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Marcus Brüggen

Publications and source records attributed to Marcus Brüggen.

At least 37 records · Page 2Linked to original sources

Classification of Radio Sources Through Self-Supervised Learning

The morphology of radio galaxies is indicative of their interaction with their surroundings, among other effects. Since modern radio surveys contain a large number of radio sources that would be impossible to analyse and classify manually, it is important to develop automatic schemes. Unlike other fields, which benefit from established theoretical frameworks and simulations, there are no such comprehensive models built for radio galaxies. This stands as a challenge to data analysis in this field and novel approaches are required. In this study, we investigate the classification of radio galaxies from the LOFAR Two-meter Sky Survey Data Release 2 (LoTSS-DR2) using self-supervised learning. Our deep clustering classification strategy involves three main steps: (i) self-supervised pre-training; (ii) fine-tuning using a labelled subsample created from the learned representations; and (iii) performing a final classification of the selected unlabelled sample. To enhance morphological information in the representations, we developed an additional random augmentation, called a random structural view (RSV). Our results demonstrate that the learned representations contain rich morphological information, enabling the creation of a labelled subsample that effectively captures the morphological diversity within the unlabelled sample. Additionally, the classification of the unlabelled sample into 12 morphological classes yields robust class probabilities. We successfully demonstrated that a subset of radio galaxies from LoTSS-DR2, encompassing diverse morphologies, can be classified using deep clustering based on self-supervised learning. The methodology developed here bridges the gap left by the absence of simulations and theoretical models, offering a framework that can readily be applied to astronomical image analyses in other bands.

astro-ph.IM↗

Simulating realistic radio continuum survey maps with diffusion models

The next generation of radio surveys is going to be transformative for cosmology and other aspects of our understanding of astrophysics. Realistic simulations of radio observations are essential for the design and planning of radio surveys. They are employed in the development of methods for tasks, such as data calibration and reduction, automated analysis and statistical studies in cosmology. We implemented a software for machine learning-assisted simulations of realistic surveys with the LOFAR telescope, resulting in a synthetic radio sky model and a corresponding artificial telescope observation. We employed a diffusion model trained on LoTSS observations to generate individual radio galaxy images with control over the angular size. Single sources are assembled into a radio sky model, using an input catalog from cosmological simulations. We then transformed this sky model into visibilities corresponding to a typical LoTSS pointing. We added realistic noise to this synthetic measurement and obtained our final simulated sky maps through deconvolution. We explored different ways to evaluate our resulting sky model. We were able to simulate realistic LOFAR observations, covering a sky patch of 5x5 degrees at an effective resolution of 8.5 arcseconds. The simulated sources have flux and size distributions that match real observations, and the resulting maps have sensitivities compatible with LoTSS observations. Our diffusion model is able to synthesize high-quality realistic radio galaxy images with precise control over the source sizes. This software can readily be applied to other instruments.

astro-ph.IM↗

The Density Distribution of Compressively-Forced Supersonic Turbulence Depends on the Driving Correlation Time

Supersonic turbulence plays a critical role in shaping astrophysical systems, from molecular clouds to the circumgalactic medium. Key properties of this turbulence include the Mach number, driving scale, and nature of the driving mechanism, which can be solenoidal (divergence-free), compressive (curl-free), or a mix of the two. A less studied property is the correlation time of the driving accelerations, $τ_{\rm a}.$ While this timescale has a minimal impact on solenoidally-driven turbulence, we show that it has a strong impact on compressively-driven turbulence. Using high-resolution simulations with tracer particles, we analyze the evolution of density fluctuations, focusing on the PDF of the logarithmic density, $s$, and its rate of change, $\frac{ds}{dt},$ and the conditional statistics of $\frac{ds}{dt}$ and $\frac{d^2s}{dt^2}$. When the driving correlation time is comparable to the eddy turnover time, $τ_{\rm a} \approx τ_{\rm e},$ compressive driving leads to the formation of large, low-density voids in which the variance of $\frac{ds}{dt}$ is large. These are directly linked to sustained accelerated expansions, which results in a strong correlation between density and the divergence of the driving acceleration field. In contrast, when $τ_{\rm a} \approx 0.1 \, τ_{\rm e}$, compressive driving does not produce such voids, resulting in a narrower, less skewed distribution. We show using analytical estimates that $τ_{\rm a}$ is may be significantly less than $τ_{\rm e}$ in supernova-driven turbulence, highlighting the need to better understand the role of the driving correlation time in shaping the density structure of turbulent astrophysical systems.

