J. C. Brown

University of Glasgow, Glasgow, SCT, United Kingdom

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Publications (148)408.01 Total impact

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    ABSTRACT: We investigate the connections between the magnetic fields and the X-ray emission from massive stars. Our study shows that the X-ray properties of known strongly magnetic stars are diverse: while some comply to the predictions of the magnetically confined wind model, others do not. We conclude that strong, hard, and variable X-ray emission may be a sufficient attribute of magnetic massive stars, but it is not a necessary one. We address the general properties of X-ray emission from "normal" massive stars, especially the long standing mystery about the correlations between the parameters of X-ray emission and fundamental stellar properties. The recent development in stellar structure modeling shows that small scale surface magnetic fields may be common. We suggest a "hybrid" scenario which could explain the X-ray emission from massive stars by a combination of magnetic mechanisms on the surface and shocks in the stellar wind. The magnetic mechanisms and the wind shocks are triggered by convective motions in sub-photospheric layers. This scenario opens the door for a natural explanation of the well established correlation between bolometric and X-ray luminosities.
    Astronomische Nachrichten 10/2011; · 1.40 Impact Factor
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    ABSTRACT: X-radiation from energetic electrons is the prime diagnostic of flare-accelerated electrons. The observed X-ray flux (and polarization state) is fundamentally a convolution of the cross-section for the hard X-ray emission process(es) in question with the electron distribution function, which is in turn a function of energy, direction, spatial location and time. To address the problems of particle propagation and acceleration one needs to infer as much information as possible on this electron distribution function, through a deconvolution of this fundamental relationship. This review presents recent progress toward this goal using spectroscopic, imaging and polarization measurements, primarily from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). Previous conclusions regarding the energy, angular (pitch angle) and spatial distributions of energetic electrons in solar flares are critically reviewed. We discuss the role and the observational evidence of several radiation processes: free-free electron-ion, free-free electron-electron, free-bound electron-ion bremsstrahlung, photoelectric absorption and Compton back-scatter (albedo), using both spectroscopic and imaging techniques. This unprecedented quality of data allows for the first time inference of the angular distributions of the X-ray-emitting electrons using albedo, improved model-independent inference of electron energy spectra and emission measures of thermal plasma. Moreover, imaging spectroscopy has revealed hitherto unknown details of solar flare morphology and detailed spectroscopy of coronal, footpoint and extended sources in flaring regions. Additional attempts to measure hard X-ray polarization were not sufficient to put constraints on the degree of anisotropy of electrons, but point to the importance of obtaining good quality polarization data.
    Space Science Reviews 10/2011; 159(1). · 5.52 Impact Factor
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    ABSTRACT: We present a comprehensive study of X-ray emission and wind properties of massive magnetic early B-type stars. Dedicated XMM-Newton observations were obtained for three stars xi1 CMa, V2052 Oph, and zeta Cas. We report the first detection of X-ray emission from V2052 Oph and zeta Cas. The observations show that the X-ray spectra of our program stars are quite soft. We compile the complete sample of early B-type stars with detected magnetic fields to date and existing X-ray measurements, in order to study whether the X-ray emission can be used as a general proxy for stellar magnetism. We find that hard and strong X-ray emission does not necessarily correlate with the presence of a magnetic field. We analyze the UV spectra of five non-supergiant B stars with magnetic fields by means of non-LTE iron-blanketed model atmospheres. The latter are calculated with the PoWR code, which treats the photosphere as well as the the wind, and also accounts for X-rays. Our models accurately fit the stellar photospheric spectra in the optical and the UV. The parameters of X-ray emission, temperature and flux are included in the model in accordance with observations. We confirm the earlier findings that the filling factors of X-ray emitting material are very high. Our analysis reveals that the magnetic early type B stars studied here have weak winds. The mass-loss rates are significantly lower than predicted by hydrodynamically consistent models. We find that, although the X-rays strongly affect the ionization structure of the wind, this effect is not sufficient in reducing the total radiative acceleration. When the X-rays are accounted for at the intensity and temperatures observed, there is still sufficient radiative acceleration to drive stronger mass-loss than we empirically infer from the UV spectral lines. (abridged)
