Entropy in the ICMEntropy in the ICM

Institute for Computational CosmologyUniversity of Durham

University of Durham

Michael Balogh

CollaboratorsCollaborators

• Mark Voit (STScI -> Michigan)– Richard Bower, Cedric Lacey

(Durham) Greg Bryan (Oxford)

• Ian McCarthy, Arif Babul (Victoria)

OutlineOutline

• 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 propertiesICM Scaling properties

Luminosity-Temperature Luminosity-Temperature RelationRelation

If cluster structure were self-similar, then we would expect L T2

Preheating by supernovae & AGNs?

Mass-Temperature Mass-Temperature RelationRelation

Cluster masses derived from resolved X-ray observations are inconsistent with simulations

Another indication of preheating?

M

T1.

5

Definition of S: S = (heat) / T Equation of state: P = K5/3

Relationship to S: S = N ln K3/2 + const.

Useful Observable: Tne-2/3 K

Characteristic Scale:

Convective stability: dS/dr > 0

Only radiative cooling can reduce Tne-2/3

Only heat input can raise Tne-2/3

Entropy: A ReviewEntropy: A Review

K200 =T200

mp (200fbcr)2/3

Dimensionless Entropy From Dimensionless Entropy From SimulationsSimulations

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 profilesEntropy profiles

Entropy profiles of Abell 1963 (2.1 keV) and Abell 1413 (6.9 keV) coincide if scaled by T0.65

Sca

led

en

trop

y: (

1+

z)2

T-1

S

Sca

led

en

trop

y: (

1+

z)2

T-0

.66

SRadius (r200) Radius (r200)

Pratt & Arnaud (2003)

Heating and CoolingHeating and Cooling

Preheating?Preheating?

Preheated gas has a minimum entropy that is preserved in clusters

Kaiser (1991)

Balogh et al. (1999)

Babul et al. (2002)

Isothermal modelM=1015 M0

Ko=400 keV cm2

300

200

100

Balogh, Babul & Patton 1999Babul, Balogh et al. 2002

log10 LX [ergs s-1]

kT [k

eV

]10

1

0.140 42 44 46

Isothermal model

Preheated modelKo=400 keV cm2

Does supernova feedback Does supernova feedback work?work?

• 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/2/3:

/avg = 0.28 (K0/100 keV cm2)-3/2

Consider the energetics for 1011 Msun of gas:

SN energy too low by at least a factor ~50

Core Entropy of Clusters & Core Entropy of Clusters & GroupsGroups

Core entropy of clusters is 100 keV cm2

at r/rvir = 0.1

Self-similar scaling

Entropy “Floor”

Ponman et al. 1999

Entropy Threshold for CoolingEntropy Threshold for Cooling

Each point inT-Tne

-2/3 planecorresponds to a uniquecooling time

Entropy Threshold for CoolingEntropy Threshold for Cooling

Entropy at which

tcool = tHubble

for 1/3 solarmetallicity is identical toobserved coreentropy!

Voit & Bryan (2001)

Entropy History of a Gas Entropy History of a Gas BlobBlob

no cooling, no feedback

cooling & feedback

Gas that remains above threshold does not cool and condense.

Gas that falls below threshold is subject to cooling and feedback.

Voit et al. 2001

Entropy Threshold for CoolingEntropy 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 L-T and the Cooling ThresholdThreshold

Gas below the cooling threshold cannot persist

Voit & Bryan (2001)Balogh, Babul & Patton (1999)Babul, Balogh et al. (2002)

log10 LX [ergs s-1]

kT [k

eV

]

10

1

0.1

40 42 44 46

Also matched by preheated, isentropic cores

L-T and the Cooling L-T and the Cooling ThresholdThreshold

Gas below the cooling threshold cannot persist

Voit & Bryan (2001)Balogh, Babul & Patton (1999)Babul, Balogh et al. (2002)

log10 LX [ergs s-1]

kT [k

eV

]

10

1

0.1

40 42 44 46

Also matched by preheated, isentropic cores

Mass-Temperature Mass-Temperature relationrelation

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 problemThe overcooling problem

Balogh et al. (2001)

