Transcript Supernovae

Supernovae
High Energy Astrophysics
[email protected]
http://www.mssl.ucl.ac.uk/
Introduction
Supernovae occur at the end of the
evolutionary history of stars. The star must
be at least 2 solar masses: the core at least
1.4 solar masses.
Stellar core collapses under force of its own
gravitation. Energy set free by collapse
expels most of star’s mass. A dense
remnant, often a neutron star, is left behind.
binding energy per nucleon
Binding energy and mass loss
A=total no. nucleons
Z=total no. protons
E b= binding energy
X Y
Fe
Change from X to Y emits
energy since Y more
tightly bound per nucleon
than X.
Y
X
A
Nuclear binding (cont.)
• Mnucleus
(A,Z) < ZMp + (A - Z)M n
• M (A,Z) = ZMp + (A - Z)M n - (E b /c 2)
• Life of a star is based on a sequence of
nuclear fusion reactions. Heat produced
counteracts gravitational attraction and
prevents collapse.
From the core outwards,
H => He, He => C, C => O, Ne, Si
Outer parts of star expand to form opaque and
relatively cool envelope (red giant phase).
Eventually, Si=>Fe: most strongly bound of
all nuclei (further fusion would absorb).
All fuel in core exhausted, then star collapses.
2 < M star < 8 solar masses
Type I SN
1.4 < Mcore< 1.9 solar masses
8 < M star< 15 solar masses
Type II SN
M core > 1.9 solar masses
If the star has less than 2 solar masses (or the
core is less than 1.4 solar masses), it
undergoes a quiet collapse, shrinking to a
stable white dwarf.
Type I: Small cores so C-burning phase
occurs catastrophically in a C-flash
explosion and star is disrupted. (may also
happen to stable wd in binary if M>1.4SM).
Type II: More massive, so when Si-burning
begins, star shrinks very rapidly.
Energy release in Supernovae
• Outer parts of star require >10 44J to form
SN… how does the implosion lead to an
explosion?
• Once the core density has reached
1017 - 1018 kg m-3 , further collapse impeded
by nucleons resistance to compression
• Shock waves form, collapse => explosion,
sphere of nuclear matter bounces back.
Shock Waves in Supernovae
• Discontinuity in velocity and density in a
flow of matter. Causes permanent change in
medium..., speed >> sound speed,
between 30,000 and 50,000 km/s.
• Shock wave may be stalled if energy goes
into breaking up nuclei into nucleons. This
consumes a lot of energy, although the
pressure (nkT) increases because n larger.
Importance of neutrinos
_
p + e => n + n
inverse b-decay
Neutrinos carry energy out of the star and
provide momentum through collisions to
throw off material.
Or they heat the material so that it expands.
They have no mass (like photons) and can
traverse large depths without being absorbed.
Thus a stalled shock wave is revived by
neutrino heating. Boundary at ~150 km:
inside, matter falls into core
outside, matter is expelled.
After expulsion of outer layers, core forms
either neutron star (Mcore < 2.5 solar masses)
or black hole (depends on gravitational field
which causes further compression).
Neutrino detectors set up in mines and tunnels
- must be screened from cosmic rays.
• Neutrino detection consistent with that
expected from SN in LMC in Feb 1987.
This was probably type II SN because
originator was massive B star (20 solar
masses)… although also individual.
• Neutrinos are rarely absorbed so energy
changed little over many x 10 9 years
(except for loss due to expansion of
Universe)… thus they are difficult to detect.
• Density of collapsing SN core is so high
however that it impedes even neutrinos!!!
Energy release up to 10 45J in type I and II SN,
accounts for >10,000 km/s initial velocity of
expanding SNR shell.
Optically, star brightens by more than 10mag
in a few hours, then decays (weeks-months)
Explosive nucleosynthesis => heavy nuclei
nuclear reactions produce ~1 solar mass
Ni which decays to Co and Fe over a
56
56
56
few months. Rate energy release consistent
with optical light curves (exponential decay
with 50-100 day time constant).
Supernova Remnants
Development of SNR (averages; end of phase)
Phase
I
II
III IV
Mass swept up
0.2
180
3600
Velocity (km/s) 3000
200
10
Radius (pc)
0.9
11
30
Time (yrs)
90 22,000 100,000
*solar masses
At time t=0, mass m 0 of gas is ejected with
velocity v 0 and total energy E 0 . This
interacts with surrounding interstellar
material with density r 0 and low-T.
Shock front, ahead
of ‘heated’ material
R
Shell velocity much
higher than sound speed
in ISM, so shock front
radius R forms.
ISM, r 0
System radiates (dE/dt)rad . Note E 0 ~10 41-45 J
SNR Development - Phase I
• Shell of swept-up material in front of shock
does not represent a significant increase in
mass of the system.
• ISM mass previously within sphere radius
R is still small.
4
3
m0 
r 0 R (t )
3
(1)
• Since momentum is conserved:
4
3
m0 v0  (m0 
r 0 R (t )). v(t )
3
(2)
• Applying condition (1) to expression (2)
shows that the velocity of the shock front
remains constant : v(t) ~ v 0
and that
R(t) ~ v 0 t
Supernova 1987a
•Star exploded in
February 1987 in Large
Magellanic Cloud.
•Shock wave is now
about one eighth of a
parsec away from the
star, and is moving at
3,000 km/s.
Dusty gas rings light up
•Two sets of dusty
gas rings surround
the star in SN1987A,
thrown off by the
massive progenitor.
•These rings were
invisible before –
light from the
supernova explosion
has lit them up.
Shock hits inner ring
The shock has hit the inner ring at 20,000 km/s, lighting
up a knot in the ring which is 160 billion km wide.
Phase II - adiabatic expansion
Radiative losses are unimportant in this phase
- no exchange of heat with surroundings.
Large amount of ISM swept-up:
4
3
m0 
r 0 R (t )
3
(3)
Thus (2) becomes :
4
3
m0 v0  (
r 0 R (t )). v(t )
3
4
dR (t ) (4)
3

