Weighing the black holes in ultraluminous X-ray sources through timing

We describe a new method to estimate the mass of black holes in Ultraluminous X-ray Sources (ULXs). The method is based on the recently discovered ``variability plane'', populated by Galactic stellar-mass black-hole candidates (BHCs) and supermassive active galactic nuclei (AGNs), in the parameter space defined by the black-hole mass, accretion rate and characteristic frequency. We apply this method to the two ULXs from which low-frequency quasi-periodic oscillations have been discovered, M82 X-1 and NGC 5408 X-1. For both sources we obtain a black-hole mass in the range 100~1300 Msun, thus providing evidence for these two sources to host an intermediate-mass black hole.Comment: 5 pages, 2 figures, Accepted by MNRA

A Stress/Displacement Virtual Element Method for Plane Elasticity Problems

The numerical approximation of 2D elasticity problems is considered, in the framework of the small strain theory and in connection with the mixed Hellinger-Reissner variational formulation. A low-order Virtual Element Method (VEM) with a-priori symmetric stresses is proposed. Several numerical tests are provided, along with a rigorous stability and convergence analysis

Ultraluminous X-ray Sources forming in low metallicity natal environments

In the last few years multiwavelength observations have boosted our understanding of Ultraluminous X-ray Sources (ULXs). Yet, the most fundamental questions on ULXs still remain to be definitively answered: do they contain stellar or intermediate mass black holes? How do they form? We investigate the possibility that the black holes hosted in ULXs originate from massive (40-120 $M_\odot$) stars in low metallicity natal environments. Such black holes have a typical mass in the range $\sim 30-90 M_\odot$ and may account for the properties of bright (above $\sim 10^{40}$ erg s$^{-1}$) ULXs. More than $\sim 10^5$ massive black holes might have been generated in this way in the metal poor Cartwheel galaxy during the last $10^7$ years and might power most of the ULXs observed in it. Support to our interpretation comes from NGC 1313 X-2, the first ULX with a tentative identification of the orbital period in the optical band, for which binary evolution calculations show that the system is most likely made by a massive donor dumping matter on a $50-100 M_\odot$ black hole.Comment: 4 pages. To appear in the Proceedings of the Conference "X-Ray Astronomy 2009: Present Status, Multiwavelength Approach and Future Perspectives", Bologna, Italy, September 2009, Eds. A. Comastri, M. Cappi, L. Angelini, 2010 AIP (in press)

The pulse profile and spin evolution of the accreting pulsar in Terzan 5, IGR J17480-2446, during its 2010 outburst

(abridged) We analyse the spectral and pulse properties of the 11 Hz transient accreting pulsar, IGR J17480-2446, in the globular cluster Terzan 5, considering all the available RXTE, Swift and INTEGRAL observations performed between October and November, 2010. By measuring the pulse phase evolution we conclude that the NS spun up at an average rate of =1.48(2)E-12 Hz/s, compatible with the accretion of the Keplerian angular momentum of matter at the inner disc boundary. Similar to other accreting pulsars, the stability of the pulse phases determined by using the second harmonic component is higher than that of the phases based on the fundamental frequency. Under the assumption that the second harmonic is a good tracer of the neutron star spin frequency, we successfully model its evolution in terms of a luminosity dependent accretion torque. If the NS accretes the specific Keplerian angular momentum of the in-flowing matter, we estimate the inner disc radius to lie between 47 and 93 km when the luminosity attains its peak value. Smaller values are obtained if the interaction between the magnetic field lines and the plasma in the disc is considered. The phase-averaged spectrum is described by thermal Comptonization of photons with energy of ~1 keV. A hard to soft state transition is observed during the outburst rise. The Comptonized spectrum evolves from a Comptonizing cloud at an electron temperature of ~20 keV towards an optically denser cloud at kT_e~3 keV. At the same time, the pulse amplitude decreases from 27% to few per cent and becomes strongly energy dependent. We discuss various possibilities to explain such a behaviour, proposing that at large accretion luminosities a significant fraction of the in-falling matter is not channelled towards the magnetic poles, but rather accretes more evenly onto the NS surface.Comment: To appear in MNRA

Lighthouses with two lights: burst oscillations from the accretion-powered millisecond pulsars

The key contribution of the discovery of nuclear-powered pulsations from the accretion-powered millisecond pulsars (AMPs) has been the establishment of burst oscillation frequency as a reliable proxy for stellar spin rate. This has doubled the sample of rapidly-rotating accreting neutron stars and revealed the unexpected absence of any stars rotating near the break-up limit. The resulting `braking problem' is now a major concern for theorists, particularly given the possible role of gravitational wave emission in limiting spin. This, however, is not the only area where burst oscillations from the AMPs are having an impact. Burst oscillation timing is developing into a promising technique for verifying the level of spin variability in the AMPs (a topic of considerable debate). These sources also provide unique input to our efforts to understand the still-elusive burst oscillation mechanism. This is because they are the only stars where we can reliably gauge the role of uneven fuel deposition and, of course, the magnetic field.Comment: Invited review, to appear in the proceedings of the workshop 'A decade of accreting millisecond x-ray pulsars' (Amsterdam, April 2008

