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At least 127 records · Page 7

Neutrino Emissivities as a Probe of the Internal Magnetic Fields of White Dwarfs

Abstract The evolution of white dwarfs (WDs) depends crucially on thermal processes. The plasma in their core can produce neutrinos that escape from the star, thus contributing to the energy loss. While in the absence of a magnetic field the main cooling mechanism is plasmon decay at high temperature and photon surface emission at low temperature, a large magnetic field in the core hiding beneath the surface even of ordinary WDs, and undetectable to spectropolarimetric measurements, could potentially leave an imprint in the cooling. In this paper, we revisit the contribution to WD cooling stemming from neutrino pair synchrotron radiation and the effects of the magnetic field on plasmon decay. Our key finding is that even if observations limit the magnetic field strength at the stellar surface, magnetic fields in the interior of WDs—with or without a surface magnetic field—can be strong enough to modify the cooling rate, with neutrino pair synchrotron emission being the most important contribution. This effect may not only be relevant for the quantification and interpretation of cooling anomalies, but suggests that the internal magnetic fields of WDs should be smaller than ∼ 6 × 10 11 G, slightly improving bounds coming from a stability requirement. While our simplified treatment of the WD structure implies that further studies are needed to reduce the systematic uncertainties, the estimates based on comparing the emissivities illustrate the potential of neutrino emission as a diagnostic tool to study the interior of WDs.

79 ASTRONOMY AND ASTROPHYSICS↗

Spectroscopic Orbits of 11 Nearby, Mid-to-late M-dwarf Binaries

We present the spectroscopic orbits of 11 nearby, mid-to-late M dwarf binary systems in a variety of configurations: 2 single-lined binaries (SB1s), 7 double-lined binaries (SB2s), 1 double-lined triple (ST2), and 1 triple-lined triple (ST3). Eight of these orbits are the first published for these systems, while five are newly identified multiples. We obtained multi-epoch, high-resolution spectra with the TRES instrument on the 1.5 m Tillinghast Reflector at the Fred Lawrence Whipple Observatory located on Mt. Hopkins in AZ. Using the TiO molecular bands at 7065–7165 Å, we calculated radial velocities for these systems, from which we derived their orbits. We find LHS 1817 to have in a 7 hr period a companion that is likely a white dwarf, due to the ellipsoidal modulation we see in our MEarth-North light-curve data. We find G 123-45 and LTT 11586 to host companions with minimum masses of 41 M {sub Jup} and 44 M {sub Jup} with orbital periods of 35 and 15 days, respectively. We find 2MA 0930+0227 to have a rapidly rotating stellar companion in a 917 day orbital period. GJ 268, GJ 1029, LP 734-34, GJ 1182, G 258-17, and LTT 7077are SB2s with stellar companions with orbital periods of 10, 96, 34, 154, 5, and 84 days; LP 655-43 is an ST3 with one companion in an 18 day orbital period and an outer component in a longer undetermined period. In addition, we present radial velocities for both components of L 870-44AB and for the outer components of LTT 11586 and LP 655-43.

79 ASTRONOMY AND ASTROPHYSICS↗

Violent mergers revisited: The origin of the fastest stars in the Galaxy

Binary systems of two carbon-oxygen white dwarfs are one of the most promising candidates for the progenitor systems of Type Ia supernovae. Violent mergers, where the primary white dwarf ignites when the secondary white dwarf smashes into it while being disrupted on its last orbit, were the first double degenerate merger scenario proposed that ignites dynamically. However, violent mergers likely contribute only a few percent to the total Type Ia supernova rate and do not yield normal Type Ia supernova light curves. Here we revisit the scenario, simulating a violent merger with better methods and, in particular, a more accurate treatment of the detonation. We find good agreement with previous simulations but with one critical difference: The secondary white dwarf being disrupted and accelerated towards the primary white dwarf and impacted by its explosion does not fully burn, and its core survives as a bound object. The explosion leaves behind a 0.16 M ⊙ star travelling 2800 km/s, making it an excellent (and so far the only) candidate to explain the origin of the fastest observed hypervelocity stars. We also show that before the explosion, 5 × 10 −3 M ⊙ of material predominantly consisting of helium, carbon, and oxygen had already been ejected at velocities above 1000 km/s. Finally, we argue that if a violent merger made the hypervelocity stars D6-1 and D6-3 and violent mergers require the most massive primary white dwarfs in binaries of two carbon-oxygen white dwarfs, there has to be a much larger population of white dwarf mergers with slightly lower mass primary white dwarfs. Because this population likely represents ≫10% of the Type Ia supernovae rate, it can essentially only give rise to normal Type Ia supernovae.

