Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: a new gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force

The innermost stable circular orbit (ISCO) delimits the transition from circular orbits to those that plunge into a black hole. In the test-mass limit, well-defined ISCO conditions exist for the Kerr and Schwarzschild spacetimes. In the finite-mass case, there are a large variety of ways to define an ISCO in a post-Newtonian (PN) context. Here I generalize the gauge-invariant ISCO condition of Blanchet & Iyer (2003) to the case of spinning (nonprecessing) binaries. The Blanchet-Iyer ISCO condition has two desirable and unexpected properties: (1) it exactly reproduces the Schwarzschild ISCO in the test-mass limit, and (2) it accurately approximates the recently-calculated shift in the Schwarzschild ISCO frequency due to the conservative-piece of the gravitational self-force [Barack & Sago (2009)]. The generalization of this ISCO condition to spinning binaries has the property that it also exactly reproduces the Kerr ISCO in the test-mass limit (up to the order at which PN spin corrections are currently known). The shift in the ISCO due to the spin of the test-particle is also calculated. Remarkably, the gauge-invariant PN ISCO condition exactly reproduces the ISCO shift predicted by the Papapetrou equations for a fully-relativistic spinning particle. It is surprising that an analysis of the stability of the standard PN equations of motion is able (without any form of "resummation") to accurately describe strong-field effects of the Kerr spacetime. The ISCO frequency shift due to the conservative self-force in Kerr is also calculated from this new ISCO condition, as well as from the effective-one-body Hamiltonian of Barausse & Buonanno (2010). These results serve as a useful point-of-comparison for future gravitational self-force calculations in the Kerr spacetime.Comment: 17 pages, 2 figures, 1 table. v2: references added; minor changes to match published versio

Gravitational-wave memory revisited: memory from the merger and recoil of binary black holes

Gravitational-wave memory refers to the permanent displacement of the test masses in an idealized (freely-falling) gravitational-wave interferometer. Inspiraling binaries produce a particularly interesting form of memory--the Christodoulou memory. Although it originates from nonlinear interactions at 2.5 post-Newtonian order, the Christodoulou memory affects the gravitational-wave amplitude at leading (Newtonian) order. Previous calculations have computed this non-oscillatory amplitude correction during the inspiral phase of binary coalescence. Using an "effective-one-body" description calibrated with the results of numerical relativity simulations, the evolution of the memory during the inspiral, merger, and ringdown phases, as well as the memory's final saturation value, are calculated. Using this model for the memory, the prospects for its detection are examined, particularly for supermassive black hole binary coalescences that LISA will detect with high signal-to-noise ratios. Coalescing binary black holes also experience center-of-mass recoil due to the anisotropic emission of gravitational radiation. These recoils can manifest themselves in the gravitational-wave signal in the form of a "linear" memory and a Doppler shift of the quasi-normal-mode frequencies. The prospects for observing these effects are also discussed.Comment: 6 pages, 2 figures; accepted to the proceedings of the 7th International LISA Symposium; v2: updated figures and signal-to-noise ratios, several minor changes to the tex

Rotational modulation of X-ray emission in Orion Nebula young stars

We investigate the spatial distribution of X-ray emitting plasma in a sample of young Orion Nebula Cluster stars by modulation of their X-ray light-curves due to stellar rotation. The study, part of the Chandra Orion Ultradeep Project (COUP), is made possible by the exceptional length of the observation: 10 days of ACIS integration during a time span of 13 days, yielding a total of 1616 detected sources in the 17x17 arcmin field of view. We here focus on a subsample of 233 X-ray-bright stars with known rotational periods. We search for X-ray modulation using the Lomb Normalized Periodogram method. X-ray modulation related to the rotation period is detected in at least 23 stars with periods between 2 and 12 days and relative amplitudes ranging from 20% to 70%. In 16 cases, the X-ray modulation period is similar to the stellar rotation period while in seven cases it is about half that value, possibly due to the presence of X-ray emitting structures at opposite stellar longitudes. These results constitute the largest sample of low mass stars in which X-ray rotational modulation has been observed. The detection of rotational modulation indicates that the X-ray emitting regions are distributed inhomogeneneously in longitude and do not extend to distances significantly larger than the stellar radius. Modulation is observed in stars with saturated activity levels (L_X/L_bol ~ 10^(-3)) showing that saturation is not due to the filling of the stellar surface with X-ray emitting regions.Comment: 41 pages, 15 figures, ApJS in press. Figure 15 (34 panels) is an on-line only figure and is not included. A pdf file which includes figure 15 as well as full resolution versions of figure 10 and 11 is available at: http://www.astropa.unipa.it/~ettoref/COUP_RotMod.pd

Inferring coronal structure from X-ray lightcurves and Doppler shifts: a Chandra study of AB Doradus

The Chandra X-ray observatory monitored the single cool star, AB Doradus, continuously for a period lasting 88 ksec (1.98 Prot) in 2002 December with the LETG/HRC-S. The X-ray lightcurve shows rotational modulation, with three peaks that repeat in two consecutive rotation cycles. These peaks may indicate the presence of compact emitting regions in the quiescent corona. Centroid shifts as a function of phase in the strongest line profile, O VIII 18.97 A, indicate Doppler rotational velocities with a semi-amplitude of 30 +/- 10 km/s. By taking these diagnostics into account along with constraints on the rotational broadening of line profiles (provided by archival Chandra HETG Fe XVII and FUSE Fe XVIII profile) we can construct a simple model of the X-ray corona that requires two components. One of these components is responsible for 80% of the X-ray emission, and arises from the pole and/or a homogeneously distributed corona. The second component consists of two or three compact active regions that cause modulation in the lightcurve and contribute to the O VIII centroid shifts. These compact regions account for 16% of the emission and are located near the stellar surface with heights of less than 0.3R*. At least one of the compact active regions is located in the partially obscured hemisphere of the inclined star, while one of the other active regions may be located at 40 degrees. High quality X-ray data such as these can test the models of the coronal magnetic field configuration as inferred from magnetic Zeeman Doppler imaging.Comment: 28 pages, 11 figures, accepted by Ap

