arXiv subjects

V. F. Suleimanov

Publications and source records attributed to V. F. Suleimanov.

At least 19 recordsLinked to original sources

arXiv2025

X-ray spectroscopy method of white dwarf mass determination in intermediate polars. External systematic uncertainties

The masses of white dwarfs (WDs) in intermediate polars (IPs) can be determined from the shape of their hard X-ray spectra. Here we study the importance of all possible systematic uncertainties in this X-ray spectroscopy method, including finite radii and rotation of magnetospheres, finite accretion column height and accretion-flow inclination relative to the WD surface. We also investigate the importance of accretion-heated envelopes on WD surfaces in IPs which are increasing WD radii. Their presence changes the commonly used mass-radius relation for cold white dwarfs. As a first approximation we use thick ($10^{-4}M_\odot$) hydrogen envelope models with a surface temperature of 30 kK. We present a new model grid of hard X-ray spectra of high-luminous IPs computed among other things with using a new mass-radius relation. This grid is used for fitting Swift/BAT spectra of 47 IPs. The average WD mass in this sample is 0.82 $M_\odot$ and coincides with the average WD mass in cataclysmic variables obtained by optical methods. This means that the calculated hard X-ray spectra and the assumptions made that the magnetospheric radii in IPs are close to the corotation radii, and the relative heights of the accretion columns are small are basically correct, because most IPs have high luminosities. But this universal grid (as well as previous universal grids) cannot give correct results for the low-luminous IPs with probably relatively tall accretion columns on the WD surfaces. Such IPs have to be investigated with individual accretion column models.

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arXiv2025

Examining the evolution of the Supersoft X-ray Source RX J0513.9-6951

Supersoft X-ray sources (SSS) are thought to be accreting white dwarfs (WDs) in close binary systems, with thermonuclear burning on their surfaces. The SSS RX J0513.9-6951 in the Large Magellanic Cloud (LMC) exhibits cyclic variations between optical low and high states, which are anti-correlated with its X-ray flux. This behaviour is believed to result from the periodic expansion and contraction of the WD due to variations in the accretion rate in the system. We analyse eight high-resolution XMM and six grating Chandra spectra of RX J0513.9-6951 with our grid of model atmosphere spectra of hot WDs computed under the assumption of local thermodynamic equilibrium. Our aim is to test a contraction model of the source variability by tracking the evolution of the WD properties. The used grid of hot WD model atmospheres spans a wide range of effective temperatures ($T_{\rm eff}=100-1000\,\rm kK$ in steps of $25\,\rm kK$) and eight values of surface gravity $\log g$. The LMC chemical composition was assumed. The obtained fitting parameters ($T_{\rm eff}$, $\log g$, and bolometric luminosity $L$) evolve on the $T_{\rm eff}- \log g$ and $T_{\rm eff}- L$ planes. This evolution follows the model tracks of WDs with masses of $1.05-1.15\,M_{\odot}$ and thermonuclear burning on the surface. The analysis has showed that the optical brightness of the system is lower when the WD is larger, more luminous, and more effectively illuminates the accretion disc. These results contradict the contraction model, which predicts the opposite behaviour of the source. We use a model, that assumes that the far UV/soft X-ray flux is reprocessed into the optical band due to multiple scattering in the cloud system above the accretion disc. More significant illumination can lead to rarefying of the cloud slab, thereby reducing the reprocessing efficiency and making the source fainter in the optical band.