Astronomy and AstroPhysics↗

Search for Magnetic Accretion in SW Sextantis Systems

SW Sextantis systems are nova-like cataclysmic variables that have unusual spectroscopic properties, which are thought to be caused by an accretion geometry having part of the mass flux trajectory out of the orbital plane. Accretion onto a magnetic white dwarf is one of the proposed scenarios for these systems. To verify this possibility, we analyzed photometric and polarimetric time-series data for a sample of six SW Sex stars. We report possible modulated circular polarization in BO Cet, SW Sex, and UU Aqr with periods of 11.1, 41.2, and 25.7 minutes, respectively, and less significant periodicities for V380 Oph at 22 minutes and V442 Oph at 19.4 minutes. We confirm previous results that LS Peg shows variable circular polarization. However, we determine a period of 18.8 minutes, which is different from the earlier reported value. We interpret these periods as the spin periods of the white dwarfs. Our polarimetric results indicate that 15% of the SW Sex systems have direct evidence of magnetic accretion. We also discuss SW Sex objects within the perspective of being magnetic systems, considering the latest findings about the demography, formation, and evolution of cataclysmic variables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Origin and Evolution of the Normal Type Ia SN 2018aoz with Infant-phase Reddening and Excess Emission

SN 2018aoz is a Type Ia SN with a B-band plateau and excess emission in infant-phase light curves ≲1 day after the first light, evidencing an over-density of surface iron-peak elements as shown in our previous study. Here, we advance the constraints on the nature and origin of SN 2018aoz based on its evolution until the nebular phase. Near-peak spectroscopic features show that the SN is intermediate between two subtypes of normal Type Ia: core normal and broad line. The excess emission may be attributable to the radioactive decay of surface iron-peak elements as well as the interaction of ejecta with either the binary companion or a small torus of circumstellar material. Nebular-phase limits on Hα and He ι favor a white dwarf companion, consistent with the small companion size constrained by the low early SN luminosity, while the absence of [O ι] and He ι disfavors a violent merger of the progenitor. Of the two main explosion mechanisms proposed to explain the distribution of surface iron-peak elements in SN 2018aoz, the asymmetric Chandrasekhar-mass explosion is less consistent with the progenitor constraints and the observed blueshifts of nebular-phase [Fe ιι] and [Ni ιι]. The helium-shell double-detonation explosion is compatible with the observed lack of C spectral features, but current 1D models are incompatible with the infant-phase excess emission, $B_{max}$--$V_{max}$ color, and weak strength of nebular-phase [Ca ιι]. Although the explosion processes of SN 2018aoz still need to be more precisely understood, the same processes could produce a significant fraction of Type Ia SNe that appear to be normal after ~1 day.

79 ASTRONOMY AND ASTROPHYSICS↗

Gemini/GMOS Transmission Spectroscopy of the Grazing Planet Candidate WD 1856+534 b

WD 1856+534 b is a Jupiter-sized, cool giant planet candidate transiting the white dwarf WD 1856+534. Here, we report an optical transmission spectrum of WD 1856+534 b obtained from ten transits using the Gemini Multi Object Spectrograph. This system is challenging to observe due to the faintness of the host star and the short transit duration. Nevertheless, our phase-folded white light curve reached a precision of 0.12%. WD 1856+534 b provides a unique transit configuration compared to other known exoplanets: the planet is 8x larger than its star and occults over half of the stellar disk during mid-transit. Consequently, many standard modeling assumptions do not hold. We introduce the concept of a “limb darkening corrected, time-averaged transmission spectrum” and propose that this is more suitable than (R pλ /R s ) 2 for comparisons to atmospheric models for planets with grazing transits. We also present a modified radiative transfer prescription. Though the transmission spectrum shows no prominent absorption features, it is sufficiently precise to constrain the mass of WD 1856+534 b to be >0.84 M J (to 2σ confidence), assuming a clear atmosphere and a Jovian composition. High-altitude cloud decks can allow lower masses. WD 1856+534 b could have formed either as a result of common envelope evolution or migration under the Kozai–Lidov mechanism. Further studies of WD 1856+534 b, alongside new dedicated searches for substellar objects around white dwarfs, will shed further light on the mysteries of post-main-sequence planetary systems.

