60,812 research outputs found

    On eigenfunction approximations for typical non-self-adjoint Schroedinger operators

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    We construct efficient approximations for the eigenfunctions of non-self-adjoint Schroedinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schroedinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima, we show that a suitable adaptation of the JWKB method is able to provide accurate lobal approximations to them.Comment: 17 pages, 11 figure

    Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples

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    This paper presents a novel power spectral density estimation technique for band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The technique employs multi-coset sampling and incorporates the advantages of compressed sensing (CS) when the power spectrum is sparse, but applies to sparse and nonsparse power spectra alike. The estimates are consistent piecewise constant approximations whose resolutions (width of the piecewise constant segments) are controlled by the periodicity of the multi-coset sampling. We show that compressive estimates exhibit better tradeoffs among the estimator's resolution, system complexity, and average sampling rate compared to their noncompressive counterparts. For suitable sampling patterns, noncompressive estimates are obtained as least squares solutions. Because of the non-negativity of power spectra, compressive estimates can be computed by seeking non-negative least squares solutions (provided appropriate sampling patterns exist) instead of using standard CS recovery algorithms. This flexibility suggests a reduction in computational overhead for systems estimating both sparse and nonsparse power spectra because one algorithm can be used to compute both compressive and noncompressive estimates.Comment: 26 pages, single spaced, 9 figure

    Are There Magnetars in High Mass X-ray Binaries? The Case of SuperGiant Fast X-Ray Transients

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    In this paper we survey the theory of wind accretion in high mass X-ray binaries hosting a magnetic neutron star and a supergiant companion. We concentrate on the different types of interaction between the inflowing wind matter and the neutron star magnetosphere that are relevant when accretion of matter onto the neutron star surface is largely inhibited; these include the inhibition through the centrifugal and magnetic barriers. Expanding on earlier work, we calculate the expected luminosity for each regime and derive the conditions under which transition from one regime to another can take place. We show that very large luminosity swings (~10^4 or more on time scales as short as hours) can result from transitions across different regimes. The activity displayed by supergiant fast X-ray transients, a recently discovered class of high mass X-ray binaries in our galaxy, has often been interpreted in terms of direct accretion onto a neutron star immersed in an extremely clumpy stellar wind. We show here that the transitions across the magnetic and/or centrifugal barriers can explain the variability properties of these sources as a results of relatively modest variations in the stellar wind velocity and/or density. According to this interpretation we expect that supergiant fast X-ray transients which display very large luminosity swings and host a slowly spinning neutron star are characterized by magnetar-like fields, irrespective of whether the magnetic or the centrifugal barrier applies. Supergiant fast X-ray transients might thus provide a new opportunity to detect and study magnetars in binary systems.Comment: Accepted for publication in ApJ. 16 pages, 6 figure

    Radio Observations of GRB Host Galaxies

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    We present 5.5 and 9.0 GHz observations of a sample of seventeen GRB host galaxies at 0.5<z<1.4, using the radio continuum to explore their star formation properties in the context of the small but growing sample of galaxies with similar observations. Four sources are detected, one of those (GRB 100418A) likely due to lingering afterglow emission. We suggest that the previously-reported radio afterglow of GRB 100621A may instead be due to host galaxy flux. We see no strong evidence for redshift evolution in the typical star formation rate of GRB hosts, but note that the fraction of `dark' bursts with detections is higher than would be expected given constraints on the more typical long GRB population. We also determine the average radio-derived star formation rates of core collapse supernovae at comparable redshift, and show that these are still well below the limits obtained for GRB hosts, and show evidence for a rise in typical star formation rate with redshift in supernova hosts.Comment: 15 pages, MNRAS accepte
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