A cluster expansion approach to renormalization group transformations

The renormalization group (RG) approach is largely responsible for the considerable success which has been achieved in developing a quantitative theory of phase transitions. This work treats the rigorous definition of the RG map for classical Ising-type lattice systems in the infinite volume limit at high temperature. A cluster expansion is used to justify the existence of the partial derivatives of the renormalized interaction with respect to the original interaction. This expansion is derived from the formal expressions, but it is itself well-defined and convergent. Suppose in addition that the original interaction is finite-range and translation-invariant. We will show that the matrix of partial derivatives in this case displays an approximate band property. This in turn gives an upper bound for the RG linearization.Comment: 13 page

HCN versus HCO+ as dense molecular gas mass tracer in Luminous Infrared Galaxies

It has been recently argued that the HCN J=1--0 line emission may not be an unbiased tracer of dense molecular gas (\rm n\ga 10^4 cm^{-3}) in Luminous Infrared Galaxies (LIRGs: $\rm L_{FIR}> 10^{11} L_{\odot}$) and HCO$^+$ J=1--0 may constitute a better tracer instead (Graci\'a-Carpio et al. 2006), casting doubt into earlier claims supporting the former as a good tracer of such gas (Gao & Solomon 2004; Wu et al. 2006). In this paper new sensitive HCN J=4--3 observations of four such galaxies are presented, revealing a surprisingly wide excitation range for their dense gas phase that may render the J=1--0 transition from either species a poor proxy of its mass. Moreover the well-known sensitivity of the HCO$^+$ abundance on the ionization degree of the molecular gas (an important issue omitted from the ongoing discussion about the relative merits of HCN and HCO$^+$ as dense gas tracers) may severely reduce the HCO$^+$ abundance in the star-forming and highly turbulent molecular gas found in LIRGs, while HCN remains abundant. This may result to the decreasing HCO$^+$/HCN J=1--0 line ratio with increasing IR luminosity found in LIRGs, and casts doubts on the HCO$^+$ rather than the HCN as a good dense molecular gas tracer. Multi-transition observations of both molecules are needed to identify the best such tracer, its relation to ongoing star formation, and constrain what may be a considerable range of dense gas properties in such galaxies.Comment: 16 pages, 4 figures, Accepted for publication in the Astrophysical Journa

Charged Rotating Black Holes on a 3-Brane

We study exact stationary and axisymmetric solutions describing charged rotating black holes localized on a 3-brane in the Randall-Sundrum braneworld. The charges of the black holes are considered to be of two types, the first being an induced tidal charge that appears as an imprint of nonlocal gravitational effects from the bulk space and the second is a usual electric charge arising due to a Maxwell field trapped on the brane. We assume a special ansatz for the metric on the brane taking it to be of the Kerr-Schild form and show that the Kerr-Newman solution of ordinary general relativity in which the electric charge is superceded by a tidal charge satisfies a closed system of the effective gravitational field equations on the brane. It turns out that the negative tidal charge may provide a mechanism for spinning up the black hole so that its rotation parameter exceeds its mass. This is not allowed in the framework of general relativity. We also find a new solution that represents a rotating black hole on the brane carrying both charges. We show that for a rapid enough rotation the combined influence of the rotational dynamics and the local bulk effects of the "squared" energy momentum tensor on the brane distort the horizon structure of the black hole in such a way that it can be thought of as composed of non-uniformly rotating null circles with growing radii from the equatorial plane to the poles. We finally study the geodesic motion of test particles in the equatorial plane of a rotating black hole with tidal charge. We show that the effects of negative tidal charge tend to increase the horizon radius, as well as the radii of the limiting photon orbit, the innermost bound and the innermost stable circular orbits for both direct and retrograde motions of the particles.Comment: RevTeX 4, 33 pages, 4 figures, new references adde

Kinetic theory for nongeodesic particle motion: Selfinteracting equilibrium states and effective viscous fluid pressures

The particles of a classical relativistic gas are supposed to move under the influence of a quasilinear (in the particle four-momenta), self-interacting force inbetween elastic, binary collisions. This force which is completely fixed by the equilibrium conditions of the gas, gives rise to an effective viscous pressure on the fluid phenomenological level. Earlier results concerning the possibility of accelerated expansion of the universe due to cosmological particle production are reinterpreted. A phenomenon such as power law inflation may be traced back to specific self-interacting forces keeping the particles of a gas universe in states of generalized equilibrium.Comment: 16 pages, latex, uses ioplppt.sty. To appear in Class. Quantum Gra

Dynamics of a self-gravitating thin cosmic string

We assume that a self-gravitating thin string can be locally described by what we shall call a smoothed cone. If we impose a specific constraint on the model of the string, then its central line obeys the Nambu-Goto equations. If no constraint is added, then the worldsheet of the central line is a totally geodesic surface.Comment: 20 pages, latex, 1 figure, final versio

Late acceleration and w=−1w=-1 crossing in induced gravity

We study the cosmological evolution on a brane with induced gravity within a bulk with arbitrary matter content. We consider a Friedmann-Robertson-Walker brane, invariantly characterized by a six-dimensional group of isometries. We derive the effective Friedmann and Raychaudhuri equations. We show that the Hubble expansion rate on the brane depends on the covariantly defined integrated mass in the bulk, which determines the energy density of the generalized dark radiation. The Friedmann equation has two branches, distinguished by the two possible values of the parameter \ex=\pm 1. The branch with \ex=1 is characterized by an effective cosmological constant and accelerated expansion for low energy densities. Another remarkable feature is that the contribution from the generalized dark radiation appears with a negative sign. As a result, the presence of the bulk corresponds to an effective negative energy density on the brane, without violation of the weak energy condition. The transition from a period of domination of the matter energy density by non-relativistic brane matter to domination by the generalized dark radiation corresponds to a crossing of the phantom divide $w=-1$.Comment: 7 pages, no figures, RevTex 4.0; (v2) new references are added, minor corrections and expanded discussion; (v3) additional comments at the end of section III, minor corrections and several new references are added, to match published version in Phys. Rev.

