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Title: Low Mach Number Modeling of Type Ia Supernovae. II. EnergyEvolution

Abstract

The convective period leading up to a Type Ia supernova (SNIa) explosion is characterized by very low Mach number flows, requiringhydrodynamical methods well-suited to long-time integration. We continuethe development of the low Mach number equation set for stellar scaleflows by incorporating the effects of heat release due to externalsources. Low Mach number hydrodynamics equations with a time-dependentbackground state are derived, and a numerical method based on theapproximate projection formalism is presented. We demonstrate throughvalidation with a fully compressible hydrodynamics code that this lowMach number model accurately captures the expansion of the stellaratmosphere as well as the local dynamics due to external heat sources.This algorithm provides the basis for an efficient simulation tool forstudying the ignition of SNe Ia.

Authors:
; ; ;
Publication Date:
Research Org.:
Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
Sponsoring Org.:
USDOE Director. Office of Science. Advanced ScientificComputing Research
OSTI Identifier:
920061
Report Number(s):
LBNL-58673-Pt.II
Journal ID: ISSN 0004-637X; ASJOAB; R&D Project: K11001; BnR: KJ0101010; TRN: US200822%%707
DOE Contract Number:
DE-AC02-05CH11231
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 649; Journal Issue: 2pt1; Related Information: Journal Publication Date: 10/02/2006
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS; ALGORITHMS; EXPLOSIONS; HEAT SOURCES; HYDRODYNAMICS; IGNITION; MACH NUMBER; SIMULATION; STELLAR ATMOSPHERES; SUPERNOVAE; VALIDATION; supernovae: general white dwarfs hydrodynamics convectionmethods:numerical

Citation Formats

Almgren, Ann S., Bell, John B., Rendleman, Charles A., and Zingale,Mike. Low Mach Number Modeling of Type Ia Supernovae. II. EnergyEvolution. United States: N. p., 2006. Web.
Almgren, Ann S., Bell, John B., Rendleman, Charles A., & Zingale,Mike. Low Mach Number Modeling of Type Ia Supernovae. II. EnergyEvolution. United States.
Almgren, Ann S., Bell, John B., Rendleman, Charles A., and Zingale,Mike. Tue . "Low Mach Number Modeling of Type Ia Supernovae. II. EnergyEvolution". United States. doi:. https://www.osti.gov/servlets/purl/920061.
@article{osti_920061,
title = {Low Mach Number Modeling of Type Ia Supernovae. II. EnergyEvolution},
author = {Almgren, Ann S. and Bell, John B. and Rendleman, Charles A. and Zingale,Mike},
abstractNote = {The convective period leading up to a Type Ia supernova (SNIa) explosion is characterized by very low Mach number flows, requiringhydrodynamical methods well-suited to long-time integration. We continuethe development of the low Mach number equation set for stellar scaleflows by incorporating the effects of heat release due to externalsources. Low Mach number hydrodynamics equations with a time-dependentbackground state are derived, and a numerical method based on theapproximate projection formalism is presented. We demonstrate throughvalidation with a fully compressible hydrodynamics code that this lowMach number model accurately captures the expansion of the stellaratmosphere as well as the local dynamics due to external heat sources.This algorithm provides the basis for an efficient simulation tool forstudying the ignition of SNe Ia.},
doi = {},
journal = {Astrophysical Journal},
number = 2pt1,
volume = 649,
place = {United States},
year = {Tue Mar 28 00:00:00 EST 2006},
month = {Tue Mar 28 00:00:00 EST 2006}
}
  • We introduce a low Mach number equation set for the large-scale numerical simulation of carbon-oxygen white dwarfs experiencing a thermonuclear deflagration. Since most of the interesting physics in a Type Ia supernova transpires at Mach numbers from 0.01 to 0.1, such an approach enables both a considerable increase in accuracy and savings in computer time compared with frequently used compressible codes. Our equation set is derived from the fully compressible equations using low Mach number asymptotics, but without any restriction on the size of perturbations in density or temperature. Comparisons with simulations that use the fully compressible equations validate themore » low Mach number model in regimes where both are applicable. Comparisons to simulations based on the more traditional an elastic approximation also demonstrate the agreement of these models in the regime for which the anelastic approximation is valid. For low Mach number flows with potentially finite amplitude variations in density and temperature, the low Mach number model overcomes the limitations of each of the more traditional models and can serve as the basis for an accurate and efficient simulation tool.« less
  • We present the first three-dimensional, full-star simulations of convection in a white dwarf preceding a Type Ia supernova, specifically the last few hours before ignition. For these long-time calculations, we use our low Mach number hydrodynamics code, MAESTRO, which we have further developed to treat spherical stars centered in a three-dimensional Cartesian geometry. The main change required is a procedure to map the one-dimensional radial base state to and from the Cartesian grid. Our models recover the dipole structure of the flow seen in previous calculations, but our long-time integration shows that the orientation of the dipole changes with time.more » Furthermore, we show the development of gravity waves in the outer, stable portion of the star. Finally, we evolve several calculations to the point of ignition and discuss the range of ignition radii.« less
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  • We compare the host galaxies of 902 supernovae (SNe), including SNe Ia, SNe II, and SNe Ibc, which are selected by cross-matching the Asiago Supernova Catalog with the Sloan Digital Sky Survey (SDSS) Data Release 7. We selected an additional 213 galaxies by requiring the light fraction of spectral observations to be >15%, which could represent well the global properties of the galaxies. Among these 213 galaxies, 135 appear on the Baldwin-Phillips-Terlevich diagram, which allows us to compare the hosts in terms of whether they are star-forming (SF) galaxies, active galactic nuclei (AGNs; including composites, LINERs, and Seyfert 2s) ormore » absorption-line galaxies (Absorps; i.e., their related emission lines are weak or non-existent). The diagrams related to the parameters D{sub n}(4000), Hδ{sub A}, stellar masses, star formation rates (SFRs), and specific SFRs for the SNe hosts show that almost all SNe II and most of the SNe Ibc occur in SF galaxies, which have a wide range of stellar masses and low D{sub n}(4000). The SNe Ia hosts as SF galaxies following similar trends. A significant fraction of SNe Ia occurs in AGNs and absorption-line galaxies, which are massive and have high D{sub n}(4000). The stellar population analysis from spectral synthesis fitting shows that the hosts of SNe II have a younger stellar population than hosts of SNe Ia. These results are compared with those of the 689 comparison galaxies where the SDSS fiber captures less than 15% of the total light. These comparison galaxies appear biased toward higher 12+log(O/H) (∼0.1 dex) at a given stellar mass. Therefore, we believe the aperture effect should be kept in mind when the properties of the hosts for different types of SNe are discussed.« less
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