The Peak of the Fallback Rate from Tidal Disruption Events: Dependence on Stellar Type
Ananya Bandopadhyay, Julia Fancher, Aluel Athian, Valentino Indelicato, Sarah Kapalanga, Angela Kumah, Daniel A. Paradiso, M. R. Todd, Eric R. Coughlin, C. J. Nixon
Abstract
Abstract A star completely destroyed in a tidal disruption event (TDE) ignites a luminous flare that is powered by the fallback of tidally stripped debris to a supermassive black hole (SMBH) of mass M • . We analyze two estimates for the peak fallback rate in a TDE, one being the “frozen-in” model, which predicts a strong dependence of the time to peak fallback rate, t peak , on both stellar mass and age, with 15 days ≲ t peak ≲ 10 yr for main sequence stars with masses 0.2 ≤ M ⋆ / M ⊙ ≤ 5 and M • = 10 6 M ⊙ . The second estimate, which postulates that the star is completely destroyed when tides dominate the maximum stellar self-gravity, predicts that t peak is very weakly dependent on stellar type, with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>peak</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mn>23.2</mml:mn> <mml:mo>±</mml:mo> <mml:mn>4.0</mml:mn> <mml:mspace width="0.25em"/> <mml:mi mathvariant="normal">days</mml:mi> </mml:mrow> </mml:mfenced> <mml:msup> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>•</mml:mo> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> for 0.2 ≤ M ⋆ / M ⊙ ≤ 5, while <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>peak</mml:mi> </mml:mrow> </mml:msub> <mml:mspace width="0.25em"/> <mml:mo>=</mml:mo> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mn>29.8</mml:mn> <mml:mo>±</mml:mo> <mml:mn>3.6</mml:mn> <mml:mspace width="0.25em"/> <mml:mi mathvariant="normal">days</mml:mi> </mml:mrow> </mml:mfenced> <mml:msup> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>•</mml:mo> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> for a Kroupa initial mass function truncated at 1.5 M ⊙ . This second estimate also agrees closely with hydrodynamical simulations, while the frozen-in model is discrepant by orders of magnitude. We conclude that (1) the time to peak luminosity in complete TDEs is almost exclusively determined by SMBH mass, and (2) massive-star TDEs power the largest accretion luminosities. Consequently, (a) decades-long extra-galactic outbursts cannot be powered by complete TDEs, including massive-star disruptions, and (b) the most highly super-Eddington TDEs are powered by the complete disruption of massive stars, which—if responsible for producing jetted TDEs—would explain the rarity of jetted TDEs and their preference for young and star-forming host galaxies.