In galactic nuclei, the gravitational potential is dominated by the central supermassive black hole, so stars follow quasi-Keplerian orbits. These orbits are distorted by gravitational forces from other stars, leading to long-term orbital relaxation. The direct numerical study of these processes is challenging because the fast orbital motion imposed by the central black hole requires very small timesteps. An alternative approach, pioneered by Gauss, is to use the secular approximation of smearing out the $N$ stars over their Keplerian orbits, using $K$ nodes along each orbit. In this study we propose three novel improvements to this method. First, we re-formulate the discretisation of the rates of change of the variables describing the orbital states to ensure that all conservation laws are exactly satisfied. Second, we replace the pairwise sum over nodes by a multipole expansion up to order $\ell_{\mathrm{max}}$, reducing the overall computational costs from $O(N^2K^2)$ to $O(NK\ell_{\mathrm{max}}^2)$. Finally, we show that the averaged dynamical system is equivalent to $2N$ interacting unit spin vectors and provide two time integrators: a second-order symplectic scheme and a fourth-order Lie-group Runge-Kutta method, both of which are straightforward to generalize to higher order. These new simulations recover the diffusion coefficients of stellar eccentricities obtained through analytical calculations of the secular dynamics.
The drift and diffusion coefficients of the inhomogeneous multi-mass degenerate Landau equation are computed to describe the self-induced resonant relaxation of a discrete self-gravitating quasi-Keplerian razor-thin axisymmetric disc orbiting a massive black hole while relying on Gauss' method. For a disc-like configuration in our Galactic centre, secular diffusion induces an adiabatic distortion of orbits. When considering a disc composed of multiple masses similarly distributed, the population of lighter stars will gain eccentricity, driving it closer to the central black hole provided the d…
Recent observations and simulations have revealed the dominance of secular processes over mergers in driving the growth of both supermassive black holes (SMBH) and galaxy evolution. Here we obtain narrowband imaging of AGN powered outflows in a sample of $12$ galaxies with disk-dominated morphologies, whose history is assumed to be merger-free. We detect outflows in $10/12$ sources in narrow band imaging of the [OIII] $5007 \unicode{x212B}$ emission using filters on the Shane-3m telescope. We calculate a mean outflow rate for these AGN of $0.95\pm0.14~\rm{M}_{\odot}~\rm{yr}^{-1}$. This exceeds…
We derive the secular evolution of the orbital elements of a stellar-mass object orbiting a spinning massive black hole. We use the post-Newtonian approximation in harmonic coordinates, with test-body equations of motion for the conservative dynamics that are valid through 3PN order, including spin-orbit, quadrupole and (spin)$^2$ effects, and with radiation-reaction contributions linear in the mass of the body that are valid through 4.5PN order, including the 4PN damping effects of spin-orbit coupling. The evolution equations for the osculating orbit elements are iterated to high PN orders us…
We investigate the orbital evolution of a system of N mutually interacting stars on initially circular orbits around the dominating central mass. We include perturbative influence of a distant axisymmetric source and an extended spherical potential. In particular, we focus on the case when the secular evolution of orbital eccentricities is suppressed by the spherical perturbation. By means of standard perturbation methods, we derive semi-analytic formulae for the evolution of normal vectors of the individual orbits. We find its two qualitatively different modes. Either the orbits interact stro…
The evolution of main sequence binaries resided in the galactic centre is influenced a lot by the central super massive black hole (SMBH). Due to this perturbation, the stars in a dense environment are likely to experience mergers or collisions through secular or non-secular interactions. In this work, we study the dynamics of the stellar binaries at galactic center, perturbed by another distant SMBH. Geometrically, such a four-body system is supposed to be decomposed into the inner triple (SMBH-star-star) and the outer triple (SMBH-stellar binary-SMBH). We survey the parameter space and deter…
