phys 3380 - astronomy the chandrasekhar limit the more massive a white dwarf, the smaller it is. ...

PHYS 3380 - Astronomy

The Chandrasekhar Limit

The more massive a white dwarf, the smaller it is.

Pressure becomes larger, until electron degeneracy pressure can no longer hold up against gravity.

WDs with more than ~ 1.4 solar masses can not exist!


･ On Main Sequence, Sun evolves slowly due to the changing chemical composition of its core - the Sun gets hotter and increases in luminosity (moving to the left and up in the HR diagram).

･ After the hydrogen is used up in the core, the helium core contracts, and heats the hydrogen rich layer just outside of the core. The hydrogen ignites in the shell around the core and the Sun moves to the right in the HR diagram.

･When the outer layers of the Sun become convective, the luminosity of the Sun shoots up and the Sun becomes a Red Giant.

･ The core continues to contract and heat up

･ The core of the Sun is supported by the hot (normal) gas of helium nuclei produced by the hydrogen burning and by degenerate electrons; the electrons already occupy many of the available energy levels up to very high energies - it will take a lot of heat in order to increase the energy of even 1 electron. The fractional increase in the kinetic energy of the electrons will be very small for a given amount of heat input. So, the pressure due to the electrons does not change very much for a given amount of heat input -the core of the Sun will not expand strongly in response to the ignition of the helium.

Summary of 1 M evolution


･ The temperature of the core rises (really the temperature of the helium nuclei gas rises) as the reactions turn-on - the reaction rate goes up - the temperature of the helium nuclei in the core goes up - the rate of reactions goes up - and so on.... Until ignition of helium burning - helium flash lasts for a few minutes or less with a peak core luminosity of up to 1 x1011 L.

･ The helium flash shuts down because, eventually, as you add enough heat to the gas, you can excite electrons to higher energy states and you eventually spread the electrons out over a large enough range of states to make the gas normal. (obey the perfect gas law).

･ The helium flash occurs in stars less massive than around 2.25 M.

･ After the helium flash, the star quiescently burns what is left of the helium in its core (for a time ~ 10 - 20 % as long as its Main Sequence lifetime).

･When the helium is converted into carbon and oxygen, the core again contracts, ignites helium burning in a shell around the core, expands, cools, and moves to the right in the HR diagram.


･When the star becomes convective, it moves up the AGB greatly increasing in luminosity at roughly constant temperature. Low mass stars are not, however, massive enough to reach the ignition temperature of carbon before the core becomes completely supported by degenerate electron pressure (which halts the contraction).

･ The nuclear evolution of the Sun ends at this point and the star is now ready to enter into its final stages of evolution; at this time the star is AGB star characterized by a carbon-oxygen core, surrounded by a helium burning shell and a hydrogen burning shell.

• For stars whose mass is greater than 2.25 M, the electrons in their cores are not

degenerate at the time of helium ignition and so there is no helium flash and they settle into a stage of quiescent helium burning before they approach the AGB.

•Star cools and moves left on the H-R diagram possibly generating a planetary nebula

•He-burning shell keeps dumping C and O onto the core. C,O core collapses and the matter becomes degenerate.

•Star becomes a white dwarf



Approximate typical timescales

Phase (yrs)

Main-sequence 9 x109

Subgiant 3 x108

Redgiant Branch 1 x109

Red clump 1 x 108

AGB evolution ~5x106

PNe ~1x105

WD cooling >8x109



Approximate typical timescales

Phase (yrs)

Main-sequence 9 x109

Subgiant 3 x109

Redgiant Branch 1 x109

Red clump 1 x 108

AGB evolution ~5x106

PNe ~1x105

WD cooling >8x109

PHYS 3380 - AstronomyLagrangian points (or libration points) - five positions in an orbital configuration where a small object affected only by gravity can maintain a stable orbital configuration with respect to two larger objects (like a satellite with respect to the Sun and Earth). Mark positions where the combined gravitational pull of the two large masses provides precisely the centripetal force required to orbit with them.

