GENERAL RELATIVITY AND PRECISE MEASUREMENTSGENERAL RELATIVITY AND PRECISE MEASUREMENTSOF PULSAR MASSESOF PULSAR MASSES

D.G. Yakovlev

Ioffe Physical Technical Institute, St.-Petersburg, Russia

• Introduction• X-ray binaries• Double neutron star binaries• Pulsar – white dwarf binaries• Summary

FFC, Pulkovo Observatory, October 10, 2013

INTRODUCIONINTRODUCIONGalaxy, stars and the SunGalaxy, stars and the Sun

Galaxy: more than 1011 starsLuminosity: L~1046 erg/s

Sun: M=2x1033 g, R=700,000 km,L=3.83x1033 erg/s, mean density of matter = 1.4 g/cm3, surface temperature ~6,000 К, internal temperature 15.7 MК.Composition: rarefied plasma, pressure P=nkT ~1017 dyn/cm2.Supported by thermonuclear reactions in central region

Giant star

WD

WD

NS

BH

NS

BH

Normal star

M<8 MSUN

Quiet removal of outer shell, birth of white dwarf (WD)

M>25 MSUN

collapse into black hole (BH)

SCHEME!

M=(8—25 ) MSUN

Core-collapsed supernova (SN II) birth of neutron star

SN Ia

i, b

b

i, b

b

36

SUN

g/cm 10~

km, 5000~

, 6.0~ :

R

MMWD

315

SUN

g/cm 10~

km, 10~

, 4.1~ :

R

MMNS

km / 3

/2 :

SUN

2

MM

cGMRBH WD, NS, BH = graveyard

i=isolatedb=binary

Extreme Physics Problem: EOS, High B, High Tc

Main mystery: EOS of super-dense core – longstanding fundamental problem of physics and astrophysics complicated by high B and Tc

Main practical problem:How to relate EOS toobservables

2 53 2

2 14 2

3 14 30

14 30

57

~ / ~ 5 10 erg ~ 0.2

~ / ~ 2 10 cm/s

3 /(4 ) 7 10 g/cm ~ (2 3)

2.8 10 g/cm standard density of nuclear matter

~ / ~ 10 = the number of baryons

In our Galaxy:

ther

b N

U GM R Mc

g GM R

M R

N M m

8 9e are ~ 10 10 neutron stars

observed ~ 2000 neutron stars

km 10~ ,4.1~ SUN RMM

MOTIVES TO ACCURATELY MEASURE NS MASSES

• Мass – most important parameter of any star

• To find critical mass which separates NSs and BHs

• To constrain EOS of superdense matter in NS core

Most massive NSs are most important!

X-ray binaries

NS

Companion inbinary system

Riccardo GiacconiNobel Prize: 2002

eaaMM ,,,, 2121

Kepler Orbits

2121 , aaaMMM

MaMaMaMa /,/ 1221 Integrals of motion:

MeaMGMJaMGME /)1(),2/( 222

21

221

Orbital period:32 /,/2 aGMP bbb

Measuring radial velocities of companion 1:

G

x

M

iMfiax

e

xKeP bb

b

231

2

32

1112

11

)sin(,sin

1,,

Measuring radial velocities of companion 2:

22 , fK

Need more parameters:

2

1

Vela X-1 Vela X-1 (=4U 0900--40)

GP Vel (=HD 77581, B0.5 Ib supergiant)

Pspin=283 s, Pb=8.96 d, e=0.09

a=50 Rsun, i>70o, R2=30 Rsun

Discovery: Chodil et al. (1967)

GP Vel: Brucato & Kristian (1972), Hiltner et al. (1972)

K2 for GP Vel: Hiltner et al. (1972)

Quaintrell et al. (2003):

1(1 ) 2.27 0.17 for 70M M i

1(1 ) 1.88 0.13 for 90M M i

K1 for Vela X-1: Rappaport et al. (1976)

