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					             Testing General Relativity
              with Relativistic Binary
                      Pulsars
                          Ingrid Stairs
                             UBC
                           GWPAW
                          Milwaukee
                         Jan. 29, 2011

Green Bank                                      Jodrell Bank
Telescope




                Parkes                Arecibo
          Outline


• Intro to pulsar timing
• Equivalence principle tests
   - “Nordtvedt”-type tests
   - Orbital decay tests
• Relativistic systems
   - Timing
   - Geodetic precession
   - Preferred-frame effects
• Looking to the future
          Pulsars and other
          compact objects probe
          theories near objects
          with strong gravitational
          binding energy. These
          tests are qualitatively
          different from Solar-system
          tests!

          WD: 0.01% of mass
          NS: 10--20% of mass
D. Page   BH: 50% of mass
          is in binding energy.
           Pulsar Timing in a Nutshell

Standard     Measure                       Observed
profile      offset                        profile




     Record the start time of the observation with the
      observatory clock (typically a maser).
     The offset gives us a Time of Arrival (TOA) for
      the observed pulse.
     Then transform to Solar System Barycentre,
      enumerate pulses and fit the timing model.
           Pulsars available for GR tests




                                            Young
                                            pulsars




Recycled
pulsars
MSPs are often very stable, nearly as good as
atomic clocks on timescales of years.

This should allow the use of an array of them
to detect gravitational waves.

This is the goal of the International Pulsar
Timing Array – European, Australian and
North American collaborations.
    Equivalence Principle Violations

Pulsar timing can:
  set limits on the Parametrized
   Post-Newtonian (PPN) parameters α1, α3 (, ζ2)
  test for violations of the Strong Equivalence
   Principle (SEP) through
     - the Nordtvedt Effect
     - dipolar gravitational radiation
     - variations of Newton's constant
(Actually, parameters modified to account for
compactness of neutron stars.)
(Damour & Esposito-Farèse 1992, CQG, 9, 2093; 1996, PRD, 53, 5541).
SEP: Nordtvedt (Gravitational Stark) Effect

 Lunar Laser Ranging: Moon's orbit is not polarized toward Sun.
                                                 Constraint:   (4.4  4.5) 10
                                                                                         4
                   10         2     2    1
  4    3         1   2  1   2
                    3         3     3    3       (Williams et al. 2009, IJMPD, 18, 1129)


                                                    
                                                 Binary pulsars: NS and WD fall
                                                 differently in gravitational
      WD                     NS                  field of Galaxy.
                                                    m grav 
                                                    inertial  1  i
                                                   m         
                                                         E grav  E grav 2
                                                    1         
                                                                              ...
                                                          mi   mi 


   Result is a polarized orbit.                  Constrain Δnet = ΔNS -ΔWD
                                                (Damour & Schäfer 1991, PRL, 66, 2549.)
                Deriving a Constraint on Δnet

                                        Use pulsar—white-dwarf binaries
                                         with low eccentricities ( <10-3).
                                        Eccentricity would contain a “forced”
                                         component along projection of
                                         Galactic gravitational force onto
                                         the orbit. This may partially
                                         cancel “natural” eccentricity.
 After Wex 1997, A&A, 317, 976.


Constraint ∝ Pb2/e. Need to estimate orbital inclination and masses.
Formerly: assume binary orbit is randomly oriented on sky.
Use all similar systems to counter selection effects (Wex).
Ensemble of pulsars: Δnet < 9x10-3 (Wex 1997, A&A, 317, 976; 2000, ASP Conf. Ser.).
Now: use information about
longitude of
periastron (previously
unused) and measured
eccentricity and a Bayesian
formulation to construct
pdfs for Δnet for each
appropriate pulsar,
representing the full
population of similar objects.
                                          Gonzalez et al., in prep.
Result: |Δnet| < 0.0045 at 95% confidence (Gonzalez
et al, nearly submitted, based on method used in
Stairs et al. 2005).
           Constraints on α1 and α3
α1: Implies existence of preferred frames.
Expect orbit to be polarized along projection of velocity (wrt CMB)
onto orbital plane. Constraint ∝ Pb1/3/e.
     Ensemble of pulsars: α1 < 1.4x10-4 (Wex 2000, ASP Conf. Ser.).
     Comparable to LLR tests (Müller et al. 1996, PRD, 54, R5927).
     This test now needs updating with Bayesian approach...