Lagrangian Points

A contour plot of the effective potential due to gravity and the centrifugal force of a two-body system in a rotating frame of reference. The arrows indicate the gradients of the potential around the five Lagrange points—downhill toward them (red) or away from them (blue).


Mass Transfer in Binary Stars

In a binary system, each star controls a finite region of space, bounded by the Roche Lobes (or Roche surfaces).

Matter can flow over from one star to another through the Inner Lagrange Point L1.

Lagrange points = points of stability, where matter can

remain without being pulled towards one of the stars.


Recycled Stellar Evolution

In some binary systems - less massive star has become a red giant - more massive star is still on main sequence - Algol paradox

Caused by mass transfer

-in a binary system can significantly alter the stars’ masses and affect their stellar evolution.


White Dwarfs in Binary Systems

Binary consisting of WD + MS or Red Giant star => WD accretes matter from the companion

Angular momentum conservation => accreted matter forms a disk, called accretion disk.

Matter in the accretion disk heats up to ~ 1 million K => X-ray emission => “X-ray binary”.

T ~ 106 K

X-ray emission


Nova Explosions

Nova Cygni 1975

Hydrogen accreted through the accretion

disk accumulates on the surface of the WD

Very hot, dense layer of non-fusing hydrogen

on the WD surface

Explosive onset of H fusion

Nova explosion

PHYS 3380 - Astronomy Recurrent Novae

Most novae are recurrent on time scales ranging from 1,000 to 100,000 years• recurrence interval for a nova is less dependent on the white dwarf's accretion rate than on its mass

• massive white dwarfs - powerful gravity - require less accretion to fuel an outburst than lower-mass ones• the interval is shorter for high-mass white dwarfs.

RS Ophiuchi eruption in Feb 2006


GK Persei

https://youtu.be/EqzJIYODSUY

https://youtu.be/EqzJIYODSUY

PHYS 3380 - Astronomy Supernovae

In the 1930’s supernovae were recognised as a separate class of objects to novae (meaning new stars).

• So-called by Fritz Zwicky, after Edwin Hubble estimated distance to Andromeda galaxy (through Cepheids)

• Hence the luminosity of the “nova” discovered in 1885 in Andromeda was determined

• Supernovae outbursts last for short periods: typically months to a few years

• Typical galaxies like the Milky Way appear to have a rate of 1-2 supernovae per 100 years

• But as they are extremely bright - even small telescopes can detect them at large cosmic distances

• Historical accounts of supernovae in our galaxy are coincident with supernovae remnants now visible


What is a Supernova ?

Stars which undergo a tremendous explosion, or sudden brightening. During this time their luminosity becomes comparable to that of the entire galaxy (which can be ~1011 stars)

SN1998bu in M96: left - reference image, right - BVI colour image


Supernovae in the Milky Way

European and far eastern written records of the following Galactic events:

Supernova Remnant Year Peak Visual mag

CasA 1680 ?

Kepler 1604 -3

Tycho 1572 -4

3C58 1181 -1

Crab 1054 -4

SN1006 1006 -9

• Supernova remnants observable in optical, radio and X-ray for thousands of years


The Crab nebula - optical (red) and X-ray (lilac) composite

Death of a massive star

Tycho’s supernova remnant in X-rays

Explosion of a white dwarf

The Menagerie Supernova Remnant

Cassiopeia A Supernova Remnant

Kepler’s Supernova Remnant

Cygnus Loop Supernova Remnant

PHYS 3380 - AstronomyThe Observed Types of Supernovae

Supernovae explosions classified into two types according to their observed properties. The two main types are Type I and Type II which are distinguished by the presence of hydrogen lines in the spectrum.

