A new low mass for the Hercules dSph: the end of a common mass scale for the dwarfs?

We present a new mass estimate for the Hercules dwarf spheroidal galaxy (dSph), based on the revised velocity dispersion obtained by Aden et al. (2009, arXiv:0908.3489). The removal of a significant foreground contamination using newly acquired Stromgren photometry has resulted in a reduced velocity dispersion. Using this new velocity dispersion of 3.72 +/- 0.91 km/s, we find a mass of M_300=1.9^{+1.1}_{-0.8} 10^6 M_sun within the central 300 pc, which is also the half-light radius, and a mass of M_433=3.7_{-1.6}^{+2.2} 10^6 M_sun within the reach of our data to 433 pc, significantly lower than previous estimates. We derive an overall mass-to-light ratio of M_433/L=103^{+83}_{-48} M_sun/L_sun. Our mass estimate calls into question recent claims of a common mass scale for dSph galaxies. Additionally, we find tentative evidence for a velocity gradient in our kinematic data of 16 +/- 3 km/s/kpc, and evidence of an asymmetric extension in the light distribution at about 0.5 kpc. We explore the possibility that these features are due to tidal interactions with the Milky Way. We show that there is a self-consistent model in which Hercules has an assumed tidal radius of r_t = 485 pc, an orbital pericentre of r_p = 18.5 +/- 5 kpc, and a mass within r_t of M_{tid,r_t}=5.2 +/- 2.7 10^6 M_sun. Proper motions are required to test this model. Although we cannot exclude models in which Hercules contains no dark matter, we argue that Hercules is more likely to be a dark matter dominated system which is currently experiencing some tidal disturbance of its outer parts.Comment: 10 pages, 3 figures, Accepted for publication by ApJ

Bivariate galaxy luminosity functions in the Sloan Digital Sky Survey

Bivariate luminosity functions (LFs) are computed for galaxies in the New York Value-Added Galaxy Catalogue, based on the Sloan Digital Sky Survey Data Release 4. The galaxy properties investigated are the morphological type, inverse concentration index, Sérsic index, absolute effective surface brightness (SB), reference frame colours, absolute radius, eClass spectral type, stellar mass and galaxy environment. The morphological sample is flux limited to galaxies with r < 15.9 and consists of 37 047 classifications to an rms accuracy of ± half a class in the sequence E, S0, Sa, Sb, Sc, Sd, Im. These were assigned by an artificial neural network, based on a training set of 645 eyeball classifications. The other samples use r < 17.77 with a median redshift of z∼ 0.08, and a limiting redshift of z < 0.15 to minimize the effects of evolution. Other cuts, for example in axis ratio, are made to minimize biases. A wealth of detail is seen, with clear variations between the LFs according to absolute magnitude and the second parameter. They are consistent with an early-type, bright, concentrated, red population and a late-type, faint, less concentrated, blue, star-forming population. This bimodality suggests two major underlying physical processes, which in agreement with previous authors we hypothesize to be merger and accretion, associated with the properties of bulges and discs, respectively. The bivariate luminosity–SB distribution is fit with the Chołoniewski function (a Schechter function in absolute magnitude and Gaussian in SB). The fit is found to be poor, as might be expected if there are two underlying processes

Spin-Peierls states of quantum antiferromagnets on the CaV4O9Ca V_4 O_9 lattice

We discuss the quantum paramagnetic phases of Heisenberg antiferromagnets on the 1/5-depleted square lattice found in $Ca V_4 O_9$. The possible phases of the quantum dimer model on this lattice are obtained by a mapping to a quantum-mechanical height model. In addition to the ``decoupled'' phases found earlier, we find a possible intermediate spin-Peierls phase with spontaneously-broken lattice symmetry. Experimental signatures of the different quantum paramagnetic phases are discussed.Comment: 9 pages; 2 eps figure

Bulk and edge correlations in the compressible half-filled quantum Hall state

We study bulk and edge correlations in the compressible half-filled state, using a modified version of the plasma analogy. The corresponding plasma has anomalously weak screening properties, and as a consequence we find that the correlations along the edge do not decay algebraically as in the Laughlin (incompressible) case, while the bulk correlations decay in the same way. The results suggest that due to the strong coupling between charged modes on the edge and the neutral Fermions in the bulk, reflected by the weak screening in the plasma analogue, the (attractive) correlation hole is not well defined on the edge. Hence, the system there can be modeled as a free Fermi gas of {\em electrons} (with an appropriate boundary condition). We finally comment on a possible scenario, in which the Laughlin-like dynamical edge correlations may nevertheless be realized.Comment: package now includes the file epsfig.sty, needed to incorporate properly the 8 magnificent figure

Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects

The fractional quantum Hall effect (FQHE) in the second orbital Landau level at filling factor 5/2 remains enigmatic and motivates our work. We consider the effect of the quasi-2D nature of the experimental FQH system on a number of FQH states (fillings 1/3, 1/5, 1/2) in the lowest, second, and third Landau levels (LLL, SLL, TLL,) by calculating the overlap, as a function of quasi-2D layer thickness, between the exact ground state of a model Hamiltonian and the consensus variational wavefunctions (Laughlin wavefunction for 1/3 and 1/5 and the Moore-Read Pfaffian wavefunction for 1/2). Using large overlap as a stability, or FQHE robustness, criterion we find the FQHE does not occur in the TLL (for any thickness), is the most robust for zero thickness in the LLL for 1/3 and 1/5 and for 11/5 in the SLL, and is most robust at finite-thickness (4-5 magnetic lengths) in the SLL for the mysterious 5/2 state and the 7/3 state. No FQHE is found at 1/2 in the LLL for any thickness. We examine the orbital effects of an in-plane (parallel) magnetic field finding its application effectively reduces the thickness and could destroy the FQHE at 5/2 and 7/3, while enhancing it at 11/5 as well as for LLL FQHE states. The in-plane field effects could thus be qualitatively different in the LLL and the SLL by virtue of magneto-orbital coupling through the finite thickness effect. In the torus geometry, we show the appearance of the threefold topological degeneracy expected for the Pfaffian state which is enhanced by thickness corroborating our findings from overlap calculations. Our results have ramifications for wavefunction engineering--the possibility of creating an optimal experimental system where the 5/2 FQHE state is more likely described by the Pfaffian state with applications to topological quantum computing.Comment: 27 pages, 20 figures, revised version (with additional author) as accepted for publication in Physical Review

Optimisation of power generation cycles using saturated liquid expansion to maximise heat recovery

The use of two-phase screw expanders in power generation cycles can achieve an increase in the utilisation of available energy from a low-temperature heat source when compared with more conventional single-phase turbines. The efficiency of screw expander machines is sensitive to expansion volume ratio, which, for given inlet and discharge pressures, increases as the expander inlet vapour dryness fraction decreases. For single-stage screw machines with low inlet dryness, this can lead to underexpansion of the working fluid and low isentropic efficiency. The cycle efficiency can potentially be improved by using a two-stage expander, consisting of a machine for low-pressure expansion and a smaller high-pressure machine connected in series. By expanding the working fluid over two stages, the built-in volume ratios of the two machines can be selected to provide a better match with the overall expansion process, thereby increasing the efficiency. The mass flow rate though both stages must be matched, and the compromise between increasing efficiency and maximising power output must also be considered. This study is based on the use of a rigorous thermodynamic screw machine model to compare the performance of single- and two-stage expanders. The model allows optimisation of the required intermediate pressure in the two-stage expander, along with the built-in volume ratio of both screw machine stages. The results allow specification of a two-stage machine, using either two screw machines or a combination of high-pressure screw and low-pressure turbine, in order to achieve maximum efficiency for a particular power output. For the low-temperature heat recovery application considered in this paper, the trilateral flash cycle using a two-stage expander and the Smith cycle using a high-pressure screw and low-pressure turbine are both predicted to achieve a similar overall conversion efficiency to that of a conventional saturated vapour organic Rankine cycle

Optimisation of two-stage screw expanders for waste heat recovery applications

It has previously been shown that the use of two-phase screw expanders in power generation cycles can achieve an increase in the utilisation of available energy from a low temperature heat source when compared with more conventional single-phase turbines. However, screw expander efficiencies are more sensitive to expansion volume ratio than turbines, and this increases as the expander inlet vapour dryness fraction decreases. For singlestage screw machines with low inlet dryness, this can lead to under expansion of the working fluid and low isentropic efficiency for the expansion process. The performance of the cycle can potentially be improved by using a two-stage expander, consisting of a low pressure machine and a smaller high pressure machine connected in series. By expanding the working fluid over two stages, the built-in volume ratios of the two machines can be selected to provide a better match with the overall expansion process, thereby increasing efficiency for particular inlet and discharge conditions. The mass flow rate though both stages must however be matched, and the compromise between increasing efficiency and maximising power output must also be considered. This research uses a rigorous thermodynamic screw machine model to compare the performance of single and two-stage expanders over a range of operating conditions. The model allows optimisation of the required intermediate pressure in the two- stage expander, along with the rotational speed and built-in volume ratio of both screw machine stages. The results allow the two-stage machine to be fully specified in order to achieve maximum efficiency for a required power output

Geometrical aspects of novel internally geared screw machine

Cylindrical helical gearing can be used in a positive displacement machine where an externally lobed inner gear rotates inside an internally lobed outer gear while maintaining continuous lines of contact between the gears. This creates a series of separate working chambers between the rotors. In this type of machine the rotors have parallel axes of rotation, and both rotors can be free to rotate about their own axes. Fixed end plates are proposed as a method of controlling the period during which fluid is allowed to enter or leave the working chambers of the internally geared screw machine. As with conventional screw machines, these internally geared rotors can then be used to achieve compression or expansion of a trapped mass of fluid. This paper describes the geometrical analysis of some simple rotor profiles and explores the effect on rotor forces for particular applications of this novel screw configuration

Internally geared screw machines with ported end plates

It is possible to design cylindrical helical gearing profiles such that an externally lobed inner gear rotates inside an internally lobed outer gear while maintaining continuous lines of contact between the gears. The continuous contact between the inner and outer rotors (analogous to the main and gate rotors in a conventional screw machine) creates a series of separate working chambers. In this type of machine the rotors have parallel axes of rotation, and if both rotors are free to rotate about their own axes, these axes can be fixed in space. The use of ported end plates is proposed to control the period during which fluid is allowed to enter or leave the working chambers of the internally geared screw machine. As with conventional screw machines, these internally geared rotors can then be used to achieve compression or expansion of a trapped mass of fluid, and the machine geometry can be designed in order to optimise performance for particular applications. This paper describes the geometrical analysis of some simple rotor profiles and explores the effect on rotor torques for particular applications of this novel screw configuration