1. High Energy Astrophysics jlc@mssl.ucl.ac.uk http://www.mssl.ucl.ac.uk/
Supernovae
High Energy Astrophysics

2. 3. Supernovae: Stellar evolution, collapse and energy release; Shock waves; Neutrinos; Phases of shock expansion; X-ray spectra [3]

3. Introduction Supernovae occur at the end of the evolutionary
history of stars.
Star must be at least 2 M; core at least 1.4 M.
Stellar core collapses under the force of its own
gravitation.
Energy set free by the collapse expels most of star’s mass.
Dense remnant, often a neutron star, remains.

4. Nuclear binding M (A, Z) < ZM + (A - Z)M → Mass deficit
M (A, Z) = ZM + (A - Z)M - (E /c )
Life of a star is based on a sequence of nuclear fusion reactions
Heat produced counteracts gravitational attraction and prevents collapse
Nuc p n 2
Nuc p n b

5. Binding energy and mass loss
A=total no. nucleons
Z=total no. protons
E = binding energy
Change from X to Y emits energy since Y is more tightly bound per nucleon than X. b
binding energy per nucleon
Fusion
Fission A X Y Fe Y X

6. Stellar Evolution and Supernovae
Stellar evolution – a series of collapses and fusions
H => He => C => Ne => O => 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 energy so an inert Fe core formed
Fuel in core exhausted hence star collapses.

7. Stellar Evolution Sequence
For large stellar mass – M > 8 M
H fusion to He  Red Giant/H-fusion shell
He fusion to C  “ “ /He- “ “
C fusion to Ne  “ “ /C- “ “
[for M < 8 M → C-flash/star explodes]
4. Ne fusion to O  “ “ /Ne- “ “
O fusion to Si  “ “ /O- “ “
Si fusion to Fe  “ “ /Si- “ “
[BUT with inert Fe core!]
Each step of the cycle is shorter than its predecessors due to
the progressively reducing element abundances

8. Stellar Evolution Schematic
Complete Star -
a Red Supergiant
Nuclear Fusion Regions
near Inert Fe Core
103 R
core

9. Stellar Mass Ranges for Supernovae
2.0 < M < 8 M
1.4 < M < 1.9 M
8.0 < M < 15 M
M > 1.9 M
15 M < M
Three possibilities:
star
Type I SN
core
Type II SN (NS)
star
core
Type II SN
(BH)
star
If the star has < 2 M or the core is < 1.4 M, it
undergoes a quiet collapse, shrinking to a stable
White Dwarf.

10. Stellar Mass Ranges (Cont.)
Type I: Small cores so C-burning phase occurs catastrophically in a C-flash explosion and star is disrupted
2.0 < M < 8 M → Disintegration/no Neutron Star
Type II: More massive, so when Si-burning begins, star shrinks very rapidly
8 < M < 15 M → Neutron Star
15 M < M → Black Hole
star
star
star

11. Stellar Collapse and Supernova Summary
Stars with a defined mass range evolve to produce cores that can collapse to form Neutron Stars
Following nuclear fuel exhaustion, core collapses gravitationally; this final collapse supplies the supernova energy
Collapse to nuclear density, in ≈ few seconds, is followed by a rebound in which the outer parts of the star are blown away
The visible/X-ray supernova results due to radiation
i From this exploded material
ii. Later from shock-heated interstellar material
Core may
Disintegrate
Collapse to a Neutron star
Collapse to a Black Hole
according to its mass which in turn depends on the mass of the original evolved star

12. Energy Release in Supernovae44
Outer parts of star require >10 J to form a Supernova… how does the implosion lead to an explosion?
Once the core density has reached kg m , further collapse impeded by nucleons resistance to compression
Shock waves form, collapse => explosion, sphere of nuclear matter bounces back. 17 18 -3

13. Shock Waves in Supernovae
Discontinuity in velocity and density in a flow of matter.
Unlike a sound wave, it causes a permanent change in the medium
Shock 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, even though the pressure (nkT) increases because n is larger.

