arXiv subjects

Charles J. Hailey

Publications and source records attributed to Charles J. Hailey.

At least 73 records · Page 4Linked to original sources

arXiv2015

Hard X-ray Morphological and Spectral Studies of The Galactic Center Molecular Cloud Sgr B2: Constraining Past Sgr A* Flaring Activity

Galactic Center (GC) molecular cloud Sgr B2 is the best manifestation of an X-ray reflection nebula (XRN) reprocessing a past giant outburst from the supermassive black hole Sgr A*. Alternatively, Sgr B2 could be illuminated by low-energy cosmic ray electrons (LECRe) or protons (LECRp). In 2013, NuSTAR for the first time resolved Sgr B2 hard X-ray emission on sub-arcminute scales. Two prominent features are detected above 10 keV - a newly emerging cloud G0.66-0.13 and the central 90" radius region containing two compact cores Sgr B2(M) and Sgr B2(N) surrounded by diffuse emission. It is inconclusive whether the remaining level of Sgr B2 emission is still decreasing or has reached a constant background level. A decreasing Fe K$α$ emission can be best explained by XRN while a constant background emission can be best explained by LECRp. In the XRN scenario, the 3-79 keV Sgr B2 spectrum can well constrain the past Sgr A* outburst, resulting in an outburst spectrum with a peak luminosity of $L_{3-79\rm~keV} \sim 5\times10^{38} \rm~erg~s^{-1}$ derived from the maximum Compton-scattered continuum and the Fe K$α$ emission consistently. The XRN scenario is preferred by the fast variability of G0.66-0.13, which could be a molecular clump located in the Sgr B2 envelope reflecting the same Sgr A* outburst. In the LECRp scenario, we derived the required CR ion power $dW/dt=(1-4)\times10^{39}\rm~erg~s^{-1}$ and the CR ionization rate $ζ_{H}=(6-10)\times 10^{-15}\rm~H^{-1}~s^{-1}$. The Sgr B2 background level X-ray emission will be a powerful tool to constrain GC CR population.

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arXiv2015

NuSTAR discovery of an unusually steady long-term spin-up of the Be binary 2RXP J130159.6-635806

We present spectral and timing analysis of NuSTAR observations of the accreting X-ray pulsar 2RXP J130159.6-635806. The source was serendipitously observed during a campaign focused on the gamma-ray binary PSR B1259-63 and was later targeted for a dedicated observation. The spectrum has a typical shape for accreting X-ray pulsars, consisting of a simple power law with an exponential cutoff starting at ~7 keV with a folding energy of E_fold=~18 keV. There is also an indication of the presence of a 6.4 keV iron line in the spectrum at the ~3 sigma significance level. NuSTAR measurements of the pulsation period reveal that the pulsar has undergone a strong and steady spin-up for the last 20 years. The pulsed fraction is estimated to be ~80%, and is constant with energy up to 40 keV. The power density spectrum shows a break towards higher frequencies relative to the current spin period. This, together with steady persistent luminosity, points to a long-term mass accretion rate high enough to bring the pulsar out of spin equilibrium.

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arXiv2015

NuSTAR observations of the powerful radio-galaxy Cygnus A

We present NuSTAR observations of the powerful radio galaxy Cygnus A, focusing on the central absorbed active galactic nucleus (AGN). Cygnus A is embedded in a cool-core galaxy cluster, and hence we also examine archival XMM-Newton data to facilitate the decomposition of the spectrum into the AGN and intracluster medium (ICM) components. NuSTAR gives a source-dominated spectrum of the AGN out to >70keV. In gross terms, the NuSTAR spectrum of the AGN has the form of a power law (Gamma~1.6-1.7) absorbed by a neutral column density of N_H~1.6x10^23 cm^-2. However, we also detect curvature in the hard (>10keV) spectrum resulting from reflection by Compton-thick matter out of our line-of-sight to the X-ray source. Compton reflection, possibly from the outer accretion disk or obscuring torus, is required even permitting a high-energy cutoff in the continuum source; the limit on the cutoff energy is E_cut>111keV (90% confidence). Interestingly, the absorbed power-law plus reflection model leaves residuals suggesting the absorption/emission from a fast (15,000-26,000km/s), high column-density (N_W>3x10^23 cm^-2), highly ionized (xi~2,500 erg cm/s) wind. A second, even faster ionized wind component is also suggested by these data. We show that the ionized wind likely carries a significant mass and momentum flux, and may carry sufficient kinetic energy to exercise feedback on the host galaxy. If confirmed, the simultaneous presence of a strong wind and powerful jets in Cygnus A demonstrates that feedback from radio-jets and sub-relativistic winds are not mutually exclusive phases of AGN activity but can occur simultaneously.

