Semester 2 - Definitions

Question 1

What is the Virial Theorem?

Answer 1

The Virial Theorem relates the potential energy and total kinetic energy in a self-gravitating sphere in hydrostatic equilibrium.

Question 2

How do we know that stars evolve?

Answer 2

Change in stars is inevitable due to the finite energy source they possess.

Question 3

Define the Jeans mass and its role in stellar evolution.

Answer 3

The Jeans mass is the maximum mass of gas stable against gravitational contraction. It determines the minimum mass required for a gas cloud to collapse and form a star.

Question 4

What are the timescales involved in stellar collapse and evolution?

Answer 4

The timescales include the freefall timescale (for collapse), Kelvin-Helmholtz timescale (for radiation-powered contraction), and nuclear timescale (for energy generation via nuclear fusion).

Question 5

What are the different types of opacity and their significance in stellar evolution?

Answer 5

Opacity types include electron scattering, free-free, bound-free, and bound-bound. They affect the transport of radiation within stars and influence their temperature profiles and evolution.

Question 6

What is initial free-fall collapse?

Answer 6

Protostars are initially accreting mass from their host molecular clouds and shrinking under their own gravity. They are not initially in H.E.

Question 7

Describe the pre-main sequence sources.

Answer 7

These low-mass objects that are bright in the optical and lie above the theoretical zero-age main sequence (ZAMS) are not fusing H-He yet. There are also signs of a protoplanetary disk.

Question 8

What are evolutionary tracks in stellar structure and evolution?

Answer 8

Evolutionary tracks represent the paths that stars take through the Hertzsprung-Russell (HR) diagram as they evolve. They help in understanding the changes in stellar properties over time.

Question 9

What are protostars and what evidence supports their existence?

Answer 9

Protostars are young stellar objects still undergoing gravitational contraction. Evidence for their existence comes from observations of redshifted absorption lines in molecular spectra.

Question 10

What are T Tauri stars and what distinguishes them from main sequence stars?

Answer 10

T Tauri stars are pre-main sequence low mass stars with high luminosity and are found in nebulae or young clusters. They are brighter than main sequence stars of similar spectral types and are often surrounded by accretion disks left over from stellar formation.

Question 11

What are Herbig Ae/Be Stars?

Answer 11

Herbig Ae/Be stars are pre-main sequence higher-mass counterparts of T Tauri stars. They are located to the right of the main sequence.

Question 12

What prevents equatorial winds in Herbig Ae/Be stars?

Answer 12

A disk of gas and dust, rotating and accreting onto the star, prevents equatorial winds.

Question 13

Explain the process of collapse in a gas cloud.

Answer 13

Gas clouds collapse under self-gravity when M > MJ. Initially the collapse is free fall but matter the gas cloud approaches H.E.

Question 14

Describe the adiabatic contraction phase.

Answer 14

In the adiabatic contraction phase, radiation produced within the cloud becomes trapped due to increasing opacity as ionization occurs. The cloud heats up, and contraction becomes adiabatic as the cloud moves towards H.E.

Question 15

What is the isothermal contraction phase and when does it end?

Answer 15

Isothermal contraction is when T~const. as potential energy released is either radiated away or absorbed without increasing T. The isothermal phase ends once all H and He in the cloud is dissociated and ionised.

Question 16

How does the Jeans mass change during adiabatic contraction and what is the line of stability?

Answer 16

During adiabatic contraction, temperature increases, leading to an increase in the Jeans mass as density increases. The line of stability, determined by the adiabatic index, separates the regime of collapse from expansion.

Question 17

What circumstances lead to instability in the adiabatic regime?

Answer 17

Instability in the adiabatic regime occurs when the adiabatic index is less than or equal to 4/3. This can happen during phase changes or with polyatomic molecules with s degrees of freedom.

Question 18

Describe the onset of hydrostatic equilibrium and the emergence of a protostar.

Answer 18

Once a collapsing cloud becomes opaque enough to trap radiation and completes dissociation and ionization, temperature and pressure start to rise. An outward pressure gradient halts contraction, leading to the establishment of H. E and the emergence of a protostar.

Question 19

Describe what temperature H.E. is established?

Answer 19

H. E is established at a T ~ 30,000K which is determined by the virial theorem.

Question 20

Describe the effect on a molecular cloud in the presence of magnetic fields?

Answer 20

Magnetic fields in molecular clouds exert pressure on the gas, resisting contraction.

Question 21

How does rotation influence the evolution of a rotating gas cloud?

Answer 21

Rotation introduces an additional centrifugal force opposing gravity.

Question 22

What are Hayashi tracks, and how do they relate to stellar evolution?

