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Sjoert van Velzen

Publications and source records attributed to Sjoert van Velzen.

At least 55 records · Page 3Linked to original sources

The first systematically identified repeating partial tidal disruption event

Tidal disruption events (TDEs) occur when a star enters the tidal radius of a supermassive black hole (SMBH). If the star only grazes the tidal radius, a fraction of the stellar mass will be accreted in a partial TDE (pTDE). The remainder can continue orbiting and may re-disrupted at pericenter, causing a repeating pTDE. pTDEs may be as or more common than full TDEs (fTDEs), yet few are known. In this work, we present the discovery of the first repeating pTDE from a systematically-selected sample, AT\,2020vdq. AT\,2020vdq was originally identified as an optically- and radio-flaring TDE. Around $3$ years after its discovery, it rebrightened dramatically and rapidly in the optical. The optical flare was remarkably fast and luminous compared to previous TDEs. It was accompanied by extremely broad (${\sim}0.1c$) optical/UV spectral features and faint X-ray emission ($L_X \sim 3\times10^{41}$\,erg\,s$^{-1}$), but no new radio-emitting component. Based on the transient optical/UV spectral features and the broadband light curve, we show that AT\,2020vdq is a repeating pTDE. We then use it to constrain TDE models; in particular, we favor a star originally in a very tight binary system that is tidally broken apart by the Hills mechanism. We also constrain the repeating pTDE rate to be $10^{-6}$ to $10^{-5}$ yr$^{-1}$ galaxy$^{-1}$, with uncertainties dominated by the unknown distribution of pTDE repeat timescales. In the Hills framework, this means the binary fraction in the galactic nucleus is of the order few percent.

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Integral Field Spectroscopy of 13 Tidal Disruption Event Hosts from the ZTF Survey

The host galaxies of tidal disruption events (TDEs) have been shown to possess peculiar properties, including high central light concentrations, unusual star-formation histories, and ``green'' colors. The ubiquity of these large-scale galaxy characteristics among TDE host populations suggests they may serve to boost the TDE rate in such galaxies by influencing the nuclear stellar dynamics. We present the first population study of integral field spectroscopy for thirteen TDE host galaxies across all spectral classes and X-ray brightnesses with the purpose of investigating their large-scale properties. We derive the black hole masses via stellar kinematics (i.e., the $M-σ$ relation) and find masses in the range $5.0 \lesssim \log(M_{\rm BH}/M_\odot) \lesssim 8.0$, with a distribution dominated by black holes with $M_{\rm BH} \sim 10^6 M_\odot$. We find one object with $M_{\rm BH} \gtrsim 10^8 M_\odot$, above the ``Hills mass'', which if the disrupted star was of solar type, allows a lower limit of $a \gtrsim 0.16$ to be placed on its spin, lending further support to the proposed connection between featureless TDEs and jetted TDEs. We also explore the level of rotational support in the TDE hosts, quantified by $(V/σ)_e$, a parameter which has been shown to correlate with stellar age and may explain the peculiar host galaxy preferences of TDEs. We find that the TDE hosts exhibit a broad range in $(V/σ)_e$ following a similar distribution as E+A galaxies, which have been shown to be overrepresented among TDE host populations.

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Tidal Disruption Event Demographics with the Zwicky Transient Facility: Volumetric Rates, Luminosity Function, and Implications for the Local Black Hole Mass Function

