arXiv subjects

S. Ansoldi

Publications and source records attributed to S. Ansoldi.

At least 37 records · Page 2Linked to original sources

arXiv2026

Detection of the distant quasar OP 313 with the first Large-Sized Telescope of CTAO

In December 2023, the Large-Sized Telescope prototype (LST-1) detected for the first time VHE $γ$-ray emission from the FSRQ OP~313 becoming the furthest blazar ever observed at VHE with z=0.997. We aim to characterize the $γ$-ray emission of OP 313 during this flare, comparing it with its average emission state in order to understand the processes leading to this detection. Its remarkable distance also enables studies on the Extragalactic Background Light (EBL), with the goal of evaluating the attenuation of VHE $γ$-ray photons. We characterize the $γ$-ray emission during the flare in December 2023 and the low emission state observed in January 2024 thanks to the LST-1 and MAGIC data and quasi-simultaneous \textit{Fermi}-LAT observations. This dataset also enables us to evaluate the EBL attenuation by systematically exploring the EBL intensity over the $γ$-ray spectrum. Finally, we study the multi-wavelength emission and interpret the broadband spectral energy distribution (SED) within blazar radiative models including the thermal contributions from the accretion disc, dusty torus and broad line region. We also characterize the flare brightness in the high-energy (HE, $E>100$~MeV) $γ$-ray band, that was found to be a factor 50 above the average emission seen by \textit{Fermi}-LAT. The HE and VHE observations allow us to set constrains to the EBL density. Finally, thanks to the extensive multi-wavelength campaign organized, we are able to construct and model the broadband SED of OP~313 within the framework of a two-zone leptonic model where the $γ$-ray emission is produced via inverse-Compton scattering of the broad line region, accretion disk and dusty torus photon fields. However the dominant external photon field remains unknown, as several combinations are able to successfully explain the $γ$-ray emission observed.

astro-ph.HE↗

arXiv2026

Long-term study of the gamma-ray emission of Cygnus X-3 with MAGIC and Fermi-LAT

Cygnus X-3 is a microquasar composed of a compact object of unknown nature closely orbiting around a Wolf-Rayet star. The particularities of this source make it a unique case among microquasars. This fact, together with its recent establishment as a PeV particle accelerator, makes Cygnus X-3 a very interesting target for the investigation of the physical processes leading to gamma-ray production. In this work, the TeV and GeV gamma-ray emission of Cygnus X-3 is studied in order to determine its origin and constrain the properties of the system. For that purpose, a point-like analysis of 130 h of data taken with the MAGIC telescopes between 2013 and 2024 was performed, which represents the largest available sample for Cygnus X-3 at $\sim$TeV energies. Additionally, contemporary data from Fermi-LAT were also analysed to better contextualize the MAGIC observations. For a more detailed investigation of the source physics, the data were divided into three subsets according to the flaring state of the source and orbital phase. No significant detection of Cygnus X-3 is found between 0.1 and 7 TeV for any of the datasets, and differential and integral flux upper limits are reported over the long-term monitoring of the source. The Fermi-LAT fluxes can be considered compatible with previous results, taking into account the different data samples used across studies. The MAGIC upper limits presented in this work represent the most constraining ones up to date at $\sim$TeV energies. An eventual detection of Cygnus X-3 at these energies would significantly constrain the source properties, and is not unreasonable to expect given that the source has already been detected in both the GeV and PeV regimes during flaring states. Further observations of Cygnus X-3 at energies above tens of GeV would be valuable for this purpose.

astro-ph.HE↗

arXiv2026

Searches for Continuous Gravitational Waves from Supernova Remnants in the first part of the LIGO-Virgo-KAGRA Fourth Observing run

We present results from directed searches for continuous gravitational waves from a sample of 15 nearby supernova remnants, likely hosting young neutron star candidates, using data from the first eight months of the fourth observing run (O4) of the LIGO-Virgo-KAGRA Collaboration. The analysis employs five pipelines: four semi-coherent methods -- the Band-Sampled-Data directed pipeline, Weave and two Viterbi pipelines (single- and dual-harmonic) -- and PyStoch, a cross-correlation-based pipeline. These searches cover wide frequency bands and do not assume prior knowledge of the targets' ephemerides. No evidence of a signal is found from any of the 15 sources. We set 95\% confidence-level upper limits on the intrinsic strain amplitude, with the most stringent constraints reaching $\sim 4 \times 10^{-26}$ near 300 Hz for the nearby source G266.2$-$1.2 (Vela Jr.). We also derive limits on neutron star ellipticity and $r$-mode amplitudes for the same source, with the best constraints reaching $\lesssim 10^{-7}$ and $\lesssim 10^{-5}$, respectively, at frequencies above 400 Hz. These results represent the most sensitive wide-band directed searches for continuous gravitational waves from supernova remnants to date.

