Potpourri of Fundamental Physics with Pulsar Binaries

Rene Breton University of Manchester

SKA Bursary Conference 29 November 2017

© SDO/AIA/AEI

© John Rowe AnimationAustralia Telescope National Facility, CSIRO

How Can We Do AstroPHYSICS?

The Sun is a very good blackbody

Astrophysical objects are far away…We rely on ‘spherical cow’ physics a lot!

How Can We Do AstroPHYSICS?

Astrophysical objects are far away…We rely on ‘spherical cow’ physics a lot!

Pulsars in binary systems are almost perfect spherical cows…Nearly perfect clockCompact object

dynamical studiestidal effects negligible

Excellent probes forgravitational studiesnuclear physics at ultra high densityextreme interaction with their environment

Pulsars in a Nutshell

Neutron stars aremacroscopic atoms

stellar massmountain size

faster than kitchen blenderspowerful magnets

Radius ~15 kmMass ~1.4 M⊙

Pspin ~1.399ms - 23.5sBdipole ~108-15 G

Density ~1014 g/cm3

Pulsars are blinking neutron stars visible through the ‘lighthouse’ effect

© Michael Kramer

The Pulsar Family

Two main observables in pulsarsspin periodspin period derivative

Rotating dipoles in vacuumagemagnetic fielddissipated energy

Binaries make 10% of populationfastest spinningoldest pulsars

Studying Gravity

Galileo’s experiment: objects fall at the same speed regardless of their massEquivalence principle: inertial mass = gravitational mass

Studying Gravity

Galileo’s experiment: objects fall at the same speed regardless of their massEquivalence principle: inertial mass = gravitational mass

Some gravitational theories agree with GR in the Solar System, but not around pulsars

Testing the Strong Equivalence Principle

Testing Gravity with Pulsars

© Arpad Horvath (Wikipedia)

Orbital Doppler shift yields Keplerian parameters(orbital period, eccentricity, etc)

masses and orbital inclination are unknown

At large velocity, Newtonian dynamics breaks downNeed ‘post-Keplerian’ parameters

phenomenological orbital perturbationsfor a theory of gravity, link Keplerian parameters and masses

Esposito-Farese (2004)

Examples of Post-Keplerian Parameter

C.M.

Einstein: Erklärung der Perilielbcvvcgiing des Merkur 831

Erklärung der Perihelbewegung des Merkur aus

der allgemeinen Relativitätstheorie.

Von A. Einstein.

In einer jüngst in diesen Berichten erschienenen Arbeit, habe ich Feld-

gleichungen der Gravitation aufgestellt, welche bezüglich beliebiger

Transformationen von der Determinante i kovariant sind. In einemNachtrage habe ich gezeigt, daß jenen Feldgleichungen allgemein

kovariante entsprechen, wenn der Skalar des Energietensors der

"Materie« verschwindet, und ich habe dargetan, daß der Einführungdieser Hypothese, durch welche Zeit und Raum der letzten Spur ob-

jektiver Realität l^eraubt werden, keine prinzipiellen Bedenken ent-

gegenstehend

In der vorliegenden Arbeit finde ich eine wichtige Bestätigung

dieser radikalsten Relativitätstheorie; es zeigt sieh nämlich, daß sie

die von Leverrier entdeckte säkulare Drehung der Merkurbahn imSinne der Bahnbewegung, welche etwa 45" im Jahrhundert beträgt

qualitativ und quantitativ erklärt, ohne daß irgendwelche besondere

Hypothese zugrunde gelegt werden müßte'".

Es ergibt sich femer, daß die Theorie eine stärkere (doppelt so

starke) Lichtstrahlenkrümmung durch Gravitationsfelder zur Konsequenzhat als gemäß meinen früheren Untersuchungen.

' In einer bald folgenden Mitteilung wird gezeigt werden, daß jene Hypotheseentbehrlich ist. Wesentlich ist nur, daß eine solche Wahl des Bezugssystems mög-lich ist, daß die Determinante \g^v\ den Wert — i annimmt. Die nachfolgende Unter-suchung ist hiervon unabhängig.