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arXiv2024

Soft X-ray emission from the classical nova AT 2018bej

Classical novae are known to demonstrate a supersoft X-ray source (SSS) state following outbursts, which is associated with residual thermonuclear burning on the white dwarf (WD) surface. During its all-sky survey (eRASS1), the eROSITA telescope onboard the Spectrum-Roentgen-Gamma observatory discovered a bright new SSS, whose position is consistent with the known classical nova AT 2018bej in the Large Magellanic Cloud. There were two eROSITA spectra obtained during eRASS1 and eRASS2 monitoring epochs and one XMM-Newton grating spectrum close to the eRASS1 epoch. We aim to describe the eROSITA and XMM-Newton spectra of AT 2018bej with our local thermodynamic equilibrium (LTE) atmosphere models. We focused on the evolution of the hot WD properties between the eRASS1 and eRASS2 epochs, especially on the change of the carbon abundance. A grid of LTE model atmosphere spectra were calculated for different values of the effective temperature (from $T_{\rm eff}= 525$ to $700\,\rm kK$), surface gravity (six values) and chemical composition with five different values of carbon and nitrogen abundances. Both eRASS1 and XMM $0.3-0.6$ keV spectral analyses yield a temperature of the WD of $T_{\rm eff}{\sim}\,600\, \rm kK$ and a WD radius of $8000-8700\,\rm km$. Simultaneous fitting of the eROSITA spectra for two epochs (eRASS1 and eRASS2) with a common WD mass parameter demonstrates a decrease in $T_{\rm eff}$ accompanied by an increase in the WD radius and a decrease in the carbon abundance. However, these changes are marginal and coincide within errors. The derived WD mass is estimated to be $1.05-1.15\, M_\odot$. We traced a minor evolution of the source on a half-year timescale accompanied by a decrease in carbon abundance and concluded that LTE model atmospheres can be used to analyse the available X-ray spectra of classical novae during their SSS stage.

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arXiv2024

Comparison of the disk precession models with the photometric behavior of TT Ari in 2021-2023

We present a comparative analysis of photometric observations of the cataclysmic variable TT Ari in its bright state, obtained by the TESS orbital observatory in 2021 and 2023 and by ground-based amateur telescopes in 2022. The light curves from 2021 and 2022 are dominated by modulations with a period slightly shorter than the orbital one (negative superhumps), 0.13292 and 0.13273 d respectively. In 2023, much stronger modulations appeared on a much longer time scale of a few days with an amplitude of up to 0.5 mag, compared to 0.2 mag in 2021. The negative superhump variability with the period of 0.1338 d was also found in the 2023 observations, but the significance of these negative superhumps is much lower than in the previous seasons. Less significant additional modulations with a period exceeding the orbital one (positive superhumps) were detected in 2021 and 2022. Their periods were 0.15106 and 0.1523 d, respectively. We also found a previously unnoticed periodic signal corresponding to the orbital period of 0.13755 d in the TESS observations in 2021. Theoretical models of tidal precession of an elliptical disk predict a decrease in the precession period (and an increase in the positive superhumps period) with increasing disk radius, which is consistent with the observed photometric behavior of the system. It enables us to estimate the mass ratio of the components in TT Ari to be $q$ in the range 0.24-0.29. The tilted disk precession model predicts a period of nodal precession whose value is in general agreement with observations.

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arXiv2024

Application of hydrostatic local thermodynamic equilibrium atmosphere models to interpretations of supersoft X-ray source spectra

Supersoft X-ray sources (SSSs) are accreting white dwarfs (WDs) with stable or recurrent thermonuclear burning on their surfaces. High-resolution X-ray spectra of such objects are rather complex, often consist of several components, and are difficult to interpret accurately. The main emission source is the hot surface of the WD and the emergent radiation can potentially be described by hot WD model atmospheres. We present a new set of such model atmosphere spectra computed in the effective temperature range from $100\rm\,kK$ to $1000\rm\,kK$, for eight values of surface gravity and three different chemical compositions. These compositions correspond to the solar one as well as to the Large and Small Magellanic Clouds, with decreased heavy element abundances, at one-half and one-tenth of the solar value. The presented model grid covers a broad range of physical parameters and, thus, it can be applied to a wide range of objects. It is also publicly available in XSPEC~format. As an illustration, we applied it here for the interpretation of \textit{Chandra} and XMM grating spectra of two classical SSSs, namely, CAL 83 (RX J0543.5$-$6823) and RX J0513.9$-$6951. The obtained effective temperatures and surface gravities of $T_{\rm eff} \approx 560$ kK, $\log g \approx 8.6-8.7$, and $T_{\rm eff} \approx 630\,{\rm kK}, \log g \approx 8.5-8.6$, respectively, are in a good agreement with previous estimations for both sources. The derived WD~mass estimations are within $1.1-1.4\,M_\odot$ for CAL 83 and $1.15-1.4\,M_\odot$ for RX J0513.9$-$6951. The mass of the WD in CAL $83$ is consistent with the mass predicted from the respective model of recurrent thermonuclear burning.

