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Central Black Hole Mass and Lifting of a Galaxy's Atmosphere

The strong correlation between atmospheric temperature and central black hole mass among massive galaxies is consistent with a linear relationship between black hole mass and the energy required to lift the atmosphere

Published onDec 07, 2022
Central Black Hole Mass and Lifting of a Galaxy's Atmosphere

Black holes at the centers of massive galaxies have masses (MBHM_{\rm BH}) that are highly correlated with circumgalactic gas temperature (kTkT), as shown by the black points (from Gaspari et al. 2019), indicating that AGN feedback tunes the masses of those black holes to the energy output (ECGME_{\rm CGM}) required to significantly lift atmospheric gas out of the halo’s potential well (blue dashed line).

The figure above is from a recent Physics Reports review article by Donahue & Voit (2020) [1]. Its black points come from a study by Gaspari et al. (2019) [2] showing that directly measured black hole masses (MBH) are highly correlated with circumgalactic gas temperature (TCGM), following

MBHM109.4(kTCGM1keV)2.7\frac {M_{\rm BH}} {M_\odot} \approx 10^{9.4} \, \left( \frac{kT_{\rm CGM}} {1 \, {\rm keV}} \right)^{2.7}

with an intrinsic scatter of only 0.21 in log MBH. This correlation is the strongest one that Gaspari et al. found, with even less scatter than the relationship between MBH and central stellar velocity dispersion (σv\sigma_v) among the galaxies in their sample.1

Interestingly, the observed MBHTCGM relation dovetails with the hypothesis that black holes grow until they have released enough energy to counteract accretion, causing cumulative black-hole feedback output to scale with the energy (ECGM) required to lift a massive galaxy’s atmosphere (e.g.,[3][4][5]). That amount of energy can be estimated from the relationship observed between halo mass (M500) and X-ray gas temperature (kTXkT_X)

M500M1013.5(kTX1keV)1.7\frac {M_{500}} {M_\odot} \approx 10^{13.5} \, \left( \frac{kT_{\rm X}} {1 \, {\rm keV}} \right)^{1.7}

among halos with masses in the 1013M10^{13} \, M_\odot to 1014M10^{14} \, M_\odot range [6]. The specific binding energy of a nearly hydrostatic atmosphere scales with TX , and so the energy required to significantly lift a halo’s baryons scales as

ECGMM500TXTX2.7E_{\rm CGM} \, \propto \, M_{500} T_{\rm X} \, \propto \, T_{\rm X}^{2.7}

for halos in this mass range.

The similarity in power-law slope between the MBHTCGM relation and ECGMTX relation strongly suggests that MBH is indeed directly proportional to ECGM. One subtlety is that TCGM and TX are usually similar but are not identical.2 However, equating them yields a simple numerical constant that connects MBH to ECGM. The dashed blue line in the figure shows the MBHTCGM relation obtained by assuming ECGM=102.3MBHc2E_{\rm CGM} = 10^{-2.3} M_{\rm BH} c^2.

Presumably, the similarity of that MBHTCGM line to the observations indicates that ~0.5% of the central black hole’s rest-mass energy has gone into lifting the surrounding CGM. Observations of the gaseous contents of galaxy groups show that something has lifted their atmospheres (e.g., [7]), and no other energy source provides enough energy. For example, the solid red line marking the upper boundary of the pink region shows that the total energy released from the central galaxy’s supernovae (ESN,central) falls far below ECGM in halos more massive than 1013M10^{13} \, M_\odot. Also, the dotted red line representing the total supernova energy from all of a halo’s stars (ESN,halo) likewise falls short of ECGM in halos more massive than 1013.3M\sim 10^{13.3} \, M_\odot.

One final feature to note about the plot is the orange dashed line (labeled LX/H0) representing an estimate of the total radiative energy losses from these atmospheres. It falls far below the blue dashed line indicating ECGM, implying that black hole feedback on group scales puts far more energy into atmospheric lifting than into replenishing radiative losses.

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