arXiv subjects

Franz Kirsten

Publications and source records attributed to Franz Kirsten.

At least 19 recordsLinked to original sources

arXiv2026

Implicit inference of the reionization history with higher-order statistics of the 21-cm signal

The Epoch of Reionization (EoR), when the first luminous sources ionised the intergalactic medium, represents a new frontier in cosmology. The Square Kilometre Array Observatory (SKAO) will offer unprecedented insights into this era through observations of the redshifted 21-cm signal, enabling constraints on the Universe's reionization history. We investigate the information content of the average neutral hydrogen fraction ($\bar{x}_{\rm HI}$) in several Gaussian (spherical and cylindrical power spectra) and non-Gaussian (Betti numbers and bispectrum) summary statistics of the 21-cm signal. Mock 21-cm observations are generated using the AA* configuration of SKAO's low-frequency telescope, incorporating noise levels for 100 and 1000 hours. We employ a state-of-the-art implicit inference framework to learn posterior distributions of $\bar{x}_{\rm HI}$ in redshift bins centred at $z=8.0,7.2$ and $6.5$, for each statistic and noise scenario, validating the posteriors through calibration tests. Using the figure of merit to assess constraining power, we find that Betti numbers alone are on average more informative than the power spectra, while the bispectrum provides limited constraints. However, combining higher-order statistics with the cylindrical power spectrum improves the mean figure of merit by $\sim$0.25 dex ($\sim33\%$ reduction in $σ(\bar{x}_{\rm HI})$). The relative contribution of each statistic varies with the stage of reionization. With SKAO observations approaching, our results show that combining power spectra with higher-order statistics can significantly increase the information retrieved from the EoR, maximising the scientific return of future 21-cm observations.

astro-ph.CO↗

arXiv2026

The Astrophysics of Fast Radio Bursts

Fast radio bursts (FRBs) provide a glimpse of high-energy astrophysical phenomena in other galaxies. They point the way to extreme conditions that are currently undetectable by any other known means. These coherent radio flashes have timescales of microseconds to milliseconds, and inferred energies that are comparable to those of the most extreme bursts seen from Galactic neutron stars. However, the nature of FRB sources remains an open question in astrophysics. Magnetically powered neutron stars known as `magnetars' are a leading candidate for explaining the FRB phenomenon, but other plausible progenitors include magnetically interacting neutron-star binaries or accreting black holes. The diversity of FRB burst types and their galactic environments hint that multiple mechanisms and progenitor types may be responsible. Here we discuss the ways in which the SKA can uncover the nature of FRBs. In particular, we focus on the key advantages of the SKA: its Southern Hemisphere location and hence overlapping sky coverage with the Vera C. Rubin Observatory, its high sensitivity compared to existing wide-field FRB surveys, its fast search timescales down to tens of $μ$s, and its broad spectral coverage with bands from 50 MHz to 15 GHz. With these capabilities, the SKA will excel in detecting FRB sources across new frequency ranges and timescales. This will aid in a better understanding of the fundamental astrophysics behind FRBs, which will in turn also contribute to their use as cosmological probes, as explored in companion chapters.

astro-ph.HE↗

arXiv2026

A steadily declining dispersion measure for the repeating fast radio burst FRB 20220529A: Evidence for an FRB engine embedded in an expanding supernova remnant

We present the discovery and subsequent 3.2 year monitoring campaign of the repeating fast radio burst FRB 20220529A with CHIME/FRB. We observe a gradual dispersion measure (DM) decline of $-0.881\pm0.001~\mathrm{pc}~\mathrm{cm}^{-3}~\mathrm{year}^{-1}$ ($-1.235\pm0.001~\mathrm{pc}~\mathrm{cm}^{-3}~\mathrm{year}^{-1}$ in the rest frame), implying a $\geq3.5\pm0.2$% decrease of the total electron column in the source environment, and we see scattering timescale variations over weeks to years. We observe a short-lived excursion in which the DM rises by $\sim 1~\mathrm{pc}~\mathrm{cm}^{-3}$, immediately preceding a transient $\sim 2000~\mathrm{rad}~\mathrm{m}^{-2}$ Faraday rotation measure (RM) increase previously reported for this source, before returning to its gradual DM decline. We identify a local line-of-sight magnetic field around FRB 20220529A during this DM/RM excursion of $3.4 \pm 0.2~\mathrm{mG}$, corresponding to one of the most strongly magnetized FRB environments. We measure a decrease in the linear polarization fraction of FRB 20220529A bursts with decreasing frequency that we attribute to depolarization from multi-path propagation in the source environment. We also place a $5σ$ upper limit on the spectral luminosity of an associated persistent radio source of $\leq 5\times10^{28}~\mathrm{erg}~\mathrm{s}^{-1}~\mathrm{Hz}^{-1}$ at 1.5 GHz. These observations are consistent with FRB 20220529A originating from a young ($\sim$ years to centuries old) expanding supernova remnant, with short-lived DM and RM variability arising from interactions with the supernova remnant or with a binary companion.

