How To Possibly Detect Graviton Mass With Gravity Waves/Pulsars.

Gravitons are the particles that mediate the force of gravity in the analogous way that photons are responsible for the electro-magnetic field.  And like photons, gravitons are thought to be massless.  In fact, assuming general relativity is correct, the mass of the graviton has an upper bound of 7x10^-32 eV which is really small. (See bold text at bottom.)  However, for alternative gravity theories this upper bound no longer holds.

                               Image via Wikipedia

Lee et al. have recently developed a new way to place a bound on the graviton mass that is general enough that it constrains this mass even in alternative theories to gravity.  This technique involves measuring correlations in the gravitational waves from the timing residuals of pulsars.

Just a reminder: fluctuations in the curvature of spacetime propagate as waves which are called gravity waves.  The top right picture shows the gravity waves given off by two neutron stars orbiting each other.  Pulsars, are "highly magnetized, rotating neutron stars" that emit a beam of light that can appear to flash the earth in very regular intervals like a lighthouse. See the lower right animation to see the "cycle of pulsed gamma rays from the Vela pulsar".

Back to the article.  Here is how the authors put it:

The pulsar timing array is a unique technique to detect nano-Hertz gravitational waves by timing millisecond pulsars, which are very stable celestial clocks. It turns out that a stochastic gravitational wave background leaves an angular dependent correlation in pulsar timing residuals for widely spaced pulsars (Hellings & Downs 1983; Lee et al. 2008). That is, the correlation C(θ) between timing residual of pulsar pairs is a function of angular separation θ between the pulsars. One can analyse the timing residual and test such a correlation between pulsar timing residuals to detect gravitational waves (Jenet et al. 2005). We find in this paper that if the graviton mass is not zero, the form of C(θ) is very different from that given by general relativity. Thus by measuring this graviton mass dependent correlation function, we can also detect the massive graviton.

So basically the correlation function between gravity waves and pulsar timing residuals puts a constraint on the graviton's mass.

Another aside: Thinking of the power spectrum of the CMB, and taking a minute to play this game may be helpful.  The power spectrum of the CMB is a correlation function of temperature fluctuations of the CMB. As that game shows, this correlation function changes significantly for changes in the amount of dark matter, dark energy, regular matter, etc...  Therefore, the shape of the power spectrum tells you a lot of physics.

Lee et al. are doing the same thing with correlation functions of gravity waves with pulsar timing residuals.  The shape of this power spectrum, which they denote as C(θ), changes significantly with graviton mass.  The plot above shows this change.  The plot on the left shows how C(θ) would look after 5 years of a bi-weekly observation and the plot on the right shows what C(θ) would look for a 10 year bi-weekly observation.

Using this technique and future gravity wave interferometers the authors claim that with 5 years of data they can place an upper bound on the graviton mass of 1x10^-22 eV and after 10 years they can place an upper bound of 3x10^-23 eV.

Now, even if the graviton does have mass, to put into preservative how light this particle must be if its mass is around these numbers, I will remind people that the mass of the electron is 510,998 eV! So a mass on the order of 10^-23 eV is mind-blowingly tiny!

Kejia Lee, Fredrick A. Jenet, Richard H. Price, Norbert Wex, & Michael Kramer (2010). Detecting massive gravitons using pulsar timing arrays Accepted by ApJ arXiv: 1008.2561v2