No hydrogen

Type I

Si He No He or Si Ia Ib Ic

Hydrogen lines

Type II

Lightcurve and spectra properties II-P, II-L, IIn, IIb, II-p


Example Spectra of Type Ia and Type II Supernovae

Typical Type II supernova observed within a few weeks of explosion

Typical Type Ia supernova observed near maximum light (i.e. when supernova is at its brightest)

H HH

Si

No H or He

S

Ca


From H Burning to Core-Collapse in Massive (> 8 M) Stars

• H in core consumed forming He core surrounded by H-burning shell

• He core contracts forming He-burning core surrounded by a H-burning shell

• Core of 12C and 16O produced, surrounded by He and H burning shells.

• The core will again contract and the temperature will rise, allowing C and O burning to Mg and Si.

• Process continues, with increasing Z, building up heavier and heavier elements until the iron group elements of Ni, Fe and Co are formed. The core is surrounded by a series of shells at lower T, and lower

• Iron core ultimately collapses, triggering an explosion that destroys the star: a supernova


Energy Production

Nuclear fusion can produce energy up to the production of iron.

Nuclear reactions that use iron cannot produce energy

- nuclear reactions can only produce energy only if proceed from from less tightly bound nuclei to more tightly bound nuclei

Binding energy due to strong force = on short range, strongest of the 4 known forces: electromagnetic, weak, strong, gravitational


• Fe core contracts as no nuclear fusion occurring, and e– become degenerate gas.

• When core mass > MCh (Chandrasekhar mass) the e– degeneracy pressure is less than self-gravity and core contracts rapidly (for Fe: MCh1.26 M )

Result:• Gas is highly degenerate, hence as core collapses T rises unconstrained, and

reaches threshold for Fe photodisintegration

• Reaction is highly endothermic - collapse turns into almost free fall. • Infall continues, T rises, and photon field energetic enough to photodissociate He

• Core contracts further, density becomes high enough for e– capture

• Neutrinos escape, removing more energy from core and accelerating collapse - complete collapse takes milliseconds

• Neutron gas becomes degenerate at densities of ~1018 kg m-3

• Neutron degeneracy pressure sufficient to balance gravity; however core has actually overshot the equilibrium point and undergoes a slight bounce, creating a shock wave which slams into the collapsing outer layers of the star.

• “Proto-neutron star" begins to form at the core

Core Collapse

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56Fe →134 He + 4n −100MeV

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e− + p → n + ν e

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He → 2n + 2 p − 25MeV


Shock wave stalls within ~0.03 s - supernova problem- inward flowing matter smothers shock wave and pushes it back into the star

What actually causes the explosion?- neutrinos reenergize the shock wave

Two stages of collapse:

-Dynamic stage (collapse, neutronization) – only e are emitted, accounting for/carry 1-3% of the binding energy (duration - 10 ms).

- Cooling stage – all neutrino flavours are emitted which carry (96-98)% of binding energy, duration - about 10 s.

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e− + p → n + ν e

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e− + e+ →ν + ν

e− + γ → e− + ν + ν

e− + nucleon → e− + ν + ν + nucleon


- Stellar gas so dense that it is actually slightly opaque to neutrinos

- ~1% of neutrino energy (1045 J) reabsorbed by the star - along with turbulent convection processes (convective overturn), reaccelerates shock wave producing an explosion.

Core collapse phase so dense and energetic that only neutrinos are able to escape the collapsing star.

- Most of gravitational potential energy of the collapse gets converted to 10 second neutrino burst

- releases about 1046 joules

PHYS 3380 - AstronomyTesting 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 m-

2. 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.


SN1987A - Confirmation of Core Collapse

Core-collapse of massive star

• Catalogued star SK-69 202

• M=17M

• Teff=17000

• Log L/ L = 5.0

• Star has disappeared

• Neutrinos confirm neutron star formation

• No pulsar or neutron star yet seen

Before At maximum

PHYS 3380 - AstronomyPrecursor

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

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.

Supernova 1987a Movie Link

http://www.eso.org/public/videos/eso1032b/

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. It is expected that, ten years from now, the ring will be roughly 100 times brighter than it is today.

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.

Light Echoes

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 the chandrasekhar limit the more massive a white dwarf, the smaller it is. ...

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