Dynamical Comptonization in spherical flows: black hole accretion and stellar winds

The transport of photons in steady, spherical, scattering flows is investigated. The moment equations are solved analytically for accretion onto a Schwarzschild black hole, taking into full account relativistic effects. We show that the emergent radiation spectrum is a power law at high frequencies with a spectral index smaller (harder spectrum) than in the non--relativistic case. Radiative transfer in an expanding envelope is also analyzed. We find that adiabatic expansion produces a drift of injected monochromatic photons towards lower frequencies and the formation of a power--law, low--energy tail with spectral index $-3$.Comment: 11 pages with 3 ps figures, MNRAS to appea

An unified timing and spectral model for the Anomalous X-ray Pulsars XTE J1810-197 and CXOU J164710.2-455216

Anomalous X-ray pulsars (AXPs) and soft gamma repeaters (SGRs) are two small classes of X-ray sources strongly suspected to host a magnetar, i.e. an ultra-magnetized neutron star with $B\approx 10^14-10^15 G. Many SGRs/AXPs are known to be variable, and recently the existence of genuinely "transient" magnetars was discovered. Here we present a comprehensive study of the pulse profile and spectral evolution of the two transient AXPs (TAXPs) XTE J1810-197 and CXOU J164710.2-455216. Our analysis was carried out in the framework of the twisted magnetosphere model for magnetar emission. Starting from 3D Monte Carlo simulations of the emerging spectrum, we produced a large database of synthetic pulse profiles which was fitted to observed lightcurves in different spectral bands and at different epochs. This allowed us to derive the physical parameters of the model and their evolution with time, together with the geometry of the two sources, i.e. the inclination of the line-of-sight and of the magnetic axis with respect to the rotation axis. We then fitted the (phase-averaged) spectra of the two TAXPs at different epochs using a model similar to that used to calculate the pulse profiles ntzang in XSPEC) freezing all parameters to the values obtained from the timing analysis, and leaving only the normalization free to vary. This provided acceptable fits to XMM-Newton data in all the observations we analyzed. Our results support a picture in which a limited portion of the star surface close to one of the magnetic poles is heated at the outburst onset. The subsequent evolution is driven both by the cooling/varying size of the heated cap and by a progressive untwisting of the magnetosphere.Comment: 15 pages, 12 figures, accepted for publication in Ap

Quantum Hypothesis Testing with Group Structure

The problem of discriminating between many quantum channels with certainty is analyzed under the assumption of prior knowledge of algebraic relations among possible channels. It is shown, by explicit construction of a novel family of quantum algorithms, that when the set of possible channels faithfully represents a finite subgroup of SU(2) (e.g., $C_n, D_{2n}, A_4, S_4, A_5$) the recently-developed techniques of quantum signal processing can be modified to constitute subroutines for quantum hypothesis testing. These algorithms, for group quantum hypothesis testing (G-QHT), intuitively encode discrete properties of the channel set in SU(2) and improve query complexity at least quadratically in $n$, the size of the channel set and group, compared to na\"ive repetition of binary hypothesis testing. Intriguingly, performance is completely defined by explicit group homomorphisms; these in turn inform simple constraints on polynomials embedded in unitary matrices. These constructions demonstrate a flexible technique for mapping questions in quantum inference to the well-understood subfields of functional approximation and discrete algebra. Extensions to larger groups and noisy settings are discussed, as well as paths by which improved protocols for quantum hypothesis testing against structured channel sets have application in the transmission of reference frames, proofs of security in quantum cryptography, and algorithms for property testing.Comment: 22 pages + 9 figures + 3 table

Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle

Recent work shows that quantum signal processing (QSP) and its multi-qubit lifted version, quantum singular value transformation (QSVT), unify and improve the presentation of most quantum algorithms. QSP/QSVT characterize the ability, by alternating ans\"atze, to obliviously transform the singular values of subsystems of unitary matrices by polynomial functions; these algorithms are numerically stable and analytically well-understood. That said, QSP/QSVT require consistent access to a single oracle, saying nothing about computing joint properties of two or more oracles; these can be far cheaper to determine given an ability to pit oracles against one another coherently. This work introduces a corresponding theory of QSP over multiple variables: M-QSP. Surprisingly, despite the non-existence of the fundamental theorem of algebra for multivariable polynomials, there exist necessary and sufficient conditions under which a desired stable multivariable polynomial transformation is possible. Moreover, the classical subroutines used by QSP protocols survive in the multivariable setting for non-obvious reasons, and remain numerically stable and efficient. Up to a well-defined conjecture, we give proof that the family of achievable multivariable transforms is as loosely constrained as could be expected. The unique ability of M-QSP to obliviously approximate joint functions of multiple variables coherently leads to novel speedups incommensurate with those of other quantum algorithms, and provides a bridge from quantum algorithms to algebraic geometry.Comment: 23 pages + 4 figures + 10 page appendix (added background information on algebraic geometry; publication in Quantum

Soybean harvest aids (1993)

Except when they have large stems, dead weeds usually cause only minor harvest problems. But unfortunately, only a hard frost will stop the growth and dry up some weeds. However, the average date of the first hard frost in most parts of Missouri is relatively late compared to the average date of soybean maturity and harvest (Figures 1 and 2). Delaying harvest until after a hard frost could result in shattering losses, further delays due to wet weather, delayed wheat planting, and delayed fall tillage. Weed problems could also be more serious in following years because of the extra time weed seeds have to reach maturity

VLT/FORS2 observations of the optical counterpart of the isolated neutron star RBS 1774

X-ray observations performed with ROSAT led to the discovery of a group (seven to date) of X-ray dim and radio-silent middle-aged isolated neutron stars (a.k.a. XDINSs), which are characterised by pure blackbody spectra (kT~40-100 eV), long X-ray pulsations (P=3-12 s), and appear to be endowed with relatively high magnetic fields, (B~10d13-14 G). RBS 1774 is one of the few XDINSs with a candidate optical counterpart, which we discovered with the VLT. We performed deep observations of RBS 1774 in the R band with the VLT to disentangle a non-thermal power-law spectrum from a Rayleigh-Jeans, whose contributions are expected to be very much different in the red part of the spectrum. We did not detect the RBS 1774 candidate counterpart down to a 3 sigma limiting magnitude of R~27. The constraint on its colour, (B-R)<0.6, rules out that it is a background object, positionally coincident with the X-ray source. Our R-band upper limit is consistent with the extrapolation of the B-band flux (assuming a 3 sigma uncertainty) for a set of power-laws F_nu ~nu^alpha with spectral indeces alpha<0.07. If the optical spectrum of RBS 1774 were non-thermal, its power-law slope would be very much unlike those of all isolated neutron stars with non-thermal optical emission, suggesting that it is most likely thermal. For instance, a Rayleigh-Jeans with temperature T_O = 11 eV, for an optically emitting radius r_O=15 km and a source distance d=150 pc, would be consistent with the optical measurements. The implied low distance is compatible with the 0.04 X-ray pulsed fraction if either the star spin axis is nearly aligned with the magnetic axis or with the line of sight, or it is slightly misaligned with respect to both the magnetic axis and the line of sight by 5-10 degreesComment: 8 pages, 8 postscript figures, accepted for publication in Astronomy & Astrophysic