Transcript PHYS3380_111615_bw - The University of Texas at Dallas

PHYS 3380 - Astronomy
Homework Set #10
11/16/15
Due 11/30/15
Chapter 13
Review Questions
7,11
Problems
5, 9
Chapter 14
Review Question
2
Problems
1, 3
PHYS 3380 - Astronomy
Testing the Model: SN1987A
Unique opportunity to test the core-collapse neutrino generating theory was
the supernova of February 1987 in the Large Magellanic Cloud.
Expected neutrino flux for the SN at this distance (about 50 kpc) was 1013 m2. How many detected ?
Two experiments (Kamiokande and IMB)
simultaneously detected neutrino burst,
and the entire neutrino capture events
lasted 12s. This occurred before the SN
was optically detected (or could have
become visible). Time for shock wave to
reach stellar surface (~1 hour).
Significant result of observations:
- neutrinos and antineutrinos both took the same time to arrive at earth difference in their arrival times less than 12 seconds.
first empirical evidence that matter, antimatter, and photons all
react similarly to gravity, which was widely predicted by standard
theories of gravity but not previously tested directly.
-allowed upper bounds on neutrino mass and charge
⇒rest mass of the electron neutrino is at most 16 eV/c2, 1/30,000 the
mass of an electron.
PHYS 3380 - Astronomy
SN1987A - Confirmation of Core Collapse
Core-collapse of
Before
massive star
• Catalogued star SK69 202
• M=17M
• Teff=17000
• Log L/ L = 5.0
• Star has
disappeared
• Neutrinos confirm
neutron star
formation
• No pulsar or neutron
star yet seen
At maximum
PHYS 3380 - Astronomy
Precursor
Sanduleak -69° 202, the precursor to SN 1987A, was a blue
supergiant presumed to have a mass of about 15 - 20 solar masses.
- required some revisions to models of high mass stellar
evolution, which had suggested that supernovae would
result from red supergiants.
Now believe star was chemically poor in elements heavier than He
- contracted and heated up after phase as cool, red
supergiant during which it lost much of its mass into space
Remnant
- rings caused by interaction
of fast stellar wind with older
slower winds - shaped by
magnetic fields
- two older winds from red and
blue supergiant stages
Supernova 1987a Movie Link
Rings must be related to the supernova because the supernova is at their center. But
they could not have been ejected by the supernova explosion.
- inner ring must have been expanding for 20,000 years to grow to this radius
- must have been ejected 20,000 years before the supernova explosion.
Movie illustrates the actual three-dimensional shape of the triple-ring system.
Astronomers really don't know why it has this structure - is one of the outstanding
mysteries of SN1987A.
Some physical effect must determine the polar axis of the rings. Possibly rotation.
But rotation of what? Many astronomers now believe that the parent star of
SN1987A was actually a close binary system. Perhaps the inner ring was ejected
while the merger took place, 20,000 years before the explosion.
Rapidly brightening "hot spots" are appearing all around the ring. These
hotspots appear where the blast wave (a kind of "sonic boom") from the
supernova explosion first strikes parts of the dense ring that protrude
inward. Intensity started to fade in 2011.
Light Echoes
Light Echoes
Light emitted in directions other than directly toward us encountered
nearby interstellar clouds and then was reflected. Luminous arcs could be
observed around the supernovae, called 'light echoes'. The two main arcs
or rings observed are due to clouds located at a distance of about 300 and
1100 light-years in front of the supernovae.
The optical light curve of SN1987A for the
first 1400 days after the explosion
- continued to brighten for the first 100
days after the initial flash, reaching a
maximum brightness of about 3rd
magnitude, bright enough to see with the
naked eye.
- then faded rapidly, with the brightness
dropping by a factor of 2 every 77 days
for the first 500 days
- almost exactly the same rate observed
in laboratories for the decay of the
radioactive nucleus Cobalt-56 into the
stable nucleus Iron-56 (the half-life of
Cobalt-56 is 77 days).
Astronomers long suspected that supernova explosions were responsible for
the formation of the heavy elements in the universe
- strongest confirmation to date of the idea that supernova explosions really
did make the heavy elements
- for the first time, we could measure exactly how much Cobalt-56 was
made (0.07 Solar masses)
PHYS 3380 - Astronomy
Supernova 1987A remnant in
different wavelengths:
ALMA data (in red infrared) shows newly formed
dust in the centre of the
remnant.
