arXiv subjects

G. Desvignes

Publications and source records attributed to G. Desvignes.

At least 55 records · Page 3Linked to original sources

arXiv2019

The Discovery of Six Recycled Pulsars from the Arecibo 327-MHz Drift-Scan Pulsar Survey

Recycled pulsars are old ($\gtrsim10^{8}$ yr) neutron stars that are descendants from close, interacting stellar systems. In order to understand their evolution and population, we must find and study the largest number possible of recycled pulsars in a way that is as unbiased as possible. In this work, we present the discovery and timing solutions of five recycled pulsars in binary systems (PSRs J0509$+$0856, J0709$+$0458, J0732$+$2314, J0824$+$0028, J2204$+$2700) and one isolated millisecond pulsar (PSR J0154$+$1833). These were found in data from the Arecibo 327-MHz Drift-Scan Pulsar Survey (AO327). All these pulsars have a low dispersion measure (DM) ($\lesssim 45 \, \rm{pc}\, cm^{-3}$), and have a DM-determined distance of $\lesssim$ 3 kpc. Their timing solutions, have data spans ranging from 1 to $\sim$ 7 years, include precise estimates of their spin and astrometric parameters, and for the binaries, precise estimates of their Keplerian binary parameters. Their orbital periods range from about 4 to 815 days and the minimum companion masses (assuming a pulsar mass of 1.4 $\rm{M_{\odot}}$) range from $\sim$ 0.06--1.11 $\rm{M_{\odot}}$. For two of the binaries we detect post-Keplerian parameters; in the case of PSR~J0709$+$0458 we measure the component masses but with a low precision, in the not too distant future the measurement of the rate of advance of periastron and the Shapiro delay will allow very precise mass measurements for this system. Like several other systems found in the AO327 data, PSRs J0509$+$0854, J0709$+$0458 and J0732$+$2314 are now part of the NANOGrav timing array for gravitational wave detection.

astro-ph.HE↗

arXiv2018

Studying the solar system with the International Pulsar Timing Array

Pulsar-timing analyses are sensitive to errors in the solar-system ephemerides (SSEs) that timing models utilise to estimate the location of the solar-system barycentre, the quasi-inertial reference frame to which all recorded pulse times-of-arrival are referred. Any error in the SSE will affect all pulsars, therefore pulsar timing arrays (PTAs) are a suitable tool to search for such errors and impose independent constraints on relevant physical parameters. We employ the first data release of the International Pulsar Timing Array to constrain the masses of the planet-moons systems and to search for possible unmodelled objects (UMOs) in the solar system. We employ ten SSEs from two independent research groups, derive and compare mass constraints of planetary systems, and derive the first PTA mass constraints on asteroid-belt objects. Constraints on planetary-system masses have been improved by factors of up to 20 from the previous relevant study using the same assumptions, with the mass of the Jovian system measured at 9.5479189(3)$\times10^{-4}$ $M_{\odot}$. The mass of the dwarf planet Ceres is measured at 4.7(4)$\times10^{-10}$ $M_{\odot}$. We also present the first sensitivity curves using real data that place generic limits on the masses of UMOs, which can also be used as upper limits on the mass of putative exotic objects. For example, upper limits on dark-matter clumps are comparable to published limits using independent methods. While the constraints on planetary masses derived with all employed SSEs are consistent, we note and discuss differences in the associated timing residuals and UMO sensitivity curves.

astro-ph.EP↗

arXiv2018

Improving timing sensitivity in the microhertz frequency regime: limits from PSR J1713$+$0747 on gravitational waves produced by super-massive black-hole binaries

We search for continuous gravitational waves (CGWs) produced by individual super-massive black-hole binaries (SMBHBs) in circular orbits using high-cadence timing observations of PSR J1713$+$0747. We observe this millisecond pulsar using the telescopes in the European Pulsar Timing Array (EPTA) with an average cadence of approximately 1.6 days over the period between April 2011 and July 2015, including an approximately daily average between February 2013 and April 2014. The high-cadence observations are used to improve the pulsar timing sensitivity across the GW frequency range of $0.008-5$ $μ$Hz. We use two algorithms in the analysis, including a spectral fitting method and a Bayesian approach. For an independent comparison, we also use a previously published Bayesian algorithm. We find that the Bayesian approaches provide optimal results and the timing observations of the pulsar place a 95 per cent upper limit on the sky-averaged strain amplitude of CGWs to be $\lesssim3.5\times10^{-13}$ at a reference frequency of 1 $μ$Hz. We also find a 95 per cent upper limit on the sky-averaged strain amplitude of low-frequency CGWs to be $\lesssim1.4\times10^{-14}$ at a reference frequency of 20~nHz.