The evolution of main sequence binaries that reside in the Galactic Centre can be heavily influenced by the central supermassive black hole (SMBH). Due to these perturbative effects, the stellar binaries in dense environments are likely to experience mergers, collisions or ejections through secular and/or non-secular interactions. More direct interactions with the central SMBH are thought to produce hypervelocity stars (HVSs) and tidal disruption events (TDEs). In this paper, we use N-body simulations to study the dynamics of stellar binaries orbiting a central SMBH primary with an outer SMBH …
We identify a gravitational-dynamical process in near-Keplerian potentials of galactic nuclei that occurs when an intermediate-mass black hole (IMBH) is migrating on an eccentric orbit through the stellar cluster towards the central supermassive black hole (SMBH). We find that, apart from conventional dynamical friction, the IMBH experiences an often much stronger systematic torque due to the secular (i.e., orbit-averaged) interactions with the cluster's stars. The force which results in this torque is applied, counterintuitively, in the same direction as the IMBH's precession and we refer to …
We study the correlations between Supermassive Black Holes (BH) and their host galaxies, using a sample of 83 BH masses collected from the most recent and reliable spatially resolved estimates available from the literature. We confirm the mono- and bivariate correlations between SMBHs and the bulges of their host galaxies, confirming that the correlation with the effective velocity dispersion is not significantly improved by higher dimensionality. Instead, pseudobulges do not seem to correlate with their SMBHs, probably because their secular evolution is often unable to trigger accretion onto …
We derive the kinetic equation that describes the secular evolution of a large set of particles orbiting a dominant massive object, such as stars bound to a supermassive black hole or a proto-planetary debris disc encircling a star. Because the particles move in a quasi-Keplerian potential, their orbits can be approximated by ellipses whose orientations remain fixed over many dynamical times. The kinetic equation is obtained by simply averaging the BBGKY equations over the fast angle that describes motion along these ellipses. This so-called Balescu-Lenard equation describes self-consistently …
Supermassive Black Holes grow at the center of galaxies in consonance with them. In this review we discuss the mass feeding mechanisms that lead to this growth in Active Galactic Nuclei (AGN), focusing on constraints derived from observations of their environment, from extragalactic down to galactic and nuclear scales. At high AGN luminosities, galaxy mergers and interactions play an important role in AGN triggering and feeding. However, gas chaotic cold accretion (CCA) in galaxy clusters can trigger radiatively inefficient AGNs in brightest cluster galaxies (BCGs). At lower luminosities, mino…
The origin of spin of low-mass supermassive black hole (SMBH) is still a puzzle at present. We here report a study on the host galaxies of a sample of radio-selected nearby ($z<0.05$) Seyfert 2 galaxies with a BH mass of $10^{6-7} M_\odot$. By modeling the SDSS $r$-band images of these galaxies through a 2-dimensional bulge+disk decomposition, we identify a new dependence of SMBH's radio power on host bulge surface brightness profile, in which more powerful radio emission comes from a SMBH associated with a more disk-like bulge. This result means low-mass and high-mass SMBHs are spun up by two…
As a natural consequence of cosmological hierarchical structure formation, sub-parsec supermassive black hole binaries (SMBHBs) should be common in galaxies but thus far have eluded spectroscopic identification. Based on four decades of optical spectroscopic monitoring, we report that the nucleus of NGC 5548, a nearby Seyfert galaxy long suspected to have experienced a major merger about one billion years ago, exhibits long-term variability with a period of 14 years in the optical continuum and broad Hbeta emission line. Remarkably, the double-peaked profile of Hbeta shows systematic velocity …
It arises a puzzle in \NGC\, how to secularly maintain the counter-rotating disc from $0.2$ to $7\,$pc unambiguously detected by recent ALMA observations of molecular gas. Upon further analysis of disc dynamics, we find that the Kelvin-Helmholtz (KH) instability (KHI) results in an unavoidable catastrophe of the disc developed at the interface between the reversely rotating parts, and demonstrate that a close binary of supermassive black holes provides tidal torques as the unique external sources to prevent the disc from the KH catastrophe. We are led to the inescapable conclusion that there m…
Statistics of the supermassive black hole gravitational wave background anisotropy
