arXiv subjects

S. P. Littlefair

Publications and source records attributed to S. P. Littlefair.

At least 19 recordsLinked to original sources

arXiv2026

V407 Vul: a triple star system with an AM CVn detectable by gravitational wave observatories

The AM CVn class includes mass transferring, ultra-compact double white dwarf binaries with orbital periods on the timescale of minutes. A long-standing puzzle is that none of the roughly fifty ultra-compact, "verification binaries" which are easily detectable in the millihertz gravitational wave regime reside in a triple star configuration. Much evidence has hinted at V407 Vul being an inspiraling, double white dwarf AM CVn with an orbital period of 569s. Yet, a decisive confirmation has proved challenging since a main sequence star dominates its visible spectrum. We present a clear confirmation of the triple star nature of the source by detecting a significant astrometric wobble of the photocentre on the 569s orbital period of the binary. The AM CVn and the main sequence components are gravitationally bound with a spatial separation of roughly 0.03-0.04'', equating to an orbital separation of approximately 120AU. A total of 23 years of orbital timing constrained the orbital decay of the AM CVn as being precise to the 1% level, critical in understanding if this class of binary survives through a period minimum or coalesce. New Hubble Space Telescope ultra-violet imaging and spectroscopic data allowed the isolated detection of the AM CVn at shorter wavelengths, revealing an approximately 58000 K accretor white dwarf, while placing a firm distance constraint of 3510+140-110 pc. At this distance, we predict that the Laser Interferometer Space Antenna (LISA) will detect V407 Vul with a 28.4+-9.2 signal-to-noise ratio in a 4yr mission time, making it the first verification binary with an outer tertiary, or "verification triple", detectable for millihertz gravitational wave observatories.

astro-ph.SR↗

arXiv2026

ZTF J021804.16+071152.93: a dead cataclysmic variable and potential solution to the missing period bouncers

It is predicted that half or more of all cataclysmic variables (CVs) should have evolved past the period minimum and now exist as so-called "period bouncers" where a white dwarf should be accreting from a Roche-lobe filling substellar companion. However, this prediction stands in stark contrast to observations, where only a few per cent of CVs are found in this evolutionary phase. A potential solution to this discrepancy is that a magnetic field emerges from within the white dwarf after the system has reached the period minimum. The transfer of angular momentum from the spin of the white dwarf into the orbit then pushes the two stars apart, detaching them for potentially billions of years. Here we present the discovery of ZTF J021804.16+071152.93, a detached $0.69\pm0.01 M_{\odot}$, 19 MG magnetic white dwarf plus $37\pm5 M_\mathrm{Jup}$ brown dwarf binary with an orbital period of 1.7 hours. The kinematics of the system indicate that it is a high probability member of the galactic thick disk. However, this strongly disagrees with the much younger age of the system obtained from the white dwarf parameters, implying that the system may have been accreting in the past. This system is therefore consistent with having detached as a result of the emergence of the magnetic field of the white dwarf when the system was still mass transferring, and may represent the ultimate fate for many (perhaps even most) CVs.

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arXiv2026

No Period Change in Two Long-Period AM CVn Binaries

Ultracompact binary systems, consisting of two compact objects in an orbit $\lesssim 0.5 R_\odot$, should exhibit measurable rates of orbital period change ($\dot{P} \neq 0$) due to the emission of gravitational waves (GWs). Measurements of \pdot\ have so far been limited to the shortest-period ultracompact binaries ($\lesssim 20$\,min). Among the AM\,CVn-type subclass, several works have proposed the presence of extra angular momentum loss beyond GW emission, with magnetic braking being a widely discussed mechanism. If present, this magnetic braking would dominate the angular momentum loss of AM\,CVn-type binaries with orbital periods $\gtrsim 30$\,min. In this work, we present a long-term eclipse timing study of two AM\,CVn-type binaries, YZ\,LMi and Gaia14aae, with respective orbital periods of 28.3\,min and 49.7\,min and continuous observations since 2006 and 2015. Both systems show $\dot{P}$ consistent with zero within $2σ$. Their $3σ$ upper limits are $1.1 \times 10^{-13}\,{\rm s \, s}^{-1}$ and $9.7 \times 10^{-14}\,{\rm s \, s}^{-1}$ respectively. These non-detections are most simply explained by a scenario in which secular angular momentum loss is not substantially stronger than GW emission at all orbital periods, but is combined with deviations from the secular $\dot{P}$ whose timescales span decades but whose amplitude is $\lesssim 10^{-13}\,{\rm s \, s}^{-1}$. %, orders of magnitude smaller than the eclipse timing variations seen in hydrogen-dominated cataclysmic variables. Our non-detections of $\dot{P}$ represent a limit on the strength of any enhanced angular momentum loss beyond pure GW emission.