    Monthly Notices of the Royal Astronomical Society 06/2011; 416. · 5.52 Impact Factor
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    ABSTRACT: Most theoretical descriptions of the production of solar flare bremsstrahlung radiation assume the collision of dilute accelerated particles with a cold, dense target plasma, neglecting interactions of the fast particles with each other. This is inadequate for situations where collisions with this background plasma are not completely dominant, as may be the case in, for example, low-density coronal sources. We aim to formulate a model of a self-interacting, entirely fast electron population in the absence of a dense background plasma, to investigate its implications for observed bremsstrahlung spectra and the flare energy budget. We derive approximate expressions for the time-dependent distribution function of the fast electrons using a Fokker-Planck approach. We use these expressions to generate synthetic bremsstrahlung X-ray spectra as would be seen from a corresponding coronal source. We find that our model qualitatively reproduces the observed behaviour of some flares. As the flare progresses, the model's initial power-law spectrum is joined by a lower energy, thermal component. The power-law component diminishes, and the growing thermal component proceeds to dominate the total emission over timescales consistent with flare observations. The power-law exhibits progressive spectral hardening, as is seen in some flare coronal sources. We also find that our model requires a factor of 7 - 10 fewer accelerated electrons than the cold, thick target model to generate an equivalent hard X-ray flux. This model forms the basis of a treatment of self-interactions among flare fast electrons, a process which affords a more efficient means to produce bremsstrahlung photons and so may reduce the efficiency requirements placed on the particle acceleration mechanism. It also provides a useful description of the thermalisation of fast electrons in coronal sources. Comment: 9 pages, 7 figures, accepted for Astronomy & Astrophysics; this version clarifies arguments around Eqs. (11) and (20)
    Astronomy and Astrophysics 03/2010; · 5.08 Impact Factor
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    N. H. Bian, E. P. Kontar, J. C. Brown
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    ABSTRACT: Aims: This work aims to investigate the spectral structure of the parallel electric field generated by strong anisotropic and balanced Alfvénic turbulence in relation with the problem of electron acceleration from the thermal population in solar flare plasma conditions. Methods: We consider anisotropic Alfvénic fluctuations in the presence of a strong background magnetic field. Exploiting this anisotropy, a set of reduced equations governing non-linear, two-fluid plasma dynamics is derived. The low-beta limit of this model is used to follow the turbulent cascade of the energy resulting from the non-linear interaction between kinetic Alfvén waves, from the large magnetohydrodynamics (MHD) scales with k⊥rho_s≪1 down to the small ``kinetic'' scales with k⊥rhos ≫1, rho_s being the ion sound gyroradius. Results: Scaling relations are obtained for the magnitude of the turbulent electromagnetic fluctuations, as a function of k⊥ and k||, showing that the electric field develops a component parallel to the magnetic field at large MHD scales. Conclusions: The spectrum we derive for the parallel electric field fluctuations can be effectively used to model stochastic resonant acceleration and heating of electrons by Alfvén waves in solar flare plasma conditions
    Astronomy and Astrophysics 01/2010; · 5.08 Impact Factor
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    ABSTRACT: Brown and Mallik (BM) recently claimed that non-thermal recombination (NTR) can be a dominant source of flare hard X-rays (HXRs) from hot coronal and chromospheric sources. However, major discrepancies between the thermal continua predicted by BM and by the Chianti database as well as RHESSI flare data, led us to discover substantial errors in the heuristic expression used by BM to extend the Kramers expressions beyond the hydrogenic case. Here we present the relevant corrected expressions and show the key modified results. We conclude that, in most cases, NTR emission was overestimated by a factor of 1-8 by BM but is typically still large enough (as much as 20-30% of the total emission) to be very important for electron spectral inference and detection of electron spectral features such as low energy cut-offs since the recombination spectra contain sharp edges. For extreme temperature regimes and/or if the Fe abundance were as high as some values claimed, NTR could even be the dominant source of flare HXRs, reducing the electron number and energy budget, problems such as in the extreme coronal HXR source cases reported by e.g. Krucker et al.
