• momentum of the baryons is not conserved
  during collapse
• (Navarro and Benz 1991, Steinmetz and Navarro
  1998, 2000,
• Sommer-Larson et al 2000)
• The j-profile mismatch
• The distribution of specific angular momentum
  in N-body simulations does not agree with
  observations
• (Bullock et al 1999, van der Bosch et al 2000)
• Other problems
• The spread in disk sizes seems to be narrower
• then the spread in ? values. (Lacey and de Jong
  2000)
• Major mergers should lead to spheroids, but they
  also
• have the highest ? values. (Gardner 2000,
  Wechsler 2000)

8
The j-profile problem

• Universal specific angular
• momentum profile
• (Bullock et al 2000)
• ? has a log-normal distribution
• There is an excess of low
• and high angular momentum
• material compared to an
• exponential disk.

9
Problems with the Standard Model

• The angular momentum catastrophe
• Hydrodynamical simulations show that the
  angular
• momentum of the baryons is not conserved
  during collapse
• (Navarro and Benz 1991, Steinmetz and Navarro
  1998, 2000,
• Sommer-Larson et al 2000)
• The j-profile mismatch
• The distribution of specific angular momentum
  in N-body simulations does not agree with
  observations
• (Bullock et al 1999, van der Bosch et al 2000)
• Other problems
• The spread in disk sizes seems to be narrower
• then the spread in ? values. (Lacey and de Jong
  2000)
• Major mergers should lead to spheroids, but they
  also
• have the highest ? values. (Gardner 2000,
  Wechsler 2000)

10
Modeling Angular Momentum

• How angular momentum is built up in halos?
• Tidal Torques
• Orbital angular momentum from mergers
• How angular momentum is transferred to the halo?
• Tidal Stripping
• Dynamical Friction
• How the baryons are related to the dark matter?
• Cooling
• Feedback

11
Tidal Torques
(Peebles 1969)
Collapsing Shells
12
Orbital-Merger

• Orbital angular momentum
• of merger is converted to
• spin angular momentum.
• (Maller et al 2002)
• We also include a slight correlation
• between the directions of incoming
• mergers as seen in N-body simulations.
• This formalism reproduces
• statistically the properties of
• the dark halo spin distribution.

13
j-profile from Orbital-Merger
Divide mass growth in to 20 equal mass bins and
assign to each bin the corresponding J that came
in with that mass. For satellites with masses
larger then the bin size the J assigned to the
bin goes as the square of the fraction of mass
in that bin. Low j material associated
with small satellites, high j material associated
with large satellites
14
Transfer of Angular Momentum

• A satellite looses mass and angular momentum
  because of tidal stripping. We can assume that
  the mass lost retains its angular momentum.
• Dynamical friction brings the satellite into the
  center of the halo, transferring its angular
  momentum to the halo.

Tidal Striping
Dynamical Friction
15
The Effect of Cooling

• When gas cools the extent of the baryons Rb will
  be much less then that of the dark matter Rdm
• Thus the baryons are not stripped from the
  satellite and instead their angular momentum is
  lost to dynamical friction.

Tidal Striping
Dynamical Friction
16
Over-cooling leads to the Angular Momentum
Catastrophe

• If the baryons cool
• rapidly and sink to
• the centers of dark
• halos, then they will
• lose their angular
• momentum.
• Taking Rb0.13 Rdm
• we see that the
• spin of the baryons
• is reduced by
• roughly an
• order of
• magnitude.

17
Heating

• The obvious solution to this problem is some form
  of heating that will prevent the baryons from
  contracting to the center of the dark halos.
• Usually people assume that this heating will keep
  the baryons exactly tracing the dark matter
  however, this is not a reasonable assumption.
  Instead we expect the effects of heating to be a
  function of the mass of the dark halo.
• Unfortunately a successful implementation of
  feedback in hydrodynamical simulations has thus
  far proven challenging (Thacker and Couchman
  2000).
• Thus we will adopt a very simplistic feedback
  recipe to explore its possible effects.

18
Simple Feedback Recipe

• Assume for some size halo feedback can
• balance the effects of cooling. Let the
• circular velocity of this halo be
• For halos with Vh Vfbfeedback will not
• balance cooling and the baryons will
• contract.
• For halos with Vh
• overcome cooling and the baryons may
• escape from the halo reducing the fraction
• in the disk.

19
Baryonic Angular Momentum
The baryonic angular momentum is reduced in
massive halos because the baryons have
condensed and the satellite spirals into the
halo before the baryons are stripped In low
mass halos the baryonic angular momentum is
reduced because there are less baryons, the
specific angular momentum is unchanged.
Vfb 95 km/s
20
Effects of Heating and Blowout
Bright Galaxies Vvir 220 km/s
Dwarf Galaxies Vvir 60 km/s
21
Comparison to Data

• The data comes from van der Bosch, Brukett and
  Swaters (2001) who analyzed the rotation curves
  of 13 dwarf galaxies to determine dark matter
  halo profiles and from them baryonic spin
  parameters and mass fractions.
• They also measured j-profiles for the galaxies in
  their sample.
• The mean viral velocity of the sample is 60 km/s
  and the
• mean baryon fraction is 0.04.
• We set the free parameter of our model Vfb by
  requiring that the mean baryon fraction in our
  model galaxies with virial velocities of 60 km/s
  is 0.04.

22
Baryon Fractions
The fraction of mass in the disk for the data and
in our model for bright and dwarf halos. Vfb
is set to 95 km/s
23
Spin Distribution of Dwarf Galaxies
Data
Dark Matter
Model Dwarfs
24
j-profiles
25
Model Dependence

• There are a wide
• range of model
• parameters that
• lead to very similar
• results as long as
• Vfb is chosen to fit
• the observed disk
• fraction.

26
Conclusions

• Heating and cooling change the angular momentum
  of baryons relative to the dark matter (Spin
  Segregation).
• The mean value of the spin parameter of baryons
  in dwarf galaxies is increased in agreement with
  observations.
• The low and high tails of the specific angular
  momentum profile are removed in agreement with
  observations.
• The spread in spin parameter values in bright
  galaxies is decreased again in agreement with
  observations.
• The low and high tails of specific angular
  momentum are sometimes removed in bright
  galaxies, allowing for large bulgeless galaxies.