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B. T. Gänsicke

Publications and source records attributed to B. T. Gänsicke.

At least 91 records · Page 5Linked to original sources

NLTT5306: The shortest Period Detached White Dwarf + Brown Dwarf Binary

We have spectroscopically confirmed a brown dwarf mass companion to the hydrogen atmosphere white dwarf NLTT5306. The white dwarf's atmospheric parameters were measured using Sloan Digital Sky Survey and X-Shooter spectroscopy as T_eff=7756+/-35K and log(g)=7.68+/-0.08, giving a mass for the primary of M_WD=0.44+/-0.04 M_sun, at a distance of 71+/-4 pc with a cooling age of 710+/-50 Myr. The existence of the brown dwarf secondary was confirmed through the near-infrared arm of the X-Shooter data and a spectral type of dL4-dL7 was estimated using standard spectral indices. Combined radial velocity measurements from the Sloan Digital Sky Survey, X-Shooter and the Hobby-Eberly Telescope's High Resolution Spectrograph of the white dwarf gives a minimum mass of 56+/-3 M_jup for the secondary, confirming the substellar nature. The period of the binary was measured as 101.88+/-0.02 mins using both the radial velocity data and i'-band variability detected with the INT. This variability indicates 'day' side heating of the brown dwarf companion. We also observe Hα emission in our higher resolution data in phase with the white dwarf radial velocity, indicating this system is in a low level of accretion, most likely via a stellar wind. This system represents the shortest period white dwarf + brown dwarf binary and the secondary has survived a stage of common envelope evolution, much like its longer period counterpart, WD0137-349. Both systems likely represent bona-fide progenitors of cataclysmic variables with a low mass white dwarf and a brown dwarf donor.

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Eclipsing Post Common Envelope Binaries from the Catalina Surveys

We analyse the Catalina Real-time Transient Survey light curves of 835 spectroscopically confirmed white dwarf plus main-sequence binaries from the Sloan Digital Sky Survey (SDSS) with g<19, in search of new eclipsing systems. We identify 29 eclipsing systems, 12 of which were previously unknown. This brings the total number of eclipsing white dwarf plus main-sequence binaries to 49. Our set of new eclipsing systems contains two with periods of 1.9 and 2.3 days making them the longest period eclipsing white dwarf binaries known. We also identify one system which shows very large ellipsoidal modulation (almost 0.3 magnitudes), implying that the system is both very close to Roche-lobe overflow and at high inclination. However, our follow up photometry failed to firmly detect an eclipse meaning that this system either contains a cool white dwarf and hence the eclipse is very shallow and undetectable in our red-sensitive photometry or that it is non-eclipsing. Radial velocity measurements for the main-sequence stars in three of our newly identified eclipsing systems imply that their white dwarf masses are lower than those inferred from modelling their SDSS spectra. 13 non-eclipsing post common envelope binaries were also identified, from either reflection or ellipsoidal modulation effects. The white dwarfs in our newly discovered eclipsing systems span a wide range of parameters, including; low mass (~0.3Msol), very hot (80,000K) and a DC white dwarf. The spectral types of the main-sequence stars range from M2 to M6. This makes our sample ideal for testing white dwarf and low-mass star mass-radius relationships as well as close binary evolution.

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IPHAS J062746.41+014811.3: a deeply eclipsing intermediate polar

We present time-resolved photometry of a cataclysmic variable discovered in the Isaac Newton Telescope Photometric Halpha Survey of the northern galactic plane, IPHAS J062746.41+014811.3 and classify the system as the fourth deeply eclipsing intermediate polar known with an orbital period of Porb=8.16 h, and spin period of Pspin=2210 s. The system shows mild variations of its brightness, that appear to be accompanied by a change in the amplitude of the spin modulation at optical wavelengths, and a change in the morphology of the eclipse profile. The inferred magnetic moment of the white dwarf is mu_wd = 6-7 x 10^33 Gcm^3, and in this case IPHAS J0627 will either evolve into a short-period EX Hya-like intermediate polar with a large Pspin\Porb ratio, or, perhaps more likely, into a synchronised polar. Swift observations show that the system is an ultraviolet and X-ray source, with a hard X-ray spectrum that is consistent with those seen in other intermediate polars. The ultraviolet light curve shows orbital modulation and an eclipse, while the low signal-to-noise ratio X-ray light curve does not show a significant modulation on the spin period. The measured X-ray flux is about an order of magnitude lower than would be expected from scaling by the optical fluxes of well-known X-ray selected intermediate polars.

