### Hellings and Downs curve

**(Hellings Downs correlation, HD correlation)**
(expected correlation in pulsar timing residuals from random waves)

The **Hellings and Downs curve** (**Hellings-Downs correlation**,
**HD correlation**), is the graphed curve
of a function that maps the angle
between two pulsars as seen from Earth
with the correlation between their
timing residuals that would result from random gravitational wave signals
from all over the sky. It has the potential usefulness for pulsar timing arrays
to help identify and quantify the background gravitational wave
signals, the gravitational wave background (GWB).
which is the signal that one would need to "subtract" when attempting
to identify a specific source.

Gravitational waves from a specific source can be recognized
only if their signal can be isolated from the combined signals
of other sources of waves at that frequency,
presumably from sources throughout the universe.
Timing residuals of pulses from pulsars (the delta between
the expected time and actual received time that is attributed
to the effect of gravitational waves) will show some correlation
just from this background signal, and such a correlation depends
upon the angle between the two pulse sources in the celestial sphere.
The Hellings and Downs curve is a calculation of the expected correlation
as a function of the angle, using some model simplifications:
that the gravitational waves are plane waves (virtually true
if the gravitational wave sources are distant), and that there
are sources in all directions and with all polarizations.
If reality is sufficiently close to these assumptions, the curve
should yield the correlation between timing residuals that
can be attributed to the background signal. This enables
quantification of the background signal, and with such quantification
at various frequencies, a power spectrum may be discerned.

(*gravitational waves*)
https://arxiv.org/pdf/1412.1142.pdf

http://adsabs.harvard.edu/full/1983ApJ...265L..39H

index