Laboratory of High Energy and Computational Physics, NICPB（高能计算物理实验室，NICPB）；Departament of Cybernetics, Tallinn University of Technology（塔林科技大学网络系）；Dipartimento di Fisica e Astronomia, Università degli Studi di Padova（帕多瓦大学物理与天文学系）；Istituto Nazionale di Fisica Nucleare, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
Tracking the assembly of supermassive black holes: a comparison of diverse models across cosmic time
Yale University（耶鲁大学）；Harvard University（哈佛大学）；Flatiron Institute（平顿研究所）；The City University of New York（纽约市立大学）；Space Telescope Science Institute（太空望远镜科学研究所）
Black Hole Binary Mergers in Galactic Nuclei: Combined Effects of Secular Dynamics and Stellar Flybys
Institute for Astronomy, School of Physics, Zhejiang University（浙江大学物理学院天文研究所）；Center for Cosmology and Computational Astrophysics, Institute for Advanced Study in Physics, Zhejiang University（浙江大学物理高等研究院宇宙学与计算天体物理中心）；Center of Gravity, Niels Bohr Institute（尼尔斯·玻尔研究所引力中心）；Niels Bohr International Academy, The Niels Bohr Institute（尼尔斯·玻尔研究所尼尔斯·玻尔国际学院）
Correlations between the mass of a supermassive black hole and the properties of its host galaxy (e.g., total stellar mass (M*), luminosity (Lhost)) suggest an evolutionary connection. A powerful test of a co-evolution scenario is to measure the relations MBH-Lhost and MBH-M* at high redshift and compare with local estimates. For this purpose, we acquired HST imaging with WFC3 of 32 X-ray-selected broad-line AGN at 1.2<z<1.7 in deep survey fields. By applying state-of-the-art tools to decompose the HST images including available ACS data, we measured the host galaxy luminosity and stellar mass…
We explore the effects of long term secular perturbations on the distribution of dark matter particles around Supermassive Black Hole (BH) binaries. We show that in the hierarchical (in separation) three-body problem, one of the BHs and a dark matter particle form an inner binary. Gravitational perturbations from the BH companion, on a much wider orbit, can cause the dark matter particle to reach extremely high eccentricities and even get accreted onto the BH, by what is known as the Eccentric Kozai-Lidov (EKL) mechanism. We show that this may produce a torus-like configuration for the dark ma…
Supermassive black holes launching plasma jets at close to speed of light, producing gamma-rays, have ubiquitously been found to be hosted by massive elliptical galaxies. Since elliptical galaxies are generally believed to be built through galaxy mergers, active galactic nuclei (AGN) launching relativistic jets are associated to the latest stages of galaxy evolution. We have discovered a pseudo-bulge morphology in the host galaxy of the gamma-ray AGN PKS 2004-447. This is the first gamma-ray emitter radio loud AGN found to be launched from a system where both black hole and host galaxy have be…
We continue to explore the relationship between globular cluster total number, $N_{\rm GC}$, and central black hole mass, $M_\bullet$, in spiral galaxies. We present here results for the Sab galaxies NGC 3368, NGC 4736 (M 94) and NGC 4826 (M 64), and the Sm galaxy NGC 4395. The globular cluster (GC) candidate selection is based on the ($u^*$ - $i^\prime$) versus ($i^\prime$ - $K_s$) color-color diagram, and $i^\prime$-band shape parameters. We determine the $M_\bullet$ versus $N_{\rm GC}$ correlation for these spirals, plus NGC 4258, NGC 253, M 104, M 81, M 31, and the Milky Way. We also redet…
We investigate the correlations between the black hole mass $M_{BH}$, the velocity dispersion $σ$, the bulge mass $M_{Bu}$, the bulge average spherical density $ρ_h$ and its spherical half mass radius $r_h$, constructing a database of 97 galaxies (31 core ellipticals, 17 power-law ellipticals, 30 classical bulges, 19 pseudo bulges) by joining 72 galaxies from the literature to 25 galaxies observed during our recent SINFONI black hole survey. For the first time we discuss the full error covariance matrix. We analyse the well known $M_{BH}-σ$ and $M_{BH}-M_{Bu}$ relations and establish the exist…
We summarize what large surveys of the contemporary universe have taught us about the physics and phenomenology of the processes that link the formation and evolution of galaxies and their central supermassive black holes. We present a picture in which the population of AGN can be divided into two distinct populations. The Radiative-Mode AGN are associated with black holes that produce radiant energy powered by accretion at rates in excess of ~1% of the Eddington Limit. They are primarily associated with less massive black holes growing in high-density pseudo-bulges at a rate sufficient to pro…
