black holes exam 3

How are stars born?

galaxies are filled with interstellar gas (very low density), gravity causes a mutual attraction over vast distances -> the gas collects and collapses in the densest concentrations -> gas pressure stops the collapse -> nuclear fusion keeps the star hot and dense at the center

What is gas pressure?

the force exerted by the random thermal motion of gas particles - the kinetic energy per particle is proportional to temperature and hotter gas has higher pressure -> hydrostatic balance (a gradient in pressure densest at the center) supports the star against gravity

What is the main sequence?

stars spend most of their life here: stars that are stable and fusing hydrogen to helium in their centers -> continues until the star runs out of hydrogen (converting H to He releases 0.7% of hydrogen's rest mass energy)

A 60 Msun star has a luminosity of 3x10^32 watts. The total energy available for fusion of H to He is the solar value (1.3 x 10^45 Joules) multiplied by 20 (1/3 the star's H). How long will this star live?

- divide total energy available by the rate energy is radiated (0.7% H lost each conversion)

3 million years:

t = {(20)(1.3x10^45 J)} /3x10^32 J/s

t= 9x10^13 s

t=3 million

how long will the sun live? (and other stars like it?)

10 billion years (massive stars live for shorter amounts of time, more luminous by using more gas)

60Msun: 3 Myr

30Msun: 11 Myr

10Msun: 32 Myr

3Msun: 370 Myr

1.5Msun: 3 Byr

1Msun: 10 Byr

0.1Msun: 1000s Byrs

if L M^3.5, what happens to the luminosity if we increase M by a factor of 5?

increases by a factor of 280

(L/L0) = (M/M0)^3.5 -> (5)^3.5 -> 280

how does a star turn into a red giant?

hydrogen shell burning: hydrogen runs out -> nuclear fusion moves into a shell of hydrogen arounnd inner core of helium -> contracts and heats -> Helium gets hot enough to fusing into carbon, oxygen, nitrogen -> envelope exapnds

(less energy, higher luminosity, shorter time)

what happens after the red giant phase when all helium in the core is used?

gravity starts to win and core begins to contract with 2 possible outcomes depending on mass

- greater than 8Msun: hot enough for carbon, oxygen to fuse -> route to supernova explosions, neutron stars, black holes

less than 8Msun: degeneracy pressure stops the contraction, end up as planetary nebulae, forms a white dwarf (the fate of the sun)

how does a star turn into a white dwarf?

stars with masses less than 8Msun: Helium and hydrogen undergo shell burning (unstable) -> outer envelopes get blown into space (planetary nebula) -> core contracts (small) and is very dense from gravity , helium, carbon, and oxygen left in core not hot enough to fuse -> electron degeneracy pressure provides support against gravity

what is the electron degeneracy pressure?

provides pressure support against gravity in white dwarfs: electrons are fermions and obey exclusion principle -> no two fermions can oppupy the same quantum state, if forced to occupy similar positions (higher density), random velocities ride and higher pressure (depends on density only)

what are the general properties of white dwarfs?

made primarily of He, C, and O (depends on mass)

mass rang: 0.2 - 1.4 Msun (chandrasekhar limit)

radii comparable to earth: ~ 7000 km

huge densities: ~ 10^9 kg/m^3

relatively dim but hot - lots of emission in the UV

higher density (more compact and small) -> faster electrons -> higher pressure

what happens when a white dwarf reaches the chandrasekhar limit?

in mass transfer binaries, gas can be accreted by a white dwarf from a mass losing evolved star -> unstable thermonuclear burning leads the white drawf to explode -> white dwarf supernova: leaves no remnant

- can outshine an entire galaxy for several days

- all have similar luminosities, can be used as standard candles to measure distances very far away

what happens to a white dwarf if it doesn't accrete and pass the chandrasekhar limit?

slowly cools, very stable - could live for > 10^30 years

if the mass transferred to a white dwarf even approaches the 1.4 Msun limit, what happens?

the star can begin undergoing unstable nuclear reactions and explode

and

the exploding star can emit as much light as many galaxies for several days

what happens to higher mass stars if lower mass stars turn into white dwarfs?

more massive stars have hotter cores than can fuse nuclei with more protons (higher temps overcome proton repulsion)

- onion shell structure: sequence of shells fusing heavier elements, with iron core at center (iron nuclei cannot obtain energy by fusion or fission)

- star continues to radiate but no fusion to balance energy losses -> core cannot maintain pressure gradient needed ->electrons removed by combining with protons to make neutrons (p+e -> n+v) - >core collapses in 1/10th second: massive star supernova

if electron degeneracy is not able to support the core of a massive star against gravity, what do you suppose happens?

the core collapses and forms a black hole, the core is supported by degeneracy pressure of neutrons, the star will explode

what happens to a massive star (above 8 Msun) when the pressure gradient cannot balance grvaity in the core?

massive star supernova: neutrons have degeneracy pressure (larger than electron pressure)

