Mass Models, Dark Matter, and MOND

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Mass Models, Dark Matter, and MOND

• Ann Martin
• Astro 620
• April 25, 2007

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Outline

• Mass Modeling Techniques in CDM
• Pressure-supported systems
• Rotationally-supported systems
• Problems with the CDM paradigm
• Assumptions uncertainties in mass models
• Cusp/core problem in CDM halos
• MOND point of view
• Basic introduction
• Predictions for dwarf galaxies
• MOND vs CDM/some results

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Motivation Why dwarf galaxies?

• May be the darkest structures in the Universe
  (Mateo 1998 review)
• CDM paradigm
• Dark matter dominates test of the nature
  of dark matter
• MOND
• Extremely low internal accelerations make them
  the perfect testing ground for MONDs most basic
  predictions
• Local dwarfs especially important high
  resolution data for internal kinematics

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Mass Models Rotationally Supported Systems

• Rotation curves (see Leis talk)
• dIrrs and very low mass spirals
• Can parameterize the rotation curve using only
  the dark matter halo (Simon et al. 2005)
• corresponding to a density profile

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Mass Models Rotation Curves

• If there are sizeable contributions from neutral
  gas a stellar disk, must include those as well.
• Following Swaters et al., circular velocity is a
  reflection of the gravitational potential with a
  radial force

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Mass Models Rotation Curves

• Total potential is the sum of the components
• Good fits usually found for an isothermal,
  spherical dark matter halo

where G is the stellar mass-to-light ratio, vd
is the rotation curve of the stellar disk for
G1, h represents the inclusion of helium, and
vh is the parameterization of the dark matter
halo profile.
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Mass Models Rotation Curves

• The Stellar Disk
• What is the vertical density variation?
  (something like sech2) How does it scale?
• What form fits the surface brightness profile?
  (usually a modified exponential)
• Should a stellar bulge or any other feature be
  included?
• How will the M/L be estimated? (Totally free
  parameter, maximum disk, minimum disk?)

• The Gaseous Disk
• Can the HI layer be assumed to be thin?
• Is the selection of the density profile
  important, or is the HI contribution small?
• How large should the correction for helium be?

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Mass Models Rotation Curves

• The Dark Matter Halo
• What form will it take?
• The isothermal sphere
• gives a rotation curve
• Later well look at the NFW profile

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Mass Models Pressure-Supported Systems

• Velocity dispersions
• dSphs and dElls (although there is some evidence
  for rotationally supported dwarfs in Virgo)
• Jeans equation determines the density
  distribution of stars for a relaxed spherical
  system
• (see Lokas Binney Tremaine for details)

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Pressure-Supported Systems
where b measures the anisotropy in the velocity
distribution, n is the 3-D stellar density, g(r)
the gravitational potential, and sr is the radial
velocity dispersion, converted from slos.
Find n by fitting the surface brightness
distribution, i.e., a King or Sersic (see below)
profile and then deprojecting
Then add a dark matter model to determine the
overall gravitational potential NFW profile or
isothermal sphere.
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Pressure-Supported Systems

• Central velocity dispersions of dSphs that arent
  satellites of the Milky Way are often highly
  uncertain (Penarrubia et al.)
• Disp. for And IX doubles is a single (possible
  member) star is included.

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CDM Problems Underlying Assumptions

• Assume a light-to-mass relationship
• A reasonable constant
• Maximum disk use the maximum stellar disk that
  doesnt, at any point, overshoot the observed
  rotation curve
• Minimum disk use stars as test particles in the
  dark matter potential

Example maximum disk models for NGC 4414
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CDM Problems Underlying Assumptions

• Implicit assumption that light traces baryonic
  matter, and that whatever tracer youve chosen is
  adequate for the kind of information you intend
  to extract.
• Assumption that the velocity dispersion is
  isotropic.
• Assumption of a model for the dark matter halo
• Only get lower limits to the halo mass, since
  there may not be test particles available to
  probe the full distribution.

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CDM Problems Underlying Uncertainties

• Velocity dispersions and CDM halos are almost
  certainly not isotropic
• Tidal interactions will have an effect on
  measured velocity dispersions
• Models are often empirical/phenomenological,
  rather than being based on first physical
  principles
• Issues of resolution (i.e. beam smearing) limits
  the usefulness of model fitting
• Large problem in HI less so in Ha and CO
  long-slit optical spectra

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CDM Problems Cusps vs. Cores

• Detailed simulations of CDM halos find that the
  density profiles are steeply cusped, with mass
  density in the inner parts of the halo r-a, a1
• Appears in simulations to hold from dwarf galaxy
  to cluster scales.

