Black Hole Mass Research Articles

Distinguishability of binary extreme-mass-ratio inspirals in low frequency band

The inspiral of compact stellar objects into massive black holes are one of the main astrophysical sources for the Laser Interferometer Space Antenna (LISA) and Taiji. These extreme-mass-ratio inspirals (EMRIs) have great potential for cosmology and fundamental physics. A binary extreme-mass-ratio inspiral (b-EMRI) describes the case where binary black holes (BBHs) are captured by a supermassive black hole. The b-EMRIs serve as multi-band gravitational wave sources and provide insights into the dynamics of nuclei and tests of general relativity. However, if the b-EMRIs can be distinguished from the normal EMRIs or not is still not clear. In this work, with a few of assumptions, and using the Teukolsky equation, we calculate the approximate gravitational waves of b-EMRIs and assess their detectability by space-based detectors. We also decouple the secondary object information from the Teukolsky equation, enabling us to calculate the energy fluxes and generate the waveforms more conveniently. Variations in the quadrupole of the binary result in small but non-negligible changes in energy fluxes and waveforms, making it possible to distinguish b-EMRI signals with data analysis. This opens up the potential of using b-EMRIs to test gravity theories and for further astrophysical studies.

Measuring source properties and quasinormal mode frequencies of heavy massive black-hole binaries with LISA

The Laser Interferometer Space Antenna (LISA) will be launched in the mid-2030s. It promises to observe the coalescence of massive black-hole (BH) binaries with signal-to-noise ratios (SNRs) reaching thousands. Crucially, it will detect some of these binaries with high SNR in both the inspiral and the merger-ringdown stages. Such signals are ideal for tests of general relativity (GR) using information from the whole waveform. Here, we consider astrophysically motivated binary systems at the high-mass end of the population observable by LISA and simulate their signals using the newly developed multipolar effective-one-body model: pSEOBNRv5HM. The merger-ringdown signal in this model depends on the binary properties (masses and spins) and also on parameters that describe fractional deviations from the GR quasinormal mode (complex) frequencies of the remnant BH. Performing full Bayesian analyses, we assess to which accuracy LISA will be able to constrain deviations from GR in the ringdown signal when using information from the whole signal. We find that these deviations can typically be constrained to within 10% and in the best cases to within 1%. We also show that with this model we can measure the binary masses and spins with great accuracy even for very massive BH systems with low SNR in the inspiral. In particular, individual source-frame masses can typically be constrained to within 10% and as precisely as 1%, and individual spins can typically be constrained to within 0.1 and, in the best cases, to within 0.001. We also probe the accuracy of the SEOBNRv5HM waveform family by performing synthetic injections of GR numerical-relativity waveforms. Using a novel method that we develop here to quantify the impact of systematic errors, we show that, already for sources with SNR O(100), we would measure erroneous deviations from GR due to waveform model inaccuracies. One of the main sources of error is the mismodeling of the relative alignment between harmonics. These results confirm the need for improving waveform models to perform tests of GR with binary BHs observed at high SNR by LISA. Published by the American Physical Society 2024

Supermassive black holes from runaway mergers and accretion in nuclear star clusters

Abstract Rapid formation of supermassive black holes occurs in dense nuclear star clusters that are initially gas-dominated. Stellar-mass black hole remnants of the most massive cluster stars sink into the core, where a massive runaway black hole forms as a consequence of combined effects of repeated mergers and Eddington-limited gas accretion. The associated gravitational-wave signals of high-redshift extreme mass-ratio inspirals are a unique signature of the nuclear star cluster scenario.

