Md Faisal Alam | Searcharxiv

arXiv2023

The NANOGrav 15-year Data Set: Observations and Timing of 68 Millisecond Pulsars

We present observations and timing analyses of 68 millisecond pulsars (MSPs) comprising the 15-year data set of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). NANOGrav is a pulsar timing array (PTA) experiment that is sensitive to low-frequency gravitational waves. This is NANOGrav's fifth public data release, including both "narrowband" and "wideband" time-of-arrival (TOA) measurements and corresponding pulsar timing models. We have added 21 MSPs and extended our timing baselines by three years, now spanning nearly 16 years for some of our sources. The data were collected using the Arecibo Observatory, the Green Bank Telescope, and the Very Large Array between frequencies of 327 MHz and 3 GHz, with most sources observed approximately monthly. A number of notable methodological and procedural changes were made compared to our previous data sets. These improve the overall quality of the TOA data set and are part of the transition to new pulsar timing and PTA analysis software packages. For the first time, our data products are accompanied by a full suite of software to reproduce data reduction, analysis, and results. Our timing models include a variety of newly detected astrometric and binary pulsar parameters, including several significant improvements to pulsar mass constraints. We find that the time series of 23 pulsars contain detectable levels of red noise, 10 of which are new measurements. In this data set, we find evidence for a stochastic gravitational-wave background.

astro-ph.HE↗

arXiv2019

Coulomb expectation values in $D=3$ and $D=3-2ε$ dimensions

We explore the quantum Coulomb problem for two-body bound states, in $D=3$ and $D=3-2ε$ dimensions, in detail, and give an extensive list of expectation values that arise in the evaluation of QED corrections to bound state energies. We describe the techniques used to obtain these expectation values and give general formulas for the evaluation of integrals involving associated Laguerre polynomials. In addition, we give formulas for the evaluation of integrals involving subtracted associated Laguerre polynomials--those with low powers of the variable subtracted off--that arise when evaluating divergent expectation values. We present perturbative results (in the parameter $ε$) that show how bound state energies and wave functions in $D=3-2ε$ dimensions differ from their $D=3$ dimensional counterparts and use these formulas to find regularized expressions for divergent expectation values such as $\big \langle \bar V^3 \big \rangle$ and $\big \langle (\bar V')^2 \big \rangle$ where $\bar V$ is the $D$-dimensional Coulomb potential. We evaluate a number of finite $D$-dimensional expectation values such as $\big \langle r^{-2+4ε} \partial_r^2 \big \rangle$ and $\big \langle r^{4ε} p^4 \big \rangle$ that have $ε\rightarrow 0$ limits that differ from their three-dimensional counterparts $\big \langle r^{-2} \partial_r^2 \big \rangle$ and $\big \langle p^4 \big \rangle$. We explore the use of recursion relations, the Feynman-Hellmann theorem, and momentum space brackets combined with $D$-dimensional Fourier transformation for the evaluation of $D$-dimensional expectation values. The results of this paper are useful when using dimensional regularization in the calculation of properties of Coulomb bound systems.

quant-ph↗