Can Heavy WIMPs Be Captured by the Earth?

If weakly interacting massive particles (WIMPs) in bound solar orbits are systematically driven into the Sun by solar-system resonances (as Farinella et al. have shown is the case for many Earth-crossing asteroids), then the capture of high-mass WIMPs by the Earth would be affected dramatically because high-mass WIMPs are captured primarily from bound orbits. WIMP capture would be eliminated for M_x>630 GeV and would be highly suppressed for M_x>~150 GeV. Annihilation of captured WIMPs and anti-WIMPs is expected to give rise to neutrinos coming from the Earth's center. The absence of such a neutrino signal has been used to place limits on WIMP parameters. At present, one does not know if typical WIMP orbits are in fact affected by these resonances. Until this question is investigated and resolved, one must (conservatively) assume that they are. Hence, limits on high-mass WIMP parameters are significantly weaker than previously believed.Comment: 8 pages + 1 figure. Submitted to Ap

No Death Star -- For Now

A star passing within \sim 10^4 \au of the Sun would trigger a comet shower that would reach the inner solar system about 0.18 Myr later. We calculate a prior probability of ~0.4% that a star has passed this close to the Sun but that the comet shower has not yet reached the Earth. We search the HIPPARCOS catalog for such recent close-encounter candidates and, in agreement with Garcia-Sanchez et al. (1997), find none. The new result reported in this Letter is an estimation of the completeness of the search. Because of the relatively bright completeness limit of the catalog itself, V~8, the search is sensitive to only about half the stars that could have had such a near encounter. On the other hand, we show that the search is sensitive to nearly all of the past encounters that would lead to a major shower in the future and conclude that it is highly unlikely that one will occur during the next 0.5 Myr.Comment: 10 pages, 1 figure. In press at The Astrophysical Journal Letter

Frequency of Solar-like Systems and of Ice and Gas Giants Beyond the Snow Line from High-magnification Microlensing Events in 2005-2008

We present the first measurement of the planet frequency beyond the "snow line," for the planet-to-star mass-ratio interval –4.5 200) microlensing events during 2005-2008. The sampled host stars have a typical mass M_(host) ~ 0.5 M_⊙, and detection is sensitive to planets over a range of planet-star-projected separations (s ^(–1)_(max)R_E, s_(max)R_E), where R_E ~ 3.5 AU(M_(host)/M_⊙)^(1/2) is the Einstein radius and s_(max) ~ (q/10^(–4.3))^(1/3). This corresponds to deprojected separations roughly three times the "snow line." We show that the observations of these events have the properties of a "controlled experiment," which is what permits measurement of absolute planet frequency. High-magnification events are rare, but the survey-plus-follow-up high-magnification channel is very efficient: half of all high-mag events were successfully monitored and half of these yielded planet detections. The extremely high sensitivity of high-mag events leads to a policy of monitoring them as intensively as possible, independent of whether they show evidence of planets. This is what allows us to construct an unbiased sample. The planet frequency derived from microlensing is a factor 8 larger than the one derived from Doppler studies at factor ~25 smaller star-planet separations (i.e., periods 2-2000 days). However, this difference is basically consistent with the gradient derived from Doppler studies (when extrapolated well beyond the separations from which it is measured). This suggests a universal separation distribution across 2 dex in planet-star separation, 2 dex in mass ratio, and 0.3 dex in host mass. Finally, if all planetary systems were "analogs" of the solar system, our sample would have yielded 18.2 planets (11.4 "Jupiters," 6.4 "Saturns," 0.3 "Uranuses," 0.2 "Neptunes") including 6.1 systems with two or more planet detections. This compares to six planets including one two-planet system in the actual sample, implying a first estimate of 1/6 for the frequency of solar-like systems

Measuring the Rotation Speed of Giant Stars From Gravitational Microlensing

During some gravitational lensing events, the lens transits the face of the star. This causes a shift in the apparent radial velocity of the star which is proportional to its rotation speed. It also changes the magnification relative to what would be expected for a point source. By measuring both effects, one can determine the rotation parameter $v\sin i$. The method is especially useful for K giant stars because these have turbulent velocities that are typically large compared with their rotation speed. By making a series of radial velocity measurements, one can typically determine $v\sin i$ to the same accuracy as the individual radial velocity measurements. There are approximately 10 microlensing transit events per year which would be suitable to make these measurements.Comment: 11 pages including 1 embedded figur

Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]

Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so contains a \textit{universal $R$-matrix} in the tensor product algebra which satisfies the Yang-Baxter equation. Applying the vector representation $\pi$, which acts on the vector module $V$, to one side of a universal $R$-matrix gives a Lax operator. In this paper a Lax operator is constructed for the $C$-type quantum superalgebras $U_q[osp(2|n)]$. This can in turn be used to find a solution to the Yang-Baxter equation acting on $V \otimes V \otimes W$ where $W$ is an arbitrary $U_q[osp(2|n)]$ module. The case $W=V$ is included here as an example.Comment: 15 page