Hubble (in green - visible)
and Chandra (in blue – x-ray)
data show the expanding
shock wave.
Estimates of the total dust - enough to build the equivalent of
200,000 Earth-mass planets. Other elements observed like
oxygen, nitrogen, sulphur, silicon, carbon and iron.
beyond expectations - helps explain why young galaxies
that we can see existing in the early Universe, which have
high rates or star birth and death, are so dusty.
PHYS 3380 - Astronomy
Type Ia Supernovae
Type Ia supernovae are seen in galaxies with only
older (>1Gyr) stellar populations e.g. elliptical
galaxies. Hence they cannot be from the deaths of
massive stars. They must come from low mass
stars.
SN1994D in
NGC4526 with HST
Lightcurves are distinctly different from
Type II supernovae. But the Type Ia form
quite a homogeneous group of events.
PHYS 3380 - Astronomy
Chandrasekhar Mass White Dwarves
MCh=1.46M
Recall the Chandrasekhar mass is the maximum possible mass for a
white dwarf star. An isolated white dwarf cools off with measured
relation and fades for rest of time.
If we add mass to a white dwarf to push it over MCh then it will be
come unstable. The mass comes from an accreting binary
companion in a close interacting binary system. Once MCh reached
then e– degeneracy pressure no longer enough to hold star up:
 C ignited under degenerate conditions - nuclear burning raises T
but not P - gas can’t expand and slow the reactions
 Thermonuclear runaway - carbon deflagration
 Incineration and complete destruction of star
Type I supernovae generally about two magnitudes brighter than
Type II
PHYS 3380 - Astronomy
Companion star expanding to fill its
Roche Lobe
White
dwarf with
mass
close to
MCh
“Roche lobe” : region within which matter is gravitationally bound to the star.
The Roche lobe of the primary and secondary meet at the Langrangian
point. Matter can be transferred.
Roche lobe is gravitational equipotential surface
PHYS 3380 - Astronomy
Exceeding the Chandrasekhar Mass
There are three models for accreting the required matter - none
of them are yet proven
1. White dwarf + main-sequence star companion: slow accretion of
mass from a binary companion on the main-sequence - observed
accretion rate is slow, timescales possibly too long e.g. U Scorpii
(recurrent nova) MWD=1.50.2M MMS=0.90.2M
2. White dwarf + red giant: the initially more massive star becomes
white dwarf . The lower mass companion (~1-2M) evolves into red
giant. Mass transferred to white dwarf . Such systems are well known
to produce novae. But mass transfer must be at just the right rate.
3. White dwarf + White dwarf merger (double degenerates): merging of
two white dwarves in binary systems, We see white dwarf binary
systems. e.g KPD 1930+2752: Mtot=1.470.01M : looses angular
momentum by gravitational radiation, merges within 200 x 106 yrs
PHYS 3380 - Astronomy
Type I and II Supernovae Light Curves
Type I: No hydrogen lines in the spectrum
Type II: Hydrogen lines in the spectrum
PHYS 3380 - Astronomy
Typical Type II supernovae have a plateau phase in their light curve
- energy comes from the expansion and cooling of the star's
outer envelope as it is blown away into space.
Both types have “tail-phase”
- luminosity source radioactive decay of 56Ni and 56Co created
explosively in supernova
-decays release energy:
3x1012 JKg-1 for 56Ni
56
56

Ni
Co

e
  e   (1/ 2  6 days)
12
-1
56
6.4x10 JKg for Co
56
Co56Fe  e    e   (1/ 2  77.1 days)
-ray lines (1.24Mev from 56Co decay) detected by space and balloon
experiments between 200-850 days.

Rate of light curve decline gives excellent match to the radioactive
energy source half-life.
Type II light curve slower than in type I, due to the efficiency of
conversion into light by all the hydrogen.
If distance is known, the mass of 56Ni can be determined. For SN1987A:
M(56Ni)= 0.075M
PHYS 3380 - Astronomy
Local Supernovae and Life on Earth
Nearby supernovae (< 50 light years) could kill many life forms on
Earth through gamma radiation and high-energy particles.
At this time, no star
capable of producing a
supernova is < 50 ly away.