Answer 22

Hayashi tracks represent evolutionary paths on the HR diagram followed by fully convective protostars.

Question 23

Describe the pre-MS evolutionary tracks for low mass stars.

Answer 23

Low-mass stars have long Hayashi tracks and remain fully convective throughout their pre-main sequence lifetimes. Low mass stars do not develop a radiative core and arrive on the hayashi track fully convective.

Question 24

What marks the arrival of a star on the main sequence, and how does it vary with mass?

Answer 24

The arrival on the main sequence occurs when nuclear fusion begins in the core. For low-mass stars, this transition occurs smoothly, while high-mass stars may exhibit deviations in their tracks due to brief periods of burning before settling onto the main sequence.

Question 25

What are brown dwarfs, and why do they not become main sequence stars?

Answer 25

Brown dwarfs are substellar objects with masses too low (< 0.08☉) to sustain hydrogen fusion in their cores. Before reaching the necessary temperature for the P-P chain, degeneracy pressure halts gravitational contraction. They may briefly burn deuterium and lithium before cooling and contracting gravitationally.

Question 26

What is the birth function, and how does it relate to the initial mass function?

Answer 26

The birth function describes the number of stars born within a given volume as a function of mass. It is distinct from the initial mass function (IMF), which describes the distribution of masses for newly formed stars.

Question 27

Describe the observations of stars in the Hertzsprung-Russell (HR) diagram.

Answer 27

HR diagrams constructed for main sequence stars show a band rather than a line. The width of the band is due to differences in chemical composition and evolutionary stages.

Question 28

How is helioseismology used to study the interior structure of the Sun?

Answer 28

Helioseismology studies the oscillations of the Sun, which can probe internal properties. Deviations between helioseismic values and model predictions provide insights into these properties.

Question 29

What do solar neutrino detectors measure?

Answer 29

Solar neutrino detectors, measure neutrinos produced in the solar core.

Question 30

What are the main consequences of nuclear burning for a star’s evolution?

Answer 30

Nuclear burning leads to changes in the mean molecular mass and thermal stabilization of the core. These are responsible for the predicted evolution on the main sequence.

Question 31

Discuss main-sequence evolution in terms of it’s nuclear timescale.

Answer 31

The main-sequence lifetime is determined by the nuclear timescale. There is a slow evolution of the star’s properties on this timescale.

Question 32

Explain the changes in composition and mean molecular mass during a star’s main sequence lifetime.

Answer 32

Over time, nuclear burning causes the fraction of hydrogen in the core to decrease while the fraction of helium increases. This change in composition leads to a change in the mean molecular mass of the core.

Question 33

Why are main sequence stars gravitationally stable?

Answer 33

Main sequence stars are gravitationally stable because the sum of internal energy and gravitational potential energy is negative in hydrostatic equilibrium. This indicates that particles do not have enough kinetic energy to escape gravity, keeping the star stable.

Question 34

Would a sudden increase in core temperature lead a main sequence star to become thermally unstable?

Answer 34

No. As T increases the star’s total energy increases. Such that |Ω| decreases. We know from the virial theorem that U must decrease. This leads to a decrease in T causing a feedback cycle.

Question 35

Describe pressure changes on the MS due to nuclear burning.

Answer 35

During nuclear burning μ changes in the core. Thermal stabilisation limits the change in core temperature. As H is converted to He, μ increases leading to a drop in core pressure.

Question 36

Describe luminosity changes on the MS due to nuclear burning.

Answer 36

The core pressure decreases as μ increases. Such that to maintain equilibrium the pressure in the rest of the star must decrease. This causes the envelope to expand such that L increases.

Question 37

Describe temperature changes on the MS due to nuclear burning.

Answer 37

In low mass stars the core temperature increases more, offsetting the increase in μ. In high mass stars the core temperature changes very little such that the increase in μ dominates.

Question 38

What happens to the core temperature of a main sequence (MS) star when the reaction rate increases?

Answer 38

The core temperature increases.

Question 39

How does the star respond when the core temperature increases?

Answer 39

The reaction rate increases (Etot increases) such that the star expands slightly.

Question 40

What is the nuclear energy generation rate dependent on?

Answer 40

It is dependent on the temperature. As temperature increases, the nuclear energy generation rate increases.

Question 41

What structural changes occur in the star due to changes in core pressure during nuclear burning?

Answer 41

Changes in core pressure lead to structural changes throughout the star.

Question 42

Describe the relationship between gas and radiation pressure in MS stars.

Answer 42

For all but the most massive MS stars, gas pressure is larger than radiation pressure in the core.

