MNRAS 499, 5562–5577 (2020) doi:10.1093/mnras/staa3127 Advance Access publication 2020 October 13 Eccentric tidal disruption event discs around supermassive black holes: dynamics and thermal emission J. J. Zanazzi 1,2‹ and Gordon I. Ogilvie 2 1Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St George Street, Toronto, Ontario M5S 1A7, Canada 2 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge Downloaded from https://academic.oup.com/mnras/article/499/4/5562/5922725 by University of Cambridge user on 11 November 2020 CB3 0WA, UK Accepted 2020 October 5. Received 2020 September 8; in original form 2020 March 26 ABSTRACT After the tidal disruption event (TDE) of a star around a supermassive black hole (SMBH), if the stellar debris stream rapidly circularizes and forms a compact disc, the TDE emission is expected to peak in the soft X-ray or far ultraviolet (UV). The fact that many TDE candidates are observed to peak in the near UV and optical has challenged conventional TDE emission models. By idealizing a disc as a nested sequence of elliptical orbits that communicate adiabatically via pressure forces, and are heated by energy dissipated during the circularization of the nearly parabolic debris streams, we investigate the dynamics and thermal emission of highly eccentric TDE discs, including the effect of general-relativistic apsidal precession from the SMBH. We calculate the properties of uniformly precessing, apsidally aligned, and highly eccentric TDE discs, and find highly eccentric disc solutions exist for realistic TDE properties (SMBH and stellar mass, periapsis distance, etc.). Taking into account compressional heating (cooling) near periapsis (apoapsis), we find our idealized eccentric disc model can produce emission consistent with the X-ray and UV/optical luminosities of many optically bright TDE candidates. Our work attempts to quantify the thermal emission expected from the shock-heating model for TDE emission, and finds stream–stream collisions are a promising way to power optically bright TDEs. Key words: accretion, accretion discs – black hole physics – hydrodynamics – radiation mechanisms: thermal – stars: black holes. Maksym, Ulmer & Eracleous 2010; Cenko et al. 2012; Donato 1 INTRODUCTION et al. 2014; Khabibullin & Sazonov 2014; Maksym, Lin & Irwin When a bright transient event occurs near the centre of an otherwise 2014; Lin et al. 2015), known as X-ray bright TDEs (Auchettl, quiescent galaxy, with a smooth power law decline in luminosity over Guillochon & Ramirez-Ruiz 2017). More sophisticated models of a time-scale of months to years and negligible corresponding colour compact accretion discs which form soon after the TDE have been or blackbody temperature evolution, the most popular interpretation able to successfully reproduce many features of X-ray bright TDEs is that we are witnessing a tidal disruption event (TDE) of a star from (e.g. Strubbe & Quataert 2009; Lodato & Rossi 2011; Jonker et al. the galaxy’s central supermassive black hole (SMBH; see review by 2020; Mummery & Balbus 2020). However, these compact TDE Komossa 2015). TDEs occur when the tidal force exerted on the disc models fail to explain the properties of optically or UltraViolet star by the SMBH exceeds the star’s self-gravity, causing the stellar (UV) bright TDEs (e.g. Gezari et al. 2006, 2008, 2009; Komossa material to be launched on highly elliptical ballistic trajectories. The et al. 2008; van Velzen et al. 2011;Wangetal.2011, 2012;Arcavi stellar debris eventually accretes on to the SMBH, powering the et al. 2014), which also have Eddington luminosities, but have much observed luminous transients (Rees 1988; Evans & Kochanek 1989). larger photosphere radii (∼1014 − 1015 cm) with lower effective An outstanding problem in astrophysics is the low effective temperatures (∼2–3 × 104 K). temperature of many of the observed TDEs. Since the earliest TDE One explanation for the low effective temperatures is that the models predicted a compact accretion disc which formed quickly TDE thermal emission does not originate from the accretion disc, from circularization of the stellar debris, with highly super-Eddington but from an outflow supported by radiation pressure from the disc’s accretion rates, the first estimates of TDE emission predicted Edding- super-Eddington accretion rate (e.g. Loeb & Ulmer 1997; Strubbe & ton luminosities (∼1044–1045 erg s−1), compact photosphere radii Quataert 2009; Lodato & Rossi 2011; Metzger & Stone 2016;Roth (∼1013 cm), and high effective temperatures (105 K; Cannizzo, et al. 2016; Curd & Narayan 2019). The TDE’s high photosphere Lee & Goodman 1990;Ulmer1999). Many TDEs detected a decade radius and low temperature can then be explained by the increased or two