    Astronomy and Astrophysics 01/2010; 515. · 5.08 Impact Factor
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    ABSTRACT: Past analyses of solar flares have ignored nonthermal recombination (NTR) emission as a means of producing Hard X-rays (HXRs) in the corona and chromosphere. However, Brown and Mallik (2008, A&A, 481, 507) have shown that NTR can be significant and even exceed nonthermal bremsstrahlung (NTB) emission for certain flare conditions that are quite common. For hot enough plasma (T > 10 MK), HXR emission of a few deka-keV has a large contribution from NTR onto highly ionized heavy elements, especially Fe. Consequently, including NTR has implications for the magnitude and the form of the inferred electron spectrum, F(E), and hence for fast-electron density and energy budgets and for the acceleration mechanisms. We show under what circumstances NTR dominates in deka-keV HXR emission. It is important to note that at high temperatures, HXR emission from thermal electrons (recombination and bremsstrahlung) becomes important. However, NTR dominates over NTB without being swamped by thermal emission in the photon energy (ε) regime of 20–30 keV and temperature range of 10–25MK (Fig. 1, left). By integrating the flux for all ε > 20keV, i.e., looking at the source luminosity function above 20 keV, we were able to show that by including NTR, the acceleration requirements are less demanding for every event, but to varying degrees based on temperature (T), spectral index (δ) and electron low-energy cut-off (Ec). Our key result is that, for T > 10MK and δ ≈ 5, including NTR reduces the demand for nonthermal electrons by up to 85%. Our paper with these results will be submitted to ApJ Letters.
    12/2009: pages 463-464;
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    ABSTRACT: Brown and Mallik (BM) recently showed that, for hot sources, recombination of non-thermal electrons (NTR) onto highly ionised heavy ions is not negligible compared to non-thermal bremsstrahlung (NTB) as a source of flare hard X-rays (HXRs) and so should be included in modelling non-thermal HXR flare emission. In view of major discrepancies between BM results for the THERMAL continua and those of the Chianti code and of RHESSI solar data, we critically re-examine and correct the BM analysis and modify the conclusions concerning the importance of NTR. Although the analytic Kramers expression used by BM is correct for the purely hydrogenic recombination cross section, the heuristic expressions used by BM to extend the Kramers expression beyond the `bare nucleus' case to which it applies had serious errors. BM results have therefore been recalculated using corrected expressions, which have been validated against the results of detailed calculations. At T ~ 10-30 MK the dominant ions are Fe 22+, 23+, 24+ for which BM erroneously overestimated NTR emission by around an order of magnitude. Contrary to the BM claim, NTR in hot flare plasmas does NOT dominate over NTB, although in some cases it can be comparable and so still very important in inversions of photon spectra to derive electron spectra, especially as NTR includes sharp edge features. The BM claim of dominance of NTR over NTB in deka-keV emission is incorrect due to a serious error in their analysis. However, the NTR contribution can still be large enough to demand inclusion in spectral fitting, the spectral edges having potentially serious effects on inversion of HXR spectra to infer fast electron spectra. Comment: 6 pages, 8 figures, 1 table
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    ABSTRACT: The collisional thick target model (CTTM) of solar hard X-ray (HXR) bursts has become an almost 'Standard Model' of flare impulsive phase energy transport and radiation. However, it faces various problems in the light of recent data, particularly the high electron beam density and anisotropy it involves.} {We consider how photon yield per electron can be increased, and hence fast electron beam intensity requirements reduced, by local re-acceleration of fast electrons throughout the HXR source itself, after injection.} {We show parametrically that, if net re-acceleration rates due to e.g. waves or local current sheet electric (${\cal E}$) fields are a significant fraction of collisional loss rates, electron lifetimes, and hence the net radiative HXR output per electron can be substantially increased over the CTTM values. In this local re-acceleration thick target model (LRTTM) fast electron number requirements and anisotropy are thus reduced. One specific possible scenario involving such re-acceleration is discussed, viz, a current sheet cascade (CSC) in a randomly stressed magnetic loop.} {Combined MHD and test particle simulations show that local ${\cal E}$ fields in CSCs can efficiently accelerate electrons in the corona and and re-accelerate them after injection into the chromosphere. In this HXR source scenario, rapid synchronisation and variability of impulsive footpoint emissions can still occur since primary electron acceleration is in the high Alfv\'{e}n speed corona with fast re-acceleration in chromospheric CSCs. It is also consistent with the energy-dependent time-of-flight delays in HXR features. Comment: 8 pages, 2 figures
    Astronomy and Astrophysics 09/2009; · 5.08 Impact Factor
  • P Mallik, J ~C Brown, A ~L MacKinnon
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    ABSTRACT: For work on my thesis dissertation, we have been studying some energetic processes in solar flares. On our work on Hard X-ray (HXR) emission from flares, we have shown that recombination emission can exceed the bremsstrahlung HXR flux for certain flare conditions. We will show some spectral features characteristic of non-thermal recombination HXR emission and will suggest how it plays a significant role in the flare HXR continuum, something that has been ignored in the past. It is important to note that these results could demand a reconsideration of the numbers of accelerated electrons since recombination can be much more efficient in producing HXR photons than bremsstrahlung. In related work on diagnosing particle acceleration in flares, we also have an interest in studying solar neutrons. To this end, we will present our work done with new-age neutron detectors developed by our colleagues at the University of New Hampshire. Using laboratory and simulated data from the detector to produce its response matrix, we then employ regularisation and deconvolution techniques to produce encouraging results for data inversion. As a corollary, we have also been reconsidering the role of inverse Compton (IC) scattering of photospheric photons. Gamma-ray observations clearly show the presence of 100 MeV electrons and positrons in the solar corona, by-products of GeV energy ions. Here we will present results of IC scattering of such photons taking proper account of radiation field geometry near the solar surface. If observed, such radiation would let us determine the number of secondary positrons produced in large flares, contributing to a full picture of ion acceleration and to predicting neutron fluxes to be encountered by future inner heliosphere space missions. This work is supported by a UK STFC Rolling Grant and a Dorothy Hodgkin's Scholarship (PM).