14. Importance of Neutrinos
Neutrinos carry energy out of the star
They can
- Provide momentum through collisions to
throw off material.
- Heat the stellar material so that it expands.
Neutrinos have no (or very little) mass (like
photons) and can traverse large depths without
being absorbed but they do interact at typical
stellar core densities r > 1015 kg m-3

15. Neutrinos (Cont.)
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 (M < 2.5 M) 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.
core

16. Neutrinos (Cont.)
Neutrinos detected consistent with number expected from supernova in LMC in Feb 1987.
Probably type II SN because originator was massive B star (20 M)
Neutrinos are rarely absorbed so energy changed little over many x 10 years (except for loss due to expansion of Universe)… thus they are very difficult to detect.
However density of collapsing SN core is so high that it impedes even neutrinos!!! 9

17. Supernovae Energy release ≤ 10 J in type I and II SN45
Energy release ≤ 10 J in type I and II SN
Accounts for v >10,000 km/s initial velocity of expanding Supernova Remnant (SNR) shell.
Optically the “star” brightens by more than 10 magnitudes in a few hours, then decays in weeks - months
Explosive nucleosynthesis:
Reactions of heavy nuclei produce ~ 1 M of
Ni which decays to Co and Fe in ~ months
Rate of energy release consistent with optical light curves (exponential decay; t ~ d) 56 56 56

18. System radiates (dE/dt) . Note E ~10 J
Shock Expansion
At time t=0, mass m of gas is ejected with velocity v and total energy E .
This interacts with surrounding interstellar material with density r and low temperature.
System radiates (dE/dt) Note E ~ J
Shock front, ahead of ‘heated’ material R
Shell velocity much higher than sound speed in ISM, so shock front of radius R forms.
ISM, r
41-45
rad

19. Supernova Remnants
Development of SNR is characterized in phases – values are averages for “end of phase”
Phase I II III
Mass swept up (M)
Velocity (km/s)
Radius (pc)
Time (yrs) , ,000
Phase IV represents disappearance of remnant

20. Summary of SNR Expansion Phases
mo >> MISM
mo < MISM - shock heated gas adiabatic due to high temperature
mo < < MISM - gas cools radiatively at constant momentum

21. 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 within sphere radius R is still small.
(1)

22. (2) Since momentum is conserved:
Applying condition (1) to expression (2) shows that the velocity of the shock front remains constant, thus :
v(t) ~ v
R(t) ~ v t
(2)
From equation 1 on the previous slide, the second term in the brackets is negligible, so
m0 x v0 ~ m0 x v(t)
Thus v(t) ~ v0 and the radius, R(t) ~ v0 x t

23. Supernova 1987A
SNR
B3 I Star exploded in February 1987 in Large Magellanic Cloud (LMC).
Shock wave now ~ 0.13 parsec away from the star, and is moving at vo~ 3,000 km/s.
This is an image of SN1987a from the Hubble Space Telescope, taken 10 years after the explosion.
The progenitor star had a mass more than six times that of our Sun, like many of the other hot stars in this picture. They are all about 12 million years old and are of the same generation of the star that went supernova. All the bright gas lying around indicates that this is a star-forming region.

24. 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.
Around the progenitor star, lay two sets of dusty gas rings. These rings were thrown off much earlier in the history of the star – the inner ring was thought to have been formed 20,000 years ago. It is not known whether these are actually rings as such, or whether they are part of an invisible sphere of gas. We may see them only as rings due to our special line of sight to the system.
Neither is it known why this material was thrown off. Massive stars do eject material in the course of their natural evolution – or a binary companion may have been dumping matter onto the progenitor, and the material was thrown off in a nova-like explosion.
X-ray and radio emission from the supernova were detected soon after the initial explosion, but was not resolvable at that time. Even the Hubble Space Telescope has only just begun to resolve the optical emission from the shock as it ploughs its way through the ISM.
The inset shows the optical shock – it’s a one-tenth light-year long dumbbell-shaped structure consisting of two blobs of debris expanding apart at nearly 3,000 km/s. It’s dumbbell-shaped because there was a ring of material around the star which has now faded.