Most massive star
known (~ 100 solar
masses) is ~ 25,000 ly
from Earth.
PHYS 3380 - Astronomy
Type Ia as Standard Candle
Light curves of nearby, low-redshift
type Ia supernovae (a) Absolute
magnitude plotted against time (in the
star’s rest frame) before
and after peak brightness. The great
majority (not all of them shown) fall
neatly onto the yellow band. The figure
emphasizes the relatively rare outliers
whose peak brightness or duration
differs noticeably from the norm. The
nesting of the light curves suggests
that one can deduce the intrinsic
brightness of an outlier from its time
scale. The brightest supernovae wax
and wane more slowly than the
faintest. (b) Simply by stretching the
time scales of individual light
curves to fit the norm, and then scaling
the brightness by an amount
determined by the required time
stretch, one gets all the type Ia light
curves to match.
PHYS 3380 - Astronomy
So type Ia offer a unique opportunity for the consistent measurement of distance out to
perhaps 1000 Mpc. Measurement at these great distances provided the first data to
suggest that the expansion rate of the universe is actually accelerating. That
acceleration implies an energy density that acts in opposition to gravity which would
cause the expansion to accelerate. This is an energy density which we have not directly
detected observationally and it has been given the name "dark energy".
PHYS 3380 - Astronomy
Neutron Stars
A supernova
explosion of a
M > 8 M star
blows away its
outer layers.
The central core will collapse into a compact object of ~ a few M.
PHYS 3380 - Astronomy
Formation of Neutron Stars
Compact objects more massive than the Chandrasekhar Limit (1.4
M) collapse further.
 Pressure becomes so
high that electrons and
protons combine to form
stable neutrons
throughout the object:
p + e-  n + ne
 Neutron Star
X-ray image of
supernova
remnant 3C58
(1181 AD)
PHYS 3380 - Astronomy
Properties of Neutron Stars
Typical size: R ~ 10 km
Mass: M ~ 1.4 – 3 M
Density: r ~ 1014 g/cm3
 Piece of neutron star matter of the size of a sugar
cube has a mass of ~ 100 million tons!!!
PHYS 3380 - Astronomy
Neutron Star Properties
Neutron stars are predicted to rotate fast and have large magnetic fields.
Simple arguments:
Angular momentum
Magnetic field
Luminosity (
Ts ~ 10 6 )
Ii i  I f  f
Bi 4 Ri2  B f 4 R 2f
L ~ 4 R 2Ts4 ~ 10 26W
M iR  i  M f R  f
R 2
i
B f  Bi 
R 

 f 
2.9 10 7
BB peak 
Angs . ~ 29 Angs.
T
2
i
2
f
R 2
i
 f   i 
R 

 f 
R f 2
Pf  Pi  
Ri 
Initial rotation period uncertain, but lets say similar to typical white dwarfs
(e.g. 40Eri B has PWD=1350s). Hence PNS ~ 4 ms
Magnetic field strengths in white dwarfs typically measured at B=5x108
Gauss, hence BNS~1014 Gauss (compare with B ~2 Gauss!)
Similar luminosity to Sun, but mostly in X-rays (optically very faint)
PHYS 3380 - Astronomy
Neutron Stars
Neutron star surface has a temperature of~ 1 million K.
Cas A in X-rays
Wien’s displacement law,
max = 3,000,000 nm / T[K]
gives a maximum wavelength of max = 3 nm, which corresponds to
X-rays.
PHYS 3380 - Astronomy
Discovery of Neutron Stars
1967: Hewish and Bell discovered regularly spaced radio pulses
P=1.337s, repeating from same point in sky
- normal star too big to pulse that fast
- star with hot spot couldn’t spin that fast - would fly apart
- pulses lasted only about 0.001 s - limited size
- star blinking on and off would create pulse smeared out by
time it takes for light to travel from one side of star to other
- In other words, an object cannot change its brightness
appreciably in an interval shorter than it takes light cross
its diameter
- therefore size had to be less than 300 km
Pulses interpreted as spin period of neutron stars
PHYS 3380 - Astronomy
Discovery of Neutron Stars
Approx. 1800 pulsars now known, with periods on range 0.002 < P <
4.3 s
Crab pulsar - embedded in Crab nebula, which is remnant of
supernova historically recorded in 1054AD
Crab pulsar emits X-ray, optical, radio
pulses P=0.033s
Spectrum is power law from hard X-rays
to the IR
 Suggestive of synchrotron radiation:
relativistic electrons spiralling around
magnetic field lines.