Question 43

What happens to the core pressure as hydrogen is converted to helium during nuclear burning?

Answer 43

The core pressure decreases.

Question 44

What is the primary reason for main-sequence evolution on the HR diagram?

Answer 44

The drop in core pressure due to the increase in helium content in the core.

Question 45

What timescale stabilizes the core temperature of a star during expansion or contraction?

Answer 45

The Kelvin-Helmholtz timescale (K-H timescale).

Question 46

How do high mass stars differ from low mass stars in terms of changes in core pressure and surface temperature?

Answer 46

High mass stars experience proportionately larger drops in core pressure, expand more, and have larger decreases in surface temperature compared to low mass stars.

Remember Teff does not equal Tcore

Question 47

How is the energy in main sequence (MS) stars primarily generated?

Answer 47

The energy in MS stars is primarily generated by the fusion of lighter elements into heavier ones.

Question 48

What is the primary outcome of the proton-proton (p-p) chain?

Answer 48

The primary outcome of the p-p chain is the production of helium-4 nuclei (4He).

Question 49

How many branches does the p-p chain have?

Answer 49

The p-p chain has three branches: PP-I, PP-II, and PP-III.

Question 50

At what core temperatures does the CNO cycle become more significant?

Answer 50

The CNO cycle becomes more significant at higher core temperatures, typically above 16MK.

Question 51

What are the catalysts in the CNO cycle, and how do they participate in the reaction?

Answer 51

Carbon (C), nitrogen (N), and oxygen (O) act as catalysts in the CNO cycle. They facilitate the fusion process without being consumed themselves.

Question 52

How are Solar neutrinos produced, and what is the estimated flux of solar neutrinos from the Sun?

Answer 52

Solar neutrinos are produced in various nuclear reactions within the Sun and carry away energy. The estimated flux of solar neutrinos from the Sun iapproximately 2 x 10^38 per second.

Question 53

What is the solar neutrino problem, and how was it resolved?

Answer 53

The solar neutrino problem refers to the discrepancy between the predicted and observed flux of solar neutrinos. It was resolved when all three flavours of neutrinos where detected and confirmed the total neutrino flux predicted by solar models.

Question 54

What can we conclude from the solar neutrino problem?

Answer 54

Neutrinos change flavour on their journey from the Sun, implying that at least some flavours have mass.

Question 55

What are the late stages of evolution for stars with M > 0.5 M☉?

Answer 55

Stars with masses greater than 0.5 M☉ often evolve into red giants and supergiants.

Question 56

What causes the complex, non-spherical shapes of planetary nebulae ejected by stars at the end of their lives?

Answer 56

The complex shapes of planetary nebulae may be due to factors such as magnetic fields, rotation, and the presence of a disk around the central stellar remnant.

Question 57

What supports white dwarfs against gravitational collapse, and what is their typical mass and radius?

Answer 57

White dwarfs are supported by electron degeneracy pressure and typically have masses of ~ 1M☉ and radii of around 10^3-10^4 km.

Question 58

What are some characteristics of neutron stars?

Answer 58

Neutron stars have a radius of approximately 10 kilometers, a mass of 1-2 solar masses (M☉), high rotation rates, surface temperatures of around 10^6 Kelvin, and are supported by neutron degeneracy pressure. They are formed in supernova explosions.

Question 59

Describe black holes.

Answer 59

Stars with very high ZAMS mass end up as black holes. This occurs when neutron degeneracy pressure can no longer support the mass of the stellar remnant. They can be detected through gravitational waves produced when they collide.

Question 60

Describe the evolution off the main sequence.

Answer 60

Hydrogen burning in the core leads to increased energy generation and increased magnitude of the temperature gradient.

Question 61

What leads to the k-mechanism?

Answer 61

When stars leave the main sequence they may undergo oscillations. Oscillating stars lie on the instability strip. Where in partially ionised zones the plasma can absorb energy without significant temperature increase. This leads to the k mechanism.

Question 62

What is the k-mechanism?

Answer 62

Pulsation requires a driving force and a restoring force. The driving force is strongest when the envelope is contracting, due to the increased opacity. This provides the outward radiation force to halt contraction and produce expansion. The cycle then reverses.

Question 63

Describe the evolutionary path of low-mass stars on the MS (M < 0.5M☉).

Answer 63

Low mass stars never develop a high enough core temperature to ignite He fusion in their cores. The core contracts and electron degeneracy pressure sets in. The star becomes a white dwarf and cools slowly.

Question 64

Describe shell burning in high-mass stars (0.5 M☉ ≤ M ≤ 8 M☉).