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arXiv2025

A milliarcsecond localization associates FRB 20190417A with a compact persistent radio source and an extreme magneto-ionic environment

We report the milliarcsecond localization of a high (1379 pc/cc) dispersion measure (DM) repeating fast radio burst, FRB 20190417A. Combining European VLBI Network detections of five repeat bursts, we confirm the FRB's host to be a low-metallicity, star-forming dwarf galaxy at z = 0.12817, similar to the hosts of FRBs 20121102A, 20190520B and 20240114A. We also confirm that it is associated with a previously reported persistent radio source (PRS), which is compact on milliarcsecond scales. Visibility-domain model fitting constrains the transverse physical size of the PRS to < 23 pc and yields an integrated flux density of 191(39) microJy at 1.4 GHz. Though we do not find significant evidence for DM evolution, FRB 20190417A exhibits a time-variable rotation measure (RM) ranging between +3958(11) and +5061(24) rad/m2 over three years. We find no evidence for intervening galaxy clusters in the FRB's line-of-sight and place a conservative lower limit on the rest-frame host DM contribution of 1228 pc/cc (90% confidence) -- the largest known for any FRB so far. This system strengthens the emerging picture of a rare subclass of repeating FRBs with large and variable RMs, above-average host DMs, and luminous PRS counterparts in metal-poor dwarf galaxies. Our results suggest that these systems are the result of environmental selection, or a distinct engine for FRB emission.

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arXiv2025

Exploring the Early Universe with Deep Learning

Hydrogen is the most abundant element in our Universe. The first generation of stars and galaxies produced photons that ionized hydrogen gas, driving a cosmological event known as the Epoch of Reionization (EoR). The upcoming Square Kilometre Array Observatory (SKAO) will map the distribution of neutral hydrogen during this era, aiding in the study of the properties of these first-generation objects. Extracting astrophysical information will be challenging, as SKAO will produce a tremendous amount of data where the hydrogen signal will be contaminated with undesired foreground contamination and instrumental systematics. To address this, we develop the latest deep learning techniques to extract information from the 2D power spectra of the hydrogen signal expected from SKAO. We apply a series of neural network models to these measurements and quantify their ability to predict the history of cosmic hydrogen reionization, which is connected to the increasing number and efficiency of early photon sources. We show that the study of the early Universe benefits from modern deep learning technology. In particular, we demonstrate that dedicated machine learning algorithms can achieve more than a $0.95$ $R^2$ score on average in recovering the reionization history. This enables accurate and precise cosmological and astrophysical inference of structure formation in the early Universe.

astro-ph.CO↗

arXiv2025

Scintillation Properties of PSR B1133+16 Measured with Very Long Baseline Interferometry

The scintillation of pulsars reveals small-scale structure of the interstellar medium. A powerful technique for characterizing the scintillating structures (screens) combines analysis of scintillation arcs and very long baseline interferometry (VLBI). We present the results of a VLBI analysis of the scintillation arcs of PSR B1133+16 from simultaneous observations with Arecibo, VLA, Jodrell Bank, Effelsberg, and Westerbork. Three arcs appear in the data set, all of which appear consistent with being the result of very anisotropic scattering screens. We are able to measure their orientations on the sky, down to uncertainties of $5\arcdeg$ for the two stronger screens, and measure distances, of $140\pm30$, $180\pm20$, and $250\pm30{\rm\,pc}$, consistent with, but substantially more precise than what was inferred previously from annual modulation patterns in the scintillation. Comparing with the differential dust extinction with distance in this direction, the two nearer screens appear associated with the wall of the Local Bubble.