79 ASTRONOMY AND ASTROPHYSICS↗

Exogeological inferences from white dwarf pollutants: the impact of stellar physics

Many white dwarfs have accreted material from their own planetary systems. These objects can be used to infer the composition of exoplanetary material and identify evidence for key geological processes. However, the white dwarf atmospheric physics distorts the inferred material composition away from the true composition, mainly through differential atomic diffusion of the accreted metals. Correcting for this effect is essential, but is dependent on various physical assumptions associated with the white dwarf itself. We first focus on the effect of assumptions related to convective overshoot and thermohaline mixing on the atomic diffusion time-scales. For white dwarfs with H-dominated atmospheres between 12000 K and 18000 K⁠, we find that including a complete treatment of convective overshoot decreases the inferred Fe and O abundances in accreted material. For these white dwarfs, we also find that including thermohaline mixing decreases Fe and O abundances. For He-dominated systems, the effect of convective overshoot is comparatively minor. We then explore the overall effect of other physical assumptions by comparing publicly available grids of diffusion time-scales. We find that the choice of model grid can have a large impact for white dwarfs with He-dominated atmospheres, notably on the inferred core to mantle ratio of accreted material. We identify several systems for which the geological interpretation is robust against these systematics. We also present a ‘discrepancy metric’ which can be used to estimate the potential impact of changing the stellar physics without requiring detailed modelling.

Astronomy and AstroPhysics↗

DAmodel: hierarchical Bayesian modelling of DA white dwarfs for spectrophotometric calibration

We use hierarchical Bayesian modelling to calibrate a network of 32 all-sky faint DA white dwarf (DA WD) spectrophotometric standards (⁠16.5 < V , 19.5⁠) alongside three CALSPEC standards, from 912 Å to 32 μm. The framework is the first of its kind to jointly infer photometric zero points and WD parameters (surface gravity log g⁠, effective temperature T eff ⁠, extinction A V ⁠, dust relation parameter R V ) by simultaneously modelling both photometric and spectroscopic data. We model panchromatic Hubble Space Telescope Wide Field Camera 3 (HST/WFC3) UVIS and IR photometry, HST/STIS UV spectroscopy, and ground-based optical spectroscopy to sub-per cent precision. Photometric residuals for the sample are the lowest yet yielding < 0.004 mag RMS on average from the UV to the NIR, achieved by jointly inferring time-dependent changes in system sensitivity and WFC3/IR count-rate nonlinearity. Our GPU-accelerated implementation enables efficient sampling via Hamiltonian Monte Carlo, critical for exploring the high-dimensional posterior space. The hierarchical nature of the model enables population analysis of intrinsic WD and dust parameters. Inferred spectral energy distributions from this model will be essential for calibrating the James Webb Space Telescope as well as next-generation surveys, including Vera Rubin Observatory’s Legacy Survey of Space and Time and the Nancy Grace Roman Space Telescope.

methods: statistical↗

Perfecting Our Set of Spectrophotometric Standard DA White Dwarfs

We verified for photometric stability a set of DA white dwarfs with Hubble Space Telescope magnitudes from the near-ultraviolet to the near-infrared and ground-based spectroscopy by using time-spaced observations from the Las Cumbres Observatory network of telescopes. The initial list of 38 stars was whittled to 32 final ones, which comprise a high-quality set of spectrophotometric standards. These stars are homogeneously distributed around the sky and are all fainter than r ~ 16.5 mag. Their distribution is such that at least two of them would be available to be observed from any observatory on the ground at any time at airmass less than 2. Light curves and different variability indices from the Las Cumbres Observatory data were used to determine the stability of the candidate standards. When available, Pan-STARRS1, Zwicky Transient Facility, and TESS data were also used to confirm the star classification. Our analysis showed that four DA white dwarfs may exhibit evidence of photometric variability, while a fifth is cooler than our established lower temperature limit, and a sixth star might be a binary. In some instances, due to the presence of faint nearby red sources, care should be used when observing a few of the spectrophotometric standards with ground-based telescopes. Light curves and finding charts for all the stars are provided.

