Transcript Stellar Remnants

Stellar Remnants
Chapter 18
Stellar Astrophysics
Review of Stellar Evolution
The Hertzsprung-Russell diagram shows the relationship between
color (temperature) and brightness (luminosity) for stars
•
About 90% of all stars
(including the Sun) lie on the
Main Sequence.
•
Stars maintain this relationship
between color and magnitude
during core hydrogen burning.
•
A star’s location along the Main
Sequence depends on mass
(higher mass stars sit at
brighter luminosities along the
Main Sequence).
•
Main Sequence is just one
phase of a star’s life
•
Astronomers use the
Hertzprung-Russell diagram to
trace the evolutionary stages of
stars of different masses.
Star Formation
Stars form out of clouds of gas and dust (which can be several
hundred light years across) in our Galaxy (the Interstellar Medium stuff between the stars). The atoms and molecules in these clouds
are moving with speeds according to the temperature of the cloud.
If the cloud is cold enough, the particles will begin to come together
due to the attractive force of gravity.
The first several stages of star formation take about 2 million years
as the densest pockets collapse first leading to fragmentation. Stars
initially form in these groups or clusters.
Pockets with mass < 0.08 Msun will not achieve high enough temps to become a star
(brown dwarfs). The following scenario is for gas spheres with 0.08 Msun < M < 7 Msun
Protostar (position 4 on HR) – after ~ million years
•the opaque center of the collapsing cloud fragment continues to
contract and gain mass as material “rains” onto it.
•The contraction leads to continued heating (position 5) which
builds pressure on the core and starts to slow the collapse.
Star (6) - after ~30 million years
• central core temperature
reaches 10 million degrees K.
• nuclear fusion begins in the
core (burning Hydrogen into
Helium and releasing
energy/light).
• contraction continues very
slowly until the star reaches
equilibrium on the Main
Sequence (position 7)
On the Main Sequence, the contraction stops because gravity
and radiation pressure exactly balance each other. The nuclear
reactions occur at exactly the right rate to balance gravity. Thus
the star’s mass determines its luminosity on the Main Sequence
(more gravitational pressure from higher mass means higher
luminosity).
Nuclear reactions slowly
convert Hydrogen to Helium
in the core. A new star
begins with about 91%
Hydrogen (H) and 9%
Helium (He).
In the core of a star with a
mass similar to the Sun, the
conversion of H to He will
take ~10 billion years (its
Main Sequence lifetime).
When the H in the core runs out:
Nuclear reactions stop
Core pressure decreases
Core contracts and gets hotter - heating
overlying layers
H to He burning moves to a shell and
reactions occur faster than before (less
gravitational pressure from upper layers)
The star becomes more luminous
The hot shell causes the outer layers to
expand and cool
The star moves off the Main Sequence
and up the Red Giant Branch (positions 8
to 9). This takes about 100 million years.
Red Giant Branch - the core continues to get hotter as the outer layers
press down (the star is called a Red Giant at this time – no longer a main
sequence star).
When the core reaches 100 million degrees, conditions are hot enough
to begin burning the Helium to Carbon
The onset of this burning causes the
temperature & luminosity to rise
sharply in a runaway explosion called
the Helium Flash (position 9).
Eventually the core expands, density
drops and equilibrium is reestablished.
The core structure is now readjusted
during Helium core burning and the
total luminosity decreases.
During core Helium burning, the star is
on the Horizontal Branch of the HR
diagram (position 10).
Helium-to-Carbon burning occurs stably in core, with Hydrogen-to-Helium
burning in a shell until the core Helium runs out in ~20-50 million years.
The increased shell burning causes the outer layers to expand and cool
once more.
The star moves up the asymptotic giant branch over the next ~10,000
years and becomes a red supergiant (position 11).
The star looks like this, with both a
Helium and Hydrogen burning shell and a
Carbon, non-burning core.
As the Carbon core continues to contract and
heat, the shell Helium burning grows more
intense.
Helium flashes occur in the shell.
Surface layers pulsate and are eventually
ejected.
The hot, tiny core is now called a White
Dwarf and is surrounding by a Planetary
Nebula (emission line nebula)
The white dwarf has ~1/2 the star’s original
mass since the other half is expelled in the
planetary nebula. They are small (about the
size of the Earth) and extremely dense (106
g/cm3).
White Dwarf
Red Giant
The white dwarf eventually gets
cooler and fainter as it no longer
produces any light via nuclear
reactions (position 13).
Unless a WD is in a binary
partner, it will become
impossible to detect after
several million years. However,
if it is in a binary system, the
WD can accrete material from
its neighbor star and can reveal
itself as a recurring event known
as a Nova.
Nova – accreted Hydrogen gas from binary
partner star onto WD surface becomes so hot
due to the strong gravitational field, it burns off
quickly and violently every few weeks to every
couple of years.
Degeneracy Pressure – supports White Dwarfs
Degenerate gas - compressed/cooled gas such that all electrons are in
lowest energy levels allowed by exclusion principle
Pauli Exclusion principle – two particles in close proximity cannot be in
the same quantum state (i.e. quantum numbers that describe energy
level, spin must differ).
Degeneracy Pressure results from the Heisenberg Uncertainty principle
Δp Δx ≥ h/2π
Since the particles’ locations are extremely confined, momentum is very
uncertain and particles are moving extremely fast  this leads to a high
pressure for a degenerate gas.
The particles have “Heisenberg speeds” of
Δv = Δp/me ~ (h/2π)ne1/3/me (eq.18.8)
Pdegen = (h/2π)2 ne5/3/me (eq.18.11)
Chandrasekhar found the maximum pressure exerted by a degenerate
electron gas with Δv  c allowing for special relativistic effects and
carbon/oxygen composition. This pressure corresponds to a maximum mass
 1.44 Msun (Chandrasakhar limit)
Mass-Radius Relationship for White Dwarfs
Equating hydrostatic equilibrium pressure with electron degeneracy pressure gives