astro-ph.GA↗

Ion densities of cold clouds driven by galactic outflows

Observations of the circumgalactic medium (CGM) often display coincident absorption from species with widely varying ionization states, providing direct evidence for complex, multiphase interactions. Motivated by these measurements, we perform a series of cloud-crushing simulations that model cold clouds traveling through the hot CGM. We analyze the ion distributions of these clouds, generate mock absorption spectra, and study their implications on quasar (QSO) absorption observations. Our results show interesting multiphase features, in which ions with significantly different ionization potentials exist in the same absorber and share similar spectral features. However, our simulations are unable to explain high ions like O \textsc{vi} and their coexistence with lower ions that appear in many observed QSO absorption systems.

astro-ph.GA↗

Accretion of self-interacting dark matter onto supermassive black holes

Dark matter (DM) spikes around supermassive black holes (SMBHs) may lead to interesting physical effects such as enhanced DM annihilation signals or dynamical friction within binary systems, shortening the merger time and possibly addressing the `final parsec problem'. They can also be promising places to study the collisionality of DM because their velocity dispersion is higher than in DM halos allowing us to probe a different velocity regime. We aim to understand the evolution of isolated DM spikes for self-interacting dark matter (SIDM) and compute the BH accretion rate as a function of the self-interaction cross-section per unit DM mass ($σ/m_χ$). We have performed the first $N$-body simulations of SIDM spikes around supermassive black holes (SMBH) and studied the evolution of the spike with an isolated BH starting from profiles similar to the ones that have been shown to be stable in analytical calculations. We find that the analytical profiles for SIDM spikes remain stable over the time-scales of hundreds of years that we have covered with our simulations. In the long-mean-free-path (LMFP) regime, the accretion rate onto the BHs grows linearly with the cross-section and flattens when we move towards the short-mean-free-path (SMFP) regime. In both regimes, our simulations match analytic expectations, which are based on the heat conduction description of SIDM. A simple model for the accretion rate allows us to calibrate the heat conduction in the gravothermal fluid prescription of SIDM. Using this prescription, we determine the maximum allowed accretion rate which occurs when $r_{\rm isco} ρ(r_{\rm isco}) σ/m_χ\sim 1$, where $r_{\rm isco}$ the radius of the innermost stable orbit. Our calibrated DM accretion rates could be used for statistical analysis of SMBH growth and incorporated into subgrid models to study BH growth in cosmological simulations.

astro-ph.CO↗

The Polarisation Sky Survey of the Universe's Magnetism (POSSUM): Science Goals and Survey Description

The Australian SKA Pathfinder (ASKAP) offers powerful new capabilities for studying the polarised and magnetised Universe at radio wavelengths. In this paper, we introduce the Polarisation Sky Survey of the Universe's Magnetism (POSSUM), a groundbreaking survey with three primary objectives: (1) to create a comprehensive Faraday rotation measure (RM) grid of up to one million compact extragalactic sources across the southern ~50 per cent of the sky (20,630 deg$^2$); (2) to map the intrinsic polarisation and RM properties of a wide range of discrete extragalactic and Galactic objects over the same area; and (3) to contribute interferometric data with excellent surface brightness sensitivity, which can be combined with single-dish data to study the diffuse Galactic interstellar medium. Observations for the full POSSUM survey commenced in May 2023 and are expected to conclude by mid-2028. POSSUM will achieve an RM grid density of around 30-50 RMs per square degree with a median measurement uncertainty of ~1 rad m$^{-2}$. The survey operates primarily over a frequency range of 800-1088 MHz, with an angular resolution of 20'' and a typical RMS sensitivity in Stokes $Q$ or $U$ of 18 $μ$Jy beam$^{-1}$. Additionally, the survey will be supplemented by similar observations covering 1296-1440 MHz over 38 per cent of the sky. POSSUM will enable the discovery and detailed investigation of magnetised phenomena in a wide range of cosmic environments, as well as the interplay between these components. This paper reviews the current science case developed by the POSSUM Collaboration and provides an overview of POSSUM's observations, data processing, outputs, and its complementarity with other radio and multi-wavelength surveys, including future work with the SKA. [Abstract abridged]

