1 / 41

Entropy in the ICM

Michael Balogh

University of Durham

Institute for Computational Cosmology University

of Durham

Collaborators

- Mark Voit (STScI -gt Michigan)
- Richard Bower, Cedric Lacey (Durham) Greg Bryan

(Oxford) - Ian McCarthy, Arif Babul (Victoria)

Outline

- Review of ICM scaling properties, and the role of

entropy - Cooling and heating
- The origin of entropy
- Lumpy vs. smooth accretion and the implications

for groups

ICM Scaling properties

Luminosity-Temperature Relation

If cluster structure were self-similar, then we

would expect L ? T2 Preheating by supernovae

AGNs?

Mass-Temperature Relation

Cluster masses derived from resolved X-ray

observations are inconsistent with

simulations Another indication of preheating?

M ? T1.5

Entropy A Review

Definition of S DS D(heat) / T Equation of

state P Kr5/3 Relationship to S S N ln K3/2

const. Useful Observable Tne-2/3 ? K

Characteristic Scale Convective

stability dS/dr gt 0 Only radiative cooling can

reduce Tne-2/3 Only heat input can raise Tne-2/3

T200

K200

mmp (200fbrcr)2/3

Dimensionless Entropy From Simulations

Simulations without cooling or feedback show

nearly linear relationship for K(Mgas) with Kmax

K200 Independent of halo mass

(Voit et al. 2003)

Simulations from Bryan Voit (2001)

Halos 2.5 x 1013 - 3.4 x 1014 h-1 MSun

Entropy profiles

Scaled entropy (1z)2 T-0.66 S

Scaled entropy (1z)2 T-1 S

Radius (r200)

Radius (r200)

Entropy profiles of Abell 1963 (2.1 keV) and

Abell 1413 (6.9 keV) coincide if scaled by T0.65

Pratt Arnaud (2003)

Heating and Cooling

Preheating?

Isothermal model

M1015 M0

Preheated gas has a minimum entropy that is

preserved in clusters Kaiser (1991) Balogh et

al. (1999) Babul et al. (2002)

Ko400 keV cm2

300

200

100

Balogh, Babul Patton 1999 Babul, Balogh et al.

2002

10

Preheated model

Ko400 keV cm2

kT keV

1

Isothermal model

0.1

40

42

44

46

log10 LX ergs s-1

Does supernova feedback work?

Consider the energetics for 1011 Msun of gas

- Local SN rate 0.002/yr (Hardin et al. 2000

Cappellaro et al. 1999) - An average supernova event releases 1044 J
- Assuming 10 is available for heating the gas

over 12.7 Gyr, total energy available is 2.5x1050

J - This corresponds to a temperature increase of

5x104 K - To achieve a minimum entropy K0 ? T/r2/3
- r/ravg 0.28 (K0/100 keV cm2)-3/2

SN energy too low by at least a factor 50

Core Entropy of Clusters Groups

Core entropy of clusters is ? 100 keV cm2 at

r/rvir 0.1

Entropy Floor

Self-similar scaling

Ponman et al. 1999

Entropy Threshold for Cooling

Each point in T-Tne-2/3 plane corresponds to a

unique cooling time

Entropy Threshold for Cooling

Entropy at which tcool tHubble for 1/3

solar metallicity is identical to observed

core entropy!

Voit Bryan (2001)

Entropy History of a Gas Blob

Gas that remains above threshold does not cool

and condense. Gas that falls below threshold is

subject to cooling and feedback.

no cooling, no feedback

cooling feedback

Voit et al. 2001

Entropy Threshold for Cooling

Updated measurements show that entropy at 0.1r200

scales as K0.1 ? T 2/3 in agreement with

cooling threshold models

Voit Ponman (2003)

L-T and the Cooling Threshold

10

kT keV

1

0.1

40

42

44

46

log10 LX ergs s-1

Also matched by preheated, isentropic cores

Gas below the cooling threshold cannot persist

Balogh, Babul Patton (1999) Babul, Balogh et

al. (2002)

Voit Bryan (2001)

L-T and the Cooling Threshold

10

kT keV

1

0.1

40

42

44

46

log10 LX ergs s-1

Also matched by preheated, isentropic cores

Gas below the cooling threshold cannot persist

Balogh, Babul Patton (1999) Babul, Balogh et

al. (2002)

Voit Bryan (2001)

Mass-Temperature relation

Both pre-heating and cooling models adequately

reproduce observed M-T relation

? Reiprich et al. (2002) Babul et al.