We conduct a systematic tidal disruption event (TDE) demographics analysis using the largest sample of optically selected TDEs. A flux-limited, spectroscopically complete sample of 33 TDEs is constructed using the Zwicky Transient Facility over three years (from October 2018 to September 2021). We infer the black hole (BH) mass ($M_{\rm BH}$) with host galaxy scaling relations, showing that the sample $M_{\rm BH}$ ranges from $10^{5.1}\,M_\odot$ to $10^{8.2}\,M_\odot$. We developed a survey efficiency corrected maximum volume method to infer the rates. The rest-frame $g$-band luminosity function (LF) can be well described by a broken power-law of $ϕ(L_g)\propto [(L_g / L_{\rm bk})^{0.3} + (L_g / L_{\rm bk})^{2.6}]^{-1}$, with $L_{\rm bk}=10^{43.1}\,{\rm erg\,s^{-1}}$. In the BH mass regime of $10^{5.3}\lesssim (M_{\rm BH}/M_\odot) \lesssim 10^{7.3}$, the TDE mass function follows $ϕ(M_{\rm BH})\propto M_{\rm BH}^{-0.25}$, which favors a flat local BH mass function ($dn_{\rm BH}/d{\rm log}M_{\rm BH}\approx{\rm constant}$). We confirm the significant rate suppression at the high-mass end ($M_{\rm BH}\gtrsim 10^{7.5}\,M_\odot$), which is consistent with theoretical predictions considering direct capture of hydrogen-burning stars by the event horizon. At a host galaxy mass of $M_{\rm gal}\sim 10^{10}\,M_\odot$, the average optical TDE rate is $\approx 3.2\times 10^{-5}\,{\rm galaxy^{-1}\,yr^{-1}}$. We constrain the optical TDE rate to be [3.7, 7.4, and 1.6$]\times 10^{-5}\,{\rm galaxy^{-1}\,yr^{-1}}$ in galaxies with red, green, and blue colors.

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The Birth of a Relativistic Jet Following the Disruption of a Star by a Cosmological Black Hole

A black hole can launch a powerful relativistic jet after it tidally disrupts a star. If this jet fortuitously aligns with our line of sight, the overall brightness is Doppler boosted by several orders of magnitude. Consequently, such on-axis relativistic tidal disruption events (TDEs) have the potential to unveil cosmological (redshift $z>$1) quiescent black holes and are ideal test beds to understand the radiative mechanisms operating in super-Eddington jets. Here, we present multi-wavelength (X-ray, UV, optical, and radio) observations of the optically discovered transient \target at $z=1.193$. Its unusual X-ray properties, including a peak observed luminosity of $\gtrsim$10$^{48}$ erg s$^{-1}$, systematic variability on timescales as short as 1000 seconds, and overall duration lasting more than 30 days in the rest-frame are traits associated with relativistic TDEs. The X-ray to radio spectral energy distributions spanning 5-50 days after discovery can be explained as synchrotron emission from a relativistic jet (radio), synchrotron self-Compton (X-rays), and thermal emission similar to that seen in low-redshift TDEs (UV/optical). Our modeling implies a beamed, highly relativistic jet akin to blazars but requires extreme matter-domination, i.e, high ratio of electron-to-magnetic field energy densities in the jet, and challenges our theoretical understanding of jets.

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The Final Season Reimagined: 30 Tidal Disruption Events from the ZTF-I Survey

Tidal disruption events (TDEs) offer a unique way to study dormant black holes. While the number of observed TDEs has grown thanks to the emergence of wide-field surveys in the past few decades, questions regarding the nature of the observed optical, UV, and X-ray emission remain. We present a uniformly selected sample of 30 spectroscopically classified TDEs from the Zwicky Transient Facility Phase I survey operations with follow-up \textit{Swift} UV and X-ray observations. Through our investigation into correlations between light curve properties, we recover a shallow positive correlation between the peak bolometric luminosity and decay timescales. We introduce a new spectroscopic class of TDE, TDE-featureless, which are characterized by featureless optical spectra. The new TDE-featureless class shows larger peak bolometric luminosities, peak blackbody temperatures, and peak blackbody radii. We examine the differences between the X-ray bright and X-ray faint populations of TDEs in this sample, finding that X-ray bright TDEs show higher peak blackbody luminosities than the X-ray faint sub-sample. This sample of optically selected TDEs is the largest sample of TDEs from a single survey yet, and the systematic discovery, classification, and follow-up of this sample allows for robust characterization of TDE properties, an important stepping stone looking forward toward the Rubin era.

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Identifying Tidal Disruption Events with an Expansion of the FLEET Machine Learning Algorithm