astro-ph.GA↗

Direction-Dependent Faraday Synthesis

Modern radio interferometers enable high-resolution polarization imaging, offering insights into cosmic magnetism through Rotation Measure (RM) synthesis. Traditional 2+1D RM synthesis treats the 2D spatial and 1D spectral transforms separately. A fully 3D approach transforms data directly from visibility-frequency space to sky-Faraday depth space using a 3D Fourier transform. Faraday synthesis uses the full dataset for improved reconstruction but requires a 3D deconvolution algorithm to subtract artifacts from the residual image. Applying this method to modern interferometers also requires corrections for direction-dependent effects (DDEs). We extend Faraday synthesis by incorporating DDE corrections, enabling accurate polarized imaging in the presence of instrumental and ionospheric effects. We implement this method within DDFACET, introducing a direction-dependent deconvolution algorithm (DDFSCLEAN) that applies DDE corrections in a faceted framework. Additionally, we parameterize the CLEAN components and evaluate the model over a larger set of frequency channels, naturally correcting for bandwidth depolarization. The method is tested on both synthetic and real data. Our results show that Faraday synthesis enables deeper deconvolution, reduces artifacts, and increases dynamic range. The depolarization correction improves recovery of polarized flux, allowing coarser frequency resolution without loss of sensitivity at high Faraday depths. From the 3D reconstruction, we identify a polarized source in a LOFAR Surveys pointing not detected by earlier RM surveys. Faraday synthesis is memory-intensive due to the large transforms between the visibility domain and the Faraday cube, and is only now becoming practical. Nevertheless, our implementation achieves comparable or faster runtimes than the 2+1D approach, making it a competitive alternative for polarization imaging.

astro-ph.IM↗

The properties of magnetised cold filaments in a cool-core galaxy cluster

Filaments of cold gas ($T\leq 10^{4}$ K) are found in the inner regions of many cool-core clusters. These structures are thought to play a major role in the regulation of feedback from active galactic nuclei (AGN). We study the morphology of the filaments, their formation, and their impact on the propagation of the outflowing AGN jets. We present a set of GPU-accelerated 3D (magneto)hydrodynamical simulations of an idealized Perseus-like cluster using the performance portable code AthenaPK. We include radiative cooling, and a self-regulated AGN feedback model that redistributes accreted material through kinetic, thermal and magnetic feedback. We confirm that magnetic fields play an important role in both the formation and evolution of the cold material. These suppress the formation of massive cold discs and favour magnetically supported filaments over clumpy structures. Achieving resolutions of $25-50$ pc, we find that filaments are not monolithic as they contain numerous and complex magnetically supported sub-structures. We find that the mass distribution of these clumps follows a $\mathrm{d}N/\mathrm{d}M \propto M^{-1.6}$ power-law for all investigated filaments. Studying the evolution of individual filaments, we find that their formation pathways can be diverse. We find examples of filaments forming through a combination of gas uplifting and condensation, as well as systems of purely infalling clumps condensing out of the intracluster medium. The density contrast between the cold gas and the outflowing hot material leads to recurring deflections of the jets, favouring inflation of bubbles.

astro-ph.GA↗

Understanding Density Fluctuations in Supersonic, Isothermal Turbulence

Supersonic turbulence occurs in many environments, particularly in astrophysics. In the crucial case of isothermal turbulence, the probability density function (PDF) of the logarithmic density, $s$, is well measured, but a theoretical understanding of the processes leading to this distribution remains elusive. We investigate these processes using Lagrangian tracer particles to track $s$ and $\frac{ds}{dt}$ in direct numerical simulations, and we show that their evolution can be modeled as a stochastic differential process with time-correlated noise. The temporal correlation functions of $s$ and $\frac{ds}{dt}$ decay exponentially, as predicted by the model, and the decay timescale is $\approx$ 1/6 the eddy turnover time. The behavior of the conditional averages of $\frac{ds}{dt}$ and $\frac{d^2s}{dt^2}$ is also well explained by the model, which shows that the density PDF arises from a balance between stochastic compressions/expansions, which tend to broaden the PDF, and the acceleration/deceleration of shocks by density gradients, which tends to narrow it.