^ Über die Unmöglichkeit, die Anonuilien der Merklirbewegung auf der Basisder NEWTONSchen Theorie befriedigend /u erkliiren, sciirieb E. Frf.undlilh jüngsteinen beaclUenswerten Aufsatz (Astr. Nachr. 4S03, Bd. 201. Juni 191 5).

Einstein: Erklärung der Perihelbewegung des Merkur 839

(in Sekunden) ein, so erhält man, wenn c die Lichtgeschwindigkeit in

cm/sec. bedeutet:

i r( I — e)

Die Rechnimg liefert für den Planeten Merkur ein Vorschreiten desPerihels um 43" in hundert Jahren, während die Astronomen 45" ±5"als unerklärten Rest zwischen Beobachtungen und NEwxoNscher Theorieangeben. Dies bedeutet volle Übereinstimmung.

Für Erde und Mars geben die Astronomen eine Vorwärtsbewegungvon I I

" bzw. 9" in hundert Jahren an, während unsere Formel nur4" bzw. I

" liefert. Es scheint jedoch diesen Angaben wegen der zugeringen Exzentrizität der Bahnen jener Planeten ein geringer Werteigen zu sein. Maßgebend für die Sicherheit der Konstatierung der

Perihelbewegung ist ihr Produkt mit der Exzentrizität (^-r-)- Be-

trachtet man die für diese Größe von Newcomb angegebenen Wertedn

"In

Merkur .... 8.48" ±0.43Venus — 0.05 ±0.25Erde 0.10+0.13Mars 0.75 ±0.35,

welche ich Hrn. Dr. Freundlich verdanke, so gewinnt man den Eindruck,

daß ein Vorrücken des Perihels überhaupt nur für Merkur wirklich

nachgewiesen ist. Ich will jedoch ein endgültiges Urteil hierüber

gerne den Fachastronomen überlassen.

Precession of orbital periastronDiscovered by Le Verrier in 1859Mercury’s orbit precesses an ‘extra’ 43” per centurySolved by Einstein in 1915

Gravitational redshiftTime dilation near massive objects

C.M.

Evidence of Gravitational Waves

Perturbations of GR field equations imply wave-like solutionsPredicted by Einstein in 1916Carry energyTwo-body orbital shrink over time

Pulsar B1913+16, the first known binary pulsarDiscovered by Hulse and Taylor (1974; Nobel 1993))Double neutron star binaryEvidence of gravitational wave radiation (Taylor et al. 1979)

Wex 2014

Taylor et al. 1979Weisberg & Taylor 2005

The Double Pulsar

© John Rowe AnimationAustralia Telescope National Facility, CSIRO

Kramer et al. (2006), Breton et al. (2008)

A dozen known DNS so farPSR J0737-3039: first and only known pulsar-pulsar system

Pulsar A (23 ms, Burgay et al. 2003)Pulsar B (2.8 s, Lyne et al. 2004)2.4 hour orbit @ e=0.08

Best test of GR in strong-field regime(Kramer et al. 2006)

Theory-independent mass ratio6 post-Keplerian parameters(Kramer et al. 2006, Breton et al. 2008)

Spin-Orbit Coupling

Like in quantum mechanics, spin-orbit couple takes place in GR

‘Geodetic precession’ can be written (Damour & Taylor, 1992, Phys. Rev. D):

In terms of observables:Spin-orbit coupling constant

The Double Pulsar is the only system providing all observables required for a theory independent test of the spin-orbit coupling(Breton et al. 2008)

Strong Equivalence Principle

Mass ratio: radio timing + optical spectroscopy

10 Freire, Wex, Esposito-Farese, Verbiest et al.

mc

Pb.

Pb.

mc

qq

Figure 5. Constraints on system masses and orbital inclination from radio and optical measurements of PSR J1738+0333 and its WDcompanion. The mass ratio q and the companion mass mc are theory-independent (indicated in black), but the constraints from themeasured intrinsic orbital decay (P Int

b , in orange) are calculated assuming that GR is the correct theory of gravity. All curves intersect,meaning that GR passes this important test. Left: cos i–mc plane. The gray region is excluded by the condition mp > 0. Right: mp–mc

plane. The gray region is excluded by the condition sin i ≤ 1. Each triplet of curves corresponds to the most likely value and standarddeviations of the respective parameters.

rived quantities that depend only on the measured TOAsand their uncertainties.

