arXiv subjects

Francesco Haardt

Publications and source records attributed to Francesco Haardt.

At least 37 records · Page 2Linked to original sources

arXiv2023

Eddington accreting Black Holes in the Epoch of Reionization

The evolution of the luminosity function (LF) of Active Galactic Nuclei (AGNs) at $z \gtrsim 5$ represents a key constraint to understand their contribution to the ionizing photon budget necessary to trigger the last phase transition in the Universe, i.e. the epoch of Reionization. Recent searches for bright high-z AGNs suggest that the space densities of this population at $z>4$ has to be revised upwards, and sparks new questions about their evolutionary paths. Gas accretion is the key physical mechanism to understand both the distribution of luminous sources and the growth of central Super-Massive Black Holes (SMBHs). In this work, we model the high-z AGN-LF assuming that high-z luminous AGN shine at their Eddington limit: we derive the expected evolution as a function of the ``duty-cycle'' ($f_{\rm dc}$), i.e. the fraction of life-time that a given SMBH spends accreting at the Eddington rate. Our results show that intermediate values ($f_{\rm dc} \simeq 0.1$) predict the best agreement with the ionizing background and photoionization rate, but do not provide enough ionizing photons to account for the observed evolution of the hydrogen neutral fraction. Smaller values ($f_{\rm dc} \lesssim 0.05$) are required for AGNs to be the dominant population responsible for Hydrogen reionization in the Early Universe. We then show that this low-$f_{\rm dc}$ evolution can be reconciled with the current constraints on Helium reionization, although it implies a relatively large number of inactive SMBHs at $z\gtrsim5$, in tension with SMBH growth models based on heavy seeding.

astro-ph.CO↗

arXiv2022

Dynamical evolution of massive black hole pairs in the presence of spin-dependent radiative feedback

The putative ubiquity of massive black holes (MBH) at the center of galaxies, and the hierarchical progress of structure formation along the cosmic history, together necessarily imply the existence of a large population of cosmic MBH binaries. Such systems are understood to be the loudest sources of gravitational waves at mHz frequencies, the regime that will be probed by the next Laser Interferometer Space Antenna (LISA). It has been proposed that the rate at which MBHs pair and then bind to form binaries is critically dependent upon the feedback exerted by the MBHs on the surrounding gaseous environment. Using the publicly available code GIZMO, we perform a suite of simulations aimed at studying the dynamics of a MBH pair embedded in a gaseous disk on 100 pc scale. By means of dedicated modules, we follow the dynamics of MBHs in the presence of different spin-dependent radiative feedback models, and compare the results to a benchmark case with no feedback at all. Our main finding is that feedback causes the secondary MBH to shrink its orbit at a reduced pace, when compared to models where feedback is absent. Moreover, such slower inspiral occurs on eccentric orbits, as feedback has the net effect of hampering the circularization process. Though idealized in many aspects, our study highlights and quantifies the importance of including spin-dependent feedback recipes in hydrodynamic simulations of MBH pairs, and ultimately in assessing the cosmological coalescence rate of such systems in view of their detection through gravitational waves.

astro-ph.GA↗

arXiv2022

On the detectability of gravitational waves from primordial black holes orbiting Sgr A*

In this work we characterize the expected gravitational wave signal detectable by the planned space-borne interferometer LISA and the proposed next generation space-borne interferometer $μ$Ares arising from a population of primordial black holes orbiting Sgr A*, the super-massive black hole at the Galactic center. Assuming that such objects indeed form the entire diffuse mass allowed by the observed orbit of S2 in the Galactic center, under the simplified assumption of circular orbits and monochromatic mass function, we assess the expected signal in gravitational waves, either from resolved and non-resolved sources. We estimate a small but non negligible chance of $\simeq$ 10% of detecting one single 1 M$_{\odot}$ primordial black hole with LISA in a 10-year-long data stream, while the background signal due to unresolved sources would essentially elude any reasonable chance of detection. On the contrary, $μ$Ares, with a $\simeq$ 3 orders-of-magnitude better sensitivity at $\simeq$ 10$^{-5}$ Hz, would be able to resolve $\simeq$ 140 solar mass primordial black holes in the same amount of time, while the unresolved background should be observable with an integrated signal-to-noise ratio $\gtrsim$ 100. Allowing the typical PBH mass to be in the range 0.01-10 M$_{\odot}$ would increase LISA chance of detection to $\simeq$ 40% towards the lower limit of the mass spectrum. In the case of $μ$Ares, instead, we find a "sweet spot" just about 1 M$_{\odot}$, a mass for which the number of resolvable events is indeed maximized.