We present an expansion of FLEET, a machine learning algorithm optimized to select transients that are most likely to be tidal disruption events (TDEs). FLEET is based on a random forest algorithm trained on the light curves and host galaxy information of 4,779 spectroscopically classified transients. For transients with a probability of being a TDE, \ptde$>0.5$, we can successfully recover TDEs with a $\approx40$\% completeness and a $\approx30$\% purity when using the first 20 days of photometry, or a similar completeness and $\approx50$\% purity when including 40 days of photometry. We find that the most relevant features for differentiating TDEs from other transients are the normalized host separation, and the light curve $(g-r)$ color during peak. Additionally, we use FLEET to produce a list of the 39 most likely TDE candidates discovered by the Zwicky Transient Facility that remain currently unclassified. We explore the use of FLEET for the Legacy Survey of Space and Time on the Vera C. Rubin Observatory (\textit{Rubin}) and the \textit{Nancy Grace Roman Space Telescope} (\textit{Roman}). We simulate the \textit{Rubin} and \textit{Roman} survey strategies and estimate that $\sim 10^4$ TDEs could be discovered every year by \textit{Rubin}, and $\sim200$ TDEs per year by \textit{Roman}. Finally, we run FLEET on the TDEs in our \textit{Rubin} survey simulation and find that we can recover $\sim 30$\% of those at a redshift $z <0.5$ with \ptde$>0.5$. This translates to $\sim3,000$ TDEs per year that FLEET could uncover from \textit{Rubin}. FLEET is provided as a open source package on GitHub https://github.com/gmzsebastian/FLEET

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Radio observations of the tidal disruption event AT2020opy: a luminous non-relativistic outflow encountering a dense circumnuclear medium

Tidal disruption events (TDEs) occur when a star passes too close to a supermassive black hole and is destroyed by tidal gravitational forces. Radio observations of TDEs trace synchrotron emission from outflowing material that may be ejected from the inner regions of the accretion flow around the SMBH or by the tidal debris stream. Radio detections of tidal disruption events are rare, but provide crucial information about the launching of jets and outflows from supermassive black holes and the circumnuclear environment in galaxies. Here we present the radio detection of the TDE AT2020opy, including three epochs of radio observations taken with the Karl G. Jansky's Very Large Array (VLA), MeerKAT, and upgraded Giant Metrewave Radio telescope. AT2020opy is the most distant thermal TDE with radio emission reported to date, and from modelling the evolving synchrotron spectra we deduce that the host galaxy has a more dense circumnuclear medium than other thermal TDEs detected in the radio band. Based on an equipartition analysis of the synchrotron spectral properties of the event, we conclude that the radio-emitting outflow was likely launched approximately at the time of, or just after, the initial optical flare. We find no evidence for relativistic motion of the outflow. The high luminosity of this event supports that a dense circumnuclear medium of the host galaxy produces brighter radio emission that rises to a peak more quickly than in galaxies with lower central densities.

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The Tidal Disruption Event AT2021ehb: Evidence of Relativistic Disk Reflection, and Rapid Evolution of the Disk-Corona System

We present X-ray, UV, optical, and radio observations of the nearby ($\approx78$ Mpc) tidal disruption event (TDE) AT2021ehb/ZTF21aanxhjv during its first 430 days of evolution. AT2021ehb occurs in the nucleus of a galaxy hosting a $\approx 10^{7}\,M_\odot$ black hole ($M_{\rm BH}$ inferred from host galaxy scaling relations). High-cadence Swift and NICER monitoring reveals a delayed X-ray brightening. The spectrum first undergoes a gradual ${\rm soft }\rightarrow{\rm hard}$ transition and then suddenly turns soft again within 3 days at $δt\approx 272$ days during which the X-ray flux drops by a factor of ten. In the joint NICER+NuSTAR observation ($δt =264$ days, harder state), we observe a prominent non-thermal component up to 30 keV and an extremely broad emission line in the iron K band. The bolometric luminosity of AT2021ehb reaches a maximum of $6.0^{+10.4}_{-3.8}\% L_{\rm Edd}$ when the X-ray spectrum is the hardest. During the dramatic X-ray evolution, no radio emission is detected, the UV/optical luminosity stays relatively constant, and the optical spectra are featureless. We propose the following interpretations: (i) the ${\rm soft }\rightarrow{\rm hard}$ transition may be caused by the gradual formation of a magnetically dominated corona; (ii) hard X-ray photons escape from the system along solid angles with low scattering optical depth ($\sim\,$a few) whereas the UV/optical emission is likely generated by reprocessing materials with much larger column density -- the system is highly aspherical; (iii) the abrupt X-ray flux drop may be triggered by the thermal-viscous instability in the inner accretion flow leading to a much thinner disk.