gr-qc↗

arXiv2026

Advanced Virgo Plus for O5 -- Design Report Overview

This document presents an overview of the design, implementation, and expected performance of the Advanced Virgo Plus (AdV+) upgrades in view of the O5 observing run. Following the experience gained during the O4 commissioning and operations, the Virgo Collaboration has revised the upgrade strategy to address limitations associated with marginally stable recycling cavities. The O5 upgrade program combines elements from the original AdV+ Phase II project with new design solutions, including the implementation of stable recycling cavities, a major modification to the central interferometer layout, and a comprehensive renewal of critical subsystems. The planned upgrades are organized in two steps, targeting progressive improvements in operational stability, noise reduction, and detector sensitivity. Key developments include new vacuum infrastructures, suspensions, mirrors, optical configurations, quantum noise reduction systems, and high-power laser technologies. The resulting configuration is expected to significantly enhance the interferometer performance, enabling a substantial increase in astrophysical reach and scientific return during O5.

astro-ph.IM↗

arXiv2026

MAGIC observations of NGC 4278. The first low-luminosity radio galaxy with compact jets detected at TeV energies

The Large High Altitude Air Shower Observatory (LHAASO) Collaboration has recently reported the first detection at TeV energies of a low-luminosity radio galaxy, NGC 4278. The aim of this work is to investigate the high-energy properties of NGC 4278 during the flaring and subsequent quasi-quiescent states with the Florian Goebel Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescopes. NGC 4278 is located in the field of view of two blazars, 1ES 1215+303 and 1ES 1218+304, previously observed by the MAGIC telescopes. Therefore, we re-analyzed MAGIC observations made between 2010 and 2024 on these sources. We also modeled the broadband spectral energy distribution of the source during and after the flaring state at TeV energies. We did not detect any statistically significant $γ$-ray emission from NGC 4278 with MAGIC. The corresponding upper limits obtained using the entire MAGIC dataset ($F_{{\rm UL, }\, >150\, \mathrm{GeV}}=1.5 \times 10^{-12}\, \mathrm{ph \, s^{-1}\, cm^{-2}}$) are consistent with the LHAASO results. The best-fit models obtained for both emission states suggest that the emitting region is strongly particle-dominated, and an efficient acceleration mechanism has to be in action in order to reach TeV energies. The transition between the flaring and quasi-quiescent state cannot be explained by a simple radiative cooling of the emitting particles. The inferred jet power, of the order of $L_{\rm jet}\sim 10^{42}\, \mathrm{erg\,s^{-1}}$, is dominated by the kinetic component in both states and it is in a good agreement with previous, time-averaged observational estimates, supporting the idea that such high-energy flares might be recurrent. The jet, however, remains too weak to break the host-galaxy confinement.

astro-ph.HE↗

arXiv2026

GWTC-4.0: Tests of General Relativity. I. Overview and General Tests

The worldwide LIGO-Virgo-KAGRA network of gravitational-wave (GW) detectors continues to increase in sensitivity, thus increasing the quantity and quality of the detected GW signals from compact binary coalescences. These signals allow us to perform ever-more sensitive tests of general relativity (GR) in the dynamical and strong-field regime of gravity. This paper is the first of three, where we present the results of a suite of tests of GR using the binary signals included in the fourth GW Transient Catalog (GWTC-4.0), i.e., up to and including the first part of the fourth observing run of the detectors (O4a). We restrict our analysis to the 91 confident signals, henceforth called events, that were measured by at least two detectors, and have false alarm rates $\le 10^{-3} \mathrm{yr}^{-1}$. These include 42 events from O4a. This first paper presents an overview of the methods, selection of events and GR tests, and serves as a guidemap for all three papers. Here we focus on the four general tests of consistency, where we find no evidence for deviations from our models. Specifically, for all the events considered, we find consistency of the residuals with noise. The final mass and final spin as inferred from the low- and high-frequency parts of the waveform are consistent with each other. We also find no evidence for deviations from the GR predictions for the amplitudes of subdominant GW multipole moments, or for non-GR modes of polarization. We thus find that GR, without new physics beyond it, is still consistent with these GW events. The results of the two additional papers in this trio also find overall consistency with vacuum GR, with more than 90% of the events being consistent with GR at the 90% credible level. While one of the ringdown analyses finds the GR value in the tails for its combined results, this may be due in part to catalog variance.