gr-qc↗

arXiv2022

Maximally informed Bayesian modelling of disc galaxies

Dissecting the underlying structure of galaxies is of main importance in the framework of galaxy formation and evolution theories. While a classical bulge+disc decomposition of disc galaxies is usually taken as granted, this is only rarely solidly founded upon the full exploitation of the richness of data arising from spectroscopic studies with integral field units. In this work we describe a fully Bayesian estimation method of the global structure of disc galaxies which makes use of the wealth of photometric, kinematic, and mass-to-light ratio data, and that can be seen as a first step towards a machine-learning approach, certainly needed when dealing with larger samples of galaxies. Ours is a novel, hybrid line of action in tackling the problem of galactic parameter estimation, neither purely photometric nor orbit-based. Being rooted on a nested sampler, our code, which is available publicly as an online repository, allows for a statistical assessment of the need for multiple components in the dissecting process. As a first case-study the GPU-optimized code is applied to the S0 galaxy NGC-7683, finding that in this galaxy a pseudo-bulge, possibly the remnant of a bar-like structure, does exist in the center of the system. These results are then tested against the publicly available, orbit-based code DYNAMITE, finding substantial agreement.

astro-ph.GA↗

arXiv2022

Misaligned Spinning Binary Black Hole Mergers in Hot Magnetized Plasma

We present general relativistic magneto-hydrodynamical simulations of equal-mass spinning black hole binary mergers embedded in a magnetized gas cloud. We focus on the effect of the spin orientation relative to the orbital angular momentum on the flow dynamics, mass accretion rate and Poynting luminosity. We find that, across the inspiral, the gas accreting onto the individual black holes concentrates into disk-like overdensities, whose angular momenta are oriented towards the spin axes and which persist until merger. We identify quasi-periodic modulations occurring in the mass accretion rate at the level of 1-20%, evolving in parallel with the gravitational wave chirp. The similarity between the accretion rate time-series and the gravitational strain is a consequence of the interplay between strong, dynamical gravitational fields and magnetic fields in the vicinity of the inspiralling black holes. This result suggests that quasi-periodicity in the pre-merger accretion rate of massive binaries is not exclusive of environments in which the black holes are embedded in a circumbinary accretion disk, and could provide an additional useful signature of electromagnetic emission concurrent to low-frequency gravitational wave detection.

astro-ph.HE↗

arXiv2022

Re-weighting dark matter in disc galaxies: a new general relativistic observational test

A recent analysis of data from the ESA Gaia mission demonstrated that the kinematics of stars in the Milky Way can be modelled without invoking the presence of dark matter whatsoever. Indeed, the higher-than-Keplerian velocities observed in outer stars can be ascribed to the properties of the general relativistic (GR) metric assumed to describe the Galaxy. Here we generalize the concept, and derive the most general exact GR model for a stationary axi-symmetric dynamically cold dust structure. We explicitly show how deviations from the commonly adopted Newtonian dynamics are indeed manifest even at low velocities and low densities. We provide for the first time a detailed description of the frequency shift experienced by photons travelling from any emission site within an external disc galaxy to the observer, relating the outcome of the shift measurement to the gravitational properties of the galaxy. Finally, we devise a novel, groundbreaking observational test potentially able to fully characterize the GR metric under the minimal set of assumptions mentioned above. The proposed experiment exploits the effects non-diagonal GR terms have on the frequency shift of photons, ultimately providing a test to evaluate whether dark matter is actually required by disc galaxy kinematics.

astro-ph.GA↗

arXiv2022

Irradiation-driven escape of primordial planetary atmospheres II. Evaporation efficiency of sub-Neptunes through hot Jupiters

