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Mutsumi Sugizaki

Publications and source records attributed to Mutsumi Sugizaki.

At least 19 recordsLinked to original sources

Investigating MAXI J1752-457 with NuSTAR in the aftermath of a superburst

We present two NuSTAR observations of the X-ray transient, MAXI J1752-457, following a superburst which was observed by MAXI/GSC in November, 2024. NuSTAR follow-up confirmed that MAXI J1752-457 is coincident with the previously observed Einstein Probe source, EP240809a. We performed a spectral analysis of the source during both NuSTAR observations, and we find that the hard X-ray spectra are consistent with the inclusion of a spherical blackbody component and a steep, non-thermal, power law component. At about 79 hours after the onset of the superburst, we find a blackbody temperature of $kT_\mathrm{bb}=0.60\pm0.1$ keV and $R_\mathrm{bb}/D_{8}=6.0^{+0.4}_{-0.3}$ km (not including corrections for scattering in the neutron star atmosphere), where $D_{8}$ is the source distance, which is not yet known, in units of 8 kpc. We found that the blackbody temperature did not change significantly in the one day interval between successive NuSTAR observations, and we performed an energy-resolved timing analysis which showed that the source variability was dominated by red noise in the power law component, suggesting coupling with an accretion disk. We infer that the source had entered an accretion-powered flux state. Furthermore, we measure a photon index of $Γ\approx4$, much steeper than those typically observed during accretion onto neutron stars at similar luminosities. This is suggestive of ongoing evolution of the electron energy distribution responsible for the power law component several days after the superburst, but the lack of hard X-ray observations prior to and throughout the superburst make it difficult to present a conclusive physical interpretation of this result.

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A simple, flexible method for timing cross-calibration of space missions

The timing (cross-)calibration of astronomical instruments is often done by comparing pulsar times-of-arrival (TOAs) to a reference timing model. In high-energy astronomy, the choice of solar system ephemerides and source positions used to barycenter the photon arrival times has a significant impact on the procedure, requiring a full reprocessing of the data each time a new convention is used. Our method, developed as part of the activities of the International Astronomical Consortium for High Energy Calibration (IACHEC), adapts an existing pulsar solution to arbitrary JPL ephemerides and source positions by simulating geocentric TOAs and refitting timing models (implemented with PINT). We validate the procedure and apply it to thousands of observations of the Crab pulsar from 15 missions spanning 1996--2025, demonstrating inter-ephemeris TOA consistency at the $\lesssim5 μ$s level, using the DE200/FK5-based Jodrell Bank Monthly Ephemeris as a common reference. We release the TOAExtractor open-source tool and a TOA database to support future calibration and scientific studies. Instrument timing performance is broadly consistent with mission specifications; the X-ray-to-radio phase offset varies with energy and time at a level that is marginally consistent with the uncertainties of the radio ephemeris, motivating coordinated multiwavelength follow-up.

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Quasi-periodic variation during a fast X-ray outburst of a high-mass X-ray binary MAXI J0709-159 / LY CMa observed by NICER

We report on a quasi-periodic variation at $\sim1$ Hz during a fast X-ray outburst of a high-mass X-ray binary MAXI J0709$-$159 / LY CMa observed by the Neutron-star interior composition explorer (NICER). The new X-ray transient MAXI J0709$-$159 was discovered on 2022 January 25. Due to the transient X-ray behavior characterized by the short (a few hours) outburst duration, rapid ($\lesssim$ 1 s) variability with spectral change, and large luminosity swing from $10^{32}$ erg s$^{-1}$ to $10^{37}$ erg s$^{-1}$, the object was considered likely to be a supergiant X-ray binary with a neutron star (NS) categorized as a Supergiant Fast X-ray Transient (SFXT). Follow-up NICER and NuSTAR observations confirmed that the position of the new X-ray object is consistent with a Be star, LY CMa, which has been also identified as a B supergiant. We analyzed the NICER data obtained from 3 hours to 6 days after the discovery. The light curve reveals that the X-ray activity continued for $\sim7$ hours in sparse short flares, each lasting $\lesssim 100$ seconds, and the luminosity instantaneously reached up to $\sim 1\times 10^{38}$ erg s$^{-1}$. The light-curve and spectral features reasonably agree with those expected from accretion of a clumpy stellar-wind onto a magnetized NS. The variability power spectrum during the brightest flare shows a broad peak at $1.1$ Hz resembling a quasi-periodic oscillation (QPO). If the QPO is attributed to the Keplerian orbital frequency at the inner edge of a transient accretion disk truncated by the NS magnetosphere, the NS surface magnetic field is estimated to be $\sim 10^{12}$ G.