α3: Violates local Lorentz invariance and conservation of
momentum. Expect orbit to be polarized, depending on cross-
product of system velocity and pulsar spin. Constraint ∝ Pb2/(eP),
same pulsars used as for Δ test.
    Ensemble of pulsars: α3 < 5.5x10-20 (Gonzalez et al. in prep.;
slightly worse limit than in Stairs et al. 2005, ApJ, 632, 1060, but
more information used).
    (Cf. Perihelion shifts of Earth and Mercury: ~2x10-7 (Will 1993,
“Theory & Expt. In Grav. Physics,” CUP))
                      Orbital Decay Tests

    These rely on measurement of or
                                             Ý
    constraint on orbital period derivative, Pb .
    This is complicated by systematic biases:
Pb 
  Ý              Pb 
                   Ý          Pb  Pb  Pb 
                                Ý        Ý        Ý                 Pb 
                                                                      Ý
                                            
Pb           Pb Accel Pb Ý Pb m Pb              Pb Dipolar
      Observed                      G         Ý
                                                        
                                                      Quadrupolar

Pb 
  Ý         Pb 
              Ý                      Pb 
                                       Ý
                            
Pb        P gravitational field Pb 
      Accel  b                         Shklovskii

P 
  Ý                 2 d
   b
             
Pb 
      Shklovskii
                      c
         Dipolar Gravitational Radiation
Difference in gravitational binding energies of NS and WD implies
dipolar gravitational radiation possible in, e.g., tensor-scalar theories.

              4  2G* m1m2
                             c1   c2 
                                          2   Damour & Esposito-Farèse
   Ý
   Pb Dipole  3                              1996, PRD, 54, 1474.
               c Pb m1  m2

  Test using pulsar—WD systems in short-period orbits. Examples:
  PSR B0655+64, 24.7-hour orbit:
          cp   0  < 2.7x10 (Arzoumanian 2003, ASP Conf. Ser. 302, 69).
                      2         -4

  PSR J1012+5307, 14.5-hour orbit:
          cp   0  < 6x10-5 (Lazaridis et al. 2009, MNRAS 400, 805).
                      2


                                           Ý
  PSR J0751+1807, 6.3-hour orbit: Pb measurement in Nice et al.
       2005 ApJ 634, 1242 has major revision with more data.
  

                             
                    PSR J1141-6545
Young pulsar with a white-dwarf companion, eccentric, 4.45-hour orbit
                                               Ý
                                     ω, γ and Pb measured
                                     through timing. Sin i
                                     measured by scintillation.
                                     
                                     Because of eccentricity, dipolar
                                     radiation predictions can be large.

                                     Agreement with GR here sets
                                     limits of  0  2.1105 for
                                                   2

                                     weakly nonlinear coupling and
                                       0  3.4 106 for strongly
                                        2

                                     nonlinear coupling (Bhat et al
                                       
  Bhat et al PRD 77, 124017 (2008)   2008).
                               
    Orbital decay tests rely on measurement of or
                                             Ý
    constraint on orbital period derivative, Pb .

    This is complicated by systematic biases:

Pb 
  Ý              Pb 
                   Ý          Pb  Pb  Pb 
                                Ý        Ý         Ý                Pb 
                                                                      Ý
                                          
Pb 
      Observed   Pb Accel Pb Ý Pb m Pb 
                                    G         Ý       Quadrupolar   Pb Dipolar
Pb 
  Ý         Pb 
              Ý                      Pb 
                                       Ý
                            
Pb        P gravitational field Pb 
      Accel  b                         Shklovskii

P 
  Ý                 2 d
   b
             
Pb 
      Shklovskii
                      c
               Variation of Newton's Constant
 Spin: Variable G changes moment of inertia of NS.
                Ý Ý
       Expect P G depending on equation of state, PM correction...
                        