Davies et al. (2019) established that for L^* galaxies the fraction of baryons in the circumgalactic medium (CGM) is inversely correlated with the mass of their central supermassive black holes (BHs) in the EAGLE hydrodynamic simulation. The interpretation is that, over time, a more massive BH has provided more energy to transport baryons beyond the virial radius, which additionally reduces gas accretion and star formation. We continue this research by focusing on the relationship between the 1) BH masses, 2) physical and observational properties of the CGM, and 3) galaxy colours for Milky Way…
Motion of short-period stars orbiting the supermassive black hole in our Galactic Center has been monitored for more than 20 years. These observations are currently offering a new way to test the gravitational theory in an unexplored regime: in a strong gravitational field, around a supermassive black hole. In this proceeding, we present three results: (i) a constraint on a hypothetical fifth force obtained by using 19 years of observations of the two best measured short-period stars S0-2 and S0-38 ; (ii) an upper limit on the secular advance of the argument of the periastron for the star S0-2…
Beyond the Merger-Quasar-Quench Paradigm I: Mergers are neither necessary nor sufficient to quench central galaxies in IllustrisTNG
Stocker AstroScience Center, Dept. of Physics, Florida International University（佛罗里达国际大学斯托克天体科学中心物理系）；Cahill Center for Astronomy and Astrophysics, California Institute of Technology（加州理工学院卡希尔天文与天体物理中心）
The complex kinematics of the young stars orbiting the supermassive black hole in the Galactic center can be explained by the presence of an intermediate mass companion of Sgr A$^\star$
Beijing Planetarium, Beijing Academy of Science and Technology（北京天文馆，北京科学院）；School of Physics and Astronom, Sun Yat-sen University（中山大学物理学院）；CSST Science Center for the Guangdong-Hong Kong-Macau Greater Bay Area（中国空间站科学中心粤港澳大湾区分中心）；Department of Astronomy and Astrophysics, University of California Santa Cruz（加州大学圣克鲁斯分校天文学与天体物理学系）；Institute for Advanced Studies, Tsinghua University（清华大学高等研究院）；Universitats-Sternwarte Munchen, Ludwig-Maximilians University Munich University Observatory（慕尼黑大学天文台）；Max-Planck Institute for Extraterrestrial Physics（马克斯·普朗克地外物理研究所）；Department of Astronomy, Westlake University（西湖大学天文学系）
The closest galaxy center, our own Central Molecular Zone (CMZ; the central 500 pc of the Milky Way), is a powerful laboratory for studying the secular processes that shape galaxies across cosmic time, from large-scale gas flows and star formation to stellar feedback and interaction with a central supermassive black hole. Research over the last decade has revealed that the process of converting gas into stars in galaxy centers differs from that in galaxy disks. The CMZ is the only galaxy center in which we can identify and weigh individual forming stars, so it is the key location to establish …
We study supermassive black holes (BHs) in merging galaxies, using a suite of hydrodynamical simulations with very high spatial (~10 pc) and temporal (~1 Myr) resolution, where we vary the initial mass ratio, the orbital configuration, and the gas fraction. (i) We address the question of when and why, during a merger, increased BH accretion occurs, quantifying gas inflows and BH accretion rates. (ii) We also quantify the relative effectiveness in inducing AGN activity of merger-related versus secular-related causes, by studying different stages of the encounter: the stochastic (or early) stage…
We report the discovery of a buried, active supermassive black hole in SDSS J085153.64+392611.76, a bulgeless Seyfert 2 (Sy2) galaxy. Keck near-infrared observations reveal a hidden broad line region, allowing for the rare case where strong constraints can be placed on both the black hole mass and bulge component. Using virial mass estimators, we obtain a black hole mass of log($M_{\rm{BH}}/M_{\odot}$) = $6.78 \pm 0.50$. This is one of the only Sy2 AGN hosted in a bulgeless galaxy with a virial black hole mass estimate and could provide important constraints on the formation scenarios of the b…
According to the general-relativistic no-hair theorem, astrophysical black holes depend only on their masses and spins and are uniquely described by the Kerr metric. Mass and spin are the first two multipole moments of the Kerr spacetime and completely determine all other moments. The no-hair theorem can be tested by measuring potential deviations from the Kerr metric which alter such higher-order moments. In this review, I discuss tests of the no-hair theorem with current and future observations of such black holes across the electromagnetic spectrum, focusing on near-infrared observations of…
School of Natural Sciences, Institute for Advanced Study（自然科学院，高等研究院）；Rudolf Peierls Centre for Theoretical Physics, University of Oxford（鲁道夫·皮尔斯理论物理中心，牛津大学）
Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation $L\propto m^p$ between the mean Lyapunov exponent $L$ of stellar orbits chaotically scattered by a supermassive black hole in the center of a galaxy and the mass parameter $m$, i.e. ratio of the mass of the black hole over the mass of the galaxy. The exponent $p$ is found numerically to obtain values in the range $p \approx 0.3$--$0.5$. We propose a theoretical interpretation of these exponents, based on estimates of local `stretching numbers', i.e. local Lyapunov exponents at succes…
Galaxy-SMBH co-evolution in 2,435 DESI disk galaxies and merger-free BH growth in bulgeless disks
University of Oxford（牛津大学）；Lancaster University（兰卡斯特大学）；University of Edinburgh（爱丁堡大学）；Masaryk University（马萨里克大学）；University of Toronto（多伦多大学）；University of Louisville（路易斯维尔大学）；Haverford College（哈弗福德学院）；University of Utah（犹他大学）
Stars bound to a supermassive black hole interact gravitationally. Persistent torques acting between stellar orbits lead to the rapid resonant relaxation of the orbital orientation vectors ("vector" resonant relaxation) and slower relaxation of the eccentricities ("scalar" resonant relaxation), both at rates much faster than two-body or non-resonant relaxation. We describe a new parallel symplectic integrator, N-ring, which follows the dynamical evolution of a cluster of N stars through vector resonant relaxation, by averaging the pairwise interactions over the orbital period and periapsis-pre…
The supermassive black holes (SMBHs) of narrow-line Seyfert 1 galaxies (NLS1s) are at the lowest end of mass function of active galactic nuclei (AGNs) and preferentially reside in late-type host galaxies with pseudobulges, which are thought to be formed by internal secular evolution. On the other hand, the population of radio-loud NLS1s presents a challenge for the relativistic jet paradigm that powerful radio jets are exclusively associated with very high mass SMBHs in elliptical hosts, which are built-up through galaxy mergers. We investigated distorted radio structures associated with the n…
We analyse the effect of stochastic torque fluctuations on the orbital evolution and the gravitational wave (GW)emission of gas-embedded sources with intermediate and extreme mass ratios. We show that gas-driven fluctuations imprint additional harmonic content in the GWs of the binary system, which we dub dirty waveforms(DWs). We find three interesting observational prospects for DWs, provided that torque fluctuations do indeed persist beyond the resolution limit of current hydrodynamical simulations. Firstly, DWs can produce a significant stochastic GW background, comparable to other GW noise…
The Environmental Switch in Black Hole Feeding: Bar-Driven vs. Merger-Driven Growth in IllustrisTNG50
Indian Institute of Science, Education and Research (IISER) Tirupati（印度科学教育与研究学院提鲁帕蒂分校）；Department of Space, Platenary and Astronomical Science and Engineering, Indian Institute of Technology (IIT), Kanpur（坎普尔印度理工学院空间、行星与天文学科学与工程系）
Collisions and interactions between gas-rich galaxies are thought to be pivotal stages in their formation and evolution, causing the rapid production of new stars, and possibly serving as a mechanism for fueling supermassive black holes (BH). Harnessing the exquisite spatial resolution (~0.5 arcsec) afforded by the first ~170 deg^2 of the Hyper Suprime-Cam (HSC) Survey, we present our new constraints on the importance of galaxy-galaxy major mergers (1:4) in growing BHs throughout the last ~8 Gyrs. Utilizing mid-infrared observations in the WISE All-Sky survey, we robustly select active galacti…
Nuclear star clusters surrounding supermassive black holes (SMBHs) in galactic nuclei contain large numbers of stars, black holes (BHs) and neutron stars (NSs), a fraction of which are likely to form binaries. These binaries were suggested to form a triple system with the SMBH, which acts as a perturber and may enhance BH and NS mergers via the Lidov-Kozai mechanism. We follow-up previous studies, but for the first time perform an extensive statistical study of BH-BH, NS-NS and BH-NS binary mergers by means of direct high-precision regularized $N$-body simulations, including Post-Newtonian (PN…
The star formation rate (SFR) in the Central Molecular Zone (CMZ, i.e. the central 500 pc) of the Milky Way is lower by a factor of >10 than expected for the substantial amount of dense gas it contains, which challenges current star formation theories. In this paper, we quantify which physical mechanisms could be responsible. On scales larger than the disc scale height, the low SFR is found to be consistent with episodic star formation due to secular instabilities or possibly variations of the gas inflow along the Galactic bar. The CMZ is marginally Toomre-stable when including gas and stars, …
