Asymptotic approximations for stellar nonradial pulsations
About: This article is published in Astrophysical Journal Supplement Series.The article was published on 1980-08-01. It has received 902 citations till now.
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TL;DR: Modules for Experiments in Stellar Astrophysics (MESA) as discussed by the authors is an open source software package for modeling the evolution of stellar structures and composition. But it is not suitable for large-scale systems such as supernovae.
Abstract: We substantially update the capabilities of the open source software package Modules for Experiments in Stellar Astrophysics (MESA), and its one-dimensional stellar evolution module, MESA star. Improvements in MESA star's ability to model the evolution of giant planets now extends its applicability down to masses as low as one-tenth that of Jupiter. The dramatic improvement in asteroseismology enabled by the space-based Kepler and CoRoT missions motivates our full coupling of the ADIPLS adiabatic pulsation code with MESA star. This also motivates a numerical recasting of the Ledoux criterion that is more easily implemented when many nuclei are present at non-negligible abundances. This impacts the way in which MESA star calculates semi-convective and thermohaline mixing. We exhibit the evolution of 3-8 M ? stars through the end of core He burning, the onset of He thermal pulses, and arrival on the white dwarf cooling sequence. We implement diffusion of angular momentum and chemical abundances that enable calculations of rotating-star models, which we compare thoroughly with earlier work. We introduce a new treatment of radiation-dominated envelopes that allows the uninterrupted evolution of massive stars to core collapse. This enables the generation of new sets of supernovae, long gamma-ray burst, and pair-instability progenitor models. We substantially modify the way in which MESA star solves the fully coupled stellar structure and composition equations, and we show how this has improved the scaling of MESA's calculational speed on multi-core processors. Updates to the modules for equation of state, opacity, nuclear reaction rates, and atmospheric boundary conditions are also provided. We describe the MESA Software Development Kit that packages all the required components needed to form a unified, maintained, and well-validated build environment for MESA. We also highlight a few tools developed by the community for rapid visualization of MESA star results.
2,761 citations
Cites methods from "Asymptotic approximations for stell..."
...The large frequency separation, ∆ν, of the model is calculated as the inverse of the sound travel time through the star, ∆ν = [2 ∫ dr/cs]−1 (Tassoul 1980; Gough 1986)....
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TL;DR: In this paper, the authors compared the neutrino predictions from a set of eight standard-like solar models and four deviant (or deficient) solar models with the results of solar neutrinos experiments.
Abstract: We calculate accurate solar models and report the detailed time dependences of important solar quantities. We use helioseismology to constrain the luminosity evolution of the Sun and report the discovery of semiconvection in evolved solar models that include diffusion. In addition, we compare the computed sound speeds with the results of p-mode observations by BiSON, GOLF, GONG, LOWL, and MDI instruments. We contrast the neutrino predictions from a set of eight standard-like solar models and four deviant (or deficient) solar models with the results of solar neutrino experiments. For solar neutrino and helioseismological applications, we present present-epoch numerical tabulations of characteristics of the standard solar model as a function of solar radius, including the principal physical and composition variables, sound speeds, neutrino fluxes, and functions needed for calculating solar neutrino oscillations.
827 citations
Cites background from "Asymptotic approximations for stell..."
...For the high-order (large radial node, n), low-degree modes that are expected to be observed in stars, the frequencies satisfy the following relation to a good approximation (e.g., Tassoul 1980) : l nl ^ * A n ] l 2 ] a B ....
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San Jose State University1, Ames Research Center2, Harvard University3, Aarhus University4, National Center for Atmospheric Research5, NASA Exoplanet Science Institute6, Lowell Observatory7, California Institute of Technology8, Space Telescope Science Institute9, University of California, Berkeley10, Massachusetts Institute of Technology11, Fermilab12, Las Cumbres Observatory Global Telescope Network13, University of Texas at Austin14, Yale University15, University of Florida16, University of California, Santa Cruz17, San Diego State University18, Lawrence Hall of Science19
TL;DR: The first Earth-size exoplanet was discovered by NASA's Kepler mission as discussed by the authors, which used transit photometry to determine the frequency of Earthsize planets in or near the habitable zone of Sun-like stars.
