Stars Crushed by Black Holes. II. A Physical Model of Adiabatic Compression and Shock Formation in Tidal Disruption Events
Abstract

We develop a Newtonian model of a deep tidal disruption event (TDE), for which the pericenter distance of the star,rp, is well within the tidal radius of the black hole,rt, i.e., whenβrt/rp≫ 1. We find that shocks form forβ≳ 3, but they are weak (with Mach numbers ∼1) for allβ, and that they reach the center of the star prior to the time of maximum adiabatic compression forβ≳ 10. The maximum density and temperature reached during the TDE follow much shallower relations withβthan the previously predicted$ρmax∝β3$and$Tmax∝β2$scalings. Belowβ≃ 10, this shallower dependence occurs because the pressure gradient is dynamically significant before the pressure is comparable to the ram pressure of the free-falling gas, while aboveβ≃ 10, we find that shocks prematurely halt the compression and yield the scalings$ρmax∝β1.62$and$Tmax∝β1.12$. We find excellent agreement between our results and high-resolution simulations. Our results demonstrate that, in the Newtonian limit, the compression experienced by the star is completely independent of the mass of the black hole. We discuss our results in the context of existing (affine) models, polytropic versus non-polytropic stars, and general relativistic effects, which become important when the pericenter of more »

Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10362619
Journal Name:
The Astrophysical Journal
Volume:
926
Issue:
1
Page Range or eLocation-ID:
Article No. 47
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
##### More Like this
1. Abstract

State transitions in black hole X-ray binaries are likely caused by gas evaporation from a thin accretion disk into a hot corona. We present a height-integrated version of this process, which is suitable for analytical and numerical studies. With radiusrscaled to Schwarzschild units and coronal mass accretion rate$ṁc$to Eddington units, the results of the model are independent of black hole mass. State transitions should thus be similar in X-ray binaries and an active galactic nucleus. The corona solution consists of two power-law segments separated at a break radiusrb∼ 103(α/0.3)−2, whereαis the viscosity parameter. Gas evaporates from the disk to the corona forr>rb, and condenses back forr<rb. Atrb,$ṁc$reaches its maximum,$ṁc,max≈0.02(α/0.3)3$. If atrrbthe thin disk accretes with$ṁd, then the disk evaporates fully before reachingrb, giving the hard state. Otherwise, the disk survives at all radii, giving the thermal state. While the basic model considers only bremsstrahlung cooling and viscous heating, we also discuss a more realistic model that includes Compton cooling and direct coronal heating by energy transport from the disk. Solutions are again independent of black hole mass, andrbremainsmore »

2. 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 as$νLν∝Rv2Teff∝t−3/2$. Despite this similarity to the mass fallback rate$Ṁfb∝t−5/3$, 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 themore »

3. Abstract

We report the discovery of MAGAZ3NE J095924+022537, a spectroscopically confirmed protocluster at$z=3.3665−0.0012+0.0009$around a spectroscopically confirmedUVJ-quiescent ultramassive galaxy (UMG;$M⋆=2.34−0.34+0.23×1011M⊙$) in the COSMOS UltraVISTA field. We present a total of 38 protocluster members (14 spectroscopic and 24 photometric), including the UMG. Notably, and in marked contrast to protoclusters previously reported at this epoch that have been found to contain predominantly star-forming members, we measure an elevated fraction of quiescent galaxies relative to the coeval field ($73.3−16.9+26.7%$versus$11.6−4.9+7.1%$for galaxies with stellar massM≥ 1011M). This high quenched fraction provides a striking and important counterexample to the seeming ubiquitousness of star-forming galaxies in protoclusters atz> 2 and suggests, rather, that protoclusters exist in a diversity of evolutionary states in the early universe. We discuss the possibility that we might be observing either “early mass quenching” or nonclassical “environmental quenching.” We also present the discovery of MAGAZ3NE J100028+023349, a second spectroscopically confirmed protocluster, at a very similar redshift of$z=3.3801−0.0281+0.0213$. We present a total of 20 protocluster members, 12 of which are photometric and eight spectroscopic including a poststarburst UMG ($M⋆=2.95−0.20+0.21×1011M⊙$). Protoclusters MAGAZ3NE J0959more »

4. Abstract

We use ALMA observations of CO(2–1) in 13 massive (M*≳ 1011M) poststarburst galaxies atz∼ 0.6 to constrain the molecular gas content in galaxies shortly after they quench their major star-forming episode. The poststarburst galaxies in this study are selected from the Sloan Digital Sky Survey spectroscopic samples (Data Release 14) based on their spectral shapes, as part of the Studying QUenching at Intermediate-z Galaxies: Gas, angu$L→ar$momentum, and Evolution ($SQuIGGL⃗E$) program. Early results showed that two poststarburst galaxies host large H2reservoirs despite their low inferred star formation rates (SFRs). Here we expand this analysis to a larger statistical sample of 13 galaxies. Six of the primary targets (45%) are detected, with$MH2≳109$M. Given their high stellar masses, this mass limit corresponds to an average gas fraction of$〈fH2≡MH2/M*〉∼7%$or ∼14% using lower stellar masses estimates derived from analytic, exponentially declining star formation histories. The gas fraction correlates with theDn4000 spectral index, suggesting that the cold gas reservoirs decrease with time since burst, as found in local K+A galaxies. Star formation histories derived from flexible stellar population synthesis modeling support thismore »

5. Abstract

The genericity of Arnold diffusion in the analytic category is an open problem. In this paper, we study this problem in the followinga prioriunstable Hamiltonian system with a time-periodic perturbation$Hε(p,q,I,φ,t)=h(I)+∑i=1n±12pi2+Vi(qi)+εH1(p,q,I,φ,t),$where$(p,q)∈Rn×Tn$,$(I,φ)∈Rd×Td$withn,d⩾ 1,Viare Morse potentials, andɛis a small non-zero parameter. The unperturbed Hamiltonian is not necessarily convex, and the induced inner dynamics does not need to satisfy a twist condition. Using geometric methods we prove that Arnold diffusion occurs for generic analytic perturbationsH1. Indeed, the set of admissibleH1isCωdense andC3open (a fortiori,Cωopen). Our perturbative technique for the genericity is valid in theCktopology for allk∈ [3, ∞) ∪ {∞,ω}.