astro-ph.HE↗

arXiv2018

Tests of Gravitational Symmetries with Pulsar Binary J1713+0747

Symmetries play an important role in modern theories of gravity. The strong equivalence principle (SEP) constitutes a collection of gravitational symmetries which are all implemented by general relativity. Alternative theories, however, are generally expected to violate some aspects of SEP. We test three aspects of SEP using observed change rates in the orbital period and eccentricity of binary pulsar J1713+0747: 1. the gravitational constant's constancy as part of locational invariance of gravitation; 2. the post-Newtonian parameter $\hatα_3$ in gravitational Lorentz invariance; 3. the universality of free fall (UFF) for strongly self-gravitating bodies. Based on the pulsar timing result of the combined dataset from the North American Nanohertz Gravitational Observatory (NANOGrav) and the European Pulsar Timing Array (EPTA), we find $\dot{G}/G = (-0.1 \pm 0.9) \times 10^{-12}\,{\rm yr}^{-1}$, which is weaker than Solar system limits, but applies for strongly self-gravitating objects. Furthermore, we obtain the constraints $|Δ|< 0.002$ for the UFF test and $-3\times10^{-20} < \hatα_3 < 4\times10^{-20}$ at 95% confidence. These are the first direct UFF and $\hatα_3$ tests based on pulsar binaries, and they overcome various limitations of previous tests.

astro-ph.HE↗

arXiv2018

PSR J1618-3921: a recycled pulsar in an eccentric orbit

PSR~J1618$-$3921 is an $11.99$-ms pulsar in a $22.7$-d orbit around a likely low-mass He white dwarf companion, discovered in a survey of the intermediate Galactic latitudes at 1400 MHz conducted with the Parkes radio telescope in the late 1990s. Although PSR~J1618$-$3921 was discovered more than 15 years ago, only limited information has been published about this pulsar which has a surprisingly large orbital eccentricity ($e \simeq 0.027$), considering its high spin frequency and likely small companion mass. The focus of this work is a precise measurement of the spin, astrometric and orbital characteristics of PSR J1618$-$3921. This was done with timing observations made at the Nançay Radio Telescope, from 2009 to 2017. We analyzed the timing data recorded at the Nançay Radio Telescope over several years to characterize the properties of PSR~J1618$-$3921. A rotation ephemeris for this pulsar was obtained by analyzing the times of arrival of the radio pulses at the telescope. We confirm the unusual eccentricity of PSR~J1618$-$3921 and discuss several hypotheses regarding its formation, in the context of other discoveries of recycled pulsars in eccentric orbits.

astro-ph.HE↗

arXiv2017

Long-term observations of pulsars in the globular clusters 47 Tucanae and M15

Multi-decade observing campaigns of the globular clusters 47 Tucanae and M15 have led to an outstanding number of discoveries. Here, we report on the latest results of the long-term observations of the pulsars in these two clusters. For most of the pulsars in 47 Tucanae we have measured, among other things, their higher-order spin period derivatives, which have in turn provided stringent constraints on the physical parameters of the cluster, such as its distance and gravitational potential. For M15, we have studied the relativistic spin precession effect in PSR B2127+11C. We have used full-Stokes observations to model the precession effect, and to constrain the system geometry. We find that the visible beam of the pulsar is swiftly moving away from our line of sight and may very soon become undetectable. On the other hand, we expect to see the opposite emission beam sometime between 2041 and 2053.

astro-ph.HE↗

arXiv2017

The discovery of two mildly-recycled binary pulsars in the Northern High Time Resolution Universe pulsar survey