astro-ph.HE↗

arXiv2025

FRB 20250316A: A Brilliant and Nearby One-Off Fast Radio Burst Localized to 13 parsec Precision

Precise localizations of a small number of repeating fast radio bursts (FRBs) using very long baseline interferometry (VLBI) have enabled multiwavelength follow-up observations revealing diverse local environments. However, the 2--3\% of FRB sources that are observed to repeat may not be representative of the full population. Here we use the VLBI capabilities of the full CHIME Outriggers array for the first time to localize a nearby (40 Mpc), bright (kJy), and apparently one-off FRB source, FRB 20250316A, to its environment on 13-pc scales. We use optical and radio observations to place deep constraints on associated transient emission and the properties of its local environment. We place a $5σ$ upper limit of $L_{\mathrm{9.9~\mathrm{GHz}}} < 2.1\times10^{25}~\mathrm{erg~s^{-1}~Hz^{-1}}$ on spatially coincident radio emission, a factor of 100 lower than any known compact persistent radio source associated with an FRB. Our KCWI observations allow us to characterize the gas density, metallicity, nature of gas ionization, dust extinction and star-formation rate through emission line fluxes. We leverage the exceptional brightness and proximity of this source to place deep constraints on the repetition of FRB 20250316A, and find it is inconsistent with all well-studied repeaters given the non-detection of bursts at lower spectral energies. We explore the implications of a measured offset of 190$\pm20$ pc from the center of the nearest star-formation region, in the context of progenitor channels. FRB 20250316A marks the beginning of an era of routine localizations for one-off FRBs on tens of mas-scales, enabling large-scale studies of their local environments.

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arXiv2024

Multiwavelength Constraints on the Origin of a Nearby Repeating Fast Radio Burst Source in a Globular Cluster

The precise origins of fast radio bursts (FRBs) remain unknown. Multiwavelength observations of nearby FRB sources can provide important insights into the enigmatic FRB phenomenon. Here, we present results from a sensitive, broadband X-ray and radio observational campaign of FRB 20200120E, the closest known extragalactic repeating FRB source (located 3.63 Mpc away in an ~10-Gyr-old globular cluster). We place deep limits on the persistent and prompt X-ray emission from FRB 20200120E, which we use to constrain possible origins for the source. We compare our results with various classes of X-ray sources, transients, and FRB models. We find that FRB 20200120E is unlikely to be associated with ultraluminous X-ray bursts, magnetar-like giant flares, or an SGR 1935+2154-like intermediate flare. Although other types of bright magnetar-like intermediate flares and short X-ray bursts would have been detectable from FRB 20200120E during our observations, we cannot entirely rule them out as a class. We show that FRB 20200120E is unlikely to be powered by an ultraluminous X-ray source or a young extragalactic pulsar embedded in a Crab-like nebula. We also provide new constraints on the compatibility of FRB 20200120E with accretion-based FRB models involving X-ray binaries. These results highlight the power of multiwavelength observations of nearby FRBs for discriminating between FRB models.

astro-ph.HE↗

arXiv2024

A search for persistent radio sources toward repeating fast radio bursts discovered by CHIME/FRB

The identification of persistent radio sources (PRSs) coincident with two repeating fast radio bursts (FRBs) supports FRB theories requiring a compact central engine. However, deep non-detections in other cases highlight the diversity of repeating FRBs and their local environments. Here, we perform a systematic search for radio sources towards 37 CHIME/FRB repeaters using their arcminute localizations and a combination of archival surveys and targeted observations. Through multi-wavelength analysis of individual radio sources, we identify two (20181030A-S1 and 20190417A-S1) for which we disfavor an origin of either star formation or an active galactic nucleus in their host galaxies and thus consider them candidate PRSs. We do not find any associated PRSs for the majority of the repeating FRBs in our sample. For 8 FRB fields with Very Large Array imaging, we provide deep limits on the presence of PRSs that are 2--4 orders of magnitude fainter than the PRS associated with FRB\,20121102A. Using Very Large Array Sky Survey imaging of all 37 fields, we constrain the rate of luminous ($\gtrsim$10$^{40}$ erg s$^{-1}$) PRSs associated with repeating FRBs to be low. Within the context of FRB-PRS models, we find that 20181030A-S1 and 20190417A-S1 can be reasonably explained within the context of magnetar, hypernebulae, gamma-ray burst afterglow, or supernova ejecta models -- although we note that both sources follow the radio luminosity versus rotation measure relationship predicted in the nebula model framework. Future observations will be required to both further characterize and confirm the association of these PRS candidates with the FRBs.