The nature of the fluorescent iron line in V 1486 Ori

The fluorescent 6.4 keV iron line provides information on cool material in the vicinity of hard X-ray sources as well as on the characteristics of the X-ray sources themselves. First discovered in the X-ray spectra of the flaring Sun, X-ray binaries and active galactic nuclei (AGN), the fluorescent line was also observed in a number of stellar X-ray sources. The young stellar object (YSO) V1486 Ori was observed in the framework of the Chandra Ultra Deep Project (COUP) as the source COUP 331. We investigate its spectrum, with emphasis on the strength and time variability of the fluorescent iron K-alpha line, derive and analyze the light curve of COUP 331 and proceed with a time-resolved spectral analysis of the observation. The light curve of V 1486 Ori shows two major flares, the first one lasting for (approx) 20 ks with a peak X-ray luminosity of 2.6*10^{32} erg/s (dereddened in the 1-10 keV band) and the second one -- only partially observed -- for >60 ks with an average X-ray luminosity of 2.4*10^{31} erg/s (dereddened). The spectrum of the first flare is very well described by an absorbed thermal model at high temperature, with a pronounced 6.7 keV iron line complex, but without any fluorescent K-alpha line. The X-ray spectrum of the second flare is characterized by even higher temperatures (>= 10 keV) without any detectable 6.7 keV Fe XXV feature, but with a very strong fluorescent iron K-alpha line appearing predominantly in the 20 ks rise phase of the flare. Preliminary model calculations indicate that photoionization is unlikely to account for the entire fluorescent emission during the rise phase.Comment: 4 pages, letter, accepted for publication in A&

Fifteen years in the high-energy life of the solar-type star HD 81809. XMM-Newton observations of a stellar activity cycle

Aims. The data set of the long-term XMM-Newton monitoring program of HD 81809 is analyzed to study its X-ray cycle, to investigate if the latter is related to the chromospheric one, to infer the structure of the corona of HD 81809, and to explore if the coronal activity of HD 81809 can be ascribed to phenomena similar to the solar ones and, therefore, considered an extension of the solar case. Methods. We analyze the observations of HD 81809 performed with XMM-Newton with a regular cadence of 6 months from 2001 to 2016 and representing one of the longest available observational baseline ($\sim 15$~yr) for a solar-like star with a well-studied chromospheric cycle (with a period of $\sim 8$~yr). We investigate the modulation of coronal luminosity and temperature and its relation with the chromospheric cycle. We interpret the data in terms of a mixture of solar-like coronal regions, adopting a methodology originally proposed to study the Sun as an X-ray star. Results. The observations show a well-defined regular cyclic modulation of the X-ray luminosity that reflects the activity level of HD 81809. The data covers approximately two cycles of coronal activity; the modulation has an amplitude of a factor of $\sim 5$ (excluding evident flares, as in the June 2002 observation) and a period of $7.3\pm 1.5$~yr, consistent with that of the chromospheric cycle. We demonstrate that the corona of HD 81809 can be interpreted as an extension of the solar case and it can be modeled with a mixture of solar-like coronal regions along the whole cycle. The activity level is mainly determined by a varying coverage of very bright active regions, similar to cores of active regions observed in the Sun. Evidence of unresolved significant flaring activity is present especially in proximity of cycle maxima.Comment: 11 pages, 5 Figures, A&A accepte

Coronal activity cycles in nearby G and K stars - XMM-Newton monitoring of 61 Cygni and Alpha Centauri

We use X-ray observations of the nearby binaries 61 Cyg A/B (K5V and K7V) and Alpha Cen A/B (G2V and K1V) to study the long-term evolution of magnetic activity in weakly to moderately active G + K dwarfs over nearly a decade. Specifically we search for X-ray activity cycles and related coronal changes and compare them to the solar behavior. For 61 Cyg A we find a regular coronal activity cycle analog to its 7.3 yr chromospheric cycle. The X-ray brightness variations are with a factor of three significantly lower than on the Sun, yet the changes of coronal properties resemble the solar behavior with larger variations occurring in the respective hotter plasma components. 61 Cyg B does not show a clear cyclic coronal trend so far, but the X-ray data matches the more irregular chromospheric cycle. Both Alpha Cen stars exhibit significant long-term X-ray variability. Alpha Cen A shows indications for cyclic variability of an order of magnitude with a period of about 12-15 years; the Alpha Cen B data suggests an X-ray cycle with an amplitude of about six to eight and a period of 8-9 years. The sample stars exhibit X-ray luminosities ranging between Lx < 1x10^26 - 3x10^27 erg s^-1 in the 0.2-2.0 keV band and have coronae dominated by cool plasma with variable average temperatures of around 1.0-2.5 MK. We find that coronal activity cycles are apparently a common phenomenon in older, slowly rotating G and K stars. The spectral changes of the coronal X-ray emission over the cycles are solar-like in all studied targets.Comment: 11 pages, 9 figures, accepted by Astronomy and Astrophysic