Gravitational wave peeps from EMRIs and their implication for LISA signal confusion noise

Scattering events around the center of massive galaxies will occasionally toss a stellar-mass compact object into an orbit around the massive black hole (MBH) at the center, beginning an extreme mass ratio inspiral (EMRI). The early stages of such a highly eccentric orbit are not likely to produce detectable gravitational waves (GWs), as the source will only be in a suitable frequency band briefly when it is close to periapsis during each long-period orbit. This repeated burst of emission, firmly in the millihertz band, is the GW peep. While a single peep is not likely to be detectable, if we consider an ensemble of such subthreshold sources, spread across the Universe, together they may produce an unresolvable background noise that could obscure sources otherwise detectable by the Laser Interferometer Space Antenna. Previous studies of the extreme mass ratio signal confusion background focused either on parabolic orbits near the MBH or events closer to merger. We seek to improve this characterization by implementing numerical kludge waveforms that can calculate highly eccentric orbits with relativistic effects. Our focus is on orbits at the point of capture that are farther away from the MBH. Here we present the waveforms and spectra of peeps generated from recent calculations of EMRIs/extreme mass ratio bursts capture parameters and discuss how these can be used to estimate the signal confusion noise generated by such events. We demonstrate the effects of changing the orbital parameters on the resulting spectra as well as showing direct comparisons to parabolic orbits and why the GW ‘peep’ needs to be studied further. The results of this study will be expanded upon in a further paper that aims to provide an update on the EMRI signal confusion noise problem.

Repainting the colour–mass diagrams by unearthing the green mountain: dust-rich S0 galaxies in the colour–(galaxy stellar mass) diagram, and the colour–(black hole mass) relations for dust-poor versus dust-rich galaxies

ABSTRACT Lenticular galaxies are notoriously misclassified as elliptical galaxies and, as such, a (disc inclination)-dependent correction for dust is often not applied to the magnitudes of dusty lenticular galaxies. This results in overly red galaxy colours, impacting their distribution in the colour–magnitude diagram. It is revealed how this has led to an underpopulation of the ‘green valley’ by hiding a ‘green mountain’ of massive dust-rich lenticular galaxies – known to be built from gas-rich major mergers – within the ‘red sequence’ of colour–(stellar mass) diagrams. Correcting for dust, a ‘green mountain’ appears at M*,gal ∼ 1011 M⊙, along with signs of an extension to lower masses producing a ‘green range’ or ‘green ridge’ on the green side of the ‘red sequence’ and ‘blue cloud.’ The ‘red sequence’ is shown to be comprised of two components: a red plateau defined by elliptical galaxies with a near-constant colour and by lower-mass dust-poor lenticular galaxies, which are mostly a primordial population but may include faded/transformed spiral galaxies. The presence of the quasi-triangular-shaped galaxy evolution sequence, previously called the ‘Triangal’, is revealed in the galaxy colour–(stellar mass) diagram. It tracks the speciation of galaxies and their associated migration through the diagram. The connection of the ‘Triangal’ to previous galaxy morphology sequences (Fork, Trident, and Comb) is also shown herein. Finally, the colour–(black hole mass) diagram is revisited, revealing how the dust correction generates a blue–green sequence for the spiral and dust-rich lenticular galaxies that is offset from a green–red sequence defined by the dust-poor lenticular and elliptical galaxies.

Resolving the vicinity of supermassive black holes with gravitational microlensing

ABSTRACT Upcoming wide-field surveys will discover thousands of new strongly lensed quasars which will be monitored with unprecedented cadence by the Legacy Survey of Space and Time (LSST). Many of these quasars will undergo caustic-crossing events over the 10-yr LSST survey, during which the quasar’s inner accretion disc crosses a caustic feature produced by an ensemble of microlenses. Such caustic-crossing events offer the unique opportunity to probe the vicinity of the central supermassive black hole, especially when combined with high cadence, multi-instrument follow-up triggered by LSST monitoring. To simulate the high-cadence optical monitoring of caustic-crossing events, we use relativistic accretion disc models which leads to strong asymmetric features. We develop analysis methods to measure the innermost stable circular orbit (ISCO) crossing time of isolated caustic-crossing events and benchmark their performance on our simulations. We also use our simulations to train a convolutional neural network (CNN) to infer the black hole mass, inclination angle, and impact angle directly from these light curves. As a pilot application of our methods, we used archival caustic-crossings of QSO 2237+0305 to estimate the black hole mass and inclination angle. From these data, two of these methods called the second derivative and wavelet methods measure an ISCO crossing time of 48.5 and 49.5 d, corresponding to a Kerr black hole mass of MBH = (1.5 ± 1.2) × 109 and (1.5 ± 1.3) × 109 M⊙, respectively. The CNN inferred log10(MBH/M⊙) = 8.35 ± 0.30 when trained on Schwarzschild black hole simulations, and a moderate inclination of i = 45 ± 23°. These measurements are found to be consistent with previous estimates.

