Download Neutron Stars, second class

th
4
lecture of “Compact
Object and Accretion”,
Master Programme at Leiden
Observatory
nd
2
Neutron Stars
class
study material: Chapter 10, ShapiroTeukolsky
these slides at
http://home.strw.leidenuniv.nl/~emr/COA/
Friday, October 16, 2015
Neutron star
observations
Friday, October 16, 2015
Gravitational time dilation
Locally, an interval in proper time is related to the
space-time metric by
An observer at rest on NS surface measures an
interval in proper time
while an observer at infinity will measures
Therefore, an intrinsic period signal of the source on time scale T0
will be observed with a period
longer periods
Friday, October 16, 2015
Einstein’s gravitational
redshift
A signal of wavelength λ0 ~ T0 will then be redshifted
where the object compactness is
Note, for White Dwarfs
This measurement may be used in principle to constrain M/R,
however, as mentione in the introduction it is difficult to detect the
surface emission and therefore line emission. In non thermal X-ray
flares is easier, e.g. Cottam et al. 2002 with XMM, z~0.35 ==>
compactness of ~0.23 in agreement with typical expectations
Friday, October 16, 2015
Neutron star cooling
(just some facts)
•
•
A NS is born very hot ~1011 K
•
When T~108 K photon cooling becomes dominant,
which corresponds to a surface T~106 K
•
Detection of thermal emission hampered by small
radius and peak emission in soft X-ray
Friday, October 16, 2015
It cool by neutrino emission for the first ~1000 yr.
Initial cooling is quite rapid: on a day timescale T
~109-1010K
Mass measurements
In binary systems, the pulsar signal is modulated by
the orbital period. The parameter T (period) and a1sin
(i) (the distance form the centre of mass of primary
projected perp. to line of sight) allows to determines a
combination of primary and secondary masses M1
and M1: Newtonian mass function from 3rd Kepler
The Doppler effect measured with lines gives a1 sin(i).
If the mass function can be also constructed for the secondary, both
mass can be determined, otherwise not. Additional uncertainty in
“i”. This is also true for WDs
Friday, October 16, 2015
Mass measurements
For binaries with two NSs, general relativistic effects help
constraining mass precisely, since effects depend on mass.
E.g. pericenter precession of orbital motion, that
“advances” at a rate:
if also other effects like, Einstein’s redshifts, period’s change due to
gravitational wave etc... can be measured, then the mass and orbital
parameter measurements become very precise, allowing for orbital
evolution predictions (e.g. Hulse & Taylor’s work)
Friday, October 16, 2015
NS + WD
Double NSs
smaller errors
Kiziltan et al. (2013)
Friday, October 16, 2015
Pulsars
how does it work ?
Friday, October 16, 2015
Description
•
pulse period P extremely
stable
•
pulse shape averaged
over ~100 or more
stable
•
pulse shape different
from pulsar to pulsar
•
two populations of
pulsars + magnetars
•
•
dP/dt >0 typically
d2P/dt2 <0 typically. P
increases slower in time
“recycled”
milli-pulsars.1-100ms
Friday, October 16, 2015
Normal pulsars:
30 ms-3 s
Glitches
•
•
•
•
sometimes the period suddenly decreases
typically, but can be up to ~4 10-6
~1%
for
for
After glitches, the period goes back to its original value
Friday, October 16, 2015
Pulsar emission model
we need to consider magnetic fields...
Friday, October 16, 2015
Basic model assumes:
1. Solid rotation with angular
frequency Ω (P = 2π/Ω).
Justified by superfluidity
2. Dipolar magnetic field
configuration, with magnetic
dipole m at angle α with rotation
axis, again good guess
3. In vacuum (not so good)
Friday, October 16, 2015
Dipolar emission
Power emitted by an
accelerated magnetic
dipole
(remember Larmor formula ?)
In a Cartesian coordinate system with z-axis = rotation axis
Let’s express “m” as a function of the polar magnetic field at the NS
surface
Friday, October 16, 2015
Dipole magnetic field in spherical coordinates with
axis (
) equal to the magnetic axis:
Polar Magnetic field at r=R ;
Solving for “m” and inserting in power
formula:
radiation power emitted by a
rotating magnetic dipole in
vacuum
Friday, October 16, 2015
law of deceleration
•
•
•
Energy is lost at the expenses of
rotational energy (mass and
gravitational energy do not
change)
Energy conservation, ignoring
GW emission from
deformation (this may not be
valid for young < 100 yr
pulsars) of NS reads :
Solving it, assuming constant
NS structure i.e. constant
moment of inertia “I”
Friday, October 16, 2015
Magnetic field
Note
the pulsar decelerates with time!
With this formula it is possible to estimate Bp, once P and
are measured
Friday, October 16, 2015
P-Pdot diagram
t
n
a
t
s
n
o
c
Line of
deceleration timescale
constant
i.e.
The higher B, the faster
deceleration. The rotational
energy power is similar for
all 3 populations
Friday, October 16, 2015
Magnetars
deceleration index
measured
it is possible to infer the deceleration index “n”
let’s understand where it comes from. If we assume
for the model developed here n=3. See deceleration
law expressed in terms of Ω
Friday, October 16, 2015
deceleration index
Note: “n” is typically a bit different from ~3, this tells
us that this simple model is too simple. Note
however, that if the energy loss was only for
gravitational waves n~5, which differs even more from
observations
Friday, October 16, 2015
deceleration timescale
= age of a pulsar
n
If we integrate
n
n
with
n
n
n
n
n
n
when n is not measured is assumed n=3. For Crabe t = 1200 yr and
we know that t= 961 yr (happened in 1054). good agreement!
Friday, October 16, 2015
deceleration timescale =
age of a pulsar
•
Classical pulsars are
younger than ~100 Myr
•
millisecond Pulsars are
older than ~100 Myr
Friday, October 16, 2015
Goldreich & Julian (1969)
Assumption of vacuum faulty: the rotating dipole induce a
strong electric field, orders of magnitude larger than gravity :
charges are accelerated from the NS crust at the poles and fill
the magnetosphere: the potential drop in vacuum is
the charges from a
“pulsar” wind that escape
through open B lines (see
next slide)
The pulsar wind carries
most of the extracted
rotational energy
Friday, October 16, 2015
Poynting flux
Goldreich & Julian (1969)
The magnetosphere structure is different: there is a corotating magnetosphere at the interior of the light cylinder RL=
c/Ω. The magnetic lines that intercepts RL are open and
particles and escape
Pulsar’s magnetosphere are larger
Poynting flux
Friday, October 16, 2015
more realistic models
Friday, October 16, 2015
•
Modern hydromagnetic simulations
showed that the G-J
model does not work
as you need to include
pair-production
•
standard view: charges
that escape along B line
emit radio via
“curvature” emission
•
standard view: charges
that heat back the NS
crust causes the crust to
heat up and emit
thermal X-ray
Open issues
• model/simulate pair production
• where the radiation, especially ϒ-rays is
generated ?
• what is
Friday, October 16, 2015
the mechanism that produce radio ?
Radiation:
observational facts
•
radiation is around/less than 10% of the
extracted rotational energy (spin-down
energy)
•
radio makes up only about
extracted energy
•
most of the radiation energy is in emitted in
ϒ-rays around ~GeV, fro most but some. E.g.
the Crab nebula emits mostly in X-ray
Friday, October 16, 2015
-4
~10
of total