r 0 R (t )
3
dt
Integrating:

(5)
m0 v0t  r 0 R 4 (t )
3
Substituting (4) for m0 v0 in (5),
R(t) = 4v(t).t, or v(t) = R(t)/4t
• Taking adiabatic shock wave into account:
1
5 2
5
 E0 
R(t )  1.17  t
 r0 
and
R (t )
v(t )  0.4
t
•Typical feature phase II – the integrated
energy lost since outburst is still small:
 dE 
  dt  RAD.dt  E0
Crab Nebula
Exploded 900 years ago. Nebula is 10 light years across.
Wisps and knots and around
the Crab pulsar
• Watch very carefully. The pulsar is the left
of the pair. There are four separate
sequences, each one successively closer in
N132D in the LMC
•Ejecta from the
supernova slam into the
ISM at more than 2,000
km/s creating shock
fronts.
•Dense ISM clouds are
heated by the SNR
shock and glow red.
Stellar debris glows
blue/green
Phase III - Rapid Cooling
• SNR cooled, => no high pressure to drive it
forward.
• Shock front is coasting
4 3
R r 0 v = constant
3
• Most material swept-up into dense, cool
shell. Residual hot gas in interior emits
weak X-rays.
Phase IV - Disappearance
• ISM has random velocities ~10 km/s.
• When velocity(SNR)=10 km/s, it merges
with ISM and is ‘lost’.
• Oversimplification!!!
- magnetic field (inhomogeneities in ISM)
- pressure of cosmic rays
Example - Cygnus Loop
- passed the end of phase II
- radiating significant fraction of its energy
Rnow ~ 20pc
vnow ~ 115 km/s (from Ha)
16
lifetime,
Rnow 20 3 10  0.4
t ~ 0.4

sec
5
vnow
= 2 x 10 12 seconds
1.1510
= 65,000 years
3
Assuming v0 = 7 x 10 km/s
and r0 = 2 x 10 -21 kg m-3 ,
from (5) we find that m0 ~10 solar masses
Density behind shock, r, can reach 4r 0 , (r0
is ISM density in front of shock.
3 m 2
Matter entering shock heated to: T 
v
16 k
( m = av. mass elements in gas)
For fully ionized plasma (65% H; 35% He)
-5
T  1.4510 v
2
(6)
Cygnus Loop: vnow ~ 105 m/s
=> T ~ 2 x 10 5 K (from (6))
But X-ray observations indicate T ~ 5 x 10 6K
implying a velocity of 600 km/s. Thus Ha
filaments more dense and slower than rest
of SNR.
Young SNRs
• Marked similarities in younger SNRs.
• Evidence for two-temp thermal plasma
- low-T < 5 keV (typically 0.5-0.6 keV)
- high-T > 5 keV (T = 1.45 x 10 -5v 2 K)
• Low-T - material cooling behind shock
High-T - bremsstrahlung from interior hot
gas
Older SNRs
• A number of older SNRs (10,000 years or
more) are also X-ray sources.
• Much larger in diameter (20 pc or more)
• X-ray emission has lower temperature essentially all emission below 2keV.
• Examples : Puppis A, Vela, Cygnus Loop all Crab-type SNRs.
Crab Nebula
• 1st visible/radio object identified with
cosmic X-ray source.
• 1964 - lunar occultation => identification
and extension
• Well-studied and calibration source (has a
well known and constant power-law
spectrum)
Crab Nebula
Exploded 900 years ago. Nebula is 10 light years across.
• No evidence of thermal component
• Rotational energy of neutron star provides
energy source for SNR
(rotational energy => radiation)
• Pulsar controls emission of nebula via
release of electrons
• Electrons interact with magnetic field to
produce synchrotron radiation
Model of the Crab
• You’re moving out from the pulsar which is
spinning around, in your line of sight to
start with.
• But the angle of orientation then changes…
Spectrum of the Crab Nebula
Watts per sq m per Hz
Log flux density
Radio
-22
IR-optical
X-ray
Log n (Hz)
-32
8
10
16
also g-rays detected up to
20
2.5x1011 eV
• Summarizing:
Bnebula ~ 10-8 Tesla to produce X-rays
nm ~ 1018 Hz (ie. peak occurs in X-rays)
E e- ~ 3 x 1013 eV
tsyn ~ 30 years
• Also, expect a break at frequency
corresponding to emission of electrons with
lifetime = lifetime of nebula. Should be at
~10 15 Hz (l~3000Angstroms). This and 30
year lifetime suggest continuous injection of
electrons.