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Rubin Observatory LSST Transients and Variable Stars Roadmap

The Vera C. Rubin Legacy Survey of Space and Time holds the potential to revolutionize time domain astrophysics, reaching completely unexplored areas of the Universe and mapping variability time scales from minutes to a decade. To prepare to maximize the potential of the Rubin LSST data for the exploration of the transient and variable Universe, one of the four pillars of Rubin LSST science, the Transient and Variable Stars Science Collaboration, one of the eight Rubin LSST Science Collaborations, has identified research areas of interest and requirements, and paths to enable them. While our roadmap is ever-evolving, this document represents a snapshot of our plans and preparatory work in the final years and months leading up to the survey's first light.

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From Data to Software to Science with the Rubin Observatory LSST

The Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) dataset will dramatically alter our understanding of the Universe, from the origins of the Solar System to the nature of dark matter and dark energy. Much of this research will depend on the existence of robust, tested, and scalable algorithms, software, and services. Identifying and developing such tools ahead of time has the potential to significantly accelerate the delivery of early science from LSST. Developing these collaboratively, and making them broadly available, can enable more inclusive and equitable collaboration on LSST science. To facilitate such opportunities, a community workshop entitled "From Data to Software to Science with the Rubin Observatory LSST" was organized by the LSST Interdisciplinary Network for Collaboration and Computing (LINCC) and partners, and held at the Flatiron Institute in New York, March 28-30th 2022. The workshop included over 50 in-person attendees invited from over 300 applications. It identified seven key software areas of need: (i) scalable cross-matching and distributed joining of catalogs, (ii) robust photometric redshift determination, (iii) software for determination of selection functions, (iv) frameworks for scalable time-series analyses, (v) services for image access and reprocessing at scale, (vi) object image access (cutouts) and analysis at scale, and (vii) scalable job execution systems. This white paper summarizes the discussions of this workshop. It considers the motivating science use cases, identified cross-cutting algorithms, software, and services, their high-level technical specifications, and the principles of inclusive collaborations needed to develop them. We provide it as a useful roadmap of needs, as well as to spur action and collaboration between groups and individuals looking to develop reusable software for early LSST science.

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Candidate Tidal Disruption Event AT2019fdr Coincident with a High-Energy Neutrino

The origins of the high-energy cosmic neutrino flux remain largely unknown. Recently, one high-energy neutrino was associated with a tidal disruption event (TDE). Here we present AT2019fdr, an exceptionally luminous TDE candidate, coincident with another high-energy neutrino. Our observations, including a bright dust echo and soft late-time X-ray emission, further support a TDE origin of this flare. The probability of finding two such bright events by chance is just 0.034%. We evaluate several models for neutrino production and show that AT2019fdr is capable of producing the observed high-energy neutrino, reinforcing the case for TDEs as neutrino sources.

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Detectability of a spatial correlation between stellar-mass black hole mergers and Active Galactic Nuclei in the Local Universe

The origin of the Binary Black Hole (BBH) mergers detected through Gravitational Waves (GWs) by the LIGO-Virgo-KAGRA (LVK) collaboration remains debated. One fundamental reason is our ignorance of their host environment, as the typical size of an event's localization volume can easily contain thousands of galaxies. A strategy around this is to exploit statistical approaches to assess the spatial correlation between these mergers and astrophysically motivated host galaxy types, such as Active Galactic Nuclei (AGN). We use a Likelihood ratio method to infer the degree of GW-AGN connection out to $z=0.2$. We simulate BBH mergers whose components' masses are sampled from a realistic distribution of the underlying population of Black Holes (BHs). Localization volumes for these events are calculated assuming two different interferometric network configurations. These correspond to the configuration of the third (O3) and of the upcoming fourth (O4) LVK observing runs. We conclude that the 13 BBH mergers detected during the third observing run at $z\leq0.2$ are not enough to reject with a \(3σ\) significance the hypothesis according to which there is no connection between GW and AGN more luminous than $\approx 10^{44.3}\rm{erg}\ \rm{s}^{-1}$, that have number density higher than \(10^{-4.75}\textrm{Mpc}^{-3}\). However, 13 detections are enough to reject this no-connection hypothesis when rarer categories of AGN are considered, with bolometric luminosities greater than $\approx 10^{45.5}\rm{erg}\ \rm{s}^{-1}$. We estimate that O4 results will potentially allow us to test fractional contributions to the total BBH merger population from AGN of any luminosity higher than \(80\%\).

