J. J. Drake

Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts, United States

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Publications (525)1488.54 Total impact

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    ABSTRACT: We present the results of a detailed numerical simulation of the circumstellar environment around three exoplanet-hosting stars. A state-of-the-art global magnetohydrodynamic (MHD) model is considered, including Alfv\'en wave dissipation as a self-consistent coronal heating mechanism. This paper contains the description of the numerical set-up, evaluation procedure, and the simulated coronal structure of each system (HD 1237, HD 22049 and HD 147513). The simulations are driven by surface magnetic field maps, recovered with the observational technique of Zeeman Doppler Imaging (ZDI). A detailed comparison of the simulations is performed, where two different implementations of this mapping routine are used to generate the surface field distributions. Quantitative and qualitative descriptions of the coronae of these systems are presented, including synthetic high-energy emission maps in the Extreme Ultra-Violet (EUV) and Soft X-rays (SXR) ranges. Using the simulation results, we are able to recover similar trends as in previous observational studies, including the relation between the magnetic flux and the coronal X-ray emission. Furthermore, for HD 1237 we estimate the rotational modulation of the high-energy emission due to the various coronal features developed in the simulation. We obtain variations, during a single stellar rotation cycle, up to 15\% for the EUV and SXR ranges. The results presented here will be used, in a follow-up paper, to self-consistently simulate the stellar winds and inner astrospheres of these systems.
    Full-text · Article · Jan 2016 · Astronomy and Astrophysics
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    ABSTRACT: COCOA-PUFS is an energy-diverse, time-domain study of the ultra-fast spinning, heavily spotted, yellow giant FK Com (HD117555; G4 III). This single star is thought to be a recent binary merger, and is exceptionally active by measure of its intense ultraviolet and X-ray emissions, and proclivity to flare. COCOA-PUFS was carried out with Hubble Space Telescope in the UV (120-300 nm), using mainly its high-performance Cosmic Origins Spectrograph, but also high-precision Space Telescope Imaging Spectrograph; Chandra X-ray Observatory in the soft X-rays (0.5-10 keV), utilizing its High-Energy Transmission Grating Spectrometer; together with supporting photometry and spectropolarimetry in the visible from the ground. This is an introductory report on the project. FK Com displayed variability on a wide range of time scales, over all wavelengths, during the week-long main campaign, including a large X-ray flare; "super-rotational broadening" of the far-ultraviolet "hot-lines" (e.g., Si IV 139 nm (T~80,000 K) together with chromospheric Mg II 280 nm and C II 133 nm (10,000-30,000 K); large Doppler swings suggestive of bright regions alternately on advancing and retreating limbs of the star; and substantial redshifts of the epoch-average emission profiles. These behaviors paint a picture of a highly extended, dynamic, hot (10 MK) coronal magnetosphere around the star, threaded by cooler structures perhaps analogous to solar prominences, and replenished continually by surface activity and flares. Suppression of angular momentum loss by the confining magnetosphere could temporarily postpone the inevitable stellar spindown, thereby lengthening this highly volatile stage of coronal evolution.
    No preview · Article · Jan 2016
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    ABSTRACT: The Chandra Cygnus OB2 Legacy Survey is a wide and deep X-ray survey of the nearby and massive Cygnus OB2 association. The survey has detected ~8,000 X-ray sources, the majority of which are pre-main sequence X-ray emitting young stars in the association itself. To facilitate quantitative scientific studies of these sources as well as the underlying OB association it is important to understand the sensitivity of the observations and the level of completeness the observations have obtained. Here we describe the use of a hierarchical Monte Carlo simulation to achieve this goal by combining the empirical properties of the observations, analytic estimates of the source verification process, and an extensive set of source detection simulations. We find that our survey reaches a 90% completeness level for a pre-main-sequence population at the distance of Cyg OB2 at an X-ray luminosity of 4 x 10^30 ergs/s and a stellar mass of 1.3 Msun for a randomly distributed population. For a spatially clustered population such as Cyg~OB2 the 90% completeness level is reached at 1.1 Msun instead, as the sources are more concentrated in areas of our survey with a high exposure. These simulations can easily be adapted for use with other X-ray observations and surveys, and we provide X-ray detection efficiency curves for a very wide array of source and background properties to allow these simulations to be easily exploited by other users.