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An accurate mass and radius measurement for an ultracool white dwarf

Studies of cool white dwarfs in the solar neighbourhood have placed a limit on the age of the Galactic disk of 8-9 billion years. However, determining their cooling ages requires the knowledge of their effective temperatures, masses, radii, and atmospheric composition. So far, these parameters could only be inferred for a small number of ultracool white dwarfs for which an accurate distance is known, by fitting their spectral energy distributions (SEDs) in conjunction with a theoretical mass-radius relation. However, the mass-radius relation remains largely untested, and the derived cooling ages are hence model-dependent. Here we report direct measurements of the mass and radius of an ultracool white dwarf in the double-lined eclipsing binary SDSS J013851.54-001621.6. We find M(WD)=0.529+/-0.010Msol and R(WD)=0.0131+/-0.0003Rsol. Our measurements are consistent with the mass-radius relation and we determine a robust cooling age of 9.5 billion years for the 3570K white dwarf. We find that the mass and radius of the low mass companion star, M(sec)=0.132+/-0.003Msol and R(sec)=0.165+/-0.001Rsol, are in agreement with evolutionary models. We also find evidence that this >9.5 Gyr old M5 star is still active, far beyond the activity lifetime for a star of its spectral type. This is likely caused by the high tidally-enforced rotation rate of the star. The companion star is close to filling its Roche lobe and the system will evolve into a cataclysmic variable in only 70 Myr. Our direct measurements demonstrate that this system can be used to calibrate ultracool white dwarf atmospheric models.

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Scars of Intense Accretion Episodes at Metal-Rich White Dwarfs

A re-evaluation of time-averaged accretion rates at DBZ-type white dwarfs points to historical, time-averaged rates significantly higher than the currently observed episodes at their DAZ counterparts. The difference between the ongoing, instantaneous accretion rates witnessed at DAZ white dwarfs, which often exceed 1e8 g/s, and those inferred over the past 1e5-1e6 yr for the DBZ stars can be a few orders of magnitude, and therefore must result from high-rate episodes of tens to hundreds of years so they remain undetected to date. This paper explores the likelihood that such brief, intense accretion episodes of gas-phase material can account for existing data. For reasonable assumptions about the circumstellar gas, accretion rates approaching or exceeding 1e15 g/s are possible, similar to rates observed in quiescent cataclysmic variables, and potentially detectable with future x-ray missions or wide-field monitoring facilities. Gaseous debris that is prone to such rapid accretion may be abundant immediately following a tidal disruption event via collisions and sublimation, or if additional bodies impinge upon an extant disk. Particulate disk matter accretes at or near the Poynting-Robertson drag rate for long periods between gas-producing events, consistent with rates inferred for dusty DAZ white dwarfs. In this picture, warm DAZ stars without infrared excesses have rates consistent with accretion from particulate disks that remain undetected. This overall picture has implications for quasi-steady state models of accretion and the derived chemical composition of asteroidal debris in DBZ white dwarfs.

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The Unseen Population of F to K-type Companions to Hot Subdwarf Stars

We present a method to select hot subdwarf stars with A to M-type companions using photometric selection criteria. We cover a wide range in wavelength by combining GALEX ultraviolet data, optical photometry from the SDSS and the Carlsberg Meridian telescope, near-infrared data from 2MASS and UKIDSS. We construct two complimentary samples, one by matching GALEX, CMC and 2MASS, as well as a smaller, but deeper, sample using GALEX, SDSS and UKIDSS. In both cases, a large number of composite subdwarf plus main-sequence star candidates were found. We fit their spectral energy distributions with a composite model in order to estimate the subdwarf and companion star effective temperatures along with the distance to each system. The distribution of subdwarf effective temperature was found to primarily lie in the 20,000 - 30,000 K regime, but we also find cooler subdwarf candidates, making up ~5-10 per cent. The most prevalent companion spectral types were seen to be main-sequence stars between F0 and K0, while subdwarfs with M-type companions appear much rarer. This is clear observational confirmation that a very efficient first stable Roche-lobe overflow channel appears to produce a large number of subdwarfs with F to K-type companions. Our samples thus support the importance of binary evolution for subdwarf formation.

