pulsar - white dwarf binaries as gravity labs

Pulsar White Dwarf Binaries as Gravity LabsJohn AntoniadisDunlap Institute, University of Toronto

14th Marcel Grossmann Meeting

(1) Quasi-stationary weak-field regime

(2) Quasi-stationary strong-field regime

(3) Radiative regime

(4) Highly relativistic regime

Solar system experiments

Binary pulsar experiments

Future GW astronomy

Gravity Regimes

Relativistic Effects in Binary Pulsars

‣Advance of Periastron


‣Time delation



‣Time delation


‣Gravitational Radiation


‣Time delation


‣Shapiro delay


B

A


‣Time delation


‣Shapiro delay

‣Relativistic spin precession



The Hulse-Taylor Binary

Orbital Decay was first detected in the Hulse-Taylor binary

Rate is -2.4085(52) x 10-12 s/s. The agreement with GR prediction is perfect!

GR GIVES A SELF-CONSISTENT ESTIMATE FOR THE MASSES OF THE TWO COMPONENTS OF THE BINARY

...but NOT the only one!!!

...and NOT the most precise!

Detected in 9 binary pulsars

TOA residual

model

fold fold

Session i Session j

Pulsar Timing

KP: Orbital Period Eccentricity Inclination

Epoch of periastron Longitude of periastron Longitude of ascension Projected semi-major axis

PK: Precession of periastron ‘‘Einstein” delay Shapiro-delay “range”

Shapiro-delay “shape” Spin precession Orbital decay

D. Champion

PK = f(K;mp,mc)

Parametrized post-Keplerian formalism

For a wide class of gravity theories:

(Damour 1988, Damour & Taylor 1992 )


! = 3

✓Pb

2⇡

◆�5/3

(T�M)2/3(1� e2)�1

�E = e

✓Pb

2⇡

◆1/3

T 2/3� M�4/3mc(mp + 2mc)

Pb = �192⇡

5

✓1 +

73

24e2 +

37

96e4◆(1� e2)�7/2T�5/3

� mpmcM�1/3

r = T�mc s = sin i

In General Relativity:

PK = f(K;mp,mc)




!


! = 3

✓Pb

2⇡

◆�5/3

(T�M)2/3(1� e2)�1

�E = e

✓Pb

2⇡

◆1/3

T 2/3� M�4/3mc(mp + 2mc)

Pb = �192⇡

5

✓1 +

73

24e2 +

37

96e4◆(1� e2)�7/2T�5/3

� mpmcM�1/3



PK = f(K;mp,mc)




!

�E


! = 3

✓Pb

2⇡

◆�5/3

(T�M)2/3(1� e2)�1

�E = e

✓Pb

2⇡

◆1/3

T 2/3� M�4/3mc(mp + 2mc)

Pb = �192⇡

5

✓1 +

73

24e2 +

37

96e4◆(1� e2)�7/2T�5/3

� mpmcM�1/3



PK = f(K;mp,mc)




!

�E

Pb


! = 3

✓Pb

2⇡

◆�5/3

(T�M)2/3(1� e2)�1

�E = e

✓Pb

2⇡

◆1/3

T 2/3� M�4/3mc(mp + 2mc)

Pb = �192⇡

5

✓1 +

73

24e2 +

37

96e4◆(1� e2)�7/2T�5/3

� mpmcM�1/3



The Double Pulsar: PSR J0737-3039A/BPreliminary results (Kramer et al., in prep.)

[Burgay et al. 2003, Lyne et al. 2004 ]

1032 WEISBERG, NICE, & TAYLOR Vol. 722

Table 3Orbital Parameters

Parameter Valuea

T0 (MJD) 52144.90097841(4)x ≡ a1 sin i (s) 2.341782(3)e 0.6171334(5)Pb (d) 0.322997448911(4)ω0 (deg) 292.54472(6)⟨ω⟩ (deg yr−1) 4.226598(5)γ (ms) 4.2992(8)Pb −2.423(1) ×10−12

Note.a Figures in parentheses represent estimated uncer-tainties in the last quoted digit. The estimated uncertain-ties range from (2–6)× the formal fitted uncertainties, inorder to reflect also the variations resulting from differentassumptions regarding timing noise, etc.

appropriate expressions for ⟨ω⟩ and γ are

⟨ω⟩ = 3G2/3c−2(Pb2π )−5/3(1 − e2)−1(m1 + m2)2/3

= 2.113323(2)!

