Estimate* the Total Mechanical Feedback Energyin Massive Clusters

Bill Mathews & Fulai Guo

University of California, Santa Cruz

*~ ±15-20%

version 2

estimate feedback energy from potential energy of gas

after each feedback heating eventcluster gas expands and feedback energy becomes PE

compare PE of gas between: (1) observed gas profiles in clusters (2) idealized gas profiles in adiabatic clusters

evolved to zero redshiftwithout:

radiative cooling non-gravitational feedback energy star formation

compare PE of (1) and (2) at same Mgas ( r)

this determines feedback energy < r independent of the time when feedback occurred

why this works:(1) NFW dark halo and adiabatic gas grow

from inside out

(2) PE is integrated from inside out

Diemand+07

cluster potential ( r) remains constant within rv(t)

total cluster potentialcluster gas density

constant-mass radiiduring halo formation

observed gas profiles in relaxed clusters

Vikhlinin+06

observed gas fraction fg = g/tot

tot

g

consider pairs of similar galaxies:

compare NFW and adiabatic cluster gas profiles

density dispersion entropy

Faltenbacher+07 using GADGET2

dmfb/(1-fb)

g

beyond small core, gas density is NFW: g = fbt

gas entropy: Sg = gg

g = [3kT/mp]1/2 (thermal dispersion)

dark matter entropy: Sdm = dmdm

dm = 3D velocity dispersion

Sdm ~ r1.2

Sg ~ r1.2

Sg = (0.70 +/- 0.25) Sdm (Faltenbacher+07)Sg ≈ Sdm => gas and dm experience identical gravitational dissipation

NFW

dm dm dm

gas gas gas

adiabatic cluster gas profiles

g

dm

grid-based adiabatic cosmogical simulations mix more and have larger density cores in cluster gas

Vazza 11

adopt two limiting assumptions for adiabatic g( r): universal baryon (1) no core: fraction

g( r) = fbt,nfw( r) fb = 0.17 (2) with core:

g( r) = c( r)fbt,nfw( r)

NFW

total cluster density

adiabatic cluster atmosphere (without density core)

total NFW cluster profile t( r) for observed Mv and c(Mv)

adiabatic cluster atmosphere

ignoring density core,adiabatic gas profile is scaled NFW ( r) = fbt( r) = 0.17t( r)

( r) contains all information about dissipative entropy-increasing events

in filaments, accretion shock, and mergers

adiabatic cluster atmosphere

using ( r) = fbt( r), integrate hydrostatic equationfor temperature and entropy S:

entropy Sad( r) ~ r1.2

(a point-slope boundary value problem)

a uniform slope near rvir is the boundary condition,but its value is not imposedin advance.

observed cluster atmosphere

obs( r) = fg(r )t,nsf( r)(Vikhlinin+06)

gas fraction for composite cluster 2 (A478 & A1413)

observed cluster atmosphere

fit to observed gas density profile:

observed cluster atmosphereusing obs( r) integrate again

for observed gas temperature( r) and entropySobs( r) which resembles observations:

Pratt+10

Sad( r)

how to recover universal adiabatic Sad( r) ~ r1.2 from Sobs( r)

Pratt+10

(assume no significant heating by recent feedback)

Sobs( r) is more sensitive to low (from old feedback)than high T (from recent feedback heating)

total feedback energy is similar, with or without core

small effect of core in adiabatic density ad( r)

total feedback energy |PE| ≈ 1-3 x 1063 ergs

Mv = 4x1014

rv = 1.9 MpcMv = 1x1015

rv = 2.7 Mpc

1063 ergs = 5 x 108 Msun c2 is huge!Lmech ≈ 1046 erg/s over tcl = 7 Gyrs

from central black hole?is spin energy needed? (McNamara+09)

obs or ad

gas outflow due to feedback(spreads metals)

review some assumptions for clusters (1,2):

1. ignore stellar baryon fraction f* :

for massive clusters (1,2) f* = 0.01 is small (Andreon10)

total stellar mass r < r500 = (0.25, 0.65)x1013

total gas mass flowing out beyond r500 = (1.9, 3.8)x1013

2. feedback energy ~1063 ergs is from central black hole (a) total supernova energy is small:

ESNII = (0.03, 0.1)x1063 ergs in r < rv

ESNIa = (0.03, 0.1)x1063 ergs in r < rv

(b) energy lost by radiation Erad is small: at cooling radius rcool = (98, 120) kpc cooling time equals age of cluster tcl ~ 7 Gyrs Erad = LX(rcool)tcl = (0.03, 0.1)x1063 ergs

(c ) most energetic known single AGN event is < 1063 ergs E ~ 1062 ergs (McNamara+05)

estimated feedback stops cooling flows!rate that unheated gas cools and flows in at rcool:

cluster (1,2)

2

1

(unrelated to feedback estimate)

estimated feedback stops cooling flows!rate that unheated gas cools and flows in at rcool:

rate that gas flows out at r due to feedback:

tcl = 7 Gyrs

M( r) tcl

an excellent independent checkof feedback estimate

< 1% of feedback energy is deposited inside rcool

cluster (1,2) 2

12

1

other recent Guo-Mathews feedback results:

dynamical jet models of -ray emitting Fermi bubbles in Milky Way

theory for expanding radio lobes in Virgo -- explains bright radio rims

Galactic coords.VLA 90 cm

b (d

egre

es)

l (degrees)

projected image of (electron) cosmic rayenergy density -- with viscosityin co-mixed plasma and CR diffusion

10

kpc

other recent Guo-Mathews feedback results:Six images of (unprojected) CR energy density with increasing viscosity in co-mixed plasma:

viscosity suppresses instabilities and makes IC image uniform

other recent Guo-Mathews feedback results:

Smooting effect of CR diffusion, increasing from left to righttop 3 images: unprojected CR energy density in kpc

bottom 3 images: projected CR energy density in Galactic coords.

(viscosity held constant)

kpc

b (d

egre

es)