79 ASTRONOMY AND ASTROPHYSICS↗

Low-metallicity Nova Explosions: A Site for Weak rp -process Nucleosynthesis

Classical novae are common cataclysmic events involving a binary system of a white dwarf and a main-sequence or red giant companion star. In metal-poor environments, these explosions produce ejecta differently from their solar counterparts due to the accretion of subsolar-metallicity material onto the white dwarf. In particular, it has been suggested that the nucleosynthesis flow in such low-metallicity nova explosions extends up to the Cu–Zn region, much beyond the expected endpoint, around Ca, predicted for solar-metallicity classical novae. This behavior resembles a weak rp-process, and such nuclear activity has never been observed in accreting white dwarf binaries with typical accretion flows. In this work, we study the characteristics of the weak rp-process for four nova models with metallicities Z = 2 × 10 −9 , 10 −7 , 2 × 10 −6 , and 2 × 10 −5 , and explore the impact of the nuclear physics uncertainties via a Monte Carlo sensitivity study. We identify nuclear reactions whose uncertainties affect the production of intermediate-mass nuclei under these conditions. These reactions and relevant nuclear quantities are targets for measurements at stable or radioactive beam facilities to reduce their rate uncertainties.

Classical novae↗

Evaporation barrier for dark matter in celestial bodies

The minimum testable dark matter (DM) mass for almost all DM signatures in celestial bodies is determined by the rate at which DM evaporates. DM evaporation has previously been calculated assuming a competition between the gravitational potential of the object, and thermal kicks from the celestial-body matter. We point out a new effect, where mediators with a range larger than the interparticle spacing induce a force proportional to the density gradient of celestial objects, forming an evaporation barrier for the DM. This effect can be so significant that evaporation does not occur even for sub-MeV DM, in stark contrast to previous calculations. This opens up a wide range of new light DM searches, many orders of magnitude in DM mass below the sensitivity of direct detection.

79 ASTRONOMY AND ASTROPHYSICS↗

Quasi-periodic Oscillations in the TESS Light Curve of TX Col, a Diskless Intermediate Polar on the Precipice of Forming an Accretion Disk

One of the fundamental properties of an intermediate polar is the dynamical nature of the accretion flow as it encounters the white dwarf’s (WD’s) magnetosphere. Many works have presumed a dichotomy between disk-fed accretion, in which the WD accretes from a Keplerian disk, and stream-fed accretion, in which the matter stream from the donor star directly impacts the WD’s magnetosphere without forming a disk. However, there is also a third, poorly understood regime in which the accretion flow consists of a torus of diamagnetic blobs that encircles the WD. This mode of accretion is expected to exist at mass-transfer rates below those observed during disk-fed accretion, but above those observed during pure stream-fed accretion. We invoke the diamagnetic-blob regime to explain the exceptional Transiting Exoplanet Survey Satellite light curve of the intermediate polar TX Col, which transitioned into and out of states of enhanced accretion during Cycles 1 and 3. Power-spectral analysis reveals that the accretion was principally stream fed. However, when the mass-transfer rate spiked, large-amplitude quasi-periodic oscillations (QPOs) abruptly appeared and dominated the light curve for weeks. The QPOs have two striking properties: they appear in a stream-fed geometry at elevated accretion rates, and they occur preferentially within a well-defined range of frequencies (∼10–25 cycle day{sup −1}). We propose that during episodes of enhanced accretion, a torus of diamagnetic blobs forms near the binary’s circularization radius and that the QPOs are beats between the white dwarf’s spin frequency and unstable blob orbits within the WD’s magnetosphere. We discuss how such a torus could be a critical step in producing an accretion disk in a formerly diskless system.

