A Different Dark Matter Potential for Modeling Cluster Atmospheres

Andisheh Mahdavi

University of Hawai’i

1/0( )n n nGM r r

Why are the shapes of cluster potentials so important?

• N-body simulations predict self-similar dark matter halos

• Shapes of potentials can constrain dark matter physics

• Clusters of galaxies probe dark matter potentials at the very largest scales.

Mass profiles in common use

3

2 20( )

rM

r r

2 20ln( )r r

2 20

2 2 20

(3 / )

( )

r r

r r

“-model” profile

00

ln(1 / )r

M r rr r

0ln(1 / )r r

r

20

1

( )r r r

NFW profile

Not analytic

Not analytic

30

1

( )n nr r r

Generalized cusp

An invertible potential with variable slope

1

001/

0 0

Consider = - ( )

nn n

n n n n n

GM rM M

r r r r

•Has finite mass M0

•Invertible:

•Useful for calculating distribution functions

•Facilitates stellar dynamics modeling

•n=1 corresponds to Hernquist’s model; n=2 gives the Plummer sphere.

An invertible potential with variable slope

2 1/20Density =

nn n nr r r

•Inner slope is 2-n; outer slope is 3+n

•n~1/2 is close to the highest resolution N-body simulations

•Generalizes classical mass profiles, but allows a free shape parameter

Hydrodynamics with the potential

Hydrostatic equilibrium: gP

0/

2 200

Luminosity ( ) diverges.

True of any potential with convergent mass.

pm kT

g

g

e

T r dr

Isothermal solutions:

Hydrodynamics with the potential

Hydrostatic equilibrium: gP

3 /

0

0 0

0 0

3 1

nn nr rg

GM m

r kT

Isothermal solutions: unphysical

Equipartition solutions: kT

Hydrodynamics with the potential

Hydrostatic equilibrium: gP

1/( 1)

0

The equipartition solution is a

polytrope with 1 1/ 3

nn ng r r

gP Equipartition solutions: kT Isothermal solutions: unphysical

Polytropic solutions:

Application

• Are clusters regular outside the very central regions?

• Many are poorly fit by the standard -model profile

• Cooling flows may not always be the cause for the surface brightness peak.

Abell 2550

Conclusion•A new surface brightness formulation is proposed, with an extra free parameter that can be tied to a physical potential

•This profile can fit clusters with rising SB without the need for a divergent power law

•The inferred value of n for Abel 2550 is 0.4, close the what high resolution simulations predict for dark matter halos

•The potential is an invertible generalization of commonly used ones, and so is useful outside X-ray astronomy:

1/0( )n n nGM r r