Radio Emission from High-redshift Active Galactic Nuclei in the JADES and CEERS Surveys

Recent calculations indicate that radio emission from quasars at z ∼ 6–7 could be detected at much earlier stages of evolution, at z ∼ 14–15, by the Next-Generation Very Large Array (ngVLA) and the Square Kilometer Array (SKA). However, the James Webb Space Telescope has now discovered less luminous active galactic nuclei (AGNs) at z > 4 and a few massive black holes (BHs) at z > 10, which may be the progenitors of supermassive black holes (SMBHs) but at different stages of growth. Radio detections of these new AGNs would provide complementary measures of their properties and those of their host galaxies. Here we estimate radio flux densities for 19 new AGNs found by the JADES, CEERS, and UNCOVER surveys. We find that ngVLA should be able to detect most of these sources in targeted surveys with integration times of 10–100 hr (and in just 1 hr for a few of them) but most would require at least 100 hr of SKA time in spite of its greater sensitivities at low frequencies. In some cases, radio emission from the BH can be distinguished from that of H ii regions and supernovae in their host galaxies, which could be used to estimate their star formation rates. Such detections would be yet another example of the useful synergies between near-infrared and radio telescopes in SMBH science in the coming decade.

Quenching massive galaxies across cosmic time with the semi-analytic model shark v2.0

ABSTRACT We introduce version 2.0 of the shark semi-analytic model of galaxy formation after many improvements to the physics included. The most significant being (i) a model describing the exchange of angular momentum (AM) between the interstellar medium and stars; (ii) a new active galactic nuclei feedback model which has two modes, a wind and a jet mode, with the jet mode tied to the jet energy production; (iii) a model tracking the development of black hole (BH) spins; (iv) more sophisticated modelling of environmental effects on satellite galaxies; and (v) automatic parameter exploration using Particle Swarm Optimization. We focus on two timely research topics: the structural properties of galaxies and the quenching of massive galaxies. For the former, sharkv2.0 is capable of producing a more realistic stellar size–mass relation with a plateau marking the transition from disc- to bulge-dominated galaxies, and scaling relations between specific AM and mass that agree well with observations. For the quenching of massive galaxies, sharkv2.0 produces massive galaxies that are more quenched than the previous version, reproducing well the observed relations between star formation rate (SFR) and stellar mass, and specific SFR and BH mass at z = 0. shark v2.0 produces a number density of massive-quiescent galaxies >1 dex higher than the previous version, in good agreement with JWST observations at z ≤ 5; predicts a stellar mass function of passive galaxies in reasonably good agreement with observations at 0.5 < z < 5; and environmental quenching to already be effective at z = 5.

Small Schwarzschild de Sitter black holes, the future boundary and islands

We continue the study of 4-dimensional Schwarzschild de Sitter black holes in the regime where the black hole mass is small compared with the de Sitter scale, following arXiv:2207.10724 [hep-th]. The de Sitter temperature is very low compared with that of the black hole. We consider the future boundary as the location where the black hole Hawking radiation is collected. Using 2-dimensional tools, we find unbounded growth of the entanglement entropy of radiation as the radiation region approaches the entire future boundary. Self-consistently including appropriate late time islands emerging just inside the black hole horizon leads to a reasonable Page curve. We also discuss other potential island solutions which show inconsistencies.

