The impact of superradiance on the spin evolution of variably accreting massive black holes

TL;DR

This work analyzes how temporally varying baryonic accretion affects black-hole spin evolution in the presence of a surrounding axion cloud responsible for superradiance. By coupling a Kerr black hole with an axion cloud growth model and an Eddington-limited accretion framework, the study derives the competition between accretion-driven angular-momentum gain and cloud-driven angular-momentum loss, tracking evolution on the Regge plane. Key findings show that strong accretion boosts prior to the superradiance drop can markedly shrink the exclusion region and shift the drop to higher masses, whereas boosts after the drop mainly produce transient deviations; the extent of impact depends on the axion mass, with lighter clouds being more sensitive. The results imply observable imprints on long-term spin distributions and offer a framework to connect axion physics with SMBH growth histories, while noting limitations such as neglecting gravitational-wave emission and assuming maximal initial spin.

Abstract

This paper explores how time-varying increases in mass accretion onto rapidly spinning black holes influence their long-term spin evolution when affected by superradiance - a process where energy is extracted from the black hole by a surrounding axion field. Using simulations the study tracks how sudden accretion boosts affect a critical spin-down phase (the superradiance drop) during which the black hole's spin rapidly decreases while its mass remains nearly constant. The black hole spin evolution is controlled by the competition between two processes: how fast angular momentum is added through accretion, and how fast it is removed by the axion cloud. One major conclusion is that boosts to the accretion rate before the superradiance drop have the strongest effect, as they can delay or reshape the drop and significantly shrink the region of the mass-spin plane depopulated due to the superradiance. In particular, a super-Eddington accretion rate of 5 times Eddington accretion, lasting for 4 Myr and occurring 30 Myr before the superradiance drop can reduce the superradiance exclusion region in the mass-spin plane by 40 percent. In contrast, boosts to the accretion rate after the superradiance drop only cause temporary changes in the black hole spin. The study also shows that black holes with lighter axion clouds are more sensitive to these early boosts and can show observable spin changes lasting tens to hundreds of millions of years. Heavier axion clouds, however, require much stronger or longer-lasting boosts to produce similar effects, making them more stable under variable accretion.

Figures (6)

• Figure 1: An illustration of the exclusion region. $f_{\rm ex}$ for LE20 is the ratio between the area of the green shaded region and the pink shaded region. $t_1$ is the start of the first superradiance drop, $t_2$ is the end of the first superradiance drop, and $t_3$ is when the black hole is maximally spinning again (the end of the simulation).
• Figure 2: Time evolution of, from top to bottom, the characteristic timescales $\, {\tau_{\rm s} }$ and $\, {\tau_{\rm acc} }$, the frequency of the lowest energy orbital $\omega_{\rm I}$, the axion cloud mass $M_{\rm S}$ and the black hole spin $a$ for the case without accretion (blue) and a case of constant accretion of $f_{\rm Edd}-0.05$.
• Figure 3: Left: The Regge plane shows that as $\Delta t_{\rm ev}$ increases, more of the exclusion region closes off. For boosts applied before the initial superradiance drop, the drop itself is pushed to higher mass levels the longer the boost. This will tend to the constant accretion trajectory for $f_{\rm Edd}=0.5$. For boosts applied after the initial superradiance drop ($t_{\rm ev} = 0.36Gyr$) the boost deviates the black hole away from the critical spin trajectory. A second drop in spin occurs when the boost is released, so the longer the duration, the longer the black hole remains deviated. Right: A longer duration boost applied before the superradiance drop means more mass is accreted into the black hole causing quicker decay in timescale as $\omega_{\rm I}$ is larger at a given time. Once the drop occurs, $\, {\tau_{\rm s} }$ establishes an equilibrium with the external mass accretion. For boosts applied after the superradiance drop, $\, {\tau_{\rm s} }$ is not faster than $\, {\tau_{\rm acc} }$ until the boost is removed. With a larger $\Delta t_{\rm ev}$ in this regime, the black hole continuously tends to the critical spin trajectory without ever losing angular momentum, establishing a new equilibrium with the $f_{\rm Edd} = 0.5$ accretion rate.
• Figure 4: Left: The Regge trajectory can be seen to be similar to the $f_{\rm Edd} = 0.5$ model. Right: The timescale decay can be seen to occur much faster than in the $f_{\rm Edd} = 0.5$ boost case since the rate at which the black hole grows is faster, decreasing $t_s$ quicker.
• Figure 5: Regge trajectory for simulations with axion mass of $10^{-18}eV$ (cyan, highaxion) and $10^{-20}eV$ (purple dashed simulation, LE30) respectively. The parameters of highaxion are set so that all $f_{\rm Edd}$ ratios are increased by a factor of 100 and any time value and duration is reduced by a factor of 100 (which is equivalent to the ratio $10^{-18}eV$ and $10^{-20}eV$) compared to the fiducial simulation LE30. This means that highaxion has a background accretion rate of $f_{\rm Edd} = 5$, which is boosted to $f_{\rm Edd} = 50$ at $t_{\rm ev} = 0.16Myr$ for $\Delta t_{\rm ev} = 30Kyr$. The overlap of the trajectories shows the universality of superradiance, and how changing the accretion parameters is degenerate with changing the axion mass.