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### Alternative gravity vs. CDM

Jerry Sellwood

Settling the argument

- Requires clear predictions that distinguish one from the other
- consistency with one or the other is not enough if both make similar predictions
- Alternative gravity is more easily falsifiable
- e.g. Milgrom predicted TFR for LSBs
- not yet regarded as decisive by the CDM folks
- but predictions must be well-worked out!

WMAP 3-year data

- Rules out all no DM models?
- No!

Falsifiable predictions of AG

- Baryonic mass should be correlated with dynamical mass. Vulnerable to:
- one rogue galaxy rotation curve
- similar light distributions with very diff. M/L
- etc.
- The shape of luminous matter should be reflected in the shape of the mass
- no misalignments or offsets, etc.

Other concerns

- Galaxy clusters
- Dwarfs & globular clusters
- Dynamical friction and galaxy mergers
- ….

Challenging CDM

- Gauntlet already thrown down:
- TFR for LSBs
- Why does MOND work?
- Issues involving gastrophysics are too murky
- Somewhat firm predictions of DM halos
- cusp/core issue – still no surrender!
- absolute density scale
- But target just moved!
- baryon/dark mass fraction
- tilted or running spectral index

The greatest challenge to CDM

- Spherically averaged density of dark matter halos seems to approximate the form:

(r) = s rs3 / [r(r+rs)3-]

- i.e. a broken power law, with 1 < < 1.5
- = 1

is “NFW”

Concentration

- s is directly related to the concentration parameter

c = r200/rs

- c correlates with mass – halos are predicted to be a 1-parameter family (e.g. Bullock et al.)

Halo density

- Dark matter halos are not as dense as predicted
- Plot from Alam et al.
- v/2 is the mean density inside the radius at which the DM rotation curve reaches vmax/2
- Points are estimates from real galaxies
- Heavy curve is for NFW and standard CDM

Tilted or running power spectrum

- Zentner & Bullock (2002):
- Lower values of v/2predicted
- by about a factor 10 in their most extreme model (n.b. 8 0.65)

1 practical difficulty

- How much mass should be assigned to the stars?
- Disk-halo degeneracy
- Low surface-brightness galaxies and dwarfs are more dominated by DM

Magnitude of discrepancy

- Weiner’s work gets around uncertainty in M/L
- Milky Way similar (Binney & Evans 2001)
- Better data are in worse agreement
- Halos are under-dense by factor

> 30 for n=1 models

> 5 for extreme tilted power spectra

- assumes =1 and ignores compression!

Effect of halo compression

- Conservative values:
- NFW halo
- baryon fraction fb=0.05
- disk scale: rs/Rd=5
- Value of v/2 increased by factor 4
- In Weiner’s cases, it would be a factor > 30

(decompression is hard)

Bar-halo friction

- Consistent with Debattista’s work on dynamical friction
- Rlast is Rc/aB when the simulation was stopped
- Rc/aB > 1.4 quickly in high-concentration models
- Bars stay fast for 30 disk rots only if c < 6

Reduce DM density?

- Feedback – Gnedin & Zhao
- points vs. dashed
- maximum possible effect – factor 2
- for a disk of reasonable size

Reduce DM density?

- Feedback – Gnedin & Zhao
- Binary BHs – Milosavljevic & Merritt
- DM particles ejected as the binary hardens
- removes about as much mass as the BHs
- but only to a radius of a few hundred pc

Reduce DM density?

- Feedback – Gnedin & Zhao
- Binary BHs – Milosavljevic & Merritt
- Bars – Weinberg & Katz

Bar-halo interaction

- Holley-Bockelmann, Weinberg & Katz (2005)
- Smaller changes reported by Weinberg & Katz (2006)
- argue problem is very challenging numerically

Density reductions

- 5 skinny, massive bars of different lengths
- flatten the cusp to about 1/3 bar length
- interesting, but unreasonable bar required

Rapid convergence with N

- Use the shortest bar
- 104 N 107
- dotted curve for unequal mass particles
- Number of terms in expansion, fine grid, etc. all make no diff.
- No evidence to support WK05 worries

Weaker bars

- Flattening of the cusp occurs only for bars that are both
- strong: axis ratio 4:1 or greater, and
- massive: Mb > 40% of enclosed halo mass
- Sudden change in density – a collective effect
- Smaller and more gradual density change for slightly weaker bars – but over a greater radial range

Maximum effect

- Rigid bar highly artificial
- increase MoI by factor 5
- more significant density reduction
- Reduction in v/2 is only by 39% in most extreme case
- Angular momentum transferred: 0.01
- i.e. most of that in the baryons
- And this was for a huge bar (a = rs)

Conclusions

- Best data on halos in galaxies indicate densities lower than LCDM prediction by factor >10
- assumes =1 and neglects compression
- No internal dynamical mechanism can reduce the density by much
- maximum 40% for most extreme bars
- results from careful simulations can be trusted
- Simply cannot unbind the halo
- not enough energy can be extracted from the baryons
- trying to make the tail wag the dog!

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