arXiv subjects

Didier Barret

Publications and source records attributed to Didier Barret.

At least 91 records · Page 5Linked to original sources

arXiv2013

Combined Analysis of Hubble and VLT Photometry of the Intermediate Mass Black Hole ESO 243-49 HLX-1

In this paper we present a combined analysis of data obtained with the Hubble Space Telescope (HST), Very Large Telescope (VLT), and Swift X-ray telescope (XRT) of the intermediate mass black hole ESO 243-49 HLX-1 that were taken 2 months apart between September and November 2010. Previous separate analyses of these data found that they were consistent with an irradiated accretion disc with contribution from either a very young or very old stellar population, and also indicated that the optical flux of the HLX-1 counterpart could be variable. Such variability could only be attributed to a varying accretion disc, so simultaneous analysis of all data sets should break the degeneracies in the model fits. We thus simultaneously fit the broad-band spectral energy distribution (SED) from near-infrared through to X-ray wavelengths of the two epochs of data with a model consisting of an irradiated accretion disc and a stellar population. We show that this combined analysis rules out an old stellar population, finding that the SED is dominated by emission from an accretion disc with moderate reprocessing in the outer disc around an intermediate mass black hole imbedded in a young (20 Myr) stellar cluster with a mass of 1E5 Msun. We also place an upper limit on the mass of an additional hidden old stellar population of 1E6 Msun. However, optical r-band observations of HLX-1 obtained with the Gemini-South telescope covering part of the decay from a later X-ray outburst are consistent with constant optical flux, indicating that the observed variability between the HST and VLT observations could be spurious caused by differences in the background subtraction applied to the two optical data sets. In this scenario the contribution of the stellar population, and thus the stellar mass of the cluster, may be higher (abridged).

astro-ph.HE↗

arXiv2013

The smooth cyclotron line in Her X-1 as seen with NuSTAR

Her X-1, one of the brightest and best studied X-ray binaries, shows a cyclotron resonant scattering feature (CRSF) near 37 keV. This makes it an ideal target for detailed study with the Nuclear Spectroscopic Telescope Array (NuSTAR), taking advantage of its excellent hard X-ray spectral resolution. We observed Her X-1 three times, coordinated with Suzaku, during one of the high flux intervals of its 35d super-orbital period. This paper focuses on the shape and evolution of the hard X-ray spectrum. The broad-band spectra can be fitted with a powerlaw with a high-energy cutoff, an iron line, and a CRSF. We find that the CRSF has a very smooth and symmetric shape, in all observations and at all pulse-phases. We compare the residuals of a line with a Gaussian optical depth profile to a Lorentzian optical depth profile and find no significant differences, strongly constraining the very smooth shape of the line. Even though the line energy changes dramatically with pulse phase, we find that its smooth shape does not. Additionally, our data show that the continuum is only changing marginally between the three observations. These changes can be explained with varying amounts of Thomson scattering in the hot corona of the accretion disk. The average, luminosity-corrected CRSF energy is lower than in past observations and follows a secular decline. The excellent data quality of NuSTAR provides the best constraint on the CRSF energy to date.

astro-ph.HE↗

arXiv2013

NuSTAR detection of hard X-ray phase lags from the accreting pulsar GS 0834-430

The NuSTAR hard X-ray telescope observed the transient Be/X-ray binary GS 0834-430 during its 2012 outburst - the first active state of this system observed in the past 19 years. We performed timing and spectral analysis, and measured the X-ray spectrum between 3-79keV with high statistical significance. We find the phase-averaged spectrum to be consistent with that observed in many other magnetized accreting pulsars. We fail to detect cyclotron resonance scattering features that would allow us to constrain the pulsar's magnetic field in either phase-averaged or phase-resolved spectra. Timing analysis shows a clearly detected pulse period of ~12.29s in all energy bands. The pulse profiles show a strong, energy-dependent hard phase lag of up to 0.3 cycles in phase, or about 4s. Such dramatic energy-dependent lags in the pulse profile have never before been reported in high-mass X-ray binary (HMXB) pulsars. Previously reported lags have been significantly smaller in phase and restricted to low-energies (E<10keV). We investigate the possible mechanisms that might produce this energy-dependent pulse phase shift. We find the most likely explanation for this effect to be a complex beam geometry.