4 GENERIC TESTS OF GRAVITY THEORIES

In order to understand the significance of the small value ofP xsb in eq. (7) — the main experimental result of this paper

— we now discuss what physical effects could in principle becontributing to it. According to Damour & Taylor (1991)

P xsb = P M

b + PTb + PD

b + P Gb , (8)

where P Mb is due to mass loss from the binary, PT

b is a con-tribution from tidal effects, PD

b is the orbital decay causedmainly by the emission of dipolar GWs (and any extramultipole modifying the general relativistic prediction) and

P Gb is a contribution from possible (yet undetected) varia-

tions of Newton’s gravitational constant (as measured by aCavendish experiment). The first two terms are the “classi-cal” terms, the last two would only be non-zero for theoriesof gravity other than general relativity.

4.1 Classical terms

4.1.1 Mass loss

In Appendix A, we derive an upper limit for the mass lossfrom the companion as a function of the total mass of thesystem. For the pulsar, the mass loss is dominated by theloss of rotational energy (Damour & Taylor 1991):

Mp

Mt=

EMtc2

= 1.5× 10−21 s−1, (9)

which is of the same order as the upper limit for Mc

Mt.

The contribution to the orbital variation due to the to-tal mass loss M = Mc + Mp is given by (Damour & Taylor1991):

P Mb = 2

MMt

Pb < 0.2 fs s−1, (10)

which is about 20 times smaller than the current uncertaintyin the measurement of P xs

b .

4.1.2 Tidal orbital decay

We now calculate the orbital decay caused by tides. Fromeqs. (3.15) and (3.19) in Smarr & Blandford (1976), we de-rive the following expression for PT

b :

PTb =

kΩc

3πq(q + 1)

!

RcPb sin ixc

"2 1τs

. (11)

Unlike the expressions in eq. (3.19), this equation is exactbecause it relates the synchronisation timescale τs (whichdescribes the change in the companion angular velocityΩc, τs = −Ωc/Ωc) to the timescale associated with thechange in the orbital period (τp = Pb/P

Tb ) assuming only

conservation of the angular momentum. In this expressionk ≡ Ic/(McR

2c), where Ic is the WD moment of inertia.

White dwarfs (particularly those with a mass much belowthe Chandrasekhar limit) are sustained by the degeneracypressure of non-relativistic electrons and can be well approx-

c⃝ 0000 RAS, MNRAS 000, 000–000

Freire et al. (2012) & Antoniadis et al. (2012)

Optical photometry + spectroscopy

Relativistic orbital decay

PSR J1738+0333 is a pulsar + white dwarf system

System parameters known from radio + optical observations

Strong Equivalence Principle

P xsb = P M

b + PTb + PD

b + P Gb

PDb ' 2 nbTmc

q

q + 1D(spsr scomp)

2 spsr,comp ' /Mpsr,compc2

perte de masse

marées ondes gravitationnelles

dipolaires

changement de la constante de gravitation

spsr 6= scompVery different binding energy

where

The most stringent test of scalar-tensor gravity. 11

Figure 6. Limits on G/G and κD derived from the measurementsof P xs

b of PSR J1738+0333 and PSR J0437−4715. The inner bluecontour level includes 68.3% and the outer contour level 95.4%of all probability. At the origin of coordinates, general relativityis well within the inner contour and close to the peak of proba-bility density. The gray band includes regions consistent with themeasured value and 1-σ uncertainty of G/G from Lunar LaserRanging (LLR). Generally only the upper half of the diagramhas physical meaning, as the radiation of dipolar GWs must nec-essarily make the system lose orbital energy.

imated by a polytropic sphere with n = 1.5. For such stars,we have k = 0.2 (Motz 1952).

The only unknown parameters in this expression areΩc and τs. If τs is much smaller than the characteristic ageof the pulsar τc = 4.1Gyr, then the WD rotation is alreadysynchronised with the orbit (Ωc = nb) and there are no tidaleffects at all. If, on the other hand, τs > τc, then Ωc can bemuch larger, but it must still be smaller than the break-upangular velocity Ωc <

!