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Initial data release of the Kepler-INT Survey

This paper describes the first data release of the Kepler-INT Survey (KIS), that covers a 116 deg2 region of the Cygnus and Lyra constellations. The Kepler field is the target of the most intensive search for transiting planets to date. Despite the fact that the Kepler mission provides superior time series photometry, with an enormous impact on all areas of stellar variability, its field lacks optical photometry complete to the confusion limit of the Kepler instrument necessary for selecting various classes of targets. For this reason, we follow the observing strategy and data reduction method used in the IPHAS and UVEX galactic plane surveys in order to produce a deep optical survey of the Kepler field. This initial release concerns data taken between May and August 2011, using the Isaac Newton Telescope on the island of La Palma. Four broadband filters were used, U, g, r, i, as well as one narrowband one, Halpha, reaching down to a 10-sigma limit of around 20th mag in the Vega system. Observations covering around 50 deg2, thus about half of the field, passed our quality control thresholds and constitute this first data release. We derive a global photometric calibration by placing the KIS magnitudes as close as possible to the Kepler Input Catalog (KIC) photometry. The initial data release catalogue containing around 6 million sources from all the good photometric fields is available for download from the KIS webpage, as well as via MAST.

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Mass ratio from Doppler beaming and Rømer delay versus ellipsoidal modulation in the Kepler data of KOI-74

We present a light curve analysis and radial velocity study of KOI-74, an eclipsing A star + white dwarf binary with a 5.2 day orbit. Aside from new spectroscopy covering the orbit of the system, we used 212 days of publicly available Kepler observations and present the first complete light curve fitting to these data, modelling the eclipses and transits, ellipsoidal modulation, reflection, and Doppler beaming. Markov Chain Monte Carlo simulations are used to determine the system parameters and uncertainty estimates. Our results are in agreement with earlier studies, except that we find an inclination of 87.0 \pm 0.4\degree, which is significantly lower than the previously published value. We find that the mass ratio derived from the radial velocity amplitude (q=0.104 \pm 0.004) disagrees with that derived from the ellipsoidal modulation (q=0.052 \pm 0.004} assuming corotation). This was found before, but with our smaller inclination, the discrepancy is even larger than previously reported. Accounting for the rapid rotation of the A-star is found to increase the discrepancy even further by lowering the mass ratio to q=0.047 \pm 0.004. These results indicate that one has to be extremely careful in using the amplitude of an ellipsoidal modulation signal in a close binary to determine the mass ratio, when a proof of corotation is not firmly established. The radial velocities that can be inferred from the detected Doppler beaming in the light curve are found to be in agreement with our spectroscopic radial velocity determination. We also report the first measurement of Rømer delay in a light curve of a compact binary. This delay amounts to -56 \pm 17 s and is consistent with the mass ratio derived from the radial velocity amplitude. The firm establishment of this mass ratio at q=0.104 \pm 0.004 leaves little doubt that the companion of KOI-74 is a low mass white dwarf.

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The fight for accretion: discovery of intermittent mass transfer in BB Doradus in the low state

Our long-term photometric monitoring of southern nova-like cataclysmic variables with the 1.3-m SMARTS telescope found BB Doradus fading from V ~ 14.3 towards a deep low state at V ~ 19.3 in April 2008. Here we present time-resolved optical spectroscopy of BB Dor in this faint state in 2009. The optical spectrum in quiescence is a composite of a hot white dwarf with Teff = 30000 +- 5000 K and a M3-4 secondary star with narrow emission lines (mainly of the Balmer series and HeI) superposed. We associate these narrow profiles with an origin on the donor star. Analysis of the radial velocity curve of the H-alpha emission from the donor star allowed the measurement of an orbital period of 0.154095 +- 0.000003 d (3.69828 +- 0.00007 h), different from all previous estimates. We detected episodic accretion events which veiled the spectra of both stars and radically changed the line profiles within a timescale of tens of minutes. This shows that accretion is not completely quenched in the low state. During these accretion episodes the line wings are stronger and their radial velocity curve is delayed by ~ 0.2 cycle, similar to that observed in SW Sex and AM Her stars in the high state, with respect to the motion of the white dwarf. Two scenarios are proposed to explain the extra emission: impact of the material on the outer edge of a cold, remnant accretion disc, or the combined action of a moderately magnetic white dwarf (B1 <~ 5 MG) and the magnetic activity of the donor star.