later had these expected properties (e.g. Bade, Komossa emitting area from the optically thick, expanding outflow, launched & Dahlem 1996; Komossa & Bade 1999; Greiner et al. 2000; from the accretion disc or SMBH. These outflows can explain the nearly constant temperatures inferred from the spectrum of optically bright TDEs (Strubbe & Quataert 2009; Miller 2015), and may lead E-mail: [email protected] to observable emission or absorption line features in the TDE’s C 2020 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society Eccentric TDE discs 5563 spectrum (Strubbe & Quataert 2011;Rothetal.2016;Roth& 2 ECCENTRIC TDE DISC STRUCTURE AND Kasen 2018). Hydrodynamical simulations show that the outflow DYNAMICS can be supported not only by radiation pressure from the compact WhenastarofmassM and radius R on a nearly parabolic orbit disc (Dai et al. 2018; Curd & Narayan 2019) but also by shocks with periapsis distance r from the SMBH of mass M• satisfies driven by stream–stream collisions during the circularization of p stellar debris (Liptai et al. 2019; Lu & Bonnerot 2020). However, 1/3 rp Rt = R(M•/M) , (1) to power the outflow, a significant fraction of the tidally disrupted 2 53 star’s rest-mass energy must be liberated (0.05 M c ∼ 10 erg), the star tidally disrupts. The stellar debris after disruption bound to much larger than the typical energy liberated by an optically bright the SMBH has a spread in specific orbital energy (assuming R Downloaded from https://academic.oup.com/mnras/article/499/4/5562/5922725 by University of Cambridge user on 11 November 2020 49 51 TDE’s early emission (∼10 –10 erg; e.g. Komossa 2015;van Rt) Velzen et al. 2020). This so-called missing energy problem has a GM•R number of proposed solutions. For instance, some argue most of the E 2 . (2) rest-mass energy is radiated in the unobservable far-UV wavelength Rt bands (e.g. Lu & Kumar 2018; Jonker et al. 2020), while others Throughout the rest of this work, we define the dimensionless stellar propose this energy is carried away by a jet whose emission is mass M¯ , radius R¯, and SMBH mass M¯ • via unobservable for most TDE viewing angles (Dai et al. 2018). Some authors suggest this energy is never emitted in the first place, but M R M• M¯ = , R¯ = , M¯ • = , (3) rather becomes trapped due to the TDE disc and outflow’s high 1M 1R 106 M optical depth (photon trapping; e.g. Curd & Narayan 2019). The normalized to typical TDE values (e.g. van Velzen et al. 2020). wind model has yet to conclusively address the missing energy After disruption, the debris is expected to re-accrete and form a problem. disc orbiting the SMBH. The shortest orbital period within the debris Contending the outflow model for optical TDE emission is the stream is stream–stream collisions model of Shiokawa et al. (2015), Piran 3 ¯ 1/2 ¯3/2 et al. (2015), and Krolik et al. (2016). Instead of optical emission = 2πGM• = √ πRt = M• R tf0 3/2 41 d, (4) (2E) 3 M¯ originating from an optically thick outflow, it instead comes from 2GM•R the accretion disc, whose annular extent remains extended (∼ The specific orbital energy of debris which re-accretes on to the TDE 1014 − 1015 cm) due to inefficient circularization of the debris stream. disc is The emission itself is powered by shock-heating from stream–stream 2/3 2/3 collisions of disc gas during formation. A prediction from this model (2πGM•) t E (t) =− =−E f0 , (5) is the broadening of H α and optical emission lines from non- f 2t 2/3 t Keplerian motion within the eccentric disc (Piran et al. 2015; Liu et al. 2017; Cao et al. 2018). This model also avoids the problem of how the where we will assume from now on that debris with orbital period tf = disc efficiently circularizes, since hydrodynamical simulations show accretes on to the disc at time t tf. The accretion rate of fallback the TDE disc remains extended and eccentric long after formation, material on to the TDE disc is then (Rees 1988; Evans & Kochanek because not enough orbital energy is dissipated to drive the disc’s 1989) eccentricity to zero (Guillochon, Manukian & Ramirez-Ruiz 2014; 5/3 Shiokawa et al. 2015;Sądowski et al. 2016; Bonnerot & Lu 2020). dMf = dMf dEf = M tf0 After the optical emission is driven by shocks from the circularization dt dEf dt 3tf0 t process, Svirski, Piran & Krolik (2017) argued that X-ray thermal η M¯ t 5/3 emission from viscous heating of the disc’s inner edge may be = ˙ f0 134 MEdd 3/2 3/2 , (6) avoided if the disc remains highly eccentric. If an elliptical disc 0.1 M¯ • R¯ t annulus loses sufficient angular momentum, its eccentricity may where M˙ = 4πGM•/(ηcκ) is the Eddington accretion rate and η is increase, allowing the disc material to cross the SMBH’s effective Edd the accretion efficiency factor.