    No preview · Article · Nov 2015
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    ABSTRACT: Tidal forces close to massive black holes can violently disrupt stars that make a close approach. These extreme events are discovered via bright X-ray and optical/UV flares in galactic centers. Prior studies based on modeling decaying flux trends have been able to estimate broad properties, such as the mass accretion rate. Here we report the detection of flows of highly ionized X-ray gas in high-resolution X-ray spectra of a nearby tidal disruption event. Variability within the absorption-dominated spectra indicates that the gas is relatively close to the black hole. Narrow line widths indicate that the gas does not stretch over a large range of radii, giving a low volume filling factor. Modest outflow speeds of a few hundred kilometers per second are observed, significantly below the escape speed from the radius set by variability. The gas flow is consistent with a rotating wind from the inner, super-Eddington region of a nascent accretion disk, or with a filament of disrupted stellar gas near to the apocenter of an elliptical orbit. Flows of this sort are predicted by fundamental analytical theory and more recent numerical simulations.
    Preview · Article · Oct 2015 · Nature
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    ABSTRACT: The results from a spectro-polarimetric study of the planet-hosting Sun-like star, HD 147513 (G5V), are presented here. Robust detections of Zeeman signatures at all observed epochs indicate a surface magnetic field, with longitudinal magnetic field strengths varying between 1.0-3.2 G. Radial velocity variations from night to night modulate on a similar timescale to the longitudinal magnetic field measurements. These variations are therefore likely due to the rotational modulation of stellar active regions rather than the much longer timescale of the planetary orbit (Porb=528 d). Both the longitudinal magnetic field measurements and radial velocity variations are consistent with a rotation period of 10 +/- 2 days, which are also consistent with the measured chromospheric activity level of the star (log R'(HK)=-4.64). Together, these quantities indicate a low inclination angle, i~18 degrees. We present preliminary magnetic field maps of the star based on the above period and find a simple poloidal large-scale field. Chemical analyses of the star have revealed that it is likely to have undergone a barium-enrichment phase in its evolution because of a higher mass companion. Despite this, our study reveals that the star has a fairly typical activity level for its rotation period and spectral type. Future studies will enable us to explore the long-term evolution of the field, as well as to measure the stellar rotation period, with greater accuracy.
    Full-text · Article · Oct 2015 · Astronomy and Astrophysics
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    Cecilia Garraffo · Jeremy J. Drake · Ofer Cohen
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    ABSTRACT: Rotation evolution of late-type stars is dominated by magnetic braking and the underlying factors that control this angular momentum loss are important for the study of stellar spin-down. In this work, we study angular momentum loss as a function of two different aspects of magnetic activity using a calibrated Alfv\'en wave-driven magnetohydrodynamic wind model: the strengths of magnetic spots and their distribution in latitude. By driving the model using solar and modified solar surface magnetograms, we show that the topology of the field arising from the net interaction of both small-scale and large-scale field is important for spin-down rates and that angular momentum loss is not a simple function of large scale magnetic field strength. We find that changing the latitude of magnetic spots can modify mass and angular momentum loss rates by a factor of two. The general effect that causes these differences is the closing down of large-scale open field at mid- and high-latitudes by the addition of the small-scale field. These effects might give rise to modulation of mass and angular momentum loss through stellar cycles, and present a problem for ab initio attempts to predict stellar spin-down based on wind models. For all the magnetogram cases considered here, from dipoles to various spotted distributions, we find that angular momentum loss is dominated by the mass loss at mid-latitudes. The spin-down torque applied by magnetized winds therefore acts at specific latitudes and is not evenly distributed over the stellar surface, though this aspect is unlikely to be important for understanding spin-down and surface flows on stars.