(m1 + m2)M⊙

"2/3

deg yr−1, (1)

γ = G2/3c−2e(Pb/2π )1/3m2(m1 + 2m2)(m1 + m2)−4/3

= 0.002936679(2)

#m2(m1 + 2m2)(m1 + m2)−4/3

M2/3⊙

$

s.

(2)

In the second line of each equation we have substituted valuesfor Pb and e from Table 3, and used the constants GM⊙/c3 =4.925490947 × 10−6 s and 1 Julian yr = 86400 × 365.25 s.The figures in parentheses represent uncertainties in the lastquoted digit, determined by propagating the uncertainties listedin Table 3. In each case, the uncertainties are dominated by theexperimental uncertainty in orbital eccentricity, e.

Equation (1) may be solved for the total mass ofthe PSR B1913+16 system, yielding M = m1 + m2 =2.828378±0.000007 M⊙. The additional constraint provided byEquation (2) permits a solution for each star’s mass individually,m1 = 1.4398 ± 0.0002 M⊙ and m2 = 1.3886 ± 0.0002 M⊙. Asfar as we know, these are the most accurately determined stellarmasses outside the solar system. It is interesting to note thatsince the value of Newton’s constant G is known to a fractionalaccuracy of only 1 × 10−4, M can be expressed more accuratelyin solar masses than in grams.

3.3. Gravitational Radiation Damping

According to general relativity a binary star system shouldradiate energy in the form of gravitational waves. Peters &Matthews (1963) showed that the resulting rate of change inorbital period should be

P GRb = − 192 π G5/3

5 c5

%Pb

2π

&−5/3 %1 +

7324

e2 +3796

e4&

× (1 − e2)−7/2 m1 m2 (m1 + m2)−1/3

= −1.699451(8) × 10−12

#m1m2(m1 + m2)−1/3

M5/3⊙

$

.

(3)

Inserting values obtained for m1 and m2 and propagatinguncertainties appropriately, we obtain the general relativistic

predicted value

P GRb = −2.402531 ± 0.000014 × 10−12. (4)

Equations (3) and (4) apply in the orbiting system’s referenceframe. Relative acceleration of that frame with respect tothe solar system barycenter will cause a small additionalcontribution to the observed Pb. Damour & Taylor (1991)presented a detailed discussion of this effect and other possiblecontributions to Pb. Recent progress in determining the galactic-structure parameters allows us to update the relevant quantitiesand compute a new value for the kinematic correction to Pb.Using R0 = 8.4 ± 0.6 kpc for the distance to the galactic centerand Θ0 = 254 ± 16 km s−1 for the circular velocity of thelocal standard of rest (Ghez et al. 2008; Gillessen et al. 2009;Reid et al. 2009), and d = 9.9 ± 3.1 kpc for the pulsar distance(Weisberg et al. 2008), we obtain the kinematic contribution,∆Pb,gal:

∆Pb,gal = −0.027 ± 0.005 × 10−12. (5)

Thus, we find the ratio of the observed-to-predicted rate oforbital period decay to be

Pb − ∆Pb,gal

P GRb

= 0.997 ± 0.002. (6)

Agreement between the observed orbital decay and the generalrelativistic prediction is illustrated in Figure 2, which showshow excess orbital phase (relative to an unchanging orbit) hasaccumulated since the pulsar’s discovery in 1974. We note thatthe overall experimental uncertainty embodied in Equation (6)is now dominated by uncertainties in the galactic parametersand pulsar distance, not the pulsar timing measurements. Evenbetter agreement between the observed and expected valuesof Pb would be obtained if the true value of R0 or d wereslightly smaller, or Θ0 slightly larger. For example, observedand expected values agree if d = 6.9 kpc, which is within theWeisberg et al. (2008) error envelope. It will be interesting tosee whether improved future estimates of these quantities willshow one or more of these conditions to be true.

