Low-mass X-ray Binary Systems Research Articles

Long-term evolution of spin and other properties of neutron star low-mass X-ray binaries: implications for millisecond X-ray pulsars

ABSTRACT A neutron star (NS) accreting matter from a companion star in a low-mass X-ray binary (LMXB) system can spin up to become a millisecond pulsar (MSP). Properties of many such MSP systems are known, which is excellent for probing fundamental aspects of NS physics when modelled using the theoretical computation of NS LMXB evolution. Here, we systematically compute the long-term evolution of NS, binary, and companion parameters for NS LMXBs using the stellar evolution code mesa. We consider the baryonic to gravitational mass conversion to calculate the NS mass evolution and show its cruciality for the realistic computation of some parameters. With computations using many combinations of parameter values, we find the general nature of the complex NS spin frequency ($\nu$) evolution, which depends on various parameters, including accretion rate, fractional mass-loss from the system, and companion star magnetic braking. Further, we utilize our results to precisely match some main observed parameters, such as $\nu$, orbital period ($P_{\rm orb}$), etc., of four accreting millisecond X-ray pulsars (AMXPs). By providing the $\nu$, $P_{\rm orb}$, and the companion mass spaces for NS LMXB evolution, we indicate the distribution and plausible evolution of a few other AMXPs. We also discuss the current challenges in explaining the parameters of AMXP sources with brown dwarf companions and indicate the importance of modelling the transient accretion in LMXBs as a possible solution.

X-ray view of emission lines in optical spectra: Spectral analysis of the two low-mass X-ray binary systems Swift J1357.2-0933 and MAXI J1305-704

X-ray view of emission lines in optical spectra: Spectral analysis of the two low-mass X-ray binary systems Swift J1357.2-0933 and MAXI J1305-704

The variable radio jet of the accreting neutron star the Rapid Burster

ABSTRACT The Rapid Burster is a unique neutron star low-mass X-ray binary system, showing both thermonuclear v-I and accretion-driven Type-II X-ray bursts. Recent studies have demonstrated how coordinated observations of X-ray and radio variability can constrain jet properties of accreting neutron stars – particularly when the X-ray variability is dominated by discrete changes. We present a simultaneous very large array, Swift, and INTErnational Gamma-Ray Astrophysics Laboratory observing campaign of the Rapid Burster to investigate whether its jet responds to Type-II bursts. We observe the radio counterpart of the X-ray binary at its faintest-detected radio luminosity, while the X-ray observations reveal prolific, fast X-ray bursting. A time-resolved analysis reveals that the radio counterpart varies significantly between observing scans, displaying a fractional variability of $38 \pm 5$ per cent. The radio faintness of the system prevents the robust identification of a causal relation between individual Type-II bursts and the evolution of the radio jet. However, based on a comparison of its low-radio luminosity with archival Rapid Burster observations and other accreting neutron stars, and on a qualitative assessment of the X-ray and radio light curves, we explore the presence of a tentative connection between bursts and jet: i.e. the Type-II bursts may weaken or strengthen the jet. The former of those two scenarios would fit with magnetorotational jet models; we discuss three lines of future research to establish this potential relation between Type-II bursts and jets more confidently.

Measuring the spin of black hole transient 4U 1543–47 Using Insight-HXMT

ABSTRACT We provided a comprehensive study of the properties of the black hole in the low-mass X-ray binary system 4U 1543-47, specifically focusing on the 2021 outburst (MJD 59380–59470). Using observations from the Insight-HXMT mission, we employed X-ray reflection fitting method and analysed spectral data to estimate key black hole parameters. Through our investigation redbased on 6 out of the 52 available observations, we estimated the spin parameter of the black hole to be $0.902_{-0.053}^{+0.054}$ and the inclination angle of the accretion disc to be $28.91_{-1.24}^{+1.82}$° (90 per cent confidence limits, statistical only), then we discussed the influence of high luminosity. Based on the relxill series models are not suitable for thick disc scenario, and in comparison with findings from other studies, we propose that our estimation of the spin value may be exaggerated.

