Observing Lense-Thirring Precession in Tidal Disruption Flares

When a star is tidally disrupted by a supermassive black hole (SMBH), the streams of liberated gas form an accretion disk after their return to pericenter. We demonstrate that Lense-Thirring precession in the spacetime around a rotating SMBH can produce significant time evolution of the disk angular momentum vector, due to both the periodic precession of the disk and the nonperiodic, differential precession of the bound debris streams. Jet precession and periodic modulation of disk luminosity are possible consequences. The persistence of the jetted x-ray emission in the Swift $J164449.3+573451$ flare suggests that the jet axis was aligned with the spin axis of the SMBH during this event.

Figure 1

Geometry of the tidal disruption of a star by a spinning SMBH. Following disruption of the star near its pericenter passage, an accretion disk will form in the star’s orbital plane. As the disk precesses, the angle $\beta$ between the SMBH spin vector ${\overrightarrow{J}}_{\mathrm{BH}}$ and the disk angular momentum vector ${\overrightarrow{L}}_{\mathrm{disk}}$ stays constant, but an associated jet may move relative to the observer’s line of sight ${\overrightarrow{r}}_{\mathrm{obs}}$.

Figure 2

Time scales for avoiding Bardeen-Peterson warping $t_{\mathrm{thin}}$ (blue, top panel) and for establishing an accretion disk $t_{\mathrm{circ}}$ (green, bottom panel) as functions of the black hole mass $M_{\mathrm{BH}}$. Dotted lines correspond to stars with a mass of $2M_{\odot }$, solid lines to $1M_{\odot }$ and dashed lines to $0.5M_{\odot }$ (with a stellar mass-radius relationship adopted from Ref. 32, p. 208). We take $n_{\mathrm{orb}}=3$ and $R_p=0.5R_t$, and conservatively plot $t_{\mathrm{thin}}$ for the outer edge of the disk, assuming $R_o=2R_p$.

Figure 3

The angular shift $\Delta {\varphi }_{\mathrm{orb}}$. The thick curves illustrate the disruption of a solar-type star with $M_{\mathrm{BH}}={10}^6{M}_{\odot }$, $a=0.8$, and $r_p=13$; the thin curves are the same but with $r_p=3$. The blue dotted lines are Eq. (8), while the green solid lines are numerical geodesic solutions. The curves do not extend prior to $t=t_{\mathrm{fall}}$, and are normalized by $\sin \beta$.

Figure 4

Regions of $a$-$\beta$ parameter space that can be excluded by continuous observations of a TDE jet with the inferred parameters in Ref. 15 and $\zeta =0$. The solid curves show contours of constant $t_{\mathrm{obs}}=T_{\mathrm{prec}}\times 2({\theta }_{\mathrm{jet}}/{10}^{-1.5})/(2\pi \sin \beta )$: the maximum number of days it would take for a jet initially in the observers’ line of sight to precess off axis, with the jet opening angle normalized to ${10}^{-1.5}$. We take $R_o=2R_p$ and $R_i=3R_{\mathrm{S}}$. Regions of parameter space to the right of the thick red contours can be excluded for the Swift $J164449.3+573451$ jet, which exhibited bright x-ray emission for over two weeks. The 14 d contours for $\zeta =-3/2$ and $\zeta =1$ are shown with black dotted and dashed lines, respectively. The effect of the DSP is negligible for these parameters, and neglected here.