astro-ph.HE↗

arXiv2013

The Hot and Energetic Universe: A White Paper presenting the science theme motivating the Athena+ mission

This White Paper, submitted to the recent ESA call for science themes to define its future large missions, advocates the need for a transformational leap in our understanding of two key questions in astrophysics: 1) How does ordinary matter assemble into the large scale structures that we see today? 2) How do black holes grow and shape the Universe? Hot gas in clusters, groups and the intergalactic medium dominates the baryonic content of the local Universe. To understand the astrophysical processes responsible for the formation and assembly of these large structures, it is necessary to measure their physical properties and evolution. This requires spatially resolved X-ray spectroscopy with a factor 10 increase in both telescope throughput and spatial resolving power compared to currently planned facilities. Feedback from supermassive black holes is an essential ingredient in this process and in most galaxy evolution models, but it is not well understood. X-ray observations can uniquely reveal the mechanisms launching winds close to black holes and determine the coupling of the energy and matter flows on larger scales. Due to the effects of feedback, a complete understanding of galaxy evolution requires knowledge of the obscured growth of supermassive black holes through cosmic time, out to the redshifts where the first galaxies form. X-ray emission is the most reliable way to reveal accreting black holes, but deep survey speed must improve by a factor ~100 over current facilities to perform a full census into the early Universe. The Advanced Telescope for High Energy Astrophysics (Athena+) mission provides the necessary performance (e.g. angular resolution, spectral resolution, survey grasp) to address these questions and revolutionize our understanding of the Hot and Energetic Universe. These capabilities will also provide a powerful observatory to be used in all areas of astrophysics.

astro-ph.HE↗

arXiv2013

The Hot and Energetic Universe: End points of stellar evolution

White dwarfs, neutron stars and stellar mass black holes are key laboratories to study matter in most extreme conditions of gravity and magnetic field. The unprecedented effective area of Athena+ will allow us to advance our understanding of emission mechanisms and accretion physics over a wide range of mass accretion rates, starting from lower and sub-luminous quiescent X-ray binaries up to super-Eddington ultra-luminous sources. Athena+ will measure stellar black hole spins in a much higher number of binaries than achievable now, opening the possibility to study how spin varies with black hole history. The high throughput and energy resolution of the X-IFU will be instrumental in establishing how disc wind properties depend on accretion state, in determining wind launching mechanism and in quantifying the impact of the wind induced mass loss on binary evolution and environment. Triggers and high quality optical and radio data originating from large wide field contemporaneous instruments will provide essential complementary information on jet launching mechanisms and on the physics of rotation powered pulsars, for instance. In addition, Athena+ will furnish multiple, independent measurements of the neutron star mass/radius relation in a wide range of environments and conditions so as to constrain the debated equation of state.

astro-ph.HE↗

arXiv2013

Soft lags in neutron star kHz Quasi Periodic Oscillations: evidence for reverberation?

High frequency soft reverberation lags have now been detected from stellar mass and super massive black holes. Their interpretation involves reflection of a hard source of photons onto an accretion disk, producing a delayed reflected emission, with a time lag consistent with the light travel time between the irradiating source and the disk. Independently of the location of the clock, the kHz Quasi-Periodic Oscillation (QPO) emission is thought to arise from the neutron star boundary layer. Here, we search for the signature of reverberation of the kHz QPO emission, by measuring the soft lags and the lag energy spectrum of the lower kHz QPOs from 4U1608-52. Soft lags, ranging from ~15 to ~40 microseconds, between the 3-8 keV and 8-30 keV modulated emissions are detected between 565 and 890 Hz. The soft lags are not constant with frequency and show a smooth decrease between 680 Hz and 890 Hz. The broad band X-ray spectrum is modeled as the sum of a disk and a thermal comptonized component, plus a broad iron line, expected from reflection. The spectral parameters follow a smooth relationship with the QPO frequency, in particular the fitted inner disk radius decreases steadily with frequency. Both the bump around the iron line in the lag energy spectrum, and the consistency between the lag changes and the inferred changes of the inner disk radius, from either spectral fitting or the QPO frequency, suggest that the soft lags may indeed involve reverberation of the hard pulsating QPO source on the disk.

astro-ph.HE↗

arXiv2013

Testing the rotating hot spot model using X-ray burst oscillations from 4U 1636-536