25. 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.

26. Chandra X-ray Images of SN 1987A
X-ray intensities (0.5 – 8.0 keV) in colour; HST Ha images as contours
Low energy X-rays
well correlated with
optical knots in ring
– dense gas ejected
by progenitor?
Higher energy X-rays
well correlated with
radio emission – fast
shock hitting
circumstellar H II
region?
No evidence yet for
emission from central
pulsar

27. Phase II - adiabatic expansion
Radiative losses are unimportant in this phase - no exchange of heat with surroundings.
Large amount of ISM swept-up:
(3)

28. Thus (2) becomes :
since mo is small
(4)
Integrating:
(5)
Substituting (4) for movo in (5)
R(t) = 4v(t).t
v(t) = R(t)/4t

29. Temperature behind the shock, T  v2, remains high – little cooling
Taking a full calculation for the adiabatic shock wave into account for a gas with g = 5/3:
and
Temperature behind the shock, T  v2, remains
high – little cooling
Typical feature of phase II – integrated energy
lost since outburst is still small:
If the calculation for the velocity and radius of the SNR are done properly, taking into account the adiabatic shock wave, then the equations shown apply (see Giacconi and Gursky, p228).
The typical feature of phase II of the SNR expansion is that the integrated radiative energy lost since outburst is still small, but note that some emission is still produced.

30. N132D in the LMC SNR age ~ 3000 years
Ejecta from the SN 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
Progenitor
The precursor to this supernova, located slightly below and left of centre in this image, is thought to have been 25 times the mass of our Sun.
Oxygen-rich stellar material is moving out at velocities of about 2,000 km/s, creating shock fronts. Shock fronts from the original SN have been reflected from dense ISM clouds. As the stellar material passes through in filaments, they glow (these are shown blue-green). The dense ISM clouds have been heated and crushed by the SN shocks – these are shown red.
This region measures 50 light years across. The SN is located in the Large Magellanic Cloud, 170,000 light years away.

31. SNR N 132D XMM-Newton CCD Image and Spectrum
X-ray image gives a
more coherent view of
the SNR
Lower ion stages
(N VII, C VI) show
T ~ 5 MK gas in ISM
filaments at limb
Higher ion stages
(Fe XXV) show
T ~ 40 – 50 MK gas
more generally
distributed

32. Phase III - Rapid Cooling
SNR cooled, => no high pressure to drive it forward.
Shock front is coasting
Most material swept-up into dense, cool shell.
Residual hot gas in interior emits weak X-rays.
= constant
During phase III, the SNR cools very rapidly. We will consider the end of this phase.
Without the high temperature behind the shock, there is no high pressure to drive it forward through the ISM. The shock front is now `coasting’ with constant radial momentum, ie. All the material in the shell moves outwards with total momentum given by the equation shown.
Most of the swept-up material is compressed into a dense, relatively cool shell (a temperature of approx. 1e4K). There is some X-ray emission from the residual gas in the interior, but this is much weaker than before.

33. XMM X-ray Observations: SNR DEM L71
Remnant in Large Magellanic Cloud (LMC):
d = 52 kpc; diam → 10 pc; age → 104 yr
0.7 – 1.0 keV
Chandra X-ray image: shell & centre
Just entering Phase III:
vshock ~ 500 km/s; Tinterior ~ 15 MK, Tshell ~ 5 MK
Shell emission dominates (XMM CCD spectra)
Emission line spectrum from XMM RGS shows:
- thermal nature of the plasma
- element abundances like LMC
Shell
Interior
XMM CCD Spectra
XMM Reflection Grating Spectrometer (RGS) spectrum

