The Bizarre Stellar Graveyard Flashcards
Degeneracy pressure supports a star’s remnant against
the crush of gravity
A degenerate star is supported by:
Electron
(e–) degeneracy pressure→ white dwarf
OR
Neutron degeneracy pressure→ neutron star (NS)
A massive remnant core, for which gravity > neutron
degeneracy pressure, can collapse out of existence
—–> black hole (BH).
White dwarf = Exposed core of a dead (Sun-like) star
that has shed its outer layers in a planetary nebula.
Progenitor star had insufficient mass to become hot enough to
fuse C
<50% of original mass left
Gravity stopped by electron (e–) degeneracy pressure .
White Dwarfs
Slide down the H-R diagram as they radiate their heat away, getting cooler& fainter. Very hot when formed→Hottest white dwarfs can radiate intense UV &X-ray light
No new energy generated→ the white dwarf eventually cools into a black dwarf
Remember: the white dwarf does NOT shrink as it cools because e– degeneracy pressure is essentially independent of T !
The composition of a white dwarf depends on the mass
of its
Very low mass→ He
~1MSun→ mainly CSize of white dwarfs
Intermediate mass→ C with large amounts of O & heavier elements.
The average white dwarf has a mass near
0.6Msun
The average white dwarf has a mass near 0.5 … 1Msun compressed into
the size of earth
describe white dwarfs part 1
Very dense→ A teaspoon of its material weighs ~10 tons (as much as a truck)! They can have various ‘compositions’: typically a C/O core with/without He and/or H2 layers, which can also be neutral or ionized. If existent, any of the remnant H & He layers must be quite thin to avoid fusion at the base of the layer
describe white dwarfs part 12
Degenerate matter obeys different laws of physics.
The larger the mass, the smaller it becomes!
Larger mass -> ↑ gravity -> ↑ density → smaller size -> e– degeneracy pressure must also ↑ to balance gravity
A 1.3 MSun white dwarf is half the diameter of one with 1 MSun , which is about the size of Earth
For white dwarfs the relation between mass & size is:
R proportional to M^(-1/3)
Heisenberg’s Uncertainty Principle sets a limit on
how massive a white dwarf can be: There is a maximum mass that creates a maximum e degeneracy pressure for which the e– reach the speed of light
Anything above this mass requires e– to travel faster than the light speed !—>impossible!
This is the Chandrasekhar Limit: no white dwarf can have a mass greater than this critical value
This limit depends slightly on the composition of the
material; for a C/O core the Chandrasekhar mass is
Mcritical =1.4MSun
Chandrasekhar predicted that
gravity will overcome e – degeneracy pressure if the white dwarf mass exceeds a certain critical value Mcritical
fangs
Sometimes white dwarfs can be energy-sucking
vampires!
They can gain mass if companion is a main-sequence
or giant star.
Falling matter forms an accretion disk
Friction in disk — . :>visible, UV & X-ray light
Differs from a protostellar disk in size (much smaller, due to stronger gravity from the white dwarf), orbital speed (much higher!) & T (much hotter!)
H build-up on white dwarf
surface—>
p&T of this thin layer of H ↑↑------> When bottom of the layer reaches T = 10mK------> Explosive fusion reaction is ignited! = NOVA! A gas shell is blown off
The white dwarf temporarily becomes brighter
—-> nova, please explain this
Minor detonation of H fusion on white dwarf’s surface
As bright as 100,000 Suns for a few days, then fade slowly
The brighter the nova, the shorter its duration.
Accretion may resume after explosion & process can repeat with a period of months to ~100,000 years (typically tens of kyears)
The larger the white dwarf mass, the shorter the period.
If enough mass is gained (1.4
MSun limit is reached!) —-> Supernova
An accreting white dwarf can
gain mass in time
Electron degeneracy pressure can no longer support star when
the accreting white dwarf reaches a mass equal to
or above the Chandrasekhar limit —> White dwarf collapses!–>
↑↑↑ core temperature–> Runaway C fusion!
(C undergoes fusion all at once) —– > Massive explosion
white dwarft supernova
type 1a supernova
Nothing is left behind !
