Neutron Star Physics a kind of introduction Ulrich R.M.E. Geppert November 4th 2011U.R.M.E., Univ. of Zielona Gora1

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


http://de.wikipedia.org/w/index.php?title=Datei:POL_Zielona_G%C3%B3ra_COA.svg&filetimestamp=20090717150257

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


Fritz Zwicky Walter Baade

1934, after the discovery of the neutron:neutron stars are in supernovae transformed out of normal stars.


http://en.wikipedia.org/wiki/File:Zwicky1.png

http://scienceworld.wolfram.com/biography/photo-credits.html

Neutron Stars First Seen as Radio Sources

Effelsberg 100m radio telescopeOne Mile Telescope completed 1964 by the Radio Astronomy Group of Cambridge University


http://en.wikipedia.org/wiki/File:One-Mile_Telescope.jpg

• 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:


Sept. 2011: Honnappa, Lewandowski, Kijak, Deshpande,Gil, Maron, Jessner: Effelsberg radiotelescope

single pulseanalysis ofPSR B1133+16

search for thecarouselcirculation time P4


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


Study of the different periodicities reveals thephysics of pulsar emissionand more.

Neutron Stars in X-Rays

XMM-NewtonNovember 4th 2011 U.R.M.E., Univ. of Zielona Gora 9

NSs in Binary Systems Bright X-ray Sourceaccr. rate ~ 7x10-9M⊙/yr, Lx ~ 1037 erg/s


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!


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


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


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


in a binary system:

~ the same problem

4. gravitational light bending

apparentsource position

true pathof lightfrom thesource


• ~ 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!!!


Observations

www.atnf.csiro.au/research/pulsar/psrcat

)(,, PPP


http://www.atnf.csiro.au/research/pulsar/psrcat

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.



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:


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.


Confirmation byX-ray Spectra!




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.


Comparison with „real“ pulsar age:

Log age [yrs] 2 4 6 8

Pin=1s

Pin=0.1s

Pin=0.01s

Quite good coincidence




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


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


A neutron star‘s life will not be boring butmay evolve through varies periods,sometimes very fast, sometimes dramatic,and sometimes very slowly.



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


Little exercise:

Epot= Ekin⇒ escape velocity ve =if ve = c ⇒ RS = gravitational redshift:

No energy (radiation) can leave the surface!!!

Schwarzschild radius


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


gravitational redshift

November 1st 2011, Maitra, Miller, Raymond, Reynolds by XMM observations:


O VIII Ly-α line

for M = 1.25 … 2M⊙ ⇒ R = 8.9 … 14.2km redshift observations ⇒ information about EoS


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


⇒ 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


the whole staris seen


incr

easi

ng c

ompa

ctne

ss

R ⇾ Rs : pulsations become less visible


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


relativistic generalization:

GR-effects:

2. spatial derivative of gravitational redshift

Schwarzschild coordinates


magnetic field decay in realistic neutron star models

increasing compactness

significant deceleration of field decay for older neutron stars


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!


2D representation of gravitational waves generatedby two neutron stars orbiting each other


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


Zielona Gora Pulsar Group:

One has to talk about the magnetic field!

Up to now no evidences against this picture !


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


ΩB

neutron vortices (SF)

proton fluxoids (SC)

Neutron Star Core Structure for T < Tc:


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


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



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


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


Strong small-scale surface B:

necessary ingredient for a PSR to flash up

Szary, Melikidze, Gil, 2011 & :

dipolar B

strong small scale B


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


Thank you!



Documents

Neutron Star Physics a kind of introduction Ulrich R.M.E. Geppert November 4th 2011U.R.M.E., Univ. of Zielona Gora1