arXiv subjects

Finn E. Christensen

Publications and source records attributed to Finn E. Christensen.

At least 55 records · Page 3Linked to original sources

arXiv2014

The Hard X-Ray View of the Young Supernova Remnant G1.9+0.3

NuSTAR observed G1.9+0.3, the youngest known supernova remnant in the Milky Way, for 350 ks and detected emission up to $\sim$30 keV. The remnant's X-ray morphology does not change significantly across the energy range from 3 to 20 keV. A combined fit between NuSTAR and CHANDRA shows that the spectrum steepens with energy. The spectral shape can be well fitted with synchrotron emission from a power-law electron energy distribution with an exponential cutoff with no additional features. It can also be described by a purely phenomenological model such as a broken power-law or a power-law with an exponential cutoff, though these descriptions lack physical motivation. Using a fixed radio flux at 1 GHz of 1.17 Jy for the synchrotron model, we get a column density of N$_{\rm H}$ = $(7.23\pm0.07) \times 10^{22}$ cm$^{-2}$, a spectral index of $α=0.633\pm0.003$, and a roll-off frequency of $ν_{\rm rolloff}=(3.07\pm0.18) \times 10^{17}$ Hz. This can be explained by particle acceleration, to a maximum energy set by the finite remnant age, in a magnetic field of about 10 $μ$G, for which our roll-off implies a maximum energy of about 100 TeV for both electrons and ions. Much higher magnetic-field strengths would produce an electron spectrum that was cut off by radiative losses, giving a much higher roll-off frequency that is independent of magnetic-field strength. In this case, ions could be accelerated to much higher energies. A search for $^{44}$Ti emission in the 67.9 keV line results in an upper limit of $1.5 \times 10^{-5}$ $\,\mathrm{ph}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}$ assuming a line width of 4.0 keV (1 sigma).

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arXiv2014

NuSTAR observation of a Type I X-ray burst from GRS 1741.9-2853

We report on two NuSTAR observations of GRS 1741.9-2853, a faint neutron star low mass X-ray binary burster located 10' away from the Galactic center. NuSTAR detected the source serendipitously as it was emerging from quiescence: its luminosity was $6\times 10^{34}$ erg~s$^{-1}$ on 2013 July 31, and $5\times 10^{35}$ erg~s$^{-1}$ in a second observation on 2013 August 3. A bright, 800-s long, H-triggered mixed H/He thermonuclear Type I burst with mild photospheric radius expansion (PRE) was present during the second observation. Assuming that the luminosity during the PRE was at the Eddington level, a H mass fraction $X=0.7$ in the atmosphere, and a neutron star mass $M=1.4 M_{\odot}$, we determine a new lower limit on the distance for this source of $6.3 \pm 0.5$ kpc. Combining with previous upper limits, this places GRS 1741.9-2853 at a distance of 7 kpc. Energy independent (achromatic) variability is observed during the cooling of the neutron star, which could result from the disturbance of the inner accretion disk by the burst. The large dynamic range of this burst reveals a long power-law decay tail. We also detect, at a 95.6\% confidence level (1.7 $σ$), a narrow absorption line at $5.46\pm0.10$ keV during the PRE phase of the burst, reminiscent of the detection by Waki et al. (1984). We propose that the line, if real, is formed in the wind above the photosphere of the neutron star by a resonant K$α$ transition from H-like Cr gravitationally redshifted by a factor $1+z=1.09$, corresponding to a radius range of 29.0 -- 41.4 km for a mass range of 1.4 -- 2.0 $M_{\odot}$.

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arXiv2014

NuSTAR Spectroscopy of Multi-Component X-ray Reflection from NGC 1068

We report on observations of NGC1068 with NuSTAR, which provide the best constraints to date on its $>10$~keV spectral shape. We find no strong variability over the past two decades, consistent with its Compton-thick AGN classification. The combined NuSTAR, Chandra, XMM-Newton, and Swift-BAT spectral dataset offers new insights into the complex reflected emission. The critical combination of the high signal-to-noise NuSTAR data and a spatial decomposition with Chandra allow us to break several model degeneracies and greatly aid physical interpretation. When modeled as a monolithic (i.e., a single N_H) reflector, none of the common Compton-reflection models are able to match the neutral fluorescence lines and broad spectral shape of the Compton reflection. A multi-component reflector with three distinct column densities (e.g., N_H~1.5e23, 5e24, and 1e25 cm^{-2}) provides a more reasonable fit to the spectral lines and Compton hump, with near-solar Fe abundances. In this model, the higher N_H components provide the bulk of the Compton hump flux while the lower N_H component produces much of the line emission, effectively decoupling two key features of Compton reflection. We note that ~30% of the neutral Fe Kalpha line flux arises from >2" (~140 pc), implying that a significant fraction of the <10 keV reflected component arises from regions well outside of a parsec-scale torus. These results likely have ramifications for the interpretation of poorer signal-to-noise observations and/or more distant objects [Abridged].