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arXiv2026

Einstein Probe discovery of EP J171159.4-333253: an eclipsing neutron star low-mass X-ray binary with clocked bursts

EP J171159.4-333253 is a new neutron-star low-mass X-ray binary discovered in outburst by the Einstein Probe (EP) on 2025 June 23, exhibiting clocked type-I X-ray bursts, eclipses and dips. In this paper, we report on the results of the X-ray spectral and timing analyses for EP J171159.4-333253 using data collected by EP and NuSTAR during the first 21 days of the outburst. The X-ray burst recurrence time can be characterized over a subset of nine bursts spanning 1.6 days around the NuSTAR observation, and the result is $t_{\rm rec}=8196 \pm 177\,$s with indications of a possible decreasing trend. From the X-ray eclipse events, the binary orbital period and the eclipse duration are estimated to be $P_{\rm orb}=6.48301 \pm 0.00003\,$hr and $D_{\star,X} = 1245.5^{+6.9}_{-6.5}\,$s, respectively. These enable an estimate of the mass and radius of the companion star and the binary inclination, which are $M_2\approx0.6-0.8\,M_\odot$, $R_2\approx0.7-0.8\,R_\odot$ and $i\approx73-75^\circ$, respectively. We also report on joint ULTRACAM and EP observations on 2025 July 21--22, detecting the source optical counterpart and covering an eclipse in both X-ray and optical bands. The optical eclipse is wavelength-dependent and broader than in X-rays, indicating that part of the optical emission arises from an extended region in the accretion flow. Despite a moderate variation in the source flux, the properties of the persistent X-ray emission are typical of a hard spectral state. We further evaluated the ratio of the accretion energy to the thermonuclear energy to be 120--130, implying helium bursts with the accreted hydrogen being depleted in-between bursts.

astro-ph.HE↗

arXiv2026

Photometric masses for long period CVs: the case study of CSS131106

We present high-speed photometry of the eclipsing cataclysmic variable CSS131106 J052412+004148. We determine the system parameters by modelling the eclipse lightcurve using the photometric eclipse method, in which the mass ratio is determined from the relative timings of the white dwarf and bright spot eclipses. Despite the blended white dwarf and bright spot ingress, typical of longer period cataclysmic variables, we perform simulations that show we are able to reliably constrain the component masses. We find a mass ratio of $q = 0.81 \pm 0.06$ and inclination $i = 78.5 \pm 0.7$ degrees. The white dwarf and donor masses were found to be $M_{w} = 0.72 \pm 0.04 \, M_{\odot}$ and $M_{d} = 0.58 \pm 0.06 \, M_{\odot}$ respectively. The white dwarf temperature was estimated to be $T_{\rm eff} = 18~500 \pm 2~000$ K, implying a moderate accretion rate of $\dot{M} = 3 \pm 1 \times 10^{-10} M_{\odot}$ yr$^{-1}$. The donor in CSS131106 J052412+004148 joins two other long-period cataclysmic variables (IP Peg and HS 0220+0031) in being unusually small for its mass, even when compared to detached M-dwarfs. The donors in all three systems are also unusually cool for their mass. We discuss possible explanations for the small radii and cool temperatures of the donors in these systems, but find no viable explanation for their properties.