High Mass Stars
•In high mass stars (> 7 M),
outer layers of star squeeze
and heat the core to ignite
Carbon…then Oxygen,
Neon, etc.
•MS life of such a star is
~30Myr(7M/M)3
•As each fuel gets
exhausted in the core, its
burning moves to a shell Onion skin structure
•Formation of Iron is the final
stage
Why is Iron formation the end of the line?
56Fe
has the highest binding energy per nucleon - very stable.
Any reaction involving iron (fission or fusion) requires energy.
With no more sources
of energy, and Fe
fusion taking energy
from the gas,
pressure support in
the star’s core is lost.
The core quickly
collapses under its
own weight….
In these higher mass stars, the iron core reaches and exceeds the
Chandrasekhar limit (1.44M) and the core cannot be supported by
electron degeneracy pressure - core continues to collapse very
quickly – less than 1/10 second!
The 56Fe atoms use any energy produced in the collapse, so the
core does not heat up.
Iron atoms get destroyed in the ever collapsing core and the
protons then combine with electrons in the star to produce neutrons
and neutrinos
e- + p = n + e
Eventually, the neutrons are so
close together they “touch”:
neutron degeneracy pressure.
The neutron core then halts the
collapse causing outer material
to bounce outward and leaving
behind a Neutron Star.
Electrons run out of room
(quantum states to occupy) and
prevent further collapse. Protons
and neutrons still free to move
Stronger gravity=>more compact
Electrons and protons
combine to make neutrons.
Neutron degeneracy
prevents further collapse.
Much more compact.
Supernova!
During the explosion,
nuclear reactions take
place rapidly and can
produce elements
heavier than iron.
Material is dispelled
into the interstellar
medium to be
incorporated into later
generations of stars.
Crab Nebula - result of a
supernova recorded by
Chinese astronomers in 1054
AD – appeared as bright as
Venus and visible in the
daytime sky
A supernovae explosion can exceed the
luminosity of an entire galaxy (max
Lsn~109Lsun)
Total energy output:
Neutrino energy ~ 1046 J
Kinetic energy of ejected gas ~ 1044 J
Photon energy ~ 1042 J
(compare with Sun’s lifetime energy
output of 1044 J)
Lightcurves show a rapid
increase in brightness
followed by fading over
several months.
Aside on Spectroscopy in Astronomy…
1
2
3
Emission line
spectra of
different elements
Absorption
line spectrum
for a star (the
Sun)
Spectra of supernovae reveal differences:
Type II SN – do show H absorption lines
Type I SN – do not show H absorption lines
Further divided:
Type Ia SN – no H or He lines
Type Ib SN – no H but do show He lines
Type II and Ib are thought to be the same thing, except that Ib completely lost their
H rich outer layers in a strong stellar wind and then underwent core collapse.
Type 1a are completely different
•WD eventually “builds up” material that
