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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!