P for Vela X-1: McClintock et al. (1976)

Masses of Neutron Stars in X-ray Binaries

SUMMARY: NEUTRON STAR MASSES IN X-RAY BINARIES

(1) There is a wide spectrum of neutron star masses in XRBs

(2) XRBs almost certainly contain massive neutron stars

(3) The best candidates are Vela X-1 (M>1.62 MSUN) Cyg X-2 4U 1700—37

(4) The prospects to accurately measure M are poor

Radio Pulsars inRadio Pulsars inCompact BinariesCompact Binaries

S

pin

axi

s Mag

netic

axi

sL

Relativistic Objects: Radio Pulsar – Compact Companion

Energy and orbital momentum:

.8

71

)1(5

32

,96

37

24

731

)1(5

32

2222/75

2/122

21

2/7

422/7255

22

21

4

eeac

MMMG

dt

dJ

eeeac

MMMG

dt

dE

Peters & Mathews (1963), Peters (1963)

Evolution of orbital parameters:

22

3/23/5

22

22/5245

213

422/7235

213

)1(

)(3

)1(

3

,2

3

304

1211

)1(15

304

96

37

24

731

)1(5

64

ce

GM

cea

GM

dt

d

dt

da

aP

dt

dP

eeac

MMMeG

dt

de

eeeac

MMMG

dt

da

bb

bb

Advantages:(1) Very precise timing P(t) (2) Point-like masses(3) GR effects

Example: Timing of pulsars and NS mass measurements

Stage 1: Measurements of Keplerian parameters

111 ,,,,, fxeKPb

Stage 2: Measurements of relativistic parameters

: 2 extra equations are required

(a) Pereastron advance: dtd /

1 2 1MAX 1MIN( 0) ; ; e M M M M M

(b) Transverse Doppler effect + gravitational dilation of signals by М2:

)0()2(

2 2212

212

22

2

e

aMc

MMeGM

cr

GM

c

v

b

(c) Shapiro parameters:

)90(,sin3

2

23/1

13/23/2

ic

GMr

MG

xMis b

(d) Orbital decay: dtdPb /

Up to 5 extra equations can be obtained !

.

Russel Hulse and Joseph Taylor

The Arecibo 305-m radio telescope(NAIC-Arecibo Observatory, NSF)

The Hulse-Taylor Pulsar (PSR B1913+16)

Discovery: 2 June 1974 (ApJ Lett, January 15, 1975) 5083 observations from 1981 to 2001

Orbit:6 0

max

0.617, 2 10 , 47

400 / , 59 , 7.75 b

e a km i

v km s P ms P hrs

Relativistic effects (Weisberg & Taylor, 2010) :

(a)

Rotation by 125о in 30 years (Mercury: 43’’ in 100 yrs)

(b)

(c)Observations:

Theoretical prediction:

Nobel Prize: 1993

.

/ 4.226598 0.000005 deg/d dt year

0.0042992 0.0000009 s

12/ (2.398 0.005) 10 /bdP dt s s

12/ (2.402531 0.000014) 10 /bdP dt s s

1

2

(2 ) (1.4398 0.0004)

(2 ) (1.3886 0.0004)

SUN

SUN

M M

M M

MASSES OFPSR B1913+16& COMPANION

(Weisberg, Nice, Taylor, 2010)

In !!!SUNM

The mass of the Hulse-Taylor Pulsar (PSR B1913+16)

Evolution of the Hulse-Taylor pulsar

)0 ifMyrs (1640 Myrs300 Myrs;1002/.

