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The no-hair theorems at work in the tidal disruption event AT2020afhd

Lorenzo Iorio

Abstract

Recently, the coprecession of both the accretion disk and the jet formed following the tidal disruption event associated with the optical transient AT2020afhd, driven by a supermassive black hole of almost ten million solar masses, were independently measured in both the X and radio bands, respectively, showing a periodicity of nearly 20 days over about 300 days. An analytical model of the general relativistic gravitomagnetic Lense-Thirring precession of the effective orbit of a fictitious test particle revolving about a spinning primary can explain the observed precessional features. It yields allowed regions in the system's parameter space which, as far as the hole's dimensionless spin parameter is concerned, are essentially in agreement with those obtained in the literature with general relativistic magnetohydrodynamic simulations. The present analytical approach can be extended to include the precession due to the hole's quadrupole mass moment as well. It breaks the degeneracy in the allowed regions occurring for negative and positive values of the spin parameter when only the Lense-Thirring effect is considered. The best estimate for the hole's mass yields the range $0.185-0.215$ for the dimensionless spin parameter. Using the same strategy with the gravitomagnetic frequency for an extended disk of finite size with a parameterized power-law mass density yields to distinct, generally non-overlapping allowed regions for each value of the power-law index adopted.

The no-hair theorems at work in the tidal disruption event AT2020afhd

Abstract

Recently, the coprecession of both the accretion disk and the jet formed following the tidal disruption event associated with the optical transient AT2020afhd, driven by a supermassive black hole of almost ten million solar masses, were independently measured in both the X and radio bands, respectively, showing a periodicity of nearly 20 days over about 300 days. An analytical model of the general relativistic gravitomagnetic Lense-Thirring precession of the effective orbit of a fictitious test particle revolving about a spinning primary can explain the observed precessional features. It yields allowed regions in the system's parameter space which, as far as the hole's dimensionless spin parameter is concerned, are essentially in agreement with those obtained in the literature with general relativistic magnetohydrodynamic simulations. The present analytical approach can be extended to include the precession due to the hole's quadrupole mass moment as well. It breaks the degeneracy in the allowed regions occurring for negative and positive values of the spin parameter when only the Lense-Thirring effect is considered. The best estimate for the hole's mass yields the range for the dimensionless spin parameter. Using the same strategy with the gravitomagnetic frequency for an extended disk of finite size with a parameterized power-law mass density yields to distinct, generally non-overlapping allowed regions for each value of the power-law index adopted.
Paper Structure (8 sections, 27 equations, 6 figures, 1 table)

This paper contains 8 sections, 27 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. The mathematical model of the no-hair disk precession
  3. Constraining the parameter space
  4. The parameter space in the most general case
  5. Narrowing the parameter space with the SMBH's mass
  6. Reducing the dimensionality of the parameter space by fixing the orbital radius
  7. A discussion on the range for the BH's spin parameter by Wang et al. 2025
  8. Summary and conclusions

Figures (6)

  • Figure 1: Radii $r_\mathrm{ISCO}^{\pm}$ of the prograde ($+$, left panel) and retrograde ($-$, right panel) ISCOs, in units of gravitational radii $R_\mathrm{g}$, as functions of the dimensionless spin parameter $a_\bullet$ of a Kerr BH.
  • Figure 2: Permitted regions in the three-dimensional parameter space $\left\{\log\left(M_\bullet/M_\odot\right),a_\bullet,r_0\right\}$ obtained by imposing the conditions that the absolute value of the NH precessional frequency of Equation (\ref{['ONH']}), calculated with Equations (\ref{['SBH']})--(\ref{['QBH']}), lies within the experimental range of Equation (\ref{['cop']}) for the observed disk-jet coprecessional one, and that the radius $r_0$ of the effective test particle orbit is larger than that of the prograde ($r^+_\mathrm{ISCO}$, left panel) and retrograde ($r^-_\mathrm{ISCO}$, right panel) equatorial ISCOs. The best estimate of the colatitude $\theta_i$ of the orbital angular momentum is taken from Table \ref{['Tab:1']}, while $\log\left(M_\bullet/M_\odot\right)$ and $a_\bullet$ are allowed to vary within their expected full ranges $6\lesssim \log\left(M_\bullet/M_\odot\right)\lesssim 8$1975Natur.254..295H2023ApJ...959..117F and $-1\leq a_\bullet \leq1$, respectively.
  • Figure 3: Permitted regions in the three-dimensional parameter space $\left\{\log\left(M_\bullet/M_\odot\right),a_\bullet,r_0\right\}$ obtained by imposing the conditions that the absolute value of the NH precessional frequency of Equation (\ref{['ONH']}), calculated with Equations (\ref{['SBH']})--(\ref{['QBH']}), lies within the experimental range of Equation (\ref{['cop']}) for the observed disk-jet coprecessional one, and that the radius $r_0$ of the effective test particle orbit is larger than that of the prograde ($r^+_\mathrm{ISCO}$, left panel) and retrograde ($r^-_\mathrm{ISCO}$, right panel) equatorial ISCOs. The range of variation for $\log\left(M_\bullet/M_\odot\right)$ and the best estimate for the colatitude $\theta_i$ of the orbital angular momentum were taken from Table \ref{['Tab:1']}, while $a_\bullet$ is allowed to vary within its full range $-1\leq a_\bullet \leq1$.
  • Figure 4: Permitted regions in the two-dimensional parameter space $\left\{\log\left(M_\bullet/M_\odot\right),a_\bullet\right\}$ obtained by imposing the condition that the absolute value of the NH precessional frequency of Equation (\ref{['ONH']}), calculated with Equations (\ref{['SBH']})--(\ref{['QBH']}), lies within the experimental range of Equation (\ref{['cop']}) for the observed disk-jet coprecessional one. The radius $r_0$ of the effective test particle orbit is set equal to the tidal disruption radius of Equation (\ref{['rtidal']}). The range of variation for $\log\left(M_\bullet/M_\odot\right)$ and the best estimate of the colatitude $\theta_i$ of the orbital angular momentum were taken from Table \ref{['Tab:1']}, while $a_\bullet$ is allowed to vary within its full range $-1\leq a_\bullet \leq1$.
  • Figure 5: Allowed regions in the $\left\{a_\bullet,T_\mathrm{prec}\right\}$ plane obtained by plotting the absolute value of Equation (\ref{['S4']}) versus $a_\bullet$ for $\zeta=0,3/5,3/4$TDELTCinesi2025. Each shaded region is delimited by the log-linear plots obtained with the maximum and minimum values of $\log\left(M_\bullet/M_\odot\right)$, as per Table \ref{['Tab:1']}. Left panel: prograde ISCO. Right panel: retrograde ISCO.
  • ...and 1 more figures