A quasar-galaxy merger at z ∼ 6.2: Black hole mass and quasar properties from the NIRSpec spectrum

We present JWST/NIRSpec integral field data of the quasar PJ308-21 at z = 6.2342. As shown by previous ALMA and HST imaging, the quasar has two companion sources, interacting with the quasar host galaxy. The high-resolution G395H/290LP NIRSpec spectrum covers the 2.87 − 5.27 μm wavelength range and shows the rest-frame optical emission of the quasar with exquisite quality (signal-to-noise ratio ∼100 − 400 per spectral element). Based on the Hβ line from the broad line region, we obtain an estimate of the black hole mass MBH, Hβ ∼ 2.7 × 109 M⊙. This value is within a factor ≲1.5 of the Hα-based black hole mass from the same spectrum (MBH, Hα ∼ 1.93 × 109 M⊙) and is consistent with a previous estimate relying on the Mg IIλ2799 line (MBH, MgII ∼ 2.65 × 109 M⊙). All these MBH estimates are within the ∼0.5 dex intrinsic scatter of the adopted mass calibrations. The high Eddington ratio of PJ308-21 λEdd, Hβ ∼ 0.67 (λEdd, Hα ∼ 0.96) is in line with the overall quasar population at z ≳ 6. The relative strengths of the [O III], Fe II, and Hβ lines are consistent with the empirical “Eigenvector 1” correlations as observed for low redshift quasars. We find evidence for blueshifted [O III] λ5007 emission with a velocity offset Δv[O III] = −1922 ± 39 km s−1 from the systemic velocity and a full width at half maximum (FWHM) FWHM([O III]) = 2776−74+75 km s−1. This may be the signature of outflowing gas from the nuclear region, despite the true values of Δv[O III] and FWHM([O III]) likely being more uncertain due to the blending with Hβ and Fe II lines. Our study demonstrates the unique capabilities of NIRSpec in capturing quasar spectra at cosmic dawn and studying their properties in unprecedented detail.

The X-ray variability of active galactic nuclei: Power spectrum and variance analysis of the Swift/BAT light curves

Aims. We study the X-ray power spectrum of active galactic nuclei (AGN) in order to investigate whether Seyfert I and II power spectra are similar or not and whether AGN variability depends on the mass and accretion rate of black holes as well as to compare the power spectra of AGN with the power spectra of Galactic X-ray black hole binaries. Method. We used 14–195 keV band light curves from the 157-month Swift/BAT hard X-ray survey, and we computed the mean power spectrum and excess variance of AGN in narrow black hole mass and AGN luminosity bins. We fitted a power-law model to the AGN power spectra, and we investigated whether the power spectrum parameters and the excess variance depend on the black hole mass, luminosity, and accretion rate of AGN. Results. We found the Seyfert I and Seyfert II power spectra to be identical, in agreement with AGN unification models. The mean AGN X-ray power spectrum has the same power-law like shape, with a slope of −1 in all AGN irrespective of their luminosity and black hole mass. We did not detect any flattening to a slope of zero at frequencies as low as 10−9 Hz. We detected an anti-correlation between the power spectral density function (PSD) amplitude and the accretion rate, similar to what has been seen in the past in the 2–10 keV band. This implies that the variability amplitude in AGN decreases with an increasing accretion rate. The universal AGN power spectrum is consistent with the mean 2–9 keV band Cyg X-1 power spectrum in its soft state. We detected a small difference in amplitude, but this is probably due to the difference in energy. Conclusions. The mean low-frequency AGN X-ray power spectrum is consistent with the extension of the mean 0.01–25 Hz Cyg X-1 power spectrum in its soft state to lower frequencies. We cannot prove that the mean AGN PSD is analogous to the mean Cyg X-1 PSD in its soft state, as we do not know the location of the high-frequency break in the hard X-ray AGN PSDs. However, if this is the case, then the accretion disc in AGN probably extends to the radius of the innermost circular stable orbit (as is probably the case with the black hole binaries in their soft state). The X-ray corona will then be located on top, illuminating the disc and producing the X-ray reflection and disc reverberation phenomena commonly observed in these objects. Furthermore, the agreement between the PSD amplitude in AGN and the Cyg X-1 (either in the soft or the hard state) over many decades in frequency indicates that the X-ray variability process is probably the same in all accreting objects, irrespective of the mass of the compact object. We plan to investigate this issue further in the near future.

