Artist's sketch of accreting neutron star, a possible source of gravitational waves. Image: NASA.

## Useful relations in gravitational wave astronomy

## Binary system merger

Two neutron stars or black holes in a close binary system emit gravitational radiation and get closer and closer together, until they merge. Gravitational wave frequency evolves as a function of time and chirp mass [1]:

## Diffraction limited resolution

Sky resolution of laser interferometers (LIGO, Virgo, Kagra, etc.) depends on a gravitational wave frequency as [2]:

## Fourier segment duration and loss of SNR

Selecting long segment durations in gravitational wave data analysis for terrestrial-based detectors leads to a higher frequency-domain resolution. However, at the same time, it may lead to a loss of SNR at high frequencies due to sidereal rotation of the Earth with respect to a gravitational wave source. If we can accept only SNR losses of 10% or less, we should constrain the Fourier segment duration by [3]:

## References

- LIGO Scientific and VIRGO Collaborations, et al. "The basic physics of the binary black hole merger GW150914." Annalen der Physik 529.1-2 (2017): 1600209.
- Goncharov, B., Thrane, E., 2018. All-sky radiometer for narrowband gravitational waves using folded data. Physical Review D, 98(6), p.064018.
- Thrane, E., Mandic, V. and Christensen, N., 2015. Detecting very long-lived gravitational-wave transients lasting hours to weeks. Physical Review D, 91(10), p.104021.

## Recent Work

Artist's representation of a GRB jets (NASA), and a 3D model of the Lomonosov satellite (MSU).