Separation angle between pulsars detecting Gravitational Waves

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zinn
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How can separation angle alone tell you about the correlation between gravitational wave signals from pulsar timing?
I’m trying to understand the Hellings and Downs curve that is being used to argue for the existence of a gravitational wave background ([NANOGrav article][1]). How can it be that the angle between two pulsars is the only variable that determines if the gravitational waves will interfere constructively (correlated) or destructively (anti-correlated). I would have imagined that distance from the observer would also be a factor.

(Image source: https://astrobites.org/2016/08/10/the-predictor-of-pulsar-timing/)
3EFC2F01-19E9-4450-9E02-914871009C04.png


I imagine that a key part of understanding this concept would be visualising the gravitational waveforms in 3D. Should I be picturing something like this? [youtube video with gravitational wave animations][2]


[1]: https://nanograv.org/15yr/Summary/Background
[2]:
[3]: https://i.stack.imgur.com/w3DSd.png
 

FAQ: Separation angle between pulsars detecting Gravitational Waves

What is the separation angle between pulsars in detecting gravitational waves?

The separation angle between pulsars in detecting gravitational waves refers to the angular distance between two pulsars as observed from Earth. This angle is crucial for determining the correlated timing residuals caused by gravitational waves passing through the space between the pulsars and Earth.

Why is the separation angle important in pulsar timing arrays (PTAs)?

The separation angle is important in PTAs because it helps in identifying the correlated signals in the timing residuals of multiple pulsars. Gravitational waves create a distinctive pattern of timing deviations that depend on the angular separation between pulsars, allowing scientists to distinguish these signals from other noise sources.

How do gravitational waves affect the timing of pulsars at different separation angles?

Gravitational waves cause variations in the time it takes for pulses from pulsars to reach Earth. These variations are correlated between different pulsars, with the degree of correlation depending on the separation angle. Pulsars with smaller separation angles will have more strongly correlated timing residuals, while those with larger separation angles will have weaker correlations.

What is the typical range of separation angles used in PTA experiments?

The typical range of separation angles used in PTA experiments varies widely, from a few degrees to over 90 degrees. A diverse range of separation angles is necessary to effectively detect and analyze the correlated signals from gravitational waves, as different angles provide different insights into the wave's properties and origins.

How does the Hellings-Downs curve relate to the separation angle between pulsars?

The Hellings-Downs curve describes the expected correlation in timing residuals between pairs of pulsars as a function of their separation angle. This curve is a key prediction of general relativity for a stochastic background of gravitational waves and serves as a benchmark for analyzing the data from PTAs. The curve shows that the correlation is highest for pulsars that are close together and decreases with increasing separation angle.

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