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					The Formation of Disk Galaxies




          Ariyeh Maller
               UMASS

           in collaboration with
           Avishai Dekel
                        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
                Some Notation

a. Angular Momentum
                    J a mv × r

                          J
b.
                       ja
     Specific Angular Momentum
                          M
                             j
                 Á' a
                        2 V vir Rvir

c. Spin parameter
 The Standard Model of Disk Formation

 Detailed Conservation of Angular Momentum
(Mestel 1963)
 Baryons initially trace dark matter
(Fall and Estafiou 1980)

                                Rd       ÁRvir

 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
   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 λ values. (Lacey and de Jong 2000)
    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
   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 λ values. (Lacey and de Jong 2000)
                       The j-profile problem

Universal specific angular
momentum profile:

     M j       Â j / j max
           =
     M vir   Â 1ƒ j / j max
(Bullock et al 2000)

μ has a log-normal distribution

There is an excess of low
and high angular momentum
material compared to an
exponential disk.
   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 λ values. (Lacey and de Jong 2000)
        Modeling Angular Momentum

1 How angular momentum is built up in halos?

   1 Tidal Torques

   2 Orbital angular momentum from mergers

 2 How angular momentum is transferred to the
                          halo?

   1 Tidal Stripping

   2 Dynamical Friction

3 How the baryons are related to the dark matter?
                    Tidal Torques

                                    (Peebles 1969)

Collapsing Shells
                                 Orbital-Merger
 Orbital angular momentum
of merger is converted to
spin angular momentum.

        J orb = 0.42V vir Rvir



(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
           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
                Transfer of Angular Momentum

msatt           M halo                             A satellite looses mass
    3       =       3                               and angular momentum
r   tidal       d   satt                            because of tidal
                                      r tidal
                                                    stripping. We can
     Tidal                                          assume that the mass
    Striping
                                                    lost retains its angular
                                                    momentum.
                           d satt


                              Dynamical            Dynamical friction
                              Friction              brings the satellite into
                                                    the center of the halo,
                                                    transferring its angular
                           The Effect of Cooling

msatt           M halo                     When gas cools the
    3       =       3                       extent of the baryons
r   tidal       d   satt
                                            Rb will be much less
     Tidal
                                            then that of the dark
    Striping                                matter Rdm
                                           Thus the baryons are
                                            not stripped from the
                                            satellite and instead
                                            their angular
                            Dynamical
                            Friction        momentum is lost to
                                            dynamical friction.
           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 Rb=0.13 Rdm
we see that the
spin of the baryons
is reduced by
roughly an
order of
magnitude.

  f d = — 0.13
        f=
                         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.
Simple Feedback Recipe
     Assume for some size halo feedback
        can
     balance the effects of cooling. Let the
     circular velocity of this halo be
                           V   fb


     For halos with Vh > Vfbfeedback will not
     balance cooling and the baryons will
     contract.            V fb ¹     1

                     Rb =                Rdm
                            V satt


     For halos with Vh < Vfb / √2 feedback
         may
     overcome cooling and the baryons may
     escape from the halo reducing the
                            V satt ¹      2


         fraction     f d=
                            2V fb
     in the disk.
               Baryonic Angular Momentum

The baryonic angular
momentum is reduced             Vfb = 95 km/s
in massive halos
because the baryons
have condensed and
the satellite spirals into
the halo before the
baryons are stripped
                             ¹ 1= 1   ¹ 2= 1
In low mass halos the
baryonic angular
momentum is reduced
because there are less
baryons, the specific
angular momentum is
unchanged.
          Effects of Heating and Blowout




Bright Galaxies Vvir = 220 km/s      Dwarf Galaxies Vvir = 60 km/s
                   ¹ 1 = ¹ 2= 1   V fb = 95km/ s
               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.
                           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
Spin Distribution of Dwarf Galaxies

                          Data:

                              Á0 = 0.063


                          Dark Matter:
                           Á0 = 0.35   È Á= 0.5


                          Model Dwarfs:

                           Á0 = 0.68   È Á= 0.61
j-profiles
                       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.

  0.8d ¹ 2 d 3.0

 0.5d ¹ 1 d 3.0

 60d V fb d 130
                  Conclusions
I. Heating and cooling change the angular
  momentum of baryons relative to the dark
  matter (Spin Segregation).
   i. The mean value of the spin parameter of
    baryons in dwarf galaxies is increased in
    agreement with observations.
   I. The low and high tails of the specific angular
    momentum profile are removed in agreement
    with observations.
   II. The spread in spin parameter values in bright
    galaxies is decreased again in agreement with
    observations.
   III. The low and high tails of specific angular

				
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posted:9/18/2012
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