-> light emitted can outshine an entire galaxy for several days, more varied in luminosity than white dwarf supernova

- collapse releases about 10^46 joules of gravitational energy mostly as neutrinos -> sudden stop of the collapse produces a shock that expands outwards through the infalling envelope, outer envelope no longer gravitationally bound and ejected into space

how could we tell observationally if a supernova is a white dwarf or massive star supernova?

white dwarf supernova leave no remnant but core collapse supernova do

and massive star supernova would show evidence of significant hydrogen in their emission but white dwarf supernova would not (outer layers of the star didn't undergo fusion)

how does core collapse end?

if/when a neutron star forms at the center -> drives a shock that moves out in to the outer envelope and causes it to explode as a core collapse

compressing matter to very high density leads to production of neutrons -> high densities so neutrons can't decay back

what is neutron degeneracy pressure?

neutrons have larger mass so they can be pushed closer together than electrons -> stronger than electron degeneracy pressure, can support more mass

what is a neutron star?

when the core collapses it leaves behind an incredibly dense neutron star -> very close to being black holes

- made by core collapse of stars above 8Msun

balanced by gravity and gradient of neutron degeneracy pressure

- spacetime curvature, strong tidal gravity, strong bending of light, significant gravitational redshift of light from the surface

- no absoprtion or emission lines

- 0.3% of all stars

At a density of 5 x 10^17 kg/m^3, what volume would one need to have a mass equivalent to the largest super tankers ~ 500,000,000 kg

(density=mass/volume) -> (volume=mass/density)

1 mm^3

Assume you had an unimpeded view of a spherical neutron star. What fraction of the surface should you be able to see at any moment?

more than 50%

- light would be nend around the neutron star, just like with black holes

Your Asgardian friend wants you to come with him on his journey to a neutron star to help him forge a giant axe a few 10s of kilometers away from the star. Is this a good idea?

no, the tidal forces from the neutron star's gravity would kill you if you got that close

What is the composition of a neutron star?

- inner core: not understood

- outer core: superfluid neurons, small number of superconducting protons, degenerate neutrons supply main pressure

- inner crust: 600m deep, heavy nuclei (iron, electrons), free neutron superfluid, electron degeneracy pressure

- outer crust: 200m deep, fluid or lattice of heavy nuclei, electron degeneracy pressure

- atmosphere: hot plasma

What is neutron star maximum mass?

the contribution of pressure to gravity means that it is very unikely to form neutron stars greater than 3Msun

- most neutron stars are near 1.4Msun

- most massive observed neutron star: 2.1Msun

what happens if a neutron star passes the maximum mass?

neutron star collapses into a black hole: time dilation makes the collapse seem to freeze as the star's outer surface approaches schwarzchild radius -> collapses into infinite density and zero volume

- proven by computers

what is thermal (blackbody) radiation?

particle that contain charges interact/collide, creating photons: spread in particle speeds and collision energy gives a spread in photon energy -> when photons and particles scatter repeatedly, we get a blackbody spectrum

- at higher temps, collisions are more violent and frequent -> spectrum shifts to shorter wavelengths/higher frequencies and gets brighter

What happens to thermal radiation if you make the source hotter?

more energy comes out at all wavelengths and the peak of the spectrum shifts blueward (the frequency rises/wavelength deacreases)

What is Wein's law?

to find the peak of the curve of thermal radiation ->

λpeak = (2,900,000nm/T)

What is the wavelength of the peak of the spectrum of a star whose surface temperature is 10,000K?

λpeak = (2,900,000 nm/10^4)

= 290 nm: ultraviolet

What is the Stefan-Boltzmann law?

to find the total energy radiated each square meter per sec (luminosity)

F= σT^4 (σ is stefan's constant, F is watt/m^2)

How much energy does each square meter of the sun radiate? surface temp: 5800 K

F = σ T^4 = 5.7 x 10^-8 x 5800^4 = 6.1 x 10^7 watt/m^2 = 61 MW/m^2

What is the temperature of a star with a peak around 600 nm?

5000 K

peak(n)= (2.9x10^6)/T ->

T= (2.9x10^6)/peak = (2.9x10^6)/600 = 5000K

What is the relationship between flux and luminosity?

Luminosity, L, is the amount of energy radiated per unit time and has units of watts = joule/s

Flux, F, is the energy radiated per unit time per unit are and has units of watts/m2

L=FA

If we want to calculate the luminosity of the sun, we only need to know its radius and surface temperature: R = 7x10^8 m and T = 5800 K. What is the sun's luminosity?

4 x 10^26 W

When the sun becomes a red giant, both its luminosity and surface area will increase. Knowing that its color will be redder than its current color, what must be true?

Its surface area increases more than its luminosity

- a redder star must have a lower temperature, making the flux lower

- since dlux is L/A, a lower area requires area to increase more than luminosity

Young neutron stars are expected to have a temperature of 10^7 K. In what part of the electromagnetic spectrum should we see their thermal emission?

x-rays

(2.9x10^6 nm)/ 10^7 = 2.9 nm = 2.9x10^-10

How were neutron stars first discovered, and what are they?

