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Abstract We present the discovery of a new double-detonation progenitor system consisting of a hot subdwarf B (sdB) binary with a white dwarf companion with aPorb= 76.34179(2) minutes orbital period. Spectroscopic observations are consistent with an sdB star during helium core burning residing on the extreme horizontal branch. Chimera light curves are dominated by ellipsoidal deformation of the sdB star and a weak eclipse of the companion white dwarf. Combining spectroscopic and light curve fits, we find a low-mass sdB star,MsdB= 0.383 ± 0.028M⊙with a massive white dwarf companion,MWD= 0.725 ± 0.026M⊙. From the eclipses we find a blackbody temperature for the white dwarf of 26,800 K resulting in a cooling age of ≈25 Myr whereas ourMESAmodel predicts an sdB age of ≈170 Myr. We conclude that the sdB formed first through stable mass transfer followed by a common envelope which led to the formation of the white dwarf companion ≈25 Myr ago. Using theMESAstellar evolutionary code we find that the sdB star will start mass transfer in ≈6 Myr and in ≈60 Myr the white dwarf will reach a total mass of 0.92M⊙with a thick helium layer of 0.17M⊙. This will lead to a detonation that will likely destroy the white dwarf in a peculiar thermonuclear supernova. PTF1 J2238+7430 is only the second confirmed candidate for a double-detonation thermonuclear supernova. Using both systems we estimate that at least ≈1% of white dwarf thermonuclear supernovae originate from sdB+WD binaries with thick helium layers, consistent with the small number of observed peculiar thermonuclear explosions.
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Polynomial bounds for chromatic number. III. Excluding a double star
Abstract A “double star” is a tree with two internal vertices. It is known that the Gyárfás–Sumner conjecture holds for double stars, that is, for every double star , there is a function such that if does not contain as an induced subgraph then (where are the chromatic number and the clique number of ). Here we prove that can be chosen to be a polynomial.
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- Award ID(s):
- 1800053
- PAR ID:
- 10369536
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Journal of Graph Theory
- Volume:
- 101
- Issue:
- 2
- ISSN:
- 0364-9024
- Page Range / eLocation ID:
- p. 323-340
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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