A Proper Motion Survey for White Dwarfs with the Wide Field Planetary Camera 2

We have performed a search for halo white dwarfs as high proper motion objects in a second epoch WFPC2 image of the Groth-Westphal strip. We identify 24 high proper motion objects with mu > 0.014 ''/yr. Five of these high proper motion objects are identified as strong white dwarf candidates on the basis of their position in a reduced proper motion diagram. We create a model of the Milky Way thin disk, thick disk and stellar halo and find that this sample of white dwarfs is clearly an excess above the < 2 detections expected from these known stellar populations. The origin of the excess signal is less clear. Possibly, the excess cannot be explained without invoking a fourth galactic component: a white dwarf dark halo. We present a statistical separation of our sample into the four components and estimate the corresponding local white dwarf densities using only the directly observable variables, V, V-I, and mu. For all Galactic models explored, our sample separates into about 3 disk white dwarfs and 2 halo white dwarfs. However, the further subdivision into the thin and thick disk and the stellar and dark halo, and the subsequent calculation of the local densities are sensitive to the input parameters of our model for each Galactic component. Using the lowest mean mass model for the dark halo we find a 7% white dwarf halo and six times the canonical value for the thin disk white dwarf density (at marginal statistical significance), but possible systematic errors due to uncertainty in the model parameters likely dominate these statistical error bars. The white dwarf halo can be reduced to around 1.5% of the halo dark matter by changing the initial mass function slightly. The local thin disk white dwarf density in our solution can be made consistent with the canonical value by assuming a larger thin disk scaleheight of 500 pc.Comment: revised version, accepted by ApJ, results unchanged, discussion expande

Arya: Nearly linear-time zero-knowledge proofs for correct program execution

There have been tremendous advances in reducing interaction, communication and verification time in zero-knowledge proofs but it remains an important challenge to make the prover efficient. We construct the first zero-knowledge proof of knowledge for the correct execution of a program on public and private inputs where the prover computation is nearly linear time. This saves a polylogarithmic factor in asymptotic performance compared to current state of the art proof systems. We use the TinyRAM model to capture general purpose processor computation. An instance consists of a TinyRAM program and public inputs. The witness consists of additional private inputs to the program. The prover can use our proof system to convince the verifier that the program terminates with the intended answer within given time and memory bounds. Our proof system has perfect completeness, statistical special honest verifier zero-knowledge, and computational knowledge soundness assuming linear-time computable collision-resistant hash functions exist. The main advantage of our new proof system is asymptotically efficient prover computation. The prover’s running time is only a superconstant factor larger than the program’s running time in an apples-to-apples comparison where the prover uses the same TinyRAM model. Our proof system is also efficient on the other performance parameters; the verifier’s running time and the communication are sublinear in the execution time of the program and we only use a log-logarithmic number of rounds

A Morphological and Multicolor Survey for Faint QSOs in the Groth-Westphal Strip

Quasars representative of the populous faint end of the luminosity function are frustratingly dim with m~24 at intermediate redshift; moreover groundbased surveys for such faint QSOs suffer substantial morphological contamination by compact galaxies having similar colors. In order to establish a more reliable ultrafaint QSO sample, we used the APO 3.5-m telescope to take deep groundbased U-band CCD images in fields previously imaged in V,I with WFPC2/HST. Our approach hence combines multicolor photometry with the 0.1" spatial resolution of HST, to establish a morphological and multicolor survey for QSOs extending about 2 magnitudes fainter than most extant groundbased surveys. We present results for the "Groth-Westphal Strip", in which we identify 10 high likelihood UV-excess candidates having stellar or stellar-nucleus+galaxy morphology in WFPC2. For m(606)<24.0 (roughly B<24.5) the surface density of such QSO candidates is 420 (+180,-130) per square degree, or a surface density of 290 (+160,-110) per square degree with an additional V-I cut that may further exclude compact emission line galaxies. Even pending confirming spectroscopy, the observed surface density of QSO candidates is already low enough to yield interesting comparisons: our measures agree extremely well with the predictions of several recent luminosity function models.Comment: 29 pages including 6 tables and 7 figures. As accepted for publication in The Astronomical Journal (minor revisions

A Slow Merger History of Field Galaxies Since z~1

Using deep infrared observations conducted with the CISCO imager on the Subaru Telescope, we investigate the field-corrected pair fraction and the implied merger rate of galaxies in redshift survey fields with Hubble Space Telescope imaging. In the redshift interval, 0.5 < z < 1.5, the fraction of infrared-selected pairs increases only modestly with redshift to 7% +- 6% at z~1. This is nearly a factor of three less than the fraction, 22% +- 8%, determined using the same technique on HST optical images and as measured in a previous similar study. Tests support the hypothesis that optical pair fractions at z~1 are inflated by bright star-forming regions that are unlikely to be representative of the underlying mass distribution. By determining stellar masses for the companions, we estimate the mass accretion rate associated with merging galaxies. At z~1, we estimate this to be 2x10^{9 +- 0.2} solar masses per galaxy per Gyr. Although uncertainties remain, our results suggest that the growth of galaxies via the accretion of pre-existing fragments remains as significant a phenomenon in the redshift range studied as that estimated from ongoing star formation in independent surveys.Comment: 5 pages, accepted for publication in ApJ Letter

A nonlinear detection algorithm for periodic signals in gravitational wave detectors

