Estimate * the Total Mechanical Feedback Energy in Massive Clusters

1. Estimate* the Total Mechanical Feedback Energyin Massive Clusters Bill Mathews & Fulai Guo University of California, Santa Cruz *~ ±15-20% version 2

2. estimate feedback energy from potential energy of gas after each feedback heating event cluster 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 redshift without: 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

3. why this works: (1) NFW dark halo and adiabatic gas grow from inside out constant-mass radii during halo formation cluster potential ( r) remains constant within rv(t) Diemand+07 (2) PE is integrated from inside out cluster gas density totalclusterpotential

4. observed gas profiles in relaxed clusters tot observed gas fraction fg = g/tot g consider pairs of similar galaxies: Vikhlinin+06

5. compare NFW and adiabatic cluster gas profiles entropy  dispersion  density  dm Sdm ~ r1.2 dm dm gas Sg ~ r1.2 gas gas dmfb/(1-fb) NFW g Faltenbacher+07 using GADGET2 beyond small core, gas density is NFW: g = fbt gas entropy: Sg = gg g = [3kT/mp]1/2 (thermal dispersion) dark matter entropy: Sdm = dmdm dm = 3D velocity dispersion Sg = (0.70 +/- 0.25) Sdm (Faltenbacher+07) Sg ≈ Sdm => gas and dm experience identical gravitational dissipation

6. adiabatic cluster gas profiles grid-based adiabatic cosmogical simulations mix more and have larger density cores in cluster gas dm adopt two limiting assumptions for adiabatic g( r): universal baryon (1) no core: fraction g( r) = fbt,nfw( r) fb = 0.17 (2) with core: g( r) = c( r)fbt,nfw( r) g NFW Vazza 11 total cluster density

7. adiabatic cluster atmosphere (without density core) total NFW cluster profile t( r) for observed Mv and c(Mv)

8. adiabatic cluster atmosphere ignoring density core, adiabatic gas profile is scaled NFW ( r) = fbt( r) = 0.17t( r) ( r) contains all information about dissipative entropy-increasing events in filaments, accretion shock, and mergers

9. adiabatic cluster atmosphere using ( r) = fbt( r), integrate hydrostatic equation for temperature  and entropy S: (a point-slope boundary value problem) entropy Sad( r) ~ r1.2 a uniform slope near rvir is the boundary condition, but its value is not imposed in advance.

10. observed cluster atmosphere gas fraction for composite cluster 2 (A478 & A1413) obs( r) = fg(r )t,nsf( r) (Vikhlinin+06)

11. observed cluster atmosphere fit to observed gas density profile:

12. observed cluster atmosphere using obs( r) integrate again for observed gas temperature ( r) and entropy Sobs( r) which resembles observations: Sad( r) Pratt+10

13. how to recover universal adiabatic Sad( r) ~ r1.2 from Sobs( r) (assume no significant heating by recent feedback) Pratt+10 Sobs( r) is more sensitive to low  (from old feedback) than high T (from recent feedback heating)

14. small effect of core in adiabatic density ad( r) total feedback energy is similar, with or without core

15. total feedback energy |PE| ≈ 1-3 x 1063 ergs obs or ad Mv = 4x1014 rv = 1.9 Mpc Mv = 1x1015 rv = 2.7 Mpc gas outflow due to feedback (spreads metals) 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)

16. 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)

17. estimated feedback stops cooling flows! rate that unheated gas cools and flows in at rcool: (unrelated to feedback estimate) cluster (1,2) 2 1

18. 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 2 cluster (1,2) 1 2 an excellent independent check of feedback estimate 1 M( r) tcl < 1% of feedback energy is deposited inside rcool

19. other recent Guo-Mathews feedback results: theory for expanding radio lobes in Virgo -- explains bright radio rims dynamical jet models of -ray emitting Fermi bubbles in Milky Way b (degrees) 10 kpc l (degrees) Galactic coords. VLA 90 cm projected image of (electron) cosmic ray energy density -- with viscosity in co-mixed plasma and CR diffusion

20. 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

21. other recent Guo-Mathews feedback results: Smooting effect of CR diffusion, increasing from left to right top 3 images: unprojected CR energy density in kpc kpc b (degrees) bottom 3 images: projected CR energy density in Galactic coords. (viscosity held constant)