Single-Degenerate Type Ia Supernovae Are Preferentially Overluminous

Recent observational and theoretical progress has favored merging and helium-accreting sub-Chandrasekhar mass white dwarfs in the double-degenerate and the double-detonation channels, respectively, as the most promising progenitors of normal Type Ia supernovae (SNe Ia). Thus the fate of rapidly-accreting Chandrasekhar mass white dwarfs in the single-degenerate channel remains more mysterious then ever. In this paper, we clarify the nature of ignition in Chandrasekhar-mass single-degenerate SNe Ia by analytically deriving the existence of a characteristic length scale which establishes a transition from central ignitions to buoyancy-driven ignitions. Using this criterion, combined with data from three-dimensional simulations of convection and ignition, we demonstrate that the overwhelming majority of ignition events within Chandrasekhar-mass white dwarfs in the single-degenerate channel are buoyancy-driven, and consequently lack a vigorous deflagration phase. We thus infer that single-degenerate SNe Ia are generally expected to lead to overluminous 1991T-like SNe Ia events. We establish that the rates predicted from both the population of supersoft X-ray sources and binary population synthesis models of the single-degenerate channel are broadly consistent with the observed rates of overluminous SNe Ia, and suggest that the population of supersoft X-ray sources are the dominant stellar progenitors of SNe 1991T-like events. We further demonstrate that the single-degenerate channel contribution to the normal and failed 2002cx-like rates is not likely to exceed 1% of the total SNe Ia rate. We conclude with a range of observational tests of overluminous SNe Ia which will either support or strongly constrain the single-degenerate scenario.Comment: 12 pages, 2 figures, accepted to Astrophysical Journal. Comments welcom

Retrieval analysis of 38 WFC3 transmission spectra and resolution of the normalisation degeneracy

A comprehensive analysis of 38 previously published Wide Field Camera 3 (WFC3) transmission spectra is performed using a hierarchy of nested-sampling retrievals: with versus without clouds, grey versus non-grey clouds, isothermal versus non-isothermal transit chords and with water, hydrogen cyanide and/or ammonia. We revisit the "normalisation degeneracy": the relative abundances of molecules are degenerate at the order-of-magnitude level with the absolute normalisation of the transmission spectrum. Using a suite of mock retrievals, we demonstrate that the normalisation degeneracy may be partially broken using WFC3 data alone, even in the absence of optical/visible data and without appealing to the presence of patchy clouds, although lower limits to the mixing ratios may be prior-dominated depending on the measurement uncertainties. With James Webb Space Telescope-like spectral resolutions, the normalisation degeneracy may be completely broken from infrared spectra alone. We find no trend in the retrieved water abundances across nearly two orders of magnitude in exoplanet mass and a factor of 5 in retrieved temperature (about 500 to 2500 K). We further show that there is a general lack of strong Bayesian evidence to support interpretations of non-grey over grey clouds (only for WASP-69b and WASP-76b) and non-isothermal over isothermal atmospheres (no objects). 35 out of 38 WFC3 transmission spectra are well-fitted by an isothermal transit chord with grey clouds and water only, while 8 are adequately explained by flat lines. Generally, the cloud composition is unconstrained.Comment: Accepted by MNRAS. 33 pages, 29 figures, 3 table

Quasi-Isometric Embeddings of Symmetric Spaces

We prove a rigidity theorem that shows that, under many circumstances, quasi-isometric embeddings of equal rank, higher rank symmetric spaces are close to isometric embeddings. We also produce some surprising examples of quasi-isometric embeddings of higher rank symmetric spaces. In particular, we produce embeddings of $SL(n,\mathbb R)$ into $Sp(2(n-1),\mathbb R)$ when no isometric embeddings exist. A key ingredient in our proofs of rigidity results is a direct generalization of the Mostow-Morse Lemma in higher rank. Typically this lemma is replaced by the quasi-flat theorem which says that maximal quasi-flat is within bounded distance of a finite union of flats. We improve this by showing that the quasi-flat is in fact flat off of a subset of codimension $2$.Comment: Exposition improved, outlines of proofs added to introduction. Typos corrected, references added. Also some discussion of the reducible case adde

Coarse differentiation of quasi-isometries II: Rigidity for Sol and Lamplighter groups

In this paper, which is the continuation of [EFW2], we complete the proof of the quasi-isometric rigidity of Sol and the lamplighter groups. The results were announced in [EFW1].Comment: 47 pages, 3 figures. Minor revisions addressing comments by the refere

Coarse differentiation of quasi-isometries I: spaces not quasi-isometric to Cayley graphs

In this paper, we prove that certain spaces are not quasi-isometric to Cayley graphs of finitely generated groups. In particular, we answer a question of Woess and prove a conjecture of Diestel and Leader by showing that certain homogeneous graphs are not quasi-isometric to a Cayley graph of a finitely generated group. This paper is the first in a sequence of papers proving results announced in [EFW0]. In particular, this paper contains many steps in the proofs of quasi-isometric rigidity of lattices in Sol and of the quasi-isometry classification of lamplighter groups. The proofs of those results are completed in [EFW1]. The method used here is based on the idea of "coarse differentiation" introduced in [EFW0].Comment: 44 pages; 4 figures; minor corrections addressing comments by the refere

System and method for progressive band selection for hyperspectral images

Disclosed herein are systems, methods, and non-transitory computer-readable storage media for progressive band selection for hyperspectral images. A system having module configured to control a processor to practice the method calculates a virtual dimensionality of a hyperspectral image having multiple bands to determine a quantity Q of how many bands are needed for a threshold level of information, ranks each band based on a statistical measure, selects Q bands from the multiple bands to generate a subset of bands based on the virtual dimensionality, and generates a reduced image based on the subset of bands. This approach can create reduced datasets of full hyperspectral images tailored for individual applications. The system uses a metric specific to a target application to rank the image bands, and then selects the most useful bands. The number of bands selected can be specified manually or calculated from the hyperspectral image's virtual dimensionality