General Form
NFW profile with a1
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CDM Problems Cusps vs. Cores

• More recent simulations allow a1.2-1.5
• Observations of dwarf galaxies find that halos
  have shallow (cored) profiles with a 0.2-0.5
  cusp/core crisis
• Note that the cusp/core problem can be solved by
  invoking exotic dark matter, but this creates
  problems all its own.

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CDM Problems Cusps vs. Cores

• Observational evidence suggests there may be no
  universal profile
• Simon et al. 2005 find that the scatter in a is
  much larger than in simulations
• Mass model degeneracies

Grey points original rot curve. Black points
stellar disk subtracted. NFW power-law fits
are similar. Here, pseudo-isothermal fit is
inferior, but is often a better fit.
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CDM Problems Cusps vs. Cores

• Caveats not that easy to compare theory to
  observation
• Beam smearing will tend to systematically lower
  slopes.
• Error bars are large enough so that cores are
  favored but cusps can usually not be ruled out
  (Hayashi et al. 2004)
• the radial range over which NFW fitting
  formulae have been validated often does not
  coincide with the scales where the disagreement
  has been identified.

• Dark matter halos are likely triaxial work is
  moving in that direction. Hayashi et al.
  simulated triaxial haloes with NFW profiles, then
  observed them, and found that cores were
  observed about 25 of the time.

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CDM Paradigm Major Questions

• What is the dark matter??
• Having no idea means that the presumed existence
  and distribution of dark matter is highly
  degenerate with the assumed laws of gravity
  (Sanders 2002).

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Introduction to MOND

• What is MOND?
• Proposed by Moti Milgrom in 1983 to explain flat
  rotation curves without resorting to dark matter

Example of a MOND fit to a galaxy rot. curve
(McGaugh)
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Introduction to MOND

• What is MOND?
• Applies only at very low accelerations single
  parameter a0 2 x 10-8 cm sec-2.
• Modifies gravity by changing the Poisson
  equation, or breaks the equivalence between
  inertial and gravitational mass

MOND
For small accs
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Introduction to MOND

• FAQs (from Stacy McGaughs MOND pages)
• Isnt it drastic to modify such a fundamental law
  as gravity?
• Sure. Just as it is drastic to fill the universe
  with non-baryonic cold dark matter consisting of
  new fundamental particles we dont actually know
  to exist. The data drive us to one of these
  extremes.
• Why is the modification based on acceleration?
• Length doesnt work. If gravity were modified at
  large length scales, then bigger galaxies would
  have a bigger mass discrepancy! (Sanders 2002)

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Introduction to MOND

• Pros
• Explains the asymptotic flatness of rotation
  curves
• Is a truly falsifiable theory
• MOND can only fit one particular shape for a
  rotation curve (single parameter theory)
• A single example of a galaxy in the MOND regime
  that exactly followed Newtonian dynamics would
  bust MOND.

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Introduction to MOND

• Pros
• Explains the slope of the Tully-Fisher relation,
  M AVflat4

Squares vcW20/2 Circles vcvflat Bothum et al
1995 Verheijen et al 1997 Eder Schombert
2000 McGaugh de Blok 1998 Matthews et al 1998
Baryonic T-F (McGaugh)
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Introduction to MOND

• Pros
• Explains the slope of the Tully-Fisher relation,
  M AVflat4

In MOND, the TF relationship is absolute,
independent of length scale or surface
brightness, and the slope has to be precisely
4.0. However, this relationship uses the
asymptotic flat rotational velocity, not the peak
rotation velocity.
Squares vcW20/2 Circles vcvflat Bothum et al
1995 Verheijen et al 1997 Eder Schombert
2000 McGaugh de Blok 1998 Matthews et al 1998
Baryonic T-F (McGaugh)
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Introduction to MOND

• Cons
• In some cases like rich clusters, and the
  recent measurement of the Bullet Cluster MOND
  proponents must admit that at least some dark
  matter is present
• And baryonic dark matter is required by
  primordial nucleosynthesis CMB constraints
• Difficult to find a general relativistic MOND
• MOND may in fact just be a way of summarizing
  actual relationships between the dark baryonic
  matter distributions in the Universe.