was not completely ejected during nova
explosions
• Added mass causes gravity to squeeze
the WD allowing Carbon to finally start
burning.
• Carbon burns all over the WD at once
(not just in core) and the star explodes in
a carbon-detonation supernova.
New Type 1a SN discovered last year in galaxy M82!
Supernova 2014J
• 11th magnitude source
• visible in amateur
telescopes
• Type Ia (exploded white
dwarf)
• debris expanding at 20,000
kilometers per second
• Distance ~ 12 million lightyears
Type II Supernova Remnants
Generally have strong
magnetic fields and
contain many charged
particles
Electrons spiral around
the field lines - spiraling
motion of charged
particles produces
synchrotron radiation polarized light
Optical Veil Nebula
IR - CasA
X-ray - CasA
Radio - CasA
Optical - SN1987A
Degeneracy Pressure – supports Neutron Stars
Neutrons obey Pauli exclusion principle similarly to
electrons and can exert degeneracy pressure at high
densities
Pn ~ (h/2π)2nn5/3/mn
(eq.18.36)
Since the star is all neutrons and  = nnmn
Pn ~ (h/2π)2 5/3/mn8/3
Recall, for electron degeneracy
Pe ~ (h/2π)2ne5/3/me
(eq.18.11)
Thus, electron degeneracy pressure is greater by mn/me ~ 1839 (at a
given density). But since the density of a neutron star is much greater
than a white dwarf, neutron degeneracy pressure is greater in a neutron
star than electron degeneracy pressure in a white dwarf.
Problem time
Compute the ratio of neutron degeneracy pressure to electron
degeneracy pressure.
Density of WD = 2x106 g/cm3
Density of NS = 2x1014 g/cm3
Pns/Pwd = (ρns/ρwd)5/3 x (me/mn)
For a 1.4M NS with r = 15km, what is the acceleration of
gravity at the surface?
gns = GMns/Rns2 = 8.3 x 1013 cm/s2
Compare with Earth’s gravity gearth = 103 cm/s2
Tidal effects are also important on the surface of a neutron star
dg/dr = 108 cm/s2/cm or 100,000 times the acceleration of
gravity on the Earth per cm.
Neutron Star size compared to New York City
Mass: 1.4 - 3 M
Radius: 10 -15 km
Density: 1011 kg/cm3
(eq 18.41)
1 cm3 weighs as much as Mt. Everest!
Neutron star rotation
Since angular momentum is
conserved, any original rotation of
the star is amplified in the
shrunken core.
J = I
(I is rotational inertia,  is angular velocity)
I = (2/5)MR2
for rotating sphere
Imagine a star like the Sun becomes a neutron star
R2 = R2
(/) = (7x105 km)/(15 km)2 = 2x109
If the Sun rotates once in 30 days, the period of the neutron star is
Pns = (2.7x106s)/(2x109) = 1.35 x 10-3s
or 1000 times per second!
Magnetic Fields
•Faraday’s Law tells us that the
magnetic flux through a surface
remains constant
•Thus, neutron stars have strong
magnetic fields since
BR2 = constant
and the star’s original magnetic
field now runs through a smaller
surface area.
•Beginning with the Sun’s
magnetic field, the neutron star
would have a field 2 x 109 times
stronger.
Detecting Neutron Stars