We report the discovery and the results of follow-up timing observations of PSR J2045+3633 and PSR J2053+4650, two binary pulsars found in the Northern High Time Resolution Universe pulsar survey being carried out with the Effelsberg radio telescope. Having spin periods of 31.7 ms and 12.6 ms respectively, and both with massive white dwarf companions, $M_{c}\, > \, 0.8\, M_{\odot}$, the pulsars can be classified as mildly recycled. PSR J2045+3633 is remarkable due to its orbital period (32.3 days) and eccentricity $e\, = \, 0.01721244(5)$ which is among the largest ever measured for this class. After almost two years of timing the large eccentricity has allowed the measurement of the rate of advance of periastron at the 5-$σ$ level, 0.0010(2)$^\circ~\rm yr^{-1}$. Combining this with a detection of the orthometric amplitude of the Shapiro delay, we obtained the following constraints on the component masses (within general relativity): $M_{p}\, = \, 1.33^{+0.30}_{-0.28}\, M_{\odot}$, and $M_{c}\, = \, 0.94^{+0.14}_{-0.13}\, M_{\odot}$. PSR J2053+4650 has a 2.45-day circular orbit inclined to the plane of the sky at an angle $i\, = \, 85.0^{+0.8}_{-0.9}\,{^\circ}$. In this nearly edge-on case the masses can be obtained from the Shapiro delay alone. Our timing observations resulted in a significant detection of this effect giving: $M_{p}\, = \, 1.40^{+0.21}_{-0.18}\, M_{\odot}$, and $M_{c}\, = \, 0.86^{+0.07}_{-0.06}\, M_{\odot}$.

astro-ph.HE↗

arXiv2017

Evidence for an intermediate-mass black hole in the globular cluster NGC 6624

PSR B1820$-$30A is located in the globular cluster NGC 6624 and is the closest known pulsar to the centre of any globular cluster. We present more than 25 years of high-precision timing observations of this millisecond pulsar and obtain four rotational frequency time derivative measurements. Modelling these higher-order derivatives as being due to orbital motion, we find solutions which indicate that the pulsar is in either a low-eccentricity ($0.33\lesssim e\lesssim0.4$) smaller orbit with a low mass companion (such as a main sequence star, white dwarf, neutron star, or stellar mass black hole) or a high-eccentricity ($e\gtrsim0.9$) larger orbit with a massive companion. The cluster mass properties and the observed properties of 4U 1820$-$30 and the other pulsars in the cluster argue against the low-eccentricity possibility. The high-eccentricity solution reveals that the pulsar is most likely orbiting around an intermediate-mass black hole (IMBH) of mass $> 7,500$~M$_\odot$ located at the cluster centre. A gravitational model for the globular cluster, which includes such a central black hole (BH), predicts an acceleration that is commensurate with that measured for the pulsar. It further predicts that the model-dependent minimum mass of the IMBH is $\sim60,000$~M$_\odot$. Accounting for the associated contribution to the observed period derivative indicates that the $γ$-ray efficiency of the pulsar should be between 0.08 and 0.2. Our results suggest that other globular clusters may also contain central black holes and they may be revealed by the study of new pulsars found sufficiently close to their centres. Note that we found an erratum in Section 5 and thus, the $\sim$60,000~M$_\odot$ mass mentioned above has to be replaced by the correct model-dependent mass limit of $\sim$20,000~M$_\odot$. See the erratum appended.

astro-ph.HE↗

arXiv2017

BlackHoleCam: fundamental physics of the Galactic center

Einstein's General Theory of Relativity (GR) successfully describes gravity. The most fundamental predictions of GR are black holes (BHs), but in spite of many convincing BH candidates in the Universe, there is no conclusive experimental proof of their existence using astronomical observations in the electromagnetic spectrum. Are BHs real astrophysical objects? Does GR hold in its most extreme limit or are alternatives needed? The prime target to address these fundamental questions is in the center of our own Galaxy, which hosts the closest and best-constrained supermassive BH candidate in the Universe, Sagittarius A* (Sgr A*). Three different types of experiments hold the promise to test GR in a strong-field regime using observations of Sgr A* with new-generation instruments. The first experiment aims to image the relativistic plasma emission which surrounds the event horizon and forms a "shadow" cast against the background, whose predicted size (~50 microarcseconds) can now be resolved by upcoming VLBI experiments at mm-waves such as the Event Horizon Telescope (EHT). The second experiment aims to monitor stars orbiting Sgr A* with the upcoming near-infrared interferometer GRAVITY at the Very Large Telescope (VLT). The third experiment aims to time a radio pulsar in tight orbit about Sgr A* using radio telescopes (including the Atacama Large Millimeter Array or ALMA). The BlackHoleCam project exploits the synergy between these three different techniques and aims to measure the main BH parameters with sufficient precision to provide fundamental tests of GR and probe the spacetime around a BH in any metric theory of gravity. Here, we review our current knowledge of the physical properties of Sgr A* as well as the current status of such experimental efforts towards imaging the event horizon, measuring stellar orbits, and timing pulsars around Sgr A*.