Quasi-periodic oscillations in rotating and deformed space–times

ABSTRACT Quasi-periodic oscillation (QPOs) analysis is important for understanding the dynamical behaviour of many astrophysical objects during transient events such as gamma-ray bursts, solar flares, magnetar flares, and fast radio bursts. In this paper, we analyse QPO data in low-mass X-ray binary (LMXB) systems, using the Lense-Thirring, Kerr, and approximate Zipoy-Voorhees metrics. We demonstrate that the inclusion of spin and quadrupole parameters modifies the well-established results for the fundamental frequencies in the Schwarzschild space–time. We interpret the QPO data within the framework of the standard relativistic precession model, allowing us to infer the values of the mass, spin, and quadrupole parameters of neutron stars in LMXBs. We explore recent QPO data sets from eight distinct LMXBs, assess their optimal parameters, and compare our findings with results in the existing literature. Finally, we discuss the astrophysical implications of our findings.

The high energy X-ray probe (HEX-P): a new window into neutron star accretion

Accreting neutron stars (NSs) represent a unique laboratory for probing the physics of accretion in the presence of strong magnetic fields (B ≳ 108 G). Additionally, the matter inside the NS itself exists in an ultra-dense, cold state that cannot be reproduced in Earth-based laboratories. Hence, observational studies of these objects are a way to probe the most extreme physical regimes. Here we present an overview of the field and discuss the most important outstanding problems related to NS accretion. We show how these open questions regarding accreting NSs in both low-mass and high-mass X-ray binary systems can be addressed with the High-Energy X-ray Probe (HEX-P) via simulated data. In particular, with the broad X-ray passband and improved sensitivity afforded by a low X-ray background, HEX-P will be able to 1) distinguish between competing continuum emission models; 2) provide tighter upper limits on NS radii via reflection modeling techniques that are independent and complementary to other existing methods; 3) constrain magnetic field geometry, plasma parameters, and accretion column emission patterns by characterizing fundamental and harmonic cyclotron lines and exploring their behavior with pulse phase; 4) directly measure the surface magnetic field strength of highly magnetized NSs at the lowest accretion luminosities; as well as 5) detect cyclotron line features in extragalactic sources and probe their dependence on luminosity in the super-Eddington regime in order to distinguish between geometrical evolution and accretion-induced decay of the magnetic field. In these ways HEX-P will provide an essential new tool for exploring the physics of NSs, their magnetic fields, and the physics of extreme accretion.

EVOLUTION OF THE X-RAY BINARY SYSTEM Sco X-1

The possible evolution of a bright low-mass X-ray binary system Sco X-1 is numerically investigated within the framework of a model assuming that the donor of the system (a satellite of a neutron star) fills its Roche lobe. The calculations take into account a strong induced stellar wind (ISW) of the donor, which occurs due to irradiation by hard radiation of an accreting relativistic star. At the same time, using the example of Sco X-1, three hypotheses are investigated, within the framework of which a high rate of mass exchange can be obtained for semi-separated X-ray binary stars. The first hypothesis is the presence of a strong ISW of the donor with standard magnetic braking. Calculations have shown that in this case it is possible to obtain a high rate of mass exchange, but at the same time the donor cannot fill the Roche lobe – it “goes under it”. The second hypothesis is an increase of magnetic braking, that is, an increase of the loss of angular momentum from the system due to the magnetic stellar wind of the donor (MSW). Such an amplification may be associated with the intense ISW of the donor in the presence of a strong magnetic field. Numerical modeling shows that with an increase of MSW by ~20 times, a high rate of mass exchange is possible when the donor fills the Roche lobe. The third hypothesis suggests the possibility of canceling the direct exchange of angular momentum between the orbital moment of the system and the moment of accreted matter passing from a low-mass donor to a more massive accretor. With such cancellation, the main process, increasing the semi-axis of the orbit, disappears. Calculations show that in this case it is possible to obtain a sufficiently high rate of mass exchange. However, the most likely reason for the increase of the rate of mass exchange in low-mass X-ray binary systems is probably the increase of magnetic braking.

