Skip to main content# 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

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 (*M*_{BH}) are highly correlated with circumgalactic gas temperature (*T*_{CGM}), following

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

with an intrinsic scatter of only 0.21 in log *M*_{BH}. This correlation is the strongest one that Gaspari et al. found, with even less scatter than the relationship between *M*_{BH} and central stellar velocity dispersion (

Interestingly, the observed *M*_{BH}–*T*_{CGM} 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 (*E*_{CGM}) 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 (*M*_{500}) and X-ray gas temperature (

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

among halos with masses in the *T*_{X} , and so the energy required to significantly lift a halo’s baryons scales as

$E_{\rm CGM} \, \propto \, M_{500} T_{\rm X} \, \propto \, T_{\rm X}^{2.7}$

for halos in this mass range.

The similarity in power-law slope between the *M*_{BH}–*T*_{CGM} relation and *E*_{CGM}–*T*_{X} relation strongly suggests that *M*_{BH} is indeed directly proportional to *E*_{CGM}. One subtlety is that *T*_{CGM} and *T*_{X} are usually similar but are not identical.2 However, equating them yields a simple numerical constant that connects *M*_{BH} to *E*_{CGM}. The dashed blue line in the figure shows the *M*_{BH}–*T*_{CGM} relation obtained by assuming

Presumably, the similarity of that *M*_{BH}–*T*_{CGM} 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 (*E*_{SN,central}) falls far below *E*_{CGM} in halos more massive than *all* of a halo’s stars (*E*_{SN,halo}) likewise falls short of *E*_{CGM} in halos more massive than

One final feature to note about the plot is the orange dashed line (labeled *L*_{X}/*H*_{0}) representing an estimate of the total radiative energy losses from these atmospheres. It falls far below the blue dashed line indicating *E*_{CGM}, implying that black hole feedback on group scales puts far more energy into atmospheric lifting than into replenishing radiative losses.