                    P       G                   Ý
                                                G
        Various millisecond pulsars, roughly:  2 1011 yr1
                                                G
                         Ý Ý
                         Pb G
Orbital
        decay: Expect           , test with circular NS-WD binaries.
                         Pb G
                                   Ý
                                 G  (1.3  2.7) 1011 yr1
   PSR B1855+09, 12.3-day orbit: G
   (Kaspi, Taylor & Ryba 1994, ApJ, 428, 713; Arzoumanian 1995, PhD thesis, Princeton).
                                                    Ý
                                                      G
                                                         (1.5  3.8) 1012 yr1
   PSR J1713+0747, 67.8-dayorbit:                   G
   (Splaver et al. 2005, ApJ, 620, 405, Nice et al. 2005, ApJ, 634, 1242).
                                                       Ý
                                                       G
                            
   PSR J0437-4715, 5.7-day orbit:                         (0.5  2.6) 1012 yr1
                                                       G
   (Verbiest et al 2008, ApJ 679, 675, 95% confidence, using slightly different assumptions).
                                                                      Ý
                                                                      G
   Not as constraining as LLR (Williams et al. 2004, PRL 93, 361101):    (4  9) 1013 yr1
                                                                    G
                   Ý
 Combined Limit on G and
          Dipolar Gravitational Radiation



                                                     Ý
     Lazaridis et al. 2009 (MNRAS 400, 805) combine thePb limits
     from J1012+5307 and J0437-4715 to form a combined limit
     on these two quantities:
                                                
            Ý
            G                   12 1
               (0.7  3.3) 10 yr
            G
                 ( cp   0 )2
     and    D         2
                                (0.3  2.5) 103

                      S

                Relativistic Binaries
Binary pulsars, especially double-neutron-star systems:
measure post-Keplerian timing parameters in a
theory-independent way (Damour & Deruelle 1986, AIHP, 44, 263).
These predict the stellar masses in any theory of gravity.
In GR:
           Pb 5 / 3
       3  T0 M    e 2 
                         2/3      1
     Ý                       1
           2 
          Pb  3 2 / 3 4 / 3
                1/

       e  T0 M m2 m1  2m2 
          2 
                       5 / 3
            192 Pb   73 2 37 4 
                                        
                              1 e  e 1  e 2  T0 5 / 3 m1m2 M 1/ 3
                                                  7 / 2
       Ý
      Pb          
              5 2   24       96 
      r  T0 m2
           Pb 2 / 3 1/ 3 2 / 3 1
      s  x  T0 M m2
           2 

      M  m1  m2
     T0  4.925490947s
      The Original System: PSR B1913+16

                                                      Highly eccentric double-NS
                                                      system, 8-hour orbit.

                                                      The  and γ parameters
                                                          Ý
                                                      predict the pulsar and
                                                      companion masses.
                                                 
                                                         Ý
                                                     The Pb parameter is in
                                                     good agreement, to ~0.2%.
                                                     Galactic acceleration
                                                   modeling now limits this test.

Weisberg & Taylor 2003, ASP Conf. Ser. 302, 93
(Courtesy Joel Weisberg)
Orbital Decay of PSR B1913+16


                The accumulated shift of
                periastron passage time,
                caused by the decay of
                the orbit.
                A good match to the
                predictions of GR!




