neutron star physics a kind of introduction ulrich r.m.e. geppert november 4th 2011u.r.m.e., univ....
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Neutron Star Physicsa kind of introduction
Ulrich R.M.E. Geppert
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 1
Great place to teach neutron star physics:
…
Zielona Gora Pulsar Group
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 2
First ideas long before first observation:
L.D.Landau 1931, talking to N.Bohrantizipation of neutron stars:
p+ + e- n
"atomic nuclei come in close contact, forming one gigantic nucleus" (published in 1932: Landau L.D.. "On the theory of stars". Phys. Z. Sowjetunion 1: 285–288.
+ 0.78MeV
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 3
Fritz Zwicky Walter Baade
1934, after the discovery of the neutron:neutron stars are in supernovae transformed out of normal stars.
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 4
Neutron Stars First Seen as Radio Sources
Effelsberg 100m radio telescopeOne Mile Telescope completed 1964 by the Radio Astronomy Group of Cambridge University
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 5
• Jocelyn Bell & Antony Hewish 1968:
- PSR B1919+21 (LGM-1)
- at radio frequencies 85 MHz…2.7 GHz
- at the Cambridge Radio Telescope
- P = 1.337 s, dP/dt = 1.3481x10-15
• start with the real story of NS observation:
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 6
Sept. 2011: Honnappa, Lewandowski, Kijak, Deshpande,Gil, Maron, Jessner: Effelsberg radiotelescope
single pulseanalysis ofPSR B1133+16
search for thecarouselcirculation time P4
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 7
P1=1.188sP4= 28.44 P1
Ruderman & Sutherland 1975
32 / PPD
PP 1
apparent drift rate
intrinsic drift rate NPP 34
2P distance between driftbands in longitude
N number of rotating sub-beams
time interval to complete onerotation around the pole
3P
4P
4P
distance between the same driftbands
4P
distance between driftbands in3P 1P
courtesy J.A. Gil
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 8
Study of the different periodicities reveals thephysics of pulsar emissionand more.
NSs in Binary Systems Bright X-ray Sourceaccr. rate ~ 7x10-9M⊙/yr, Lx ~ 1037 erg/s
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 10
X-ray spectral fit for cooling NS B0656+14
BB1~8.7•105K
BB2~1.4•106K
PL (magnetospheric)
A2/A1=(6.8±3.7)•10-3
Neutron star surfacehas non-uniformtemperature!
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 11
First direct observationof a NS in visible lightwith the HST in 1997:RX J1856.5-3754
- no pulsation- d ≈ 117 pc ≈ (344 ly ≈ 3.6x1015km)- parallax ~ DM!
spectral fits:non-uniform Ts
Neutron Stars in Visible Light
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 12
How can a neutron star call attention to themselves?
1. emission of electromagnetic radiation
- radio
- IR
- visible
- UV
- X-ray
only close-by ones (< 1kpc)
thermal (surface) or magnetospheric emission
⇒ magnetospheric,…
bursting and/orcontinuous
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 13
2. trapping a companion
- if main sequence, red giant, or white dwarf
⇒ wind or Roche lobe overflow accretion may onset
3. emission of gravitational waves
⇒ LIGO (U.S.), LISA (NASA & ESA)
power of a rotating mass quadrupole
Tiny! ⇒ rapid rotation andlarge Q demanded.
isolated:
revival of an old dead pulsar orswitch-on of a bright X-ray source
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 14
in a binary system:
~ the same problem
4. gravitational light bending
apparentsource position
true pathof lightfrom thesource
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 15
• ~ 2500 NSs, majority: Radio-PSRs,
• ~ binary NSs, X-rays, Γ-rays, optical, UV
• ~ 0.001 s < P < 10 s
• ~ 10-20 < dP/dt < 10-10
• ~ small sample of NSs in our galaxy
(1SN/30yrs, age ~ 1010yrs 3·10⇒ 8 NSs)
Summary of Observations
It returns a lot of fun!!!
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 16
Observations
www.atnf.csiro.au/research/pulsar/psrcat
)(,, PPP
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 17
Comparison with Pulsar Watches
• Japanese „Pulsar“ company advertises: our watches run slow only by about 1s per year….