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arXiv2026

Long-term eclipse time variations in white dwarf binaries

The overwhelming majority of eclipsing white dwarf (WD) binary systems show quasi-periodic variations in eclipse timings on many year timescales. Currently, the mechanism behind these eclipse time variations (ETVs) is not known, with the main competing theories being the planetary hypothesis and the Applegate/Lanza mechanisms. Here, we present a comprehensive study of 43 WD binary systems, the vast majority of which have more than a decade of eclipse timing measurements, analysing their global properties to determine which driving force is the likely origin of the observed ETVs. Long-term, high-speed photometry data obtained with ULTRACAM, ULTRASPEC and HiPERCAM have allowed us to track the evolution of the ETVs in these systems, and analyse any previously unseen trends. From this analysis, we find a clear difference in the level of observed ETVs past the fully convective boundary, where systems with partially radiative companion stars consistently showing high levels of variation. While some systems may be affected by the presence of an unknown planet, the results from this study strongly indicates that an Applegate- or Lanza-like mechanism is the most likely driving force for the timing variations seen in the majority of systems in this sample. However, as found in previous studies, the Applegate/Lanza mechanisms are still not able to reproduce the large and rapid timing variations seen in the vast majority of systems, with the companion star to the WD unable to provide sufficient energy on these short timescales.

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arXiv2025

SN 2024cld: unveiling the complex mass-loss histories of evolved supergiant progenitors to core collapse supernovae

Pre-explosion mass loss in supernova (SN) progenitors is a crucial unknown factor in stellar evolution, yet has been illuminated recently by the diverse zoo of interacting transients. We present SN2024cld, a transitional core-collapse SN at a distance of 39 Mpc, straddling the boundary between SN II and SN IIn, showing persistent interaction with circumstellar material (CSM) similar to H-rich SN1998S and PTF11iqb. The SN was discovered and classified just 12h post-explosion via the GOTO-FAST high-cadence program. Optical spectroscopy, photometry, and polarimetry over 220d chart the complex, long-lived interaction in this transient. Early evolution is dominated by CSM interaction, showing a 14d rise to a peak absolute magnitude of g=-17.6 mag, with clear flash-ionisation signatures. SN2024cld also shows a slowly-evolving late time light curve powered by CSM interaction, with high-velocity (6000 km/s) shoulders on a strong multi-component H-alpha profile. Dense polarimetric coverage reveals marked evolution in the photospheric geometry -- peaking at p=2% 10 days post-explosion, and rotating approx. 60 deg as the ejecta sweep more distant CSM. We observe a narrow 60 km/s H-alpha P Cygni feature throughout, associated with pre-shock CSM. SN2024cld represents among the best-observed 98S-like SNe to date, revealing a multi-component CSM structure: a dense, inner aspherical envelope, CSM disk/torus, and tenuous, extended wind. We propose this SN arose from an evolved supergiant progenitor experiencing multiple mass loss episodes in its terminal years, with binary interaction plausibly generating the CSM disk. SN2024cld constrains the progenitors and mass-loss paradigms of 98S-like SNe, unveiling the chaotic ends of evolved supergiant stars from afar.

astro-ph.HE↗

arXiv2025

Constraints on an optical counterpart for the long-period radio transient GPM J1839-10

Long period radio transients (LPTs) are periodic radio sources showing pulsed emission on timescales from minutes to hours. The underlying sources behind this emission are currently unclear. There are two leading candidates: neutron stars or white dwarfs. Neutron stars could emit at LPT timescales as magnetars, binaries, or precessing sources. White dwarfs on the other hand have only been observed to emit in radio as binary systems with companions that provide charged particles through their wind. A key distinction is that an optical counterpart is much more likely in the white dwarf scenario. GPM J1839-10 is an LPT with a radio period of 21 min for which the white dwarf scenario has been favoured, but no optical counterpart is confirmed. Using HiPERCAM, a high-speed multi-colour photometer that observes simultaneously in ugriz filters, we probe the existence of a white dwarf in GPM J1839-10. We do not directly detect a white dwarf, but cannot rule out its presence given the uncertain distance and reddening of GPM J1839-10. On the other hand, we find evidence in our data for periodic behaviour in harmonics of the radio period, as expected from the white dwarf scenario.

astro-ph.SR↗

arXiv2025

A Sibling of AR Scorpii: SDSS J230641.47$+$244055.8 and the Observational Blueprint of White Dwarf Pulsars

