Download Neutron Star Magnetic Fields Observations, 0rigin, Evolution, Effects

Neutron Star Physics
a 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.Bohr
antizipation of neutron stars:
p+
+
e-
+ 0.78MeV
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.
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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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
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Neutron Stars First Seen as Radio Sources
One Mile Telescope completed
1964 by the Radio Astronomy
Group of Cambridge University
November 4th 2011
Effelsberg 100m radio telescope
U.R.M.E., Univ. of Zielona Gora
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• start with the real story of NS observation:
• 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
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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Sept. 2011: Honnappa, Lewandowski, Kijak, Deshpande,
Gil, Maron, Jessner:
Effelsberg radiotelescope
single pulse
analysis of
PSR B1133+16
search for the
carousel
circulation time P4
P1=1.188s
P4= 28.44 P1
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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courtesy J.A. Gil
apparent drift rate
D  P2 / P3
distance between
driftbands in longitude
P2

Study of
P the different
P
P

periodicities
reveals the
P PN
P

physics of pulsar emission
P P
and more.

4
distance between
driftbands in 1
3
intrinsic drift rate
3
N

November 4th 2011
3
number of rotating sub-beams
1
P4
Ruderman & Sutherland 1975
4
distance between
the same driftbands
time interval to complete one
4 rotation around the pole
P
U.R.M.E., Univ. of Zielona Gora
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Neutron Stars in X-Rays
XMM-Newton
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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NSs in Binary Systems Bright X-ray Source
accr. rate ~ 7x10-9M⊙/yr, Lx ~ 1037 erg/s
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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X-ray spectral fit for cooling NS B0656+14
Neutron star surface
has non-uniform
temperature!
BB1~8.7•105K
BB2~1.4•106K
PL (magnetospheric)
A2/A1=(6.8±3.7)•10-3
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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Neutron Stars in Visible Light
First direct observation
of a NS in visible light
with the HST in 1997:
RX J1856.5-3754
- no pulsation
- d ≈ 117 pc
≈ (344 ly ≈ 3.6x1015km)
- parallax ~ DM!
spectral fits:
non-uniform Ts
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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How can a neutron star call attention to themselves?
1. emission of electromagnetic radiation
bursting and/or
continuous
- radio
- IR
only close-by ones (< 1kpc)
- visible
- UV
thermal (surface) or magnetospheric emission
- X-ray
⇒ magnetospheric,…
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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2. trapping a companion
revival
of an
pulsar or
- if main sequence,
redold
giant, dead
or white dwarf
switch-on
a lobe
bright
⇒ wind or of
Roche
overflowX-ray
accretionsource
may onset
3. emission of gravitational waves
⇒ LIGO (U.S.), LISA (NASA & ESA)
isolated:
power of a rotating
mass quadrupole
Tiny! ⇒ rapid rotation and
large Q demanded.
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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in a binary system:
~ the same problem
4. gravitational light bending
true path
of light
from the
source
apparent
source
position
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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Summary of Observations
•
•
•
•
~ 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 ⇒ 3·108 NSs)
It returns a lot of fun!!!
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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Observations
www.atnf.csiro.au/research/pulsar/psrcat



P, P, ( P)
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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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
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First Rough Ideas Based on P(t)
• Limit on emitting area: cΔt ~ cP ~ 300 km
• Limit on mean density:
Idea about the compactness,
4
 2  GmM
i.e.mR
the
 internal
mR
, M  ofR 
  structure
R
3
 P 
neutron stars.
2
2
3
2
3
  2 1.5 1013 gcm 3
PG
⇒ compact object, more compact than WD but no BH
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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Energy Loss by Rotating Multipoles
Larmor formula for magnetic dipole:



2  2  1

Emdr   3 m m  B p R 3 (e|| cos   e sin  cos t  e' sin  sin t )
3c
2
E mdr  
Bp2 R 6  4 sin 2 
6c 3
For Crab-PSR data:
R

38 

Eem  6.4 10 

6
 1.2 10 cm 
November 4th 2011
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 P 


 0.0331s 
4
2
Bp


-1


erg
s
12

5
.
2

10
G


U.R.M.E., Univ. of Zielona Gora
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First Models for PSR Magnetic Field
loss of rotational energy ~ power of magneto-dipole radiation:
B R  sin 

I 
3
6c
2
6
4
2
Idea about the 19magnetic
field

B  3.2 10 PP
strength of neutron stars.
8
15
B ~ 10 ...10 G
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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Confirmation by
X-ray Spectra!
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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First Models for PSR Age
 