gr-qc↗

arXiv2026

GWTC-4.0: Tests of General Relativity. III. Tests of the Remnants

This is the third paper of the set recording the results of the suite of tests of general relativity (GR) performed on the signals from the fourth Gravitational-Wave Transient Catalog (GWTC-4.0), where we focus on the remnants of the binary mergers. We examine for the first time 42 events from the first part of the fourth observing run of the LIGO-Virgo-KAGRA detectors, alongside events from the previous observation runs, restricting our analysis to the confident signals, which were measured in at least two detectors and that have false alarm rates $\le 10^{-3} \mathrm{yr}^{-1}$. This paper focuses on seven tests of the coalescence remnants. Three of these are tests of the ringdown and its consistency with the expected quasinormal mode spectrum of a Kerr black hole. Specifically, two tests analyze just the ringdown in the time domain, and the third test analyzes the entire signal in the frequency domain. Four tests allow for the existence of possible echoes arriving after the end of the ringdown, which are not expected in GR. We find overall consistency of the remnants with GR. When combining events by multiplying likelihoods (hierarchically), one analysis finds that the GR prediction lies at the boundary of the $98.6^{+1.4}_{-9.4}\%$ ($99.3^{+0.7}_{-4.5}\%$) credible region, an increase from $93.8^{+6.1}_{-20.0}\%$ ($94.9^{+4.4}_{-18.2}\%$) for GWTC-3.0. Here the ranges of values comes from bootstrapping to account for the finite number of events analyzed and suggest that some of the apparently significant deviation could be attributed to variance due to the finite catalog. Since the significance also decreases to 92.2% (96.2%) when including the more recent very loud event GW250114, there is no strong evidence for a GR deviation. We find no evidence for post-merger echoes in the events that were analyzed. (Abridged)

gr-qc↗

arXiv2026

All-sky Searches for Continuous Gravitational Waves from Isolated Neutron Stars in the Data from the First Part of the Fourth LIGO-Virgo-KAGRA Observing Run

We present results from an all-sky search for continuous gravitational waves, using three different methods applied to the first eight months of LIGO data from the fourth LIGO-Virgo-KAGRA Collaboration s observing run. We aim at signals potentially emitted by rotating, non-axisymmetric isolated neutron star in the Milky Way. The analysis spans a frequency range from 20 Hz to 2000 Hz and accommodates frequency derivative magnitudes up to $10^{-8}$ Hz/s. No statistically significant periodic gravitational wave signals were detected. We establish 95% confidence-level (CL) frequentist upper limits on the dimensionless strain amplitudes. The most stringent population-averaged strain upper limits reach 9.7 $\times$ $10^{-26}$ near 290 Hz, matching the best previous constraints from 250 to $\sim$1700 Hz while extending coverage to a much broader spin-down range. At higher frequencies, the new limits improve upon previous results by factors of approximately $\sim$1.6. These constraints are applied to three astrophysical scenarios: 1) the distribution of galactic neutron stars as a function of spin frequency and ellipticity; 2) the contribution of millisecond pulsars to the GeV excess near the galactic center; and 3) the possible dark matter fraction composed of nearby inspiraling primordial binary black holes with asteroid-scale masses.