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Optical Observations of the High Mass X-ray Binary MAXI J0709$-$159/LY CMa

We report on the optical spectroscopic monitoring of the X-ray transient MAXI J0709$-$159 (identified as the Be star LY CMa) performed for about 1.5 months after the X-ray detection with MAXI. The observed spectrum showed a double-peaked H$α$ line with a peak-to-peak separation of $\sim 230$ km s$^{-1}$, suggestive of the Be disk origin. We also detected a broad wing of the H$α$ line with a line-of-sight velocity of $\gtrsim 900$ km s$^{-1}$, which could be explained by the accretion disk of the compact object or a stellar wind from the Be star. Initially the H$α$ line showed an asymmetric profile with an enhanced blue peak, and then the blue peak decreased in $\sim$ 3 weeks to a similar strength to the red peak. We suggest that the evolution of the blue peak is associated with the X-ray activity and generated by the turbulence of the Be disk due to the passage of the compact object. We also investigated flux variation using the archival TESS data and found quasi-periodic variations with frequencies of $\sim 1$ and $\sim 2$ day$^{-1}$, which were likely caused by the pulsation of the B star. The overall variability properties on timescales of $\sim$ day were similar to those in Be X-ray binaries, rather than supergiant X-ray binaries.

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{\it Insight}-HXMT View of the BHC Swift J1727.8-1613 during its outburst in 2023

The transient Galactic black hole candidate Swift\,J1727.8-1613 went through an outburst for the very first time in August 2023 and lasted for almost 6 months. We study the timing and spectral properties of this source using publicly available archival {\it Insight}-HXMT data for the first 10 observation IDs that last from MJD 60181 to 60198 with a total of 92 exposures for all three energy bands. We have detected quasi-periodic oscillations (QPOs) in a frequency range of $0.21 \pm 0.01$ - $1.86 \pm 0.01$ Hz by fitting the power density spectrum. Based on the model-fitted parameters and properties of the QPOs, we classify them as type-C in nature. We also conclude that the origin of the QPOs could be the shock instabilities in the transonic advective accretion flows around black holes. The spectral analysis was performed using simultaneous data from the three on-board instruments LE, ME, and HE of \textit{Insight}-HXMT in the broad energy band of $2-150 $ keV. To achieve the best fit, spectral fitting required a combination of models e.g. interstellar absorption, power-law, multi-color disk-blackbody continuum, Gaussian emission/absorption, and reflection by neutral material. From the spectral properties, we found that the source was in an intermediate state at the start of the analysis period and was transitioning to the softer states. The inner edge of the accretion disk moved inward in progressive days following the spectral nature. We found that the source has a high inclination of $78^\circ-86^\circ$. The hydrogen column density from the model fitting varied in the range of $(0.12 \pm 0.02 - 0.39 \pm 0.08)\times10^{22}$ cm$^{-2}$.