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arXiv2014

A Hard X-Ray Power-Law Spectral Cutoff in Centaurus X-4

The low-mass X-ray binary Cen X-4 is the brightest and closest (<1.2 kpc) quiescent neutron star transient. Previous 0.5-10 keV X-ray observations of Cen X-4 in quiescence identified two spectral components: soft thermal emission from the neutron star atmosphere and a hard power-law tail of unknown origin. We report here on a simultaneous observation of Cen X-4 with NuSTAR (3-79 keV) and XMM-Newton (0.3-10 keV) in 2013 January, providing the first sensitive hard X-ray spectrum of a quiescent neutron star transient. The 0.3-79 keV luminosity was 1.1 x 10^(33) erg/s (for D=1kpc), with around 60 percent in the thermal component. We clearly detect a cutoff of the hard spectral tail above 10 keV, the first time such a feature has been detected in this source class. We show that thermal Comptonization and synchrotron shock origins for the hard X-ray emission are ruled out on physical grounds. However, the hard X-ray spectrum is well fit by a thermal bremsstrahlung model with an 18 keV electron temperature, which can be understood as arising either in a hot layer above the neutron star atmosphere or in a radiatively-inefficient accretion flow (RIAF). The power-law cutoff energy may be set by the degree of Compton cooling of the bremsstrahlung electrons by thermal seed photons from the neutron star surface. Lower thermal luminosities should lead to higher (possibly undetectable) cutoff energies. We compare Cen~X-4's behavior with PSR J1023+0038, IGR J18245-2452, and XSS J12270-4859, which have shown transitions between LMXB and radio pulsar modes at a similar X-ray luminosity.

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arXiv2014

NuSTAR Discovery of a Cyclotron Line in the Be/X-ray Binary RX J0520.5-6932 During Outburst

We present spectral and timing analysis of NuSTAR observations of RX J0520.5$-$6932 in the 3-79 keV band collected during its outburst in January 2014. The target was observed on two epochs and we report the detection of a cyclotron resonant scattering feature with central energies of $E_\mathrm{CRSF} = 31.3_{-0.7}^{+0.8}$ keV and $31.5_{-0.6}^{+0.7}$ keV during the two observations, respectively, corresponding to a magnetic field of $B \approx 2 \times10^{12}$ G. The 3-79 keV luminosity of the system during the two epochs assuming a nominal distance of 50 kpc was $3.667\pm0.007\times 10^{38}\,\mathrm{erg\,s^{-1}}$ and $3.983\pm0.007\times10^{38}\,\mathrm{erg\,s^{-1}}$. Both values are much higher than the critical luminosity of $\approx1.5\times10^{37}\,\mathrm{erg\,s^{-1}}$ above which a radiation dominated shock front may be expected. This adds a new object to the sparse set of three systems that have a cyclotron line observed at luminosities in excess of $10^{38}\,\mathrm{erg\,s^{-1}}$. A broad ($σ\approx0.45$ keV) Fe emission line is observed in the spectrum at a central energy of $6.58_{-0.05}^{+0.05}$ keV in both epochs. The pulse profile of the pulsar was observed to be highly asymmetric with a sharply rising and slowly falling profile of the primary peak. We also observed minor variations in the cyclotron line energy and width as a function of the rotation phase.% As in observations of other cyclotron absorption line sources, there is a small ($Δϕ\lesssim0.1$) phase difference between the peak of the cyclotron energy variation and the peak of the flux variation.