etPPt deathspinspinPSR

At birth: yrdtdhrPcmae b deg/12.3/,93.9,103.2,666.0 11

Now:11

31

0.617, 2.0 10 , 7.75 , / 4.23 deg/ ,

7.77 10 /

b

G

e a cm P hr d dt yr

L erg s

In 200 Myr: yrdtdhrPcmae b deg/5.11/,64.3,102.1,439.0 11

The last 10 Years of the Hulse-Taylor Pulsar

10 years before death:41

0.00081, 17300 , 23 , / 39.6 deg/ ,

1.2 10 /

b

G

e a km P s d dt hr

L erg s

1 ms before death : sergLmsPkma Gb /10,1,40 55

M31

Time to merging = 300 Myr

Geodetic precession of the Hulse-Taylor pulsar

M

M

eac

GMbprec 3

1)1(

3 122

2Barker & O’Connell (1975):

yrsPyr precprec 300,deg/21.1

yrttt outouton 240;2025;1940

27),(;22),( Bspinprecspin

Ideal Wolszczan Pulsar (PSR B1534+12)

Discovery: Wolszczan (1991)

0

37.9 , 10.1 , 0.274, / 1.76 deg/

77

bP ms P hr e d dt yr

i

All 5 GR parameters measured:

/ , , / , , bd dt dP dt s r

1

2

(2 ) (1.3332 0.0020)

(2 ) (1.3452 0.0020)

SUN

SUN

M M

M M

Neutron star masses (Stairs et al. 2003):

J0737-3039 A and B: Double Pulsar Binary

PulsarА Burgay et al. (2003) Observation:

4.5 min in August 2001 + systematic observations since 2003 (5 months)

yrdtdehrPmsP b deg/17/,0878.0,45.2,7.22

SunMM )02.058.2(

Pulsar B Lyne et al. (2004)

Systematic observations since May 2003 (7 months)

SunSun MMMM

isrfsP

)005.0250.1()1(,)005.0337.1()1(

87,;,773.2

21

2

Results:

Myrstdeath 86 Fifth binary with short lifetime

yrstyrst precprec 71,75 21 Radio eclipses

Double Neutron Star Binaries

MASSES OF DOUBLE NEUTRON STAR BINARIES

• 5 DNSB = 10 neutron star masses accurately measured

• All masses are in narrow range

• HT pulsar is most massive among them

• No recent progress with these objects

RADIO PULSARS AND WHITE DWARFS(or other compact companions)

Advantages:• Compact stars – point-like masses• Often – recycled millisecond pulsars: pulsars can be massive, short periods – good timing, weak magnetic fields – no glitches or pulsar noise

Disadvantages:• Underwent active accretion phase – as a rule, almost circular orbits = difficult to measure periastron advance and gamma-parameter• Low-mass companions – difficult to measure Shapiro effect and dPb/dt

Specific feature:• Often observed in globular clusters

Neutron Stars and White DwarfsWhite dwarfs: M2—Pb

Neutron Stars and White Dwarfs

Ideal System Radio Pulsar—White Dwarf (PSR J1141—6545)

Discovery: Kaspi et al. (2000)

0

394 , 4.75 , 0.172, / 5.3 deg/

~ 76

bP ms P hr e d dt yr

i

Three GR parameters measured:

/ , , /bd dt dP dt

1

2

PSR: (2 ) (1.30 0.04)

WD: (2 ) (0.99 0.04)

SUN

SUN

M M

M M

Masses (Bailes et al. 2003):

Ideal Binary Radio Pulsar—White Dwarf (PSR J1909—3744)

Discovery: Jacoby et al. (2003)

72.9 , 1.53 , ~ 10 , 86.6bP ms P d e i

Two relativistic parameters measures: s, r

1

2

PSR: (1 ) (1.438 0.024)

WD: (1 ) (0.2038 0.022)

SUN

SUN

M M

M M

Masses of stars (Jacoby et al. 2005):

Fallen Down AngelRadio Pulsar—White Dwarf (PSR J0751+1807)

Discovery: Lundgren et al. (1995)

3.48 , 6.3 , 0.000003bP ms P hr e

One relativistic parameter measured: dPb/dtShapiro effect is poorly pronounced: i~65-850

0.41 0.5

2

PSR: (2 ) 2.1

WD: (2 ) (0.19 0.03)