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Accretion spin-up and a strong magnetic field in the slow-spinning Be X-ray binary MAXI J0655-013

We present MAXI and NuSTAR observations of the Be X-ray binary, MAXI J0655-013, in outburst. NuSTAR observed the source once early in the outburst, when spectral analysis yields a bolometric (0.1--100 keV), unabsorbed source luminosity of $L_{\mathrm{bol}}=5.6\times10^{36}\mathrm{erg\,s^{-1}}$, and a second time 54 days later, by which time the luminosity dropped to $L_{\mathrm{bol}}=4\times10^{34}\,\mathrm{erg\,s^{-1}}$ after first undergoing a dramatic increase. Timing analysis of the NuSTAR data reveals a neutron star spin period of $1129.09\pm0.04$ s during the first observation, which decreased to $1085\pm1$ s by the time of the second observation, indicating spin-up due to accretion throughout the outburst. Furthermore, during the first NuSTAR observation, we observed quasiperiodic oscillations with centroid frequency $ν_0=89\pm1$ mHz, which exhibited a second harmonic feature. By combining the MAXI and NuSTAR data with pulse period measurements reported by Fermi/GBM, we are able to show that apparent flaring behavior in the MAXI light-curve is an artifact introduced by uneven sampling of the pulse profile, which has a large pulsed fraction. Finally, we estimate the magnetic field strength at the neutron star surface via three independent methods, invoking a tentative cyclotron resonance scattering feature at $44$ keV, QPO production at the inner edge of the accretion disk, and spin-up via interaction of the neutron star magnetic field with accreting material. Each of these result in a significantly different value. We discuss the strengths and weaknesses of each method and infer that MAXI J0655-013 is likely to have a high surface magnetic field strength, $B_{s}>10^{13}$ G.

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Discovery of a new supergiant fast X-ray transient MAXI J0709-159 associated with the Be star LY CMa

We report on the discovery of a new supergiant fast X-ray transient (SFXT), MAXI J0709$-$159, and its identification with LY CMa (also known as HD 54786). On 2022 January 25, a new flaring X-ray object named MAXI J0709$-$159, was detected by Monitor of All-sky X-ray Image (MAXI). Two flaring activities were observed in the two scans of $\sim 3$ hours apart, where the 2-10 keV flux reached $5\times 10^{-9}$ erg cm$^{-2}$ s$^{-1}$. During the period, the source exhibited a large spectral change suggesting that the absorption column density $N_\mathrm{H}$ increased from $10^{22}$ cm$^{-2}$ to $10^{23}$ cm$^{-2}$. NuSTAR follow-up observation on January 29 identified a new X-ray source with a flux of $6\times 10^{-13}$ erg cm$^{-2}$ s$^{-1}$ at the position consistent with LY CMa, which has been identified as B supergiant as well as Be star, located at the 3 kpc distance. The observed X-ray activity characterized by the short ($\lesssim$ several hours) duration, the rapid ($\lesssim$ a few seconds) variabilities accompanied with spectral changes, and the large luminosity swing ($10^{32}$-$10^{37}$ erg s$^{-1}$) agree with those of SFXT. On the other hand, optical spectroscopic observations of LY CMa revealed a broad $Hα$ emission line, which may indicate the existence of a Be circumstellar disk. These obtained results suggest that the optical companion, LY CMa, certainly has a complex circumstellar medium including dense clumps.

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MAXI and NuSTAR observations of the faint X-ray transient MAXI J1848-015 in the GLIMPSE-C01 Cluster

We present the results of MAXI monitoring and two NuSTAR observations of the recently discovered faint X-ray transient MAXI J1848-015. Analysis of the MAXI light-curve shows that the source underwent a rapid flux increase beginning on 2020 December 20, followed by a rapid decrease in flux after only $\sim5$ days. NuSTAR observations reveal that the source transitioned from a bright soft state with unabsorbed, bolometric ($0.1$-$100$ keV) flux $F=6.9 \pm 0.1 \times 10^{-10}\,\mathrm{erg\,cm^{-2}\,s^{-1}}$, to a low hard state with flux $F=2.85 \pm 0.04 \times 10^{-10}\,\mathrm{erg\,cm^{-2}\,s^{-1}}$. Given a distance of $3.3$ kpc, inferred via association of the source with the GLIMPSE-C01 cluster, these fluxes correspond to an Eddington fraction of order $10^{-3}$ for an accreting neutron star of mass $M=1.4M_\odot$, or even lower for a more massive accretor. However, the source spectra exhibit strong relativistic reflection features, indicating the presence of an accretion disk which extends close to the accretor, for which we measure a high spin, $a=0.967\pm0.013$. In addition to a change in flux and spectral shape, we find evidence for other changes between the soft and hard states, including moderate disk truncation with the inner disk radius increasing from $R_\mathrm{in}\approx3\,R_\mathrm{g}$ to $R_\mathrm{in}\approx8\,R_\mathrm{g}$, narrow Fe emission whose centroid decreases from $6.8\pm0.1$ keV to $6.3 \pm 0.1$ keV, and an increase in low-frequency ($10^{-3}$-$10^{-1}$ Hz) variability. Due to the high spin we conclude that the source is likely to be a black hole rather than a neutron star, and we discuss physical interpretations of the low apparent luminosity as well as the narrow Fe emission.