Detecting Population III Stars through Tidal Disruption Events in the Era of JWST and Roman

The first-generation metal-free stars, referred to as Population III (Pop III) stars, are believed to be the first objects to form out of the pristine gas in the very early Universe. Pop III stars have different structures from the current generation of stars and are important for generating heavy elements and shaping subsequent star formation. However, it is very challenging to directly detect Pop III stars given their high redshifts and short lifetimes. In this Letter, we propose a novel method for detecting Pop III stars through their tidal disruption events (TDEs) by massive black holes. We model the emission properties and calculate the expected rates for these unique TDEs in the early Universe at z ∼ 10. We find that Pop III star TDEs have much higher mass fallback rates and longer evolution timescales compared to solar-type star TDEs in the local Universe, which enhances the feasibility of their detection, although a good survey strategy will be needed for categorizing these sources as transients. We further demonstrate that a large fraction of the flare emissions are redshifted to infrared wavelengths, which can be detected by the JWST and the Nancy Grace Roman Space Telescope (Roman). Last but not least, we find a promising Pop III star TDE detection rate of up to a few tens per year using Roman, based on our current understanding of the black hole mass function in the early Universe.

The doomsday of black hole evaporation

Abstract By assuming simultaneously the unitarity of the Hawking evaporation and the universality of Bekenstein entropy bound as well as the validity of cosmic censorship conjecture, we find that the black hole evaporation rate could evolve from the usual inverse square law in black hole mass into a constant evaporation rate near the end of the Hawking evaporation before quantum gravity could come into play, inferring a slightly longer lifetime for lighter black holes.

Discovery of Optically Emitting Circumgalactic Nebulae around the Majority of UV-luminous Quasars at Intermediate Redshift

We report the discovery of large, ionized, [O ii]-emitting circumgalactic nebulae around the majority of 30 UV-luminous quasars at z = 0.4–1.4 observed with deep, wide-field integral field spectroscopy with the Multi-Unit Spectroscopy Explorer (MUSE) by the Cosmic Ultraviolet Baryon Survey and MUSE Quasar Blind Emitters Survey. Among the 30 quasars, seven (23%) exhibit [O ii]-emitting nebulae with major axis sizes greater than 100 kpc, 20 greater than 50 kpc (67%), and 27 (90%) greater than 20 kpc. Such large, optically emitting nebulae indicate that cool, dense, and metal-enriched circumgalactic gas is common in the halos of luminous quasars at intermediate redshift. Several of the largest nebulae exhibit morphologies that suggest interaction-related origins. We detect no correlation between the sizes and cosmological-dimming-corrected surface brightnesses of the nebulae and quasar redshift, luminosity, black hole mass, or radio-loudness, but find a tentative correlation between the nebulae and rest-frame [O ii] equivalent width in the quasar spectra. This potential trend suggests a relationship between interstellar medium content and gas reservoirs on CGM scales. The [O ii]-emitting nebulae around the z ≈ 1 quasars are smaller and less common than Lyα nebulae around z ≈ 3 quasars. These smaller sizes can be explained if the outer regions of the Lyα halos arise from scattering in more neutral gas, by evolution in the cool circumgalactic medium content of quasar-host halos, by lower-than-expected metallicities on ≳50 kpc scales around z ≈ 1 quasars, or by changes in quasar episodic lifetimes between z = 3 and 1.