SUN

SUN

M M

M M

Masses of companions (Nice, Splaver, Stairs 2004, 2005):

After 2007 (Nice, Stairs, Kasian 2008):

1

2

PSR: (2 ) (1.26 0.28)

WD: ~ 0.2

SUN

SUN

M M

M M

Radio Pulsar—White Dwarf (PSR J1911—5958A)

Discovery: D’Amico et al. (2001)

3.26 , 0.84 , 0.000003bP ms P d e

No relativistic parameters measured

Bassa et al. (2006), Cocozza et al. (2006) – radial velocity curve and mass of white dwarf are measured in optical observations

0.161 0.10

2

PSR: (1 ) 1.40

WD: (1 ) (0.18 0.02)

SUN

SUN

M M

M M

PSR J1903+0327 (2009)

Discovery: Cordes et al. (2006)

2.15 , 95 , 0.44bP ms P d e

1

2

PSR: (1 ) 1.67 0.01

MS: (1 ) 1.028 0.004

SUN

SUN

M M

M M

The first eccentric binary MCP in the galactic diskCompanion: MS star, M~1 MSUN

Evolutionary scenario: unclearMeasured: periastron advance + s, r

Problem: large size of companion can affect periastron advance Perspective: timing, refined measurements of periastron advance, s, r

Most Massive Known Neutron StarPSR J1614-2230 + WD

63.15 , 8.69 , 1.3 10 , 89.17obP ms P d e i

1

2

PSR: (1 ) 1.97 0.04

WD: (1 ) 0.500 0.006

SUN

SUN

M M

M M

Measured: Shapiro effect, s, r

Most massive neutron star currently known

28 0ct. 2010, Nature 467, 1081

Discovery: 2002 (Hessels et al. 2005)

Most Massive Known Neutron StarShapiro delay in PSR J1614-2230 + WD

0 0.5 1.0

Orbital phase

Tim

e re

sid

ual

, mic

rose

con

ds

Demorest et al. (2010)

THE SECOND MOST MASSIVE NEUTRON STARPSR J0348+0432 + WD

Radio observations: Green Bank (USA) 2007Publication: Lynch et al. (2013)

Science, 26 April 2013, Vol. 340, Issue 6131, 448

39 , 2.46 , 40.2 , 2.1 kpcobP ms P h i d

Pulsar: moderately spun up by accretionWD: low-massive, He coreAge of the system: about 3 Gyrs

Measured: radial velocities of PSR and WD and spectroscopic WD mass

1

2

PSR: (1 ) 2.01 0.04

WD: (1 ) 0.172 0.003

SUN

SUN

M M

M M

0.07 130.11

13

/ 2.58 10

/ ( 2.73 0.45) 10

b

b

dP dt

dP dt

Checked by orbital decay:

Theory

Observations

Time to merging: 400 Myr

Ideal binary for checking GR!

Measured without GR effects

THE SECOND MOST MASSIVE NEUTRON STARPSR J0348+0432 + WD

Summary of NS-WD and NS-NS binaries

Kiziltan et al. (2013)

MOST MASSIVE NEUTRON STAR VERSUS TIME

PSR B1913+16

PSR J0751+1807

PSR J1903+0327

PSR J1614—2230 PSR J0348+0432

HT pulsar

PSR J1614-2230PSR J0348+0432

GeneralRelativityCausality

Mass—Radius Diagram for Exploring EOS of Superdense

RESULTS• General Relativity Theory was tested Gravitational radiation discovered Geodetic precession discovered• Double neutron star mergers were discovered• Gravitational observatories of new generation are built• General Relativity has become useful tool• Masses of some neutron stars accurately measured Currently: Mmax>2 MSUN => soft and moderate EOSs are ruled out

=> EOS is stiff => little room for exotic matter

Unsolved Problems

• MMAX = ?

• Stiff EOS = just stiff or superstiff?

Main feature at present: Rapid progress!