The Eccentric Nature of Eccentric Tidal Disruption Events

Upon entering the tidal sphere of a supermassive black hole, a star is ripped apart by tides and transformed into a stream of debris. The ultimate fate of that debris, and the properties of the bright flare that is produced and observed, depends on a number of parameters, including the energy of the center of mass of the original star. Here we present the results of a set of smoothed particle hydrodynamics simulations in which a 1M ⊙, γ = 5/3 polytrope is disrupted by a 106 M ⊙ supermassive black hole. Each simulation has a pericenter distance of r p = r t (i.e., β ≡ r t/r p = 1 with r t the tidal radius), and we vary the eccentricity e of the stellar orbit from e = 0.8 up to e = 1.20 and study the nature of the fallback of debris onto the black hole and the long-term fate of the unbound material. For simulations with eccentricities e ≲ 0.98, the fallback curve has a distinct, three-peak structure that is induced by self-gravity. For simulations with eccentricities e ≳ 1.06, the core of the disrupted star reforms following its initial disruption. Our results have implications for, e.g., tidal disruption events produced by supermassive black hole binaries.

SMART: A new implementation of Schwarzschild’s Orbit Superposition technique for triaxial galaxies and its application to an N-body merger simulation

We present SMART, a new 3D implementation of the Schwarzschild Method and its application to a triaxial N-body merger simulation. SMART fits full line-of-sight velocity distributions (LOSVDs) to determine the viewing angles, black hole, stellar and dark matter (DM) masses and the stellar orbit distribution of galaxies. Our model uses a 5D orbital starting space to ensure a representative set of stellar trajectories adaptable to the integrals-of-motion space and it is designed to deal with non-parametric stellar and DM densities. SMART’s efficiency is demonstrated by application to a realistic N-body merger simulation including supermassive black holes which we model from five different projections. When providing the true viewing angles, 3D stellar luminosity profile and normalized DM halo, we can (i) reproduce the intrinsic velocity moments and anisotropy profile with a precision of $\sim 1\%$ and (ii) recover the black hole mass, stellar mass-to-light ratio and DM normalization to better than a few percent accuracy. This precision is smaller than the currently discussed differences between initial-stellar-mass functions and scatter in black hole scaling relations. Further tests with toy models suggest that the recovery of the anisotropy in triaxial galaxies is almost unique when the potential is known and full LOSVDs are fitted. We show that orbit models even allow the reconstruction of full intrinsic velocity distributions, which contain more information than the classical anisotropy parameter. Surprisingly, the orbit library for the analysed N-body simulation’s gravitational potential contains orbits with net rotation around the intermediate axis that is stable over some Gyrs.

Disentangling the formation history of galaxies via population-orbit superposition: method validation

ABSTRACT We present population-orbit superposition models for external galaxies based on Schwarzschild’s orbit-superposition method, by tagging the orbits with age and metallicity. The models fit the density distributions, kinematic, and age and metallicity maps from integral field unit (IFU) spectroscopy observations. We validate the method and demonstrate its power by applying it to mock data, similar to those obtained by the Multi-Unit Spectroscopic Explorer (MUSE) IFU on the Very Large Telescope (VLT). These mock data are created from Auriga galaxy simulations, viewed at three different inclination angles (ϑ = 40°, 60°, 80°). Constrained by MUSE-like mock data, our model can recover the galaxy’s stellar orbit distribution projected in orbital circularity λz versus radius r, the intrinsic stellar population distribution in age t versus metallicity Z, and the correlation between orbits’ circularity λz and stellar age t. A physically motivated age–metallicity relation improves the recovering of intrinsic stellar population distributions. We decompose galaxies into cold, warm, and hot+counter-rotating components based on their orbit circularity distribution, and find that the surface density, velocity, velocity dispersion, and age and metallicity maps of each component from our models well reproduce those from simulation, especially for projections close to edge-on. These galaxies exhibit strong global age versus σz relation, which is well recovered by our model. The method has the power to reveal the detailed build-up of stellar structures in galaxies, and offers a complement to local resolved, and high-redshift studies of galaxy evolution.

A study of stellar orbit fractions: simulated IllustrisTNG galaxies compared to CALIFA observations

ABSTRACT Motivated by the recently discovered kinematic ‘Hubble sequence’ shown by the stellar orbit-circularity distribution of 260 CALIFA galaxies, we make use of a comparable galaxy sample at z = 0 with a stellar mass range of $M_{*}/\mathrm{M}_{\odot }\in [10^{9.7},\, 10^{11.4}]$ selected from the IllustrisTNG simulation and study their stellar orbit compositions in relation to a number of other fundamental galaxy properties. We find that the TNG100 simulation broadly reproduces the observed fractions of different orbital components and their stellar mass dependences. In particular, the mean mass dependences of the luminosity fractions for the kinematically warm and hot orbits are well reproduced within model uncertainties of the observed galaxies. The simulation also largely reproduces the observed peak and trough features at $M_{*}\approx 1\rm {-}2\times 10^{10}\, \mathrm{M}_{\odot }$ in the mean distributions of the cold- and hot-orbit fractions, respectively, indicating fewer cooler orbits and more hotter orbits in both more- and less-massive galaxies beyond such a mass range. Several marginal disagreements are seen between the simulation and observations: the average cold-orbit (counter-rotating) fractions of the simulated galaxies below (above) $M_{*}\approx 6\times 10^{10}\, \mathrm{M}_{\odot }$ are systematically higher than the observational data by $\lesssim 10{{\ \rm per\ cent}}$ (absolute orbital fraction); the simulation also seems to produce more scatter for the cold-orbit fraction and less so for the non-cold orbits at any given galaxy mass. Possible causes that stem from the adopted heating mechanisms are discussed.