               Weisberg, Nice & Taylor, 2010
               (Courtesy Joel Weisberg)
                                          Mass-mass diagram for
                                          the double pulsar
                                          J0737-3039A and B.
                                          In addition to 5 PK
                                          parameters (for A), we
                                          measure the
                                          mass ratio R. This
                                          is independent of
                                          gravitational theory
                                          ⇒ whole new
                                          constraint on gravity
                                          compared to other
                                          double-NS systems.
As of July 2010; Kramer et al. in prep.
     Numbers reported in 2006 (Kramer et al, Science):
     We can use the measured values of R = 0.9336±0.0005
     and  = 16.8995±0.0007 o/year to get the masses and
          Ý
     then compute the other parameters as expected in GR:
     Expected in GR:             Observed:

     γ = 0.38418(22) ms          γ = 0.3856 ± 0.0026ms
     P = -1.24787(13)×10-12
     Ý
     b                           P = (-1.252 ± 0.017)×10-12
                                 Ý
                                 b

     r = 6.153(26) ms             r = 6.21 ± 0.33 ms
                                             0.00016
                0.00013
     s  0.999870.00048       s  0.999740.00039
                                 Pb 
                                   Ý
                                          104   Deller et al 2008, Science
     In particular:              Pb 
                                       Accel



         obs
                               This was a 0.05% test of
     s                           strong-field GR – now down to
             0.99987 0.00050
     s pred                    a ~0.02% test!
         Using Multiple Pulsars


                             Strong constraints on
                             parameters in
                             alternate theories can be
                             achieved by combining
                             information from multiple
                             pulsars plus solar-system
                             tests (Damour &
                             Esposito-Farese).



Damour and Esposito-Farese
          Geodetic Precession

Precession of either NS's spin axis about
the total (~ orbital) angular momentum.
Why would we expect this?

Before the second
supernova:
all AM vectors
aligned.
Before the second
supernova:
all AM vectors
aligned.

After second supernova:
orbit tilted,
misalignment angle δ
(shown for recycled A);
B spin pointed
elsewhere (defined
by kick?).
                            Geodetic Precession
Precession period: 300 years for B1913+16, 700 years for B1534+12,
265 years for J1141-6545 and only ~70 years for the J0737-3039 pulsars.


                                             Observed in B1534+12
                                             (Arzoumanian 1995)
                                             and measured by
                                             comparison to
                                             orbital aberration:
                                                                   0.48 o/yr
                                               spin
                                                1       0.44      0.16

                                             (68% confidence)
                                             cf GR prediction:
 Observed in PSR B1913+16,                   0.51 o/yr
 (Weisberg et al 1989, Kramer 1998)        (Stairs et al 2004)
 which will disappear ~2025.
 Kramer 1998
What about the double pulsar?

There appear to be no changes
in A's profile (Manchester
et al 2005, Ferdman et al 2008).


This starts to put strong
constraints on the
misalignment angle:
<37o for one-pole model,
<14o for two-pole model
(95.4% confidence limits,
Ferdman PhD thesis, UBC 2008;
plot updated to 2009).
     But B has changed a lot....
      and has now disappeared completely!

Dec. 2003




                                                   Jan. 2009



                             Perera et al., 2010
B's effects on A
provide another
avenue to precession:

Eclipses of A by B
occur every orbit
(Lyne et al 2004,
Kaspi et al 2004).
A's flux is
modulated by the
dipolar emission
from B.
                        McLaughlin et al. 2004a
See Lyutikov &
Thompson 2005
for a simple
geometrical model,
illustrated here for
April 2007 data
by Breton et al. 2008.
René Breton
See Lyutikov &
Thompson 2005
for a simple
geometrical model,
illustrated here for
April 2007 data
by Breton et al. 2008.

This model makes
concrete
predictions if B
precesses...
           Eclipse geometry, Breton et al 2008.
           If B precesses, ϕ will change with
           time, and the structure of the
           eclipse modulation should also
           change... and it does!


         Dec. 2003



         Nov. 2007


Courtesy René Breton
The angles α and θ stay
constant, but ϕ
changes at a rate of
4.77+0.66-0.65o yr-1. This is
nicely consistent with the
rate predicted by GR:
5.0734(7) o yr-1.

