# As of 2021 in how many binary systems has the period decrease due to gravitational waves been measured?

I am searching for data for the period decrease of binary systems due to gravitational waves. I am aware of three systems in which it was possible to measure this period decrease:

• The Hulse-Taylor binary PSR 1913+16
• the double pulsar PSR J0737-3039
• the pulsar-neutron-star-binary PSR B1534+12

However I know of these three from the book von gravitational waves from Maggiore which is from 2006. Have there been any new binary sytems entered the list, from which the period decrease has been measured up to this date? I'm thankful for any help.

I am especially interested in the question whether there have been any measurements comparing results not only to the famous period decrease formula that can be derived from the quadrupole-approximaion of gravitational radiation

$$$$\dot{P}_b=-\frac{192\pi G^\frac{5}{3}}{5c^5}\Biggl(\frac{P_b}{2\pi}\Biggr)^{-\frac{5}{3}}\frac{m_1m_2}{(m_1+m_2)^\frac{1}{3}}\frac{1+\frac{73}{24}e^2+\frac{37}{96}e^4}{(1-e^2)^\frac{7}{2}}$$$$

but to higher Post-Newtonian formulas that may exist...

• There are obviously all the gravitational wave merger sources (about 50) in which the post-Newtonian contributions are important. Perhaps you need to be more specific? Commented Sep 2, 2021 at 11:49
• Yes, of course. I was referring only to those kind of systems, where gravitational waves are not measured directly by interferrometers, but indirectly by measuring the back reaction they have on the periodic motion of the source. Commented Sep 2, 2021 at 12:14
• This Living review by Cliff Will may be of use to you: link.springer.com/article/10.12942/lrr-2014-4 Commented Sep 3, 2021 at 8:25

According to the Australia National Telescope Facility Pulsar Catalogue, there are currently 31 pulsar binaries with a measured negative value for the derivative of the period.

For an overview of what tests of gravity have been performed using these binaries see this Living Review by Cliff Will, or this 2020 review by Wex and Kramer.

• This helps a lot, indeed. Thank you! Commented Sep 3, 2021 at 15:24
• The list from ANTF contains pulsars with positive $\dot{P}_B$, not negative. The Hulse-Taylor pulsar (J1915+1606 or J1913+16) is not in the list Commented Sep 3, 2021 at 19:51
• @PaulT. I fixed the typo in the search link. Commented Sep 9, 2021 at 9:46

Three things can affect the observed binary period of a pulsar system: GW emission, relative acceleration, and the Shklovskii effect. All three can be fit as part of a binary model using the same $$\dot{P}_B$$ parameter (or PBDOT in the ANTF pulsar catalogue naming). Here's search for all pulsars with positive or negative $$\dot{P}_B$$ from ANTF. (the parameter C1 is PBDOT, which I can't seem to get to display with the right tag)

GW emission causes the period to decay resulting in negative $$\dot{P}_B$$.

Relative acceleration doesn't affect the actual orbit but causes the observed orbital period to change. The pulsar timing model is based in the solar system barycenter (SSB) frame, so it appears as $$\dot{P}_B$$. If a pulsar system has a significantly different galactic gravitation potential relative to the solar system, that would show up as a relative acceleration. A host globular cluster could also cause this. For instance globular cluster 47 Tucanae hosts many pulsars including several binaries with observed $$\dot{P}_B$$ (e.g. J0024-7204E, H, I, ...). A relative acceleration can result a positive or negative $$\dot{P}_B$$.

Finally, the Shklovskii effect is the result of transverse motion of the binary system relative to the line of sight. It's sometimes called secular acceleration. Like relative accelerations it doesn't affect the true binary period just the observed period in the SSB frame. The Shklovskii effect causes positive $$\dot{P}_B$$.

In order to measure the GW part of the orbital decay one must first account for the others. Since transverse motion shows up in other parts of the timing model, I believe the Shklovskii effect can be pretty straightforwardly corrected.

It turns out there are 31 pulsars in the ATNF catalogue with negative $$\dot{P}_B$$. Unfortunately I am unsure which have been confirmed to be the result of GW driven decay and not some other effect.

• I'm not sure why anybody would down vote this answer. Commented Sep 9, 2021 at 9:47