79 ASTRONOMY AND ASTROPHYSICS↗

Radial velocity variability and the evolution of hot subdwarf stars

Hot subdwarf stars represent a late and peculiar stage in the evolution of low-mass stars, since they are likely formed by close binary interactions. In this work, we perform a radial velocity (RV) variability study of a sample of 646 hot subdwarfs with multi-epoch radial velocities based on spectra from Sloan Digital Sky Survey (SDSS) and Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST). The atmospheric parameters and RVs were taken from the literature. For stars with archival spectra but without literature values, we determined the parameters by fitting model atmospheres. In addition, we redetermined the atmospheric parameters and RVs for all the He-enriched sdO/Bs. This broad sample allowed us to study RV-variability as a function of the location in theT eff - log g- and T eff - log n (He)/n (H) diagrams in a statistically significant way. We used the fraction of RV-variable stars and the distribution of the maximum RV variations ΔRV max as diagnostics. Both indicators turned out to be quite inhomogeneous across the studied parameter ranges. A striking feature is the completely dissimilar behaviour of He-poor and He-rich hot subdwarfs. While the former have a high fraction of close binaries, almost no significant RV variations could be detected for the latter. This has led us to the conclusion that there is likely no evolutionary connection between these subtypes. On the other hand, intermediate He-rich- and extreme He-rich sdOB/Os are more likely to be related. Furthermore, we conclude that the vast majority of this population is formed via one or several binary merger channels. Hot subdwarfs with temperatures cooler than ~24 000 K tend to show fewer and smaller RV-variations. These objects might constitute a new subpopulation of binaries with longer periods and late-type or compact companions. The RV-variability properties of the extreme horizontal branch (EHB) and corresponding post-EHB populations of the He-poor hot subdwarfs match and confirm the predicted evolutionary connection between them. Stars found below the canonical EHB at somewhat higher surface gravities show large RV variations and a high RV variability fraction. These properties are consistent with most of them being low-mass EHB stars or progenitors of low-mass helium white dwarfs in close binaries.

79 ASTRONOMY AND ASTROPHYSICS↗

R Coronae Borealis Star Evolution: Simulating 3D Merger Events to 1D Stellar Evolution Including Large-scale Nucleosynthesis

R Coronae Borealis (RCB) stars are rare hydrogen-deficient carbon-rich variable supergiants thought to be the result of dynamically unstable white dwarf mergers. In this article, we attempt to model RCB stars through all the relevant timescales by simulating a merger event in Octo-tiger, a 3D adaptive mesh refinement (AMR) hydrodynamics code, and mapping the post-merger object into MESA, a 1D stellar evolution code. We then post-process the nucleosynthesis on a much larger nuclear reaction network to study the enhancement of s-process elements. We present models that match observations or previous studies in most surface abundances, isotopic ratios, early evolution, and lifetimes. We also observe similar mixing behavior to previous modeling attempts that result in the partial He-burning products visible on the surface in observations. However, we do note that our subsolar models lack any enhancement in s-process elements, which we attribute to a lack of hydrogen in the envelope. We also find that the 16 O/ 18 O isotopic ratio is very sensitive to initial hydrogen abundance and increases outside of the acceptable range with a hydrogen mass fraction greater than 10 -4 .

79 ASTRONOMY AND ASTROPHYSICS↗

Dimming the Lights: 2D Simulations of Deflagrations of Hybrid C/O/Ne White Dwarfs Using FLASH

The dimmest and most numerous outlier of the Type Ia supernova population, the Type Iax event, is increasingly being found in the results of observational campaigns. There is currently no single accepted model to describe these events. This 2D study explores the viability of modeling Type Iax events as a hybrid C/O/Ne white dwarf progenitor undergoing a deflagration using the multiphysics software FLASH. This hybrid was created using the stellar evolution code MESA, and its C-depleted core and mixed structure have demonstrated lower yields than traditional C/O progenitors in previous deflagration-to-detonation studies. To generate a sample, 30 “realizations” of this simulation were performed, the only difference being the shape of the initial match head used to start the deflagration. Consistent with earlier work, these realizations produce the familiar hot dense bound remnant surrounded by sparse ejecta. Our results indicate that the majority of the star remains unburned (∼70%) and bound (>90%). Our realizations produce total ejecta yields on the order of 10 −2 –10 −1 M ☉ , ejected 56 Ni yields on the order of 10 −4 –10 −2 M ☉ , and ejecta kinetic energies on the order of 10 48 –10 49 erg. Compared to yields inferred from recent observations of the dimmest Type Iax events—SN 2007qd, SN 2008ha, SN 2010ae, SN 2019gsc, SN 2019muj, SN 2020kyg, and SN 2021fcg—our simulation produces comparable 56 Ni yields but too-small total yields and kinetic energies. Reignition of the remnant is also seen in some realizations.