Precise and accurate measurements of neutron star masses and radii would provide valuable information about the still uncertain properties of cold matter at supranuclear densities. One promising approach to making such measurements involves analysis of the X-ray flux oscillations often seen during thermonuclear (type 1) X-ray bursts. These oscillations are almost certainly produced by emission from hotter regions on the stellar surface modulated by the rotation of the star. One consequence of the rotation is that the oscillation should appear earlier at higher photon energies than at lower energies. Ford (1999) found compelling evidence for such a hard lead in the tail oscillations of one type 1 burst from Aql X-1. We have therefore analyzed individually the oscillations observed in the tails of the four type 1 bursts from 4U 1636-536 that, when averaged, provided the strongest evidence for a soft lead in the analysis by Muno et al. (2003). We have also analyzed the oscillation observed during the superburst from this star. We find that the data from these five bursts, treated both individually and jointly, are fully consistent with a rotating hot spot model. Unfortunately, the uncertainties in these data are too large to provide interesting constraints on the mass and radius of this star.

astro-ph.HE↗

arXiv2013

XMM-Newton Observations of the TeV γ-ray Source HESS J1804-216

We have analyzed three XMM-Newton observations of the central part of the unidentified TeV γ-ray source HESS J1804-216. We focus on two X-ray sources 2XMMi J180442.0-214221 (Src 1) and 2XMMi J180432.5-214009 (Src 2), which were suggested to be the possible X-ray counterparts to the TeV source. We discover a 2.93 hr X-ray periodicity from Src 1, with the pulse profile explained with a self-eclipsing pole in an eclipsing polar. Src 2 exhibits a strong Fe emission line (FWHM ~0.3 keV and equivalent width ~0.8 keV) and large X-ray variability on timescales of hours and is probably an intermediate polar. Thus Src 1 and Src 2 are probably two field sources not responsible for the TeV emission. The observations were contaminated by strong straylight from a nearby bright source, and we see no clear extended X-ray emission that can be attributed to the supernova remnant G8.7-0.1, a popular possible association with the TeV source. The other possible association, the pulsar wind nebula candidate PSR J1803-2137, shows little long-term variability, compared with a previous Chandra observation. Many point sources were serendipitously detected, but most of them are probably normal stars. Three new candidate compact object systems (other than Src 1, Src 2 and PSR J1803-2137) are also found. They are far away from the TeV source and are probably also magnetic cataclysmic variables, thus unlikely to be responsible for the TeV emission.

astro-ph.HE↗

arXiv2012

Calibration strategies for the LAD instrument on-board LOFT

The Scientific objectives of the LOFT mission, e.g., the study of the Neutron Star equation of state and of the Strong Gravity, require accurate energy, time and flux calibration for the 500k channels of the SDD detectors, as well as the knowledge of the detector dead-time and of the detector response with respect to the incident angle of the photons. We report here the evaluations made to asses the calibration issues for the LAD instrument. The strategies for both ground and on-board calibrations, including astrophysical observations, show that the goals are achievable within the current technologies.

astro-ph.IM↗

arXiv2012

Classification of X-ray Sources in the XMM-Newton Serendipitous Source Catalog

We carry out classification of 4330 X-ray sources in the 2XMMi-DR3 catalog. They are selected under the requirement of being a point source with multiple XMM-Newton observations and at least one detection with the signal-to-noise ratio larger than 20. For about one third of them we are able to obtain reliable source types from the literature. They mostly correspond to various types of stars (611), active galactic nuclei (AGN, 753) and compact object systems (138) containing white dwarfs, neutron stars, and stellar-mass black holes. We find that about 99% of stars can be separated from other source types based on their low X-ray-to-IR flux ratios and frequent X-ray flares. AGN have remarkably similar X-ray spectra, with the power-law photon index centered around 1.91+-0.31, and their 0.2-4.5 keV flux long-term variation factors have a median of 1.48 and 98.5% less than 10. In contrast, 70% of compact object systems can be very soft or hard, highly variable in X-rays, and/or have very large X-ray-to-IR flux ratios, separating them from AGN. Using these results, we derive a source type classification scheme to classify the other sources and find 644 candidate stars, 1376 candidate AGN and 202 candidate compact object systems, whose false identification probabilities are estimated to be about 1%, 3% and 18%, respectively. There are still 320 associated with nearby galaxies and 151 in the Galactic plane, which we expect to be mostly compact object systems or background AGN. We also have 100 candidate ultra-luminous X-ray sources. They are found to be much less variable than other accreting compact objects.