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arXiv2024

SRG/ART-XC discovery of SRGAJ144459.2-604207: a well-tempered bursting accreting millisecond X-ray pulsar

We report on the discovery of the new accreting millisecond X-ray pulsar SRGAJ144459.2-604207 using the SRG/ART-XC data. The source was observed twice in February 2024 during the declining phase of the outburst. Timing analysis revealed a coherent signal near 447.8~Hz modulated by the Doppler effect due to the orbital motion. The derived parameters for the binary system are consistent with the circular orbit with a period of $\sim5.2$~h. The pulse profiles of the persistent emission, showing a sine-like part during half a period with a plateau in between, can well be modelled by emission from two circular spots partially eclipsed by the accretion disk. Additionally, during our 133~ks exposure observations, we detected 19 thermonuclear X-ray bursts. All bursts have similar shapes and energetics, and do not show any signs of photospheric radius expansion. The burst rate decreases linearly from one per $\sim$1.6~h at the beginning of observations to one per $\sim$2.2~h at the end and anticorrelates with the persistent flux. Spectral evolution during the bursts is consistent with the models of the neutron star atmospheres heated by accretion and imply a neutron star radius of 11--12~km and the distance to the source of 8--9~kpc. We also detected pulsations during the bursts and showed that the pulse profiles differ substantially from those observed in the persistent emission. However, we could not find a simple physical model explaining the pulse profiles detected during the bursts.

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arXiv2024

Magnetospheric Flows in X-ray Pulsars I: Instability at super-Eddington regime of accretion

Within the magnetospheric radius, the geometry of accretion flow in X-ray pulsars is shaped by a strong magnetic field of a neutron star. Starting at the magnetospheric radius, accretion flow follows field lines and reaches the stellar surface in small regions located close to the magnetic poles of a star. At low mass accretion rates, the dynamic of the flow is determined by gravitational attraction and rotation of the magnetosphere due to the centrifugal force. At the luminosity range close to the Eddington limit and above it, the flow is additionally affected by the radiative force. We construct a model simulating accretion flow dynamics over the magnetosphere, assuming that the flow strictly follows field lines and is affected by gravity, radiative and centrifugal forces only. The magnetic field of a NS is taken to be dominated by the dipole component of arbitrary inclination with respect to the accretion disc plane. We show that accretion flow becomes unstable at high mass accretion rates and tends to fluctuate quasi-periodically with a typical period comparable to the free-fall time from the inner disc radius. The inclination of a magnetic dipole with respect to the disc plane and strong anisotropy of X-ray radiation stabilise the mass accretion rate at the poles of a star, but the surface density of material covering the magnetosphere fluctuates even in this case.

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arXiv2023

X-ray polarimetry of X-ray pulsar X Persei: another orthogonal rotator?

X Persei is a persistent low-luminosity X-ray pulsar of period of $\sim$835 s in a Be binary system. The field strength at the neutron star surface is not known precisely, but indirect signs indicate a magnetic field above $10^{13}$ G, which makes the object one of the most magnetized known X-ray pulsars. Here we present the results of observations X Persei performed with the Imaging X-ray Polarimetry Explorer (IXPE). The X-ray polarization signal was found to be strongly dependent on the spin phase of the pulsar. The energy-averaged polarization degree in 3-8 keV band varied from several to $\sim$20 per cent over the pulse with a positive correlation with the pulsed X-ray flux. The polarization angle shows significant variation and makes two complete revolutions during the pulse period resulting in nearly nil pulse-phase averaged polarization. Applying the rotating vector model to the IXPE data we obtain the estimates for the rotation axis inclination and its position angle on the sky as well as for the magnetic obliquity. The derived inclination is close to the orbital inclination reported earlier for X Persei. The polarimetric data imply a large angle between the rotation and magnetic dipole axes, which is similar to the result reported recently for the X-ray pulsar GRO J1008$-$57. After eliminating the effect of polarization angle rotation over the pulsar phase using the best-fitting rotating vector model, the strong dependence of the polarization degree with energy was discovered with its value increasing from 0% at $\sim$2 keV to 30% at 8 keV.