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Discovery of the black hole X-ray binary transient MAXIJ1348-630

We report the first half-year monitoring of the new Galactic black hole candidate MAXI J1348-630, discovered on 2019 January 26 with the Gas Slit Camera (GSC) on-board MAXI. During the monitoring period, the source exhibited two outburst peaks, where the first peak flux (at T=14 day from the discovery of T =0) was ~4 Crab (2-20 keV) and the second one (at T =132 day) was ~0.4 Crab (2-20 keV). The source exhibited distinct spectral transitions between the high/soft and low/hard states and an apparent "q"-shape curve on the hardness-intensity diagram, both of which are well-known characteristics of black hole binaries. Compared to other bright black hole transients, MAXI J1348-630 is characterized by its low disk-temperature (~0.75 keV at the maximum) and high peak flux in the high/soft state. The low peak-temperature leads to a large innermost radius that is identified as the Innermost Stable Circular Orbit (ISCO), determined by the black hole mass and spin. Assuming the empirical relation between the soft-to-hard transition luminosity (Ltrans) and the Eddington luminosity (LEdd), Ltrans/LEdd ~ 0.02, and a face-on disk around a non-spinning black hole, the source distance and the black hole mass are estimated to be D ~ 4 kpc and ~7 (D/4 kpc) Mo, respectively. The black hole is more massive if the disk is inclined and the black hole is spinning. These results suggest that MAXI J1348-630 may host a relatively massive black hole among the known black hole binaries in our Galaxy.

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X-ray emission evolution of the Galactic ultra-luminous X-ray pulsar Swift J0243.6+6124 during the 2017-2018 outburst observed by the MAXI GSC

This paper reports on the X-ray emission evolution of the ultra-luminous Galactic X-ray pulsar, Swift J0243.6+6124, during the 2017-2018 giant outburst observed by the MAXI GSC. The 2-30 keV light curve and the energy spectra confirm that the luminosity $L_\mathrm{X}$ reached $2.5\times 10^{39}$ erg s$^{-1}$, 10 times higher than the Eddington limit. When the source was luminous with $L_\mathrm{X}\gtrsim 0.9\times 10^{38}$ erg s$^{-1}$, it exhibited a negative correlation on a hardness-intensity diagram. However, two hardness ratios, a soft color ($=$ 4-10 keV / 2-4 keV) and a hard color ($=$ 10-20 keV / 4-10 keV), showed somewhat different behavior across a characteristic luminosity of $L_\mathrm{c}\simeq 5\times 10^{38}$ erg s$^{-1}$. The soft color changed more than the hard color when $L_\mathrm{X} < L_\mathrm{c}$, whereas the opposite was observed above $L_\mathrm{c}$. The spectral change above $L_\mathrm{c}$ was represented by a broad enhanced feature at $\sim 6$ keV. The pulse profiles made a transition from a single-peak to a double-peak one as the source brightened across $L_\mathrm{c}$. These spectral and pulse-shape properties can be interpreted by a scenario that the accretion columns on the neutron star surface, producing the Comptonized X-ray emission, gradually became taller as $L_\mathrm{X}$ increased. The broad 6 keV enhancement could be a result of cyclotron-resonance absorption at $\sim 10$ keV, corresponding to a surface magnetic field $B_\mathrm{s}\simeq 1.1\times 10^{12}$ G. The spin-frequency derivatives calculated with the Fermi GBM data showed a smooth correlation with $L_\mathrm{X}$ up to the outburst peak, and its linear coefficient is comparable to those of X-ray binary pulsars whose $B_\mathrm{s}$ are $(1-8)\times 10^{12}$ G. These results suggest that $B_\mathrm{s}$ of Swift J0243.6$+$6124 is a few times $10^{12}$ G.