4. OTHER RELATIVISTIC EFFECTS

Two other relativistic phenomena are potentially measurablein the PSR B1913+16 system: geodetic precession and gravita-tional propagation delay. Spin–orbit coupling should cause thepulsar’s spin axis to precess (Damour & Ruffini 1974; Barker& O’Connell 1975a, 1975b), which should lead to observablepulse shape changes. Weisberg et al. (1989) first detected suchchanges, which were observed and modeled further by Kramer(1998). Weisberg & Taylor (2002) and Clifton & Weisberg(2008) found that the pulsar beam is elongated in the latitudedirection and becomes wider in longitude with increasing dis-tance from the beam axis in latitude. These models suggest thatin the next decade or so, precession may move the beam farenough that the pulsar will become unobservable from Earth forsome decades, before eventually returning to view.

The excess propagation delay (Shapiro 1964) caused by thepassage of pulsar signals through the curved spacetime ofthe companion is largest at the pulsar’s superior conjunction.The maximum amplitude varies with time because the impactparameter at superior conjunction strongly depends on thecurrent value of ω. In this respect, the orbital geometry wasparticularly unfavorable in the mid-1990s (see Damour & Taylor





Parameter Valuea




⟨ω⟩ = 3G2/3c−2(Pb2π )−5/3(1 − e2)−1(m1 + m2)2/3

= 2.113323(2)!

(m1 + m2)M⊙

"2/3

deg yr−1, (1)

γ = G2/3c−2e(Pb/2π )1/3m2(m1 + 2m2)(m1 + m2)−4/3

= 0.002936679(2)

#m2(m1 + 2m2)(m1 + m2)−4/3

M2/3⊙

$

s.

(2)





P GRb = − 192 π G5/3

5 c5

%Pb

2π

&−5/3 %1 +

7324

e2 +3796

e4&

× (1 − e2)−7/2 m1 m2 (m1 + m2)−1/3

= −1.699451(8) × 10−12

#m1m2(m1 + m2)−1/3

M5/3⊙

$

.

(3)


predicted value

P GRb = −2.402531 ± 0.000014 × 10−12. (4)


∆Pb,gal = −0.027 ± 0.005 × 10−12. (5)


Pb − ∆Pb,gal

P GRb

= 0.997 ± 0.002. (6)





0.05%





Parameter Valuea




⟨ω⟩ = 3G2/3c−2(Pb2π )−5/3(1 − e2)−1(m1 + m2)2/3

= 2.113323(2)!

(m1 + m2)M⊙

"2/3

deg yr−1, (1)

γ = G2/3c−2e(Pb/2π )1/3m2(m1 + 2m2)(m1 + m2)−4/3

= 0.002936679(2)

#m2(m1 + 2m2)(m1 + m2)−4/3

M2/3⊙

$

s.

(2)





P GRb = − 192 π G5/3

5 c5

%Pb

2π

&−5/3 %1 +

7324

e2 +3796

e4&

× (1 − e2)−7/2 m1 m2 (m1 + m2)−1/3

= −1.699451(8) × 10−12

#m1m2(m1 + m2)−1/3

M5/3⊙

$

.

(3)


predicted value

P GRb = −2.402531 ± 0.000014 × 10−12. (4)


∆Pb,gal = −0.027 ± 0.005 × 10−12. (5)


Pb − ∆Pb,gal

P GRb

= 0.997 ± 0.002. (6)





0.05%



See talks by Rene Breton and Marcel Kehl for more details

The Double Pulsar: PSR J0737-3039A/BKramer et al. 2006

Beyond the Double Pulsar

There are several orbital effects predicted by alternative theories of gravity that depend on the difference of the compactness between the two objects of the binary Hard to detect in DNSs

[Damour & Esposito-Farèse, PhR 1993, PhRD 1996]

E.g. when gravity is mediated by additional fields (tensor, vector, scalar...)