    AAS/Solar Physics Division Meeting #40; 05/2009
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    ABSTRACT: The polarimetric and photometric variability of Wolf-Rayet (WR) stars as caused by clumps in the winds, is revisited. In the model which is improved from Li et al. 2000, the radial expansion of the thickness is accounted for, but we retain the dependence on the beta velocity law, stellar occultation effects. We again search for parameters that can yield results consistent with observations in regards to the mean polarization, the ratio of polarimetric to photometric variability, and the volume filling factor. Clump generation and spatial distribution are randomized by the Monte Carlo method so as to produce clumps which are, in the mean, distributed uniformly in space and have time intervals with a Gaussian distribution. The generated clumps move radially outward with a velocity law determined by a beta index, and the angular size of the clumps is assumed to keep fixed. By fitting the observational results and the volume filling factor, the clump velocity law index beta and clump ejection rate are inferred, and are found to be well constrained. In addition, the subpeak features on broad emission lines seem to support the clump ejection rate. Meanwhile, the fraction of the total mass loss rate that is contained in the clumps is obtained by fitting the observed polarization. We conclude that this picture for the clump properties produces a valuable diagnostic of WR wind structure. Comment: 28 pages, 13 figures, accepted for publication in RAA
    Research in Astronomy and Astrophysics 03/2009; · 1.35 Impact Factor
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    ABSTRACT: Context. An abstract should be given Aims. An abstract should be given Methods. An abstract should be given Results. An abstract should be given Conclusions. An abstract should be given We consider the polarization arising from scattering in an en- velope illuminated by a central anisotropic source. This work ex- tends the theory introduced in a previous paper (Al-Malki et al. 1999) in which scattering polarization from a spherically sym- metric envelope illuminated by an anisotropic point source was considered. Here we generalize to account for the more realis- tic expectation of a non-spherical envelope shape. Spherical har- monics are used to describe both the light source anisotropy and the envelope density distribution functions of the scatter ing par- ticles. This framework demonstrates how the net resultant polar- ization arises from a superposition of three basic "shape" f unc- tions: the distribution of source illumination, the distri bution of envelope scatterers, and the phase function for dipole scat tering. Specific expressions for the Stokes parameters and scattere d flux are derived for the case of an ellipsoidal light source insid e an ellipsoidal envelope, with principal axes that are general ly not aligned. Two illustrative examples are considered: (a) axisym- metric mass loss from a rapidly rotating star, such as may apply to some Luminous Blue Variables, and (b) a Roche-lobe filling star in a binary system with a circumstellar envelope. As a gen- eral conclusion, the combination of source anisotropy with dis- torted scattering envelopes leads to more complex polarimetric behavior such that the source characteristics should be car efully considered when interpreting polarimetric data. Polarization - Stars: circumstellar - Stars: binaries - Sta rs: rotation - Stars: winds
    Astronomy and Astrophysics 03/2009; 496(2). · 5.08 Impact Factor
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    ABSTRACT: We consider the polarization arising from scattering in an envelope illuminated by a central anisotropic source. Spherical harmonics are used to describe both the light source anisotropy and the envelope density distribution functions of the scattering particles. This framework demonstrates how the net resultant polarization arises from a superposition of three basic "shape" functions: the distribution of source illumination, the distribution of envelope scatterers, and the phase function for dipole scattering. Specific expressions for the Stokes parameters and scattered flux are derived for the case of an ellipsoidal light source inside an ellipsoidal envelope, with principal axes that are generally not aligned. Two illustrative examples are considered: (a) axisymmetric mass loss from a rapidly rotating star, such as may apply to some Luminous Blue Variables, and (b) a Roche-lobe filling star in a binary system with a circumstellar envelope. As a general conclusion, the combination of source anisotropy with distorted scattering envelopes leads to more complex polarimetric behavior such that the source characteristics should be carefully considered when interpreting polarimetric data.