PHYS 3380 - Astronomy
Lighthouse Model of Pulsars
A pulsar’s magnetic
field has a dipole
structure. Charged
particles (e-) are
accelerated along
magnetic field lines radiation is beamed in
the the acceleration
direction - mostly
along the magnetic
poles.
If spin and
magnetic
axes are not
aligned,
leads to the
“lighthouse
effect
PHYS 3380 - Astronomy
PHYS 3380 - Astronomy
Pulsar Light Curves
Combination of strong magnetic field
and the rapid rotation produces
extremely powerful electric fields,
with electric potential in excess of
1,000,000,000,000 volts. Electrons
are accelerated to high velocities by
these strong electric fields.
These electrons produce radiation (light) in two general ways: (1) Acting as a
coherent plasma, the electrons work together to produce radio emission by a
process whose details remain poorly understood; and (2) Acting individually, the
electrons interact with photons or the magnetic field to produce high-energy
emission such as optical, X-ray and gamma-ray. The exact locations where the
radiation is produced are uncertain and may be different for different types of
radiation, but they must occur somewhere above the magnetic poles.
PHYS 3380 - Astronomy
Light Curves of the Crab Pulsar
Only very young pulsars - like the Crab Pulsar - would be energetic
enough to produce radiation a short wavelengths and produce visible
light.
Possible explanation for differences in observed pulsar
light curves
PHYS 3380 - Astronomy
Pulsar Periods
Pulsar energy generated by
rotation - as it blows away
pulsar wind and blasts
radiation outward, it slows
down.
So, over time, pulsars lose
energy and angular
momentum Pulsar rotation gradually
slows down
Oldest about 10 million years
Glitches consequences of angular momentum transfer between a solid crust,
which rotates at the measured pulsar periodicity, and a more rapidly rotating
"loose' component of the neutron star interior. Possibly caused by
“starquakes” or vortices in fluid (neutron) interior.
PHYS 3380 - Astronomy
The Crab Pulsar
Pulsar wind + jets
Remnant of a supernova observed in A.D. 1054
PHYS 3380 - Astronomy
Pulsar Wind
Combination of rapid rotating and strong
magnetic field generate jets of matter and
anti-matter moving away from the north
and south poles and an intense wind
flowing out in the equatorial direction carry 99.9% of energy released from
slowing down of pulsar rotation rate.
Chandra X-ray Image of Crab Nebula
Inner X-ray ring thought to be shock wave
marking boundary between surrounding
nebula and the pulsar wind. Energetic
electrons and positrons move outward
from this ring to brighten the outer ring
and produce an extended X-ray glow.
Fingers, loops, and bays indicate that magnetic field of the nebula and filaments of
cooler matter are controlling the motion of the electrons and positrons. The particles
can move rapidly along the magnetic field and travel several light years before
radiating away their energy - move much more slowly perpendicular to the magnetic
field, and travel only a short distance before losing their energy.
This effect can explain the long, thin, fingers and loops, as well as the sharp
boundaries of the bays. The conspicuous dark bays on the lower right and left are
likely due to the effects of a toroidal magnetic field - a relic of the progenitor star.
PHYS 3380 - Astronomy
Composite X-ray (Chandra - left) and visible (Hubble) movie
PHYS 3380 - Astronomy
Proper Motion of Neutron Stars
Some neutron stars are moving
rapidly through interstellar space
- might be a result of anisotropies
during the supernova explosion
forming the neutron star
Composite X-ray (red/white) and optical (green/blue)
image of Black Widow Pulsar - shows elongated cloud,
or cocoon, of high-energy particles flowing behind the
rapidly rotating pulsar moving at a speed of almost a
million kilometers per hour. Bow shock wave due to this
motion optically visible - the greenish crescent shape.
Pressure behind the bow shock creates a second shock
wave that sweeps the cloud of high-energy particles
back from the pulsar to form the cocoon.
PHYS 3380 - Astronomy
The vela Pulsar
moving through
interstellar space
A recent change appears to
be connected to the
occurrence of a glitch
rotation speed, which
presumably released a burst
of energy that was carried
outward at near the speed of
light by the pulsar wind.