skip to main content


Title: The Luminosity Function of Tidal Disruption Events from Fallback-powered Emission: Implications for the Black Hole Mass Function
Abstract

Tidal disruption events (TDEs), in which a star is destroyed by the gravitational field of a supermassive black hole (SMBH), are being observed at a high rate owing to the advanced state of survey science. One of the properties of TDEs that is measured with increasing statistical reliability is the TDE luminosity function,dṄTDE/dL, which is the TDE rate per luminosity (i.e., how many TDEs are within a given luminosity range). Here we show that if the luminous emission from a TDE is directly coupled to the rate of return of tidally destroyed debris to the SMBH, then the TDE luminosity function is in good agreement with observations and scales as ∝L−2.5for high luminosities, provided that the SMBH mass functiondN/dM—the number of SMBHs (N) per SMBH mass (M)—is approximately flat in the mass range over which we observe TDEs. We also show that there is a cutoff in the luminosity function at low luminosities that is a result of direct captures, and this cutoff has been tentatively observed. IfdN/dMis flat, which is in agreement with some observational campaigns, these results suggest that the fallback rate feeds the accretion rate in TDEs. Contrarily, ifdN/dlogMis flat, which has been found theoretically and is suggested by other observational investigations, then the emission from TDEs is likely powered by another mechanism. Future observations and more TDE statistics, provided by the Rubin Observatory/LSST, will provide additional evidence as to the reality of this tension.

 
more » « less
Award ID(s):
2006684
NSF-PAR ID:
10414517
Author(s) / Creator(s):
;
Publisher / Repository:
DOI PREFIX: 10.3847
Date Published:
Journal Name:
The Astrophysical Journal Letters
Volume:
948
Issue:
2
ISSN:
2041-8205
Format(s):
Medium: X Size: Article No. L22
Size(s):
["Article No. L22"]
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    We conduct a systematic tidal disruption event (TDE) demographics analysis using the largest sample of optically selected TDEs. A flux-limited, spectroscopically complete sample of 33 TDEs is constructed using the Zwicky Transient Facility over 3 yr (from 2018 October to 2021 September). We infer the black hole (BH) mass (MBH) with host galaxy scaling relations, showing that the sampleMBHranges from 105.1Mto 108.2M. We developed a survey efficiency corrected maximum volume method to infer the rates. The rest-frameg-band luminosity function can be well described by a broken power law ofϕ(Lg)Lg/Lbk0.3+Lg/Lbk2.61, withLbk= 1043.1erg s−1. In the BH mass regime of 105.3≲ (MBH/M) ≲ 107.3, the TDE mass function followsϕ(MBH)MBH0.25, which favors a flat local BH mass function (dnBH/dlogMBHconstant). We confirm the significant rate suppression at the high-mass end (MBH≳ 107.5M), which is consistent with theoretical predictions considering direct capture of hydrogen-burning stars by the event horizon. At a host galaxy mass ofMgal∼ 1010M, the average optical TDE rate is ≈3.2 × 10−5galaxy−1yr−1. We constrain the optical TDE rate to be [3.7, 7.4, and 1.6] × 10−5galaxy−1yr−1in galaxies with red, green, and blue colors.

     
    more » « less
  2. 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 massM. 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,tpeak, on both stellar mass and age, with 15 days ≲tpeak≲ 10 yr for main sequence stars with masses 0.2 ≤M/M≤ 5 andM= 106M. The second estimate, which postulates that the star is completely destroyed when tides dominate the maximum stellar self-gravity, predicts thattpeakis very weakly dependent on stellar type, withtpeak=23.2±4.0daysM/106M1/2for 0.2 ≤M/M≤ 5, whiletpeak=29.8±3.6daysM/106M1/2for a Kroupa initial mass function truncated at 1.5M. 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.

