PHYS 3380 - Astronomy Homework Set #10 11/16/15 Due 11/30/15 Chapter 13 Review Questions 7,11...

PHYS 3380 - Astronomy

Homework Set #1011/16/15

Due 11/30/15

Chapter 13

Review Questions 7,11

Problems5, 9

Chapter 14

Review Question2Problems1, 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 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.

-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.


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. Intensity started to fade in 2011.

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.

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)


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.

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.


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.


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


“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

White dwarf with mass close to MCh

Companion star expanding to fill its Roche Lobe

PHYS 3380 - AstronomyExceeding 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=1.50.2M MMS=0.90.2M

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=1.470.01M : looses angular momentum by gravitational radiation, merges within 200 x 106 yrs


Type I and II Supernovae Light Curves

Type I: No hydrogen lines in the spectrum

Type II: Hydrogen lines in the spectrum

PHYS 3380 - AstronomyTypical 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

6.4x1012 JKg-1 for 56Co

-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

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56Ni→56Co+ e+ + ν e + γ (τ 1/ 2 = 6 days)56Co→56Fe + e+ + ν e + γ (τ 1/ 2 = 77.1 days)


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.


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) beforeand after peak brightness. The great majority (not all of them shown) fall neatly onto the yellow band. The figureemphasizes 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 intrinsicbrightness 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 lightcurves 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.


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".


Neutron Stars

The central core will collapse into a compact object of ~ a few M.

A supernova explosion of a M > 8 M star blows away its outer layers.


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)


Properties of Neutron Stars

Typical size: R ~ 10 kmMass: 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:

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)

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Angular momentum Magnetic field Luminosity (Ts ~ 106)

Iiωi = I fω f Bi4πRi2 = B f 4πR f

2 L ~ 4πR2σTs4 ~ 1026W

M iRi2ωi = M fR f

2ω f B f = BiRiR f

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2

λ BB− peak =2.9 ×107

TAngs. ~ 29 Angs.

ω f =ωiRiR f

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2

Pf = PiR fRi

⎛

⎝ ⎜

⎞

⎠ ⎟

2

PHYS 3380 - Astronomy Neutron Stars

Wien’s displacement law,

max = 3,000,000 nm / T[K]

gives a maximum wavelength of max = 3 nm, which corresponds to X-rays.

Cas A in X-rays

Neutron star surface has a temperature of~ 1 million K.

PHYS 3380 - AstronomyDiscovery 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 - AstronomyDiscovery 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.


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


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.

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.

Pulsar Light Curves

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.


The Crab Pulsar

Remnant of a supernova observed in A.D. 1054

Pulsar wind + jets

PHYS 3380 - Astronomy Pulsar WindCombination 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.

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.Chandra X-ray Image of Crab Nebula

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.


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.


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.

PHYS 3380 - Astronomy Homework Set #10 11/16/15 Due 11/30/15 Chapter 13 Review Questions 7,11...

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Transcript of PHYS 3380 - Astronomy Homework Set #10 11/16/15 Due 11/30/15 Chapter 13 Review Questions 7,11...