Correlations due to localization in quantum eigenfunctions of disordered microwave cavities

Non-universal correlations due to localization are observed in statistical properties of experimental eigenfunctions of quantum chaotic and disordered microwave cavities. Varying energy {E} and mean free path {l} enable us to experimentally tune from localized to delocalized states. Large level-to-level Inverse Participation Ratio (IPR I_{2}) fluctuations are observed for the disordered billiards, whose distribution is strongly asymmetric about . The density auto-correlations of eigenfunctions are shown to decay exponentially and the decay lengths are experimentally determined. All the results are quantitatively consistent with calculations based upon nonlinear sigma-models.Comment: 4 pages, LaTex, 5 .jpg figures. This paper with 5 embedded postscript figures available (PS,PDF) at http://sagar.physics.neu.edu/preprints

Photometric identification of blue horizontal branch stars

We investigate the performance of some common machine learning techniques in identifying BHB stars from photometric data. To train the machine learning algorithms, we use previously published spectroscopic identifications of BHB stars from SDSS data. We investigate the performance of three different techniques, namely k nearest neighbour classification, kernel density estimation and a support vector machine (SVM). We discuss the performance of the methods in terms of both completeness and contamination. We discuss the prospect of trading off these values, achieving lower contamination at the expense of lower completeness, by adjusting probability thresholds for the classification. We also discuss the role of prior probabilities in the classification performance, and we assess via simulations the reliability of the dataset used for training. Overall it seems that no-prior gives the best completeness, but adopting a prior lowers the contamination. We find that the SVM generally delivers the lowest contamination for a given level of completeness, and so is our method of choice. Finally, we classify a large sample of SDSS DR7 photometry using the SVM trained on the spectroscopic sample. We identify 27,074 probable BHB stars out of a sample of 294,652 stars. We derive photometric parallaxes and demonstrate that our results are reasonable by comparing to known distances for a selection of globular clusters. We attach our classifications, including probabilities, as an electronic table, so that they can be used either directly as a BHB star catalogue, or as priors to a spectroscopic or other classification method. We also provide our final models so that they can be directly applied to new data.Comment: To appear in A&A. 19 pages, 22 figures. Tables 7, A3 and A4 available electronically onlin

Combinatorial identities for binary necklaces from exact ray-splitting trace formulae

Based on an exact trace formula for a one-dimensional ray-splitting system, we derive novel combinatorial identities for cyclic binary sequences (P\'olya necklaces).Comment: 15 page

Kinematic Structure in the Galactic Halo at the North Galactic Pole: RR Lyrae and BHB Stars show different kinematics

Space motions are given for 38 RR Lyrae (RRL) stars and 79 blue horizontal branch (BHB) stars in a ~200 deg2 area around the North Galactic Pole (NGP) using a homogeneous distance scale consistent with (m-M)0=18.52 for the LMC. The kinematics of the 26 RRL and 52 BHB stars in the 10.4 cubic kpc volume that have Z<8 kpc are not homogeneous. Our BHB sample (like that of Sirko et al. 2004b) has a zero galactic rotation (V_phi) and roughly isotropic velocity dispersions. The RRL sample shows a definite retrograde rotation (V_phi = -95+/-29 km/s) and non-isotropic velocity dispersions. The combined BHB and RRL sample has a retrograde galactic rotation (V) that is similar to that found by Majewski (1992) for his sample of subdwarfs in SA 57. The velocity dispersion of the RRL stars that have a positive W motion is significantly smaller than the dispersion of those "streaming down" with a negative W. One component of our sample (rich in RRL's) shows retrograde rotation and the streaming motion that we associate with the accretion process. The other (traced by the BHB stars) shows essentially no rotation and less evidence of streaming. These two components have HB morphologies that suggest that they may be the field star equivalents of the young and old halo globular clusters respectively.Comment: Accepted for publication on MNRAS. 20 pages, 7 figures, 12 table

Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak

The baryon acoustic oscillations are a promising route to the precision measure of the cosmological distance scale and hence the measurement of the time evolution of dark energy. We show that the non-linear degradation of the acoustic signature in the correlations of low-redshift galaxies is a correctable process. By suitable reconstruction of the linear density field, one can sharpen the acoustic peak in the correlation function or, equivalently, restore the higher harmonics of the oscillations in the power spectrum. With this, one can achieve better measurements of the acoustic scale for a given survey volume. Reconstruction is particularly effective at low redshift, where the non-linearities are worse but where the dark energy density is highest. At z=0.3, we find that one can reduce the sample variance error bar on the acoustic scale by at least a factor of 2 and in principle by nearly a factor of 4. We discuss the significant implications our results have for the design of galaxy surveys aimed at measuring the distance scale through the acoustic peak.Comment: 5 pages, LaTeX. Submitted to the Astrophysical Journa

Exact trace formulae for a class of one-dimensional ray-splitting systems

Based on quantum graph theory we establish that the ray-splitting trace formula proposed by Couchman {\it et al.} (Phys. Rev. A {\bf 46}, 6193 (1992)) is exact for a class of one-dimensional ray-splitting systems. Important applications in combinatorics are suggested.Comment: 14 pages, 3 figure