Spectral analysis of the LMXB XTE J1810−189 with NICER data

ABSTRACT X-ray Timing Explorer J1810−189 is a low-mass X-ray binary transient system hosting a neutron star, which underwent a three-month-long outburst in 2020. In order to study its spectral evolution during this outburst, we analysed all the available observations performed by Neutron star Interior Composition Explorer, in the 1–10 keV energy band. First, we fitted the spectra with a thermal Comptonization model. Our analysis revealed the lack of a significant direct emission from a blackbody-like component, therefore we calculated the optical depth of the Comptonizing region, deriving an upper limit of 4.5, which suggests the presence of a moderately thick corona. We also attempted to fit the spectrum with an alternative model, i.e. a cold Comptonized emission from a disc and a direct thermal component from the neutron star, finding a similarly good fit. The source did not enter a full high luminosity/soft state throughout the outburst, with a photon index ranging from ∼1.7 to ∼2.2, and an average unabsorbed flux in the 1–10 keV band of ∼3.6 × 10−10 erg cm−2 s−1. We searched for the presence of Fe K-shell emission lines in the range ∼6.4–7 keV, significantly detecting a broad component only in a couple of observations. Finally, we conducted a time-resolved spectral analysis of the detected type-I X-ray burst, observed during the outburst, finding no evidence of a photospheric radius expansion. The type-I burst duration suggests a mix of H/He fuel.

X-ray reprocessing: Through the eclipse spectra of low mass X-ray binaries with XMM-Newton

Eclipsing X-ray binaries make an ideal condition to study reprocessed X-rays, as the X-rays detected during eclipse are purely reprocessed while the much brighter primary X-rays are blocked by the companion star. We carried out a comprehensive study of X-ray reprocessing with four eclipsing Low Mass X-ray Binary (LMXB) systems by comparing X-ray spectra during and outside eclipse with XMM-Newton EPIC pn observations. The 17 observations of MXB 1659−298, AX J1745.6−2901, EXO 0748−676 and XTE J1710−281 give unique features of the systems. For example, X-ray reprocessing characteristics in AX J1745.6−2901 is found to be nearly same irrespective of the intensity state; there is an indication of different types of variable warp structures in the inner accretion disk in EXO 0748−676, a high out-of-eclipse to eclipse flux ratio in XTE J1710−281 in spite of a large size of the accretion disk perhaps indicates low scale height of the accretion disk. The eclipse spectra for some of the LMXB sources are reported for the first time. We have derived the fractional visible area of the accretion disk during maximum eclipse phase for various obscuration geometries. The out-of-eclipse to eclipse flux ratio in LMXBs observed to be smaller compared to that found in High Mass X-ray Binaries. This indicates greater reprocessing in LMXBs despite having less dense, less extended stellar wind from the companion. The X-ray reprocessing efficiencies observed in LMXBs indicate large dependencies of X-ray reprocessing on the scale height of the accretion disk, relative size of the disk compared to the companion and some other unknown factors.

An evolutionary model for the V404 Cyg system

V404 Cyg is a low mass X-Ray binary (LMXB) system that has undergone outbursts in 1938, 1989, and 2015. During these events, it has been possible to make determinations for the relevant data of the system. This data include the mass of the compact object (i.e., a black hole; BH) and its companion, the orbital period, the companion spectral type, and luminosity class. Remarkably, the companion star has a metallicity value that is appreciably higher than solar. All these data allow for the construction of theoretical models to account for its structure, determine its initial configuration, and predict its fate. Assuming that the BH is already formed when the primary star reaches the zero age main sequence, we used our binary evolution code for this purpose. We find that the current characteristics of the system are nicely accounted for by a model with initial masses of 9 M⊙ for the BH, 1.5 M⊙ for the companion star and an initial orbital period of 1.5 d, while also considering that at most 30% of the mass transferred by the donor is accreted by the BH. The metallicity of the donor for our best fit is Z = 0.028 (twice solar metallicity). We also studied the evolution of the BH spin parameter, assuming that is not rotating initially. Remarkably, the spin of the BHs in our models is far from reaching the available observational determination. This may indicate that the BH in V404 Cyg was initially spinning, a result that may be relevant for understanding the formation BHs in the context of LMXB systems.