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Monitoring the Superorbital Period Variation and the Spin Period Evolution of SMC X-1

The X-ray pulsar SMC X-1 shows a superorbital modulation with an unstable cycle length in the X-ray band. We present its timing behaviors, including the spin, orbital, and superorbital modulations, beyond the end of the Rossi X-ray Timing Explorer mission. The time-frequency maps derived by the wavelet Z-transform and the Hilbert-Huang transform suggest that a new superorbital period excursion event occurred in ~MJD 57100 (2015 March). This indicates the excursion is recurrent and probably (quasi)periodic. The hardness ratio obtained with the Monitor of All-sky X-ray Image (MAXI) suggests increased absorption during the transition from the high to the low state in the superorbital cycle. Compared to the regular epochs, the superorbital profile during the excursion epochs has a shallower and narrower valley, likely caused by a flatter warp. By tracking the spin period evolution with the MAXI Gas Slit Camera in 2-20 keV, we derive an averaged spin-up rate of $\dotν=2.515(3)\times10^{-11}$ s$^{-2}$ during the period between MJD 55141 (2009 November) and 58526 (2019 February). We obtain no positive correlation between the spin frequency residual and the superorbital frequency, but a torque change accompanying the superorbital period excursion is possible. We suggest that the accretion torque on the neutron star could be changed by various mechanisms, including the change of mass accretion rate and the warp angle. We update the value of the orbital decay as $\dot{P}_{\rm{orb}}/P_{\rm{orb}}=-3.380(6)\times10^{-6}$ yr$^{-1}$. Finally, we reconfirm the detection of the superorbital modulation in the optical band and its coherence in phase with the X-ray modulation.

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An enigmatic hump around 30 keV in Suzaku spectra of Aquila X-1 in the Hard State

The typical accreting neutron star, Aquila X-1, was observed with Suzaku seven times in the decay phase of an outburst in 2007 September-October. Among them, the second to the fourth observations were performed 10 to 22 days after the outburst peak, when the source was in the hard state with a luminosity of 2x10^36 erg/sec. A unified spectral model for this type of objects approximately reproduced the 0.8--100~keV spectra obtained in these 3 observations. However, the spectra all exhibited an enigmatic hump-like excess around 30 keV, above the hard X-ray continuum which is interpreted as arising via Comptonization. The excess feature was confirmed to be significant against statistical and systematic uncertainties. It was successfully represented by a Gaussian centered at ~32 keV, with a width (sigma) of ~6 keV and an equivalent width of ~8.6 keV. Alternatively, the feature can also be explained by a recombination edge model, that produces a quasi-continuum above an edge energy of ~27 keV with an electron temperature of ~11 keV and an equivalent width of ~6.3 keV. These results are discussed in the context of atomic features of heavy elements synthesized via rapid-proton capture process during thermonuclear flashes.