We present an algorithm for the detection of periodic sources of gravitational waves with interferometric detectors that is based on a special symmetry of the problem: the contributions to the phase modulation of the signal from the earth rotation are exactly equal and opposite at any two instants of time separated by half a sidereal day; the corresponding is true for the contributions from the earth orbital motion for half a sidereal year, assuming a circular orbit. The addition of phases through multiplications of the shifted time series gives a demodulated signal; specific attention is given to the reduction of noise mixing resulting from these multiplications. We discuss the statistics of this algorithm for all-sky searches (which include a parameterization of the source spin-down), in particular its optimal sensitivity as a function of required computational power. Two specific examples of all-sky searches (broad-band and narrow-band) are explored numerically, and their performances are compared with the stack-slide technique (P. R. Brady, T. Creighton, Phys. Rev. D, 61, 082001).Comment: 9 pages, 3 figures, to appear in Phys. Rev.

Evolution of the Near-Infrared Tully-Fisher Relation: Constraints on the Relationship Between the Stellar and Total Masses of Disk Galaxies since z=1

Using a combination of Keck spectroscopy and near-infrared imaging, we investigate the K-band and stellar mass Tully-Fisher relation for 101 disk galaxies at 0.2 < z < 1.2, with the goal of placing the first observational constraints on the assembly history of halo and stellar mass. Our main result is a lack of evolution in either the K-band or stellar mass Tully-Fisher relation from z = 0 - 1.2. Furthermore, although our sample is not statistically complete, we consider it suitable for an initial investigation of how the fraction of total mass that has condensed into stars is distributed with both redshift and total halo mass. We calculate stellar masses from optical and near-infrared photometry and total masses from maximum rotational velocities and disk scale lengths, utilizing a range of model relationships derived analytically and from simulations. We find that the stellar/total mass distribution and stellar-mass Tully-Fisher relation for z > 0.7 disks is similar to that at lower redshift, suggesting that baryonic mass is accreted by disks along with dark matter at z < 1, and that disk galaxy formation at z < 1 is hierarchical in nature. We briefly discuss the evolutionary trends expected in conventional structure formation models and the implications of extending such a study to much larger samples.Comment: ApJ, in press, 9 page

Warm dark matter at small scales: peculiar velocities and phase space density

We study the scale and redshift dependence of the power spectra for density perturbations and peculiar velocities, and the evolution of a coarse grained phase space density for (WDM) particles that decoupled during the radiation dominated stage. The (WDM) corrections are obtained in a perturbative expansion valid in the range of redshifts at which N-body simulations set up initial conditions, and for a wide range of scales. The redshift dependence is determined by the kurtosis $\beta_2$ of the distribution function at decoupling. At large redshift there is an enhancement of peculiar velocities for $\beta_2 > 1$ that contributes to free streaming and leads to further suppression of the matter power spectrum and an enhancement of the peculiar velocity autocorrelation function at scales smaller than the free streaming scale. Statistical fluctuations of peculiar velocities are also suppressed on these scales by the same effect. In the linearized approximation, the coarse grained phase space density features redshift dependent (WDM) corrections from gravitational perturbations determined by the power spectrum of density perturbations and $\beta_2$. For $\beta_2 > 25/21$ it \emph{grows logarithmically} with the scale factor as a consequence of the suppression of statistical fluctuations. Two specific models for WDM are studied in detail. The (WDM) corrections relax the bounds on the mass.Comment: 22 pages, 9 figs, more explanations. Published versio

New "Einstein Cross" Gravitational Lens Candidates in HST WFPC2 Survey Images

We report the serendipitous discovery of ``Einstein cross'' gravitational lens candidates using the Hubble Space Telescope. We have so far discovered two good examples of such lenses, each in the form of four faint blue images located in a symmetric configuration around a red elliptical galaxy. The high resolution of HST has facilitated the discovery of this optically selected sample of faint lenses with small (~1 arcsec) separations between the (I ~ 25-27) lensed components and the much brighter (I ~ 19-22) lensing galaxies. The sample has been discovered in the routine processing of HST fields through the Medium Deep Survey pipeline, which fits simple galaxy models to broad band filter images of all objects detected in random survey fields using WFPC2. We show that the lens configuration can be modeled using the gravitational field potential of a singular isothermal ellipsoidal mass distribution. With this model the lensing potential is very similar, both in ellipticity and orientation, to the observed light distribution of the elliptical galaxy, as would occur when stars are a tracer population. The model parameters and associated errors have been derived by 2-dimensional analysis of the observed images. The maximum likelihood procedure iteratively converges simultaneously on the model for the lensing elliptical galaxy and the source of the lensed components. A systematic search is in progress for other gravitational lens candidates in the HST Medium Deep Survey. This should eventually lead to a good statistical estimate for lensing probabilities, and enable us to probe the cosmological component of the observed faint blue galaxy population.Comment: Accepted for Astrophysical Journal Letters, 1995 November 1 LaTex, 10 pages, includes 2 figures 1 table, tarred gzip uuencoded using uufiles scrip

Cosmological Fluctuations of Short Wavelength

This paper presents a completely analytic treatment of cosmological fluctuations whose wavelength is small enough to come within the horizon well before the energy densities of matter and radiation become equal. This analysis yields a simple formula for the conventional transfer function T(k) at large wave number k, which agrees very well with computer calculations of T(k). It also yields an explicit formula for the microwave background multipole coefficient C_ell at very large ell.Comment: 15 pages, no figure