astro-ph.GA↗

Simulating images of radio galaxies with diffusion models

With increasing amounts of data in astronomy, automated analysis methods have become crucial. Synthetic data are required for developing and testing such methods. Current simulations often suffer from insufficient detail or inaccurate representation of source type occurrences. To overcome those deficiencies, we implemented a deep generative model trained on observations to generate realistic radio galaxy images with full control over the flux and source morphology. We used a diffusion model, trained with continuous time steps to reduce sampling time without quality impairments. Two models were trained on two different datasets, respectively. One set was a selection of images from the second data release of the LOFAR Two-Metre Sky Survey (LoTSS). The model is conditioned on peak flux values to preserve signal intensity information after re-scaling image pixel values. The other, smaller set was obtained from the VLA survey of Faint Images of the Radio Sky at Twenty-Centimeters (FIRST). In that set, every image was provided with a morphological class label the corresponding model was conditioned on. Conditioned sampling is realized with classifier-free diffusion guidance. We evaluated the quality of generated images by comparing distributions of different quantities over the real and generated data, including results from the standard source-finding algorithms. The class conditioning was evaluated by training a classifier and comparing its performance on both real and generated data. We were able to generate realistic images of high quality using 25 sampling steps, which is unprecedented in the field of radio astronomy. The generated images are visually indistinguishable from the training data and the distributions of different image metrics were replicated. The classifier performs equally well for real and generated images, indicating strong sampling control over morphological properties.

astro-ph.IM↗

The SRG/eROSITA All-Sky Survey: View of the Virgo Cluster

As the closest galaxy cluster, the Virgo Cluster is an exemplary environment for the study of the large-scale filamentary structure and physical effects that are present in cluster outskirts but absent from the more easily studied inner regions. Here, we present an analysis of the SRG/eROSITA data from five all-sky surveys. eROSITA allows us to resolve the entire Virgo cluster and its outskirts on scales between 1 kpc and 3 Mpc, covering a total area on the sky of about 25$^\circ$ by 25$^\circ$. We utilized image manipulation techniques and surface brightness profiles to search for extended emission, surface brightness edges, and features in the outskirts. We employed a method of comparing mean and median profiles to measure gas clumping out to and beyond the virial radius. Surface brightness analysis of the cluster and individual sectors of the cluster reveal the full extent of previously identified cold fronts to the north and south. The emissivity bias due to gas clumping, which we quantify over three orders of magnitude in the radial range, is found to be mild, consistent with previous findings. We find uniform clumping measurements in all directions, with no enhancements along candidate filaments. We find an estimated virial gas mass of $M_{\mathrm{gas},r<r_{200}} = (1.98 \pm 0.70) \times 10^{13}$ M$_\odot$. Through imaging analysis we detect the presence of extended emission spanning 320\,kpc to the southwest of M49. The extension has a significance of 3.15$σ$ and is coincident with radio emission detected with LOFAR, which could be evidence of an accretion shock or turbulent reacceleration as the M49 group or background W' cloud falls into the cluster and interacts with the intracluster medium.

astro-ph.CO↗

1-arcsecond imaging of ELAIS-N1 field at 144MHz using the LoTSS survey with international LOFAR telescope

We present the first wide area (2.5 x 2.5 deg^2) LOFAR High Band Antenna image at a resolution of 1.2'' x 2'' with a median noise of approximately 80 microJy per beam. It was made from an 8-hour International LOFAR Telescope (ILT) observation of the ELAIS-N1 field at frequencies ranging from 120 to 168 MHz with the most up-to-date ILT imaging methods. This intermediate resolution falls between the highest possible resolution (0.3'') achievable by using all International LOFAR Telescope (ILT) baselines and the standard 6-arcsecond resolution in the LoTSS (LOFAR Two-meter Sky Survey) image products utilising the LOFAR Dutch baselines only. This is the first demonstration of the feasibility of imaging using the ILT at a resolution of around 1'', which provides unique information on source morphology at scales that fall below the surface brightness limits at higher resolutions. The total calibration and imaging computational time is approximately 52,000 core hours, nearly 5 times more than required to produce a 6'' resolution image. We also present a radio source catalogue containing 2263 sources detected over the 2.5 x 2.5 deg^2 image of the ELAIS-N1 field, with a peak intensity threshold of 5.5 sigma. The catalogue has been cross-matched with the LoTSS deep ELAIS-N1 field radio catalogue, and its flux density and positional accuracy have been investigated and corrected accordingly. We find that approximately 80% of sources which we expect to be detectable based on their peak brightness in the LoTSS 6'' resolution image are detected in this image, which is approximately a factor of two higher than for 0.3'' resolution imaging in the Lockman Hole, implying there is a wealth of information on these intermediate scales.