GMc/R3c = 0.038 rad s−1. These

conditions for Ωc and τs yield PTb < 1.4 fs s−1. Thus, even

if the WD were rotating near break-up velocity, PTb would

still be smaller than the uncertainty in the measurementof P xs

b . We note, however, that the progenitor of the WDwas very likely synchronised with the orbit. This impliesthat, when the WD formed, its rotational frequency waswithin one order of magnitude of the orbital frequency, i.e.,Ωc ! 2×10−3 rad s−1 (for the reasoning, see, e.g., AppendixB2.2 of Bassa et al. (2006)).

4.2 Test of GR and generic tests of alternative

gravity theories

The smallness of the classical terms implies that the mea-surement of P xs

b (eq. (7)) is a direct test of GR. Unlike

many alternative theories of gravity, GR predicts P Gb = 0,

PDb = 0 and therefore P xs

b = 0. As discussed in Sec-tion 3.3, this is consistent with observations, which meansthat GR passes the test posed by the measurement of P xs

b forPSR J1738+0333. In this respect PSR J1738+0333 consti-tutes a verification of GR’s quadrupole formula with a pre-cision of about 15% at the 1-σ level. In view of more strin-gent tests with other binary pulsars (Kramer et al. 2006;Weisberg, Nice & Taylor 2010) this result by itself does not

seem particularly interesting. However, the large differencein the compactness of the two components of this binarysystem makes PSR J1738+0333 a remarkable laboratory foralternative gravity theories, in particular those which predictthe emission of dipolar gravitational radiation. In Sections5 and 6, we will confront our observations with two specificclasses of gravity theories. In the present section, we follow amore generic approach, valid for gravity theories where non-perturbative strong-field effects are absent and higher-ordercontributions in powers of the gravitational binding energiesof the bodies can be neglected, at least to a point where onedoes not care about multiplicative factors <

∼ 2. As an exam-ple, the well known Jordan-Fierz-Brans-Dicke scalar-tensortheory falls into this group.

Under the assumptions above, we can write for thechange in the orbital period caused by dipolar gravitationalradiation damping in a low-eccentricity binary pulsar system

PDb ≃ −2π nbT⊙mc

qq + 1

κDS2 +O"

s3p,c#

, (12)

where S = sp−sc is the body-dependent term which is givenby the difference in the “sensitivities” of the pulsar, sp, andthe companion, sc [see Will (1993) for the definition of sp,c].The quantity κD is a body-independent constant that quan-tifies the dipolar self-gravity contribution, and takes differ-ent values for different theories of gravity.3 For the purposeof this section, we have neglected higher-order correctionsin powers of the sensitivities in the equation above (Theyactually vanish in the Jordan-Fierz-Brans-Dicke case). Thefull non-linearity will be taken into account in Sections 5and 6 (anticipating on the notation defined there, the terms∝ s3p,c are negligible when the absolute value of the non-linear matter-scalar coupling constant, |β0|, is significantlysmaller than 2).

The value of sp,c depends on the theory of gravity, theexact form of the equation of state and the mass of thepulsar; for a Mp = 1.4M⊙ neutron star, it is generally ofthe order of 0.15, the value we use in our calculations. Foran asymmetric system like PSR J1738+0333, the sensitivityof the companion WD has a negligible value: in the post-Newtonian limit, it is given by ϵ/Mcc

2 ∼ 10−4, where ϵis the gravitational binding energy of the WD (Will 2006).Therefore, S = sp − sc ≃ sp = 0, which implies that ifκD = 0, then there must be emission of dipolar GWs, andan associated orbital decay according to eq. (12). In a doubleneutron star system we would have sp ≈ sc and thereforeS ≈ 0, which means that we should observe PD

b ≈ 0 even ifκD = 0. It is for this reason that, despite the low relativeprecision of the radiative test in PSR J1738+0333, it rep-resents such a powerful constraint on alternative theoriesof gravity (see, e.g. Eardley 1975; Bhat, Bailes & Verbiest2008). Apart from this, the use of optical data is very im-portant because they provide estimates of q and mc that arefree of explicit strong field effects — unlike in the case of thebinary pulsar PSR B1913+16 (see Weisberg, Nice & Taylor2010), or for many of the parameters of the double pulsar(Kramer et al. 2006).

3 In general scalar-tensor theories of gravity, we have κD =2η2

!