Spectroscopy of Bright QUEST RR Lyrae Stars: Velocity Substructures toward Virgo

Using a sample of 43 bright (V<16.1, distance <13 kpc) RR Lyrae stars (RRLS) from the QUEST survey with spectroscopic radial velocities and metallicities, we find that several separate halo substructures contribute to the Virgo overdensity (VOD). While there is little evidence for halo substructure in the spatial distribution of these stars, their distribution in radial velocity reveals two moving groups. These results are reinforced when the sample is combined with a sample of blue horizontal branch stars that were identified in the SDSS, and the combined sample provides evidence for one additional moving group. These groups correspond to peaks in the radial velocity distribution of a sample of F type main-sequence stars that was recently observed in the same directon by SEGUE, although in one case the RRLS and F star groups may not lie at the same distance. One of the new substructures has a very narrow range in metallicity, which is more consistent with it being the debris from a destroyed globular cluster than from a dwarf galaxy. A small concentration of stars have radial velocities that are similar to the Virgo Stellar Stream (VSS) that was identified previously in a fainter sample of RRLS. Our results suggest that this feature extends to distances as short as ~12 kpc from its previous detection at ~19 kpc. None of the new groups and only one star in the sample have velocities that are consistent with membership in the leading tidal stream from the Sagittarius Dwarf Spheroidal Galaxy, which some authors have suggested is the origin of the VOD.Comment: Accepted for publication in the A

The Case for the Dual Halo of the Milky Way

Carollo et al. have recently resolved the stellar population of the Milky Way halo into at least two distinct components, an inner halo and an outer halo. This result has been criticized by Schoenrich et al., who claim that the retrograde signature associated with the outer halo is due to the adoption of faulty distances. We refute this claim, and demonstrate that the Schoenrich et al. photometric distances are themselves flawed because they adopted an incorrect main-sequence absolute magnitude relationship from the work of Ivezi\'c et al. When compared to the recommended relation from Ivezi\'c et al., which is tied to a Milky Way globular cluster distance scale and accounts for age and metallicity effects, the relation adopted by Schoenrich et al. yields up to 18% shorter distances for stars near the main-sequence turnoff (TO). Use of the correct relationship yields agreement between the distances assigned by Carollo et al. and Ivezi\'{c} et al. for low-metallicity dwarfs to within 6-10%. Schoenrich et al. also point out that intermediate-gravity stars (3.5 <= log g <= 4.0) with colors redder than the TO region are likely misclassified, with which we concur. We implement a new procedure to reassign luminosity classifications for the TO stars that require it. New derivations of the rotational behavior demonstrate that the retrograde signature and high velocity dispersion of the outer-halo population remains. We summarize additional lines of evidence for a dual halo, including a test of the retrograde signature based on proper motions alone, and conclude that the preponderance of evidence strongly rejects the single-halo interpretation.Comment: 46 pages, 2 tables, 15 figures, Accepted for publication in the Astrophysical Journa

From chaos to disorder: Statistics of the eigenfunctions of microwave cavities

We study the statistics of the experimental eigenfunctions of chaotic and disordered microwave billiards in terms of the moments of their spatial distributions, such as the Inverse Participation Ratio (IPR) and density-density auto-correlation. A path from chaos to disorder is described in terms of increasing IPR. In the chaotic, ballistic limit, the data correspond well with universal results from random matrix theory. Deviations from universal distributions are observed due to disorder induced localization, and for the weakly disordered case the data are well-described by including finite conductance and mean free path contributions in the framework of nonlinear sigma models of supersymetry.Comment: 5 pages + 2 JPG figure

The Century Survey Galactic Halo Project III: A Complete 4300 deg^2 Survey of Blue Horizontal Branch Stars in the Metal-Weak Thick Disk and Inner Halo

We present a complete spectroscopic survey of 2414 2MASS-selected blue horizontal branch (BHB) candidates selected over 4300 deg^2 of the sky. We identify 655 BHB stars in this non-kinematically selected sample. We calculate the luminosity function of field BHB stars and find evidence for very few hot BHB stars in the field. The BHB stars located at a distance from the Galactic plane |Z|<4 kpc trace what is clearly a metal-weak thick disk population, with a mean metallicity of [Fe/H]= -1.7, a rotation velocity gradient of dv_{rot}/d|Z|= -28+-3.4 km/s in the region |Z|<6 kpc, and a density scale height of h_Z= 1.26+-0.1 kpc. The BHB stars located at 5<|Z|<9 kpc are a predominantly inner-halo population, with a mean metallicity of [Fe/H]= -2.0 and a mean Galactic rotation of -4+-31 km/s. We infer the density of halo and thick disk BHB stars is 104+-37 kpc^-3 near the Sun, and the relative normalization of halo to thick-disk BHB stars is 4+-1% near the Sun.Comment: 12 pages in emulateapj format, accepted for publication in February A