astro-ph.IM↗

Concept Study of a Storage Ring-based Gravitational Wave Observatory: Gravitational Wave Strain and Synchrotron Radiation Noise

This work for the first time addresses the feasibility of measuring millihertz gravitational waves (mHz GWs) with a storage ring-based detector. While this overall challenge consists of several partial problems, here we focus solely on quantifying design limitations imposed by the kinetic energy and radiated power of circulating ions at relativistic velocities. We propose an experiment based on the measurement of the time-of-flight signal of an ion chain. One of the dominant noise sources inherent to the measurement principle for such a GW detector is the shot noise of the emitted synchrotron radiation. We compute the noise amplitude of arrival time signals obtained by analytical estimates and simulations of ions with different masses and velocities circulating in a storage ring with the circumference of the Large Hadron Collider (LHC). Thereby, we show that our experiment design could reduce the noise amplitude due to the synchrotron radiation in the frequency range $10^{-4} - 10^{-2}$ Hz to one or two orders of magnitude below the expected GW signals from of astrophysical sources, such as super-massive binary black holes or extreme mass-ratio inspirals. Other key requirements for building a working storage ring-based GW detector include the generation and acceleration of heavy ion chains with the required energy resolution, their injection and continued storage, as well as the detection method to be used for the determination of the particle arrival time. However, these are not the focus of the work presented here, in which we instead concentrate on the definition of a working principle in terms of ion type, kinetic energy, and ring design, which will later serve as a starting point when addressing a more complete experimental setup.

gr-qc↗

Cosmological simulations of the generation of cluster-scale radio emission from turbulent re-acceleration

Context. The recent discovery of so-called mega radio halos as a new class of diffuse, steep-spectrum radio sources in clusters of galaxies has raised questions about the origin and the evolution of cluster-wide radio emission. Aims. We investigate whether the formation mechanisms of radio halos and mega radio halos differ, or whether they can be produced by different modalities of the same (re)acceleration mechanism. Here we present results of a cosmological simulation of a disturbed galaxy cluster, with the aim to study the origin of mega radio halos. Methods. We analysed the evolution of cosmic-ray electrons, subject to gains and losses using a Fokker-Planck solver. In particular, we included the effects of Adiabatic Stochastic Acceleration (ASA) which is caused by the stochastic interaction of cosmic rays with diffusing magnetic field lines in super-Alfvenic turbulence. Moreover, we included shock acceleration and the seeding of cosmic-ray electrons by galaxies. Results. Our simulations generate cluster-scale radio sources during mergers, with properties that are in agreement with those observed for real radio halos. Furthermore, we find evidence of additional emission on larger scales. This emission resembles the radial distribution and the spectrum of a mega radio halo, but only when viewed close to the merger axis. Conclusions. In our simulation, the mechanism responsible for the formation of diffuse radio emission, both in the form of classical and mega radio halos, is cosmic-ray re-acceleration by turbulence. This turbulence is more solenoidal and more subsonic in the classical radio halo region, than in the mega radio halo region.

astro-ph.HE↗

Semi-Supervised Rotation Measure Deconvolution and its application to MeerKAT observations of galaxy clusters

Faraday rotation contains information about the magnetic field structure along the line of sight and is an important instrument in the study of cosmic magnetism. Traditional Faraday spectrum deconvolution methods such as RMCLEAN face challenges in resolving complex Faraday dispersion functions and handling large datasets. We develop a deep learning deconvolution model to enhance the accuracy and efficiency of extracting Faraday rotation measures from radio astronomical data, specifically targeting data from the MeerKAT Galaxy Cluster Legacy Survey (MGCLS). We use semi-supervised learning, where the model simultaneously recreates the data and minimizes the difference between the output and the true signal of synthetic data. Performance comparisons with RMCLEAN were conducted on simulated as well as real data for the galaxy cluster Abell 3376. Our semi-supervised model is able to recover the Faraday dispersion with great accuracy, particularly for complex or high-RM signals, maintaining sensitivity across a broad RM range. The computational efficiency of this method is significantly improved over traditional methods. Applied to observations of Abell 3376, we find detailed magnetic field structures in the radio relics, and several AGN. We also apply our model to MeerKAT data of Abell 85, Abell 168, Abell 194, Abell 3186 and Abell 3667.

