The Formation of Disk Galaxies

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The Formation of Disk Galaxies
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Literature

• Freeman, 1970, ApJ 160, 811
• Fall Efstathiou, 1980, MNRAS 193, 189
• White, 1984, ApJ, 286, 38
• Navarro, Frenk White, 1996, ApJ 462, 563
• Mo, Mao White, 1998, MNRAS 295, 319

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Classification of Galaxies

• Hubble Sequence
• Todays lecture
• How do disks form
• Future lecture why do some disks have bars

Galaxien und aktive Kerne
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Properties of disk galaxies

• actively star forming
• substantial amounts of gas (gt10)
• ordered motion, stars on nearly circular orbits
  around galactic center
• Flat rotation curves
• low velocity dispersion, in particular for young
  stars
• exponential surface density profile

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Exponential disks
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Vertical Structure of Disk

• Many disks have a vertical structure that follow
• Most spirals have two disk components
• Thin disk MW z0225pc
• Thick disk MW z01kpc

van der Kruit Searle 1981
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Rotation Curve of the Milky Way
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Rotation curves of spiral galaxies
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Dark Matter in Disk Galaxies
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Stellar populations

• Population II
• old stars
• in bulge and halo (globular clusters) of the
  Milky Way
• metal poor, in particular in the halo
• a-enriched (C,O,Ne,Mg,Si,S ...) are
  over-abundant compared to the Sun
• high velocity w.r.t. the local standard of rest

• Population I
• young stars
• in the disk of the Milky Way
• metal abundance similar to that of the Sun
• similar fraction of a-elements as in the Sun
• low velocity w.r.t. the local standard of rest.

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Non-linear collapse
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Spherical top hat model
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Spherical top hat

• Consider an overdense region at ti t0, i.e. for
  background universe it can be assumed O1
• Compare with Friedmanns equation

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Spherical top hat

• 1st integral
• For Elt0 this ODE has the parametric solution
• Maximum radius Rm is reached at time tm

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Spherical top hat

• Rm and tm are linked by
• For small fluctuations
• i.e. consistent with linear perturbation theory

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Spherical top hat 3 phases

• Turn around ( ? ? )
• Overdensity w.r.t background by comparison with
  shell that follows Hubble expansion
• Collapse ( ? 2? )
• Linearly extrapolated density contrast
• Perfect collapse never occurs. Small deviation
  from spherical symmetry result in random motions

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Spherical top hat 3 phases

• Energy
• Kinetic energy K initially Kinit 0
• Potential energy V
• Virialization
• Virial theorem V -2K
• Energy conservation Vfinal Kfinal E
  Vinit? Vfinal 2Vinitial or Rfinal
  ½Rinitial
• Estimated average overdensity

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from Rix IMPRS lecture 2008
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Spherical top hat for O?1

• Minimum overdensity required to collapse at all

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A simple halo model

• Dark matter halos have no obvious edge
• Simple model define halo as region that is
  causally connected.
• Consequently, one obtains for radius and mass

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A simple halo model

• Ignoring the ?dependence (?2/3), we obtain very
  simple relations
• For Milky Way (vc220 km/s)
• rhalo 350kpc, i.e. Andromeda and MW overlap
• Mhalo 50 Mdisk
• For a given vc, halos in a low O universe are
  more massive!
• Tully-Fisher like velocity scaling is intriguing
• Virial mass corresponds to an average overdensity
  (compared to the critical density) of

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Properties of Dark Matter Halos
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The Density Profile of Cold Dark Matter Halos

• Mass profiles of dark halos are independent of
  halo mass and cosmological parameters

Density
Navarro, Frenk White 1997
Radius
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The Density Profile of Cold Dark Matter Halos

• There is no obvious density plateau or core
  near the center
• The profile is shallower than isothermal near the
  center

Density
Navarro, Frenk White 1997
Radius
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The Density Profile of Cold Dark Matter Halos

• Halo fitting ? two parameters
• Circular velocity vc
• Concentration c Rvir/Rs
• Cosmology (?, ?, ?8 , power spectrum) determines
  c
• for CDM-type models cRvir/Rs ? 10for
  galaxy halos

Density
Radius
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Halo profiles for different CDM and WDM
cosmologies
?8
?
vc
WDM
Eke, Navarro Steinmetz 2001
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Halo profiles for non-hierarchical models
Huss, Jain Steinmetz 1999
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Concentration as inferred from LSBs
? best fit c?2 ? c?10 (CDM)
McGaugh et al. 2002
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The Origin of Galactic Spin
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Angular momentum of a Lagrangean fluid element

• Zeldovich
• or for the angular momentum

F Taylor expanded
moment of inertia
tidal field
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Angular momentum of a Lagrangean fluid element

• For Om1 L?t
• L grows until turnaroundcollapse ? Ijk ? a-2
• Spherically symmetric objects dont gain any
  angular momentum, axisymmetric object no AM along
  symmetry axis. Also no AM if f is isocontour of
  ??
• Angular momentum ? vorticity !

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Piontek Steinmetz 2009
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Tidal Torques and Angular Momentum

• The angular momentum of galaxies originates
  in tidal torques exerted by external
  material during the expansion phase
• It is relatively inefficient (?0.05),
  implying that dark matter halos must be
  present to spin up baryonic material during
  collapse

• The leading cause is a misalignment between the
  principal axes of the inertia momentum tensor
  (Iij) and of the shear tensor (?2F/?xi?xj)
• Most effective near turnaround, when Iij is
  largest.

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Tidal Torques and Angular Momentum
Given the tendency of matter to collapse on large
scale sheets crisscrossed by filaments, this
implies that the spin axis should lie on the
plane traced by the surrounding large scale
structure.
z0 configuration of matter within a 5 Mpc sphere
in the initial conditions
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Galactic Spin Direction and Large Scale Structure
The direction of galactic spin is easiest to
estimate in edge-on spiral disks.
Navarro et al. 2005
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Dark matter form a timing argument

• Spin parameter of cosmic structures (tidal torque
  theory)for an analytical derivation see,
  e.g. Steinmetz Bartelmann, 1995
• Typical self-gravitating disk ?0.5 ? spin-up
  by factor 10 ? energy dissipation factor of 100
• E ? R-1 ? collapse by factor of 100
• This takes more than a Hubble time
• Need for dark matter v given by DM halo ? r
  vconst. ? only collapse by factor 1/?
  required

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Standard Model of Disk Formation
Jf
Ji
DM
Cooling
Gas
AM Conservation Ji Jf Adiabatic compression
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Why have disks exponential surface density
profiles?

• Freeman, 1970 Self-gravitating exponential disk
  and rigidly rotating homogeneous sphere have
  simular angular momentum distributions

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Is it that simple?
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Angular momentum conserved?

• Angular momentum is transferred from the baryons
  to the dark matter during mergers
• It is not easy to form disk galaxies that
  resemble observed spirals in CDM models!

Steinmetz Navarro 1999
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Piontek Steinmetz 2009
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Angular momentum of simulated disks
specific angular momentum
mass
Navarro Steinmetz 1997
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The specific angular momentum of model galaxies
Overall, the system is dominated by a slowly
rotation spheroid. The size of the disk
component is, however, comparable to other
spirals of similar rotation speed.
Specific Angular Momentum
Rotation Speed
Abadi et al 2003