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    ABSTRACT: Under suitable conditions, hard X-rays (HXRs) may be emitted by a neutralized proton beam due to the "heating" of the electrostatically dragged electrons in collisions with a nearly neutral background atmosphere. A simple estimate is made generalizing this HXR emission mechanism to heavier ions dragging a neutralizing electron current. Recent gamma-ray results on the energy content of flare ions of ≥1 MeV nucleon-1 are used to estimate the total HXR yield above 20 keV or so which would be expected from these processes, and in 19 flares the results are compared with HXR data in the same events. It is found that only in two flares are the neutral beam HXRs clearly important and that in a few others they may be significant. In most events, however, the neutral beam HXR contribution is small, though the ion energy is comparable with that of electrons.
    The Astrophysical Journal 12/2008; 541(2):1104. · 6.73 Impact Factor
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    ABSTRACT: Context. Hard X-ray bremsstrahlung continuum spectra, such as from solar flares, are commonly described in terms of power-law fits, either to the photon spectra themselves or to the electron spectra responsible for them. In applications various approximate relations between electron and photon spectral indices are often used for energies both above and below electron low-energy cutoffs.Aims. We examine the form of the exact relationships in various situations, and for various cross-sections, showing that empirical relations sometimes used can be highly misleading especially at energies below the low-energy cutoff, and consider how to improve fitting procedures.Methods. We obtain expressions for photon spectra from single, double and truncated power-law electron spectra for a variety of cross-sections and for the thin and thick target models and simple analytic expressions for the non-relativistic Bethe-Heitler case.Results. We show that below the low-energy cutoff Kramers and other constant spectral index forms commonly used are very poor approximations to accurate results, but that our analytical forms are a good match; and that above a low-energy cutoff, the Kramers and non-relativistic Bethe-Heitler results match reasonably well with results for up to energies around $100$ keV.Conclusions. Analytical forms of the non-relativistic Bethe-Heitler photon spectra from general power-law electron spectra are good match to exact results for both thin and thick targets and they enable much faster spectral fitting than evaluation of the full spectral integrations.
    Astronomy and Astrophysics 08/2008; · 5.08 Impact Factor
  • S Stoiser, JC Brown, AM Veronig
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    ABSTRACT: We present simple analytic models which predict the peak X-ray emission measure and temperature attained in flares in which the chromospheric evaporation process takes place either in a single ‘monolithic’ loop or in a loop consisting of several filaments that are created successively as the energy release process proceeds in time. As possible mechanisms driving chromospheric evaporation we consider both classical heat conduction from the loop top and non-thermal electron beams. The model predictions are tested for a set of 18 well studied RHESSI microflares. The results suggest beam driven evaporation in filamented loops as being capable of accounting for the observed emission measures and temperatures though there are issues with the very high beam densities needed. On the other hand, estimates of the emission measures achieved by conductive evaporation which are derived by using the Rosner – Tucker – Vaiana (RTV) scaling law are much larger than the observed ones. Possible reasons for this discrepancy are discussed.
    Solar Physics 01/2008; · 3.26 Impact Factor
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    ABSTRACT: The puzzle of the origin of Be star disks is discussed. Contrary to recently published claims, it is argued that the magnetically torqued disk (MTD) type models of Cassinelli et al. offer a viable scenario for a successful model with all the key ingredients. MTD models involve disk compression by equatorial collision of stellar wind streams that are steered and torqued by a dipole-like magnetic field. While the growing disk density tends to lead to the gas breaking out centrifugally from the field, it is proposed that the onset of viscous effects can lead to an eventual stable, slowly outflowing, Keplerian disk. It is then shown that the resulting very dense (wind compressed) disk need have only a very slow subsonic outflow to satisfy mass continuity. Consequently, line profile data do not preclude steadily expanding disks of high density. It is also shown that the time taken to reach the steady state would typically be of the order of 104 wind flow times R/v∞. This is far longer than the run times of recent numerical MHD simulations that displayed bursty breakout behavior, which may therefore only be transients induced by unrealistic initial conditions.