astro-ph.HE↗

arXiv2024

A Repeating Fast Radio Burst Source in a Low-Luminosity Dwarf Galaxy

We present the localization and host galaxy of FRB 20190208A, a repeating source of fast radio bursts (FRBs) discovered using CHIME/FRB. As part of the PRECISE repeater localization program on the EVN, we monitored FRB 20190208A for 65.6 hours at $\sim1.4$ GHz and detected a single burst, which led to its VLBI localization with 260 mas uncertainty (2$σ$). Follow-up optical observations with the MMT Observatory ($i\gtrsim 25.7$ mag (AB)) found no visible host at the FRB position. Subsequent deeper observations with the GTC, however, revealed an extremely faint galaxy ($r=27.32 \pm0.16$ mag), very likely ($99.95 \%$) associated with FRB 20190208A. Given the dispersion measure of the FRB ($\sim580$ pc cm$^{-3}$), even the most conservative redshift estimate ($z_{\mathrm{max}}\sim0.83$) implies that this is the lowest-luminosity FRB host to date ($\lesssim10^8L_{\odot}$), even less luminous than the dwarf host of FRB 20121102A. We investigate how localization precision and the depth of optical imaging affect host association, and discuss the implications of such a low-luminosity dwarf galaxy. Unlike the other repeaters with low-luminosity hosts, FRB 20190208A has a modest Faraday rotation measure of a few tens of rad m$^{-2}$, and EVN plus VLA observations reveal no associated compact persistent radio source. We also monitored FRB 20190208A for 40.4 hours over 2 years as part of the ÉCLAT repeating FRB monitoring campaign on the Nançay Radio Telescope, and detected one burst. Our results demonstrate that, in some cases, the robust association of an FRB with a host galaxy will require both high localization precision, as well as deep optical follow-up.

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arXiv2023

Milliarcsecond Localisation of the Hyperactive Repeating FRB 20220912A

We present very-long-baseline interferometry (VLBI) observations of the hyperactive repeating FRB 20220912A using the European VLBI Network (EVN) with an EVN-Lite setup. We detected 150 bursts from FRB 20220912A over two observing epochs in October 2022. Combining the data of these bursts allows us to localise FRB 20220912A to a precision of a few milliarcseconds, corresponding to a transverse scale of less than 10 pc at the distance of the source. The precision of this localisation shows that FRB 20220912A lies closer to the centre of its host galaxy than previously found, although still significantly offset from the host galaxy's nucleus. On arcsecond scales, FRB 20220912A is coincident with a persistent continuum radio source known from archival observations, however, we find no compact persistent emission on milliarcsecond scales. The persistent radio emission is thus likely to be from star-formation in the host galaxy. This is in contrast to some other active FRBs, such as FRB 20121102A and FRB 20190520B.

astro-ph.HE↗

arXiv2023

Constraints on the persistent radio source associated with FRB 20190520B using the European VLBI Network

We present very-long-baseline interferometry (VLBI) observations of a continuum radio source potentially associated with the fast radio burst source FRB 20190520B. Using the European VLBI network (EVN), we find the source to be compact on VLBI scales with an angular size of $<2.3$ mas ($3σ$). This corresponds to a transverse physical size of $<9$ pc (at the $z=0.241$ redshift of the host galaxy), confirming it to be an FRB persistent radio source (PRS) like that associated with the first-known repeater FRB 20121102A. The PRS has a flux density of $201 \pm 34 \rm{μJy}$ at 1.7 GHz and a spectral radio luminosity of $L_{1.7 \rm GHz} = (3.0 \pm 0.5) \times 10^{29}\,\mathrm{erg s^{-1} Hz^{-1}}$ (also similar to the FRB 20121102A PRS). Comparing to previous lower-resolution observations, we find that no flux is resolved out on milliarcsecond scales. We have refined the PRS position, improving its precision by an order of magnitude compared to previous results. We also report the detection of a FRB 20190520B burst at 1.4 GHz and find the burst position to be consistent with the PRS position, at $\lesssim20$ mas. This strongly supports their direct physical association and the hypothesis that a single central engine powers both the bursts and the PRS. We discuss the model of a magnetar in a wind nebula and present an allowed parameter space for its age and the radius of the putative nebula powering the observed PRS emission. Alternatively, we find that an accretion-powered 'hypernebula' model also fits our observational constraints.