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A tidal disruption event coincident with a high-energy neutrino

Cosmic neutrinos provide a unique window into the otherwise-hidden mechanism of particle acceleration in astrophysical objects. A flux of high-energy neutrinos was discovered in 2013, and the IceCube Collaboration recently reported the likely association of one high-energy neutrino with a flare from the relativistic jet of an active galaxy pointed towards the Earth. However a combined analysis of many similar active galaxies revealed no excess from the broader population, leaving the vast majority of the cosmic neutrino flux unexplained. Here we present the likely association of a radio-emitting tidal disruption event, AT2019dsg, with a second high-energy neutrino. AT2019dsg was identified as part of our systematic search for optical counterparts to high-energy neutrinos with the Zwicky Transient Facility. The probability of finding any coincident radio-emitting tidal disruption event by chance is 0.5%, while the probability of finding one as bright in bolometric energy flux as AT2019dsg is 0.2%. Our electromagnetic observations can be explained through a multi-zone model, with radio analysis revealing a central engine, embedded in a UV photosphere, that powers an extended synchrotron-emitting outflow. This provides an ideal site for PeV neutrino production. Assuming that the association is genuine, our observations suggest that tidal disruption events with mildly-relativistic outflows contribute to the cosmic neutrino flux.

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Reverberation in tidal disruption events: dust echoes, coronal emission lines, multi-wavelength cross-correlations, and QPOs

Stellar tidal disruption events (TDEs) are typically discovered by transient emission due to accretion or shocks of the stellar debris. Yet this luminous flare can be reprocessed by gas or dust that inhabits a galactic nucleus, resulting in multiple reverberation signals. Nuclear dust heated by the TDE will lead to an echo at infrared wavelengths (1-10 $μ$m) and transient coronal lines in optical spectra of TDEs trace reverberation by gas that orbits the black hole. Both of these signal have been detected, here we review this rapidly developing field. We also review the results that have been extracted from TDEs with high-quality X-ray light curves: quasi periodic oscillations (QPOs), reverberation lags of fluorescence lines, and cross-correlations with emission at other wavelengths. The observational techniques that are covered in this review probe the emission from TDEs over a wide range of scales: from light years to the innermost parts of the newly formed accretion disk. They provide insights into important properties of TDEs such as their bolometric output and the geometry of the accretion flow. While reverberation signals are not detected for every TDE, we anticipate they will become more commonplace when the next generation of X-ray and infrared instruments become operational.

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Discovery of a Fast Iron Low-ionization Outflow in the Early Evolution of the Nearby Tidal Disruption Event AT2019qiz

We report the results of ultraviolet (UV) and optical photometric and spectroscopic analysis of the tidal disruption event (TDE) AT2019qiz. Our follow-up observations started $<$10 days after the source began to brighten in the optical and lasted for a period of six months. Our late-time host-dominated spectrum indicates that the host galaxy likely harbors a weak active galactic nucleus. The initial {\it Hubble Space Telescope (HST)} spectrum of AT2019qiz exhibits an iron and low-ionization broad absorption line (FeLoBAL) system that is seen for the first time in a TDE. This spectrum also bears a striking resemblance to that of Gaia16apd, a superluminous supernova. Our observations provide insights into the outflow properties in TDEs and show evidence for a connection between TDEs and engine-powered supernovae at early phase, as originally suggested in Metzger & Stone (2016). In a time frame of 50 days, the UV spectra of AT2019qiz started to resemble previous TDEs with only high-ionization BALs. The change in UV spectral signatures is accompanied by a decrease in the outflow velocity, which began at $15,000$ km s$^{-1}$ and decelerated to $\sim10,000$ km s$^{-1}$. A similar evolution in the H$α$ emission line width further supports the speculation that the broad Balmer emission lines are formed in TDE outflows. In addition, we detect narrow absorption features on top of the FeLoBAL signatures in the early HST UV spectrum of AT2019qiz. The measured HI column density corresponds to a Lyman-limit system whereas the metal absorption lines, such as NV, CIV, FeII, and MgII, are likely probing the circumnuclear gas and interstellar medium in the host galaxy.