astro-ph.HE↗

arXiv2016

Detection of the magnetar SGR J1745-2900 up to 291 GHz with evidence of polarized millimetre emission

In Torne et al. (2015), we showed detections of SGR J1745-2900 up to 225 GHz (1.33 mm); at that time the highest radio frequency detection of pulsar emission. In this work, we present the results of new observations of the same magnetar with detections up to 291 GHz (1.03 mm), together with evidence of linear polarization in its millimetre emission. SGR J1745-2900 continues to show variability and is, on average, a factor $\sim$4 brighter in the millimetre band than in our observations of July 2014. The new measured spectrum is slightly inverted, with $\left<α\right> = +0.4\pm0.2$ (for $S_ν \propto ν^α)$. However, the spectrum does not seem to be well described by a single power law, which might be due to the intrinsic variability of the source, or perhaps a turn-up somewhere between 8.35 and 87 GHz. These results may help us to improve our still incomplete model of pulsar emission and, in addition, they further support the search for and study of pulsars located at the Galactic Centre using millimetre wavelengths.

astro-ph.HE↗

arXiv2016

21-year timing of the black-widow pulsar J2051-0827

Timing results for the black-widow pulsar J2051-0827 are presented, using a 21-year dataset from four European Pulsar Timing Array telescopes and the Parkes radio telescope. This dataset, which is the longest published to date for a black-widow system, allows for an improved analysis that addresses previously unknown biases. While secular variations, as identified in previous analyses, are recovered, short-term variations are detected for the first time. Concurrently, a significant decrease of approx. 2.5x10-3 cm-3 pc in the dispersion measure associated with PSR J2051-0827 is measured for the first time and improvements are also made to estimates of the proper motion. Finally, PSR J2051-0827 is shown to have entered a relatively stable state suggesting the possibility of its eventual inclusion in pulsar timing arrays.

astro-ph.HE↗

arXiv2016

A glitch in the millisecond pulsar J0613-0200

We present evidence for a small glitch in the spin evolution of the millisecond pulsar J0613$-$0200, using the EPTA Data Release 1.0, combined with Jodrell Bank analogue filterbank TOAs recorded with the Lovell telescope and Effelsberg Pulsar Observing System TOAs. A spin frequency step of 0.82(3) nHz and frequency derivative step of ${-1.6(39) \times 10^{-19}\,\text{Hz} \ \text{s}^{-1}}$ are measured at the epoch of MJD 50888(30). After PSR B1821$-$24A, this is only the second glitch ever observed in a millisecond pulsar, with a fractional size in frequency of ${Δν/ν=2.5(1) \times 10^{-12}}$, which is several times smaller than the previous smallest glitch. PSR J0613$-$0200 is used in gravitational wave searches with pulsar timing arrays, and is to date only the second such pulsar to have experienced a glitch in a combined 886 pulsar-years of observations. We find that accurately modelling the glitch does not impact the timing precision for pulsar timing array applications. We estimate that for the current set of millisecond pulsars included in the International Pulsar Timing Array, there is a probability of $\sim 50$% that another glitch will be observed in a timing array pulsar within 10 years.