astro-ph.HE↗

arXiv2023

The Radio Parallax of the Crab Pulsar: A First VLBI Measurement Calibrated with Giant Pulses

We use four observations with the European VLBI network to measure the first precise radio parallax of the Crab Pulsar. We found two in-beam extragalactic sources just outside the Crab Nebula, with one bright enough to use as a background reference source in our data. We use the Crab Pulsar's giant pulses to determine fringe and bandpass calibration solutions, which greatly improved the sensitivity and reliability of our images and allowed us to determine precise positional offsets between the pulsar and the background source. From those offsets, we determine a parallax of $π=0.53\pm0.06\rm{\;mas}$ and proper motion of $(μ_α,μ_δ)=(-11.34\pm0.06,2.65\pm0.14)\rm{\;mas\;yr^{-1}}$, yielding a distance of $d=1.90^{+0.22}_{-0.18}\rm{\;kpc}$ and transverse velocity of $v_{\perp}=104^{+13}_{-11}\rm{\;km\;s^{-1}}$. These results are consistent with the Gaia 3 measurements, and open up the possibility of far more accurate astrometry with further VLBI observations.

astro-ph.HE↗

arXiv2023

Resolving the Emission Regions of the Crab Pulsar's Giant Pulses II. Evidence for Relativistic Motion

The Crab Pulsar is the prime example of an emitter of giant pulses. These short, very bright pulses are thought to originate near the light cylinder, at $\sim\!1600{\rm\;km}$ from the pulsar. The pulsar's location inside the Crab Nebula offers an unusual opportunity to resolve the emission regions, using the nebula, which scatters radio waves, as a lens. We attempt to do this using a sample of 61998 giant pulses found in coherently combined European VLBI network observations at $18{\rm\;cm}$. These were taken at times of relatively strong scattering and hence good effective resolution, and from correlations between pulse spectra, we show that the giant pulse emission regions are indeed resolved. We infer apparent diameters of $\sim\!2000$ and $\sim\!2400{\rm\;km}$ for the main and interpulse components, respectively, and show that with these sizes the correlation amplitudes and decorrelation timescales and bandwidths can be understood quantitatively, both in our observations and in previous ones. Using pulse-spectra statistics and correlations between polarizations, we also show that the nebula resolves the nanoshots that comprise individual giant pulses. The implied diameters of $\sim\!1100{\rm\;km}$ far exceed light travel-time estimates, suggesting the emitting plasma is moving relativistically, with $γ\simeq10^{4}$, as inferred previously from drifting bands during the scattering tail of a giant pulse. If so, the emission happens over a region extended along the line of sight by $\sim\!10^{7}{\rm\;km}$. We conclude that relativistic motion likely is important for producing giant pulses, and may be similarly for other sources of short, bright radio emission, such as fast radio bursts.

astro-ph.HE↗

arXiv2021

The 60 pc Environment of FRB 20180916B

Fast Radio Burst FRB 20180916B in its host galaxy SDSS J015800.28+654253.0 at 149 Mpc is by far the closest-known FRB with a robust host galaxy association. The source also exhibits a 16.35-day period in its bursting. Here we present optical and infrared imaging as well as integral field spectroscopy observations of FRB 20180916B with the WFC3 camera on the Hubble Space Telescope and the MEGARA spectrograph on the 10.4-m Gran Telescopio Canarias. The 60-90 milliarcsecond (mas) resolution of the Hubble imaging, along with the previous 2.3-mas localization of FRB 20180916B, allow us to probe its environment with a 30-60 pc resolution. We constrain any point-like star-formation or HII region at the location of FRB 20180916B to have an H$α$ luminosity $L_\mathrm{Hα} \lesssim 10^{37}\,\mathrm{erg\,s^{-1}}$ and, correspondingly, constrain the local star-formation rate to be $\lesssim10^{-4}\,\mathrm{M_\odot\,yr^{-1}}$. The constraint on H$α$ suggests that possible stellar companions to FRB 20180916B should be of a cooler, less massive spectral type than O6V. FRB 20180916B is 250 pc away (in projected distance) from the brightest pixel of the nearest young stellar clump, which is $\sim380$\,pc in size (full-width at half maximum). With the typical projected velocities of pulsars, magnetars, or neutron stars in binaries (60-750 km s$^{-1}$), FRB 20180916B would need 800 kyr to 7 Myr to traverse the observed distance from its presumed birth site. This timescale is inconsistent with the active ages of magnetars ($\lesssim10$ kyr). Rather, the inferred age and observed separation are compatible with the ages of high-mass X-ray binaries and gamma-ray binaries, and their separations from the nearest OB associations.