Possible existence of neutron stars was first realized
in the 1930s in theory only.

Believed to be too small to be observed (although some
nearby and recently formed NS have hot enough surfaces (T~106K and L~0.2Lsun)
to be detected in X-rays)

In 1967 an accidental discovery in radio astronomy
revived interest in neutron stars via the discovery of
the first pulsar.
The first pulsar was discovered in 1967 by a graduate student,
Jocelyn Bell, who measured this radio signal from an unresolved
source (named LGM-1).
Her advisor Antony Hewish was studying the scintillation
(twinkling) of radio light from distant sources caused by charged
particles in our solar system.
This required observations with time resolution of ~1/10th second
– not previously attempted for radio sources.
The rapidly varying
source they detected
showed a regular
pulsation with a period of
1.337 s.
Since then, about 500
pulsars have been
discovered in our Galaxy
For a rotating star, the rotation must not be so fast that objects on
the surface lose contact with the surface (i.e. gravity must be
greater than the force required to keep a point moving in a circular
path).
where P is the period, R is radius
R = [(G/4π2)mP2]1/3
Rules out normal stars and WD which do not have strong enough
surface gravity leaving neutron stars as the best candidates.
1)
Strong magnetic fields
capture particles from NS
atmosphere and produce
“hot spots” at the magnetic
poles.
2)
Accelerated particles at hot
spots emit beamed
synchrotron radiation.
3)
If the rotation axis is different
than the magnetic field axis,
then the radiation beam
rotates like a searchlight.
4) The rotating
searchlight is like a
lighthouse, which we
see as a pulsar if we
happen to lie in the
searchlight beam.
5) Not all neutron stars
will be observed by us
as pulsars because the
searchlight might not
intercept Earth. The
pulsar would visible to
about ~20% of
potential observers
The pulse period gives
the rotation period of the
neutron star.
Typical periods are 0.03
to 1 seconds, or 1 to 30
rotations per second
The beamed radiation appears in
the radio, but sometimes also in
X-rays, visible, infrared. Emission
mechanism not entirely
understood though most is likely
synchrotron radiation – magnetic
field accelerates charged particles
which spiral around field lines.
Visible light images of the Crab
Pulsar during “on” and “off”
separated by only hundredths of a
second
Crab Pulsar P = 0.033s
This pulsar is responsible for
replacing much of the
energy radiated away via
synchrotron emission from
the remnant (about 105 Lsun)
Chandra X-ray (left) and
HST optical (right) movie
showing real time shock
waves from the pulsar into
the surrounding interstellar
medium
More than half of all stars are in
binaries.
White dwarfs in close binaries
lead to novae (mass transfer
followed by Hydrogen burning
on the surface of the white
dwarf).
Neutron star binaries can behave
similarly (mass transfer followed
by Hydrogen burning on the
surface).
Neutron star
Time scales are shorter (explodes
every few hours) and the bursts
are hotter (appearing in X-rays)
because stronger surface gravity.
X-Ray Bursters
Neutron stars in Close Binaries
The hot accretion disk and hot spot
are constant sources of X-rays,
with bursts (fueled by fusion) going
off every few hours.
Millisecond Pulsars:
Infalling accreted material
orbits faster than the NS spin
and can spin-up the rotation
over time causing some
neutron stars to spin almost
~1000 times a second
Stellar Black Holes

Just as there is a limit to the mass that can be
supported by electron degeneracy, there is a
limit to the mass supported by neutron
degeneracy (Tolman-Oppenheimer-Volkoff limit: ~3Msun)

If mass is greater than this, there is nothing to
halt gravitational collapse

The result is a stellar core that becomes a
black hole
Detection of Black Hole candidates in binary systems
BH in binary system
with normal star
As star evolves, it
evolves and swells to
size larger than Roche
limit
Tidal force of BH strips
away outer layer. Gas
is compressed and
heated to 106K.
Forms accretion disk
with characteristic
spectrum - X-rays from
innermost (hottest)
parts with visible–
infrared from outer part
We measure masses from orbital
parameters (Kepler’s Laws).
If dark companion has M > 3 Msun,
likely BH candidate.
Observational Evidence for Black Holes: Cygnus X-1
•Bright X-ray source
•Optical images show an O type star (blue supergiant) with mv=9
implying a mass of 15 Msun
•Spectroscopic binary with P=5.6 days
•Variability of 0.07mag implies orbit inclination of 30 degrees
•Period combined with velocities from orbital parameters yields
total system mass of ~23Msun
•Mass of unseen companion: 8Msun (or at least more than 4Msun)
•X-ray variability implies small source of origin (5ms -- <1500km)
•Black hole!
Gamma-ray image
X-ray variability over 1
minute
Observational Evidence for Black Holes: Cygnus X-1
Problems with black hole conclusion
•Possible that the spectrum of the companion is produced by
different mass star
•Orbit inclination has some uncertainty
•Triple-star system?
For years, Cyg X-1 was the only
strong candidate for stellar black
hole, but there are currently over
~30 likely black hole candidates
in our Galaxy
See http://www.johnstonsarchive.net/relativity/bhctable.html and
http://blackholes.stardate.org/objects/ for current lists
Other examples:
LMCX-3
•X-ray source in Large Magellanic Cloud
•Companion is 17th mag B3V star
•Spectroscopic binary - P=1.7 days
•Does not eclipse - constrains inclination
•Estimated mass of compact object: 4 to 11Msun
Nova Mon 1975
•Transient X-ray source
•Optical companion is a K-dwarf (better mass estimate)
•Spectroscopic binary - P=7.8 hours
•Estimated lower-limt mass of compact object: 3 Msun
V404 Cygni
•spectroscopic binary
•P=6.47 days
•Cool subgiant (0.6Msun) orbiting dark companion with M=6Msun