In <1% of the cases, it is believed that a white dwarf may NOT explode as a Type Ia supernova but instead undergoes a process known as an accretion-induced collapse to form a rapidly rotating neutron star. However, NO accretion-induced collapse event has yet been directly observed experimentally
White dwarf supernovae are different from those
generated by Fe catastrophe (massive star collapse)
:type II supernovae
How are supernovae classified?
Based on the presence or absence of certain elements → from the spectra of their maximum emitted light
From the explosion’s luminosity: its peak value & variation in time
Hypernova
is an extremely luminous supernovae:
a stellar explosion with an energy of over 100 supernovae ,when the star’s core collapses → only for very massive stars, typically with Mstar > ~40MSun
shine most brilliantly
Type Ia supernovae shine most brilliantly: 10b Suns.
Can temporarily
be as bright as a
whole galaxy!
Supernovae types distinguished by their
luminosity & its
variation in time
White dwarf supernovae (Type Ia) lack
H absorption lines & after a short high peak their luminosity fades steadily with time
Supernovae of massive stars fade in
in 2 or more distinct stages
White dwarf supernovae always occur when the
1.4MSun limit is reached —> same maximum luminosities!
Excellent distance indicators
More luminous than Cepheid variable stars
Can measure much greater distances
No mass limit for
massive star supernovae.
Distance measurement with white dwarf supernovae
White dwarf supernovae always occur when the 1.4
MSun limit is reached—>same maximum luminosities!
Excellent distance indicators
More luminous than Cepheid variable stars
Can measure much greater distances
No mass limit for massive star supernovae.
Knowing the energy (because
M is always the same, Mcritical = 1.4MSun!) of a white dwarf supernova–>Luminosity of ANY such Type Ia event is known–>Distance to the white dwarf supernova (& its galaxy) can be determined using the inverse square law:
Distance measurement with white dwarf supernovae
Apparent
brightness = Luminosity/4πd^2
Neutron star (NS) =
leftover core from the Fe core
collapse of a massive star’s supernova.
Neutron degeneracy pressure stops
collapse of cores with masses <3MSun .
Gravity crush cannot be stopped for Mcore>3MSun
—->
black hole
Neutron Star Tremendous crush of gravity:
The gravitational acceleration at surface = 1011g (i.e. 100gb)
Escape velocity is ~0.5c!
Neutron stars are very dense:
Mass ave≅ 1.3…1.5MSun with
diameter of ~10…20 km
ρ=1012 g/cm3→ denser than the atomic nucleus! A paperclip of this density outweighs Mount Everest!
Densest matter known!!!
In very dense matter, neutrons are stable
What is it’s a neutron’s star structure?
~90% is made of neutrons
The state of matter varies with depth inside a neutron
star
:
Surface: a thin solid crust of &
e– & + nuclei
Deep inside: A heavy liquid interior in which immense pressure
disintegrates atomic nuclei & recombines
e– with protons —> neutrons (hence the name). Various superfluids, e.g. superfluid of free neutrons & a superconducting fluid of protons are probably found at different depths
Neutron stars are also very hot:
T = 1mK≅ 170TSun (almost perfect blackbody radiators!)
Hence, applying Stefan-Boltzmann’s law ->L = 0.3LSun
Applying Wien’s displacement law-> λpeak
≅3 nm !, i.e. almost all light is emitted as X-rays
Hence, we can find neutron stars in the Universe by observing the X-ray range. Still, some can be observed in visible light, and some (pulsars) with radio telescopes
Neutron stars cool down by 2 possible key mechanisms
Also EM radiation, but most importantly: by neutrino emission
In pulsars, also by radiation emission jets → also carry away angular momentum
gradual slow down of the spin (spin-down rate ∝ mgn. field strength)
Despite their density and age, they still have a very
agitated life:
Quakes → violent crust dynamics (cracked by the mgn. field??)
Spin variations that shake the interior → confirm the interior is fluid
Rapid & drastic mgn. field rearrangements —> GRBs in magnetars
Pulsars discovery
Graduate student Jocelyn Bell & her advisor discovered a
radio source in the Cygnus constellation in 1967.