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AGN on the move: A search for off-nuclear AGN from recoiling SMBHs and ongoing galaxy mergers with the Zwicky Transient Facility

A supermassive black hole (SMBH) ejected from the potential well of its host galaxy via gravitational wave recoil carries important information about the mass ratio and spin alignment of the pre-merger SMBH binary. Such a recoiling SMBH may be detectable as an active galactic nucleus (AGN) broad line region offset by up to 10\,kpc from a disturbed host galaxy. We describe a novel methodology using forward modeling with \texttt{The Tractor} to search for such offset AGN in a sample of 5493 optically variable AGN detected with the Zwicky Transient Facility (ZTF). We present the discovery of 9 AGN which may be spatially offset from their host galaxies and are candidates for recoiling SMBHs. Five of these offset AGN exhibit double-peaked broad Balmer lines which may arise from unobscured accretion disk emission and four show radio emission indicative of a relativistic jet. The fraction of double-peaked emitters in our spatially offset AGN sample is significantly larger than the 16\% double-peaked emitter fraction observed for ZTF AGN overall. In our sample of variable AGN we also identified 52 merging galaxies, including a new spectroscopically confirmed dual AGN. Finally, we detected the dramatic rebrightening of SDSS1133, a previously discovered variable object and recoiling SMBH candidate, in ZTF. The flare was accompanied by the re-emergence of strong P-Cygni line features indicating that it may be an outbursting luminous blue variable star.

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Rapid accretion state transitions following the tidal disruption event AT2018fyk

Following a tidal disruption event (TDE), the accretion rate can evolve from quiescent to near-Eddington levels and back over months - years timescales. This provides a unique opportunity to study the formation and evolution of the accretion flow around supermassive black holes (SMBHs). We present two years of multi-wavelength monitoring observations of the TDE AT2018fyk at X-ray, UV, optical and radio wavelengths. We identify three distinct accretion states and two state transitions between them. These appear remarkably similar to the behaviour of stellar-mass black holes in outburst. The X-ray spectral properties show a transition from a soft (thermal-dominated) to a hard (power-law dominated) spectral state around L$_{\rm bol} \sim $few $ \times 10^{-2}$ L$_{\rm Edd}$, and the strengthening of the corona over time $\sim$100--200 days after the UV/optical peak. Contemporaneously, the spectral energy distribution (in particular, the UV-to-X-ray spectral slope $α_{ox}$) shows a pronounced softening as the outburst progresses. The X-ray timing properties also show a marked change, initially dominated by variability at long ($>$day) timescales while a high frequency ($\sim$10$^{-3}$ Hz) component emerges after the transition into the hard state. At late times ($\sim$500 days after peak), a second accretion state transition occurs, from the hard into the quiescent state, as identified by the sudden collapse of the bolometric (X-ray+UV) emission to levels below 10$^{-3.4}$ L$_{\rm Edd}$. Our findings illustrate that TDEs can be used to study the scale (in)variance of accretion processes in individual SMBHs. Consequently, they provide a new avenue to study accretion states over seven orders of magnitude in black hole mass, removing limitations inherent to commonly used ensemble studies.

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Forward Modeling Populations of Flares from Tidal Disruptions of Stars by Super-massive Black Holes

Detections of the tidal disruption flares (TDFs) of stars by supermassive black holes (SMBHs) are rapidly accumulating as optical surveys improve. These detections may provide constraints on SMBH demographics, stellar dynamics, and stellar evolution in galaxies. To maximize this scientific impact, we require a better understanding of how astrophysical parameters interact with survey selection effects in setting the properties of detected flares. We develop a framework for modeling the distributions of optical TDF detections in surveys across attributes of the host galaxies and the flares themselves. This model folds in effects of the stellar disruption rate in each galaxy, the flare luminosity and temperature distributions, the effects of obscuration and reddening by dust in the host galaxy, and survey selection criteria. We directly apply this model to the sample of TDFs detected by the Zwicky Transient Facility and find that the overall flare detection rate is in line with simple theoretical expectation. The model can also reproduce the distribution of total stellar mass and redshift of the host galaxies, but fails to match all details of the detected flares, such as their luminosity and temperature distributions. We also find that dust obscuration likely plays an important role in suppressing the TDF detection rate in star-forming galaxies. While we do not find that the unusual preference of TDFs to have hosts in post-starburst galaxies in the "green valley" can be entirely explained by selection effects, our model can help to quantify the true rate enhancement in those galaxies.

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