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MOND Predictions for Dwarf Galaxies

• Little guys at the bottom left (triangles are
  dSphs)
• Solid line shows MOND-predicted relationship for
  a0 10-8 cm s-2 dashed lines are 5x and
  one-fifth

• Sanders McGaugh (2002)
• Velocity dispersion vs. model-dependent
  characteristic radius for pressure-supported
  systems.

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MOND Predictions for Dwarf Galaxies Low Mass
Spirals

• Milgrom Sanders, 2007
• MOND found success with massive spirals, and
  low-mass counterparts (with increasing pressure
  support) probe another regime
• Additionally, in small objects (with small
  accelerations), inclination and distance affect
  only the normalization (not the shape!) of the
  MOND curve

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Low Mass Spirals

• Points are rotation curve (from 21 cm obs)
• Solid line MOND rotation curve
• Dotted/dashed Newtonian rotation curves for
  stars/gas
• MOND curves predicted by

Where aN is the Newtonian a that would be
calculated from the mass distribution, assuming
M/L and a good measurement of distance (for HI
mass)
Milgrom Sanders, 2007
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MOND Predictions for Dwarf Galaxies UCDs

• Because these systems are so compact, one would
  expect that the acceleration due to the
  gravitational potential would be everywhere
  greater than a0.
• Predicts that UCDs should exhibit no mass
  discrepancy (Scarpa) direct test of the
  difference between CDM and MOND
• Prediction has been satisfied thus far, but
  further observations of UCDs are needed.

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MOND Predictions for Dwarf Galaxies UCDs
If intermediate mass UCDs were found, they
might resemble nucleated dwarfs, but be smaller,
simpler, and more regular. In that case, we may
be able to probe the region of the switchover
from Newtonian to MONDian dynamics.
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Dark Matter vs. MOND Local Group dSphs

• MOND changes the tidal effect that a galaxy like
  the Milky Way has on its satellites. The external
  field of the host galaxy has a very large
  impact on dynamical mass estimates from velocity
  dispersions
• Must introduce a measurement of isolation, h
  ratio of a systems internal acceleration to the
  external tidal pull.
• For isolated, spherically symmetric, low density
  objects

Sanders McGaugh, 2002
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Dark Matter vs. MOND Local Group dSphs

• For objects dominated by galactic fields use
  Newtonian estimate, but multiply the
  gravitational constant by
• Figure estimates of mass-to-light ratios as a
  function of h using the MOND formalism. Is
  improving with time.

Sanders McGaugh, 2002
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Dark Matter vs. MOND Local Group dSphs

• Lokas (2001) comparison of dark matter and MOND
  for the Fornax dSph
• Take-home message very difficult to distinguish
  the two with the data currently available
• Dark matter model gives a reasonable 1.5 x 109
  Msun
• MOND model requires a0 2.1 x 10-8 cm s-2, in line
  with MOND paradigm

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Summary

• Uncertainties and modeling degeneracies leave CDM
  MOND on equally firm footing.
• CDM struggles to answer questions of galaxy
  formation, including missing satellites, cusps
  vs. cores, and structure in voids.
• MOND struggles to convince us that a modification
  of gravity is not only called for, its less
  drastic than a modification of matter.

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References

• Hayashi, E. et al. astro-ph/0408132
• Lokas, E.L. 2001, MNRAS, 327, L21.
  astro-ph/0107479
• Mateo, M. 1998, ARAA, 36, 435-506.
• Stacy McGaughs MOND pages, http//www.astro.umd.e
  du/ssm/mond
• Milgrom, M., Sanders, R.H. 2007, ApJ, 658, L17
• Penarrubia, J., McConnachie, A., Navarro, J.F.
  ApJ (submitted). Astro-ph/0701780
• Sanders, R.H., McGaugh, S.S. 2002, ARAA, 40,
  263
• Scarpa, R. astro-ph/0504051
• Simon, J.D., Bolatto, A.D., Leroy, A., Blitz, L.,
  Gates, E.L. 2005, ApJ, 621, 757
• Swaters, R.A., Madore, B.B, van den Bosch, F.C.,
  Balcells, M. 2003, ApJ, 583, 732