Planet migration and gap formation by tidally-induced shocks

Gap formation in a gas disk triggered by disk-planet tidal interaction is considered. Density waves launched by the planet are assumed to be damped as a result of their nonlinear evolution leading to shock formation and its subsequent dissipation. As a consequence wave angular momentum is transferred to the disk,leading to evolution of its surface density. Planetary migration is an important ingredient of the theory; effects of the planet-induced surface density perturbations on the migration speed are considered. A gap is assumed to form when a stationary solution for the surface density profile is no longer possible in the frame of reference migrating with the planet. An analytical limit on the planetary mass necessary to open a gap in an inviscid disk is derived. The critical mass turns out to be smaller than mass M_1 for which planetary Hill's radius equals disk scaleheight by a factor of at least Q^{5/7} (Q is the Toomre stability parameter) depending on the strength of the migration feedback. In viscous disks the critical planetary mass could vary from about 0.1M_1 to M_1, depending on the disk viscosity. This implies that a gap could be formed by a planet with mass 1-10 times bigger than the Earth mass depending on the disk aspect ratio, viscosity, and planet's location in the nebula.Comment: AASTeX, 31 pages, 7 figures, 1 table, submitted to Ap

Catalogue of 12CO(J=1-0) and 13CO(J=1-0) Molecular Clouds in the Carina Flare Supershell

We present a catalogue of 12CO(J=1-0) and 13CO(J=1-0) molecular clouds in the spatio-velocity range of the Carina Flare supershell, GSH 287+04-17. The data cover a region of ~66 square degrees and were taken with the NANTEN 4m telescope, at spatial and velocity resolutions of 2.6' and 0.1 km/s. Decomposition of the emission results in the identification of 156 12CO clouds and 60 13CO clouds, for which we provide observational and physical parameters. Previous work suggests the majority of the detected mass forms part of a comoving molecular cloud complex that is physically associated with the expanding shell. The cloud internal velocity dispersions, degree of virialization and size-linewidth relations are found to be consistent with those of other Galactic samples. However, the vertical distribution is heavily skewed towards high-altitudes. The robust association of high-z molecular clouds with a known supershell provides some observational backing for the theory that expanding shells contribute to the support of a high-altitude molecular layer.Comment: To be published in PASJ Vol. 60, No. 6. (Issued on December 25th 2008). 35 pages (including 13 pages of tables), 7 figures. Please note that formatting problems with the journal macro result in loss of rightmost data columns in some long tables. These will be fixed in the final published issue. In the meantime, please contact the authors for missing dat

Interchain interactions and magnetic properties of Li2CuO2

An effective Hamiltonian is constructed for an insulating cuprate with edge-sharing chains Li2CuO2.The Hamiltonian contains the nearest and next-nearest neighboring intrachain and zigzag-type interchain interactions.The values of the interactions are obtained from the analysis of the magnetic susceptibility, and this system is found to be described as coupled frustrated chains.We calculate the dynamical spin correlation function S(q,\omega) by using the exact diagonalization method, and show that the spectra of S(q,\omega) are characterized by the zigzag-type interchain interactions. The results of the recent inelastic neutron scattering experiment are discussed in the light of the calculated spectra.Comment: 4 pages, 3 figures, RevTe

The optical counterpart of an Ultra-luminous X-Ray Source in NGC 5204

Ultra-luminous X-Ray sources are extra-nuclear point sources in external galaxies with $L_X=10^{39}$--$10^{41}$ erg/s and are among the most poorly understood X-ray sources. To help understand their nature, we are trying to identify their optical counterparts by combining images from the Hubble Space Telescope and the Chandra Observatory. Here we report upon the optical counterpart for the ULX in NGC 5204, which has average X-ray luminosity of $\sim3\times10^{39}$ erg/s and has varied by a factor of 50% over the last 10 years. A unique optical counterpart to this ULX is found by carefully comparing the Chandra ACIS images and HST WFPC2 and ACS/HRC images. The spectral energy distribution and the HST/STIS FUV spectrum of this object show that it is a B0 Ib supergiant star with peculiarities, including the $\lambda$1240 N V emission line that is uncommon in B stellar spectra but has been predicted for X-ray illuminated accretion disks and seen in some X-ray binaries. Study of its FUV spectrum leads to a binary model for this ULX in which the B0 Ib supergiant is overflowing its Roche Lobe and accreting onto the compact primary, probably a black hole. This picture predicts an orbital period of $\sim10$ days for different black hole mass, which can be tested by future observations

Power Law of Customers' Expenditures in Convenience Stores

In a convenience store chain, a tail of the cumulative density function of the expenditure of a person during a single shopping trip follows a power law with an exponent of -2.5. The exponent is independent of the location of the store, the shopper's age, the day of week, and the time of day.Comment: 9 pages, 5 figures. Accepted for publication in Journal of the Physical Society of Japan Vol.77No.

Static black hole uniqueness and Penrose inequality

Under certain conditions, we give a new way to prove the uniqueness of static black hole in higher dimensional asymptotically flat spacetimes. In the proof, the Penrose inequality plays a key role in higher dimensions as well as four dimensions.Comment: 6 page

Molecular clouds towards RCW 49 and Westerlund 2; Evidence for cluster formation triggered by cloud-cloud collision

We have made CO(J=2-1) observations towards the HII region RCW 49 and its ionizing source, the rich stellar cluster Westerlund 2 (hereafter Wd2), with the NANTEN2 sub-mm telescope. These observations have revealed that two molecular clouds in velocity ranges of -11 to +9 km/s and 11 to 21 km/s respectively, show remarkably good spatial correlations with the Spitzer IRAC mid-infrared image of RCW 49, as well a velocity structures indicative of localized expansion around the bright central regions and stellar cluster. This strongly argues that the two clouds are physically associated with RCW 49. We obtain a new kinematic distance estimate to RCW 49 and Wd2 of 5.4^{+ 1.1}_{- 1.4} kpc, based on the mean velocity and velocity spread of the associated gas. We argue that acceleration of the gas by stellar winds from Wd2 is insufficient to explain the entire observed velocity dispersion of the molecular gas, and suggest a scenario in which a collision between the two clouds ~4 Myrs ago may have triggered the formation of the stellar cluster.Comment: A version with higher resolution figures is available from http://www.a.phys.nagoya-u.ac.jp/~naoko/research/apjl2009/fur09_rev_highreso.pd

Temperature and Density Distribution in the Molecular Gas Toward Westerlund 2: Further Evidence for Physical Association

Furukawa et al. 2009 reported the existence of a large mass of molecular gas associated with the super star cluster Westerlund 2 and the surrounding HII region RCW49, based on a strong morphological correspondence between NANTEN2 12CO(J=2-1) emission and Spitzer IRAC images of the HII region. We here present temperature and density distributions in the associated molecular gas at 3.5 pc resolution, as derived from an LVG analysis of the 12CO(J=2-1), 12CO(J=1-0) and 13CO(J=2-1) transitions. The kinetic temperature is as high as 60-150 K within a projected distance of 5-10 pc from Westerlund 2 and decreases to as low as 10 K away from the cluster. The high temperature provides robust verification that the molecular gas is indeed physically associated with the HII region, supporting Furukawa et al.'s conclusion. The derived temperature is also roughly consistent with theoretical calculations of photo dissociation regions (PDRs), while the low spatial resolution of the present study does not warrant a more detailed comparison with PDR models. We suggest that the molecular clouds presented here will serve as an ideal laboratory to test theories on PDRs in future higher resolution studies.Comment: 23 pages, 5 figures, accepted for publication in Ap