    Preview · Article · Sep 2015 · The Astrophysical Journal
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    ABSTRACT: V745 Sco is a recurrent nova, with the most recent eruption occurring in February 2014. V745 Sco was first observed by Swift a mere 3.7 h after the announcement of the optical discovery, with the super-soft X-ray emission being detected around 4 d later and lasting for only ∼2 d, making it both the fastest follow-up of a nova by Swift and the earliest switch-on of super-soft emission yet detected. Such an early switch-on time suggests a combination of a very high velocity outflow and low ejected mass and, together with the high effective temperature reached by the super-soft emission, a high mass white dwarf (>1.3 M⊙). The X-ray spectral evolution was followed from an early epoch where shocked emission was evident, through the entirety of the super-soft phase, showing evolving column density, emission lines, absorption edges, and thermal continuum temperature. UV grism data were also obtained throughout the super-soft interval, with the spectra showing mainly emission lines from lower ionization transitions and the Balmer continuum in emission. V745 Sco is compared with both V2491 Cyg (another nova with a very short super-soft phase) and M31N 2008-12a (the most rapidly recurring nova yet discovered). The longer recurrence time compared to M31N 2008-12a could be due to a lower mass accretion rate, although inclination of the system may also play a part. Nova V745 Sco (2014) revealed the fastest evolving super-soft source phase yet discovered, providing a detailed and informative data set for study.
    Preview · Article · Sep 2015 · Monthly Notices of the Royal Astronomical Society
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    ABSTRACT: We estimate the accretion rates of 235 Classical T Tauri star (CTTS) candidates in the Lagoon Nebula using ugri H α photometry from the VST Photometric H α survey+. Our sample consists of stars displaying H α excess, the intensity of which is used to derive accretion rates. For a subset of 87 stars, the intensity of the u-band excess is also used to estimate accretion rates. We find the mean variation in accretion rates measured using H α and u-band intensities to be ∼0.17 dex, agreeing with previous estimates (0.04–0.4 dex) but for a much larger sample. The spatial distribution of CTTS align with the location of protostars and molecular gas suggesting that they retain an imprint of the natal gas fragmentation process. Strong accretors are concentrated spatially, while weak accretors are more distributed. Our results do not support the sequential star-forming processes suggested in the literature.
    Full-text · Article · Aug 2015 · Monthly Notices of the Royal Astronomical Society
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    ABSTRACT: We estimate the accretion rates of 235 Classical T Tauri star (CTTS) candidates in the Lagoon Nebula using $ugri$H$\alpha$ photometry from the VPHAS+ survey. Our sample consists of stars displaying H$\alpha$-excess, the intensity of which is used to derive accretion rates. For a subset of 87 stars, the intensity of the $u$-band excess is also used to estimate accretion rates. We find the mean variation in accretion rates measured using H$\alpha$ and $u$-band intensities to be $\sim$ 0.17 dex, agreeing with previous estimates (0.04-0.4 dex) but for a much larger sample. The spatial distribution of CTTS align with the location of protostars and molecular gas suggesting that they retain an imprint of the natal gas fragmentation process. Strong accretors are concentrated spatially, while weak accretors are more distributed. Our results do not support the sequential star forming processes suggested in the literature.
    Full-text · Article · Jul 2015
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    ABSTRACT: Recent developments in instrumentation and observational techniques have opened a new window for stellar magnetic field studies. In particular Zeeman Doppler Imaging (ZDI) is now routinely used to recover the large scale magnetic field topologies of stars different from the Sun, including several planet-hosting stars. These stellar magnetic fields intimately affect the environment around late-type stars by driving the coronal high-energy radiation (EUV/X-rays), transient events (e.g. flares and coronal mass ejections), and the development of stellar winds and astrospheres. These elements can have a strong impact in the evolution of planetary systems via star-planet interactions and erosion of exoplanetary atmospheres. In this context, the initial results from ZDI data-driven, detailed 3D MHD modeling of the coronal conditions and circumstellar environment around three planet hosting stars are presented. For one of the considered systems (HD 1237), we investigate the interactions of the magnetized stellar wind with the exoplanet, assuming a Jupiter-like magnetosphere around it.
    Full-text · Conference Paper · Jul 2015
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    ABSTRACT: We analyse the magnetic activity characteristics of the planet hosting Sun-like star, HD 1237, using HARPS spectro-polarimetric time-series data. We find evidence of rotational modulation of the magnetic longitudinal field measurements consistent with our ZDI analysis, with a period of 7 days. We investigate the effect of customising the LSD mask to the line depths of the observed spectrum and find that it has a minimal effect on shape of the extracted Stokes V profile but does result in a small increase in the S/N ($\sim$ 7%). We find that using a Milne-Eddington solution to describe the local line profile provides a better fit to the LSD profiles in this slowly rotating star, which also impacts the recovered ZDI field distribution. We also introduce a fit-stopping criterion based on the information content (entropy) of the ZDI maps solution set. The recovered magnetic field maps show a strong (+90 G) ring-like azimuthal field distribution and a complex radial field dominating at mid latitudes ($\sim$45 degrees). Similar magnetic field maps are recovered from data acquired five months apart. Future work will investigate how this surface magnetic field distribution impacts the coronal magnetic field and extended environment around this planet-hosting star.