Jocelyn Bell: noticed regular radio pulses -> came from a spinning neutron star: magnetic fields created by electric current in neutron star -> two beams of radiation emitted along magnetic axis, sweep out wikth rotation (like a lighthouse)

very hot but not very luminous due to small emitting area, also dim x-ray sources

broad range of rotation periods

spin rapidly but spin down as rotational energy is lost in electromagnetic wind

accretion from a binary companion can spin up the neutron star

What would happen if the beam from a spinning neutron star hit the Earth

We would call it a pulsar

Why were pulsars first discovered in radio rather than in X-rays?

Sensitive radio telescopes existed before sensitive x-ray telescopes

If any tiny amount of angular momentum makes it hard for gas to fall directly into the black hole, how does anything end up there?

Gas can interact with itself so that some gas loses and some gains angular momentum allowing a fraction of the gas to fall in

Once gas forms circular orbits, why does it accrete at all? What is needed for gas to accrete?

friction due to magnetic turbulence generated by magnetorotational instability

We know gas can fall into a black hole. Why does this matter?

Gas falling into a black hole loses gravitational potential energy and some of that can be radiated as light

Where does the gravitational potential energy lost by matter falling into a black hole go?

Half of it is radiated away as light, black holes can be the most luminous objects for their mass

What is the theoretical model for black hole jets?

magnetic fields are twisted into helical shapes by rotation and rotational energy of a spinning black hole or accretion disk, produced flux of electromagnetic energy used to accelerate particles, causing radiation

What is the relationship between luminosity, accretion rate, and efficiency?

L=ηMc^2

(M = mass accreted per unit time)

Suppose a supernova destroys a 20Msun star in a binary system with a low mass star. What happens to the low mass star?

Gravity pulling on low mass star is reduced suddenly as the supernova ejecta passes by the orbit, binary is typically unbound and flies off into space

How does a binary system become an accreting black hole?

Binary system must have a small orbital separation -> leads to mass transfer of mass between the stars, also sharing a single envelope

Why do we think common envelope phases must occur?

The final separation of some binaries with black holes or neutron stars are smaller than the radii of the original star

What do astronomers need to measure the masses of black holes in binaries?

Orbital period, Doppler shift, and viewing angle

- if m>3Msun: black hole candidate

-m<3Msun: neutron star - pulsars, thermonuclear bursts

Why would accretion disks be so hot that their thermal emission is in X-rays?

Large luminosity and small emitting area

What are the relativistic effects on black hole/neutron star accretion disks?

lensed by black hole: can see the backside of the disk

doppler: approaching side is blue, receding is red

beaming: approaching is bright, receding is dimmed

Black hole spin affects all of the following aspects of accretion in black hole x-ray binaries. What is most important for astronomers studying black holes?

a. Spin affects the structure of the black hole inside the event horizon.

b. Spin determines the effective inner edge of the blackhole accretion disk (the ISCO).

c. Spin determines the amount of Hawking radiation.

d. Spin affects the vertical thickness of the accretion disk.

b. spin determines the effective inner edge of the black hole accretion disk

What are gravitational waves?

perturbations to curvature of spacetime that propagate at speed of light and carry energy

caused by any non-axisymmetric motion

What are strong sources of gravitational waves?

A rotating neutron star with a mountain on the surface or binary stars

Why would merging black hole binaries be stronger sources of gravitational waves than merging stars of the same mass?

The black holes are compact enough that they can get very close to each other before merging

How do you detect gravitational waves?

Interferometers: bounces a laser between mirrors for arms at right angles to one another allows very precise measurements in changes in length of the arms

- LIGO detectors

How does the LIGO interferometer work?

It measures changes in the distance between mirrors as the gravitational wave passes

Why build 2 LIGO detectors separated by thousands of kilometers?

So that geographically local sources of noise that mimic gravitational waves could be rules out if they showed up in only one detector

When was the first detection of gravitational waves?

September 14, 2015

- result of 2 black holes merging 1 B years

- lost 3Msun as gravitational wave energy

- put out as much energy as all stars in the observable universe for 10 milliseconds

Where did the energy of gravitational waves come from in the observed 1 byr old black hole merger?

The gravitational potential energy of the black holes as their orbit shrank, the orbital energy of the black holes as their orbit shrank, and the rest mass energy of the black holes that was lost when they merged

How do neutron star mergers differ from black hole mergers?

have a weaker signal than black hole mergers, could produce gamma rays or other electromagnetic signal (light)

When was the first detection of a neutron star merger?

2025: using LIGO and VIRGO detectors

- coincident with gamma ray bursts detected by the Fermi telescope

- astronomers where able to identify an electromagneted counterpart to the gravitational wave source -> thought to come from material ejected during merger: ejecta is now thoguht to be significant source of heavy elements (gold)