    The Astrophysical Journal 01/2008; · 6.73 Impact Factor
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    ABSTRACT: X-ray properties of the stellar population in the Carina OB1 association are examined with special emphasis on early-type stars. Their spectral characteristics provide some clues to understanding the nature of X-ray formation mechanisms in the winds of single and binary early-type stars. A timing and spectral analysis of five observations with XMM-Newton is performed using various statistical tests and thermal spectral models. 235 point sources have been detected within the field of view. Several of these sources are probably pre-main sequence stars with characteristic short-term variability. Seven sources are possible background AGNs. Spectral analysis of twenty three sources of type OB and WR 25 was performed. We derived spectral parameters of the sources and their fluxes in three energy bands. Estimating the interstellar absorption for every source and the distance to the nebula, we derived X-ray luminosities of these stars and compared them to their bolometric luminosities. We discuss possible reasons for the fact that, on average, the observed X-ray properties of binary and single early type stars are not very different, and give several possible explanations. Comment: 20 pages, 16 figures
    Astronomy and Astrophysics 11/2007; · 5.08 Impact Factor
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    ABSTRACT: We focus attention on the Oe/Be stars to test the concept that the disks of these stars form by magnetic channeling of wind material toward the equator. Calculations are made of the X-rays expected from the Magnetically Torqued Disk (MTD) model for Be stars discussed by Cassinelli et al. (2002), by Maheswaran (2003), and by Brown et al. (2004). The dominant parameters in the model are the $\beta$ value of the velocity law, the rotation rate of the star, $S_o$, and the ratio of the magnetic field energy density to the disk gravitational energy density, $\gamma$. The model predictions are compared with the $ROSAT$ observations obtained for an O9.5 star $\zeta$ Oph from \Berghofer et al. (1996) and for 7 Be stars from Cohen et al. (1997). Extra considerations are also given here to the well studied Oe star $\zeta$ Oph for which we have $Chandra$ observations of the X-ray line profiles of the triad of He-like lines from the ion Mg XI. Comment: 28 pages with 6 figures. Accepted for publication in ApJ
    The Astrophysical Journal 10/2007; · 6.73 Impact Factor
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    ABSTRACT: X-ray catalogue of sources detected with XMM-Newton in the Carina OB1 association is presented. X-ray count rates in three energy bands and the X-ray variability status are given. Cross-identifications of X-ray sources with optical and infrared catalogues are also presented. (2 data files).
    VizieR Online Data Catalog. 10/2007;

Publication Stats

1k Citations
408.01 Total Impact Points


  • 1980–2011
    • University of Glasgow
      • School of Physics and Astronomy
      Glasgow, SCT, United Kingdom
    • The University of Waikato
      • Department of Mathematics
      Hamilton, Waikato, New Zealand
  • 2005–2007
    • University of Wisconsin, Madison
      • Department of Astronomy
      Mississippi, United States
  • 2006
    • Karl-Franzens-Universität Graz
      • Institute of Physics
      Graz, Styria, Austria
  • 2004
    • University of Delaware
      • Bartol Research Institute
      Delaware, United States
  • 1998–2004
    • University of Alabama in Huntsville
      • Department of Physics
      Huntsville, Alabama, United States
    • INFN - Istituto Nazionale di Fisica Nucleare
      Frascati, Latium, Italy
    • Università degli Studi di Genova
      • Department of Physics
      Genova, Liguria, Italy
  • 2000
    • National Center for Atmospheric Research
      • High Altitude Observatory
      Boulder, Colorado, United States
  • 1990
    • University of São Paulo
      San Paulo, São Paulo, Brazil
    • Observatoire de Paris
      Lutetia Parisorum, Île-de-France, France
  • 1988
    • Brandeis University
      Waltham, Massachusetts, United States
  • 1987
    • University of California, San Diego
      • Center for Astrophysics and Space Sciences (CASS)
      San Diego, CA, United States
  • 1984
    • California Institute of Technology
      Pasadena, California, United States