    Full-text · Article · Jul 2015 · Astronomy and Astrophysics
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    Cecilia Garraffo · Jeremy J. Drake · Ofer Cohen
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    ABSTRACT: Observations of young open clusters have revealed a bimodal distribution of fast and slower rotation rates that has proven difficult to explain with predictive models of spin down that depend on rotation rates alone. The Metastable Dynamo Model proposed recently by Brown, employing a stochastic transition probability from slow to more rapid spin down regimes, appears to be more successful but lacks a physical basis for such duality. Using detailed 3D MHD wind models computed for idealized multipole magnetic fields, we show that surface magnetic field complexity can provide this basis. Both mass and angular momentum losses decline sharply with increasing field complexity. Combined with observation evidence for complex field morphologies in magnetically active stars, our results support a picture in which young, rapid rotators lose angular momentum in an inefficient way because of field complexity. During this slow spin-down phase, magnetic complexity is eroded, precipitating a rapid transition from weak to strong wind coupling.
    Full-text · Article · Jun 2015
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    ABSTRACT: We study the interaction between the atmospheres of Venus-like, non-magnetized exoplanets orbiting an M-dwarf star, and the stellar wind using a multi-species Magnetohydrodynaic (MHD) model. We focus our investigation on the effect of enhanced stellar wind and enhanced EUV flux as the planetary distance from the star decreases. Our simulations reveal different topologies of the planetary space environment for sub- and super-Alfvenic stellar wind conditions, which could lead to dynamic energy deposition in to the atmosphere during the transition along the planetary orbit. We find that the stellar wind penetration for non-magnetized planets is very deep, up to a few hundreds of kilometers. We estimate a lower limit for the atmospheric mass-loss rate and find that it is insignificant over the lifetime of the planet. However, we predict that when accounting for atmospheric ion acceleration, a significant amount of the planetary atmosphere could be eroded over the course of a billion years.
    Full-text · Article · Apr 2015 · The Astrophysical Journal
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    D. Takei · J. J. Drake · H. Yamaguchi · P. Slane · Y. Uchiyama · S. Katsuda
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    ABSTRACT: We report on a second epoch of Chandra X-ray imaging spectroscopy of the spatially-resolved old nova remnant GK Persei. An ACIS-S3 observation of 97.4 ks was conducted in November 2013 after a lapse of 13.8 years from the last visit in 2000. The X-ray emitting nebula appeared more faint and patchy compared with the first epoch. The flux decline was particularly evident in fainter regions and the mean decline was 30-40 % in the 0.5-1.2 keV energy band. A typical expansion of the brightest part of the remnant was 1.9 arcsec, which corresponds to an expansion rate of 0.14 arcsec yr^{-1}. The soft X-ray spectra extracted from both the 2000 and 2013 data can be explained by a non-equilibrium ionization collisional plasma model convolved with interstellar absorption, though do not allow us to constrain the origin of the flux evolution. The plasma temperature has not significantly evolved since the 2000 epoch and we conclude that the fading of the X-ray emission is due largely to expansion. This implies that recent expansion has been into a lower density medium, a scenario that is qualitatively consistent with the structure of the circumstellar environment photographed soon after the initial explosion more than a century ago. Fainter areas are fading more quickly than brighter areas, indicating that they are fainter because of a lower ambient medium density and consequently more rapid expansion.