gr-qc↗

arXiv2026

First detection of VHE gamma-ray signal from the FSRQ TON 0599

TON\,0599 (z=0.7247) belongs to the few flat spectrum radio quasars (FSRQs) detected in the very high energy (VHE, $E > 100$\,GeV) gamma-ray band. Its redshift makes it currently one of the farthest VHE gamma-ray sources. It was detected for the first time with the MAGIC telescopes on 2017 December 15, and observed until December 29. The flux reached a maximum of about 50 per cent of the Crab Nebula flux above 80 GeV on the second night of observation, after which we witnessed a gradual decrease of the flux. The VHE gamma-ray spectrum connects smoothly to the one in the high energy ($E > 100$\,MeV) band obtained from simultaneous observations with {\textit Fermi}-LAT. It features a cut-off at energies around 50\,GeV, indicating the location of the gamma-ray emission zone beyond the broad line region. In addition, we were able to follow the spectral evolution during the fading phase of the flare. Multiwavelength analysis based on observations in optical, near-infrared, and radio bands acquired by the Whole Earth Blazar Telescope (WEBT) Collaboration from November to March, as well as observations in X-ray and optical--UV bands with instruments on board the \textit{Swift} satellite, shows strong correlation between different bands. We model the broadband emission with a simple one-zone leptonic model, where the high-energy peak is predominantly produced by external Compton (EC) scattering of photons from the dusty torus.

astro-ph.HE↗

arXiv2026

Time-Dependent Modeling of the Sub-Hour Spectral Evolution During the 2013 Outburst of Mrk 421

In April 2013, the TeV blazar Markarian~421 underwent one of its most powerful emission outbursts to date. An extensive multi-instrument campaign featuring MAGIC, VERITAS, and \textit{NuSTAR} provided comprehensive very-high-energy (VHE; $E > 100$\,GeV) and X-ray coverage over nine consecutive days. In this work, we perform a detailed spectral analysis of the X-ray and VHE emissions on sub-hour timescales throughout the flare. We identify several clockwise spectral hysteresis loops in the X-rays, revealing a spectral evolution more complex than a simple harder-when-brighter trend. The VHE spectrum extends beyond 10\,TeV, and its temporal evolution closely mirrors the behavior in the X-rays. We report the first evidence of VHE spectral hysteresis occurring simultaneously with the X-ray loops. To interpret these findings, we apply a time-dependent leptonic model to 240 broadband spectral energy distributions (SEDs) binned on a 15-minute scale, allowing us to self-consistently track the particle distribution's history. Our modeling shows that the majority of the sub-hour flux and spectral variations are driven by changes in the luminosity and slope of the injected electron distribution. The required variations in the electron slope are difficult to reconcile with magnetic reconnection but are consistent with a shock-acceleration scenario where the shock compression ratio evolves by a factor of $\sim2$. The model also points to a relatively stable magnetic field and emitting region size, favoring a scenario where the emission originates from a stationary feature in the jet, such as a recollimation shock. However, this scenario requires a jet Lorentz factor that significantly exceeds values from VLBI measurements to account for the high minimum electron energy implied by the lack of variability in the optical band.

astro-ph.HE↗

arXiv2026

GWTC-4.0: Searches for Gravitational-Wave Lensing Signatures

Gravitational waves can be gravitationally lensed by massive objects along their path. Depending on the lens mass and the lens--source geometry, this can lead to the observation of a single distorted signal or multiple repeated events with the same frequency evolution. We present the results for gravitational-wave lensing searches on the data from the first part of the fourth LIGO--Virgo--KAGRA observing run (O4a). We search for strongly lensed events in the newly acquired data by (1) searching for an overall phase shift present in an image formed at a saddle point of the lens potential, (2) looking for pairs of detected candidates with consistent frequency evolution, and (3) identifying sub-threshold counterpart candidates to the detected signals. Beyond strong lensing, we also look for lensing-induced distortions in all detected signals using an isolated point-mass model. We do not find evidence for strongly lensed gravitational-wave signals and use this result to constrain the rate of detectable strongly lensed events and the merger rate density of binary black holes at high redshift. In the search for single distorted lensed signals, we find one outlier: GW231123_135430, for which we report more detailed investigations. While this event is interesting, the associated waveform uncertainties make its interpretation complicated, and future observations of the populations of binary black holes and of gravitational lenses will help determine the probability that this event could be lensed.