Radio pulsating white dwarf (WD) systems, known as WD pulsars, are non-accreting binary systems where the rapidly spinning WD interacts with a low-mass companion producing pulsed non-thermal emission that can be observed across the entire electromagnetic spectrum. Only two such systems are known: AR Sco and eRASSU J191213.9$-$441044. Here we present the discovery of a third WD pulsar, SDSS J230641.47$+$244055.8. The optical spectrum is dominated by molecular bands from an M-dwarf companion, with additional narrow emission lines from the Balmer series and He I. The long-term optical light-curve folded on its orbital period ($P_\mathrm{orb} = 3.49$ h) exhibits large scatter (roughly 10 per cent). High-cadence photometry reveals a short period signal, which we interpret to be the spin period of the WD primary ($P_\mathrm{spin} \simeq 92$ s). The WD spin period is slightly shorter than that of AR Sco ($\rm \sim 117$ s), the WD pulsar prototype. Time-resolved spectroscopy reveals emission from the irradiated companion and Na I absorption lines approximately tracing its centre of mass, which yields a binary mass function of $f(M) \simeq 0.2 {\rm M_\odot}$. The H$α$ emission includes a low-amplitude broad component, resembling the energetic emission line flashes seen in AR Sco. Using spectral templates, we classify the companion to be most likely a $\rm M4.0\pm 0.5$ star with $T_\mathrm{\rm eff} \approx 3300$ K. Modelling the stellar contribution constrains the secondary mass ($0.19\,{\rm M_\odot}\lesssim M_2\lesssim 0.28\,{\rm M_\odot}$), system distance ($\simeq1.25\,{\rm kpc}$), and inclination ($i \simeq 45-50^\circ$). We discuss the proposed evolutionary scenarios and summarize the observational properties of all three known WD pulsars, establishing a benchmark for identifying and classifying future members of this emerging class.

astro-ph.SR↗

arXiv2025

A targeted search for binary white dwarf pulsars using Gaia and WISE

After its discovery in 2016, the white dwarf binary AR Scorpii (AR Sco) remained for several years the only white dwarf system to show pulsed radio emission associated with a fast-spinning white dwarf. The evolutionary origin and the emission mechanism for AR Sco are not completely understood, with different models proposed. Testing and improving these models requires observational input. Here we report the results of a targeted search for other binary white dwarf pulsars like AR Sco. Using data from Gaia and WISE, we identified 56 candidate systems with similar properties to AR Sco, of which 26 were previously uncharacterised. These were subject to spectroscopic and photometric follow-up observations. Aside from one new binary white dwarf pulsar found, J191213.72-441045.1, which was reported in a separate work, we find no other systems whose characteristics are akin to AR Sco. The newly characterised systems are primarily young stellar objects (with 10 found) or cataclysmic variables (7 identifications), with the remaining being either blended or non-variable on short timescales.

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arXiv2025

Two almost planetary mass survivors of common envelope evolution

White dwarfs are often found in close binaries with stellar or even substellar companions. It is generally thought that these compact binaries form via common envelope evolution, triggered by the progenitor of the white dwarf expanding after it evolved off the main-sequence and engulfing its companion. To date, a handful of white dwarfs in compact binaries with substellar companions have been found, typically with masses greater than around 50 M$_\mathrm{Jup}$. Here we report the discovery of two eclipsing white dwarf plus brown dwarf binaries containing very low mass brown dwarfs. ZTF J1828+2308 consists of a hot ($15900\pm75$ K) $0.610\pm0.004$ M$_{\odot}$ white dwarf in a 2.7 hour binary with a $0.0186\pm0.0008$ M$_{\odot}$ ($19.5\pm0.8$ M$_\mathrm{Jup}$) brown dwarf. ZTF J1230$-$2655 contains a cool ($10000\pm110$ K) $0.65\pm0.02$ M$_{\odot}$ white dwarf in a 5.7 hour binary with a companion that has a mass of less than 0.0211 M$_{\odot}$ (22.1 M$_\mathrm{Jup}$). While the brown dwarf in ZTF J1828+2308 has a radius consistent with its mass and age, ZTF J1230$-$2655 contains a roughly 20 per cent overinflated brown dwarf for its age. We are only able to reconstruct the common envelope phase for either system if it occurred after the first thermal pulse, when the white dwarf progenitor had already lost a significant fraction of its original mass. This is true even for very high common envelope ejection efficiencies ($α_\mathrm{CE}\sim 1$), unless both systems have extremely low metallicities. It may be that the lowest mass companions can only survive a common envelope phase if it occurs at this very late stage.