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Constraints on the Lifetimes of Disks Resulting from Tidally Destroyed Rocky Planetary Bodies

Spitzer IRAC observations of 15 metal-polluted white dwarfs reveal infrared excesses in the spectral energy distributions of HE 0110-5630, GD 61, and HE 1349-2305. All three of these stars have helium-dominated atmospheres, and their infrared emissions are consistent with warm dust produced by the tidal destruction of (minor) planetary bodies. This study brings the number of metal-polluted, helium and hydrogen atmosphere white dwarfs surveyed with IRAC to 53 and 38 respectively. It also nearly doubles the number of metal-polluted helium-rich white dwarfs found to have closely orbiting dust by Spitzer. From the increased statistics for both atmospheric types with circumstellar dust, we derive a typical disk lifetime of log[t_{disk} (yr)] = 5.6+-1.1 (ranging from 3*10^4 - 5*10^6 yr). This assumes a relatively constant rate of accretion over the timescale where dust persists, which is uncertain. We find that the fraction of highly metal-polluted helium-rich white dwarfs that have an infrared excess detected by Spitzer is only 23 per cent, compared to 48 per cent for metal-polluted hydrogen-rich white dwarfs, and we conclude from this difference that the typical lifetime of dusty disks is somewhat shorter than the diffusion time scales of helium-rich white dwarf. We also find evidence for higher time-averaged accretion rates onto helium-rich stars compared to the instantaneous accretion rates onto hydrogen-rich stars; this is an indication that our picture of evolved star-planetary system interactions is incomplete. We discuss some speculative scenarios that can explain the observations.

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Discovery of a stripped red giant core in a bright eclipsing binary star

We report the serendipitous discovery from WASP archive photometry of a binary star in which an apparently normal A-type star (J0247-25A) eclipses a smaller, hotter subdwarf star (J0247-25B). The kinematics of J0247-25A show that it is a blue-straggler member of the Galactic thick-disk. We present follow-up photometry and spectroscopy from which we derive approximate values for the mass, radius and luminosity for J0247-25B assuming that J0247-25A has the mass appropriate for a normal thick-disk star. We find that the properties of J0247-25B are well matched by models for a red giant stripped of its outer layers and currently in a shell hydrogen-burning stage. In this scenario, J0247-25B will go on to become a low mass white dwarf (M~0.25 solar masses) composed mostly of helium. J0247-25B can be studied in much greater detail than the handful of pre helium white dwarfs (pre-He-WD) identified to-date. These results have been published by Maxted et al., 2011. We also present a preliminary analysis of more recent observations of J0247-25 with the UVES spectrograph, from which we derive much improved masses for both stars in the binary. We find that both stars are more massive than expected and that J0247-25A rotates sub-synchronously by a factor of about 2. We also present lightcurves for 5 new eclipsing pre-He-WD subsequently identified from the WASP archive photometry, 4 of which have mass estimates for the subdwarf companion based on a pair of radial velocity measurements.

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A Trio of Metal-Rich Dust and Gas Disks Found Orbiting Candidate White Dwarfs with K-Band Excess

This paper reports follow-up photometric and spectroscopic observations, including warm Spitzer IRAC photometry of seven white dwarfs from the SDSS with apparent excess flux in UKIDSS K-band observations. Six of the science targets were selected from 16,785 DA star candidates identified either spectroscopically or photometrically within SDSS DR7, spatially cross-correlated with HK detections in UKIDSS DR8. Thus the selection criteria are completely independent of stellar mass, effective temperature above 8000 K, and the presence (or absence) of atmospheric metals. The infrared fluxes of one target are compatible with a spatially-unresolved late M or early L-type companion, while three stars exhibit excess emissions consistent with warm circumstellar dust. These latter targets have spectral energy distributions similar to known dusty white dwarfs with high fractional infrared luminosities (thus the K-band excesses). Optical spectroscopy reveals the stars with disk-like excesses are polluted with heavy elements, denoting the ongoing accretion of circumstellar material. One of the disks exhibits a gaseous component - the fourth reported to date - and orbits a relatively cool star, indicating the gas is produced via collisions as opposed to sublimation, supporting the picture of a recent event. The resulting statistics yield a lower limit of 0.8% for the fraction dust disks at DA-type white dwarfs with cooling ages less than 1 Gyr. Two overall results are noteworthy: all stars whose excess infrared emission is consistent with dust are metal-rich; and no stars warmer than 25,000 K are found to have this type of excess, despite sufficient sensitivity.