(2002) Voit et al. (2002)

The overcooling problem

Observations imply W/Wb ? 0.05

fcool

Fraction of condensed gas in simulations is

much larger, depending on numerical resolution

Observed fraction

1

10

kT (keV)

Balogh et al. (2001)

Heating-Cooling Tradeoff

Many mixtures of heating and cooling can explain

L-T relation If only 10 of the baryons are

condensed, then 0.7 keV of excess energy implied

in groups

Voit et al. (2002)

Heating Cooling

Start with Babul et al. (2002) cluster models,

which have isentropic cores Allow to cool for

time t in small timesteps, readjusting to

hydrostatic equilibrium after each step Develops

power-law profile with K ? r1.1

McCarthy et al. in prep

Entropy profiles of CF clusters

Observed cooling flow clusters show entropy

gradients in core Well matched by dynamic

cooling model from initially isentropic core

Model

Observations

McCarthy et al. in prep

Simple coolingheating models

Data from Horner et al., uncorrected for cooling

flows

McCarthy et al. in prep

Simple coolingheating models

Data from Horner et al., uncorrected for cooling

flows Non-CF clusters well matched by preheated

model of Babul et al. (2002) CF cluster

properties matched if gas is allowed to cool for

up to a Hubble time

McCarthy et al. in prep

The origin of entropy

Voit, Balogh, Bower, Lacey Bryan

ApJ, in press

astro-ph/0304447

Important Entropy Scales

Characteristic entropy scale associated with halo

mass M200

v2acc

Entropy generated by accretion shock

Ksm

3 (4rin)2/3

(Mt)2/3

?

(d ln M / d ln t)2/3

Dimensionless Entropy From Simulations

How is entropy generated initially? Expect

merger shocks to thermalize energy of accreting

clumps But what happens to the density?

(Voit et al. 2003)

Simulations from Bryan Voit (2001)

Halos 2.5 x 1013 - 3.4 x 1014 h-1 MSun

Smooth vs. Lumpy Accretion

SMOOTH

LUMPY

Smooth accretion produces 2-3 times more entropy

than hierarchical accretion (but similar profile

shape)

Voit et al. 2003

Preheated smooth accretion

- If pre-shock entropy K1Ksm, gas is no longer

pressureless

K2 Ksm 0.84K1, for Ksm/K1 0.25

0.84K1

Note adiabatic heating decreases post-shock

entropy

Lumpy accretion

- Assume all gas in haloes with mean density Dfbrcr
- K(t) (r1/ Dfbrcr)2/3 Ksm(t)
- 0.1 Ksm(t)
- Two solutions K ? vin2/r
- 1. distribute kinetic energy through turbulence

(i.e. at constant density) - 2. vsh 2 vac (i.e. if shock occurs well within

R200)

Preheating and smooth accretion

M(to)1013h-1Mo

Kmod

Ksm

K1

K200

Kc(T200)

Early accretion is isentropic leads to

nearly-isentropic groups

Voit et al. 2003

Entropy gradients in groups

Entropy in groups

Scaled entropy (1z)2T-0.66S

Scaled entropy (1z)2T-1S

Radius (r200)

Radius (r200)

Entropy profiles of Abell 1963 (2.1 keV) and

Abell 1413 (6.9 keV) coincide if scaled by

T0.65 Cores are not isentropic

Pratt Arnaud (2003)

Excess entropy in groups

Entropy measured at r500 ( 0.6r200) exceeds

the amount hierarchical accretion can generate by

hundreds of keV cm2

Entropy gradients in groups

Mo51013 h-1 Mo

Lx/T3lum (1042 h-3 erg s-1 keV-3

0.1 1 10

0.1 1 10 1000

Lx/T3lum (1042 h-3 erg s-1 keV-3

geff5/3

geff1.2

1 10

100 1000

Tlum (keV)

K(0.1r200) keV cm2

Voit et al. 2003

Excess entropy at R200

Entropy gradients in groups with elevated core

entropy naturally leads to elevated entropy at

R200

geff 1.2

geff 1.3

Voit et al. 2003

Excess Entropy at R500

Entropy measured at r500 ( 0.6r200) exceeds

the amount hierarchical accretion can generate by

hundreds of keV cm2

Smooth accretion on groups?

- Groups are not isentropic, but do match the

expectations from smooth accretion models - Relatively small amounts of preheating may eject

gas from precursor haloes, effectively smoothing

the distribution of accreting gas. - Self-similarity broken because groups accrete

mostly smooth gas, while clusters accrete most

gas in clumps

Conclusions

- Feedback and cooling both required to match

cluster properties and condensed baryon fraction - Smooth accretion models match group profiles
- Difficult to generate enough entropy through

simple shocks when accretion is clumpy - Similarity breaking between groups and clusters

may be due to the effects of preheating on the

density of accreted material