Secular spin-down of the AMP XTE J1751-305

Context. Of the 13 known accreting millisecond pulsars, only a few showed more than one outburst during the RXTE era. XTE J1751-305 showed, after the main outburst in 2002, other three dim outbursts. We report on the timing analysis of the latest one, occurred on October 8, 2009 and serendipitously observed from its very beginning by RXTE. Aims. The detection of the pulsation during more than one outburst permits to obtain a better constraint of the orbital parameters and their evolution as well as to track the secular spin frequency evolution of the source. Methods. Using the RXTE data of the last outburst of the AMP XTE J1751-305, we performed a timing analysis to improve the orbital parameters. Because of the low statistics, we used an epoch folding search technique on the whole data set to improve the local estimate of the time of ascending node passage. Results. Using this new orbital solution we epoch folded data obtaining three pulse phase delays on a time span of 1.2 days, that we fitted using a constant spin frequency model. Comparing this barycentric spin frequency with that of the 2002 outburst, we obtained a secular spin frequency derivative of -0.55(12) x 10^{-14} Hz s^{-1}. In the hypothesis that the secular spin-down is due to a rotating magneto-dipole emission, consistently with what is assumed for radio pulsars, we estimate the pulsar's magnetic dipole value. We derive an estimate of the magnetic field strength at the polar cap of B_{PC} = 4.0(4) x 10^8 Gauss, for a neutron star mass of 1.4M\odot, assuming the Friedman Pandharipande Skyrme equation of state.Comment: 7 pages, 4 figures, accepted for publication on A&

Timing of the 2008 Outburst of SAX J1808.4-3658 with XMM-Newton: A Stable Orbital Period Derivative over Ten Years

We report on a timing analysis performed on a 62-ks long XMM-Newton observation of the accreting millisecond pulsar SAX J1808.4-3658 during the latest X-ray outburst that started on September 21, 2008. By connecting the time of arrivals of the pulses observed during the XMM observation, we derived the best-fit orbital solution and a best-fit value of the spin period for the 2008 outburst. Comparing this new set of orbital parameters and, in particular, the value of the time of ascending-node passage with the orbital parameters derived for the previous four X-ray outbursts of SAX J1808.4-3658 observed by the PCA on board RXTE, we find an updated value of the orbital period derivative, which turns out to be $\dot P_{\rm orb} = (3.89 \pm 0.15) \times 10^{-12}$ s/s. This new value of the orbital period derivative agrees with the previously reported value, demonstrating that the orbital period derivative in this source has remained stable over the past ten years. Although this timespan is not sufficient yet for confirming the secular evolution of the system, we again propose an explanation of this behavior in terms of a highly non-conservative mass transfer in this system, where the accreted mass (as derived from the X-ray luminosity during outbursts) accounts for a mere 1% of the mass lost by the companion.Comment: 4 pages, 3 figures. Final version, including editing corrections, to appear on A&A Letter

Measuring the neutron star equation of state using X-ray timing

One of the primary science goals of the next generation of hard X-ray timing instruments is to determine the equation of state of the matter at supranuclear densities inside neutron stars, by measuring the radius of neutron stars with different masses to accuracies of a few percent. Three main techniques can be used to achieve this goal. The first involves waveform modelling. The flux we observe from a hotspot on the neutron star surface offset from the rotational pole will be modulated by the star's rotation, giving rise to a pulsation. Information about mass and radius is encoded into the pulse profile via relativistic effects, and tight constraints on mass and radius can be obtained. The second technique involves characterising the spin distribution of accreting neutron stars. The most rapidly rotating stars provide a very clean constraint, since the mass-shedding limit is a function of mass and radius. However the overall spin distribution also provides a guide to the torque mechanisms in operation and the moment of inertia, both of which can depend sensitively on dense matter physics. The third technique is to search for quasi-periodic oscillations in X-ray flux associated with global seismic vibrations of magnetars (the most highly magnetized neutron stars), triggered by magnetic explosions. The vibrational frequencies depend on stellar parameters including the dense matter equation of state. We illustrate how these complementary X-ray timing techniques can be used to constrain the dense matter equation of state, and discuss the results that might be expected from a 10m$^2$ instrument. We also discuss how the results from such a facility would compare to other astronomical investigations of neutron star properties. [Modified for arXiv]Comment: To appear in Reviews of Modern Physics as a Colloquium, 23 pages, 9 figure

Direct imaging of defect formation in strained organic flexible electronics by Scanning Kelvin Probe Microscopy

The development of new materials and devices for flexible electronics depends crucially on the understanding of how strain affects electronic material properties at the nano-scale. Scanning Kelvin-Probe Microscopy (SKPM) is a unique technique for nanoelectronic investigations as it combines non-invasive measurement of surface topography and surface electrical potential. Here we show that SKPM in non-contact mode is feasible on deformed flexible samples and allows to identify strain induced electronic defects. As an example we apply the technique to investigate the strain response of organic thin film transistors containing TIPS-pentacene patterned on polymer foils. Controlled surface strain is induced in the semiconducting layer by bending the transistor substrate. The amount of local strain is quantified by a mathematical model describing the bending mechanics. We find that the step-wise reduction of device performance at critical bending radii is caused by the formation of nano-cracks in the microcrystal morphology of the TIPS-pentacene film. The cracks are easily identified due to the abrupt variation in SKPM surface potential caused by a local increase in resistance. Importantly, the strong surface adhesion of microcrystals to the elastic dielectric allows to maintain a conductive path also after fracture thus providing the opportunity to attenuate strain effects