    Preview · Article · Mar 2015 · The Astrophysical Journal
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    ABSTRACT: We present the results of an intensive multiwavelength campaign on nova LMC 2012. This nova evolved very rapidly in all observed wavelengths. The time to fall two magnitudes in the V band was only 2 days. In X-rays the super soft phase began 13 ± 5 days after discovery and ended around day 50 after discovery. During the super soft phase, the Swift/XRT and Chandra spectra were consistent with the underlying white dwarf (WD) being very hot, ∼1 MK, and luminous, ∼1038 erg s−1. The UV, optical, and near-IR photometry showed a periodic variation after the initial and rapid fading had ended. Timing analysis revealed a consistent 19.24 ± 0.03 hr period in all UV, optical, and near-IR bands with amplitudes of ∼0.3 mag which we associate with the orbital period of the central binary. No periods were detected in the corresponding X-ray data sets. A moderately high inclination system, i = 60 ± 10, was inferred from the early optical emission lines. The HST/STIS UV spectra were highly unusual with only the N v (1240 Å) line present and superposed on a blue continuum. The lack of emission lines and the observed UV and optical continua from four epochs can be fit with a low mass ejection event, ∼10−6 , from a hot and massive WD near the Chandrasekhar limit. The WD, in turn, significantly illuminated its subgiant companion which provided the bulk of the observed UV/optical continuum emission at the later dates. The inferred extreme WD characteristics and low mass ejection event favor nova LMC 2012 being a recurrent nova of the U Sco subclass.
    No preview · Article · Mar 2015 · The Astronomical Journal
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    ABSTRACT: Context. Transient short-period (<100 s) oscillations have been found in the X-ray light curves of three novae during their super-soft source (SSS) phase and in one persistent SSS. Aims. We pursue an observational approach to determine possible driving mechanisms and relations to fundamental system parameters such as the white dwarf mass. Methods. We performed a systematic search for short-period oscillations in all available XMM-Newton and Chandra X-ray light curves of persistent SSS and novae during their SSS phase. To study time evolution, we divided each light curve into short time-segments and computed power spectra. We then constructed a dynamic power spectrum from which we identified transient periodic signals even when only present for a short time. We base our confidence levels on simulations of false-alarm probability for the chosen oversampling rate of 16, corrected for multiple testing based on the number of time segments. From all time segments of each system, we computed fractions of time when periodic signals were detected. Results. In addition to the previously known systems with short-period oscillations, RS Oph (35 s), KT Eri (35 s), V339 Del (54 s), and Cal 83 (67 s), we found one additional system, LMC 2009a (33 s), and also confirm the 35 s period from Chandra data of KT Eri. The oscillation amplitudes are of about <15% of the respective count rates and vary without any clear dependence on the X-ray count rate. The fractions of the time when the respective periods were detected at 2σ significance (duty cycle) are 11.3%, 38.8%, 16.9%, 49.2%, and 18.7% for LMC 2009a, RS Oph, KT Eri, V339 Del, and Cal 83, respectively. The respective highest duty cycles found in a single observation are 38.1%, 74.5%, 61.4%, 67.8%, and 61.8%. Conclusions. Since fast rotation periods of the white dwarfs as origin of these transient oscillations are speculative, we concentrate on pulsation mechanisms. We present initial considerations predicting the oscillation period to scale linearly with the white dwarf radius (and thus mass), weakly with the pressure at the base, and luminosity. Estimates of the size of the white dwarf could be useful for determining whether these systems are more massive than typical white dwarfs, and thus whether they are growing from accretion over time. Signs of such mass growth may have implications for whether some of these systems are attractive as Type Ia supernova progenitors.
    Full-text · Article · Feb 2015 · Astronomy and Astrophysics
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    Paola Testa · Steve Saar · Jeremy J Drake
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    ABSTRACT: Observations of the coronae of the Sun and of solar-like stars provide complementary information to advance our understanding of stellar magnetic activity, and of the processes leading to the heating of their outer atmospheres. While solar observations allow us to study the corona at high spatial and temporal resolution, the study of stellar coronae allows us to probe stellar activity over a wide range of ages and stellar parameters. Stellar studies therefore provide us with additional tools for understanding coronal heating processes, as well as the long-term evolution of solar X-ray activity. We discuss how recent studies of stellar magnetic fields and coronae contribute to our understanding of the phenomenon of activity and coronal heating in late-type stars.
