Faint blue objects on the Hubble Deep Field North & South as possible nearby old halo white dwarfs

Using data derived from the deepest and finest angular resolution images of the universe yet acquired by astronomers at optical wavelengths using the Hubble Space Telescope (HST) in two postage-stamp sections of the sky (Williams et al. 1996a,b), plus simple geometrical and scaling arguments, we demonstrate that the faint blue population of point-source objects detected on those two fields (M\'endez et al. 1996) could actually be ancient halo white dwarfs at distances closer than about 2 kpc from the Sun. This finding has profound implications, as the mass density of the detected objects would account for about half of the missing dark matter in the Milky-Way (Bahcall and Soneira 1980), thus solving one of the most controversial issues of modern astrophysics (Trimble 1987, Ashman 1992). The existence of these faint blue objects points to a very large mass locked into ancient halo white dwarfs. Our estimate indicates that they could account for as much as half of the dark matter in our Galaxy, confirming the suggestions of the MACHO microlensing experiment (Alcock et al. 1997). Because of the importance of this discovery, deep follow-up observations with HST within the next two years would be needed to determine more accurately the kinematics (tangential motions) for these faint blue old white dwarfs.Comment: Accepted for publication on The Astrophysical Journal, Part 1. 8 pages (AAS Latex macros V4.0), 1 B&W postscript figure, 2 color postscript figure

Semismall perturbations, semi-intrinsic ultracontractivity, and integral representations of nonnegative solutions for parabolic equations

We consider nonnegative solutions of a parabolic equation in a cylinder D \timesI, where $D$ is a noncompact domain of a Riemannian manifold and $I =(0,T)$ with $0 < T \le \infty$ or $I=(-\infty,0)$. Under the assumption [SSP] (i.e., the constant function 1 is a semismall perturbation of the associated elliptic operator on $D$), we establish an integral representation theorem of nonnegative solutions: In the case $I =(0,T)$, any nonnegative solution is represented uniquely by an integral on $(D \times \{0 \}) \cup (\partial_M D \times [0,T))$, where $\partial_M D$ is the Martin boundary of $D$ for the elliptic operator; and in the case $I=(-\infty,0)$, any nonnegative solution is represented uniquely by the sum of an integral on $\partial_M D \times (-\infty,0)$ and a constant multiple of a particular solution. We also show that [SSP] implies the condition [SIU] (i.e., the associated heat kernel is semi-intrinsically ultracontractive).Comment: 35 page

Stressed and Strapped: Caregivers in California

Profiles the demographics and self-reported physical and mental health status of informal caregivers caring for a family member or friend, including high blood pressure, diabetes, and heart disease; psychological distress; and unhealthy behaviors

On the kHz QPO frequency correlations in bright neutron star X-ray binaries

We re-examine the correlation between the frequencies of upper and lower kHz quasi-periodic oscillations (QPO) in bright neutron-star low-mass X-ray binaries. By including the kHz QPO frequencies of the X-ray binary Cir X-1 and two accreting millisecond pulsars in our sample, we show that the full sample does not support the class of theoretical models based on a single resonance, while models based on relativistic precession or Alfven waves describe the data better. Moreover, we show that the fact that all sources follow roughly the same correlation over a finite frequency range creates a correlation between the linear parameters of the fits to any sub-sample.Comment: Accepted for publication in MNRAS; 7 pages, 4 figure