astro-ph.HE↗

arXiv2012

The Spectral Evolution along the Z track of the Bright Neutron Star X-ray Binary GX 17+2

Z sources are bright neutron-star X-ray binaries, accreting at around the Eddington limit. We analyze the 68 RXTE observations (270 ks) of Sco-like Z source GX 17+2 made between 1999 October 3-12, covering a complete Z track. We create and fit color-resolved spectra with a model consisting of a thermal multicolor disk, a single-temperature-blackbody boundary layer and a weak Comptonized component. We find that, similar to what was observed for XTE J1701-462 in its Sco-like Z phase, the branches of GX 17+2 can be explained by three processes operating at a constant accretion rate Mdot into the disk: increase of Comptonization up the horizontal branch, transition from a standard thin disk to a slim disk up the normal branch, and temporary fast decrease of the inner disk radius up the flaring branch. We also model the Comptonization in an empirically self-consistent way, with its seed photons tied to the thermal disk component and corrected for to recover the pre-Comptonized thermal disk emission. This allows us to show a constant Mdot along the entire Z track based on the thermal disk component. We also measure the upper kHz QPO frequency and find it to depend on the apparent inner disk radius R_in (prior to Compton scattering) approximately as frequency \propto R_in^(-3/2), supporting the idenfitication of it as the Keplerian frequency at R_in. The horizontal branch oscillation is probably related to the dynamics in the inner disk as well, as both its frequency and R_in vary significantly on the horizontal branch but become relatively constant on the normal branch.

astro-ph.HE↗

arXiv2012

A comparison of broad iron emission lines in archival data of neutron star low-mass X-ray binaries

Relativistic X-ray disk-lines have been found in multiple neutron star low-mass X-ray binaries, in close analogy with black holes across the mass-scale. These lines have tremendous diagnostic power and have been used to constrain stellar radii and magnetic fields, often finding values that are consistent with independent timing techniques. Here, we compare CCD-based data from Suzaku with Fe K line profiles from archival data taken with gas-based spectrometers. In general, we find good consistency between the gas-based line profiles from EXOSAT, BeppoSAX and RXTE and the CCD data from Suzaku, demonstrating that the broad profiles seen are intrinsic to the line and not broad due to instrumental issues. However, we do find that when fitting with a Gaussian line profile, the width of the Gaussian can depend on the continuum model in instruments with low spectral resolution, though when the different models fit equally well the line widths generally agree. We also demonstrate that three BeppoSAX observations show evidence for asymmetric lines, with a relativistic disk-line model providing a significantly better fit than a Gaussian. We test this by using the posterior predictive p-value method, and bootstrapping of the spectra to show that such deviations from a Gaussian are unlikely to be observed by chance.

astro-ph.HE↗

arXiv2012

kHz QPOs from the 2000 and 2010 X-ray transients located in the globular cluster Terzan 5: EXO1745-248 and IGR J17480-2446

EXO1745-248 is a transient neutron star low-mass X-ray binary located in the globular cluster Terzan 5. It was in outburst in 2000 and displayed during one Rossi X-ray Timing Explorer observation a highly coherent quasi-periodic oscillation (QPO) at frequencies between 670 and 715 Hz. Applying a maximum likelihood method to fit the X-ray power density spectrum, we show that the QPO can be detected on segments as short as T=48 seconds. We find that its width is consistent with being constant, while previous analysis based on longer segment duration (200 s) found it variable. If the QPO frequency variations in EXO1745-248 follows a random walk (i.e. the contribution of the drift to the measured width increases like square root of T), we derive an intrinsic width of about 2.3 Hz. This corresponds to an intrinsic quality factor of about 297+/-50 at 691 Hz. We also show that Q is consistent with being constant between 2.5 and 25 keV. IGR J17480-2446 is another X-ray transient located in Terzan 5. It is a very interesting object showing accretion powered pulsations and burst oscillations at 11 Hz. We report on the properties of its kHz QPOs detected between October 18th and October 23rd, soon after the source had moved from the so-called Atoll to the Z state. Its QPOs are typical of persistent Z sources; in the sense that they have low Q factors (about 30) and low RMS amplitudes (about 5 %). The highest frequency (at 870 Hz), if orbital, sets a lower limit on the inner disk radius of about 18.5 km, and an upper limit to the dipole moment of the magnetic field 5 x 10^26 G cm^3.