A new dynamically self-consistent version of the Besançon Galaxy model

Context. Dynamically self-consistent galactic models are necessary for analysing and interpreting star counts, stellar density distributions, and stellar kinematics in order to understand the formation and the evolution of our Galaxy. Aims. We modify and improve the dynamical self-consistency of the Besançon Galaxy model in the case of a stationary and axisymmetric gravitational potential. Methods. Each stellar orbit is modelled by determining a Stäckel approximate integral of motion. Generalised Shu distribution functions (DFs) with three integrals of motion are used to model the stellar distribution functions. Results. This new version of the Besançon model is compared with the previous axisymmetric BGM2014 version and we find that the two versions have similar densities for each stellar component. The dynamically self-consistency is improved and can be tested by recovering the forces and the potential through the Jeans equations applied to each stellar distribution function. Forces are recovered with an accuracy better than one per cent over most of the volume of the Galaxy.

General relativistic effects on the orbit of the S2 star with GRAVITY

Context. The first observations of the GRAVITY instrument obtained in 2016, have shown that it should become possible to probe the spacetime close to the supermassive black hole Sagittarius A* (Sgr A*) at the Galactic center by using accurate astrometric positions of the S2 star. Aims. The goal of this paper is to investigate the detection by GRAVITY of different relativistic effects affecting the astrometric and/or spectroscopic observations of S2 such as the transverse Doppler shift, the gravitational redshift, the pericenter advance and higher-order general relativistic (GR) effects, in particular the Lense-Thirring effect due to the angular momentum of the black hole. Methods. We implement seven stellar-orbit models to simulate both astrometric and spectroscopic observations of S2 beginning near its next pericenter passage in 2018. Each model takes into account a certain number of relativistic effects. The most accurate one is a fully GR model and is used to generate the mock observations of the star. For each of the six other models, we determine the minimal observation times above which it fails to fit the observations, showing the effects that should be detected. These threshold times are obtained for different astrometric accuracies as well as for different spectroscopic errors. Results. Transverse Doppler shift and gravitational redshift can be detected within a few months by using S2 observations obtained with pairs of accuracies (σA,σV) = (10−100 μas, 1−10 km s-1) where σA and σV are the astrometric and spectroscopic accuracies, respectively. Gravitational lensing can be detected within a few years with (σA,σV) = (10 μas, 10 km s-1). Pericenter advance should be detected within a few years with (σA,σV) = (10 μas, 1−10 km s-1). Cumulative high-order photon curvature contributions, including the Shapiro time delay, affecting spectroscopic measurements can be observed within a few months with (σA,σV) = (10 μas, 1 km s-1). By using a stellar-orbit model neglecting relativistic effects on the photon path except the major contribution of gravitational lensing, S2 observations obtained with accuracies (σA,σV) = (10 μas, 10 km s-1), and a black hole angular momentum (a,i′,Ω′) = (0.99,45°,160°), the 1σ error on the spin parameter a is of about 0.4, 0.2, and 0.1 for a total observing run of 16, 30, and 47 yr, respectively. The 1σ errors on the direction of the angular momentum reach σi′ ≈ 25° and σΩ′ ≈ 40° when considering the three orbital periods run. We found that the uncertainties obtained with a less spinning black hole (a = 0.7) are similar to those evaluated with a = 0.99. Conclusions. The combination of S2 observations obtained with the GRAVITY instrument and the spectrograph SINFONI (Spectrograph for INtegral Field Observations in the Near Infrared) also installed at the VLT (Very Large Telescope) will lead to the detection of various relativistic effects. Such detections will be possible with S2 monitorings obtained within a few months or years, depending on the effect. Strong constraints on the angular momentum of Sgr A* (e.g., at 1σ = 0.1) with the S2 star will be possible with a simple stellar-orbit model without using a ray-tracing code but with approximating the gravitational lensing effect. However, long monitorings are necessary, and we thus must rely on the discovery of closer-in stars near Sgr A* if we want to efficiently constrain the black hole parameters with stellar orbits in a short time, or monitor the flares if they orbit around the black hole.

A Quasi-Stationary Twisted Disk Formed as a Result of a Tidal Disruption Event

In this note we briefly review the main results of our recent study of the formation of misaligned accretion disks after the tidal disruption of stars by rotating supermassive black holes. Since the accretion rates in such disks initially exceed the Eddington limit they are initially advection dominated. Assuming the α model for the disk viscosity implies that the disk can become thermally unstable when the accretion rate is comparable to, or smaller than, the Eddington value, while still being radiation pressure dominated. It then undergoes cyclic transitions between high and low states. During these transitions the aspect ratio varies from ~1 to ~10−3, which is reflected in changes in the degree of disk misalignment at the stream impact location. For maximal black hole rotation and sufiociently large values of the viscosity parameter, α ≳ 0.01–0.1, the ratio of the disk inclination to that of the initial stellar orbit is estimated to be 0.1–0.2 in the advection dominated state, while reaching order unity in the low state. Misalignment decreases with decrease of α, but increases as the black hole rotation parameter decreases. Thus, it is always significant when the latter is small.