arXiv subjects

Andrew Mummery

Publications and source records attributed to Andrew Mummery.

At least 55 records · Page 3Linked to original sources

arXiv2024

Continuum emission from within the plunging region of black hole discs

The thermal continuum emission observed from accreting black holes across X-ray bands has the potential to be leveraged as a powerful probe of the mass and spin of the central black hole. The vast majority of existing ``continuum fitting'' models neglect emission sourced at and within the innermost stable circular orbit (ISCO) of the black hole. Numerical simulations, however, find non-zero emission sourced from these regions. In this work we extend existing techniques by including the emission sourced from within the plunging region, utilising new analytical models which reproduce the properties of numerical accretion simulations. We show that in general the neglected intra-ISCO emission produces a hot-and-small quasi-blackbody component, but can also produce a weak power-law tail for more extreme parameter regions. A similar hot-and-small blackbody component has been added in by hand in an ad-hoc manner to previous analyses of X-ray binary spectra. We show that the X-ray spectrum of MAXI J1820+070 in a soft-state outburst is extremely well described by a full Kerr black hole disc, while conventional models which neglect intra-ISCO emission are unable to reproduce the data. We believe this represents the first robust detection of intra-ISCO emission in the literature, and allows additional constraints to be placed on the MAXI J1820+070 black hole spin which must be low $a_\bullet < 0.5$ to allow a detectable intra-ISCO region. Emission from within the ISCO is the dominant emission component in the MAXI J1820+070 spectrum between $6$ and $10$ keV, highlighting the necessity of including this region. Our continuum fitting model is made publicly available.

astro-ph.HE↗

arXiv2024

The turbulent variability of accretion discs observed at high energies

We use numerical stochastic-viscous hydrodynamic simulations and new analytical results from thin disc theory to probe the turbulent variability of accretion flows, as observed at high energies. We show that the act of observing accretion discs in the Wien tail exponentially enhances small-scale temperature variability in the flow, which in a real disc will be driven by magnetohydrodynamic turbulence, to large amplitude luminosity fluctuations (as predicted analytically). In particular, we demonstrate that discs with more spatially coherent turbulence (as might be expected of thicker discs), and relativistic discs observed at larger inclinations, show significantly enhancement in their Wien-tail variability. We believe this is the first analysis of relativistic viewing-angle effects on turbulent variability in the literature. Using these results we argue that tidal disruption events represent particularly interesting systems with which to study accretion flow variability, and may in fact be the best astrophysical probes of small scale disc turbulence. This is a result of a typical tidal disruption event disc being naturally observed in the Wien-tail and likely having a somewhat thicker disc and cleaner X-ray spectrum than other sources. We argue for dedicated X-ray observational campaigns of tidal disruption events, with the aim of studying accretion flow variability.

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arXiv2024

A Case for a Binary Black Hole System Revealed via Quasi-Periodic Outflows

Binaries containing a compact object orbiting a supermassive black hole are thought to be precursors of gravitational wave events, but their identification has been extremely challenging. Here, we report quasi-periodic variability in X-ray absorption which we interpret as quasi-periodic outflows (QPOuts) from a previously low-luminosity active galactic nucleus after an outburst, likely caused by a stellar tidal disruption. We rule out several models based on observed properties and instead show using general relativistic magnetohydrodynamic simulations that QPOuts, separated by roughly 8.3 days, can be explained with an intermediate-mass black hole secondary on a mildly eccentric orbit at a mean distance of about 100 gravitational radii from the primary. Our work suggests that QPOuts could be a new way to identify intermediate/extreme-mass ratio binary candidates.

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arXiv2024

The maximum mass of a black hole which can tidally disrupt a star: measuring black hole spins with tidal disruption events