astro-ph.HE↗

arXiv2011

Maximum likelihood fitting of X-ray power density spectra: Application to high-frequency quasi-periodic oscillations from the neutron star X-ray binary 4U1608-522

High frequency quasi-periodic oscillations (QPOs) from weakly magnetized neutron stars display rapid frequency variability and high coherence with quality factors up to at least 200 at frequencies around 850 Hz. Their parameters have been estimated so far from standard min(chi2) fitting techniques, after combining a large number of Power Density Spectra (PDS), as to have the powers normally distributed. Accounting for the statistical properties of PDS, we apply a maximum likelihood method to derive the QPO parameters in the non Gaussian regime. The method presented is general, easy to implement and can be applied to fitting individual PDS, several PDS simultaneously or their average, and is obviously not specific to the analysis of kHz QPO data. It applies to the analysis of any PDS optimized in frequency resolution and for low frequency variability or PDS containing features whose parameters vary on short timescales, as is the case for kHz QPOs. It is equivalent to the standard chi^2 minimization fitting when the number of PDS fitted is large. The accuracy, reliability and superiority of the method is demonstrated with simulations of synthetic PDS. We show that the maximum likelihood estimates of the QPO parameters are asymptotically unbiased, and have negligible bias when the QPO is reasonably well detected. By contrast, we show that the standard min(chi2) fitting method gives biased parameters with larger uncertainties. The maximum likelihood fitting method is applied to a subset of archival Rossi X-ray Timing Explorer (RXTE) data of the neutron star X-ray binary 4U1608-522. We show that the kHz QPO parameters can be measured on 8 second timescales and that the time evolution of the frequency is consistent with a random walk. This enables us to estimate the intrinsic quality factor of the QPO to be around 260, whereas previous analysis indicated a maximum value around 200 (abridged).

astro-ph.HE↗

arXiv2011

X-ray Variability and Hardness of ESO 243-49 HLX-1: Clear Evidence for Spectral State Transitions

The ultra-luminous X-ray (ULX) source ESO 243-49 HLX-1 currently provides the strongest evidence for the existence of intermediate mass black holes. We conduct an ongoing monitoring campaign with the Swift X-ray Telescope and found that HLX-1 showed two fast rise and exponential decay with increases in the count rate of a factor ~40 separated by 375+/-13 days. We obtained new XMM-Newton and Chandra dedicated pointings that were triggered at the lowest and highest luminosities, respectively. The unabsorbed luminosities ranged from 1.9x10^40 to 1.25x10^42 erg/s. We confirm here the detection of spectral state transitions from HLX-1 reminiscent of Galactic black hole binaries: at high luminosities, the X-ray spectrum showed a thermal state dominated by a disk component with temperatures of 0.26 keV at most, and at low luminosities the spectrum is dominated by a hard power law with a photon index in the range 1.4-2.1, consistent with a hard state. The source was also observed in a steep power law state. In the thermal state, the luminosity of the disk component appears to scale with the fourth power of the inner disk temperature which supports the presence of an optically thick, geometrically thin accretion disk. The low fractional variability (rms of 9+/-9%) in this state also suggests the presence of a dominant disk. The spectral changes and long-term variability of the source cannot be explained by variations of the beaming angle and are not consistent with the source being in a super-Eddington accretion state. HLX-1 is thus an unusual ULX as it is similar to Galactic black hole binaries, which have non-beamed and sub-Eddington emission, but with luminosities 3 orders of magnitude higher. In this picture, a lower limit on the mass of the black hole of >9000 M_sun can be derived, and the disk temperature in the thermal state also suggests the presence of a black hole of a few 10^3 M_sun.

astro-ph.HE↗

arXiv2011

GRAVITAS : General Relativistic Astrophysics VIa Timing And Spectroscopy: An ESA M3 mission proposal