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An application of the Ghosh & Lamb model to the accretion powered X-ray pulsar X Persei

The accretion-induced pulse-period changes of the Be/X-ray binary pulsar X Persei were investigated over a period of 1996 January to 2017 September. This study utilized the monitoring data acquired with the RXTE/ASM in 1.5$-$12 keV and MAXI/GSC in 2$-$20 keV. The source intensity changed by a factor of 5$-$6 over this period. The pulsar was spinning down for 1996$-$2003, and has been spinning up since 2003, as already reported. The spin up/down rate and the 3$-$12 keV flux, determined every 250 d, showed a clear negative correlation, which can be successfully explained by the accretion torque model proposed by Ghosh & Lamb (1979). When the mass, radius and distance of the neutron star are allowed to vary over a range of 1.0$-$2.4 solar masses, 9.5$-$15 km, and 0.77$-$0.85 kpc, respectively, the magnetic field strength of $B=(4-25) \times10^{13}\ \rm G$ gave the best fits to the observation. In contrast, the observed results cannot be explained by the values of $B\sim10^{12}\ \rm G$ previously suggested for X Persei, as long as the mass, radius, and distance are required to take reasonable values. Assuming a distance of $0.81\pm0.04$ kpc as indicated by optical astrometry, the mass of the neutron star is estimated as $M=2.03\pm0.17$ solar masses.

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The 7-year MAXI/GSC X-ray Source Catalog in the High Galactic-Latitude Sky (3MAXI)

We present the third MAXI/GSC catalog in the high Galactic-latitude sky ($|b| > 10^\circ$) based on the 7-year data from 2009 August 13 to 2016 July 31, complementary to that in the low Galactic-latitude sky ($|b| < 10^\circ$; Hori et al. 2018). We compile 682 sources detected at significances of $s_{\rm D,4-10~keV} \geq 6.5$ in the 4--10 keV band. A two-dimensional image fit based on the Poisson likelihood algorithm ($C$-statistics) is adopted for the detections and constraints on their fluxes and positions. The 4--10 keV sensitivity reaches $\approx 0.48$ mCrab, or $\approx 5.9 \times 10^{-12}$ erg cm$^{-2}$ s$^{-1}$, over the half of the survey area. Compared with the 37-month catalog (Hiroi et al. 2013), which adopted a threshold of $s_{\rm D,4-10~keV} \geq 7$, the source number increases by a factor of $\sim$1.4. The fluxes in the 3--4 keV and 10--20 keV bands are further estimated, and hardness ratios (HRs) are calculated using the 3--4 keV, 4--10 keV, 3--10 keV, and 10--20 keV band fluxes. We also make the 4--10 keV lightcurves in one year bins for all the sources and characterize their variabilities with an index based on a likelihood function and the excess variance. Possible counterparts are found from five major X-ray survey catalogs by Swift, Uhuru, RXTE, XMM-Newton, and ROSAT, and an X-ray galaxy-cluster catalog (MCXC). Our catalog provides the fluxes, positions, detection significances, HRs, one-year bin lightcurves, variability indices, and counterpart candidates.

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Correlation between the luminosity and spin-period changes during outbursts of 12 Be binary pulsars observed by the MAXI/GSC and the Fermi/GBM

To observationally study spin-period changes of accreting pulsars caused by the accretion torque, the present work analyzes X-ray light curves of 12 Be binary pulsars obtained by the MAXI/GSC all-sky survey and their pulse periods measured by the Fermi/GBM pulsar project, both covering more than 6 years from 2009 August to 2016 March. The 12 objects were selected because they are accompanied by clear optical identification, and accurate measurements of surface magnetic fields. The luminosity $L$ and the spin-frequency derivatives $\dotν$, measured during large outbursts with $L\gtrsim 1\times 10^{37}$ erg s$^{-1}$, were found to approximately follow the theoretical relations in the accretion torque models, represented by $\dotν \propto L^α$ ($α\simeq 1$), and the coefficient of proportionality between $\dotν$ and $L^α$, agrees, within a factor of $\sim 3$, with that proposed by Ghosh & Lamb (1979). In the course of the present study, the orbital elements of several sources were refined.

