Tests of General Relativity
with Pulsar Timing Arrays
Andrea N. Lommen
International Liaison for NANOGrav
Associate Professor of Physics and Astronomy
Head of Astronomy Program
Director of Grundy Observatory
Franklin and Marshall College
Lancaster, PA
Different geometries
R=9km
R=12km
R=16 km
What is
a
pulsar?
Timing residuals versus time:
J1713+0747
J1909-3744
Slide
courtesy of
Paul
Demorest
Photo Courtesy of Virgo
Pulsar1
Pulsar2
Earth
Adapted from NASA figure
Detectability of a Waveform
g    h
dt 2
dx j dx k dx j dx k
r

h jk t, x 
    jk
d 
d d d d
1  km n m
 dt   d  1 k n m
m
r
 dn n h jk t , x 
j
k



h0
m
m
Residual  e jk n n
1

k
n
f
t

f
t

L
1
k
n


 m  0
 m 
0
2
r
r
ˆ
where h jk t, x   h0 f  t  k  x e and L is the dist ance to the pulsar.
j
k


A sense of what’s detectable
h
M
5
3
2
P 3d
  hP
5
3
M P

d
1
3
5

 3  P  3
M

 

9
2  10 M  1year
  50ns
 d 


100Mpc 
1
NANOGrav Residuals
Adapted
from
Demorest
et al
(2013) by
David
Nice
NANOGrav 5-year timing results summary
Demorest
et al
(2013)
Orbital Motion in the Radio Galaxy 3C 66B: Evidence for a
Supermassive Black Hole Binary Sudou, Iguchi, Murata, Taniguchi
(2003) Science 300: 1263-1265.
Residual(s)
Residual(s)
Constraining the Properties of Supermassive Black Hole Systems
Using Pulsar Timing: Application to 3C 66b, Jenet, Lommen, Larson
and Wen (2004) ApJ 606:799-803. (NANOGrav)
10
0
-10
Simulated residuals due to 3c66b
10
0
-10
Data from Kaspi, Taylor, Ryba 1994
15
The shape of the GW
response
Thanks Bill Coles
A 5 x 109 solar-mass black hole binary coalescing 100 Mpc away.
30 IPTA pulsars, improved by 10, sampled once a day.
Maximum Entropy based on Summerscales, Burrows, Finn and Ott 2008
Thank you to Manuela Campanelli, Carlos O. Lousto, Hiroyuki Nakano, and Yosef Zlochower
for waveforms. Phys.Rev.D79:084010 (2009). http://ccrg.rit.edu/downloads/waveforms
Hellings and Downs Curve
(Overlap Reduction Function)
Courtesy of
Rick Jenet
(NANOGrav)
and George
Hobbs
(PPTA).
Original
figure from
Hellings and
Downs
(1983).
Yardley et al 2011 (PPTA)
Response maps from
alternate polarizations
Chamberlin et al, PhRvD (2012)
Lee et al. (2008)
for biweekly observations made for five years with rms timing accuracy of 100 ns,
detecting non-Einsteinian modes will require:
pulsars in the case of the longitudinal mode;
•60
•60 for the two spin-1 ‘‘shear’’ modes; and
•40 for the spin-0 ‘‘breathing’’ mode
Sydney Chamberlin (UW Milwaukee,
NANOGrav) Non-Einsteinian
gravitational waves using PTAs
Chamberlin et al, PhRvD (2012)
Figure by Paul Demorest, NANOGrav (see
arXiv:0902.2968 and arXiv:1201.6641)
Measuring the Graviton Mass
KJ Lee et al, ApJ (2010)
Measuring the Graviton Mass
KJ Lee et al, ApJ (2010)
Optimization
Amounts to redistributing observing time
among pulsars
• To detect a single source, observe only halfdozen best of your pulsars (Burt, Lommen &
Finn 2011 and recent work by Xavi Siemens)
• To detect the stochastic background, maximize
the number of pulsars
• To detect (or rule-out) longitudinal modes,
observe a few sources close together in the sky
The Pulsar Data Challenge
• Opened a week ago (March 23)
• Will close in Sept
• Go to www.ipta4gw.org
Question #0
• How much do the tests on GR that you
can do with binary pulsars matter?
Question #1
• How should we optimize the pulsar
timing array?
Question #2
• What is the best method for detecting
alternate modes?
– Bayesian analysis
– Frequentist
– What would convince you?
Question #3
• What effect would other theories of
gravity (besides the conservative notion
I’ve taken here that it’s GR but not
standard polarization) have on pulsar
timing and how would I test those?
Question #4
• Can we do tests on the existing IPTA
data challenge data? Is there a
different data set we need to ask them
to produce in order to test alternate
theories?
Questions
• 0. How much do the tests on GR using binary pulsars
matter?
• 1. How should PTAs be optimized? Which pulsars
should we observe most?
• 2. What is the best method for detecting alternate
modes?
• 3. What effect would other theories of gravity have on
pulsar timing and how would I test those?
• 4. Can you do tests of alternative theories of gravity
on the existing IPTA data challenge data?