astro-ph.HE↗

arXiv2016

A millisecond pulsar in an extremely wide binary system

We report on 22 yrs of radio timing observations of the millisecond pulsar J1024$-$0719 by the telescopes participating in the European Pulsar Timing Array (EPTA). These observations reveal a significant second derivative of the pulsar spin frequency and confirm the discrepancy between the parallax and Shklovskii distances that has been reported earlier. We also present optical astrometry, photometry and spectroscopy of 2MASS J10243869$-$0719190. We find that it is a low-metallicity main-sequence star (K7V spectral type, $\mathrm{[M/H]}=-1.0$, $T_\mathrm{eff}=4050\pm50$ K) and that its position, proper motion and distance are consistent with those of PSR J1024$-$0719. We conclude that PSR J1024$-$0719 and 2MASS J10243869$-$0719190 form a common proper motion pair and are gravitationally bound. The gravitational interaction between the main-sequence star and the pulsar accounts for the spin frequency derivatives, which in turn resolves the distance discrepancy. Our observations suggest that the pulsar and main-sequence star are in an extremely wide ($P_\mathrm{b}>200$ yr) orbit. Combining the radial velocity of the companion and proper motion of the pulsar, we find that the binary system has a high spatial velocity of $384\pm45$ km s$^{-1}$ with respect to the local standard of rest and has a Galactic orbit consistent with halo objects. Since the observed main-sequence companion star cannot have recycled the pulsar to millisecond spin periods, an exotic formation scenario is required. We demonstrate that this extremely wide-orbit binary could have evolved from a triple system that underwent an asymmetric supernova explosion, though find that significant fine-tuning during the explosion is required. Finally, we discuss the implications of the long period orbit on the timing stability of PSR J1024$-$0719 in light of its inclusion in pulsar timing arrays.

astro-ph.HE↗

arXiv2016

High-precision timing of 42 millisecond pulsars with the European Pulsar Timing Array

We report on the high-precision timing of 42 radio millisecond pulsars (MSPs) observed by the European Pulsar Timing Array (EPTA). This EPTA Data Release 1.0 extends up to mid-2014 and baselines range from 7-18 years. It forms the basis for the stochastic gravitational-wave background, anisotropic background, and continuous-wave limits recently presented by the EPTA elsewhere. The Bayesian timing analysis performed with TempoNest yields the detection of several new parameters: seven parallaxes, nine proper motions and, in the case of six binary pulsars, an apparent change of the semi-major axis. We find the NE2001 Galactic electron density model to be a better match to our parallax distances (after correction from the Lutz-Kelker bias) than the M2 and M3 models by Schnitzeler (2012). However, we measure an average uncertainty of 80\% (fractional) for NE2001, three times larger than what is typically assumed in the literature. We revisit the transverse velocity distribution for a set of 19 isolated and 57 binary MSPs and find no statistical difference between these two populations. We detect Shapiro delay in the timing residuals of PSRs J1600$-$3053 and J1918$-$0642, implying pulsar and companion masses $m_p=1.22_{-0.35}^{+0.5} \text{M}_{\odot}$, $m_c = 0.21_{-0.04}^{+0.06} \text{M}_{\odot }$ and $m_p=1.25_{-0.4}^{+0.6} \text{M}_{\odot}$, $m_c = 0.23_{-0.05}^{+0.07} \text{M}_{\odot }$, respectively. Finally, we use the measurement of the orbital period derivative to set a stringent constraint on the distance to PSRs J1012$+$5307 and J1909$-$3744, and set limits on the longitude of ascending node through the search of the annual-orbital parallax for PSRs J1600$-$3053 and J1909$-$3744.

astro-ph.HE↗

arXiv2016

From Spin Noise to Systematics: Stochastic Processes in the First International Pulsar Timing Array Data Release

We analyse the stochastic properties of the 49 pulsars that comprise the first International Pulsar Timing Array (IPTA) data release. We use Bayesian methodology, performing model selection to determine the optimal description of the stochastic signals present in each pulsar. In addition to spin-noise and dispersion-measure (DM) variations, these models can include timing noise unique to a single observing system, or frequency band. We show the improved radio-frequency coverage and presence of overlapping data from different observing systems in the IPTA data set enables us to separate both system and band-dependent effects with much greater efficacy than in the individual PTA data sets. For example, we show that PSR J1643$-$1224 has, in addition to DM variations, significant band-dependent noise that is coherent between PTAs which we interpret as coming from time-variable scattering or refraction in the ionised interstellar medium. Failing to model these different contributions appropriately can dramatically alter the astrophysical interpretation of the stochastic signals observed in the residuals. In some cases, the spectral exponent of the spin noise signal can vary from 1.6 to 4 depending upon the model, which has direct implications for the long-term sensitivity of the pulsar to a stochastic gravitational-wave (GW) background. By using a more appropriate model, however, we can greatly improve a pulsar's sensitivity to GWs. For example, including system and band-dependent signals in the PSR J0437$-$4715 data set improves the upper limit on a fiducial GW background by $\sim 60\%$ compared to a model that includes DM variations and spin-noise only.