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arXiv2022

Likely optical counterpart of the cool middle-aged pulsar J1957+5033

The 840 kyr old pulsar PSR J1957+5033, detected so far only in $γ$- and X-rays, is a nearby and rather cool neutron star with a temperature of 0.2--0.3 MK, a distance of $\la$1 kpc, and a small colour reddening excess $E(B-V) \approx 0.03$. These properties make it an ideal candidate to detect in the optical to get additional constraints on its parameters. We thus performed the first deep optical observations of the pulsar with the 10.4-meter Gran Telescopio Canarias in the $g'$ band and found its possible counterpart with $g'=27.63\pm 0.26$. The counterpart candidate position is consistent with the X-ray coordinates of the pulsar within the 0.5 arcsec accuracy. Assuming that this is the real counterpart, we analysed the pulsar X-ray spectrum together with the derived optical flux density. As a result, we found that the thermal emission from the bulk surface of the cooling neutron star can significantly contribute to its optical flux. Our multi-wavelength spectral analysis favours the pulsar nature of the detected optical source, since it provides physically adequate parameters of the pulsar emission. We show that the optical data can provide new constraints on the pulsar temperature and distance.

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arXiv2021

Middle aged $γ$-ray pulsar J1957+5033 in X-rays: pulsations, thermal emission and nebula

We analyze new XMM-Newton and archival Chandra observations of the middle-aged $γ$-ray radio-quiet pulsar J1957+5033. We detect, for the first time, X-ray pulsations with the pulsar spin period of the point-like source coinciding by position with the pulsar. This confirms the pulsar nature of the source. In the 0.15--0.5 keV band, there is a single pulse per period and the pulsed fraction is $\approx18\pm6$ per cent. In this band, the pulsar spectrum is dominated by a thermal emission component that likely comes from the entire surface of the neutron star, while at higher energies ($\gtrsim0.7$ keV) it is described by a power law with the photon index $Γ\approx 1.6$. We construct new hydrogen atmosphere models for neutron stars with dipole magnetic fields and non-uniform surface temperature distributions with relatively low effective temperatures. We use them in the spectral analysis and derive the pulsar average effective temperature of $\approx(2-3)\times10^5$ K. This makes J1957+5033 the coldest among all known thermally emitting neutron stars with ages below 1 Myr. Using the interstellar extinction--distance relation, we constrain the distance to the pulsar in the range of 0.1--1 kpc. We compare the obtained X-ray thermal luminosity with those for other neutron stars and various neutron star cooling models and set some constraints on latter. We observe a faint trail-like feature, elongated $\sim 8$ arcmin from J1957+5033. Its spectrum can be described by a power law with a photon index $Γ=1.9\pm0.5$ suggesting that it is likely a pulsar wind nebula powered by J1957+5033.

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arXiv2020

Measuring the masses of magnetic white dwarfs: A NuSTAR Legacy Survey

The hard X-ray spectrum of magnetic cataclysmic variables can be modelled to provide a measurement of white dwarf mass. This method is complementary to radial velocity measurements, which depend on the (typically rather uncertain) binary inclination. Here we present results from a Legacy Survey of 19 magnetic cataclysmic variables with NuSTAR. We fit accretion column models to their 20-78 keV spectra and derive the white dwarf masses, finding a weighted average $\bar{M}_{\rm WD}=0.77\pm0.02$ $M_{\odot}$, with a standard deviation $σ=0.10$ $M_{\odot}$, when we include the masses derived from previous NuSTAR observations of seven additional magnetic cataclysmic variables. We find that the mass distribution of accreting magnetic white dwarfs is consistent with that of white dwarfs in non-magnetic cataclysmic variables. Both peak at a higher mass than the distributions of isolated white dwarfs and post-common-envelope binaries. We speculate as to why this might be the case, proposing that consequential angular momentum losses may play a role in accreting magnetic white dwarfs and/or that our knowledge of how the white dwarf mass changes over accretion-nova cycles may also be incomplete.