astro-ph.CO↗

Simulations of galaxy cluster mergers with velocity-dependent, rare and frequent self-interactions

Self-interacting dark matter (SIDM) has been proposed to solve small-scale problems in $Λ$CDM cosmology. In previous work, constraints on the self-interaction cross-section of dark matter have been derived assuming that the self-interaction cross-section is independent of velocity. However, a velocity-dependent cross-section is more natural in most theories of SIDM. Using idealized $N$-body simulations without baryons, we study merging clusters with velocity-dependent SIDM. In addition to the usual rare scattering in the isotropic limit, we also simulate these systems with anisotropic, small-angle (frequent) scatterings. We find that the collision-less brightest cluster galaxy (BCG) has an offset from the DM peak that grows at later stages. Finally, we also extend the existing upper bounds on the velocity-independent, isotropic self-interaction cross-section to the parameter space of rare and frequent velocity-dependent self-interactions by studying the central densities of dark matter-only isolated haloes. For these upper-bound parameters, the DM-BCG offsets just after the first pericentre in the dark matter-only simulations are found to be $\leq$ 10 kpc. On the other hand, because of BCG oscillations, we speculate that the distribution of BCG offsets in a relaxed cluster is a statistically viable probe. Therefore, this motivates further studies of BCG off-centring in hydrodynamic cosmological simulations.

astro-ph.CO↗

Zooming in on the Circumgalactic Medium with GIBLE: Tracing the Origin and Evolution of Cold Clouds

We use the GIBLE suite of cosmological zoom-in simulations of Milky Way-like galaxies with additional super-Lagrangian refinement in the circumgalactic medium (CGM) to quantify the origin and evolution of CGM cold gas clouds. The origin of $z$\,$=$\,$0$ clouds can be traced back to recent ($\lesssim$\,$2$\,Gyr) outflows from the central galaxy ($\sim$\,45\,$\%$), condensation out of the hot phase of the CGM in the same time frame ($\sim$\,45\,$\%$), and to a lesser degree to satellite galaxies ($\lesssim$\,5\,$\%$). We find that in-situ condensation results from rapid cooling around local over-densities primarily seeded by the dissolution of the previous generation of clouds into the hot halo. About $\lesssim$\,10\,$\%$ of the cloud population is long lived, with their progenitors having already assembled $\sim$\,$2$\,Gyr ago. Collective cloud-cloud dynamics are crucial to their evolution, with coalescence and fragmentation events occurring frequently ($\gtrsim$\,20\,Gyr$^{-1}$). These interactions are modulated by non-vanishing pressure imbalances between clouds and their interface layers. The gas content of clouds is in a constant state of flux, with clouds and their surroundings exchanging mass at a rate of \mbox{$\gtrsim$\,$10^3$\,M$_\odot$\,Myr$^{-1}$}, depending on cloud relative velocity and interface vorticity. Furthermore, we find that a net magnetic tension force acting against the density gradient is capable of inhibiting cloud-background mixing. Our results show that capturing the distinct origins of cool CGM clouds, together with their physical evolution, requires high-resolution, cosmological galaxy formation simulations with both stellar and supermassive black hole feedback-driven outflows.

astro-ph.GA↗

Detection of gravitational waves in circular particle accelerators II. Response analysis and parameter estimation using synthetic data

We simulate the response of a Storage Ring Gravitational-Wave Observatory (SRGO) to astrophysical millihertz (mHz) gravitational waves (GWs), numerically obtaining its sensitivity curve and optimal choices for some controllable experiment parameters. We also generate synthetic noisy GW data and use Markov Chain Monte Carlo (MCMC) methods to perform parameter estimation of the source properties and their degeneracies. We show that a single SRGO could potentially localize the GW source in the sky using Earth's rotation. We also study the source sky localization area, mass and distance estimation errors as functions of noise, data sampling rate, and observing time. Finally, we discuss, along with its implications, the capacity of an SRGO to detect and constrain the parameters of millihertz GW events.

gr-qc↗