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arXiv2014

No Time for Dead Time: Timing analysis of bright black hole binaries with NuSTAR

Timing of high-count rate sources with the NuSTAR Small Explorer Mission requires specialized analysis techniques. NuSTAR was primarily designed for spectroscopic observations of sources with relatively low count-rates rather than for timing analysis of bright objects. The instrumental dead time per event is relatively long (~2.5 msec), and varies by a few percent event-to-event. The most obvious effect is a distortion of the white noise level in the power density spectrum (PDS) that cannot be modeled easily with the standard techniques due to the variable nature of the dead time. In this paper, we show that it is possible to exploit the presence of two completely independent focal planes and use the cross power density spectrum to obtain a good proxy of the white noise-subtracted PDS. Thereafter, one can use a Monte Carlo approach to estimate the remaining effects of dead time, namely a frequency-dependent modulation of the variance and a frequency-independent drop of the sensitivity to variability. In this way, most of the standard timing analysis can be performed, albeit with a sacrifice in signal to noise relative to what would be achieved using more standard techniques. We apply this technique to NuSTAR observations of the black hole binaries GX 339-4, Cyg X-1 and GRS 1915+105.

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arXiv2014

A broadband X-ray study of the Geminga pulsar with NuSTAR and XMM-Newton

We report on the first hard X-ray detection of the Geminga pulsar above 10 keV using a 150 ks observation with the NuSTAR observatory. The double-peaked pulse profile of non-thermal emission seen in the soft X-ray band persists at higher energies. Broadband phase-integrated spectra over the 0.2-20 keV band with NuSTAR and archival XMM-Newton data do not fit to a conventional two-component model of a blackbody plus power-law, but instead exhibit spectral hardening above ~5 keV. We find two spectral models fit the data well: (1) a blackbody (kT1 ~ 42 eV) with a broken power-law (Gamma1 ~ 2.0, Gamma2 ~ 1.4 and Ebreak ~ 3.4 keV), and (2) two blackbody components (kT1 ~ 44 eV and kT2 ~ 195 eV) with a power-law component (Gamma ~ 1.7). In both cases, the extrapolation of the Rayleigh-Jeans tail of the thermal component is consistent with the UV data, while the non-thermal component overpredicts the near-infrared data, requiring a spectral flattening at E ~ 0.01 - 1 keV. While strong phase variation of the power-law index is present below ~5 keV, our phase-resolved spectroscopy with NuSTAR indicates that another hard non-thermal component with Gamma ~ 1.3 emerges above ~5 keV. The spectral hardening in non-thermal X-ray emission as well as spectral flattening between the optical and X-ray bands argue against the conjecture that a single power-law may account for multi-wavelength non-thermal spectra of middle-aged pulsars.

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arXiv2014

NuSTAR Observations of the Magnetar 1E 2259+586

We report on new broad band spectral and temporal observations of the magnetar 1E 2259+586, which is located in the supernova remnant CTB 109. Our data were obtained simultaneously with the Nuclear Spectroscopic Telescope Array (NuSTAR) and Swift, and cover the energy range from 0.5-79 keV. We present pulse profiles in various energy bands and compare them to previous RXTE results. The NuSTAR data show pulsations above 20 keV for the first time and we report evidence that one of the pulses in the double-peaked pulse profile shifts position with energy. The pulsed fraction of the magnetar is shown to increase strongly with energy. Our spectral analysis reveals that the soft X-ray spectrum is well characterized by an absorbed double-blackbody or blackbody plus power-law model in agreement with previous reports. Our new hard X-ray data, however, suggests that an additional component, such as a power-law, is needed to describe the NuSTAR and Swift spectrum. We also fit the data with the recently developed coronal outflow model by Beloborodov for hard X-ray emission from magnetars. The outflow from a ring on the magnetar surface is statistically preferred over outflow from a polar cap.

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arXiv2014

High-Energy X-ray Imaging of the Pulsar Wind Nebula MSH~15-52: Constraints on Particle Acceleration and Transport