The tidal acceleration experienced by an object at the event horizon of a black hole decreases as one over the square of the black hole's mass. As such there is a maximum mass at which a black hole can tidally disrupt an object outside of its event horizon and potentially produce observable emission. This maximum mass is known as the ``Hills mass'', and in full general relativity is a function of both the black hole's spin $a_\bullet$ and the inclination angle of the incoming object's orbit with respect to the black hole's spin axis $ψ$. In this paper we demonstrate that the Hills mass can be represented by a simple analytical function of $a_\bullet$ and $ψ$, the first general solution of this problem. This general solution is found by utilising the symmetries of a class of critical Kerr metric orbits known as the innermost bound spherical orbits. Interestingly, at fixed black hole spin the maximum Hills mass can lie at incoming orbital inclinations outside of the black hole's equatorial plane $ψ\neq π/2$. When compared to previous results in the literature this effect can lead to an increase in the maximum Hills mass (at fixed spin) by as much as a factor of $\sqrt{11/5} \simeq 1.48$ for a maximally rotating black hole. We then demonstrate how Bayesian inference, coupled with an estimate of the mass of a black hole in a tidal disruption event, can be used to place conservative constraints on that black hole's spin. We provide a publicly available code tidalspin which computes these spin distributions.

gr-qc↗

arXiv2024

The dynamics of accretion flows near to the innermost stable circular orbit

Accretion flows are fundamentally turbulent systems, yet are classically modelled with viscous theories only valid on length scales significantly greater than the typical size of turbulent eddies in the flow. We demonstrate that, while this will be a reasonable bulk description of the flow at large radii, this must break down as the flow approaches absorbing boundaries, such as the innermost stable circular orbit (ISCO) of a black hole disc. This is because in a turbulent flow large velocity fluctuations can carry a fluid element over the ISCO from a finite distance away, from which it will not return, a process without analogy in conventional models. This introduces a non-zero directional bias into the velocity fluctuations in the near-ISCO disc. By studying reduced random walk problems, we derive a number of implications of the presence of an absorbing boundary in an accretion context. In particular, we show that the average velocity with which a typical fluid element crosses the ISCO is much larger than is assumed in traditional theories. This enhanced velocity modifies the thermodynamic properties of black hole accretion flows on both sides of the ISCO. In particular, thermodynamic quantities for larger ISCO stresses no longer display pronounced cusps at the ISCO in this new formalism, a result with relevance for a number of observational probes of the intra-ISCO region. Finally, we demonstrate that these extended models reproduce the trans-ISCO behaviour observed in GRMHD simulations of thin discs.

astro-ph.HE↗

arXiv2024

Reflecting on naked singularities: iron line fitting as a probe of the cosmic censorship conjecture

We demonstrate that the X-ray iron line fitting technique can be leveraged as a powerful probe of the cosmic censorship conjecture. We do this by extending existing emission line models to arbitrary spin parameters of the Kerr metric, no longer restricted to black hole metrics with $|a_\bullet |< 1$. We show that the emission lines from naked singularity metrics ($|a_\bullet| > 1$) show significant differences to their black hole counterparts, even for those metrics with identical locations of the innermost stable circular orbit, i.e., emission line fitting does not suffer from the degeneracy which affects continuum fitting approaches. These differences are entirely attributable to the disappearance of the event horizon for $|a_\bullet| > 1$. We highlight some novel emission line features of naked singularity metrics, such as ``inverted'' emission lines (with sharp red wings and extended blue wings) and ``triple lines''. The lack of detection of any of these novel features provides support of the cosmic censorship conjecture. We publicly release {\tt XSPEC} packages {\tt skline} and {\tt skconv} which can now be used to probe the cosmic censorship conjecture in Galactic X-ray binaries and Active Galactic Nuclei. The inclusion of super-extremal spacetimes can be alternatively posed as a way of stress-testing conventional models of accretion.

astro-ph.HE↗

arXiv2023

Testing theories of accretion and gravity with super-extremal Kerr discs

Fitting the thermal continuum emission of accreting black holes observed across X-ray bands represents one of the principle means of constraining the properties (mass and spin) of astrophysical black holes. Recent ''continuum fitting'' studies of Galactic X-ray binaries in the soft state have found best fitting dimensionless spin values which run into the prior bounds placed on traditional models ($a_\star = 0.9999$). It is of critical importance that these results are robust, and not a result solely of the presence of these prior bounds and deficiencies in conventional models of accretion. Motivated by these results we derive and present superkerr, an XSPEC model comprising of a thin accretion disc solution valid in the Kerr geometry for arbitrary spin parameter $a_\star$, extending previous models valid only for black holes ($|a_\star| < 1$). This extension into ''superextremal'' spacetimes with $|a_\star| > 1$ includes solutions which describe discs evolving around naked singularities, not black holes. While being valid solutions of Einstein's field equations these naked singularities are not expected to be present in nature. We discuss how the ''measurement'' of a Kerr spin parameter $1 < a_\star < 5/3$ would present compelling evidence for the requirement of a rethink in either standard accretion theory, or our theories of gravity.