34. Phase IV - Disappearance
ISM has random velocities ~10 km/s.
When velocity (SNR) is ~ 10 km/s, it merges with the ISM and is ‘lost’.
Entire four-phase model represents an
oversimplification!!!
- magnetic field (inhomogeneities in ISM)
- pressure of cosmic rays
- shock interacts with interstellar clouds
(velocity and temperature decrease and radiation increases)
Although we have regarded the ISM so far as being a cold, stationary gas, it has random velocities of approx 10 km/s. Once the SNR shell becomes this slow, it merges with the ISM in front of it and is lost.
However, this is an oversimplification in that the ISM has a magnetic field and may present inhomogeneities to the SNR. Moreover, the pressure of cosmic rays must be taken into account. Both of these factors affect the expansion of the SNR.
The magnetic field may help the coupling of the ejected matter with the ISM so that a shock wave can develop. Inhomogeneities of the ISM are also important, since the shock velocity and radiation intensity are both a function of density; as the shock enters a dense cloud, the velocity decreases and the radiation increases.

35. Example – Nature of Cygnus Loop
- passed the end of phase II
- radiating significant fraction of its energy R ~ 20pc v ~ 115 km/s (from Ha filaments)
Lifetime,
= 2 x seconds = 65,000 years
now
now
t ~
We will now take the case of the Cygnus Loop, which has probably past the end of phase II and is radiating a significant fraction of its energy.
Using the equation t=0.4R(t)/v(t) (see equation (5) onwards) and substituting the values for R(now) and v(now), gives a lifetime for the Cygnus Loop SNR of approximately years. 12

36. Assuming v = 7 x 10 km/s and r = 2 x 10 kg m3
Assuming v = 7 x 10 km/s and r = 2 x kg m
from (5) we find that m ~10 M
Density behind shock, r, can reach 4r
(r is ISM density in front of shock)
Matter entering shock heated to:
( = av. mass of particles in gas)
-21 -3
These are average values for a SNR of this type.
The density immediately behind the shock front, which can be identified with the density in SNR shell, can reach a maximum of 4 times the initial density, ie 4 times the density of the IS material which lies in front of the shock.
The matter which enters the shock from the ISM is heated to the temperature as shown, where the mean mass is the average mass of all of the elements in the gas. k is Boltzmann’s constant

37. For fully ionized plasma (65% H; 35% He)
Cygnus Loop: v ~ 10 m/s → 100 km/s
=> T ~ 2 x 10 K (from (6))
But X-ray observations indicate T ~ 5 x 10 K
implying a velocity of 600 km/s.
Thus Ha filaments are denser and slower
than rest of the SNR structures.
(6) 5
now 5 6
Using this equation and assuming a fully ionized plasma which is composed of 65% hydrogen and 35% helium, the temperature is then given by equation (6).
The observed velocity of the SNR measured from the Halpha line emission is 100 km/s and this corresponds to a temperature of 200,000K. However, X-ray observations indicate a temperature of 5 million K, implying a much higher velocity of 600 km/s. Thus the Halpha filaments must be more dense and slower than the rest of the SNR.
This is also observed in Cas A and Tycho, and is evidence of inhomogeneities in the ISM.

38. Young SNRs Marked similarities in younger SNRs.
Evidence for two-tempertaure thermal plasma low-T < 5 keV (typically keV) high-T > 5 keV (T = 1.45 x 10 v K)
Low-T - material cooling behind shock
High-T - bremsstrahlung from interior hot gas -5 2
Marked similarities have been observed between the younger SNRs, eg. Cassiopeia A, Tycho and Kepler which are all about 400 years old.
The data may be explained as thermal emission from a plasma, but not at a single temperature: a high-temperature component dominates above ~5keV and a low-temperature component below ~5keV.
The equivalent temperature of the high-T component is about 40million degrees K for these young SNRs. The low-T component is probably due to material which is cooling behind the shock front. The high-T component is bremsstrahlung emission from hot gas in the interior of the SNR and dominates the SNR emission.