And because we measure
both orbital semi-major
axes, this actually constrains
a generalized set of
gravitational strong-field
theories for the first time!     Breton et al 2008
          Preferred-frame effects with double-NS
          systems




Wex & Kramer 2007


Wex & Kramer showed that pulsars similar to the double pulsar
are sensitive to preferred-frame effects (within semi-conservative
theories) via their orbital parameters. Here they show that the
double pulsar (left), a similar system at the Galactic centre
(middle) and their combination can lead to strong constraints on
the directionality of the preferred frame (PFE antenna).
              Future Telescopes
                        The Galactic Census with the
                        Square Kilometre Array
                        should provide:
                        ~30000 pulsars
                        ~1000 millisecond pulsars
                        ~100 relativistic binaries
                        1—10 pulsar – black-hole
                           systems.


With suitable PSR—BH systems, we may be able to
               c spin
measure the BH 2 S                        c4 Q
                          and quadrupoleqmoment
                                        2 3
               GM                         G M
, testing

                    q   2
the Cosmic Censorship conjecture and
                                 
the No-hair theorem        .
  Pulsar with 100 μs timing precision in 0.1-year, eccentricity 0.4
  orbit around Sgr A*: weekly observations over 3 years lead to a
  measurement of the spin (via frame-dragging) and quadrupole
  moment (below) to high precision, assuming Sgr A* is an extreme
  Kerr BH.
Wex et al., in prep.


                                                 ΔS/S ~ 10-4...10-3




                                                ΔQ/Q = 0.008


                                                  The challenge
                                                  will be finding
                                                  such pulsars!!
                Future Prospects
Long-term timing of pulsar – white dwarf systems
                   Ý
⇒ better limits on G /G and dipolar gravitational radiation, as
   well as PPN-type parameters
⇒ better limits on gravitational-wave background
Long-term timing of relativistic systems
          
⇒ improved tests of strong-field GR.
                                            
Potential to measure higher-order terms inÝ in 0737A: we may be
able to measure the neutron-star moment of inertia!
Profile changes and eclipses in relativistic binaries
⇒ better tests of precession rates, geometry determinations.
Large-scale surveys, large new  telescopes...
⇒ more systems of all types... and maybe some new “holy grails”
such as a pulsar—black hole system... stay tuned!
α3 can also be tested by isolated pulsars.
Self-acceleration and Shklovskii effect contribute to observed
period derivatives:




Physics,”CUP).
                Constraints on α3 (and ζ2)




1996, CQG, 13, 3121).




so not really a good test.
                            ˙
                            P = n a self

                             ˙
                               3
                                   P
                                   c
                                    ⋅
                             P pm = P 2
                                        d
                                        c

Young pulsars: α3 < 2x10-10 (Will 1993, “Theory & Expt. In Grav.

Millisecond pulsars: α3 < ~10-15 (Bell 1996, ApJ, 462, 287; Bell & Damour


α3+ζ2 also accelerate the CM of a binary system ⇒ variable P
                                                                    .
in eccentric PSR B1913+16: (α3+ζ2) < 4x10-5 (Will 1992, ApJ, 393, L59).
But geodetic precession and timing noise can mimic this effect,
                        PSR B1534+12

                                            Measure same parameters as
                                            for B1913+16, plus Shapiro
                                            delay.

                                            The parameters ˙ , s and γ
                                            form a complementary test
                                            of GR.

                                                             ˙
                                            The measuredP b contains
                                            a large Shklovskii v2/d
                                            contribution. If GR is correct,
                                            the distance to the pulsar is
After Stairs 2005, ASP Conf. Ser. 328, 3.
                                            1.05 ± 0.05 kpc.
What about the double pulsar?

Geodetic precession
appears not
to be happening
in 0737A, despite
short 75-year period.

No pulse shape
changes over 14.5
months, plus back to
discovery observation
(Manchester et al 2005).
But B has shown evidence of
orbital (likely due to A)
changes and long-term (likely
precession) changes from the
start.

Burgay et al. 2005
See Lyutikov &
Thompson 2005
for a simple
geometrical model,
illustrated here for
April 2007 data
by Breton et al. 2008.

				
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