### 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 pairs of pulsars as seen from Earth
with the correlation between such pairs'
timing residuals that would result from random gravitational wave (GW) signals
from all over the sky, i.e., an isotropic, unpolarized stochastic
gravitational-wave background.
The curve has potential usefulness for pulsar timing arrays
to help identify and quantify the gravitational wave background (GWB)
(random waves from many distant sources),
which is the signal that one would need to "subtract" when attempting
to identify a specific source.
Other sources of randomness, such as measurement errors,
would not show the same correlation.

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
throughout the universe.
Timing residuals of pulses from pulsars (the delta between
the expected time and actual received time that can be
the effect of gravitational waves) will show some correlation
merely 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 this 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 a correlation to the curve is found in the data, characteristics
of the GW background are confirmed (e.g., whether it is isotropic),
its quantification is obtained, and with such quantification at
various frequencies, an angular power spectrum may be discerned.
Furthermore, use of PTAs to search for GWs is proved valid and means
is provided to isolate any specific GW signal, e.g., from those of
some specific binary SMBH.

(*gravitational waves*)
**Further reading:**

https://ui.adsabs.harvard.edu/abs/2015AmJPh..83..635J/abstract

https://ui.adsabs.harvard.edu/abs/1983ApJ...265L..39H/abstract

https://astrobites.org/2016/08/10/the-predictor-of-pulsar-timing/

https://ui.adsabs.harvard.edu/abs/2017LRR....20....2R/abstract

http://ipta.phys.wvu.edu/files/student-week-2014/Lindley_Lentati_IPTA2014_Student_Week.pdf

http://nanograv.org/research/

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