The Bizarre Stellar Graveyard

Question 1

Degeneracy pressure supports a star’s remnant against

Answer 1

the crush of gravity

Question 2

A degenerate star is supported by:

Answer 2

 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 .

Question 3

White Dwarfs

Answer 3

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 !

Question 4

The composition of a white dwarf depends on the mass

of its

Answer 4

 Very low mass→ He
~1MSun→ mainly CSize of white dwarfs
 Intermediate mass→ C with large amounts of O & heavier elements.

Question 5

The average white dwarf has a mass near

Answer 5

0.6Msun

Question 6

The average white dwarf has a mass near 0.5 … 1Msun compressed into

Answer 6

the size of earth

Question 7

describe white dwarfs part 1

Answer 7

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

Question 8

describe white dwarfs part 12

Answer 8

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)

Question 9

Heisenberg’s Uncertainty Principle sets a limit on

Answer 9

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

Question 10

Chandrasekhar predicted that

Answer 10

gravity will overcome e – degeneracy pressure if the white dwarf mass exceeds a certain critical value Mcritical

Question 11

fangs

Answer 11

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!)

Question 12

H build-up on white dwarf

surface—>

Answer 12

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

Question 13

The white dwarf temporarily becomes brighter

—-> nova, please explain this

Answer 13

 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

Question 14

An accreting white dwarf can

Answer 14

gain mass in time

Question 15

Electron degeneracy pressure can no longer support star when

Answer 15

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

Question 16

white dwarft supernova

Answer 16

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

Question 17

White dwarf supernovae are different from those

Answer 17

generated by Fe catastrophe (massive star collapse)

:type II supernovae

Question 18

How are supernovae classified?

Answer 18

 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

Question 19

Hypernova

Answer 19

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

Question 20

shine most brilliantly

Answer 20

Type Ia supernovae shine most brilliantly: 10b Suns.
 Can temporarily
be as bright as a
whole galaxy!

Question 21

Supernovae types distinguished by their

Answer 21

luminosity & its

variation in time

Question 22

White dwarf supernovae (Type Ia) lack

Answer 22

H absorption lines & after a short high peak their luminosity fades steadily with time

Question 23

 Supernovae of massive stars fade in

Answer 23

in 2 or more distinct stages

Question 24

White dwarf supernovae always occur when the

Answer 24

1.4MSun limit is reached —> same maximum luminosities!
 Excellent distance indicators
 More luminous than Cepheid variable stars
 Can measure much greater distances

Question 25

No mass limit for

Answer 25

massive star supernovae.

Question 26

Distance measurement with white dwarf supernovae

Answer 26

 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

Question 27

Neutron star (NS) =

Answer 27

leftover core from the Fe core | collapse of a massive star’s supernova.

Question 28

 Neutron degeneracy pressure stops

Answer 28

collapse of cores with masses <3MSun .

Question 29

Gravity crush cannot be stopped for Mcore>3MSun | ---->

Answer 29

black hole

Question 30

Neutron Star  Tremendous crush of gravity:

Answer 30

 The gravitational acceleration at surface = 1011g (i.e. 100gb) Escape velocity is ~0.5c!

Question 31

 Neutron stars are very dense:

Answer 31

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

Question 32

What is it’s a neutron’s star structure?

Answer 32

 ~90% is made of neutrons

Question 33

The state of matter varies with depth inside a neutron star :

Answer 33

 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

Question 34

Neutron stars are also very hot:

Answer 34

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

Question 35

Neutron stars cool down by 2 possible key mechanisms

Answer 35

 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

Question 36

Pulsars discovery

Answer 36

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.

Question 37

Pulsars

Answer 37

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!!)

Question 38

Magnetar =

Answer 38

another type of neutron star: with an ultra-strong magnetic field

Question 39

Mgn. field of a neutron star:

Answer 39

1…10t× Earth’s

Question 40

Pulsars Rotate rapidly with periods of

Answer 40

0.03…4 s. Due to angular momentum conserv. during & after collapse

Question 41

potent electrical generator

Answer 41

The strong mgn. field & rapid rotation of a neutron | star make it a very potent electrical generator.

Question 42

Pulsars continue s'il vous plait

Answer 42

 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

Question 43

Pulsars are

Answer 43

Neutron Stars!