Gravitational radiation from thermal mountains on accreting neutron stars: sources of temperature non-axisymmetry

ABSTRACT The spin distribution of accreting neutron stars in low-mass X-ray binary systems shows a concentration of pulsars well below the Keplerian break-up limit. It has been suggested that their spin frequencies may be limited by the emission of gravitational waves, due to the presence of large-scale asymmetries in the internal temperature profile of the star. These temperature asymmetries have been demonstrated to lead to a non-axisymmetric mass distribution, or ‘mountain’, that generates gravitational waves at twice the spin frequency. The presence of a toroidal magnetic field in the interior of accreting neutron stars has been shown to introduce such anisotropies in the star’s thermal conductivity, by restricting the flow of heat orthogonal to the magnetic field and establishing a non-axisymmetric temperature distribution within the star. We revisit this mechanism, extending the computational domain from (only) the crust to the entire star, incorporating more realistic microphysics, and exploring different choices of outer boundary condition. By allowing a magnetic field to permeate the core of the neutron star, we find that the likely level of temperature asymmetry in the inner crust (ρ ∼ 1013 g cm−3) can be up to 3 orders of magnitude greater than the previous estimate, improving prospects for one day detecting continuous gravitational radiation. We also show that temperature asymmetries sufficiently large to be interesting for gravitational wave emission can be generated in strongly accreting neutron stars if crustal magnetic fields can reach ∼1012 G.

ERASSt J040515.6 − 745202, an X-ray burster in the Magellanic Bridge

Context. During the third all-sky survey (eRASS3), eROSITA, the soft X-ray instrument aboard Spectrum-Roentgen-Gamma, detected a new hard X-ray transient, eRASSt J040515.6 − 745202, in the direction of the Magellanic Bridge. Aims. We arranged follow-up observations and searched for archival data to reveal the nature of the transient. Methods. Using X-ray observations with XMM-Newton, NICER, and Swift, we investigated the temporal and spectral behaviour of the source for over about 10 days. Results. The X-ray light curve obtained from the XMM-Newton observation with an ∼28 ks exposure revealed a type-I X-ray burst with a peak bolometric luminosity of at least 1.4 × 1037 erg s−1. The burst energetics are consistent with a location of the burster at the distance of the Magellanic Bridge. The relatively long exponential decay time of the burst of ∼70 s indicates that it ignited in a H-rich environment. The non-detection of the source during the other eROSITA surveys, twelve and six months before and six months after eRASS3, suggests that the burst was discovered during a moderate outburst which reached 2.6 × 1036 erg s−1 in persistent emission. During the NICER observations, the source showed alternating flux states with the high level at a similar brightness as during the XMM-Newton observation. This behaviour is likely caused by dips as also seen during the last hour of the XMM-Newton observation. Evidence for a recurrence of the dips with a period of ∼21.8 h suggests eRASSt J040515.6 − 745202 is a low-mass X-ray binary (LMXB) system with an accretion disk seen nearly edge on. We identify a multi-wavelength counterpart to the X-ray source in UVW1 and g, r, i, and z images obtained by the optical/UV monitor on XMM-Newton and the Dark Energy Camera at the Cerro Tololo Inter-American Observatory. The spectral energy distribution is consistent with radiation from an accretion disk which dominates the UV and from a cool late-type star detected in the optical to infrared wavelengths. Conclusions. After the discovery of X-ray bursts in M 31, the Magellanic Bridge is only the second location outside of the Milky Way where an X-ray burster was found. The burst uniquely identifies eRASSt J040515.6 − 745202 as an LMXB system with a neutron star. Its location in the Magellanic Bridge confirms the existence of an older stellar population which is expected if the bridge was formed by tidal interactions between the Magellanic Clouds, which stripped gas and stars from the clouds.

Spectral analysis of the AMXP IGR J17591–2342 during its 2018 outburst

ABSTRACT The Accreting Millisecond X-ray Pulsar IGR J17591–2342 is a Low Mass X-ray Binary (LMXB) system that went in outburst on 2018 August and it was monitored by the NICER observatory and partially by other facilities. We aim to study how the spectral emission of this source evolved during the outburst by exploiting the whole X-ray data repository of simultaneous observations. The continuum emission of the combined broad-band spectra is on average well described by an absorbed Comptonization component scattering blackbody-distributed photons peaking at (0.8 ± 0.5) keV by a moderately optically thick corona (τ = 2.3 ± 0.5) with temperature of (34 ± 9) keV. A blackbody component with temperature and radial size of (0.8 ± 0.2) keV and (3.3 ± 1.5) km, respectively, is required by some of the spectra and suggests that part of the central emission, possibly a fraction of the neutron star surface, is not efficiently scattered by the corona. The continuum at low energies is characterized by significant residuals suggesting the presence of an absorption edge of O viii and of emission lines of Ne ix ions. Moreover, broad Fe i and Fe xxv Kα emission lines are detected at different times of the outburst, suggesting the presence of reflection in the system.