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arXiv2020

Burst-induced coronal cooling in GS 1826-24 The clock wagging its tail

Type I X-ray bursts in GS 1826-24, and in several other systems, may induce cooling of the hot inner accretion flow that surrounds the bursting neutron star. Given that GS 1826-24 remained persistently in the hard state over the period 2003-2008 and presented regular bursting properties, we stacked the spectra of the X-ray bursts detected by INTEGRAL (JEM-X and ISGRI) and XMM-Newton (RGS) during that period to study the effect of the burst photons on the properties of the Comptonizing medium. The extended energy range provided by these instruments allows the simultaneous observation of the burst and persistent emission spectra. We detect an overall change in the shape of the persistent emission spectrum in response to the burst photon shower. For the first time, we observe simultaneously a drop in the hard X-ray emission, together with a soft X-ray excess with respect to the burst blackbody emission. The hard X-ray drop can be explained by burst-induced coronal cooling, while the bulk of the soft X-ray excess can be described by fitting the burst emission with an atmosphere model, instead of a simple blackbody model. Traditionally, the persistent emission was assumed to be invariant during X-ray bursts, and more recently to change only in normalization but not in spectral shape; the observed change in the persistent emission level during X-ray bursts may thus trigger the revision of existing neutron star mass-radius constraints, as the derived values rely on the assumption that the persistent emission does not change during X-ray bursts. The traditional burst fitting technique leads to up to a 10% overestimation of the bolometric burst flux in GS 1826-24, which significantly hampers the comparisons of the KEPLER and MESA model against this 'textbook burster'.

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arXiv2018

Accretion heated atmospheres of X-ray bursting neutron stars

Some thermonuclear (type I) X-ray bursts at the neutron star surfaces in low-mass X-ray binaries take place during hard persistent states of the systems. Spectral evolution of these bursts is well described by the atmosphere model of a passively cooling neutron star when the burst luminosity is high enough. The observed spectral evolution deviates from the model predictions when the burst luminosity drops below a critical value of 20-70% of the maximum luminosity. We suggest that these deviations are induced by the additional heating of the accreted particles. We present a method for computation of the neutron star atmosphere models heated by accreted particles assuming that their energy is released via Coulomb interactions with electrons. We compute the temperature structures and the emergent spectra of the atmospheres of various chemical compositions and investigate the dependence of the results on the other model parameters. We show that the heated atmosphere develops the hot (20--100 keV) corona-like surface layer cooled by Compton scattering, and the deeper, almost isothermal optically thick region with a temperature of a few keV. The emergent spectra deviate strongly from those of undisturbed neutron star atmospheres, with the main differences being the presence of a high-energy tail and a strong excess in the low-energy part of the spectrum. They also lack the iron absorption edge, which is visible in the spectra of undisturbed low-luminosity atmospheres with solar chemical composition. Using the computed spectra, we obtained the dependences of the dilution and color-correction factors as functions of relative luminosities for pure helium and solar abundance atmospheres. We show that the helium model atmosphere heated by accretion corresponding to 5% of the Eddington luminosity describes well the late stages of the X-ray bursts in 4U 1820-30.

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arXiv2018

Testing the equation of state of neutron stars with electromagnetic observations

Neutron stars are the densest, directly observable stellar objects in the universe and serve as unique astrophysical laboratories to study the behavior of matter under extreme physical conditions. This book chapter is devoted to describing how electromagnetic observations, particularly at X-ray, optical and radio wavelengths, can be used to measure the mass and radius of neutron stars and how this leads to constraints on the equation of state of ultra-dense matter. Having accurate theoretical models to describe the astrophysical data is essential in this effort. We will review different methods to constrain neutron star masses and radii, discuss the main observational results and theoretical developments achieved over the past decade, and provide an outlook of how further progress can be made with new and upcoming ground-based and space-based observatories.

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arXiv2017

Superhumps linked to X-ray emission. The superoutbursts of SSS J122221.7-311525 and GW Lib

[Abridged] We present more than 4 years of Swift X-ray observations of the 2013 superoutburst, subsequent decline and quiescence of the WZ Sge-type dwarf nova SSS J122221.7-311525 (SSS122222) from 6 days after discovery. Only a handful of WZ Sge-type dwarf novae have been observed in X-rays, and until recently GW Lib was the only binary of this type with complete coverage of an X-ray light curve throughout a superoutburst. We collected extensive X-ray data of a second such system to understand the extent to which the unexpected properties of GW Lib are common to the WZ Sge class. We analysed the X-ray light curve and compared it with the behaviour of superhumps which were detected in the optical light curve. We also performed spectral analysis of the data. The results were compared with the properties of GW Lib, for which new X-ray observations were also obtained. SSS122222 was variable and around five times brighter in 0.3-10 keV X-rays during the superoutburst than in quiescence, mainly because of a significant strengthening of a high-energy component of the X-ray spectrum. The post-outburst decline of the X-ray flux lasted at least 500 d. The data show no evidence of the expected optically thick boundary layer in the system during the outburst. SSS122222 also exhibited a sudden X-ray flux change in the middle of the superoutburst, which occurred exactly at the time of the superhump stage transition. A similar X-ray behaviour was also detected in GW Lib. This result demonstrates a relationship between the outer disc and the white dwarf boundary layer for the first time, and suggests that models for accretion discs in high mass ratio accreting binaries are currently incomplete. The very long decline to X-ray quiescence is also in strong contrast to the expectation of low viscosity in the disc after outburst.