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Large X-ray Flares on Stars Detected with MAXI/GSC: A Universal Correlation between the Duration of a Flare and its X-ray Luminosity

23 giant flares from 13 active stars (eight RS CVn systems, one Algol system, three dMe stars and one YSO) were detected during the first two years of our all-sky X-ray monitoring with the gas propotional counters (GSC) of the Monitor of All-sky X-ray Image (MAXI). The observed parameters of all of these MAXI/GSC flares are found to be at the upper ends for stellar flares with the luminosity of 10^(31-34) ergs s-1 in the 2-20 keV band, the emission measure of 10^(54-57) cm-3, the e-folding time of 1 hour to 1.5 days, and the total radiative energy released during the flare of 10^(34-39) ergs. Notably, the peak X-ray luminosity of 5(3-9)*10^33 ergs s-1 in the 2-20 keV band was detected in one of the flares on II Peg, which is one of the, or potentially the, largest ever observed in stellar flares. X-ray flares were detected from GT Mus, V841 Cen, SZ Psc, and TWA-7 for the first time in this survey. Whereas most of our detected sources are multiple-star systems, two of them are single stars (YZ CMi and TWA-7). Among the stellar sources within 100 pc distance, the MAXI/GSC sources have larger rotation velocities than the other sources. This suggests that the rapid rotation velocity may play a key role in generating large flares. Combining the X-ray flare data of nearby stars and the sun, taken from literature and our own data, we discovered a universal correlation of tau~L_X^0.2 for the flare duration tau and the intrinsic X-ray luminosity L_X in the 0.1-100 keV band, which holds for 5 and 12 orders of magnitude in tau and L_X, respectively. The MAXI/GSC sample is located at the highest ends on the correlation.

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Hard-tail emission in the soft state of low-mass X-ray binaries and their relation to the neutron star magnetic field

Average hard-tail X-ray emission in the soft state of nine bright Atoll low-mass X-ray binaries containing a neutron star (NS-LMXBs) are investigated by using the light curves of MAXI/GSC and Swift/BAT. Two sources (4U 1820$-$30 and 4U 1735$-$44) exhibit large hardness ratio (15--50 keV$/$2--10 keV: {\it HR} $>$ 0.1), while the other sources distribute at {\it HR} $\ltsim$ 0.1. In either case, {\it HR} does not depend on the 2--10 keV luminosity. Therefore the difference of {\it HR} is due to the 15--50 keV luminosity, which is Comptonized emission. The Compton cloud is assumed to be around the neutron star. The size of the Compton cloud would affect the value of {\it HR}. Although the magnetic field of NS-LMXB is weak, we could expect a larger Alfvén radius than the innermost stable circular orbit or the neutron star radius in some sources. In such cases, the accretion inflow is stopped at the Alfvén radius and would create relatively large Compton cloud. It would result in the observed larger Comptonized emission. By attributing the difference of the size of Compton cloud to the Alfvén radius, we can estimate the magnetic fields of neutron star. The obtained lower/upper limits are consistent with the previous results.

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Application of the Ghosh & Lamb Relation to the Spin-up/down Behavior in the X-ray Binary Pulsar 4U 1626-67

We analyzed continuous MAXI/GSC data of the X-ray binary pulsar 4U 1626-67 from 2009 October to 2013 September, and determined the pulse period and the pulse-period derivative for every 60-d interval by the epoch folding method. The obtained periods are consistent with those provided by the Fermi/GBM pulsar project. In all the 60-d intervals, the pulsar was observed to spin up, with the spin-up rate positively correlated with the 2-20 keV flux. We applied the accretion torque model proposed by Ghosh & Lamb (1979, ApJ, 234, 296) to the MAXI/GSC data, as well as the past data including both spin-up and spin-down phases. The Ghosh & Lamb relation was confirmed to successfully explain the observed relation between the spin-up/down rate and the flux. By comparing the model-predicted luminosity with the observed flux, the source distance was constrained as 5-13 kpc, which is consistent with that by Chakrabarty (1998, ApJ, 492, 342). Conversely, if the source distance is assumed, the data can constrain the mass and radius of the neutron star, because the Ghosh & Lamb model depends on these parameters. We attempted this idea, and found that an assumed distance of, e.g., 10 kpc gives a mass in the range of 1.81-1.90 solar mass, and a radius of 11.4-11.5 km, although these results are still subject to considerable systematic uncertainties other than that in the distance.

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