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arXiv2024

Calibrating the clock of JWST

JWST, despite not being designed to observe astrophysical phenomena that vary on rapid time scales, can be an unparalleled tool for such studies. If timing systematics can be controlled, JWST will be able to open up the sub-second infrared timescale regime. Rapid time-domain studies, such as lag measurements in accreting compact objects and Solar System stellar occultations, require both precise inter-frame timing and knowing when a time series begins to an absolute accuracy significantly below 1s. In this work we present two long-duration observations of the deeply eclipsing double white dwarf system ZTF J153932.16+502738.8, which we use as a natural timing calibrator to measure the absolute timing accuracy of JWST's clock. From our two epochs, we measure an average clock accuracy of $0.12\pm0.06$s, implying that JWST can be used for sub-second time-resolution studies down to the $\sim100$ms level, a factor $\sim5$ improvement upon the pre-launch clock accuracy requirement. We also find an asymmetric eclipse profile in the F322W2 band, which we suggest has a physical origin.

astro-ph.IM↗

arXiv2024

A Survey for Radio Emission from White Dwarfs in the VLA Sky Survey

Radio emission has been detected from tens of white dwarfs, in particular in accreting systems. Additionally, radio emission has been predicted as a possible outcome of a planetary system around a white dwarf. We searched for 3 GHz radio continuum emission in 846,000 candidate white dwarfs previously identified in Gaia using the Very Large Array Sky Survey (VLASS) Epoch 1 Quick Look Catalogue. We identified 13 candidate white dwarfs with a counterpart in VLASS within 2". Five of those were found not to be white dwarfs in follow-up or archival spectroscopy, whereas seven others were found to be chance alignments with a background source in higher-resolution optical or radio images. The remaining source, WDJ204259.71+152108.06, is found to be a white dwarf and M-dwarf binary with an orbital period of 4.1 days and long-term stochastic optical variability, as well as luminous radio and X-ray emission. For this binary, we find no direct evidence of a background contaminant, and a chance alignment probability of only ~2 per cent. However, other evidence points to the possibility of an unfortunate chance alignment with a background radio and X-ray emitting quasar, including an unusually poor Gaia DR3 astrometric solution for this source. With at most one possible radio emitting white dwarf found, we conclude that strong (> 1-3 mJy) radio emission from white dwarfs in the 3 GHz band is virtually nonexistent outside of interacting binaries.

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arXiv2024

Soft X-ray prompt emission from a high-redshift gamma-ray burst EP240315a

Long gamma-ray bursts (GRBs) are believed to originate from core collapse of massive stars. High-redshift GRBs can probe the star formation and reionization history of the early universe, but their detection remains rare. Here we report the detection of a GRB triggered in the 0.5--4 keV band by the Wide-field X-ray Telescope (WXT) on board the Einstein Probe (EP) mission, designated as EP240315a, whose bright peak was also detected by the Swift Burst Alert Telescope and Konus-Wind through off-line analyses. At a redshift of $z=4.859$, EP240315a showed a much longer and more complicated light curve in the soft X-ray band than in gamma-rays. Benefiting from a large field-of-view ($\sim$3600 deg$^2$) and a high sensitivity, EP-WXT captured the earlier engine activation and extended late engine activity through a continuous detection. With a peak X-ray flux at the faint end of previously known high-$z$ GRBs, the detection of EP240315a demonstrates the great potential for EP to study the early universe via GRBs.

astro-ph.HE↗

arXiv2024

The double low-mass white dwarf eclipsing binary system J2102-4145 and its possible evolution

Approximately 150 low-mass white dwarfs, with masses below 0.4Msun, have been discovered. The majority of these low-mass WDs are observed in binary systems as they cannot be formed through single-star evolution within the Hubble time. In this study, we present a comprehensive analysis of the double low-mass WD eclipsing binary system J2102-4145. Our investigation involved an extensive observational campaign, resulting in the acquisition of approximately 28 hours of high-speed photometric data across multiple nights using NTT/ULTRACAM, SOAR/Goodman, and SMARTS-1m telescopes. These observations have provided critical insights into the orbital characteristics of this system, including parameters such as inclination and orbital period. To disentangle the binary components of J2102-4145, we employed the XT GRID spectral fitting method with GMOS/Gemini-South and X-Shooter data. Additionally, we used the PHOEBE package for light curve analysis on NTT/ULTRACAM high-speed time-series photometry data to constrain the binary star properties. Our analysis reveals remarkable similarities between the two components of this binary system. For the primary star, we determined Teff1 = 13688 +- 65 K, log g1 = 7.36 +- 0.01, R1 = 0.0211 +- 0.0002 Rsun, and M1 = 0.375 +- 0.003 Msun, while the secondary star is characterized by Teff2 = 12952 +- 53 K, log g2 = 7.32 +- 0.01, R2 = 0.0203 +- 0.0002 Rsun, and M2 = 0.31 +- 0.003 Msun. Furthermore, we observe a notable discrepancy between Teff and R of the less massive WD compared to evolutionary sequences for WDs from the literature, which has significant implications for our understanding of WD evolution. We discuss a potential formation scenario for this system that might explain this discrepancy and explore its future evolution. We predict that this system will merge in about 800 Myr, evolving into a helium-rich hot subdwarf star and later into a hybrid He/CO WD.