We present the first images of the pulsar wind nebula (PWN) MSH 15-52 in the hard X-ray band (>8 keV), as measured with the Nuclear Spectroscopic Telescope Array (NuSTAR). Overall, the morphology of the PWN as measured by NuSTAR in the 3-7 keV band is similar to that seen in Chandra high-resolution imaging. However, the spatial extent decreases with energy, which we attribute to synchrotron energy losses as the particles move away from the shock. The hard-band maps show a relative deficit of counts in the northern region towards the RCW 89 thermal remnant, with significant asymmetry. We find that the integrated PWN spectra measured with NuSTAR and Chandra suggest that there is a spectral break at 6 keV which may be explained by a break in the synchrotron-emitting electron distribution at ~200 TeV and/or imperfect cross calibration. We also measure spatially resolved spectra, showing that the spectrum of the PWN softens away from the central pulsar B1509-58, and that there exists a roughly sinusoidal variation of spectral hardness in the azimuthal direction. We discuss the results using particle flow models. We find non-monotonic structure in the variation with distance of spectral hardness within 50" of the pulsar moving in the jet direction, which may imply particle and magnetic-field compression by magnetic hoop stress as previously suggested for this source. We also present 2-D maps of spectral parameters and find an interesting shell-like structure in the NH map. We discuss possible origins of the shell-like structure and their implications.

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arXiv2014

The variable hard X-ray emission of NGC4945 as observed by NuSTAR

We present a broadband (~0.5-79 keV) spectral and temporal analysis of multiple NuSTAR observations combined with archival Suzaku and Chandra data of NGC4945, the brightest extragalactic source at 100 keV. We observe hard X-ray (> 10 keV) flux and spectral variability, with flux variations of a factor 2 on timescales of 20 ksec. A variable primary continuum dominates the high energy spectrum (>10 keV) in all the states, while the reflected/scattered flux which dominates at E< 10 keV stays approximately constant. From modelling the complex reflection/transmission spectrum we derive a Compton depth along the line of sight of tau_Thomson ~ 2.9, and a global covering factor for the circumnuclear gas of ~ 0.15. This agrees with the constraints derived from the high energy variability, which implies that most of the high energy flux is transmitted, rather that Compton-scattered. This demonstrates the effectiveness of spectral analysis in constraining the geometric properties of the circumnuclear gas, and validates similar methods used for analyzing the spectra of other bright, Compton-thick AGN. The lower limits on the e-folding energy are between 200-300 keV, consistent with previous BeppoSAX, Suzaku and Swift BAT observations. The accretion rate, estimated from the X-ray luminosity and assuming a bolometric correction typical of type 2 AGN, is in the range ~0.1-0.3 lambda_Edd depending on the flux state. The substantial observed X-ray luminosity variability of NGC4945 implies that large errors can arise from using single-epoch X-ray data to derive L/L_Edd values for obscured AGNs.

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arXiv2014

Initial Results from NuSTAR Observations of the Norma Arm

Results are presented for an initial survey of the Norma Arm gathered with the focusing hard X-ray telescope NuSTAR. The survey covers 0.2 deg$^2$ of sky area in the 3-79 keV range with a minimum and maximum raw depth of 15 ks and 135 ks, respectively. Besides a bright black-hole X-ray binary in outburst (4U 1630-47) and a new X-ray transient (NuSTAR J163433-473841), NuSTAR locates three sources from the Chandra survey of this region whose spectra are extended above 10 keV for the first time: CXOU J163329.5-473332, CXOU J163350.9-474638, and CXOU J163355.1-473804. Imaging, timing, and spectral data from a broad X-ray range (0.3-79 keV) are analyzed and interpreted with the aim of classifying these objects. CXOU J163329.5-473332 is either a cataclysmic variable or a faint low-mass X-ray binary. CXOU J163350.9-474638 varies in intensity on year-long timescales, and with no multi-wavelength counterpart, it could be a distant X-ray binary or possibly a magnetar. CXOU J163355.1-473804 features a helium-like iron line at 6.7 keV and is classified as a nearby cataclysmic variable. Additional surveys are planned for the Norma Arm and Galactic Center, and those NuSTAR observations will benefit from the lessons learned during this pilot study.

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arXiv2014

In-flight PSF calibration of the NuSTAR hard X-ray optics

We present results of the point spread function (PSF) calibration of the hard X-ray optics of the Nuclear Spectroscopic Telescope Array (NuSTAR). Immediately post-launch, NuSTAR has observed bright point sources such as Cyg X-1, Vela X-1, and Her X-1 for the PSF calibration. We use the point source observations taken at several off-axis angles together with a ray-trace model to characterize the in-orbit angular response, and find that the ray-trace model alone does not fit the observed event distributions and applying empirical corrections to the ray-trace model improves the fit significantly. We describe the corrections applied to the ray-trace model and show that the uncertainties in the enclosed energy fraction (EEF) of the new PSF model is < 3% for extraction apertures of R > 60" with no significant energy dependence. We also show that the PSF of the NuSTAR optics has been stable over a period of ~300 days during its in-orbit operation.