Making use of the publicly available 1D photoionization hydrodynamics code ATES we set out to investigate the combined effects of planetary gravitational potential energy ($ϕ_p\equiv GM_p/R_p$) and stellar X-ray and Extreme Ultraviolet (XUV) irradiation ($F_{\rm XUV}$) on the evaporation efficiency ($η$) of moderately-to-highly irradiated gaseous planets, from sub-Neptunes through hot Jupiters. We show that the (known) existence of a threshold potential above which energy-limited escape (i.e., $η\simeq 1$) is unattainable can be inferred analytically. For $\log ϕ_p\gtrsim \log ϕ_p^{\rm thr}\approx [12.9-13.2]$ (in cgs units), most of the energy absorption occurs where the average kinetic energy acquired by the ions through photo-electron collisions is insufficient for escape. This causes the evaporation efficiency to plummet with increasing $ϕ_p$,. Whether or not planets with $ϕ_p\lesssim ϕ_p^{\rm thr}$ exhibit energy-limited outflows is regulated primarily by the stellar irradiation level. Specifically, for low-gravity planets, above $F_{\rm XUV}\simeq 10^{4-5}$ erg cm$^{-2}$s$^{-1}$ Ly$α$ losses overtake adiabatic and advective cooling and the evaporation efficiency of low-gravity planets drops below the energy-limited approximation, albeit remaining largely independent of $ϕ_p$Further, we show that whereas $η$ increases as $F_{\rm XUV}$ increases for planets above $ϕ^{\rm thr}_p$, the opposite is true for low-gravity planets. This behavior can be understood by examining the relative fractional contributions of advective and radiative losses as a function of atmospheric temperature. This novel framework enables a reliable, physically motivated prediction of the expected evaporation efficiency for a given planetary system; an analytical approximation of the best-fitting $η$ is given in the appendix.

astro-ph.EP↗

arXiv2021

Irradiation-driven escape of primordial planetary atmospheres I. The ATES photoionization hydrodynamics code

Intense X-ray and ultraviolet stellar irradiation can heat and inflate the atmospheres of closely orbiting exoplanets, driving mass outflows that may be significant enough to evaporate a sizable fraction of the planet atmosphere over the system lifetime. The recent surge in the number of known exoplanets, together with the imminent deployment of new ground and space-based facilities for exoplanet discovery and characterization, requires a prompt and efficient assessment of the most promising targets for intensive spectroscopic follow-ups. To this purpose, we developed ATES (ATmospheric EScape); a new hydrodynamics code that is specifically designed to compute the temperature, density, velocity and ionization fraction profiles of highly irradiated planetary atmospheres, along with the current, steady-state mass loss rate. ATES solves the one-dimensional Euler, mass and energy conservation equations in radial coordinates through a finite-volume scheme. The hydrodynamics module is paired with a photoionization equilibrium solver that includes cooling via bremsstrahlung, recombination and collisional excitation/ionization for the case of a primordial atmosphere entirely composed of atomic hydrogen and helium, whilst also accounting for advection of the different ion species. Compared against the results of 14 moderately-to-highly irradiated planets simulated with The PLUTO-CLOUDY Interface (TPCI), ATES yields remarkably good agreement at a significantly smaller fraction of the computational time. A convergence study shows that ATES recovers stable, steady-state hydrodynamic solutions for systems with $\log(-ϕ_p) \lesssim 12.9 + 0.17\log F_{\rm XUV}$. Incidentally, atmospheres of systems above this threshold are generally thought to be undergoing Jeans escape. The code, which also features a user-friendly graphic interface, is available publicly as an online repository.