gr-qc↗

arXiv2026

Constraints on gravitational waves from the 2024 Vela pulsar glitch

Among known neutron stars, the Vela pulsar is one of the best targets for gravitational-wave searches. It is also one of the most prolific in terms of glitches, sudden frequency changes in a pulsar's rotation. Such glitches could cause a variety of transient gravitational-wave signals. Here we search for signals associated with a Vela glitch on 29 April 2024 in data of the two LIGO detectors from the fourth LIGO--Virgo--KAGRA observing run. We search both for seconds-scale burst-like emission, primarily from fundamental (f-)mode oscillations, and for longer quasi-monochromatic transients up to four months in duration, primarily from quasi-static quadrupolar deformations. We find no significant detection candidates, but for the first time we set direct observational upper limits on gravitational strain amplitude that are stricter than what can be indirectly inferred from the overall glitch energy scale. We discuss the short- and long-duration observational constraints in the context of specific emission models. These results demonstrate the potential of gravitational-wave probes of glitching pulsars as detector sensitivity continues to improve.

gr-qc↗

arXiv2025

All-sky search for continuous gravitational-wave signals from unknown neutron stars in binary systems in the first part of the fourth LIGO-Virgo-KAGRA observing run

We present the results of a blind all-sky search for continuous gravitational-wave signals from neutron stars in binary systems using data from the first part of the fourth observing run (O4a) using LIGO detectors data. Rapidly rotating, non-axisymmetric neutron stars are expected to emit continuous gravitational waves, whose detection would significantly improve our understanding of the galactic neutron star population and matter under extreme conditions, while also providing valuable tests of general relativity. Neutron stars in binary systems likely constitute a substantial fraction of the unobserved galactic population and, due to potential mass accretion, may emit stronger gravitational-wave signals than their isolated counterparts. This search targets signals from neutron stars with frequencies in the 100-350 Hz range, with orbital periods between 7 and 15 days and projected semi-major axes between 5 and 15 light-seconds. The analysis employs the GPU-accelerated fasttracks pipeline. No credible astrophysical signals were identified, and, in the absence of a detection, we report search sensitivity estimates on the population of neutron stars in binary systems in the Milky Way.

gr-qc↗

arXiv2025

Tests of General Relativity with GWTC-3

The ever-increasing number of detections of gravitational waves (GWs) from compact binaries by the Advanced LIGO and Advanced Virgo detectors allows us to perform ever-more sensitive tests of general relativity (GR) in the dynamical and strong-field regime of gravity. We perform a suite of tests of GR using the compact binary signals observed during the second half of the third observing run of those detectors. We restrict our analysis to the 15 confident signals that have false alarm rates $\leq 10^{-3}\, {\rm yr}^{-1}$. In addition to signals consistent with binary black hole (BH) mergers, the new events include GW200115_042309, a signal consistent with a neutron star--BH merger. We find the residual power, after subtracting the best fit waveform from the data for each event, to be consistent with the detector noise. Additionally, we find all the post-Newtonian deformation coefficients to be consistent with the predictions from GR, with an improvement by a factor of ~2 in the -1PN parameter. We also find that the spin-induced quadrupole moments of the binary BH constituents are consistent with those of Kerr BHs in GR. We find no evidence for dispersion of GWs, non-GR modes of polarization, or post-merger echoes in the events that were analyzed. We update the bound on the mass of the graviton, at 90% credibility, to $m_g \leq 2.42 \times 10^{-23} \mathrm{eV}/c^2$. The final mass and final spin as inferred from the pre-merger and post-merger parts of the waveform are consistent with each other. The studies of the properties of the remnant BHs, including deviations of the quasi-normal mode frequencies and damping times, show consistency with the predictions of GR. In addition to considering signals individually, we also combine results from the catalog of GW signals to calculate more precise population constraints. We find no evidence in support of physics beyond GR.

gr-qc↗

arXiv2025

GW231123: a Binary Black Hole Merger with Total Mass 190-265 $M_{\odot}$

On 2023 November 23 the two LIGO observatories both detected GW231123, a gravitational-wave signal consistent with the merger of two black holes with masses $137^{+23}_{-18}\, M_\odot$ and $101^{+22}_{-50}\, M_\odot$ (90\% credible intervals), at luminosity distance 0.7-4.1 Gpc and redshift of $0.40^{+0.27}_{-0.25}$, and a network signal-to-noise ratio of $\sim$20.7. Both black holes exhibit high spins, $0.9^{+0.10}_{-0.19}$ and $0.80^{+0.20}_{-0.52}$ respectively. A massive black hole remnant is supported by an independent ringdown analysis. Some properties of GW231123 are subject to large systematic uncertainties, as indicated by differences in inferred parameters between signal models. The primary black hole lies within or above the theorized mass gap where black holes between 60-130 $M_\odot$ should be rare due to pair instability mechanisms, while the secondary spans the gap. The observation of GW231123 therefore suggests the formation of black holes from channels beyond standard stellar collapse, and that intermediate-mass black holes of mass $\sim$200 $M_\odot$ form through gravitational-wave driven mergers.