I
Bp2 R 6  4 sin 2 
6c 3
   K ( B , R ) 3
, i.e. 
p

d 1 


 K  with K   3 and T     :

2 

dt  2 


2




T

1   the
  characteristic
Idea
t  about
a
2    i  


age of neutron stars.
 P
if       

 2P
a
2
i
P and dP/dt of Crab PSR : 1243 yrs ⇒ 955 yrs real age ⇒ quite good!
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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Comparison with „real“ pulsar age:
Pin=1s
Pin=0.1s
Pin=0.01s
Log age [yrs] 2
4
6
8
Quite good coincidence
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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November 4th 2011
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November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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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 ≳ 108 yrs
• millisecond pulsars:P≲0.01s, B≲ 108G,
age ≳ 109 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
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young NSs
old NSs
: stronger field
: weaker field
magnetic field decay
NSs in binaries : weaker field
millisecond PSRs : rapid rotation
accretion spins up &
decreases magnetic field
magnetars
strong magnetic field
brakes rotation efficiently
November 4th 2011
: slow rotation
U.R.M.E., Univ. of Zielona Gora
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A neutron star‘s life will not be boring but
may evolve through varies periods,
sometimes very fast, sometimes dramatic,
and sometimes very slowly.
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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Radius ~ 10km, Mass ~ 1.4M⊙
Neutron stars are the only stellar objects
where 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
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Little exercise:
Epot= Ekin⇒ escape velocity ve =
if ve = c ⇒ RS =
Schwarzschild radius
gravitational redshift:
No energy (radiation) can leave the surface!!!
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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Radius
Mass
Sun
M⊙
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
R⊙
Mean Density (g/cc)
Surface Pot.(GM/Rc2 = Rs/R )
Object
1
10-6
proper time and length at the surface
36
general relativistic effects
neutron stars
• 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
- energy of elm waves (light) ⇒ light bending
- magnetic energy dissipation
- thermal energy transfer
⇒ decelerated cooling
- rot. energy (spin, orbital)
⇒ gravitational waves
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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gravitational redshift
November 1st 2011, Maitra, Miller, Raymond, Reynolds by XMM observations:
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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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
curved space trajectory
flat space trajectory
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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a part of a neutron star‘s back side is seen
⇒ gravitational light bending makes a larger
part of the neutron star surface „visible“
⇒ consequences for the interpretation of
surface features and lightcurves
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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the whole star
is seen
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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increasing compactness
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
R ⇾ Rs :
pulsations
become
less visible
43
relativistic heat transfer – decelerated cooling
relativistic field diffusion – decelerated decay
thermal energy
magnetic energy
~ mass
⇒ subject to and source
of gravitation
less
important
flat space:
constant conductivities:
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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relativistic generalization:
Schwarzschild coordinates
GR-effects:
2. spatial derivative of gravitational redshift
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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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
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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 agreement
with loss of energy due to gravitational waves
as predicted by GR!
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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2D representation of gravitational waves generated
by two neutron stars orbiting each other
November 4th 2011
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theoretical curve
rate of decrease of
orbital period: 76,5 μs/yr
observed
change in the epoch
of periastron with date
rate of decrease of
semimajor axis: 3,5 m/yr
1993 Nobel Prize
Calculated lifetime to
final inspiral: 300000 yrs
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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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
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Neutron Star Core Structure for T < Tc:
Ω
B
proton fluxoids (SC)
neutron vortices (SF)
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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Forces acting upon a fluxoid:
Fn
Fb
1 c
Fcrust
vp 4


  
E  B  dA
core
Fd
Flux expulsion from balance of forces:
Fb + Fd(vp) + Fn + Fcrust(vp) = 0
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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Core Magnetic Field Evolution
Bcore will be re-arranged in the SF core
but
can be dissipated only in the crust
⇒ decay determined by conductive properties of the inner crust
 ohm
σic
4l 2

c2
~ 1028s-1, lic
~ 105cm
Core field decays on time scales > 108 yrs!
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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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
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November 4th 2011
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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
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Crustal Magnetic Field Evolution
magnetization parameter
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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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
• ⇒Hall induction equation:


2



 1 
 
c
B   curl  curlB    (curlBe )  
B
B  
  
4
 0

diffusion & dissipation
Hall drift
Non-linear B-decay in the crust!
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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Hall-Drift ⇒ Hall-Instability
σ=const, B0=f(z)ex, small perturbations in y-direction,
small scale strong B
perfect conductor boundary
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
vacuum boundary
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
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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
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Thank you!
November 4th 2011
U.R.M.E., Univ. of Zielona Gora
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November 4th 2011
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November 4th 2011
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