1− γPPN"−1

, where η ≡ 4βPPN−γPPN−3 is the Nordtvedtparameter, a combination of PPN parameters related to the vio-lation of the strong equivalence principle.

c⃝ 0000 RAS, MNRAS 000, 000–000

Violation of strong equivalence principleDipolar gravitational wave emissionOnly if self-energy of two bodies is different

‘Excess’ of orbital decay

Freire et al. (2012) & Antoniadis et al. (2012)

Nuclear Physics at Ultra High Density

Demorest et al. 2010

J1614-2230

J0348+0432

Neutron stars explore different regime of nuclear physics than heavy ion collisionsUltra high density particularly sensitive to symmetry energyExotic particles / state transition near the core?Bulk properties (mass, radius, moment of inertia) can be used as probes

PSR-NS

PSR-WD Redbacks

Black widowsBlack widows

Redbacks

B1957+20

J1311-3430

J0348+0432

J1614-2230

The Pulsar Mass Landscape .

How to measure masses?Where to look?

Radio timing and…

relativistic effects

optical observations(velocity, spectral type)

optical observations(velocity, light curve)

Spiders Taxonomy

Fast millisecond pulsars (⪅5 ms)Compact orbits (75 minutes - 26 hours)Energetic pulsar (Edot = few 1034 erg/s)

Black Widows Redbacks

Same behaviours, different species…

Irradiated companionRadio eclipses (0 - 70% of the orbit)Optical flux/colour modulation

First: PSR B1957+20 (Fruchter et al. 1988)Very low companion mass (~0.02 M⊙)?

First: PSR J1023+0038 (Archibald et al. 2009)Low companion mass (~0.2 M⊙)Some show state transitions ‘MSP ⟷ LMXB’

The Fermi Revolution

Number of known spiders (in the Galactic field)Pre-Fermi: ~4Now: 4-5 dozens

Credit: Fermi-LAT 5 Years

Most discoveries in deep radio searches of Fermi point sources (e.g. Ray et al. 2012, Camilo et al. 2015)

Evident bias in the radio: strongly eclipsed systemsGamma-ray is luminosity-limited (i.e. infinite optical depth)

Stellar ‘Braai’

Determining the system geometry is ‘possible’ using

Pulsar radio timing5 Keplerian parameters(Unknown masses and orbital inclination)

Optical follow-up of the companionLight curves orbital inclination, temperatures, companion sizeSpectroscopy mass ratio (from projected velocity)

van Kerkwijk et al. 2011

Extreme Pulsar Interaction #1

A majority of ‘spider’ binaries show radio eclipsesMass stripped from companionFull evaporation within Hubble time?Exact mechanism unknown

In ‘original’ black widow, PSR B1957+20, later concluded not sufficient mass-loss rate(Eichler & Levinson 1988)

Comprehensive set of eclipsing spiders observed with LOFAR (110-190 MHz)

Low frequency is key window to probe:Local changes in electron column densityOut-gasing / ablation physics

Modern Take on Radio Eclipses

E. Polzin (JBCA) J1810+1744 eclipse DM and scattering December 4, 2016 2 / 5

Imaging

Calibrated using standard LOFAR software and imaged with CASA,using 1 minute time intervals

Flux extracted with PyBDSF

Non-eclipse Eclipse

E. Polzin (JBCA) The eclipses of black widow pulsar J1810+1744 10 / 12

Polzin et al. in prep Time

Puls

e ph

ase

Important findings:Radio flux completely absorbed (confirming Broderick et al. 2016)Eclipse region must be clumpy

Radio Eclipse Studies

Polzin et al. in prep

Eclipses of PSR J1810+1744 11

Figure 7. Normalised flux density for the full eclipses observed on 2011June 6 (WSRT) and 2013 July 25 (LOFAR). The flux densities as measuredin each of the frequency sub-bands centred on 118 (blue), 134 (green), 154(red), 176 (cyan), 321 (pink), 344 (yellow) and 369 MHz (purple) are shown.Wider eclipses are observed for lower frequency sub-bands. The black curvesshow least squares fits of Fermi-Dirac functions to the ingresses and egressesin each frequency sub-band.