Abstract: NASA's Kepler Mission uses transit photometry to determine the frequency of Earth-size planets in or near the habitable zone of Sun-like stars. The mission reached a milestone toward meeting that goal: the discovery of its first rocky planet, Kepler-10b. Two distinct sets of transit events were detected: (1) a 152 ± 4 ppm dimming lasting 1.811 ± 0.024 hr with ephemeris T [BJD] = 2454964.57375^(+0.00060)_(–0.00082) + N * 0.837495^(+0.000004)_(–0.000005) days and (2) a 376 ± 9 ppm dimming lasting 6.86 ± 0.07 hr with ephemeris T [BJD] = 2454971.6761^(+0.0020)_(–0.0023) + N * 45.29485^(+0.00065) _(–0.00076) days. Statistical tests on the photometric and pixel flux time series established the viability of the planet candidates triggering ground-based follow-up observations. Forty precision Doppler measurements were used to confirm that the short-period transit event is due to a planetary companion. The parent star is bright enough for asteroseismic analysis. Photometry was collected at 1 minute cadence for >4 months from which we detected 19 distinct pulsation frequencies. Modeling the frequencies resulted in precise knowledge of the fundamental stellar properties. Kepler-10 is a relatively old (11.9 ± 4.5 Gyr) but otherwise Sun-like main-sequence star with T_(eff) = 5627 ± 44 K, M_⋆ = 0.895 ± 0.060 M_⊙ , and R_⋆ = 1.056 ± 0.021 R_⊙. Physical models simultaneously fit to the transit light curves and the precision Doppler measurements yielded tight constraints on the properties of Kepler-10b that speak to its rocky composition: M_P = 4.56^9+1.17)_(–1.29) M_⊕, R_P = 1.416^(+0.033)_(–0.036) R_⊕, and ρ_P = 8.8^(+2.1)_(–2.9) g cm^(–3). Kepler-10b is the smallest transiting exoplanet discovered to date.
623 citations
Cites background from "Asymptotic approximations for stell..."
...(2010b) and described in more detail by Steffen et al. (2010). The discovery of the planets orbiting Kepler-9 (Holman et al....
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...Five such candidate systems were included in the catalog of Borucki et al. (2010b) and described in more detail by Steffen et al. (2010)....
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TL;DR: Observations of gravity-mode period spacings in red giants that permit a distinction between evolutionary stages to be made, using high-precision photometry obtained by the Kepler spacecraft to measure oscillations in several hundred red giants.
Abstract: Red giants are evolved stars that have exhausted the supply of hydrogen in their cores and instead burn hydrogen in a surrounding shell. Once a red giant is sufficiently evolved, the helium in the core also undergoes fusion. Outstanding issues in our understanding of red giants include uncertainties in the amount of mass lost at the surface before helium ignition and the amount of internal mixing from rotation and other processes. Progress is hampered by our inability to distinguish between red giants burning helium in the core and those still only burning hydrogen in a shell. Asteroseismology offers a way forward, being a powerful tool for probing the internal structures of stars using their natural oscillation frequencies. Here we report observations of gravity-mode period spacings in red giants that permit a distinction between evolutionary stages to be made. We use high-precision photometry obtained by the Kepler spacecraft over more than a year to measure oscillations in several hundred red giants. We find many stars whose dipole modes show sequences with approximately regular period spacings. These stars fall into two clear groups, allowing us to distinguish unambiguously between hydrogen-shell-burning stars (period spacing mostly ~50 seconds) and those that are also burning helium (period spacing ~100 to 300 seconds)
620 citations
TL;DR: A review of the current state of the field can be found in this article, with a particular emphasis on recent advances provided by the Kepler and COROT (Convection, Rotation & Planetary Transits) space missions.
Abstract: We are entering a golden era for stellar physics driven by satellite and telescope observations of unprecedented quality and scope. New insights on stellar evolution and stellar interiors physics are being made possible by asteroseismology, the study of stars by the observation of natural, resonant oscillations. Asteroseismology is proving to be particularly significant for the study of solar-type and red-giant stars. These stars show rich spectra of solar-like oscillations, which are excited and intrinsically damped by turbulence in the outermost layers of the convective envelopes. In this review we discuss the current state of the field, with a particular emphasis on recent advances provided by the Kepler and COROT (Convection, Rotation & Planetary Transits) space missions and the wider significance to astronomy of the results from asteroseismology, such as stellar populations studies and exoplanet studies.
499 citations
Additional excerpts
...…the periods, Πnl, i.e., Πnl = ν −1 nl ≃ ∆Πl (n+ ǫg) , (11) where the period separation ∆Πl (analagous to ∆ν for p modes) is given by: ∆Πl = 2π2 √ l(l + 1) ( ∫ r2 r1 N dr r )−1 , (12) assuming that N2 ≥ 0 in the convectively stable region bounded by [r1, r2], with N = 0 at r1 and r2 (Tassoul 1980)....
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