Observed a sharp pulse recurring every 1.33 s
300 pc (978 light years) away
They called it a pulsar
(pulsating radio source).
Pulses came at very precise intervals.
Man-made? Artificial??
Mystery solved by late 1968 when a pulsar was
discovered in the heart of Crab Nebula
Pulsations: due to rapidly spinning neutron star.
Pulsars
The magnetic field at the surface of a collapsing star
grows in strength as the surface area of the star
decreases (↓ in radius leads to↑ mgn. field strength ~ 1/10^5) —> Huge magnetic field strengths at
the surfaces of neutron stars (even larger for
magnetars!!)
Magnetar =
another type of neutron star: with an ultra-strong magnetic field
Mgn. field of a neutron star:
1…10t× Earth’s
Pulsars Rotate rapidly with periods of
0.03…4 s. Due to angular momentum conserv. during & after collapse
potent electrical generator
The strong mgn. field & rapid rotation of a neutron
star make it a very potent electrical generator.
Pulsars continue s’il vous plait
The electric field generated by the rotating magnetized neutron star can be strong enough to rip charged particles (such as e–) away from its surface——->
The charged particles follow the mgn. field lines to the N & S mgn. poles of the neutron star and are accelerated —> Produce (not yet known how exactly) intense but narrow beams of radiation, pointing away from the two mgn. poles ————>
Radio emission
concentrated at mgn.
poles of neutron star
& focused into a beam
Pulsars are
Neutron Stars!
Magnetic poles usually do NOT coincide
with
rotational poles
“lighthouse” effect
Beam of radiation sweeps round &
round when poles are not aligned with
rotation axis:
The star’s orientation determines
whether we ‘see’ it as a pulsar:
Pulsar: We see a pulse of light/radiation each time the beam sweeps by Earth’s direction once each rotation No pulsar if polar beam always points away from Earth Pulsar≡ neutron star. Neutron star != Pulsar.
The youngest pulsars have the
shortest periods
(thought to have resulted from supernova explosion).
Rotate as fast as 625 times per second
Rotation rate gradually slows as neutron star ages.
Energy & angular momentum carried away by EM fields created from the continual twirling of magnetic field
Crab nebula pulsar currently rotates at ~30 Hz → rotates less than half as fast 2,000 years later after its birth
several ‘ms pulsars’ are observed in globular
clusters → very old
These must have spun-up due to in-falling matter from a companion star Matter infalling onto the neutron star adds angular momentum (spin) to it
Neutron stars in close binary systems can also
steal matter from companion
----------->accretion disk Similar to white dwarf binaries Mass transfer speeds up the (pulsar) rotation Can become as high as ~1,000 Hz Known as ‘millisecond pulsars’
Neutron stars gravitation is much stronger than
that of white dwarfs
In-falling matter releases enormous energy → Accretion disk becomes hot enough to emit X-rays
Close binaries containing neutron
stars are known as X-ray binaries
(XRBins).
X-ray bursters
H gas accretes onto the surface of the neutron star :
A 1 m thick H shell forms on the neutron star
Pressure at the bottom of this
layer is high enough for H to
fuse steadily on the surface
A He layer forms underneath
Its T steadily ↑ —> when it reaches 100m K, He fuses instantly & emits a huge energy burst
Neutron star “novae” are called X-ray bursters.
A burst lasts a few seconds & repeats every few hours to days
Each burst radiates as much as 100,000 Suns!!
Anomalous X-ray Pulsars (AXPs)→
→ A different kind of X-ray emitters, solely due to events on the surface of a magnetar
Double neutron star system
Many neutron star (NS) pairs are now known.
These stars spiral toward each other in an orbital decay, emitting space-warping gravity waves.
Similar to light waves radiating outward like ripples on a pond
Eventually collide & merge, possibly becoming a black hole (BH)
Such pairs have given us the first (indirect) evidence of the existence of gravitational waves
The radioactive material released in the merger heats up and expands, emitting a burst of light called a
kilonova as well as a slew of γ rays in a GRB. While kilonovas are 1,000 times brighter than a nova, they’re 1/10th to 1/100th the brightness of a typical supernova.
kilonova = NS+NS or NS+BH merger
Double neutron star system 2
How can very heavy elements be produced by stars?