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The low states of CVs at the upper edge of the period gap

We review our knowledge of the origin and phenomenology of low states (also known as VY Scl states) in cataclysmic variables, making special emphasis on the cataclysmic variable population found just above the period gap. This orbital period range between approximately 3 and 4 hours is the preferred land for the elusive SW Sextantis stars, which are believed to be about to enter the gap when their donor stars become fully convective. Despite their main role in our understanding of the whole picture of cataclysmic variable evolution, the study of their component stars is almost impossible due to the extreme veiling brightness of the accretion disc during the high state. Here we present the first steps toward the characterisation of the white dwarfs and the donor stars in these VY Scl systems in the low state, and the discovery of sporadic accretion events and satellite emission lines like those observed in the AM Her systems in the low state, which are likely related to magnetic activity of the fast rotating secondary stars.

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A precision study of two eclipsing white dwarf plus M dwarf binaries

We use a combination of X-shooter spectroscopy, ULTRACAM high-speed photometry and SOFI near-infrared photometry to measure the masses and radii of both components of the eclipsing post common envelope binaries SDSS J1212-0123 and GK Vir. For both systems we measure the gravitational redshift of the white dwarf and combine it with light curve model fits to determine the inclinations, masses and radii. For SDSS J1212-0123 we find a white dwarf mass and radius of 0.439 +/- 0.002 Msun and 0.0168 +/- 0.0003 Rsun, and a secondary star mass and radius of 0.273 +/- 0.002 Msun and 0.306 +/- 0.007 Rsun. For GK Vir we find a white dwarf mass and radius of 0.564 +/- 0.014 Msun and 0.0170 +/- 0.0004 Rsun, and a secondary star mass and radius of 0.116 +/- 0.003 Msun and 0.155 +/- 0.003 Rsun. The mass and radius of the white dwarf in GK Vir are consistent with evolutionary models for a 50,000K carbon-oxygen core white dwarf. Although the mass and radius of the white dwarf in SDSS J1212-0123 are consistent with carbon-oxygen core models, evolutionary models imply that a white dwarf with such a low mass and in a short period binary must have a helium core. The mass and radius measurements are consistent with helium core models but only if the white dwarf has a very thin hydrogen envelope, which has not been predicted by evolutionary models. The mass and radius of the secondary star in GK Vir are consistent with evolutionary models after correcting for the effects of irradiation by the white dwarf. The secondary star in SDSS J1212-0123 has a radius ~9 per cent larger than predicted.

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Post-common-envelope binaries from SDSS. XIII: Mass dependencies of the orbital period distribution

Post-common-envelope binaries (PCEBs) consisting of a white dwarf (WD) and a main-sequence secondary star are ideal systems to constrain models of common-envelope (CE) evolution. Until very recently, observed samples of PCEBs have been too small to fully explore this potential, however the recently identified large and relatively homogenous sample of PCEBs from the Sloan Digital Sky Survey (SDSS) has significantly changed this situation. We here analyze the orbital period distributions of PCEBs containing He- and C/O-core WDs separately and investigate whether the orbital period of PCEBs is related to the masses of their stellar components. We performed standard statistical tests to compare the orbital period distributions and to determine the confidence levels of possible relations. The orbital periods of PCEBs containing He-core WDs are significantly shorter than those of PCEBs containing C/O-core WDs. While the He-core PCEB orbital period distribution has a median value of Porb ~ 0.28 d, the median orbital period for PCEBs containing C/O-core WDs is Porb ~ 0.57 d. We also find that systems containing more massive secondaries have longer post-CE orbital periods, in contradiction to recent predictions. Our observational results provide new constraints on theories of CE evolution. However we suggest future binary population models to take selection effects into account that still affect the current observed PCEB sample.