astro-ph.HE↗

arXiv2015

Revisiting the birth locations of pulsars B1929+10, B2020+28,and B2021+51

We present new proper motion and parallax measurements obtained with the European VLBI Network (EVN) at 5$\,$GHz for the three isolated pulsars B1929+10, B2020+28, and B2021+51. For B1929+10 we combined our data with earlier VLBI measurements and confirm the robustness of the astrometric parameters of this pulsar. For pulsars B2020+28 and B2021+51 our observations indicate that both stars are almost a factor of two closer to the solar system than previously thought, placing them at a distance of $1.39_{-0.06}^{+0.05}$ and $1.25_{-0.17}^{+0.14}\,$kpc. Using our new astrometry, we simulated the orbits of all three pulsars in the Galactic potential with the aim to confirm or reject previously proposed birth locations. Our observations ultimately rule out a claimed binary origin of B1929+10 and the runaway star $ζ$ Ophiuchi in Upper Scorpius. A putative common binary origin of B2020+28 and B2021+51 in the Cygnus Superbubble is also very unlikely.

astro-ph.SR↗

arXiv2014

Precision astrometry of pulsars and other compact radio sources in the globular cluster M15

The globular cluster (GC) M15 (NGC 7078) is host to at least eight pulsars and two low mass X-ray binaries (LMXBs) one of which is also visible in the radio regime. Here we present the results of a multi-epoch global very long baseline interferometry (VLBI) campaign aiming at i) measuring the proper motion of the known compact radio sources, ii) finding and classifying thus far undetected compact radio sources in the GC, and iii) detecting a signature of the putative intermediate mass black hole (IMBH) proposed to reside at the core of M15. We measure the sky motion in right ascension ($μ_α$) and declination ($μ_δ$) of the pulsars M15A and M15C and of the LMXB AC211 to be $(μ_α,\,μ_δ)_{\text{M15A}}=(-0.54\pm0.14,\,-4.33\pm0.25)\,$mas$\,$yr$^{-1}$, $(μ_α,\,μ_δ)_{\text{M15C}}=(-0.75\pm0.09,\,-3.52\pm0.13)\,$mas$\,$yr$^{-1}$, and $(μ_α,\,μ_δ)_{\text{AC211}}=(-0.46\pm0.08,\,-4.31\pm0.20)\,$mas$\,$yr$^{-1}$, respectively. Based on these measurements we estimate the global proper motion of M15 to be $(μ_α,\,μ_δ)=(-0.58\pm0.18,\,-4.05\pm0.34)\,$mas$\,$yr$^{-1}$. We detect two previously known but unclassified compact sources within our field of view. Our observations indicate that one them is of extragalactic origin while the other one is a foreground source, quite likely an LMXB. The double neutron star system M15C became fainter during the observations, disappeared for one year and is now observable again---an effect possibly caused by geodetic precession. The LMXB AC211 shows a double lobed structure in one of the observations indicative of an outburst during this campaign. With the inclusion of the last two of a total of seven observations we confirm the upper mass limit for a putative IMBH to be M$_{\bullet}<500$ M$_{\odot}$.

astro-ph.HE↗

arXiv2014

Variability in Ultra-luminous X-ray Sources

Many upcoming surveys, particularly in the radio and optical domains, are designed to probe either the temporal and/or the spatial variability of a range of astronomical objects. In the light of these high resolution surveys, we review the subject of ultra-luminous X-ray (ULX) sources, which are thought to be accreting black holes for the most part. We also discuss the sub-class of ULXs known as the hyper-luminous X-ray sources, which may be accreting intermediate mass black holes. We focus on some of the open questions that will be addressed with the new facilities, such as the mass of the black hole in ULXs, their temporal variability and the nature of the state changes, their surrounding nebulae and the nature of the region in which ULXs reside.

astro-ph.HE↗