Unlike elements like C, Si or Fe, Au or U cannot be created within the core of a star.
Kilonovas = NS+NS and NS+BH mergers create
significant quantities of neutron-rich radioactive
nuclei via the so-called r-process = the rapid neutron capture process
When the spiralling NSs finally merge, the matter
reaches unimaginable temperatures (1011 K). A few
percent of the matter is ejected in the form of spiral arms, which cool rapidly. It is in these arms that the important
nuclear physics takes place which creates elements
heavier than Fe, a list that includes Au, Hg, Pt, U, Th, and more.
Gravity’s ultimate victory: Black holes
The core of a massive star with
Mcore>3 MSun after supernova will collapse without end.
Gravity too strong for even neutron degeneracy to stop the collapse
Gravity final wins! ——-> The star becomes infinitely small ——-> Creates a “hole” in the universe
This is what we call a black hole
This is what we call a black hole
huge mass compressed into an infinitely small space has extremely large gravity!—> Black hole = an object so dense that escape velocity exceeds c
A singularity!
Newton’s law of gravity no longer valid!
According to the Theory of
Relativity, gravity is not a
force but the
warping of spacetime (the 4D Universe) about
an object with mass ——-»»>Gravity imposes a curvature on the space-time ‘fabric’.
Space-time extremely distorted near a black hole
Path of light through space is bent
Even light (no mass) is affected by gravity.
event horizon
Once one enters a black hole, (s)he leaves the
observable universe & can never return.
Matter/light cannot climb out once within a
boundary known as the event horizon:
the boundary around a black hole at
which the escape velocity equals the speed of
light (c)
.
Tidal forces could be tremendous near event horizon
The entering object could be “spaghettified”
event horizon 2
Boundary between the inside of black hole & the Universe → defined by a sphere of radius RS around the black hole
Inside of black hole = the actual singularity but also its close vicinity
Point of no return for objects entering black hole
Also defines the size of black hole
The Schwarzchild radius,
RS
RS = 3M (Rs in [km] if M is in [MSun])
Black hole with the mass of the Sun: RS = 3 km
Black hole with 10MSun: RS = 30 km
Stellar core within event horizon elaborate
Hidden from view
Contains all the mass & exerts full
gravity of the mass
All matter crushed to an infinitely tiny & dense point
singularity
Very far away from a black hole, space-time is less
curved and its gravity is indistinguishable from
ANY other mass
A black hole at a distance exerts gravity according to Newton’s Law:
Planets’ orbits the same if a 1MSun black hole replace our Sun
It does not suck in everything around it!
Gravity increases from Newton’s predictions only at a 3RS distance from the black hole
Properties of a black hole (continued)
The black hole destroys nearly all information about
matter that falls into it—->We CANNOT answer the question “What lies inside a
black hole?”→ because no information can ever
emerge from within the event horizon
Conservation of angular momentum dictates that black holes should rotate very rapidly when they form in the collapse of a rotating star–>It will drag neighbouring regions of space-time around it in circles
Effect known as frame-dragging
Frame-dragging will tend to
accelerate infalling objects in
the direction of rotation, instead of falling straight forward —– > Fast spinning accretion disk
Friction between adjacent zones of the accretion disk causes it to become
extremely hot and emit large amounts of X-rays
Friction between adjacent zones of the accretion disk
causes it to become extremely hot and emit large
amounts of X-rays
This heating is extremely efficient: can convert 10…50% of the mass energy of an object into radiation, as opposed to nuclear fusion which can only convert a few % of the mass to energy
Other predicted effects are narrow jets of particles at relativistic speeds squirting off along the disk’s axis
Light near a black hole
Light is trapped due to effects of general relativity:
space-time is severely warped within the event horizon.
Light coming from a region close to a black hole is bent (if not radial) & red-shifted.