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arXiv2014

NuSTAR Observations of the State Transition of Millisecond Pulsar Binary PSR J1023+0038

We report NuSTAR observations of the millisecond pulsar - low mass X-ray binary (LMXB) transition system PSR J1023+0038 from June and October 2013, before and after the formation of an accretion disk around the neutron star. Between June 10-12, a few days to two weeks before the radio disappearance of the pulsar, the 3-79 keV X-ray spectrum was well fit by a simple power law with a photon index of Gamma=1.17 +/-0.08 (at 90% confidence) with a 3-79 keV luminosity of 7.4+/-0.4 x 10^32 erg/s. Significant orbital modulation was observed with a modulation fraction of 36+/-10%. During the October 19-21 observation, the spectrum is described by a softer power law (Gamma=1.66+/-0.06) with an average luminosity of 5.8+/-0.2 x 10^33 erg/s and a peak luminosity of ~1.2 x 10^34 erg/s observed during a flare. No significant orbital modulation was detected. The spectral observations are consistent with previous and current multi-wavelength observations and show the hard X-ray power law extending to 79 keV without a spectral break. Sharp edged, flat bottomed `dips' are observed with widths between 30-1000 s and ingress and egress time-scales of 30-60 s. No change in hardness ratio was observed during the dips. Consecutive dip separations are log-normal in distribution with a typical separation of approximately 400 s. These dips are distinct from dipping activity observed in LMXBs. We compare and contrast these dips to observations of dips and state changes in the similar transition systems PSR J1824-2452I and XSS J1227.0-4859 and discuss possible interpretations based on the transitions in the inner disk.

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arXiv2014

NuSTAR observations of X-ray bursts from the magnetar 1E 1048.1-5937

We report the detection of eight bright X-ray bursts from the 6.5-s magnetar 1E 1048.1-5937, during a 2013 July observation campaign with the Nuclear Spectroscopic Telescope Array (NuSTAR). We study the morphological and spectral properties of these bursts and their evolution with time. The bursts resulted in count rate increases by orders of magnitude, sometimes limited by the detector dead time, and showed blackbody spectra with kT=6-8 keV in the T90 duration of 1-4 s, similar to earlier bursts detected from the source. We find that the spectra during the tail of the bursts can be modeled with an absorbed blackbody with temperature decreasing with flux. The bursts flux decays followed a power-law of index 0.8-0.9. In the burst tail spectra, we detect a ~13 keV emission feature, similar to those reported in previous bursts from this source as well as from other magnetars observed with the Rossi X-ray Timing Explorer (RXTE). We explore possible origins of the spectral feature such as proton cyclotron emission, which implies a magnetic field strength of B~2X10^15 G in the emission region. However, the consistency of the energy of the feature in different objects requires further explanation.

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arXiv2014

NuSTAR study of Hard X-Ray Morphology and Spectroscopy of PWN G21.5-0.9

We present NuSTAR high energy X-ray observations of the pulsar wind nebula (PWN)/supernova remnant G21.5-0.9. We detect integrated emission from the nebula up to ~40 keV, and resolve individual spatial features over a broad X-ray band for the first time. The morphology seen by NuSTAR agrees well with that seen by XMM-Newton and Chandra below 10 keV. At high energies NuSTAR clearly detects non-thermal emission up to ~20 keV that extends along the eastern and northern rim of the supernova shell. The broadband images clearly demonstrate that X-ray emission from the North Spur and Eastern Limb results predominantly from non-thermal processes. We detect a break in the spatially integrated X-ray spectrum at ~9 keV that cannot be reproduced by current SED models, implying either a more complex electron injection spectrum or an additional process such as diffusion compared to what has been considered in previous work. We use spatially resolved maps to derive an energy-dependent cooling length scale, $L(E) \propto E^{m}$ with $m = -0.21 \pm 0.01$. We find this to be inconsistent with the model for the morphological evolution with energy described by Kennel & Coroniti (1984). This value, along with the observed steepening in power-law index between radio and X-ray, can be quantitatively explained as an energy-loss spectral break in the simple scaling model of Reynolds (2009), assuming particle advection dominates over diffusion. This interpretation requires a substantial departure from spherical magnetohydrodynamic (MHD), magnetic-flux-conserving outflow, most plausibly in the form of turbulent magnetic-field amplification.