astro-ph.HE↗

arXiv2025

Cosmological and High Energy Physics implications from gravitational-wave background searches in LIGO-Virgo-KAGRA's O1-O4a runs

We search for gravitational-wave background signals produced by various early Universe processes in the Advanced LIGO O4a dataset, combined with the data from the earlier O1, O2, and O3 (LIGO-Virgo) runs. The absence of detectable signals enables powerful constraints on fundamental physics. We derive gravitational-wave background energy density upper limits from the O1-O4a data to constrain parameters associated with various possible processes in the early Universe: first-order phase transitions, cosmic strings, domain walls, stiff equation of state, axion inflation, second-order scalar perturbations, primordial black hole binaries, and parity violation. In our analyses, the presence of an astrophysical background produced by compact (black hole and neutron star) binary coalescences throughout the Universe is also considered. We address the implications for various cosmological and high energy physics models based on the obtained parameter constraints. We conclude that LIGO-Virgo data already yield significant constraints on numerous early Universe scenarios.

gr-qc↗

arXiv2025

GW241011 and GW241110: Exploring Binary Formation and Fundamental Physics with Asymmetric, High-Spin Black Hole Coalescence

We report the observation of gravitational waves from two binary black hole coalescences during the fourth observing run of the LIGO--Virgo--KAGRA detector network, GW241011 and GW241110. The sources of these two signals are characterized by rapid and precisely measured primary spins, non-negligible spin--orbit misalignment, and unequal mass ratios between their constituent black holes. These properties are characteristic of binaries in which the more massive object was itself formed from a previous binary black hole merger, and suggest that the sources of GW241011 and GW241110 may have formed in dense stellar environments in which repeated mergers can take place. As the third loudest gravitational-wave event published to date, with a median network signal-to-noise ratio of $36.0$, GW241011 furthermore yields stringent constraints on the Kerr nature of black holes, the multipolar structure of gravitational-wave generation, and the existence of ultralight bosons within the mass range $10^{-13}$--$10^{-12}$ eV.

astro-ph.HE↗

arXiv2025

Directional Search for Persistent Gravitational Waves: Results from the First Part of LIGO-Virgo-KAGRA's Fourth Observing Run

The angular distribution of gravitational-wave power from persistent sources may exhibit anisotropies arising from the large-scale structure of the Universe. This motivates directional searches for astrophysical and cosmological gravitational-wave backgrounds, as well as continuous-wave emitters. We present results of such a search using data from the first observing run through the first portion of the fourth observing run of the LIGO-Virgo-KAGRA Collaborations. We apply gravitational-wave radiometer techniques to generate skymaps and search for both narrowband and broadband persistent gravitational-wave sources. Additionally, we use spherical harmonic decomposition to probe spatially extended sources. No evidence of persistent gravitational-wave signals is found, and we set the most stringent constraints to date on such emissions. For narrowband point sources, our sensitivity estimate to effective strain amplitude lies in the range $(0.03 - 8.4) \times 10^{-24}$ across all sky and frequency range $(20 - 160)$ Hz. For targeted sources -- Scorpius X-1, SN 1987A, the Galactic Center, Terzan 5, and NGC 6397 -- we constrain the strain amplitude with best limits ranging from $\sim 1.1 \times 10^{-25}$ to $6.5 \times 10^{-24}$. For persistent broadband sources, we constrain the gravitational-wave flux $F_{α, \hat{n}}^{95\%, \mathrm{UL}}(25\, \mathrm{Hz}) < (0.008 - 5.5) \times 10^{-8}\, \mathrm{erg\, cm^{-2}\, s^{-1}\, Hz^{-1}}$, depending on the sky direction $\hat{n}$ and spectral index $α=0,\,2/3,\,3$. Finally, for extended sources, we place upper limits on the strain angular power spectrum $C_\ell^{1/2} < (0.63 - 17) \times 10^{-10} \,\mathrm{sr}^{-1}$.

gr-qc↗