Peculiar X-ray transient SRGA J043520.9+552226/AT2019wey discovered with SRG/ART-XC

Context. During its ongoing all-sky survey, the Mikhail Pavlinsky ART-XC (Astronomical Roentgen Telescope - X-ray Concentrator) telescope on board the Spectrum-Roentgen-Gamma (SRG) observatory is set to discover new X-ray sources, many of which can be transient. Here we report the discovery and multiwavelength follow-up of a peculiar X-ray source SRGA J043520.9+552226 = SRGe J043523.3+552234. This is the high-energy counterpart of the optical transient AT2019wey. Aims. Through its sensitivity and the survey strategy, the Mikhail Pavlinsky ART-XC telescope uncovers poorly studied weak transient populations. Using the synergy with current public optical surveys, we aim to reveal the nature of these transients to study their parent populations. SRGA J043520.9+552226 is the first transient detected by ART-XC that has a bright optical counterpart suitable for further studies. Methods. We used available public X-ray and optical data and observations with SRG, INTEGRAL, NuSTAR, NICER, Swift, and ground-based telescopes to investigate the spectral energy distributions of the source in different phases of the outburst. Results. Based on X-ray spectral and timing properties derived from space observations, optical spectroscopy, and photometry obtained with the 2.5 m and RC600 telescopes of the Caucasian Mountain Observatory of the Sternberg Astronomical Institute of Moscow State University, we propose that the source is a black hole in a low-mass close X-ray binary system.

Millisecond pulsars from accretion-induced collapse as the origin of the Galactic Centre gamma-ray excess signal

Gamma-ray data from the Fermi-Large Area Telescope reveal an unexplained, apparently diffuse, signal from the Galactic bulge that peaks near 2 GeV with an approximately spherical intensity profile $\propto r^{-2.4}$ that extends to angular radial scales of at least 10 degrees, possibly to 20 degrees. The origin of this "Galactic Centre Excess" (GCE) has been debated with proposed sources prominently including self-annihilating dark matter and a hitherto undetected population of millisecond pulsars (MSPs). However, the conventional channel for the generation of MSPs has been found to predict too many low mass X-ray binary (LMXB) systems and, because of the expected large natal kicks, may not accommodate the close spatial correspondence between the GCE signal and stars in the bulge. Here we report a binary population synthesis forward model that demonstrates that an MSP population arising from the accretion induced collapse (AIC) of O-Ne white dwarfs in Galactic bulge binaries can naturally reproduce the morphology, spectral shape, and intensity of the GCE signal while also obeying LMXB constraints. Synchrotron emission from MSP-launched cosmic ray electrons and positrons may simultaneously explain the mysterious, microwave "haze" from the inner Galaxy

Multi-wavelength Observations of AT2019wey: a New Candidate Black Hole Low-mass X-ray Binary

Abstract AT2019wey (SRGA J043520.9+552226, SRGE J043523.3+552234) is a transient first reported by the ATLAS optical survey in 2019 December. It rose to prominence upon detection, three months later, by the Spektrum-Roentgen-Gamma (SRG) mission in its first all-sky survey. X-ray observations reported in Yao et al. suggest that AT2019wey is a Galactic low-mass X-ray binary (LMXB) with a black hole (BH) or neutron star (NS) accretor. Here we present ultraviolet, optical, near-infrared, and radio observations of this object. We show that the companion is a short-period (P ≲ 16 hr) low-mass (<1 M ⊙) star. We consider AT2019wey to be a candidate BH system since its locations on the L radio–L X and L opt–L X diagrams are closer to BH binaries than NS binaries. We demonstrate that from 2020 June to August, despite the more than 10 times brightening at radio and X-ray wavelengths, the optical luminosity of AT2019wey only increased by 1.3–1.4 times. We interpret the UV/optical emission before the brightening as thermal emission from a truncated disk in a hot accretion flow and the UV/optical emission after the brightening as reprocessing of the X-ray emission in the outer accretion disk. AT2019wey demonstrates that combining current wide-field optical surveys and SRG provides a way to discover the emerging population of short-period BH LMXB systems with faint X-ray outbursts.