Observations imply */b 0.05

f co

ol

0.1

0.6

0.5

0.4

0.3

0.2

Fraction of condensed gas in simulations is much larger, depending on numerical resolution

Pearce et al. (2000)

Lewis et al. (2000)

Katz & White (1993)

kT (keV)1 10

Observed fraction

Heating-Cooling TradeoffHeating-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 + CoolingHeating + Cooling

McCarthy et al. in prep

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

Entropy profiles of CF Entropy profiles of CF clustersclusters

McCarthy et al. in prep

Observed cooling flow clusters show entropy gradients in core

Well matched by dynamic cooling model from initially isentropic core

Obser

vatio

ns

Model

Simple cooling+heating Simple cooling+heating modelsmodels

McCarthy et al. in prep

Data from Horner et al., uncorrected for cooling flows

Simple cooling+heating Simple cooling+heating modelsmodels

McCarthy et al. in prep

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

The origin of entropyThe origin of entropyVoit, Balogh, Bower, Lacey & Bryan ApJ, in press astro-ph/0304447

Important Entropy ScalesImportant Entropy Scales

K200 =T200

mp (200fbcr)2/3

Characteristic entropy scale associated with halo mass M200

Ksm =v2

acc

(4in)2/3

Entropy generated by accretion shock

(Mt)2/3

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

Dimensionless Entropy From Dimensionless Entropy From SimulationsSimulations

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 AccretionSmooth vs. Lumpy Accretion

Smooth accretion produces ~2-3 times more entropy than hierarchical accretion(but similar profile shape)

SMOOTH

LUMPY

Voit et al. 2003

Preheated smooth Preheated smooth accretionaccretion

• If pre-shock entropy K1≈Ksm, gas is no longer pressureless

=(M2-1)2

M2

48/3Ksm

5 K1

K2 ≈ Ksm + 0.84K1, for Ksm/K1» 0.25

+ 0.84K1 vin

2

3(41)2/3 ≈

Note adiabatic heating decreases post-shock entropy

Lumpy accretionLumpy accretion

• Assume all gas in haloes with mean density fbcr

K(t) ≈ (1/ fbcr)2/3 Ksm(t)

≈ 0.1 Ksm(t)

Two solutions: K vin2/

1. distribute kinetic energy through turbulence (i.e. at constant density)

2. vsh ≈ 2 vac (i.e. if shock occurs well within R200)

Entropy gradients in Entropy gradients in groupsgroups

Entropy in groupsEntropy in groups

Entropy profiles of Abell 1963 (2.1 keV) and Abell 1413 (6.9 keV) coincide if scaled by T0.65

Cores are not isentropic

Sca

led

en

trop

y (1

+z)

2T

-1S

Sca

led

en

trop

y (1

+z)

2T

-0.6

6S

Radius (r200) Radius (r200)

Pratt & Arnaud (2003)

Excess entropy in groupsExcess entropy in groups

Entropy “measured” at r500 (~ 0.6r200) exceeds the amount hierarchical accretion can generate by hundreds of keV cm2

Entropy gradients in Entropy gradients in groupsgroups

1 10 0.1

1

1

0

Tlum (keV)

Lx/

T3

lum (

10

42 h

-3 e

rg s

-1 k

eV

-3

Lx/

T3

lum (

10

42 h

-3 e

rg s

-1 k

eV

-3

Mo=5×1013 h-1 Mo

eff=5/3

eff=1.2

100 1000

0

.1

1

10

1

00

0

K(0.1r200) keV cm2

Voit et al. 2003

Excess entropy at RExcess entropy at R200200

Entropy gradients in groups with elevated core entropy naturally leads to elevated entropy at R200

Voit et al. 2003

eff = 1.2

eff = 1.3

≈ 2.6K(R200)

K200

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

≈ 3.5 for 1013 h-1Mo

≈ 1.7 for 1015 h-1Mo

Excess Entropy at RExcess Entropy at R500500

Entropy “measured” at r500 (~ 0.6r200) exceeds the amount hierarchical accretion can generate by hundreds of keV cm2

Smooth accretion on Smooth accretion on groups?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

ConclusionsConclusions• 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