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arXiv2023

The donor star radial velocity curve in the cataclysmic variable GY Cnc confirms white dwarf eclipse modelling mass

A large number of white dwarf and donor masses in cataclysmic variables have been found via modelling the primary eclipse, a method that relies on untested assumptions. Recent measurements of the mass of the white dwarf in the cataclysmic variable GY Cnc, obtained via modelling its ultraviolet spectrum, conflict with the mass obtained via modelling the eclipse light curve. Here we measure the radial velocity of the absorption lines from the donor star in GY Cnc to be $K_{\rm abs} = 280 \pm 2$ kms$^{-1}$, in excellent agreement with the prediction based on the masses derived from modelling the eclipse light curve. It is possible that the white dwarf mass derived from the ultraviolet spectrum of GY Cnc is affected by the difficulty of disentangling the white dwarf spectrum from the accretion disc spectrum.

astro-ph.SR↗

arXiv2023

TIC 378898110: A Bright, Short-Period AM CVn Binary in TESS

AM CVn-type systems are ultracompact, helium-accreting binary systems which are evolutionarily linked to the progenitors of thermonuclear supernovae and are expected to be strong Galactic sources of gravitational waves detectable to upcoming space-based interferometers. AM CVn binaries with orbital periods $\lesssim$ 20--23 min exist in a constant high state with a permanently ionised accretion disc. We present the discovery of TIC 378898110, a bright ($G=14.3$ mag), nearby ($309.3 \pm 1.8$ pc), high-state AM CVn binary discovered in TESS two-minute-cadence photometry. At optical wavelengths this is the third-brightest AM CVn binary known. The photometry of the system shows a 23.07172(6) min periodicity, which is likely to be the `superhump' period and implies an orbital period in the range 22--23 min. There is no detectable spectroscopic variability. The system underwent an unusual, year-long brightening event during which the dominant photometric period changed to a shorter period (constrained to $20.5 \pm 2.0$ min), which we suggest may be evidence for the onset of disc-edge eclipses. The estimated mass transfer rate, $\log (\dot{M} / \mathrm{M_\odot} \mathrm{yr}^{-1}) = -6.8 \pm 1.0$, is unusually high and may suggest a high-mass or thermally inflated donor. The binary is detected as an X-ray source, with a flux of $9.2 ^{+4.2}_{-1.8} \times 10^{-13}$ erg cm$^{-2}$ s$^{-1}$ in the 0.3--10 keV range. TIC 378898110 is the shortest-period binary system discovered with TESS, and its large predicted gravitational-wave amplitude makes it a compelling verification binary for future space-based gravitational wave detectors.

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arXiv2023

An Eclipsing 47 minute Double White Dwarf Binary at 400 pc

We present the discovery of the eclipsing double white dwarf (WD) binary WDJ 022558.21-692025.38 that has an orbital period of 47.19 min. Following identification with the Transiting Exoplanet Survey Satellite, we obtained time-series ground based spectroscopy and high-speed multi-band ULTRACAM photometry which indicate a primary DA WD of mass 0.40 +- 0.04 Msol and a 0.28 +- 0.02 Msol mass secondary WD, which is likely of type DA as well. The system becomes the third-closest eclipsing double WD binary discovered with a distance of approximately 400 pc and will be a detectable source for upcoming gravitational wave detectors in the mHz frequency range. Its orbital decay will be measurable photometrically within 10 yrs to a precision of better than 1%. The fate of the binary is to merge in approximately 41 Myr, likely forming a single, more massive WD.

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