astro-ph.EP↗

arXiv2021

The Evolution of the Lyman-Alpha Luminosity Function During Reionization

The time frame in which hydrogen reionization occurred is highly uncertain, but can be constrained by observations of Lyman-alpha (Ly$α$) emission from distant sources. Neutral hydrogen in the intergalactic medium (IGM) attenuates Ly$α$~photons emitted by galaxies. As reionization progressed the IGM opacity decreased, increasing Ly$α$~visibility. The galaxy Ly$α$~luminosity function (LF) is thus a useful tool to constrain the timeline of reionization. In this work, we model the Ly$α$~LF as a function of redshift, $z=5-10$, and average IGM neutral hydrogen fraction, $\overline{x}_\textsc{hi}$. We combine the Ly$α$~luminosity probability distribution obtained from inhomogeneous reionization simulations with a model for the UV LF to model the Ly$α$~LF. As the neutral fraction increases, the average number density of Ly$α$~emitting galaxies decreases, and are less luminous, though for $\overline{x}_\textsc{hi} \lesssim 0.4$ there is only a small decrease of the Ly$α$~LF. We use our model to infer the IGM neutral fraction at $z=6.6, 7.0, 7.3$ from observed Ly$α$~LFs. We conclude that there is a significant increase in the neutral fraction with increasing redshift: $\overline{x}_\textsc{hi}(z=6.6)=0.08^{+ 0.08}_{- 0.05}, \, \overline{x}_\textsc{hi}(z=7.0)=0.28 \pm 0.05$ and $\overline{x}_\textsc{hi}(z=7.3)=0.83^{+ 0.06}_{- 0.07}$. We predict trends in the Ly$α$~luminosity density and Schechter parameters as a function of redshift and the neutral fraction. We find that the Ly$α$~luminosity density decreases as the universe becomes more neutral. Furthermore, as the neutral fraction increases, the faint-end slope of the Ly$α$~LF steepens, and the characteristic Ly$α$~luminosity shifts to lower values, concluding that the evolving shape of the Ly$α$~LF -- not just its integral -- is an important tool to study reionization.

astro-ph.GA↗

arXiv2021

Fully General Relativistic Magnetohydrodynamic Simulations of Accretion Flows onto Spinning Massive Black Hole Binary Mergers

We perform the first suite of fully general relativistic magnetohydrodynamic simulations of spinning massive black hole binary mergers. We consider binary black holes with spins of different magnitudes aligned to the orbital angular momentum, which are immersed in a hot, magnetized gas cloud. We investigate the effect of the spin and degree of magnetization (defined through the fluid parameter $β^{-1}\equiv p_{\mathrm{mag}}/p_{\mathrm{fluid}}$) on the properties of the accretion flow. We find that magnetized accretion flows are characterized by more turbulent dynamics, as the magnetic field lines are twisted and compressed during the late inspiral. Post-merger, the polar regions around the spin axis of the remnant Kerr black hole are magnetically dominated, and the magnetic field strength is increased by a factor $\sim$10$^2$ (independently from the initial value of $β^{-1}$). The magnetized gas in the equatorial plane acquires higher angular momentum, and settles in a thin circular structure around the black hole. We find that mass accretion rates of magnetized configurations are generally smaller than in the unmagnetized cases by up to a factor $\sim$3. Black hole spins have also a suppressing effect on the accretion rate, as large as $\sim$48\%. As a potential driver for electromagnetic emission we follow the evolution of the Poynting luminosity, which increases after merger up to a factor $\sim2$ with increasing spin, regardless of the initial level of magnetization of the fluid. Our results stress the importance of taking into account both spins and magnetic fields when studying accretion processes onto merging massive black holes.

astro-ph.HE↗

arXiv2021

Proof of CMB-driven X-ray brightening of high-z radio galaxies

We present a definitive assessment of the role of Inverse Compton scattering of Cosmic Microwave Background photons (IC/CMB) in the context of radio galaxies. Owing to the steep increase of the CMB radiation energy density, IC/CMB is supposed to become progressively more important with respect to radio synchrotron cooling as the redshift increases. For typical energies at play, this process will up-scatter the CMB photons into the X-ray band, and is thus expected to yield a redshift-dependent, concurrent X-ray brightening and radio dimming of the jet-powered structures. Here we show how a conclusive proof of this effect hinges on high-resolution imaging data in which the extended lobes can be distinguished from the compact hot spots where synchrotron-self-Compton dominates the X-ray emission regardless of redshift. We analyze Chandra and Very Large Array data of 11 radio galaxies between 1.3 3 radio galaxies below <1 mJy, IC/CMB alone can not be responsible for a deficit in high-z, radio-loud AGN if--as we argue--such AGN typically have bright, compact hot spots.

