Estimate* the Total Mechanical Feedback Energy in Massive Clusters Bill Mathews & Fulai Guo...
-
date post
22-Dec-2015 -
Category
Documents
-
view
213 -
download
0
Transcript of Estimate* the Total Mechanical Feedback Energy in Massive Clusters Bill Mathews & Fulai Guo...
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 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)