General form of the function [formula omitted] using cylindrically static spacetime

We find an exact static solution in four dimensions to the field equations of the f(Q) gravity by using a cylindrically static spacetime with two different ansatz, ν(r) and μ(r). This solution is derived without imposing any conditions on f(Q). The black hole solution involves four constants: c1, c2, c3, and c4. Among these, c1 is linked to the cosmological constant, c2 to the black hole's mass, while c3 and c4 are responsible for the deviation of the solution from the linear form of f(Q). We demonstrate how the analytical function f(Q) relies on c3. When c3 is zero, f(Q) becomes a constant function, leading to the non-metricity case. We investigate the singularity of this solution and show that the Kretschmann invariant has a much milder singularity compared to the non-metricity case. We produce a black hole that rotates with non-vanishing values of Q and f(Q) by using a coordinate transformation. Then, we analyze the laws of thermodynamics to determine the physical characteristics of this black hole solution and demonstrate that it is locally thermodynamically stable.

Machine learning applications in studies of the physical properties of active galactic nuclei based on photometric observations

Context. We investigate the physical nature of active galactic nuclei (AGNs) using machine learning (ML) tools. Aims. We show that the redshift, z, bolometric luminosity, LBol, central mass of the supermassive black hole (SMBH), MBH, Eddington ratio, λEdd, and AGN class (obscured or unobscured) can be reconstructed through multi-wavelength photometric observations only. Methods. We trained a random forest regressor (RFR) ML-model on 7616 spectroscopically observed AGNs from the SPIDERS-AGN survey, which had previously been cross-matched with soft X-ray observations (from ROSAT or XMM), WISE mid-infrared photometry, and optical photometry from SDSS ugriz filters. We built a catalog of 21 050 AGNs that were subsequently reconstructed with the trained RFR; for 9687 sources, we found archival redshift measurements. All AGNs were classified as either type 1 or type 2 using a random forest classifier (RFC) algorithm on a subset of known sources. All known photometric measurement uncertainties were incorporated via a simulation-based approach. Results. We present the reconstructed catalog of 21 050 AGNs with redshifts ranging from 0 < z < 2.5. We determined z estimations for 11 363 new sources, with both accuracy and outlier rates within 2%. The distinction between type 1 or type 2 AGNs could be identified with respective efficiencies of 94% and 89%. The estimated obscuration level, a proxy for AGN classification, of all sources is given in the dataset. The LBol, MBH, and λEdd values are given for 21 050 new sources with their estimated error. These results have been made publicly available. Conclusions. The release of this catalog will advance AGN studies by presenting key parameters of the accretion history of 6 dex in luminosity over a wide range of z. Similar applications of ML techniques using photometric data only will be essential in the future, with large datasets from eROSITA, JSWT, and the VRO poised to be released in the next decade.

Impact of primordial black holes on heavy neutral leptons searches in the framework of resonant leptogenesis

We investigate the effects on sub-TeV resonant leptogenesis of primordial black holes with masses from 106 g to ∼109 g. The latter might dominate the energy content of the Universe altering its evolution and, eventually, diluting the final baryon asymmetry. We find that, depending on the mass and abundance of primordial black holes, the parameter space of sub-TeV resonant leptogenesis shrinks towards higher right-handed neutrino masses and smaller active-sterile mixing. Remarkably, this translates into important implications for the experimental searches of heavy neutral leptons. Conversely, we demonstrate that a possible future detection of sub-TeV heavy neutral leptons would disfavor regions of the parameter space of primordial black holes currently allowed. Published by the American Physical Society 2024

Exploring Low-mass Black Holes through Tidal Disruption Events in the Early Universe: Perspectives in the Era of the JWST, Roman Space Telescope, and LSST Surveys