• Crab pulsar slows down by about 1.6x10-5s per year, i.e. 1 second in 60.000 years
if you can‘t look on the atomic time clock of the NIST in Fort Collins CO:
better look on a PSR!November 4th 2011 U.R.M.E., Univ. of Zielona Gora 18
First Rough Ideas Based on P(t)
• Limit on emitting area: cΔt ~ cP ~ 300 km
3132
32
22
gcm105.13
3
4,
2
GP
RMR
GmM
PmRmR
⇒ compact object, more compact than WD but no BH
• Limit on mean density:Idea about the compactness,i.e. the internal structure of neutron stars.
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 19
Energy Loss by Rotating Multipoles
)sinsincossincos(2
1
3
2 '||
32
3mdr teteeRBmmc
E p
3
2462p
mdr 6
sin
c
RBE
Larmor formula for magnetic dipole:
1-
2
12
46
638
em s ergG102.5s0331.0cm102.1
104.6
pBPR
E
For Crab-PSR data:
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 21
First Models for PSR Magnetic Field
loss of rotational energy ~ power of magneto-dipole radiation:
G10...10~
102.3
6
sin
158
19
3
2462
B
PPB
c
RBI
Idea about the magnetic fieldstrength of neutron stars.
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 22
First Models for PSR Age
PP
t
KKt
RBKc
RBI
22ai
a
2
i
32
3p3
2462p
if
12
T
:Tandwith 2
1
d
d
),( i.e.,6
sin
P and dP/dt of Crab PSR : 1243 yrs ⇒ 955 yrs real age ⇒ quite good!
Idea about the characteristicage of neutron stars.
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 26
Comparison with „real“ pulsar age:
Log age [yrs] 2 4 6 8
Pin=1s
Pin=0.1s
Pin=0.01s
Quite good coincidence
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 27
different classes of neutron stars
• radio pulsars: P~0.1…5s, B~1012…13G,
age ≲ 107 yrs
• pulsars in binary systems: P≲0.1s, B≲ 1010G, age 10≳ 8 yrs
• millisecond pulsars:P≲0.01s, B≲ 108G,
age 10≳ 9 yrs• pulsars SNR: 0.01<P<1s, B > 1012G,
age ≲ 105 yrs• magnetars: P~ 10s, B > 1014G, age ≲ 105 yrs
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 30
young NSs : stronger fieldold NSs : weaker field
magnetic field decay
NSs in binaries : weaker fieldmillisecond PSRs : rapid rotation
accretion spins up &decreases magnetic field
magnetars : slow rotation strong magnetic fieldbrakes rotation efficiently
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 31
A neutron star‘s life will not be boring butmay evolve through varies periods,sometimes very fast, sometimes dramatic,and sometimes very slowly.
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 32
Radius ~ 10km, Mass ~ 1.4M⊙Neutron stars are the only stellar objectswhere relativistic effects play a role.
Quantity that estimates the importance of general relativity:
= compactness
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 34
Little exercise:
Epot= Ekin⇒ escape velocity ve =if ve = c ⇒ RS = gravitational redshift:
No energy (radiation) can leave the surface!!!
Schwarzschild radius
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 35
Object Mass Radius Mean Density (g/cc) Surface Pot.(GM/Rc2 = Rs/R )
Sun M⊙ R ⊙ 1 10 -6
WD ≲ M⊙ ∼ 10-2 R ⊙ ≲ 107 ∼10-4
NS 1…3 M⊙ ∼ 10-5 R ⊙ ≲ 1015 ∼10-1
BH arbitrary 2GM/c2 ∼ M/R3 ∼1
proper time and length at the surface
36
general relativistic effects neutron stars
- energy of elm waves (light) ⇒ light bending
- magnetic energy dissipation ⇒ decelerated cooling- thermal energy transfer
- rot. energy (spin, orbital) ⇒ gravitational waves
• gravitational field carries energy ⇒ it is by its own a source of the field ⇒ non-linearity of the field equations• all kinds of energy have the property of inertia (E=mc2) ⇒ all kinds of energy are subject to gravitation
- energy of emitted photons ⇒ gravitational redshift
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 37
gravitational redshift
November 1st 2011, Maitra, Miller, Raymond, Reynolds by XMM observations:
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 38
O VIII Ly-α line
for M = 1.25 … 2M⊙ ⇒ R = 8.9 … 14.2km redshift observations ⇒ information about EoS
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 39
light bending
- first approvement of GR by use of the solar eclipse in 1919 by Sir Arthur Eddington ⇒ Einstein became a superstar
flat space trajectory
curved space trajectory
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 40
⇒ gravitational light bending makes a larger part of the neutron star surface „visible“
⇒ consequences for the interpretation of surface features and lightcurves
a part of a neutron star‘s back side is seen
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 41
incr
easi
ng c
ompa
ctne
ss
R ⇾ Rs : pulsations become less visible
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 43
relativistic heat transfer – decelerated coolingrelativistic field diffusion – decelerated decay
thermal energy magnetic energy ~ mass
⇒ subject to and source of gravitation
flat space:
constant conductivities:
lessimportant
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 44
relativistic generalization:
GR-effects:
2. spatial derivative of gravitational redshift
Schwarzschild coordinates
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 45
magnetic field decay in realistic neutron star models
increasing compactness
significant deceleration of field decay for older neutron stars
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 46
gravitational waves emitted by rotating neutron stars
1. neutron star spin + mass quadrupolar moment
2. neutron star orbital rotation in a binary system
Hulse-Taylor pulsar PSR B1913 + 16
Orbit decayed since 1975 in precise agreementwith loss of energy due to gravitational waves as predicted by GR!