CO Emission in Low Luminosity, HI Rich Galaxies

We present 12CO 1-0 observations of eleven low luminosity M_B > -18), HI--rich dwarf galaxies. Only the three most metal-rich galaxies, with 12+log(O/H) ~ 8.2, are detected. Very deep CO spectra of six extremely metal-poor systems (12+log(O/H) < 7.5) yield only low upper limits on the CO surface brightness, I_CO < 0.1 K km/s. Three of these six have never before been observed in a CO line, while the others now have much more stringent upper limits. For the very low metallicity galaxy Leo A, we do not confirm a previously reported detection in CO, and the limits are consistent with another recent nondetection. We combine these new observations with data from the literature to form a sample of dwarf galaxies which all have CO observations and measured oxygen abundances. No known galaxies with 12+log(O/H) < 7.9 (Z < 0.1 solar) have been detected in CO. Most of the star-forming galaxies with higher (12+log(O/H) > 8.1) metallicities are detected at similar or higher I_CO surface brightnesses. The data are consistent with a strong dependence of the I_CO/M_H_2 = X_CO conversion factor on ambient metallicity. The strikingly low upper limits on some metal-poor galaxies lead us to predict that the conversion factor is non-linear, increasing sharply below approximately 1/10 of the solar metallicity (12+log(O/H) < 7.9).Comment: 25 pages, 4 figures, 3 tables. Accepted for publication in AJ Tables replaced -- now formated for landscape orientatio

The Origin of the Dust Arch in the Halo of NGC 4631: An Expanding Superbubble?

We study the nature and the origin of the dust arch in the halo of the edge-on galaxy NGC 4631 detected by Neininger & Dumke (1999). We present CO observations made using the new On-The-Fly mapping mode with the FCRAO 14m telescope, and find no evidence for CO emission associated with the dust arch. Our examination of previously published HI data shows that if previous assumptions about the dust temperature and gas/dust ratio are correct, then there must be molecular gas associated with the arch, below our detection threshold. If this is true, then the molecular mass associated with the dust arch is between 1.5 x 10^8 M(sun)and 9.7 x 10^8 M(sun), and likely towards the low end of the range. A consequence of this is that the maximum allowed value for the CO-to-H_2 conversion factor is 6.5 times the Galactic value, but most likely closer to the Galactic value. The kinematics of the HI apparently associated with the dust arch reveal that the gas here is not part of an expanding shell or outflow, but is instead two separate features (a tidal arm and a plume of HI sticking out into the halo) which are seen projected together and appear as a shell. Thus there is no connection between the dust "arch" and the hot X-ray emitting gas that appears to surround the galaxy Wang et al. (2001).Comment: 14 pages, including 4 figures. Accepted by A.J. for March 200

Star formation in the giant HII regions of M101

The molecular components of three giant HII regions (NGC 5461, NGC 5462, NGC 5471) in the galaxy M101 are investigated with new observations from the James Clerk Maxwell Telescope, the NRAO 12-meter, and the Owens Valley millimeter array. Of the three HII regions, only NGC 5461 had previously been detected in CO emission. We calculate preliminary values for the molecular mass of the GMCs in NGC 5461 by assuming a CO-to-H_2 factor (X factor) and then compare these values with the virial masses. We conclude that the data in this paper demonstrate for the first time that the value of X may decrease in regions with intense star formation. The molecular mass for the association of clouds in NGC 5461 is approximately 3x10^7 Mo and is accompanied by 1-2 times as much atomic mass. The observed CO emission in NGC 5461 is an order of magnitude stronger than in NGC 5462, while it was not possible to detect molecular gas toward NGC 5471 with the JCMT. An even larger ratio of atomic to molecular gas in NGC 5471 was observed, which might be attributed to efficient conversion of molecular to atomic gas. The masses of the individual clouds in NGC 5461, which are gravitationally bound, cover a range of (2-8) x 10^5 Mo, comparable with the masses of Galactic giant molecular clouds (GMCs). Higher star forming efficiencies, and not massive clouds, appear to be the prerequisite for the formation of the large number of stars whose radiation is required to produce the giant HII regions in M101.Comment: 32 pages, 5 figures, accepted for publication in the Astrophysical Journa

On the dual interpretation of zero-curvature Friedmann-Robertson-Walker models

Two possible interpretations of FRW cosmologies (perfect fluid or dissipative fluid)are considered as consecutive phases of the system. Necessary conditions are found, for the transition from perfect fluid to dissipative regime to occur, bringing out the conspicuous role played by a particular state of the system (the ''critical point '').Comment: 13 pages Latex, to appear in Class.Quantum Gra