gr-qc↗

arXiv2023

Fundamental scaling relationships revealed in the optical light curves of tidal disruption events

We present fundamental scaling relationships between properties of the optical/UV light curves of tidal disruption events (TDEs) and the mass of the black hole that disrupted the star. We have uncovered these relations from the late-time emission of TDEs. Using a sample of 63 optically-selected TDEs, the latest catalog to date, we observed flattening of the early-time emission into a near-constant late-time plateau for at least two-thirds of our sources. Compared to other properties of the TDE lightcurves (e.g., peak luminosity or decay rate) the plateau luminosity shows the tightest correlation with the total mass of host galaxy ($p$-value of $2 \times 10^{-6}$, with a residual scatter of 0.3 dex). Physically this plateau stems from the presence of an accretion flow. We demonstrate theoretically and numerically that the amplitude of this plateau emission is strongly correlated with black hole mass. By simulating a large population of TDEs, we determine a plateau luminosity-black hole mass scaling relationship well described by $ \log_{10} \left(M_{\bullet}/M_{\odot} \right) = 1.50 \log_{10} \left( L_{\rm plat}/10^{43} {\rm erg \, s^{-1}} \right) + 9.0 $. The observed plateau luminosities of TDEs and black hole masses in our large sample are in excellent agreement with this simulation. Using the black hole mass predicted from the observed TDE plateau luminosity, we reproduce the well-known scaling relations between black hole mass and galaxy velocity dispersion. The large black hole masses of 10 of the TDEs in our sample allow us to provide constraints on their black hole spins, favouring rapidly rotating black holes. We add 49 (34) black hole masses to the galaxy mass (velocity dispersion) scaling relationships, updating and extending these correlations into the low black hole mass regime.

astro-ph.HE↗

arXiv2023

Late time HST UV and optical observations of AT~2018cow: extracting a cow from its background

The bright, blue, rapidly evolving AT2018cow is a well-studied peculiar extragalactic transient. Despite an abundance of multi-wavelength data, there still is no consensus on the nature of the event. We present our analysis of three epochs of Hubble Space Telescope (HST) observations spanning the period from 713-1474 days post burst, paying particular attention to uncertainties of the transient photometry introduced by the complex background in which AT2018cow resides. Photometric measurements show evident fading in the UV and more subtle but significant fading in the optical. During the last HST observation, the transient's optical/UV colours were still bluer than those of the substantial population of compact, young, star-forming regions in the host of AT2018cow, suggesting some continued transient contribution to the light. However, a compact source underlying the transient would substantially modify the resulting spectral energy distribution, depending on its contribution in the various bands. In particular, in the optical filters, the complex, diffuse background poses a problem for precise photometry. An underlying cluster is expected for a supernova occurring within a young stellar environment or a tidal-disruption event (TDE) within a dense older one. While many recent works have focused on the supernova interpretation, we note the substantial similarity in UV light-curve morphology between AT2018cow and several tidal disruption events around supermassive black holes. Assuming AT2018cow arises from a TDE-like event, we fit the late-time emission with a disc model and find $M_{BH} = 10^{3.2{\pm}0.8}$ M$_{\odot}$. Further observations are necessary to determine the late-time evolution of the transient and its immediate environment.

astro-ph.HE↗

arXiv2023

Extending the theory of propagating fluctuations: the first fully relativistic treatment and analytical Fourier-Green's functions

The aperiodic variability ubiquitously observed from accreting black hole X-ray binary systems is generally analysed within the framework of the so-called ``theory of propagating fluctuations''. In this paper we derive the Fourier transforms of the Green's function solutions of the thin disc equations. These solutions suffice to describe all possible solutions through standard convolution techniques. Solutions are found for both Newtonian discs and general relativistic solutions with a vanishing ISCO stress. We use this new relativistic theory to highlight the Kerr black hole spin dependence of a number of observable variability properties of black hole discs. The phase lags, coherence, and power density spectra of Kerr discs are shown to be strong functions of black hole spin. Observations of the aperiodic variability of black hole accretion sources may now, at least in principle, offer a new avenue to directly constrain black hole spins.

