[Paper Review] Observable gravitational waves from tidal disruption events and their electromagnetic counterpart

Toscani, M., Lodato, G.|arXiv (Cornell University)|Jan 1, 2022

Pulsars and Gravitational Waves ResearchPhysics and Astronomy90 references20 citations

TL;DR

This paper estimates the detectability of tidal disruption events (TDEs) via future gravitational wave (GW) detectors, particularly LISA and next-generation missions like Decigo. Using semi-analytical modeling of GW emission and stellar population rates, it finds that LISA will likely detect no TDEs unless black holes are embedded in young stellar populations with massive stars (m★,max ≳60 M⊙), in which case up to a few dozen events may be observed. Next-generation detectors could detect thousands of TDEs annually, enabling population studies of black hole masses and stellar environments, with electromagnetic counterparts expected in X-ray or optical bands.

ABSTRACT

We estimate the rate of tidal disruption events (TDEs) that will be detectable with future gravitational wave detectors as well as the most probable properties of these events and their possible electromagnetic counterpart. To this purpose we combine standard gravitational waves and electromagnetic results with detailed rates estimates. We find that the \emph{Laser Interferometer Space Antenna} (LISA) should not detect any TDEs, unless black holes (BHs) are typically embedded by a young stellar population which, in this situation, could lead up to few 10 events during the duration of the mission. If there are gravitational wave observations, these events should also be observable in the X-ray or the optical/UV part of the electromagnetic spectrum, which may open up the multi-messenger era for TDEs. The generation of detectors following LISA will at least yearly observe $10^4$ TDEs at cosmological distances, allowing to do population studies and constrain the black hole mass function. In all cases, most probable events should be around black holes with a mass such that the Keplerian frequency at the Schwarzschild radius is similar to the optimal frequency of the detector and with a large penetration factor.

Motivation & Objective

• To estimate the rate of tidal disruption events (TDEs) detectable by future gravitational wave detectors such as LISA and Decigo.
• To determine the most probable physical properties of detectable TDEs, including black hole mass, stellar mass, and penetration factor.
• To assess whether detectable GW events from TDEs would have observable electromagnetic counterparts in X-ray or optical/UV bands.
• To explore how non-detections or detections with LISA could constrain the age of stellar populations around black holes.
• To provide a framework for interpreting future multi-messenger observations of TDEs using combined GW and EM data.

Proposed method

• The study uses a semi-analytical model to compute the gravitational wave strain and frequency from TDEs based on the star-BH system's mass, radius, and orbital parameters.
• It derives the characteristic strain (ℎGW) and observed frequency (𝑓obs) using relativistic and Newtonian approximations, incorporating redshift and comoving distance (χ(z)) under a ΛCDM cosmology.
• The model includes a penetration factor β = rT/rp, with β ≤ βmax = rT/(2rSch) to ensure stars are not directly captured, and assumes a Kroupa-like stellar mass function with extrapolated high-mass cutoffs.
• The TDE rate is computed by combining the GW detectability threshold (S/Nlim) with galaxy-wide stellar and black hole mass functions, using empirical BH mass functions from Davidzon+17 and Reines+15.
• Electromagnetic detectability is assumed based on standard TDE luminosity models, with X-ray and optical/UV flares expected for non-direct plunge events.
• The analysis includes Monte Carlo-style sampling of parameters and computes observable rates across different detectors and stellar population models.

Experimental results

Research questions

• RQ1 Can LISA detect gravitational waves from tidal disruption events involving stars and stellar-mass or supermassive black holes?
• RQ2 What are the most probable physical parameters (BH mass, stellar mass, penetration factor) of TDEs detectable by future GW detectors?
• RQ3 Are detectable GW events from TDEs likely to have observable electromagnetic counterparts in X-ray or optical/UV bands?
• RQ4 How do non-detections or detections by LISA constrain the age and mass distribution of stellar populations around black holes?
• RQ5 What is the expected detection rate of TDEs with next-generation GW detectors like Decigo, ALIA, and BBO across cosmological redshifts?

Key findings

• LISA is unlikely to detect any TDEs unless black holes are embedded in young stellar populations with a maximum stellar mass m★,max ≳60 M⊙, in which case up to a few dozen events could be detected over its 4-year mission.
• For such young stellar populations, the maximum redshift for detectable TDEs with LISA is zmax ≈ 0.1, corresponding to a characteristic strain threshold of ℎGW ≈ 10−22.
• Next-generation detectors like Decigo are expected to detect 10^4 to 10^6 TDEs per year at cosmological distances, enabling detailed studies of the black hole mass function.
• The most probable TDEs detected by any GW instrument are those involving black holes with a mass such that the Keplerian frequency at the critical radius (κ×rSch) matches the detector’s optimal frequency.
• All TDEs detectable in gravitational waves by LISA or Decigo are expected to have bright electromagnetic counterparts in X-ray or optical/UV bands, enabling multi-messenger follow-up.
• The TDE rate is significantly lower (by a factor of ~5) for monochromatic stellar populations compared to Kroupa-like initial mass functions, highlighting the importance of stellar mass distribution in rate estimates.