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arXiv2015

Deep NuSTAR and Swift Monitoring Observations of the Magnetar 1E 1841-045

We report on a 350-ks NuSTAR observation of the magnetar 1E 1841-045 taken in 2013 September. During the observation, NuSTAR detected six bursts of short duration, with $T_{90}<1$ s. An elevated level of emission tail is detected after the brightest burst, persisting for $\sim$1 ks. The emission showed a power-law decay with a temporal index of 0.5 before returning to the persistent emission level. The long observation also provided detailed phase-resolved spectra of the persistent X-ray emission of the source. By comparing the persistent spectrum with that previously reported, we find that the source hard-band emission has been stable over approximately 10 years. The persistent hard X-ray emission is well fitted by a coronal outflow model, where $e^{+/-}$ pairs in the magnetosphere upscatter thermal X-rays. Our fit of phase-resolved spectra allowed us to estimate the angle between the rotational and magnetic dipole axes of the magnetar, $α_{mag}=0.25$, the twisted magnetic flux, $2.5\times10^{26}\rm \ G\ cm^2$, and the power released in the twisted magnetosphere, $L_j=6\times10^{36}\rm \ erg\ s^{-1}$. Assuming this model for the hard X-ray spectrum, the soft X-ray component is well fit by a two-blackbody model, with the hotter blackbody consistent with the footprint of the twisted magnetic field lines on the star. We also report on the 3-year Swift monitoring observations obtained since 2011 July. The soft X-ray spectrum remained stable during this period, and the timing behavior was noisy, with large timing residuals.

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arXiv2015

Broadband X-ray Properties of the Gamma-ray Binary 1FGL J1018.6-5856

We report on NuSTAR, XMM-Newton and Swift observations of the gamma-ray binary 1FGL J1018.6-5856. We measure the orbital period to be 16.544+/-0.008 days using Swift data spanning 1900 days. The orbital period is different from the 2011 gamma-ray measurement which was used in the previous X-ray study of An et al. (2013) using ~400 days of Swift data, but is consistent with a new gamma-ray solution reported in 2014. The light curve folded on the new period is qualitatively similar to that reported previously, having a spike at phase 0 and broad sinusoidal modulation. The X-ray flux enhancement at phase 0 occurs more regularly in time than was previously suggested. A spiky structure at this phase seems to be a persistent feature, although there is some variability. Furthermore, we find that the source flux clearly correlates with the spectral hardness throughout all orbital phases, and that the broadband X-ray spectra measured with NuSTAR, XMM-Newton, and Swift are well fit with an unbroken power-law model. This spectrum suggests that the system may not be accretion-powered.

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arXiv2015

Broadband X-ray Imaging and Spectroscopy of the Crab Nebula and Pulsar with NuSTAR

We present broadband (3 -- 78 keV) NuSTAR X-ray imaging and spectroscopy of the Crab nebula and pulsar. We show that while the phase-averaged and spatially integrated nebula + pulsar spectrum is a power-law in this energy band, spatially resolved spectroscopy of the nebula finds a break at $\sim$9 keV in the spectral photon index of the torus structure with a steepening characterized by $ΔΓ\sim0.25$. We also confirm a previously reported steepening in the pulsed spectrum, and quantify it with a broken power-law with break energy at $\sim$12 keV and $ΔΓ\sim0.27$. We present spectral maps of the inner 100\as\ of the remnant and measure the size of the nebula as a function of energy in seven bands. These results find that the rate of shrinkage with energy of the torus size can be fitted by a power-law with an index of $γ= 0.094\pm 0.018$, consistent with the predictions of Kennel and Coroniti (1984). The change in size is more rapid in the NW direction, coinciding with the counter-jet where we find the index to be a factor of two larger. NuSTAR observed the Crab during the latter part of a $γ$-ray flare, but found no increase in flux in the 3 - 78 keV energy band.