astro-ph.HE↗

arXiv2023

Accretion within the innermost stable circular orbit: analytical thermodynamic solutions in the adiabatic limit

We present analytical solutions for the thermodynamic (temperature, pressure, density, etc.) properties of thin accretion flows in the region within the innermost stable circular orbit (ISCO) of a Kerr black hole, the first analytical solutions of their kind. These solutions are constructed in the adiabatic limit and neglect radiative losses, an idealisation valid for a restricted region of parameter space. We highlight a number of remarkable properties of these solutions, including that these solutions cool for radii $r_I/2 < r < r_I$, before increasing in temperature for $0 < r < r_I/2$, independent of black hole spin and assumptions regarding the equation of state of the accretion flow. The radiative temperature of these solutions can, for some values of the free parameters of the theory, peak within the ISCO and not in the main body of the disc. These solutions represent a fundamentally new class of analytical accretion solutions, which are both non-circular and non-radial in character.

astro-ph.HE↗

arXiv2023

A complete characterisation of the orbital shapes of the non-circular Kerr geodesic solutions with circular orbit constants of motion

We present analytical solutions describing a family of both inwardly and outwardly spiralling orbits in the Kerr spacetime. The solutions are exact, and remarkable for their simplicity. These orbits all have the angular momentum and energy of a circular orbit at some radius $r_c$, but are not restricted to remaining on that circular orbit, a property not possible in Newtonian gravity. We demonstrate that there are five distinct orbital solutions which terminate at the black hole singularity, and three solutions which either escape to infinity or remain bound. The different orbital solutions are characterised entirely by the black hole spin $a$ and the location of $r_c$. Photon orbits spiralling into or out of their (unstable) circular orbit radii are also analysed. These have properties similar to the hyperbolic class of massive particle orbits discussed herein.

gr-qc↗

arXiv2023

From X-rays to physical parameters: a comprehensive analysis of thermal tidal disruption event X-ray spectra

We perform a comprehensive analysis of a population of 19 X-ray bright tidal disruption events (TDEs), fitting their X-ray spectra with a new, physically self consistent, relativistic accretion disc model. Not all of the TDEs inhabit regions of parameter space where the model is valid, or have sufficient data for a detailed analysis, and physically interpretable parameters for a sub-sample of 11 TDEs are determined. These sources have thermal (power-law free) X-ray spectra. The radial sizes measured from these spectra lie at values consistent with the inner-most stable circular orbit of black holes with masses given by the $M_{\rm BH}-σ$ relationship, and can be used as an independent measurement of $M_{\rm BH}$. The bolometric disc luminosity can also be inferred from X-ray data. All of the TDEs have luminosities which are sub-Eddington ($L_{\rm bol, disc} \lesssim L_{\rm edd}$), and larger than the typical hard-state transitional luminosity of X-ray binary discs ($L_{\rm bol, disc} \gtrsim 0.01 L_{\rm edd}$). The {\it peak} bolometric luminosity is found to be linearly correlated with the $M_{\rm BH}-σ$ mass. The TDE X-ray-to-bolometric correction can reach values up to $\sim 100$, and grows exponentially at late times, resolving the missing energy problem. We show that the peak disc luminosities of some TDEs are smaller than their observed optical luminosities, implying that not all of the early time optical emission can be sourced from reprocessed disc emission. Our results are supportive of the hypothesis that thermal X-ray bright TDEs are in accretion states analogous to the ``soft'' accretion state of X-ray binaries, and that black hole accretion processes are scale (mass) invariant.

astro-ph.HE↗

arXiv2022

Asymptotic Green's function solutions of the general relativistic thin disc equations

The leading order Green's function solutions of the general relativistic thin disc equations are computed, using a pseudo-Newtonian potential and asymptotic Laplace mode matching techniques. This solution, valid for a vanishing ISCO stress, is constructed by ensuring that it reproduces the leading order asymptotic behaviour of the near-ISCO, Newtonian, and global WKB limits. Despite the simplifications used in constructing this solution, it is typically accurate, for all values of the Kerr spin parameter $a$ and at all radii, to less than a percent of the full numerically calculated solutions of the general relativistic disc equations. These solutions will be of use in studying time-dependent accretion discs surrounding Kerr black holes.

