Plasma-photon interaction in curved spacetime. II. Collisions, thermal corrections, and superradiant instabilities

Motivated by electromagnetic-field confinement due to plasma near accreting black holes, we continue our exploration of the linear dynamics of an electromagnetic field propagating in curved spacetime in the presence of plasma by including three effects that were neglected in our previous analysis: collisions in the plasma, thermal corrections, and the angular momentum of the background black hole spacetime. We show that: (i) the plasma-driven long-lived modes survive in a collisional plasma except when the collision timescale is unrealistically small; (ii) thermal effects, which might be relevant for accretion disks around black holes, do not affect the axial long-lived modes; (iii) in the case of a spinning black hole the plasma-driven modes become superradiantly unstable at the linear level; (iv) the polar sector in the small-frequency regime admits a reflection point due to the resonant properties of the plasma. Dissipative effects such as absorption, formation of plasma waves, and nonlinear dynamics play a crucial role in the vicinity of this resonant point.

Figure 1

Imaginary (top) and real (bottom) part of the axial $l=1$ mode for the quasibound states of a cold, collisional plasma in a Schwarzschild background as a function of the collision timescale $\tau$, normalized by the plasma frequency. For large collision time $\tau \gg 1/{\omega }_{\mathrm{pl}}$, the results are identical to the collisionless case discussed in Paper I. When the collision time becomes very short, $\tau \ll 1/{\omega }_{\mathrm{pl}}$, the collisions between electrons and protons shorten the lifetime of the bound states.

Figure 2

Same as in Fig. 1 but for the polar sector. The behavior of the modes is the same as in the axial case, and a quenching occurs as $\tau {\omega }_{\mathrm{pl}}\ll 1$.

Figure 3

Absolute value squared of the polar $l=1$ wavefunction $u_{(3)}$ for different values of the collision parameter $\tau$ at $M{\omega }_{\mathrm{pl}}=0.35$. As plasma becomes more collisional, the resonance at the reflection point is smoothed out.

Figure 4

Imaginary part of the axial $l=1=m$ mode for different values of the plasma frequency ${\omega }_{\mathrm{pl}}$. The imaginary part of the mode changes sign and becomes superradiant when the superradiant condition ${\omega }_R<m{\mathrm{\Omega }}_H$ is met. Black dots represent Proca modes with $l=1=m$. The difference between the two spectra is always less than 2%.

Figure 5

Superradiant axial modes with $l=1=m$ in a Bondi accretion model [see Eq. (56)] with plasma asymptotic frequency ${\omega }_{\infty }=0.05/M$, for different values of the plasma frequency at the horizon, ${\omega }_{\mathrm{pl}}\approx {\omega }_{\mathrm{B}}$. The imaginary part of the modes is some orders of magnitude smaller than in the ${\omega }_{\mathrm{pl}}=\text{const}$. case, and can become comparable to the Salpeter time (marked as a dashed line for the case of $M=10M_{\odot }$).