Violation of the Strong Equivalence Principle that results in emission of dipolar gravitational radiation

Beyond the Double Pulsar

There are several orbital effects predicted by alternative theories of gravity that depend on the difference of the compactness between the two objects of the binary Hard to detect in DNSs

[Damour & Esposito-Farèse, PhR 1993, PhRD 1996]

Example: Scalar-Tensor Gravity: Gravity mediated by Tensor+Scalar Fields

gµ⌫ = g⇤µ⌫A(�) = g⇤µ⌫(2↵0�+ �0�2 + . . . )field-dependent coupling with matter:

Dipole Radiation

We need Pulsar-White Dwarf systems with short orbits to test it!!!

Problem: Suitable systems are rare!

Only a handful of relativistic systems with Pb < 1 day

Difficult to constraint the masses!

PSR J1012+5307 (Lazaridis et al. MNRAS, 2009, Caballero et al. in prep.) PSR J1738+0333 (JA et al. MNRAS, 2012, Freire et al. MNRAS 2012) PSR J0348+0432 (JA et al. Science, 2013)

PSR J1738+0333

Freire et al. MNRAS 2012

✴ Millisecond pulsar (spin period ~5.8 ms)

✴ Binary: white dwarf companion, orbital period ~ 8.5 hours

✴ Discovered in 2001 with the Parkes telescope

✴ Timed with Arecibo and Effelsberg

Pspin = 0.005850095859775683± 0.000000000000000005 s

Pspin = (2.411991± 0.000014)⇥ 10�20 s s�1

x = 0.343429130± 0.000000017 ls

Pb = 0.3547907398724± 0.0000000000013 days

e = 0.00000034± 0.00000011

Pb = �0.0000000000000259± 0000000000000032 s s�1

(µ↵, µ�) = (+7.037± 0.005,+5.073± 0.012)mas yr�1

⇡x

= 0.68± 0.05

PSR J1738+0333


q =MPSR

MWD= 8.1± 0.2

Te↵ = 9130± 150K

log g = 6.55± 0.10

PSR J1738+0333

Gemini-S

Keck

Model

Gemini - Model

JA et al. MNRAS 2012

MWD = 0.181+0.007�0.005 M�

RWD = 0.037+0.004�0.003 R�

mc

Pb.

Pb.

mc

qq

PSR J1738+0333

Models calibrated against observations of PSR J1909-3744 for which independent measurements of mass and radius are available from pulsar-timing [JA, 2013] + lot’s of follow-up work.... JA & van Kerkwijk 2015. Istrate, Tauris, Langer & JA, 2014a Istrate, Tauris & JA, 2015, in prep

MNS = 1.46+0.06�0.05 M�

JA et al. MNRAS 2012

LLR

LLR

SEP

J1141–6545

B1534+12

B1913+16J0737–3039

J1738+0333

−6 −4 −2 2 4 60

0

0

0|

10

10

10

10

10

Cassini

PSR J1738+0333

↵p = ↵p(↵0;�0; EOS)

A(�) = exp[↵0(�� 0) +1

2

�0(�� 0)2+ . . . ]

PXSb = P Int

b � PGRb = +2.0+3.7

�3.6 ⇥ 10�15

P Intb /PGR

b = 0.93± 0.13

“Excess” orbital decay:

Gives a limit on:


LIGO/VIRGO

LLR

LLR

SEP

J1141–6545

B1534+12

B1913+16J0737–3039

J1738+0333

−6 −4 −2 2 4 60

0

0

0|

10

10

10

10

10

Cassini

PSR J1738+0333

↵p = ↵p(↵0;�0; EOS)

A(�) = exp[↵0(�� 0) +1

2

�0(�� 0)2+ . . . ]

PXSb = P Int

b � PGRb = +2.0+3.7

�3.6 ⇥ 10�15

P Intb /PGR

b = 0.93± 0.13

“Excess” orbital decay:

Gives a limit on:


LIGO/VIRGO

See talk by Anne Archibald for potential improvements

Limits on TeVeS

Tensor-Vector-Scalar theories (based on Bekenstein’s 2004 TeVeS theory) can also be constrained, but in this case J1738 is not enough.