Figure 8. Eclipse duration, eclipse, taken as full-width at half-maximumof out-of-eclipse flux density, for observed full eclipses. The error barscorrespond to 1 uncertainties from the Fermi-Dirac fits to the measuredflux densities. The dashed line shows a best fit power law with ↵ = 0.41.Dierent colours represent separate eclipses.

apparent clumpy nature of the eclipsing medium, and very shallowfrequency dependence for the 100–200 MHz eclipse ingress couldallow refraction to have some role in the process. Additionally,refraction would provide an explanation for observed features suchas the brief enhancements in flux density seen in the egress inFig. 3(k), where the line-of-sight could pass a caustic.For free-free absorption, using Equation (11) of Thompson et al.(1994) with an electron column density from the 345 MHz egress,Ne 3 1016 cm2, and absorption length equal to the eclipsewidth of 5.61010 cm, we find a required temperature of the eclipsemedium, T . 103 f 2/3

cl K, with clumping factor fcl =n2

e↵/hnei,

Figure 9. Ingress and egress durations, taken as |0.25 phase of half-maximum flux density |. Top: four LOFAR and one WSRT egress observa-tions, the dashed line shows a best fit power law with ↵ = 0.35. Bottom:three LOFAR and one WSRT ingress observations, the dotted line shows abest fit power law with ↵ = 0.41. The error bars correspond to 1 uncer-tainties from the Fermi-Dirac fits to the measured flux densities. Dierentcoloured symbols represent separate eclipses. Durations, taken at 118, 134,154, 176, 321, 344 and 369 MHz, are plotted with small frequency osetsfor clarity.

for an optical depth > 1. The same temperature constraint isfound for the 149 MHz eclipse parameters. This is equal to thelimit calculated for PSR B1957+20 in Thompson et al. (1994) andis understood to be orders of magnitude colder than that expectedin such a medium with a realistic clumping factor.Should the eclipse region material increase in density closer tothe companion (as expected from the observations), o-axis radiobeams could reflect or refract from the higher density regions intothe line-of-sight radio beam, causing induced Compton scatteringin the line-of-sight radiation. As explained in Thompson et al.(1994) this would alter the observed radiation spectrum, appearingto act as absorption of low-frequency radiation. Using Equation (26)of Thompson et al. (1994) with the measured flux density of PSRJ1810+1744, S0

= 480 mJy, a spectral index ↵ = 2.3 (Murphyet al. 2017), electron column density Ne 1016 cm2, a sourcedistance of d = 2.0 kpc and orbital separation a = 9.3 1010 cmfrom Breton et al. (2013), we find an optical depth at 149 MHzof ind . 0.5M , where M (RC/2r)2 is the magnification factorof the reflected radio beam, RC is the radius of curvature of thereflecting region and r is the distance from the centre of curvatureto the scattering region (Section 2.4.1. of Thompson et al. 1994).For PSR J1810+1744 we estimate the radius of curvature of

MNRAS 000, 1–13 (2017)

Asymmetry and chromatic effects indicate sweptback trailing material

Evaporation rate:

150 MHz: 6x10-13 M/yr

350 MHz: 10-12 M/yr

Ablation in 5 Gyr: 9x10-12 M/yr

Black widows might become isolated after all

Extreme Pulsar Interaction #2

(23 ms)

(2.8 s)

A

B

The Double Pulsar is also a radio eclipsing systemPulsar A eclipsed by Pulsar B every orbit for ~30 secCaused by synchrotron absorption in closed field line of B’s magnetosphere

The Double Pulsar Eclipses

Direct probe of magnetosphere on 10,000 km scaleCanonical dipolar magnetic field works!

Large plasma density requiredSharp outer boundary to plasmasphere

Spin precession made Pulsar B in 2009.Will be back in 2024!

Conclusions

Eccentricity

Orb

ital P

erio

d

PSR + NS

PSR + WD

spin-orbit coupling

dipolar GW

tensor-scalar

TeVeS/MOND

NS EoS

SEP violation

preferred frame effects (statistical)

G time-variation

relativistic effectsPSR + BD*

Binary pulsars offer great tools to studygravitationmatter at extreme densityextreme interaction

preferred frame effects (individual)

pulsar magnetospheresirradiation physicsbinary evolution