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arXiv2015

Locating the most energetic electrons in Cassiopeia A

We present deep ($>$2.4 Ms) observations of the Cassiopeia A supernova remnant with {\it NuSTAR}, which operates in the 3--79 keV bandpass and is the first instrument capable of spatially resolving the remnant above 15 keV. We find that the emission is not entirely dominated by the forward shock nor by a smooth "bright ring" at the reverse shock. Instead we find that the $>$15 keV emission is dominated by knots near the center of the remnant and dimmer filaments near the remnant's outer rim. These regions are fit with unbroken power-laws in the 15--50 keV bandpass, though the central knots have a steeper ($Γ\sim -3.35$) spectrum than the outer filaments ($Γ\sim -3.06$). We argue this difference implies that the central knots are located in the 3-D interior of the remnant rather than at the outer rim of the remnant and seen in the center due to projection effects. The morphology of $>$15 keV emission does not follow that of the radio emission nor that of the low energy ($<$12 keV) X-rays, leaving the origin of the $>$15 keV emission as an open mystery. Even at the forward shock front we find less steepening of the spectrum than expected from an exponentially cut off electron distribution with a single cutoff energy. Finally, we find that the GeV emission is not associated with the bright features in the {\it NuSTAR} band while the TeV emission may be, suggesting that both hadronic and leptonic emission mechanisms may be at work.

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arXiv2014

NuSTAR Detection Of A Cyclotron Line In The Supergiant Fast X-ray Transient IGR J17544-2619

We present NuSTAR spectral and timing studies of the Supergiant Fast X-ray Transient (SFXT) IGR J17544-2619. The spectrum is well-described by a ~1 keV blackbody and a hard continuum component, as expected from an accreting X-ray pulsar. We detect a cyclotron line at 17 keV, confirming that the compact object in IGR J17544-2619 is indeed a neutron star. This is the first measurement of the magnetic field in a SFXT. The inferred magnetic field strength, B = (1.45 +/- 0.03) * 10^12 G * (1+z) is typical of neutron stars in X-ray binaries, and rules out a magnetar nature for the compact object. We do not find any significant pulsations in the source on time scales of 1-2000 s.

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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

The Broadband XMM-Newton and NuSTAR X-ray Spectra of Two Ultraluminous X-ray Sources in the Galaxy IC 342

We present results for two Ultraluminous X-ray Sources (ULXs), IC 342 X-1 and IC 342 X-2, using two epochs of XMM-Newton and NuSTAR observations separated by $\sim$7 days. We observe little spectral or flux variability above 1 keV between epochs, with unabsorbed 0.3--30 keV luminosities being $1.04^{+0.08}_{-0.06} \times 10^{40}$ erg s$^{-1}$ for IC 342 X-1 and $7.40\pm0.20 \times 10^{39}$ erg s$^{-1}$ for IC 342 X-2, so that both were observed in a similar, luminous state. Both sources have a high absorbing column in excess of the Galactic value. Neither source has a spectrum consistent with a black hole binary in low/hard state, and both ULXs exhibit strong curvature in their broadband X-ray spectra. This curvature rules out models that invoke a simple reflection-dominated spectrum with a broadened iron line and no cutoff in the illuminating power-law continuum. X-ray spectrum of IC 342 X-1 can be characterized by a soft disk-like black body component at low energies and a cool, optically thick Comptonization continuum at high energies, but unique physical interpretation of the spectral components remains challenging. The broadband spectrum of IC 342 X-2 can be fit by either a hot (3.8 keV) accretion disk, or a Comptonized continuum with no indication of a seed photon population. Although the seed photon component may be masked by soft excess emission unlikely to be associated with the binary system, combined with the high absorption column, it is more plausible that the broadband X-ray emission arises from a simple thin blackbody disk component. Secure identification of the origin of the spectral components in these sources will likely require broadband spectral variability studies.

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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

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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