astro-ph.IM↗

arXiv2016

The International Pulsar Timing Array: First Data Release

The highly stable spin of neutron stars can be exploited for a variety of (astro-)physical investigations. In particular arrays of pulsars with rotational periods of the order of milliseconds can be used to detect correlated signals such as those caused by gravitational waves. Three such "Pulsar Timing Arrays" (PTAs) have been set up around the world over the past decades and collectively form the "International" PTA (IPTA). In this paper, we describe the first joint analysis of the data from the three regional PTAs, i.e. of the first IPTA data set. We describe the available PTA data, the approach presently followed for its combination and suggest improvements for future PTA research. Particular attention is paid to subtle details (such as underestimation of measurement uncertainty and long-period noise) that have often been ignored but which become important in this unprecedentedly large and inhomogeneous data set. We identify and describe in detail several factors that complicate IPTA research and provide recommendations for future pulsar timing efforts. The first IPTA data release presented here (and available online) is used to demonstrate the IPTA's potential of improving upon gravitational-wave limits placed by individual PTAs by a factor of ~2 and provides a 2-sigma limit on the dimensionless amplitude of a stochastic GWB of 1.7x10^{-15} at a frequency of 1 yr^{-1}. This is 1.7 times less constraining than the limit placed by (Shannon et al. 2015), due mostly to the more recent, high-quality data they used.

astro-ph.IM↗

arXiv2016

The gamma-ray millisecond pulsar deathline, revisited - New velocity and distance measurements

Millisecond pulsars (MSPs) represent nearly half of the more than 160 currently known $γ$-ray pulsars detected by the Large Area Telescope on the \textit{Fermi} satellite, and a third of all known MSPs are seen in $γ$ rays. The least energetic $γ$-ray MSPs enable us to probe the so-called deathline for high-energy emission, i.e., the spin-down luminosity limit under which pulsars (PSRs) cease to produce detectable high-energy radiation. Characterizing the MSP luminosity distribution helps to determine their contribution to the Galactic diffuse $γ$-ray emission. We made use of the high-quality pulsar timing data recorded at the Nançay Radio Telescope over several years to characterize the properties of a selection of MSPs. For one of the pulsars, the dataset was complemented with Westerbork Synthesis Radio Telescope observations. The rotation ephemerides derived from this analysis were also used to search the LAT data for new $γ$-ray MSPs. For the MSPs considered in this study, we obtained new transverse proper motion measurements or updated the existing ones, and placed new distance constraints for some of them, with four new timing parallax measurements. We discovered significant GeV $γ$-ray signals from four MSPs, i.e., PSRs J0740+6620, J0931$-$1902, J1455$-$3330, and J1730$-$2304. The latter is now the least energetic $γ$-ray pulsar found to date. Despite the improved $\dot E$ and $L_γ$ estimates, the relationship between these two quantities remains unclear, especially at low $\dot E$ values.

astro-ph.HE↗

arXiv2016

The noise properties of 42 millisecond pulsars from the European Pulsar Timing Array and their impact on gravitational wave searches

The sensitivity of Pulsar Timing Arrays to gravitational waves depends on the noise present in the individual pulsar timing data. Noise may be either intrinsic or extrinsic to the pulsar. Intrinsic sources of noise will include rotational instabilities, for example. Extrinsic sources of noise include contributions from physical processes which are not sufficiently well modelled, for example, dispersion and scattering effects, analysis errors and instrumental instabilities. We present the results from a noise analysis for 42 millisecond pulsars (MSPs) observed with the European Pulsar Timing Array. For characterising the low-frequency, stochastic and achromatic noise component, or "timing noise", we employ two methods, based on Bayesian and frequentist statistics. For 25 MSPs, we achieve statistically significant measurements of their timing noise parameters and find that the two methods give consistent results. For the remaining 17 MSPs, we place upper limits on the timing noise amplitude at the 95% confidence level. We additionally place an upper limit on the contribution to the pulsar noise budget from errors in the reference terrestrial time standards (below 1%), and we find evidence for a noise component which is present only in the data of one of the four used telescopes. Finally, we estimate that the timing noise of individual pulsars reduces the sensitivity of this data set to an isotropic, stochastic GW background by a factor of >9.1 and by a factor of >2.3 for continuous GWs from resolvable, inspiralling supermassive black-hole binaries with circular orbits.

astro-ph.IM↗