Flaring of tidally compressed dark-matter clumps

We explore the physics and observational consequences of tidal compression events (TCEs) of dark-matter clumps (DMCs) by supermassive black holes (SMBHs). Our analytic calculations show that a DMC approaching a SMBH much closer than the tidal radius undergoes significant compression along the axis perpendicular to the orbital plane, shortly after pericenter passage. For DMCs composed of self-annihilating dark-matter particles, we find that the boosted DMC density and velocity dispersion lead to a flaring of the annihilation rate, most pronounced for a velocity-dependent annihilation cross section. If the end products of the annihilation are photons, this results in a gamma-ray flare, detectable (and possibly already detected) by the Fermi telescope for a range of model parameters. If the end products of dark-matter annihilation are relativistic electrons and positrons and the local magnetic field is large enough, TCEs of DMCs can lead to flares of synchrotron radiation. Finally, TCEs of DMCs lead to a burst of gravitational waves, in addition to the ones radiated by the orbital motion alone, and with a different frequency spectrum. These transient phenomena provide interesting new avenues to explore the properties of dark matter.

Figure 1

Trajectories of test particles with respect to the center of mass of the DMC, perpendicular to the orbital plane, for a penetration factor $\beta =10$. Specifically, we show trajectories with initial height $z/R_{\mathrm{cl}}\in [-1,1]$ and initial vertical velocity from $-1$ to 1 times the virial velocity. The curves are started and ended at entry and exit from the tidal radius.

Figure 2

Velocities of test particles with respect to the center of mass of the DMC, perpendicular to the orbital plane, for a penetration factor $\beta =10$. For each curve, the initial conditions match those of the line with identical color in Fig. 1.

Figure 3

Compression factor perpendicular to the orbital plane, as a function of the true anomaly $f$ (focusing on the interval $-\pi /4<f<\pi /4$), for several values of the penetration factor $\beta$. Pericenter passage occurs at $f=0$.

Figure 4

Orbital plane deformation of the DMC, with a penetration factor of $\beta =10$. At any given moment, tidal forces tend to stretch the DMC along the axis connecting it to the SMBH and compress it in the perpendicular direction. This figure illustrates the delayed response of the DMC as it moves along its parabolic orbit.

Figure 5

Compression factor in the orbital plane, as a function of the true anomaly $f$, for several $\beta ={10}^2$ (red lines) and ${10}^4$ (blue lines). The dashed lines illustrate the compression factor that one would obtain if neglecting random velocities (or setting $\mathit{B}$ to zero).

Figure 6

Gamma-ray light curves from DM annihilation in tidally compressed DM clumps at a distance of 100 Mpc, assuming $M_{\mathrm{cl}}=0.1M_{\odot }$, ${\rho }_{\mathrm{cl}}=10^{-10}\mathrm{g}{\mathrm{cm}}^{-3}$, $m_{\chi }=1\mathrm{GeV}$, and a total number of 10 gamma-ray photons produced per annihilation event. The assumed annihilation cross section is normalized such that $⟨\sigma v{⟩}_0=3\times {10}^{-28}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ before the DMC enters the tidal radius. The three rightmost (blue) curves correspond to a penetration factor $\beta =10$, and the two leftmost (red) curves to $\beta =100$. The labels $s$, $p$, $d$ indicate the type of annihilation ($s$-wave, $p$-wave, or $d$-wave, respectively).