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Post common envelope binaries from SDSS. XII: The orbital period distribution

The complexity of the common envelope phase and of magnetic stellar wind braking currently limits our understanding of close binary evolution. Because of their intrinsically simple structure, observational population studies of white dwarf plus main sequence (WDMS) binaries hold the potential to test theoretical models and constrain their parameters. The Sloan Digital Sky Survey (SDSS) has provided a large and homogeneously selected sample of WDMS binaries, which we are characterising in terms of orbital and stellar parameters. We have obtained radial velocity information for 385 WDMS binaries from follow-up spectroscopy, and for an additional 861 systems from the SDSS sub-spectra. Radial velocity variations identify 191 of these WDMS binaries as post common envelope binaries (PCEBs). Orbital periods of 58 PCEBs were subsequently measured, predominantly from time-resolved spectroscopy, bringing the total number of SDSS PCEBs with orbital parameters to 79. Observational biases inherent to this PCEB sample were evaluated through extensive Monte Carlo simulations. We find that 21-24% of all SDSS WDMS binaries have undergone common envelope evolution, which is in good agreement with published binary population models and high-resolution HST imaging of WDMS binaries unresolved from the ground. The bias corrected orbital period distribution of PCEBs ranges from 1.9 h to 4.3 d and follows approximately a normal distribution in log(Porb), peaking at ~10.3 h. There is no observational evidence for a significant population of PCEBs with periods in the range of days to weeks. The large and homogeneous sample of SDSS WDMS binaries provides the means to test fundamental predictions of binary population models, and hence to observationally constrain the evolution of all close compact binaries.

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The shortest period detached white dwarf + main-sequence binary

We present high-speed ULTRACAM and SOFI photometry and X-shooter spectroscopy of the recently discovered 94 minute orbital period eclipsing white dwarf / main-sequence binary SDSS J085746.18+034255.3 (CSS 03170) and use these observations to measure the system parameters. We detect a shallow secondary eclipse and hence are able to determine an orbital inclination of 85.5 +/- 0.2 deg. The white dwarf has a mass of 0.51 +/- 0.05 Msun and a radius of 0.0247 +/- 0.0008 Rsun. With a temperature of 35,300 +/- 400K the white dwarf is highly over-inflated if it has a carbon-oxygen core, however if it has a helium core then its mass and radius are consistent with evolutionary models. Therefore, the white dwarf in SDSS J085746.18+034255.3 is most likely a helium core white dwarf with a mass close to the upper limit expected from evolution. The main-sequence star is an M8 dwarf with a mass of 0.09 +/- 0.01 Msun and a radius of 0.110 +/- 0.004 Rsun placing it close to the hydrogen burning limit. The system emerged from a common envelope ~20 million years ago and will reach a semi-detached configuration in ~400 million years, becoming a cataclysmic variable with a period of 66 minutes, below the period minimum.

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Post-common-envelope binaries from SDSS. XI: The white dwarf mass distributions of CVs and pre-CVs

We have known for a long time that many of the measured white dwarf (WD) masses in cataclysmic variables (CVs) significantly exceed the mean mass of single WDs. This was thought to be related to observational biases, but recent high-precision measurements of WD masses in a great number of CVs are challenging this interpretation. We review the measured WD masses of CVs, determine the WD-mass distribution of an extensive sample of post-common-envelope binaries (PCEBs) that are representative for the progenitors of the current CV population (pre-CVs) and compare both distributions. We calculate the CV formation time of the PCEBs in our sample by determining the post common-envelope (CE) and the main-sequence evolution of the binary systems and define a pre-CV to be a PCEB that evolves into a semi-detached configuration with stable mass transfer within less than the age of the Galaxy. Possible observational biases affecting the WD-mass distribution for the pre-CV and the CV samples are discussed. The mean WD mass among CVs is =0.83\pm0.23 Msun, much larger than that found for pre-CVs, =0.67\pm0.21 Msun. Selection effects cannot explain the high WD masses observed in CVs and we here suggest two possible explanations, both of which imply substantial revisions to the standard model of CV evolution: either most CVs have formed above the orbital-period gap (which requires a high WD mass to initiate stable mass transfer or a previous phase of thermal-timescale mass transfer), or the mass of the WDs in CVs grows through accretion (which strongly disagrees with the predictions of classical nova models). Both options may imply that CVs contribute to the single-degenerate progenitors of Type Ia supernovae. The number of He-core WDs found in CVs (<=10%) is roughly consistent with the number of He-core WDs in pre-CVs (<=17+-8%), which indicates a low value of the CE efficiency.

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