Light can orbit a black hole at a radius of 1.5RS
Falling in a black hole
Time slows down near a black hole. What would it be like to plunge into a black hole
What would it be like to
plunge into a black
hole 1
An astronaut takes a probe to go into the black hole
From the astronaut’s point of view, time neither speeds up nor slows down, but he’d say that the mother-ship time runs increasingly fast & its light gets blue-shifted
From the mother-ship’s point of view, the probe’s on-board clock ticks more slowly & light from probe is red-shifted → because the photon must spend energy to overcome the hole’s gravity. This energy can come only by “giving up” of the initial energy by increasing its wavelength
What would it be like to
plunge into a black
hole 2
Probe eventually disappears from view as light is red-shifted beyond radio & time on clock stops
From the mother-ship point of view, the astronaut never crosses the event horizon, will asymptotically be approaching it FOREVER.
If the black hole is small (e.g. 10
MSun , with RS= 30 km) —> the
astronaut is “spaghettified” & torn apart by tidal forces
If the black hole is supermassive (e.g. 10^9MSun , with RS= 3bkm) —–>the tidal forces are much smaller & non-lethal
A black hole by itself emits no light
difficult to detect
A black hole is the only object that can be
so massive & yet small enough to be invisible → 3 main ways to detect them
A black hole is the only object that can be so massive & yet small enough to be invisible → 3 main ways to detect them
1) Infer its presence from the effect exerted on its
companion in X-ray binaries which contain a black
hole.
2) Gravitational lensing
3) Observe sources of strong radiation (γ, X-ray) &
emission jets.
Gravitational lensing
Gravitation of any huge mass curves space so that light travels on a curved path—> the mass acts as a lens
Another effect: the star being lensed by a foreground mass gets brighter when the mass passes in front of the star.
It is possible to measure the mass of the “lens”
Observe sources of strong radiation (γ, X-ray) &
emission jets.
Now we know that almost any galaxy must have a huge black hole at its center (usually supermassive, 10^6MSun at center of Milky Way)
The ‘light signatures’ (particularly the X-ray spectrum) from the
accretion disk & radiation jet emitted by a BH are different from
those coming from a NS and also the intensity variation in time
Still, it is not always possible to tell with certainty what object is at the center of the accretion disk
Just like white dwarfs & neutron stars, a black hole can also be
one component of a binary system
Just like white dwarfs & neutron stars, a black hole can also be one component of a binary system
an accretion disk will form & emit hard radiation (as shown earlier)
But is there any binary system formed ONLY of black
holes?
When 2 galaxies merge with one another —> was experimentally confirmed recently
Astronomical binaries of massive stars might also lead to the formation of binary black holes.
Black holes can also
merge or collide
Huge amount of radiation emitted as gravitational waves during the final second before the two black holes merge: could be 5% of the total mass of the system —> more energy than a star of comparable mass emits in optical radiation throughout its billions of years of life-time.
Black hole binaries could well be Nature’s most luminous objects!
Gamma Ray Bursts (GRBs)
The most powerful bursts of energy that ever occur in
the universe
Total luminosity of a burst can briefly exceed combined
luminosities of 1m galaxies like our Milky Way!
Cosmic γ-rays observed above Earth’s atmosphere since 1960s.
Satellites detected strong bursts, which occurred only for a few minutes or less, but almost daily
Hard to focus, pass through telescopes
Unable to determine direction
Afterglows of some GRBs detected at other wavelengths since 1997.
Pinpoint their sources to distant galaxies
Some can even be seen with binoculars!
Two types of GRBs:
Short (duration <2 s)
Long (duration >2 s)
grb explain more pls: Short bursts tend to be
10 × dimmer and have more highly-energetic (hard)
γ rays than long ones.
Short bursts
the energy conversion of the source/phenomenon into γ rays ↓ as the burst progresses, unlike long bursts where it appears to remain constant throughout the burst
what causes short ray grbs
Long bursts → Supernovae or even hypernovae = gigantic supernovae of very massive stars (rapidly rotating core) forming black holes
.
Short bursts → thought to be due to catastrophic
collisions of 2 very massive stellar objects in a binary
system ( 2 neutron stars, or neutron star & black hole).