astro-ph.HE↗

arXiv2021

Intermediate mass black holes from stellar mergers in young star clusters

Intermediate mass black holes (IMBHs) in the mass range $10^2-10^5\,\mathrm{M_{\odot}}$ bridge the gap between stellar black holes (BHs) and supermassive BHs. Here, we investigate the possibility that IMBHs form in young star clusters via runaway collisions and BH mergers. We analyze $10^4$ simulations of dense young star clusters, featuring up-to-date stellar wind models and prescriptions for core collapse and (pulsational) pair instability. In our simulations, only 9 IMBHs out of 218 form via binary BH mergers, with a mass $\sim{}100-140$ M$_\odot$. This channel is strongly suppressed by the low escape velocity of our star clusters. In contrast, IMBHs with masses up to $\sim{}438$ M$_{\odot}$ efficiently form via runaway stellar collisions, especially at low metallicity. Up to $\sim{}0.2$~% of all the simulated BHs are IMBHs, depending on progenitor's metallicity. The runaway formation channel is strongly suppressed in metal-rich ($Z=0.02$) star clusters, because of stellar winds. IMBHs are extremely efficient in pairing with other BHs: $\sim{}70$% of them are members of a binary BH at the end of the simulations. However, we do not find any IMBH-BH merger. More massive star clusters are more efficient in forming IMBHs: $\sim{}8$% ($\sim{}1$%) of the simulated clusters with initial mass $10^4-3\times{}10^4$ M$_\odot$ ($10^3-5\times{}10^3$ M$_\odot$) host at least one IMBH.

astro-ph.GA↗

arXiv2020

Unveiling early black hole growth with multi-frequency gravitational wave observations

Third Generation ground based Gravitational Wave Interferometers, like the Einstein Telescope (ET), Cosmic Explorer (CE), and the Laser Interferometer Space Antenna (LISA) will detectcoalescing binary black holes over a wide mass spectrum and across all cosmic epochs. We track the cosmological growth of the earliest light and heavy seeds that swiftly transit into the supermassive domain using a semi analytical model for the formation of quasars at $z=6.4$, 2 and $0.2$, in which we follow black hole coalescences driven by triple interactions. We find that light seed binaries of several $10^2$ M$_\odot$ are accessible to ET with a signal-to-noise ratio ($S/N$) of $10-20$ at $6 20$). Mergers involving heavy seeds ($\sim 10^5 M_\odot - 10^6 M_\odot$) would be within reach up to $z=20$ in the LISA frequency domain. The lower-z model predicts $11.25(18.7)$ ET(LISA) events per year, overall.

astro-ph.GA↗

arXiv2020

Binary black holes in young star clusters: the impact of metallicity

Young star clusters are the most common birth-place of massive stars and are dynamically active environments. Here, we study the formation of black holes (BHs) and binary black holes (BBHs) in young star clusters, by means of 6000 N-body simulations coupled with binary population synthesis. We probe three different stellar metallicities (Z=0.02, 0.002 and 0.0002) and two initial density regimes (density at the half-mass radius $ρ_{\rm h}\ge{}3.4\times10^4$ and $\ge{1.5\times10^2}$ M$_\odot$ pc$^{-3}$ in dense and loose star clusters, respectively). Metal-poor clusters tend to form more massive BHs than metal-rich ones. We find $\sim{}6$, $\sim{}2$, and $<1$% of BHs with mass $m_{\rm BH}>60$ M$_\odot$ at Z=0.0002, 0.002 and 0.02, respectively. In metal-poor clusters, we form intermediate-mass BHs with mass up to $\sim{}320$ M$_\odot$. BBH mergers born via dynamical exchanges (exchanged BBHs) can be more massive than BBH mergers formed from binary evolution: the former (latter) reach total mass up to $\sim{}140$ M$_\odot$ ($\sim{}80$ M$_\odot$). The most massive BBH merger in our simulations has primary mass $\sim{}88$ M$_\odot$, inside the pair-instability mass gap, and a mass ratio of $\sim{}0.5$. Only BBHs born in young star clusters from metal-poor progenitors can match the masses of GW170729, the most massive event in O1 and O2, and those of GW190412, the first unequal-mass merger. We estimate a local BBH merger rate density $\sim{}110$ and $\sim{}55$ Gpc$^{-3}$ yr$^{-1}$, if we assume that all stars form in loose and dense star clusters, respectively.

astro-ph.HE↗

arXiv2020

Extended X-ray emission from the z=4.26 radio galaxy 4C 63.20

We report on deep Chandra X-ray Telescope imaging observations of 4C 63.20, one of the few known radio galaxies at z>3.5. The X-ray counterpart is resolved into a core plus two off-nuclear sources that (combined) account for close to 30% of the total X-ray flux. Their morphology and orientation are consistent with a diffuse, lobe-like nature, albeit compact hotspots cannot be ruled out. The broadband spectral energy distribution of 4C 63.20 can be reproduced with a jet model where the majority of the radio flux can be ascribed to synchrotron emission from the hotspots, whereas the (non-nuclear) X-ray emission is produced via Inverse Compton (IC) off of Cosmic Microwave Background (CMB) photons within the extended lobes. This scenario is broadly consistent with the expectation from highly magnetized lobes in a hotter CMB, and supports the view that IC/CMB may quench less extreme radio lobes at high redshifts.