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 47
2D representation of gravitational waves generatedby two neutron stars orbiting each other
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 48
theoretical curve
observedchange in the epochof periastron with date
rate of decrease of orbital period: 76,5 μs/yrrate of decrease of semimajor axis: 3,5 m/yrCalculated lifetime tofinal inspiral: 300000 yrs
1993 Nobel Prize
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 49
Zielona Gora Pulsar Group:
One has to talk about the magnetic field!
Up to now no evidences against this picture !
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 50
What does the core centered field?
- it is large scale field, i.e. it has a long range
⇒ it is responsible for pulsar braking
- it is based in the SF/SC neutron star core
⇒ it decays very slowly
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 51
ΩB
neutron vortices (SF)
proton fluxoids (SC)
Neutron Star Core Structure for T < Tc:
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 52
Forces acting upon a fluxoid:
Fb
Fn
Fd
Fcrust ABE
c
v
d
4
1
corep
Flux expulsion from balance of forces:
Fb + Fd(vp) + Fn + Fcrust(vp) = 0November 4th 2011 U.R.M.E., Univ. of Zielona Gora 53
Core Magnetic Field Evolution
Core field decays on time scales > 108 yrs!
2
2
ohm
4
c
l
Bcore will be re-arranged in the SF corebutcan be dissipated only in the crust
⇒ decay determined by conductive properties of the inner crust
σic ~ 1028s-1, lic ~ 105cm
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 54
Crustal Magnetic Field Evolution
Observational evidences:
● PSR activity at all: demands small scale (l ~ 105…106cm) and strong (B ≳ 1014G) fields!
● Evidence of Joule heating ⇒ finite σ
● Magnificent Seven: non-isotropic surface temperature Ts
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 55
Crustal B-decay: Pulsars
Ruderman & Sutherland 1975: B-curvature ~ 106cm ⇒ no dipolar!
Gil & Melikidze since ~2002: B ≳ 1014G
Strong, small scale B-components necessary!November 4th 2011 U.R.M.E., Univ. of Zielona Gora 57
Crustal Magnetic Field Evolution
magnetization parameterNovember 4th 2011 U.R.M.E., Univ. of Zielona Gora 58
Small scale B-modes in outer crust:
Ohmic decay in 104…105 years
➽ modes have to be „re-created“
Hall-Drift
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 59
Creation of Spot-like Bs
)Bcurl(Bcurl
0
1curl
4
2eBBcB
diffusion & dissipation Hall drift
• ⇒Hall induction equation:
Non-linear B-decay in the crust!November 4th 2011 U.R.M.E., Univ. of Zielona Gora 60
Hall-Drift ⇒ Hall-Instabilityσ=const, B0=f(z)ex, small perturbations in y-direction,
vacuum boundary
perfect conductor boundary
small scale strong B
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 61
Strong small-scale surface B:
necessary ingredient for a PSR to flash up
Szary, Melikidze, Gil, 2011 & :
dipolar B
strong small scale B
November 4th 2011 U.R.M.E., Univ. of Zielona Gora 62
I have not talked about:
- prozess of neutron star creation in a supernova
- establishment of an MHD equilibrium after birth
- decision: magnetar or standard neutron star
- magnetar observations (SGR, AXP) and physics
- mechanisms that create ultrastrong magnetic fields
- appearance of hot spots at a neutron star‘s surface
- spin-up of neutron stars to millisecon pulsars in accreting binary systems- …November 4th 2011 U.R.M.E., Univ. of Zielona Gora 63
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