Implications of binary black hole detections on the merger rates of double neutron stars and neutron star-black holes

We show that the inferred merger rate and chirp masses of binary black holes (BBHs) detected by advanced LIGO (aLIGO) can be used to constrain the rate of double neutron star (DNS) and neutron star - black hole (NSBH) mergers in the universe. We explicitly demonstrate this by considering a set of publicly available population synthesis models of \citet{Dominik:2012kk} and show that if all the BBH mergers, GW150914, LVT151012, GW151226, and GW170104, observed by aLIGO arise from isolated binary evolution, the predicted DNS merger rate may be constrained to be $2.3-471.0$~\rate~ and that of NSBH mergers will be constrained to $0.2-48.5$~\rate. The DNS merger rates are not constrained much but the NSBH rates are tightened by a factor of $\sim 4$ as compared to their previous rates. Note that these constrained DNS and NSBH rates are extremely model dependent and are compared to the unconstrained values $2.3-472.5$ \rate~ and $0.2-218$ \rate, respectively, using the same models of \citet{Dominik:2012kk}. These rate estimates may have implications for short Gamma Ray Burst progenitor models assuming they are powered (solely) by DNS or NSBH mergers. While these results are based on a set of open access population synthesis models which may not necessarily be the representative ones, the proposed method is very general and can be applied to any number of models thereby yielding more realistic constraints on the DNS and NSBH merger rates from the inferred BBH merger rate and chirp mass.Comment: 5 pages, no figures, 4 tables, v2: matches published versio

Contrast Interferometry Using Bose-Einstein Condensates to Measure h/m and the Fine Structure Constant

The kinetic energy of an atom recoiling due to absorption of a photon was measured as a frequency using an interferometric technique called ``contrast interferometry''. Optical standing wave pulses were used as atom-optical elements to create a symmetric three-path interferometer with a Bose-Einstein condensate. The recoil phase accumulated in different paths was measured using a single-shot detection technique. The scheme allows for additional photon recoils within the interferometer and its symmetry suppresses several random and systematic errors including those from vibrations and ac Stark shifts. We have measured the photon recoil frequency of sodium to $7$ppm precision, using a simple realization of this scheme. Plausible extensions should yield a sufficient precision to bring within reach a ppb-level determination of $h/m$ and the fine structure constant $\alpha$

Heavy Quarkonium Potential Model and the 1P1{}^1P_1 State of Charmonium

A theoretical explanation of the observed splittings among the P~states of charmonium is given with the use of a nonsingular potential model for heavy quarkonia. We also show that the recently observed mass difference between the center of gravity of the ${}^3P_J$ states and the ${}^1P_1$ state of $c\bar{c}$ does not provide a direct test of the color hyperfine interaction in heavy quarkonia. Our theoretical value for the mass of the ${}^1P_1$ state is in agreement with the experimental result, and its E1 transition width is 341.8~keV. The mass of the $\eta_c'$ state is predicted to be 3622.3~MeV.Comment: 15 page REVTEX documen