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arXiv2014

NuSTAR J163433-4738.7: A Fast X-ray Transient in the Galactic Plane

During hard X-ray observations of the Norma spiral arm region by the Nuclear Spectroscopic Telescope Array (NuSTAR) in 2013 February, a new transient source, NuSTAR J163433-4738.7, was detected at a significance level of 8-sigma in the 3-10 keV bandpass. The source is consistent with having a constant NuSTAR count rate over a period of 40 ks and is also detected simultaneously by Swift at lower significance. The source is not significantly detected by NuSTAR, Swift, or Chandra in the days before or weeks after the discovery of the transient, indicating that the strong X-ray activity lasted for between ~0.5 and 1.5 days. Near-IR imaging observations were carried out before and after the X-ray activity, but we are not able to identify the counterpart. The combined NuSTAR and Swift energy spectrum is consistent with a power-law with a photon index of Gamma = 4.1(+1.5)(-1.0) (90% confidence errors), a blackbody with kT = 1.2+/-0.3 keV, or a bremsstrahlung model with kT = 3.0(+2.1)(-1.2) keV. The reduced-chi2 values for the three models are not significantly different, ranging from 1.23 to 1.44 for 8 degrees of freedom. The spectrum is strongly absorbed with NH = 2.8(+2.3)(-1.4)e23 cm-2, 9(+15)(-7)e22 cm-2, and 1.7(+1.7)(-0.9)e23 cm-2, for the power-law, blackbody, and bremsstrahlung models, respectively. Although the high column density could be due to material local to the source, it is consistent with absorption from interstellar material along the line of sight at a distance of 11 kpc, which would indicate an X-ray luminosity >1e34 erg/s. Although we do not reach a definitive determination of the nature of NuSTAR J163433-4738.7, we suggest that it may be an unusually bright active binary or a magnetar.

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arXiv2014

Confirmation of a High Magnetic Field in GRO J1008-57

GRO J1008$-$57 is a high-mass X-ray binary for which several claims of a cyclotron resonance scattering feature near 80 keV have been reported. We use NuSTAR, Suzaku, and Swift data from its giant outburst of November 2012 to confirm the existence of the 80 keV feature and perform the most sensitive search to date for cyclotron scattering features at lower energies. We find evidence for a 78$^{+3}_{-2}$ keV line in the NuSTAR and Suzaku data at $> 4σ$ significance, confirming the detection using Suzaku alone by Yamamoto et al. (2014). A search of both the time-integrated and phase-resolved data rules out a fundamental at lower energies with optical depth larger than 5% of the 78 keV line. These results indicate that GRO J1008$-$57 has a magnetic field of $6.7\times10^{12} (1+z)$ G, the highest of known accreting pulsars.

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arXiv2014

NuSTAR detection of high-energy X-ray emission and rapid variability from Sagittarius A* flares

Sagittarius A* harbors the supermassive black hole that lies at the dynamical center of our Galaxy. Sagittarius A* spends most of its time in a low luminosity emission state but flares frequently in the infrared and X-ray, increasing up to a few hundred fold in brightness for up to a few hours at a time. The physical processes giving rise to the X-ray flares are uncertain. Here we report the detection with the NuSTAR observatory in Summer and Fall 2012 of four low to medium amplitude X-ray flares to energies up to 79 keV. For the first time, we clearly see that the power-law spectrum of Sagittarius A* X-ray flares extends to high energy, with no evidence for a cut off. Although the photon index of the absorbed power-law fits are in agreement with past observations, we find a difference between the photon index of two of the flares (significant at the 95% confidence level). The spectra of the two brightest flares (~55 times quiescence in the 2-10 keV band) are compared to simple physical models in an attempt to identify the main X-ray emission mechanism, but the data do not allow us to significantly discriminate between them. However, we confirm the previous finding that the parameters obtained with synchrotron models are, for the X-ray emission, physically more reasonable than those obtained with inverse-Compton models. One flare exhibits large and rapid (< 100 s) variability, which, considering the total energy radiated, constrains the location of the flaring region to be within ~10 Schwarzschild radii of the black hole.

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