Question 44

Magnetic poles usually do NOT coincide | with

Answer 44

rotational poles

Question 45

“lighthouse” effect

Answer 45

Beam of radiation sweeps round & round when poles are not aligned with rotation axis:

Question 46

The star’s orientation determines | whether we ‘see’ it as a pulsar:

Answer 46

```  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. ```

Question 47

The youngest pulsars have the

Answer 47

shortest periods (thought to have resulted from supernova explosion). Rotate as fast as 625 times per second

Question 48

Rotation rate gradually slows as neutron star ages.

Answer 48

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

Question 49

several ‘ms pulsars’ are observed in globular | clusters → very old

Answer 49

```  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 ```

Question 50

Neutron stars in close binary systems can also | steal matter from companion

Answer 50

``` ----------->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’ ```

Question 51

Neutron stars gravitation is much stronger than | that of white dwarfs

Answer 51

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).

Question 52

X-ray bursters

Answer 52

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!!

Question 53

Anomalous X-ray Pulsars (AXPs)→

Answer 53

→ A different kind of X-ray emitters, solely due to events on the surface of a magnetar

Question 54

Double neutron star system

Answer 54

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

Question 55

Double neutron star system 2

Answer 55

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.

Question 56

Gravity’s ultimate victory: Black holes

Answer 56

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

Question 57

This is what we call a black hole

Answer 57

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!

Question 58

According to the Theory of Relativity, gravity is not a force but the

Answer 58

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.

Question 59

event horizon

Answer 59

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”

Question 60

event horizon 2

Answer 60

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

Question 61

The Schwarzchild radius, | RS

Answer 61

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

Question 62

Stellar core within event horizon elaborate

Answer 62

Hidden from view  Contains all the mass & exerts full gravity of the mass

Question 63

All matter crushed to an infinitely tiny & dense point

Answer 63

singularity

Question 64

Very far away from a black hole, space-time is less curved and its gravity is indistinguishable from ANY other mass

Answer 64

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

Question 65

Properties of a black hole (continued)

Answer 65

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

Question 66

Frame-dragging will tend to

Answer 66

accelerate infalling objects in | the direction of rotation, instead of falling straight forward ----- > Fast spinning accretion disk

Question 67

Friction between adjacent zones of the accretion disk causes it to become

Answer 67

extremely hot and emit large amounts of X-rays

Question 68

Friction between adjacent zones of the accretion disk causes it to become extremely hot and emit large amounts of X-rays

Answer 68

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

Question 69

Light near a black hole

Answer 69

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

Question 70

Falling in a black hole

Answer 70

``` Time slows down near a black hole. What would it be like to plunge into a black hole ```

Question 71

What would it be like to plunge into a black hole 1

Answer 71

 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

Question 72

What would it be like to plunge into a black hole 2

Answer 72

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

Question 73

A black hole by itself emits no light

Answer 73

difficult to detect

Question 74

A black hole is the only object that can be

Answer 74

so massive & yet small enough to be invisible → 3 main ways to detect them

Question 75

A black hole is the only object that can be so massive & yet small enough to be invisible → 3 main ways to detect them

Answer 75

 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.

Question 76

Gravitational lensing

Answer 76

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"

Question 77

Observe sources of strong radiation (γ, X-ray) & | emission jets.

Answer 77

 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

Question 78

Just like white dwarfs & neutron stars, a black hole can also be

Answer 78

one component of a binary system

Question 79

Just like white dwarfs & neutron stars, a black hole can also be one component of a binary system

Answer 79

an accretion disk will form & emit hard radiation (as shown earlier)

Question 80

But is there any binary system formed ONLY of black | holes?

Answer 80

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.

Question 81

Black holes can also

Answer 81

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!

Question 82

Gamma Ray Bursts (GRBs)

Answer 82

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!

Question 83

Cosmic γ-rays observed above Earth’s atmosphere since 1960s.

Answer 83

 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

Question 84

Afterglows of some GRBs detected at other wavelengths since 1997.

Answer 84

 Pinpoint their sources to distant galaxies |  Some can even be seen with binoculars!

Question 85

Two types of GRBs:

Answer 85

 Short (duration <2 s) |  Long (duration >2 s)

Question 86

grb explain more pls: Short bursts tend to be

Answer 86

10 × dimmer and have more highly-energetic (hard) | γ rays than long ones.

Question 87

Short bursts

Answer 87

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

Question 88

what causes short ray grbs

Answer 88

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).