    Preview · Article · Feb 2015 · Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences
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    ABSTRACT: A fine analysis of spectral line widths and Doppler shifts employing Fourier transform and cross-correlation techniques has been applied to Chandra HETG spectra obtained in 1999 October of the rapidly rotating young star AB Doradus in order to investigate its coronal topology. The observation lasted 52.3ks, covering 1.2 rotation periods. The X-ray light curve obtained from integrating the dispersed signal revealed a moderate intensity flare midway through the exposure in which the count rate increased sharply by about 50% and subsequently decayed over the next 10ks. We find no significant Doppler shifts in the spectra or modulation of the light curve that could be attributed to rotation of dominant coronal structures at this epoch. Individual spectral line widths are statistically consistent with thermal broadening and formally require no rotational broadening, while the $1\sigma$ limit to rotational broadening corresponds to a compact corona restricted to latitudes $>57\deg$. Fourier analysis suggests a small amount of rotational broadening is present consistent with a corona restricted largely to the poles, and excludes models with surface rotational broadening or greater. These results present direct spectroscopic evidence that the dominant coronal activity on rapidly-rotating active stars is associated with the dark polar spots commonly seen in photospheric Doppler images, and support models in which these spots are of mixed magnetic polarity that forms closed loops.
    Preview · Article · Jan 2015 · The Astrophysical Journal
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    ABSTRACT: The young massive OB association Cygnus OB2, in the Cygnus X complex, is the closest (1400 pc) star forming region to the Sun hosting thousands of young low mass stars and up to 1000 OB stars, among which are some of the most massive stars known in our Galaxy. This region holds great importance for several fields of modern astrophysics, such as the study of the physical properties of massive and young low-mass stars and the feedback provided by massive stars on star and planet formation process. Cygnus OB2 has been recently observed with Chandra/ACIS-I as part of the 1.08Msec Chandra Cygnus OB2 Legacy Project. This survey detected 7924 X-ray sources in a square degree area centered on Cyg OB2. Since a proper classification and study of the observed X-ray sources also requires the analysis of their optical and infrared counterparts, we combined a large and deep set of optical and infrared catalogs available for this region with our new X-ray catalog. In this paper we describe the matching procedure and present the combined catalog containing 5703 sources. We also briefly discuss the nature of the X-ray sources with optical and infrared counterparts using their position in the color-magnitude and color-color diagrams.
    Preview · Article · Jan 2015
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    ABSTRACT: We present the results of a numerical simulation of the corona and wind structure of the Sun-like exoplanet-host GJ 3021 using a global magnetohydrodynamic (MHD) model. The simulation is driven by the radial component of the surface magnetic field recovered with the Zeeman Doppler Imaging (ZDI) technique. We consider two different ZDI input maps, which have similar large-scale structures but different spatial resolutions and field strengths. These maps arise from different but comparable models used to fit the observed circularly polarised spectra of the star. Our simulations show that the structure of the inner corona is consistent among the considered cases. Larger discrepancies are found in the wind structure, in particular in the radial wind speed and the Alfvén surface topology. These elements can have a significant impact on the mass loss and angular momentum loss predicted for this system and in other studies based on this numerical data-driven approach.
    Full-text · Conference Paper · Jan 2015

Publication Stats

6k Citations
1,488.54 Total Impact Points

Institutions

  • 1925-2015
    • Harvard-Smithsonian Center for Astrophysics
      • Smithsonian Astrophysical Observatory
      Cambridge, Massachusetts, United States
  • 2014
    • The University of Warwick
      • Department of Physics
      Coventry, England, United Kingdom
  • 2010-2014
    • Idenix Pharmaceuticals, Inc.
      Cambridge, Massachusetts, United States
  • 2005-2013
    • United States Naval Observatory
      Вашингтон, Maine, United States
    • University of Zurich
      • Institut für Theoretische Physik
      Zürich, Zurich, Switzerland
  • 2011
    • University of Wisconsin - Whitewater
      • Department of Physics
      Whitewater, WI, United States
  • 1993-2011
    • University of Leicester
      • Department of Physics and Astronomy
      Leiscester, England, United Kingdom
    • The Ohio State University
      • Department of Astronomy
      Columbus, OH, United States
  • 2009
    • Tokyo Metropolitan University
      Edo, Tōkyō, Japan
    • Rikkyo University
      • Department of Physics
      Tokyo, Tokyo-to, Japan
  • 1993-2009
    • University of California, Berkeley
      • Space Sciences Laboratory
      Berkeley, California, United States
  • 2008
    • The University of Edinburgh
      • Institute for Astronomy (IfA)
      Edinburgh, Scotland, United Kingdom
  • 2001
    • Arizona State University
      • School of Earth and Space Exploration
      Phoenix, Arizona, United States
  • 1993-2000
    • Villanova University
      노리스타운, Pennsylvania, United States
  • 1991
    • University of Oxford
      Oxford, England, United Kingdom