gr-qc↗

arXiv2022

The high energy probability distribution of accretion disc luminosity fluctuations

The probability density function of accretion disc luminosity fluctuations at high observed energies (i.e., energies larger than the peak temperature scale of the disc) is derived, under the assumption that the temperature fluctuations are log-normally distributed. Thin disc theory is used throughout. While log-normal temperature fluctuations would imply that the disc's bolometric luminosity is also log-normal, the observed Wien-like luminosity behaves very differently. For example, in contrast to a log-normal distribution, the standard deviation of the derived distribution is not linearly proportional to its mean. This means that these systems do not follow a linear rms-flux relationship. Instead they exhibit very high intrinsic variance, and undergo what amounts to a phase transition, in which the mode of the distribution (in the statistical sense) ceases to exist, even for physically reasonable values of the underlying temperature variance. The moments of this distribution are derived using asymptotic expansion techniques. A result that is important for interpreting observations is that the theory predicts that the fractional variability of these disc systems should increase as the observed frequency is increased. The derived distribution will be of practical utility in quantitatively understanding the variability of disc systems observed at energies above their peak temperature scale, including X-ray observations of tidal disruption events.

astro-ph.HE↗

arXiv2022

Inspirals from the innermost stable circular orbit of Kerr black holes: Exact solutions and universal radial flow

We present exact solutions of test particle orbits spiralling inward from the innermost stable circular orbit (ISCO) of a Kerr black hole. Our results are valid for any allowed value of the angular momentum $a$-parameter of the Kerr metric. These solutions are of considerable physical interest. In particular, the radial 4-velocity of these orbits is both remarkably simple and, with the radial coordinate scaled by its ISCO value, universal in form, otherwise completely independent of the black hole spin.

gr-qc↗

arXiv2021

Tidal disruption event discs are larger than they seem: removing systematic biases in TDE X-ray spectral modelling

The physical sizes of TDE accretion discs are regularly inferred, from the modelling of the TDEs X-ray spectrum as a single temperature blackbody, to be smaller than the plausible event horizons of the black holes which they occur around - a clearly unphysical result. In this Letter we demonstrate that the use of single-temperature blackbody functions results in the systematic underestimation of TDE accretion disc sizes by as much as an order-of-magnitude. In fact, the radial `size' inferred from fitting a single temperature blackbody to an observed accretion disc X-ray spectrum does not even positively correlate with the physical size of that accretion disc. We further demonstrate that the disc-observer inclination angle and absorption of X-ray photons may both lead to additional underestimation of the radial sizes of TDE discs, but by smaller factors. To rectify these issues we present a new fitting function which accurately reproduces the size of an accretion disc from its 0.3-10 keV X-ray spectrum. Unlike traditional approaches, this new fitting function does not assume that the accretion disc has reached a steady state configuration, an assumption which is unlikely to be satisfied by most TDEs. An XSPEC implementation of this new fitting function is available at github.com/andymummeryastro/TDEdiscXraySpectrum.

astro-ph.HE↗

arXiv2021

An upper observable black hole mass scale for tidal disruption events with thermal X-ray spectra

We comprehensively model the X-ray luminosity emergent from time dependent relativistic accretion discs, developing analytical models of the X-ray luminosity of thermal disc systems as a function of black hole mass $M$, disc mass $M_d$, and disc $α$-parameter. The X-ray properties of these solutions will be directly relevant for understanding TDE observations. We demonstrate an extremely strong suppression of thermal X-ray luminosity from large mass black holes, $L_X \sim \exp(-m^{7/6})$, where $m$ is a dimensionless mass, roughly the the black hole mass in unity of $10^6$M$_\odot$. This strong suppression results in upper-observable black hole mass limits, which we demonstrate to be of order $M_{\rm lim} \simeq 3 \times 10^7 M_\odot$, above which thermal X-ray emission will not be observable. This upper observable black hole mass limit is a function of the remaining disc parameters, and the full dependence can be described analytically (eq. 82). We demonstrate that the current population of observed X-ray TDEs is indeed consistent with an upper black hole mass limit of order $M \sim 10^7M_\odot$, consistent with our analysis.

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