astro-ph.HE↗

arXiv2020

Lyman Continuum Escape Fraction from Low-mass Starbursts at z=1.3

We present a new constraint on the Lyman Continuum (LyC) escape fraction at z~1.3. We obtain deep, high sensitivity far-UV imaging with the Advanced Camera for Surveys (ACS) Solar Blind Channel (SBC) on the Hubble Space Telescope (HST), targeting 11 star-forming galaxies at 1.2 190 Å, low stellar mass (M* < 10^10 M_sun) and U-band magnitude of U<24.2. These criteria identify young, low metallicity star bursting populations similar to the primordial star-forming galaxies believed to have reionized the universe. We do not detect any LyC signal (with S/N >3) in the individual galaxies or in the stack in the far-UV images. We place $3σ$ limits on the relative escape fraction of individual galaxies to be f_{esc,rel}<[0.10-0.22] and a stacked $3σ$ limit of f_{esc,rel}<0.07. Comparing to the confirmed LyC emitters from the literature, the galaxies in our sample span similar ranges of various galaxy properties including stellar mass, dust attenuation, and star formation rate (SFR). In particular, we compare the distribution of H$α$ and [OIII] EWs of confirmed LyC emitters and non-detections including the galaxies in this study. Finally, we discuss if a dichotomy seen in the distribution of H$α$ EWs can perhaps distinguish the LyC emitters from the non-detections.

astro-ph.GA↗

arXiv2020

Binary black holes in the pair-instability mass gap

Pair instability (PI) and pulsational PI prevent the formation of black holes (BHs) with mass $\gtrsim{}60$ M$_\odot$ from single star evolution. Here, we investigate the possibility that BHs with mass in the PI gap form via stellar mergers and multiple stellar mergers, facilitated by dynamical encounters in young star clusters. We analyze $10^4$ simulations, run with the direct N-body code nbody6++gpu coupled with the population synthesis code MOBSE. We find that up to $\sim{}6$~% of all simulated BHs have mass in the PI gap, depending on progenitor's metallicity. This formation channel is strongly suppressed in metal-rich (Z = 0.02) star clusters, because of stellar winds. BHs with mass in the PI gap are initially single BHs but can efficiently acquire companions through dynamical exchanges. We find that $\sim{}$21%, 10% and 0.5% of all binary BHs have at least one component in the PI mass gap at metallicity Z = 0.0002, 0.002 and 0.02, respectively. Based on the evolution of the cosmic star formation rate and metallicity, and under the assumption that all stars form in young star clusters, we predict that $\sim{}5$~% of all binary BH mergers detectable by advanced LIGO and Virgo at their design sensitivity have at least one component in the PI mass gap.

astro-ph.HE↗

arXiv2020

On the eccentricity evolution of massive black hole binaries in stellar backgrounds

We study the dynamical evolution of eccentric massive black hole binaries (MBHBs) interacting with unbound stars by means of an extensive set of three body scattering experiments. Compared to previous studies, we extend the investigation down to a MBHB mass ratio of $q=m_2/m_1=10^{-4}$, where $m_1$ and $m_2$ are the masses of the primary and secondary hole respectively. Contrary to a simple extrapolation from higher mass ratios, we find that for $q\lesssim 10^{-3}$ the eccentricity growth rate becomes negative, i.e., the binary {\it circularises} as it shrinks. This behaviour is due to the subset of interacting stars captured in metastable counter-rotating orbits; those stars tend to extract angular momentum from the binary, promoting eccentricity growth for $q>10^{-3}$, but tend to inject angular momentum into the binary driving it towards circularisation for $q<10^{-3}$. The physical origin of this behaviour requires a detailed study of the orbits of this subset of stars and is currently under investigation. Our findings might have important consequences for intermediate MBHs (IMBHs) inspiralling onto MBHs (e.g. a putative $10^3\rm M_{\odot}$ black hole inspiralling onto SgrA$^*$).

astro-ph.GA↗