Blank field submm sources, failed stars, and the dark matter

I discuss the possibility that a significant fraction (possibly a third) of the faint SCUBA sources are not in fact high redshift galaxies, but actually local cold dark dusty gas clouds emitting only in the submm, with a temperature around 7K. I show that the observational constraints on such a population - dynamical limits on missing matter, the FIR-mm background, and the absence of gross high-latitude extinction features - constrains the mass of such objects to be in the range 0.1 - 10 Jupiter masses. The characteristics deduced are closely similar to those of the objects proposed by Walker and Wardle (1998) to explain halo dark matter. However, such objects, if they explain a large fraction of the SCUBA sources, cannot extend through the halo without greatly exceeding the FIR-mm background. Instead, I deduce the characteristic distance of the SCUBA sources to be around 100 pc, consistent with being drawn from a disk population with a scale height of few hundred parsecs. Regardless of the dark matter problem, the possible existence of such compact sub-stellar but non-degenerate objects is intriguing. They may be seen as "failed stars", representing an alternative end-point to brown dwarfs. It is possible that they greatly outnumber both stars and brown dwarfs. The nearest such object could be a fraction of a parsec away. Several relatively simple observations could critically test this hypothesis.Comment: 25 pages, 1 figure, to be published in Monthly Notices of the RA

Unbounded Symmetric Homogeneous Domains in Spaces of Operators

We define the domain of a linear fractional transformation in a space of operators and show that both the affine automorphisms and the compositions of symmetries act transitively on these domains. Further, we show that Liouville's theorem holds for domains of linear fractional transformations, and, with an additional trace class condition, so does the Riemann removable singularities theorem. We also show that every biholomorphic mapping of the operator domain $I < Z^*Z$ is a linear isometry when the space of operators is a complex Jordan subalgebra of ${\cal L}(H)$ with the removable singularity property and that every biholomorphic mapping of the operator domain $I + Z_1^*Z_1 < Z_2^*Z_2$ is a linear map obtained by multiplication on the left and right by J-unitary and unitary operators, respectively. Readers interested only in the finite dimensional case may identify our spaces of operators with spaces of square and rectangular matrices

Tax Enforcement for Gamers: High Penalties or Strict Disclosure Rules?

This essay responds to Alex Raskolnikov’s proposal to replace the current federal income tax compliance regime with a two-track approach based on taxpayer choice. The “deterrence regime” (DR) would be designed to be chosen by “gamers”, and the “compliance regime” (CR) would be designed to be chosen by all other taxpayers. Penalty rates would be significantly higher in the DR than in the CR. In this response, Lawrence Zelenak notes that the tax shelter disclosure rules of current law can also be viewed as a way of imposing a special compliance regime-featuring high odds of detection rather than high penalty rates-on gamers. Zelenak compares Raskolnikov’s proposal with the current regime, and suggests that there are plausible grounds for preferring the current regime to the proposal

Ram Selection and Ewe Culling

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For Better and Worse: The Differing Income Tax Treatments of Marriage at Different Income Levels

Although both marriage penalties and marriage bonuses exist at all income levels under the federal income tax, the system is tilted toward penalties for lower-income couples, toward bonuses for middle-income couples, and back toward penalties for upper income couples. This Article begins by explaining how the tax rules produce these differing treatments of marriage at different points in the income distribution. It then argues that the increase in recent decades in the social acceptability and prevalence of cohabitation makes tax marriage effects a more serious concern--in terms of both behavioral, effects and fairness-than in earlier decades. After demonstrating that Congress has never offered any justification for the differing tax treatments of marriage at different income levels, and that no plausible defense exists for the current distribution of penalties and bonuses, the Article offers several policy recommendations. The most basic and most important recommendation is simply that, whatever Congress does in this area, it should make conscious decisions about the appropriate distributions of penalties and bonuses at various income levels, instead of following its current practice of stumbling into a set of poorly understood and almost-impossible-to-defend effects