39. 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 2 keV.
Examples : Puppis A, Vela, Cygnus Loop
The comparisons shown are relative to the younger SNRs discussed in the previous slides.

40. Crab Nebula
First visible/radio object identified with a cosmic X-ray source.
lunar occultation => identification and extension
Well-studied and calibration source (has a well known and constant power-law spectrum)
The Crab Nebula was the first visible or radio object to be identified with a cosmic X-ray source.
In 1964, the lunar occultation of the Crab Nebula confirmed its identification and showed that the source was also extended.
It is one of the most studied objects at X-ray wavelengths. Furthermore, it is often used as a calibration source in X-rays in-flight because its spectral shape (which is a power-law) and flux are well determined and constant with time.

41. Crab Nebula Exploded 900 years ago. Nebula is 10 light years across.
Pulsar
The progenitor of the Crab pulsar exploded 900 years ago and is thus in phase II. The blue glow shown in the Palomar image, is due to synchrotron emission from electrons fed by the pulsar into the nebula. The green, red and yellow filaments towards the edges of the filament are remnants of the progenitor star.
The nebula measures 10 light years across and lies 7,000 light years away.
The pulsar can be seen in the HST image – it’s the left hand star of the pair in the centre of the image. The pulsar is surrounded by knots and wisps which change with time. The wisps stream away with time creating a stripy effect which changes every few days. The nebula is a lot more dynamic than was previously thought, but the reason for this is not well understood.
Exploded 900 years ago. Nebula is 10 light years across.

42. 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
There is no evidence for any thermal component in the X-ray spectrum of the Crab Nebula. It is generally accepted that the energy source for the nebula is the rotational energy of the neutron star. The mechanism for converting rotational energy into radiation involves processes occurring in rapidly varying, intense magnetic field. We will see the details of this when we treat pulsars in general in the very near future.
But briefly, the emission of the nebula is controlled by the pulsar. Electrons are released from the atmosphere of the spinning neutron star and into the nebula itself. Here, the interaction of the electrons with the magnetic field gives rise to synchrotron radiation, over essentially all of the electromagnetic spectrum.

43. Spectrum of the Crab Nebula
Log flux density
-22
-32
Watts per sq m per Hz
also g-rays detected up to 2.5x10 eV
Radio
IR-optical
X-ray
This is the observed spectrum of the Crab Nebula which extends from the radio to X-rays and continues into the gamma-rays, reaching energies of 2.5e11 eV (equivalent to 5e25 Hz) and higher.
For more information, see Giaconni and Gursky, p282. 8 10 16 20
Log n (Hz) 11

44. Summarizing: B ~ 10 Tesla to produce X-rays n ~ 10 Hz (i. e
Summarizing: B ~ Tesla to produce X-rays n ~ Hz (i.e. peak occurs in X-rays) E ~ 3 x 10 eV
t ~ 30 years
Also, expect a break at frequency corresponding to emission of electrons with lifetime = lifetime of nebula. Should be at ~10 Hz (l~3000Angstroms). This and 30 year lifetime suggest continuous injection of electrons. -8
nebula 18 m 13 e-
syn
From previous work calculating properties of synchrotron emission from the Crab Nebula, the magnetic field in the nebula must be approx 1e-8 Tesla to produce X-rays, the peak in the emission must occur at 1e18Hz, the energy in the electrons must be ~3e13eV and the lifetime for the synchrotron emission assuming these parameters is about 30 years.
We have also seen that we can expect a break in the spectrum at a frequency corresponding to the emission of electrons with a lifetime equal to that of the nebula. This should be at about 1e15 Hz (a wavelength of about 3000A, ie in the blue). If there is a break, it is not sharp. This, and the synchrotron lifetime of about 30 years, suggest that a continuous injection of electrons must be occurring. 15

45. SUPERNOVAE
END OF TOPIC