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arXiv2017

Stable accretion from a cold disc in highly magnetized neutron stars

The aim of this paper is to investigate the transition of a strongly magnetized neutron star into the accretion regime with very low accretion rate. For this purpose we monitored the Be-transient X-ray pulsar GRO J1008-57 throughout a full orbital cycle. The current observational campaign was performed with the Swift/XRT telescope in the soft X-ray band (0.5-10 keV) between two subsequent Type I outbursts in January and September 2016. The expected transition to the propeller regime was not observed. However, the transitions between different regimes of accretion were detected. In particular, after an outburst the source entered a stable accretion state characterised by the accretion rate of ~10^14-10^15 g/s. We associate this state with accretion from a cold (low-ionised) disc of temperature below ~6500 K. We argue that a transition to such accretion regime should be observed in all X-ray pulsars with certain combination of the rotation frequency and magnetic field strength. The proposed model of accretion from a cold disc is able to explain several puzzling observational properties of X-ray pulsars.

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arXiv2017

Neutron star mass and radius measurements from atmospheric model fits to X-ray burst cooling tail spectra

Observations of thermonuclear X-ray bursts from accreting neutron stars (NSs) in low-mass X-ray binary systems can be used to constrain NS masses and radii. Most previous work of this type has set these constraints using Planck function fits as a proxy: both the models and the data are fit with diluted blackbody functions to yield normalizations and temperatures which are then compared against each other. Here, for the first time, we fit atmosphere models of X-ray bursting NSs directly to the observed spectra. We present a hierarchical Bayesian fitting framework that uses state-of-the-art X-ray bursting NS atmosphere models with realistic opacities and relativistic exact Compton scattering kernels as a model for the surface emission. We test our approach against synthetic data, and find that for data that are well-described by our model we can obtain robust radius, mass, distance, and composition measurements. We then apply our technique to Rossi X-ray Timing Explorer observations of five hard-state X-ray bursts from 4U 1702-429. Our joint fit to all five bursts shows that the theoretical atmosphere models describe the data well but there are still some unmodeled features in the spectrum corresponding to a relative error of 1-5% of the energy flux. After marginalizing over this intrinsic scatter, we find that at 68% credibility the circumferential radius of the NS in 4U 1702-429 is R = 12.4+-0.4 km, the gravitational mass is M=1.9+-0.3 Msun, the distance is 5.1 < D/kpc < 6.2, and the hydrogen mass fraction is X < 0.09.

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arXiv2017

The remarkable outburst of the highly evolved post-period-minimum dwarf nova SSS J122221.7-311525

We report extensive 3-yr multiwavelength observations of the WZ Sge-type dwarf nova SSS J122221.7-311525 during its unusual double superoutburst, the following decline and in quiescence. The second segment of the superoutburst had a long duration of 33 d and a very gentle decline with a rate of 0.02 mag/d, and it displayed an extended post-outburst decline lasting at least 500 d. Simultaneously with the start of the rapid fading from the superoutburst plateau, the system showed the appearance of a strong near-infrared excess resulting in very red colours, which reached extreme values (B-I~1.4) about 20 d later. The colours then became bluer again, but it took at least 250 d to acquire a stable level. Superhumps were clearly visible in the light curve from our very first time-resolved observations until at least 420 d after the rapid fading from the superoutburst. The spectroscopic and photometric data revealed an orbital period of 109.80 min and a fractional superhump period excess <0.8 per cent, indicating a very low mass ratio q<0.045. With such a small mass ratio the donor mass should be below the hydrogen-burning minimum mass limit. The observed infrared flux in quiescence is indeed much lower than is expected from a cataclysmic variable with a near-main-sequence donor star. This strongly suggests a brown-dwarf-like nature for the donor and that SSS J122221.7-311525 has already evolved away from the period minimum towards longer periods, with the donor now extremely dim.

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