Planet formation around stars of various masses: The snow line and the frequency of giant planets

We use a semi-analytic circumstellar disk model that considers movement of the snow line through evolution of accretion and the central star to investigate how gas giant frequency changes with stellar mass. The snow line distance changes weakly with stellar mass; thus giant planets form over a wide range of spectral types. The probability that a given star has at least one gas giant increases linearly with stellar mass from 0.4 M_sun to 3 M_sun. Stars more massive than 3 M_sun evolve quickly to the main-sequence, which pushes the snow line to 10-15 AU before protoplanets form and limits the range of disk masses that form giant planet cores. If the frequency of gas giants around solar-mass stars is 6%, we predict occurrence rates of 1% for 0.4 M_sun stars and 10% for 1.5 M_sun stars. This result is largely insensitive to our assumed model parameters. Finally, the movement of the snow line as stars >2.5 M_sun move to the main-sequence may allow the ocean planets suggested by Leger et. al. to form without migration.Comment: Accepted to ApJ. 12 pages of emulateap

Second and higher-order quasi-normal modes in binary black hole mergers

Black hole (BH) oscillations known as quasi-normal modes (QNMs) are one of the most important gravitational wave (GW) sources. We propose that higher perturbative order of QNMs, generated by nonlinear gravitational interaction near the BHs, are detectable and worth searching for in observations and simulations of binary BH mergers. We calculate the metric perturbations to second-order and explicitly regularize the master equation at the horizon and spatial infinity. We find that the second-order QNMs have frequencies twice the first-order ones and the GW amplitude is up to ~10% that of the first-order one. The QNM frequency would also shift blueward up to ~1%. This provides a new test of general relativity as well as a possible distance indicator.Comment: 5 pages, 1 figure, accepted for publication in PRD Rapid Communication

Cohomology and Support Varieties for Lie Superalgebras II

In \cite{BKN} the authors initiated a study of the representation theory of classical Lie superalgebras via a cohomological approach. Detecting subalgebras were constructed and a theory of support varieties was developed. The dimension of a detecting subalgebra coincides with the defect of the Lie superalgebra and the dimension of the support variety for a simple supermodule was conjectured to equal the atypicality of the supermodule. In this paper the authors compute the support varieties for Kac supermodules for Type I Lie superalgebras and the simple supermodules for $\mathfrak{gl}(m|n)$. The latter result verifies our earlier conjecture for $\mathfrak{gl}(m|n)$. In our investigation we also delineate several of the major differences between Type I versus Type II classical Lie superalgebras. Finally, the connection between atypicality, defect and superdimension is made more precise by using the theory of support varieties and representations of Clifford superalgebras.Comment: 28 pages, the proof of Proposition 4.5.1 was corrected, several other small errors were fixe

Drude Weight of the Two-Dimensional Hubbard Model -- Reexamination of Finite-Size Effect in Exact Diagonalization Study --

The Drude weight of the Hubbard model on the two-dimensional square lattice is studied by the exact diagonalizations applied to clusters up to 20 sites. We carefully examine finite-size effects by consideration of the appropriate shapes of clusters and the appropriate boundary condition beyond the imitation of employing only the simple periodic boundary condition. We successfully capture the behavior of the Drude weight that is proportional to the squared hole doping concentration. Our present result gives a consistent understanding of the transition between the Mott insulator and doped metals. We also find, in the frequency dependence of the optical conductivity, that the mid-gap incoherent part emerges more quickly than the coherent part and rather insensitive to the doping concentration in accordance with the scaling of the Drude weight.Comment: 9 pages with 10 figures and 1 table. accepted in J. Phys. Soc. Jp

Complexity for Modules Over the Classical Lie Superalgebra gl(m|n)

Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus \mathfrak{g}_{\bar{1}}$ be a classical Lie superalgebra and $\mathcal{F}$ be the category of finite dimensional $\mathfrak{g}$-supermodules which are completely reducible over the reductive Lie algebra $\mathfrak{g}_{\bar{0}}$. In an earlier paper the authors demonstrated that for any module $M$ in $\mathcal{F}$ the rate of growth of the minimal projective resolution (i.e., the complexity of $M$) is bounded by the dimension of $\mathfrak{g}_{\bar{1}}$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. In both cases we show that the complexity is related to the atypicality of the block containing the module.Comment: 32 page

Quark condensate in nuclear matter based on Nuclear Schwinger-Dyson formalism

The effects of higher order corrections of ring diagrams for the quark condensate are studied by using the bare vertex Nuclear Schwinger Dyson formalism based on $\sigma$-$\omega$ model. At the high density the quark condensate is reduced by the higher order contribution of ring diagrams more than the mean field theory or the Hartree-Fock

The relationship between the COPD Assessment Test score and airflow limitation in Japan in patients aged over 40 years with a smoking history.

BACKGROUND: A large number of chronic obstructive pulmonary disease (COPD) patients in Japan remain undiagnosed, primarily due to the underuse of spirometry. Two studies were conducted to see whether the COPD Assessment Test (CAT) in primary care has the potential to identify those patients who need spirometry for a diagnosis of COPD and to determine whether patients with cardiovascular disease had airflow limitation, which could be detected by CAT. MATERIALS AND METHODS: Two multicenter, noninterventional, prospective studies (studies 1 and 2) were conducted across Japan. Patients in both studies were ≥40 years old with a smoking history. Those in study 1 were seen in primary care and had experienced repeated respiratory tract infections, but had no diagnosis of COPD. Patients in study 2 were identified in cardiovascular disease clinics when routinely visiting for their cardiovascular disease. All patients completed the CAT prior to lung-function testing by hand-held spirometry. The presence of airflow limitation was defined as a forced expiratory volume in 1 second (FEV1)/FEV6 ratio<0.73. RESULTS: A total of 3,062 subjects completed the CAT (2,067 in study 1, 995 in study 2); 88.8% were male, and the mean age (±standard deviation) was 61.5±11.6 years. Airflow limitation was found in 400 (19.4%) patients in study 1, and 269 (27.0%) in study 2. The CAT score in patients with airflow limitation was significantly higher than in patients without airflow limitation in both studies: 8.6 (95% confidence interval [CI] 7.9-9.2) versus 7.4 (95% CI 7.1-7.6) in study 1, and 8.3 (95% CI 7.5-9.2) versus 6.4 (95% CI 6.0-6.8) in study 2 (both P<0.001). CONCLUSION: These findings suggest that the CAT has the potential to identify patients with cardiovascular disease or a history of frequent chest infections who need spirometry to diagnose COPD