Hydrodynamical simulations↗

Improving White Dwarfs as Chronometers with Gaia Parallaxes and Spectroscopic Metallicities

White dwarfs (WDs) offer unrealized potential in solving two problems in astrophysics: stellar age accuracy and precision. WD cooling ages can be inferred from surface temperatures and radii, which can be constrained with precision by high-quality photometry and parallaxes. Accurate and precise Gaia parallaxes along with photometric surveys provide information to derive cooling and total ages for vast numbers of WDs. Here we analyze 1372 WDs found in wide binaries with main-sequence (MS) companions and report on the cooling and total age precision attainable in these WD+MS systems. The total age of a WD can be further constrained if its original metallicity is known because the MS lifetime depends on metallicity at fixed mass, yet metallicity is unavailable via spectroscopy of the WD. We show that incorporating spectroscopic metallicity constraints from 38 wide binary MS companions substantially decreases internal uncertainties in WD total ages compared to a uniform constraint. Averaged over the 38 stars in our sample, the total (internal) age uncertainty improves from 21.04% to 16.77% when incorporating the spectroscopic constraint. Higher mass WDs yield better total age precision; for eight WDs with zero-age MS masses ≥2.0 M ⊙ , the mean uncertainty in total ages improves from 8.61% to 4.54% when incorporating spectroscopic metallicities. We find that it is often possible to achieve 5% total age precision for WDs with progenitor masses above 2.0 M ⊙ if parallaxes with ≤1% precision and Pan-STARRS g, r, and i photometry with ≤0.01 mag precision are available.

79 ASTRONOMY AND ASTROPHYSICS↗

Heavy dark matter in white dwarfs: multiple-scattering capture and thermalization

We present an improved treatment for the scattering of heavy dark matter from the ion constituents of a white dwarf. In the heavy dark matter regime, multiple collisions are required for the dark matter to become gravitationally captured. Our treatment incorporates all relevant physical effects including the dark matter trajectories, nuclear form factors, and radial profiles for the white dwarf escape velocity and target number densities. Our capture rates differ by orders of magnitude from previous estimates, which have typically used approximations developed for dark matter scattering in the Earth. We also compute the time for the dark matter to thermalize in the center of the white dwarf, including in-medium effects such as phonon emission and absorption from the ionic lattice in the case where the star has a crystallized core. We find much shorter thermalization timescales than previously estimated, especially if the white dwarf core has crystallized. We illustrate the importance of our improved approach by determining the cross section required for accumulated asymmetric dark matter to self-gravitate.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Astrometric gravitational-wave detection via stellar interferometry

Here, we evaluate the potential for gravitational-wave (GW) detection in the frequency band from 10 nHz to 1 μ Hz using extremely high-precision astrometry of a small number of stars. In particular, we argue that nonmagnetic, photometrically stable, hot white dwarfs (WD) located at ~kpc distances may be optimal targets for this approach. Previous studies of astrometric GW detection have focused on the potential for less precise surveys of large numbers of stars; our work provides an alternative optimization approach to this problem. Interesting GW sources in this band are expected at characteristic strains around h c ~10 -17 × (μHz/ $f$ GW ). The astrometric angular precision required to see these sources is Δθ~h c after integrating for a time T~1/$f$GW. We show that jitter in the photometric center of WD of this type due to starspots is bounded to be small enough to permit this high-precision, small-N approach. We discuss possible noise arising from stellar reflex motion induced by orbiting objects and show how it can be mitigated. The only plausible technology able to achieve the requisite astrometric precision is a space-based stellar interferometer. Such a future mission with few-meter-scale collecting dishes and baselines of $\mathscr{O}$(100 km ) is sufficient to achieve the target precision. This collector size is broadly in line with the collectors proposed for some formation-flown, space-based astrometer or optical synthetic-aperture imaging-array concepts proposed for other science reasons. The proposed baseline is however somewhat larger than the km-scale baselines discussed for those concepts, but we see no fundamental technical obstacle to utilizing such baselines. A mission of this type thus also holds the promise of being one of the few ways to access interesting GW sources in this band.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