Absolute timing of the Crab pulsar with the INTEGRAL/SPI telescope

We have investigated the pulse shape evolution of the Crab pulsar emission in the hard X-ray domain of the electromagnetic spectrum. In particular, we have studied the alignment of the Crab pulsar phase profiles measured in the hard X-rays and in other wavebands. To obtain the hard X-ray pulse profiles, we have used six year (2003-2009, with a total exposure of about 4 Ms) of publicly available data of the SPI telescope on-board of the INTEGRAL observatory, folded with the pulsar time solution derived from the Jodrell Bank Crab Pulsar Monthly Ephemeris. We found that the main pulse in the hard X-ray 20-100 keV energy band is leading the radio one by $8.18\pm0.46$ milliperiods in phase, or $275\pm15 \mu s$ in time. Quoted errors represent only statistical uncertainties.Our systematic error is estimated to be $\sim 40 \mu s$ and is mainly caused by the radio measurement uncertainties. In hard X-rays, the average distance between the main pulse and interpulse on the phase plane is $0.3989\pm0.0009$. To compare our findings in hard X-rays with the soft 2-20 keV X-ray band, we have used data of quasi-simultaneous Crab observations with the PCA monitor on-board the Rossi X-Ray Timing Explorer (RXTE) mission. The time lag and the pulses separation values measured in the 3-20 keV band are $0.00933\pm0.00016$ (corresponding to $310\pm6 \mu s$) and $0.40016\pm0.00028$ parts of the cycle, respectively. While the pulse separation values measured in soft X-rays and hard X-rays agree, the time lags are statistically different. Additional analysis show that the delay between the radio and X-ray signals varies with energy in the 2 - 300 keV energy range. We explain such a behaviour as due to the superposition of two independent components responsible for the Crab pulsed emission in this energy band

Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions

We develop general criteria that ensure that any non-zero solution of a given second-order difference equation is differentially transcendental, which apply uniformly in particular cases of interest, such as shift difference equations, q-dilation difference equations, Mahler difference equations, and elliptic difference equations. These criteria are obtained as an application of differential Galois theory for difference equations. We apply our criteria to prove a new result to the effect that most elliptic hypergeometric functions are differentially transcendental

The High Energy Emission of the Crab Nebula from 20 keV to 6 MeV with INTEGRAL

The SPI spectrometer aboard the INTEGRAL mission observes regularly the Crab Nebula since 2003. We report on observations distributed over 5.5 years and investigate the variability of the intensity and spectral shape of this remarkable source in the hard X-rays domain up to a few MeV. While single power law models give a good description in the X-ray domain (mean photon index ~ 2.05) and MeV domain (photon index ~ 2.23), crucial information are contained in the evolution of the slope with energy between these two values. This study has been carried out trough individual observations and long duration (~ 400 ks) averaged spectra. The stability of the emission is remarkable and excludes a single power law model. The slopes measured below and above 100 keV agree perfectly with the last values reported in the X-ray and MeV regions respectively, but without indication of a localized break point. This suggests a gradual softening in the emission around 100 keV and thus a continuous evolution rather than an actual change in the mechanism parameters. In the MeV region, no significant deviation from the proposed power law model is visible up to 5-6 MeV. Finally, we take advantage of the spectroscopic capability of the instrument to seek for previously reported spectral features in the covered energy range with negative results for any significant cyclotron or annihilation emission on 400 ks timescales. Beyond the scientific results, the performance and reliability of the SPI instrument is explicitly demonstrated, with some details about the most appropriate analysis method.Comment: accepted for publication in ApJ; 4 figures, 2 table

The emission of Cygnus X-1: observations with INTEGRAL SPI from 20 keV to 2 MeV

We report on Cyg X-1 observations performed by the SPI telescope onboard the INTEGRAL mission and distributed over more than 6 years. We investigate the variability of the intensity and spectral shape of this peculiar source in the hard X-rays domain, and more particularly up to the MeV region. We first study the total averaged spectrum which presents the best signal to noise ratio (4 Ms of data). Then, we refine our results by building mean spectra by periods and gathering those of similar hardness. Several spectral shapes are observed with important changes in the curvature between 20 and 200 keV, even at the same luminosity level. In all cases, the emission decreases sharply above 700 keV, with flux values above 1 MeV (or upper limits) well below the recently reported polarised flux (Laurent et al. 2011), while compatible with the MeV emission detected some years ago by CGRO/COMPTEL (McConnell et al., 2002). Finally, we take advantage of the spectroscopic capability of the instrument to seek for spectral features in the 500 keV region with negative results for any significant annihilation emission on 2 ks and days timescales, as well as in the total dataset.Comment: 14 pages, 10 figures, accepted for publication in Ap

On the morphology of the electron-positron annihilation emission as seen by SPI/INTEGRAL

The 511 keV positron annihilation emission remains a mysterious component of the high energy emission of our Galaxy. Its study was one of the key scientific objective of the SPI spectrometer on-board the INTEGRAL satellite. In fact, a lot of observing time has been dedicated to the Galactic disk with a particular emphasis on the central region. A crucial issue in such an analysis concerns the reduction technique used to treat this huge quantity of data, and more particularly the background modeling. Our method, after validation through a variety of tests, is based on detector pattern determination per ~6 month periods, together with a normalisation variable on a few hour timescale. The Galactic bulge is detected at a level of ~70 sigma allowing more detailed investigations. The main result is that the bulge morphology can be modelled with two axisymmetric Gaussians of 3.2 deg. and 11.8 deg. FWHM and respective fluxes of 2.5 and 5.4 x 10^-4 photons/(cm^2.s^1). We found a possible shift of the bulge centre towards negative longitude at l=-0.6 +/- 0.2 degrees. In addition to the bulge, a more extended structure is detected significantly with flux ranging from 1.7 to 2.9 x10^-3 photons/(cm^2.s^1) depending on its assumed geometry (pure disk or disk plus halo). The disk emission is also found to be symmetric within the limits of the statistical errors.Comment: This paper has 12 pages and 14 figures. Accepted for publication by the Astrophysical Journa

A single sub-km Kuiper Belt object from a stellar Occultation in archival data

The Kuiper belt is a remnant of the primordial Solar System. Measurements of its size distribution constrain its accretion and collisional history, and the importance of material strength of Kuiper belt objects (KBOs). Small, sub-km sized, KBOs elude direct detection, but the signature of their occultations of background stars should be detectable. Observations at both optical and X-ray wavelengths claim to have detected such occultations, but their implied KBO abundances are inconsistent with each other and far exceed theoretical expectations. Here, we report an analysis of archival data that reveals an occultation by a body with a 500 m radius at a distance of 45 AU. The probability of this event to occur due to random statistical fluctuations within our data set is about 2%. Our survey yields a surface density of KBOs with radii larger than 250 m of 2.1^{+4.8}_{-1.7} x 10^7 deg^{-2}, ruling out inferred surface densities from previous claimed detections by more than 5 sigma. The fact that we detected only one event, firmly shows a deficit of sub-km sized KBOs compared to a population extrapolated from objects with r>50 km. This implies that sub-km sized KBOs are undergoing collisional erosion, just like debris disks observed around other stars.Comment: To appear in Nature on December 17, 2009. Under press embargo until 1800 hours London time on 16 December. 19 pages; 7 figure