V404 Cygni with Fermi-LAT

ABSTRACT We revisit the well-studied outburst of the low-mass X-ray binary (LMXB) system V404 Cygni, and claims of γ-ray excesses observed with the Fermi-LAT instrument. Upon analysing an 11.5 yr data set with the 8-yr LAT point source catalogue and 8-yr background models, we find no evidence to suggest that there is high energy γ-ray emission during the outburst period (or at any other time) from V404 Cygni. This is due to the proximity of V404 Cygni to the γ-ray emitting blazar B2023+336, a luminous source approximately 0.3○ away, which causes source confusion at the position of V404 Cygni, the luminous γ-ray background, and the use of older background models and catalogues in previous studies.

Convection and rotation boosted prescription of magnetic braking: application to the formation of extremely low-mass white dwarfs

ABSTRACT Extremely low-mass white dwarfs (ELM WDs) are the result of binary evolution in which a low-mass donor star is stripped by its companion leaving behind a helium-core white dwarf (WD). We explore the formation of ELM WDs in binary systems considering the Convection And Rotation Boosted magnetic braking treatment. Our evolutionary sequences were calculated using the Modules for Experiments in Stellar Astrophysics code, with initial masses of 1.0 and 1.2 M⊙ (donor), and 1.4 (accretor), compatible with low-mass X-ray binary (LMXB) systems. We obtain ELM models in the range 0.15–0.27 M⊙ from a broad range of initial orbital periods, 1–25 d. The bifurcation period, where the initial period is equal to the final period, ranges from 20 to 25 d. In addition to LMXBs, we show that ultracompact X-ray binaries (UCXBs) and wide-orbit binary millisecond pulsars can also be formed. The relation between mass and orbital period obtained is compatible with the observational data from He WD companions to pulsars.

The evolution of rapid optical/X-ray timing correlations in the initial hard state of MAXI J1820+070

ABSTRACT We report on a multiepoch campaign of rapid optical/X-ray timing observations of the superbright 2018 outburst of MAXI J1820+070, a black hole low-mass X-ray binary system. The observations spanned 80 d in the initial hard state and were taken with NTT/ULTRACAM and GTC/HiPERCAM in the optical (usgsrsiszs filters at time resolutions of 8–300 Hz) and with ISS/NICER in X-rays. We find (i) a growing anticorrelation between the optical and X-ray light curves, (ii) a steady, positive correlation at an optical lag of ∼0.2 s (with a longer lag at longer wavelengths) present in all epochs, and (iii) a curious positive correlation at negative optical lags in the last, X-ray softest epoch, with longer wavelengths showing a greater correlation and a more negative lag. To explain these, we postulate the possible existence of two synchrotron-emitting components – a compact jet and a hot flow. In our model, the significance of the jet decreases over the outburst, while the hot flow remains static (thus, relatively, increasing in significance). We also discuss a previously discovered quasi-periodic oscillation and note how it creates coherent optical time lags, stronger at longer wavelengths, during at least two epochs.

Optical and ultraviolet monitoring of the black hole X-ray binary MAXI J1820+070/ASASSN-18ey for 18 months

ABSTRACT MAXI J1820+070 is a low-mass black hole X-ray binary system with high luminosity in both optical and X-ray bands during its outburst periods. We present extensive photometry in the X-ray, ultraviolet, and optical bands, as well as densely cadenced optical spectra, covering the phase from the beginning of the optical outburst to ∼550 days. During the rebrightening process, the optical emission precedes the X-ray by 20.80 ± 2.85 days. The spectra are characterized by blue continua and emission features of Balmer series, He i, and He ii lines and a broad Bowen blend. The pseudo equivalent widths (pEWs) of emission lines are found to show anticorrelations with the X-ray flux measured at comparable phases, due to increased suppression by the optical continuum. At around the X-ray peak, the full widths at half-maximum (FWHMs) of Hβ and He ii λ4686 tend to stabilize at 19.4 and 21.8 Å, corresponding to the line-forming regions at radii of 1.7 and 1.3 R⊙ within the disc. We further analysed the absolute fluxes of the lines and found that the fluxes of Hβ and He ii λ4686 show positive correlations with the X-ray flux, favouring the suggestion that the irradiation model is responsible for the optical emission. However, the fact that X-ray emission experiences a dramatic flux drop at t ∼ 200 days after the outburst, while the optical flux only shows a little variation, suggests that additional energy such as viscous energy may contribute to the optical radiation, in addition to X-ray irradiation.