GRAVITAS is an X-ray observatory, designed and optimised to address the ESA Cosmic Vision theme of "Matter under extreme conditions". It was submitted as a response to the call for M3 mission proposals. The concept centres around an X-ray telescope of unprecedented effective area, which will focus radiation emitted from close to the event horizon of black holes or the surface of neutron stars. To reveal the nature and behaviour of matter in the most extreme astrophysical environments, GRAVITAS targets a key feature in the X-ray spectra of compact objects: the iron Kalpha line at ~6.5 keV. The energy, profile, and variability of this emission line, and the properties of the surrounding continuum emission, shaped by General Relativity (GR) effects, provide a unique probe of gravity in its strong field limit. Among its prime targets are hundreds of supermassive black holes in bright Active Galactic Nuclei (AGN), which form the perfect laboratory to help understand the physical processes behind black hole growth. Accretion plays a fundamental role in the shaping of galaxies throughout cosmic time, via the process of feedback. Modest (~sub-arcmin) spatial resolution would deliver the necessary sensitivity to extend high quality X-ray spectroscopy of AGN to cosmologically-relevant distances. Closer to home, ultra-high count rate capabilities and sub-millisecond time resolution enable the study of GR effects and the equation of state of dense matter in the brightest X-ray binaries in our own Galaxy, using multiple probes, such as the broad iron line, the shape of the disk continuum emission, quasi-periodic oscillations, reverberation mapping, and X-ray burst oscillations. Despite its breakthrough capabilities, all enabling technologies for GRAVITAS are already in a high state of readiness. It is based on ultra light-weight X-ray optics and a focal plane detector using silicon technology.

astro-ph.HE↗

arXiv2011

Discovery of an Ultrasoft X-ray Transient Source in the 2XMM Catalog: a Tidal Disruption Event Candidate

We have discovered an ultrasoft X-ray transient source, 2XMMi J184725.1-631724, which was detected serendipitously in two XMM-Newton observations in the direction of the center of the galaxy IC 4765-f01-1504 at a redshift of 0.0353. These two observations were separated by 211 days, with the 0.2-10 keV absorbed flux increasing by a factor of about 9. Their spectra are best described by a model dominated by a thermal disk or a single-temperature blackbody component (contributing >80% of the flux) plus a weak power-law component. The thermal emission has a temperature of a few tens of eV, and the weak power-law component has a photon index of ~3.5. Similar to the black hole X-ray binaries in the thermal state, our source exhibits an accretion disk whose luminosity appears to follow the $L\propto T^4$ relation. This would indicate that the black hole mass is about 10^5-10^6 M_sun using the best-fitting inner disk radius. Both XMM-Newton observations show variability of about 21% on timescales of hours, which can be explained as due to fast variations in the mass accretion rate. The source was not detected by ROSAT in an observation in 1992, indicating a variability factor of >64 over longer timescales. The source was not detected again in X-rays in a Swift observation in 2011 February, implying a flux decrease by a factor of >12 since the last XMM-Newton observation. The transient nature, in addition to the extreme softness of the X-ray spectra and the inactivity of the galaxy implied by the lack of strong optical emission lines, makes it a candidate tidal disruption event. If this is the case, the first XMM-Newton observation would have been in the rising phase, and the second one in the decay phase.

astro-ph.HE↗

arXiv2011

The Cool Accretion Disk in ESO 243-49 HLX-1: Further Evidence of an Intermediate Mass Black Hole

With an inferred bolometric luminosity exceeding 10^42 erg/s, HLX-1 in ESO 243-49 is the most luminous of ultraluminous X-ray sources and provides one of the strongest cases for the existence of intermediate mass black holes. We obtain good fits to disk-dominated observations of the source with BHSPEC, a fully relativistic black hole accretion disk spectral model. Due to degeneracies in the model arising from the lack of independent constraints on inclination and black hole spin, there is a factor of 100 uncertainty in the best-fit black hole mass M. Nevertheless, spectral fitting of XMM-Newton observations provides robust lower and upper limits with 3000 Msun < M < 3 x 10^5 Msun, at 90% confidence, placing HLX-1 firmly in the intermediate-mass regime. The lower bound on M is entirely determined by matching the shape and peak energy of the thermal component in the spectrum. This bound is consistent with (but independent of) arguments based solely on the Eddington limit. Joint spectral modelling of the XMM-Newton data with more luminous Swift and Chandra observations increases the lower bound to 6000 Msun, but this tighter constraint is not independent of the Eddington limit. The upper bound on M is sensitive to the maximum allowed inclination i, and is reduced to M < 10^5 Msun if we limit i < 75 deg.

astro-ph.HE↗