Pulsar-WD binaries are insensitive to original TeVeS but the double pulsar can constraint regions near the linear coupling

TeVeS and all non-linear friends may soon be proven to be unnaturally fine-tuned theories


Tensor-Vector-Scalar theories (based on Bekenstein’s 2004 TeVeS theory) can also be constrained, but in this case J1738 is not enough.

Pulsar-WD binaries are insensitive to original TeVeS but the double pulsar can constraint regions near the linear coupling

TeVeS and all non-linear friends may soon be proven to be unnaturally fine-tuned theories

Courtesy of G. Esposito-Farese

Limits on TeVeS

Discovery & basic parameters: Lynch et al. ApJ, V. 763, p. 81 (2013) Astro-ph:1209:4296

Pb ⇠ 2.46 h

Pspin ⇠ 39 ms

Mc � 0.08 M�

PSR J0348+0432

PSR J0348+0432

PSR B1913+16

PSR J0737-3039A/B

Sun

PSR J0348+0432

N. Wex

KWD = 351± 4 km s�1

KPSR = 30.008235± 0.00016 km s�1

q ⌘ MPSR/MWD = KWD/KPSR

= 11.70± 0.13

PSR J0348+0432

JA et al. Science, 2013

Te↵ = (10130± 30stat ± 65sys) K

log g = (6.045± 0.032stat ± 0.065sys)

PSR J0348+0432


MWD = 0.172± 0.003 M�

0.165 � 0.185 M� (99.72% C.L.)

MPSR = 2.01± 0.04 M�

1.90 � 2.15 M� (99.72% C.L.)

PSR J0348+0432


PSR J0348+0432

PSR J0348+0432

↵p = 1 =) Pb = �110 000 µs/yr

GR =) Pb = �8.2 µs/yr

Observations =) Pb = �8.6± 1.4 µs/yr

Solar SystemJ1738+0333

PSR J0348+0432

Einstein-Aether and Hořava gravity

Yagi et al, PRD 2014

See talk by Diego Blas for details

PSR J0348+0432

MWD MWD

P.b

P.b qq

PSR J0348+0432

P.bP

.b

MWD MWD

q q

PSR J0348+0432

April 2014

Will 1994, Damour & Esposito-Farèse PhR D (1998)

PSR J0348+0432

General Relativity

+ DipolarΔN


With current constraints: We lose less than half a circle!

6 8 10 12 14 16 18 200.0

0.5

1.0

1.5

2.0

2.5

3.0

Radius @km D

Mass@S

olarMassesD

GRCausality

Rotation

Quark Matter

FPS GS1AP3

PSR J0348+0432

qLMXBs+PRE+J0348

Data from Steiner et al. 2013

Constraints on the Equation of State

6 8 10 12 14 16 18 200.0

0.5

1.0

1.5

2.0

2.5

3.0

Radius @km D

Mass@S

olarMassesD

GRCausality

Rotation

Quark Matter

FPS GS1AP3

PSR J0348+0432

>2.3 Msol MSPs?

qLMXBs+PRE+J0348

qLMXBs + PRE + 2.3 Msol

Data from Steiner et al. 2013

Constraints on the Equation of State

Conclusions

‣Improvements in white dwarf modeling and observing techniques have al lowed ~one order-of-magnitude improvement in mass measurements of pulsar-white dwarf systems

‣Mass measurements + radio timing allowed the first high-precision tests for the existence of gravitational dipolar radiation, a prediction of numerous alternatives to GR

‣Null results rule out a large number of GR alternatives

‣PSR J0348+0432 provides a test of GR in a strong-field regime, qualitatively very different from what was available in the past

‣Both PSRs J0348+0432 and J1738+0333 provide strong experimental support for the use of GR-based gravitational-wave templates for the direct detection of GWs with ground-based detectors

Thank you!