The James Webb Space Telescope (JWST) has recently uncovered the presence of low-luminosity active galactic nuclei (AGNs) at z = 4–11. Spectroscopic observations have provided estimates of the nuclear black hole (BH) masses for these sources, extending the low-mass boundary down to M • ∼ 106–7 M ⊙. Despite this breakthrough, the observed lowest mass of BHs is still ≳1–2 orders of magnitude heavier than the predicted mass range of their seed population, thereby leaving the initial mass distribution of massive BHs poorly constrained. In this paper, we focus on UV-to-optical (in the rest frame) flares of stellar tidal disruption events (TDEs) embedded in low-luminosity AGNs as a tool for exploring low-mass BH populations with ≲104–6 M ⊙. We provide an estimate of the TDE rate over z = 4–11, associated with the properties of JWST-detected AGN host galaxies, and we find that deep and wide survey programs with JWST and the Roman Space Telescope (RST) can detect and identify TDEs up to z ≃ 4–7. The predicted detection numbers of TDEs at z > 4 in 1 yr are NTDE∼2–10(0.2–2) for the JADES-Medium (and COSMOS-Web) survey with JWST and NTDE∼2–10(8–50) for the deep (and wide) tiers of the High Latitude Time Domain Survey with RST. We further discuss survey strategies for hunting for transient high-redshift TDEs in wide-field surveys with RST, as well as a joint observation campaign with the Vera C. Rubin Observatory for enhancing the detection number. The high-redshift TDE search will give us a unique opportunity to probe the mass distribution of early BH populations.

EIGER. V. Characterizing the Host Galaxies of Luminous Quasars at z ≳ 6

Abstract We report JWST/NIRCam measurements of quasar host galaxy emissions and supermassive black hole (SMBH) masses for six quasars at 5.9 < z < 7.1 in the Emission-line galaxies and Intergalactic Gas in the Epoch of Reionization (EIGER) project. We obtain deep NIRCam imaging in the F115W, F200W, and F356W bands, as well as F356W grism spectroscopy of the quasars. We use bright unsaturated stars to construct models of the point-spread functions (PSFs) and estimate the errors of these PSFs. We then measure or constrain the fluxes and morphology of the quasar host galaxies by fitting the quasar images as a point source plus an exponential disk. We successfully detect the host galaxies of three quasars, which have host-to-quasar-flux ratios of ∼1%–5%. Spectral energy distribution fitting suggests that these quasar host galaxies have stellar masses of M * ≳ 1010 M ⊙. For quasars with host galaxy nondetections, we estimate the upper limits of their stellar masses. We use the grism spectra to measure the Hβ line profile and the continuum luminosity, then estimate the SMBH masses for the quasars. Our results indicate that the positive relation between SMBH masses and host galaxy stellar masses already exists at redshift z ≳ 6. The quasars in our sample show a high BH-to-stellar-mass ratio of M BH/M * ∼ 0.15, which is about ∼2 dex higher than local relations. We find that selection effects only contribute partially to the high M BH/M * ratios of high-redshift quasars. This result hints at a possible redshift evolution of the M BH–M * relation.

Observing gravitational waves with solar system astrometry

The subtle influence of gravitational waves on the apparent positioning of celestial bodies offers novel observational windows [1,2,3,4]. We calculate the expected astrometric signal induced by an isotropic Stochastic Gravitational Wave Background (SGWB) in the short distance limit. Our focus is on the resultant proper motion of Solar System objects, a signal on the same time scales addressed by Pulsar Timing Arrays (PTA). We derive the corresponding astrometric deflection patterns, finding that they manifest as distinctive dipole and quadrupole correlations or, in some cases, may not be present. Our analysis encompasses both Einsteinian and non-Einsteinian polarisations. We estimate the upper limits for the amplitude of SGWBs that could be obtained by tracking the proper motions of large numbers of solar system objects such as asteroids. We find that for SGWBs with negative spectral indices, such as that generated by Super Massive Black Hole Binaries (SMBHB), the constraints from these observations could rival those from PTAs. With the Gaia satellite and the Vera C. Rubin Observatory poised to track an extensive sample of asteroids — ranging from 𝒪(105) to 𝒪(106), we highlight the significant future potential for similar surveys to contribute to our understanding of the SGWB.