     
    more » « less
  3. Abstract

    We present a toy model for the thermal optical/UV/X-ray emission from tidal disruption events (TDEs). Motivated by recent hydrodynamical simulations, we assume that the debris streams promptly and rapidly circularize (on the orbital period of the most tightly bound debris), generating a hot quasi-spherical pressure-supported envelope of radiusRv∼ 1014cm (photosphere radius ∼1015cm) surrounding the supermassive black hole (SMBH). As the envelope cools radiatively, it undergoes Kelvin–Helmholtz contractionRvt−1, its temperature risingTefft1/2while its total luminosity remains roughly constant; the optical luminosity decays asνLνRv2Tefft3/2. Despite this similarity to the mass fallback rateṀfbt5/3, envelope heating from fallback accretion is subdominant compared to the envelope cooling luminosity except near optical peak (where they are comparable). Envelope contraction can be delayed by energy injection from accretion from the inner envelope onto the SMBH in a regulated manner, leading to a late-time flattening of the optical/X-ray light curves, similar to those observed in some TDEs. Eventually, as the envelope contracts to near the circularization radius, the SMBH accretion rate rises to its maximum, in tandem with the decreasing optical luminosity. This cooling-induced (rather than circularization-induced) delay of up to several hundred days may account for the delayed onset of thermal X-rays, late-time radio flares, and high-energy neutrino generation, observed in some TDEs. We compare the model predictions to recent TDE light-curve correlation studies, finding both agreement and points of tension.

     
    more » « less
  4. Abstract

    The tidal disruption of stars by supermassive black holes (SMBHs) probes relativistic gravity. In the coming decade, the number of observed tidal disruption events (TDEs) will grow by several orders of magnitude, allowing statistical inferences of the properties of the SMBH and stellar populations. Here we analyze the probability distribution functions of the pericenter distances of stars that encounter an SMBH in the Schwarzschild geometry, where the results are completely analytic, and the Kerr metric. From this analysis we calculate the number of observable TDEs, defined to be those that come within the tidal radiusrtbut outside the direct capture radius (which is, in general, larger than the horizon radius). We find that relativistic effects result in a steep decline in the number of stars that have pericenter distancesrp≲ 10rg, whererg=GM/c2, and that for maximally spinning SMBHs the distribution function ofrpat such distances scales asfrprp4/3, or in terms ofβrt/rpscales asfββ−10/3. We find that spin has little effect on the TDE fraction until the very-high-mass end, where instead of being identically zero the rate is small (≲1% of the expected rate in the absence of relativistic effects). Effectively independent of spin, if the progenitors of TDEs reflect the predominantly low-mass stellar population and thus have masses ≲1M, we expect a substantial reduction in the rate of TDEs above 107M.

     
    more » « less
  5. Abstract

    We present13CO(J= 1 → 0) observations for the EDGE-CALIFA survey, which is a mapping survey of 126 nearby galaxies at a typical spatial resolution of 1.5 kpc. Using detected12CO emission as a prior, we detect13CO in 41 galaxies via integrated line flux over the entire galaxy and in 30 galaxies via integrated line intensity in resolved synthesized beams. Incorporating our CO observations and optical IFU spectroscopy, we perform a systematic comparison between the line ratio12/13I[12CO(J=10)]/I[13CO(J=10)]and the properties of the stars and ionized gas. Higher12/13values are found in interacting galaxies compared to those in noninteracting galaxies. The global12/13slightly increases with infrared colorF60/F100but appears insensitive to other host-galaxy properties such as morphology, stellar mass, or galaxy size. We also present azimuthally averaged12/13profiles for our sample up to a galactocentric radius of 0.4r25(∼6 kpc), taking into account the13CO nondetections by spectral stacking. The radial profiles of12/13are quite flat across our sample. Within galactocentric distances of 0.2r25, the azimuthally averaged12/13increases with the star formation rate. However, Spearman rank correlation tests show the azimuthally averaged12/13does not strongly correlate with any other gas or stellar properties in general, especially beyond 0.2r25from the galaxy centers. Our findings suggest that in the complex environments in galaxy disks,12/13is not a sensitive tracer for ISM properties. Dynamical disturbances, like galaxy interactions or the presence of a bar, also have an overall impact on12/13, which further complicates the interpretations of12/13variations.

     
    more » « less