Answer 64

Depending on their mass they undergo a series of core and shell burning starting with hydrogen shell burning. The core is supported by the pressure of the inert helium. The mass limit that can be supported by this is known as the Schonberg-Chandrasekhar limit.

Question 65

Describe the evolutionary path of high mass stars on the MS.

Answer 65

High mass stars start with Core H burning on the MS. It eventually stops causing the core to contract leading to H shell burning. The triple alpha process then starts in the core.

Question 66

Describe helium ignition.

Answer 66

At the end of H shell burning in high mass stars the triple alpha process occurs when the core contracts. The ignition of triple alpha in a degenerate core results in a helium flash leading to a runaway reaction.

Question 67

Describe the helium main sequence.

Answer 67

A shorter phase with less energy available. The energy generation rate depends highly on temperature ~T^30.

Question 68

When does thermal pulsing occur and what is the result of this?

Answer 68

Thermal pulsing occurs in AGB stars due to the interaction between the helium-burning shell and the hydrogen-burning shell. This leads to periodic episodes of increased nuclear activity and mass loss.

Question 69

Describe the onset of He shell burning.

Answer 69

As the core He burns, the core μ increases. At 10 μ the core starts to contract accompanied by the cooling of the envelope. After the inert C core contracts He shell burning starts, forcing the overlying H-burning shell to expand.

Question 70

Describe RGB, HB and AGB.

Answer 70

The red giant branch consists of stars which are undergoing only shell H burning.

The horizontal branch corresponds to stars on the helium main sequence, with an H-burning shell.

The asymptotic giant branch corresponds to He shell burning, with an inert C/O core.

Question 71

What causes thermal pulses?

Answer 71

The interaction between He-burning shell and the H-burning shell.

Question 72

Describe the mass loss on the RGB and AGB.

Answer 72

The increase in luminosity and radius on the RGB and AGB leads to strong stellar winds.

AGB stars lose their envelope more rapidly compared to the other evolutionary timescales.

Question 73

How are heavy elements formed in asymptotic giant branch (AGB) stars?

Answer 73

Heavy elements are formed in AGB stars primarily through the slow-process, which involves neutron capture. During thermal pulses in AGB stars, neutrons are released through the reaction 13C(a,n)16O.

Question 74

What happens to the remnant core of a star depending on mass?

Answer 74

After the AGB phase, the remnant core contracts and heats up. Part of the remnant becomes degenerate. If the mass of the core is ≲ 8☉, it becomes a white dwarf, supported by electron degeneracy pressure. However, if the core mass exceeds this it leads to a core-collapse supernova.

Question 75

What is the Chandrasekhar limiting mass, and what is its significance?

Answer 75

The Chandrasekhar limiting mass is the maximum mass of a stable white dwarf supported entirely by relativistic electron degeneracy pressure. It is significant because beyond this mass, no stable solution exists.

Question 76

How does core burning proceed in stars with masses ≳ 8 M☉?

Answer 76

In stars with masses ≳ 8 M☉, core burning proceeds similarly to less massive stars until the HB stage. During the AGB phase, helium shell burning adds mass to the C/O core, leading to carbon burning. This process produces heavier elements.

Question 77

What triggers the collapse of the iron core in massive stars?

Answer 77

After 56Fe reactions become endothermic known as photodisintegration and core fission stops. The core is supported primarily by degeneracy pressure. The core mass increases due to Si burning. Once it exceeds the Chandrasekhar mass the core begins to collapse.

Question 78

What accelerates the collapse of the iron core?

Answer 78

Photodisintegration, electrons captured in inverse beta decay and neutrinos streaming out taking energy with them from inverse beta decay.

Question 79

Describe the end result of a core collapse supernova.

Answer 79

The end result of a core collapse in a massive star is the formation of a neutron star this is due to shock waves driving off the exterior of the star in a supernova explosion.

Question 80

How are supernovae classified, and what distinguishes Type I from Type II supernovae?

Answer 80

Supernovae are classified based on the presence or absence of hydrogen lines in their early spectra. Type I supernovae lack hydrogen lines, indicating that the progenitor star had lost most of its envelope prior to core collapse, while Type II supernovae exhibit hydrogen lines, suggesting a significant envelope at the time of collapse.

Question 81

Describe the phases through which a collapsing gas cloud passes before becoming a protostar.

Answer 81

Initial free fall, isothermal contraction (dissociation and ionisation), adiabatic contraction and the onset of H.E.

Question 82

What effect would halt contraction earliest for low mass stars

Answer 82

Rotation

Question 83

Describe the evolutionary track during free fall.

Answer 83

During free fall we start with approximately isothermal contraction. This ends when ionisation is complete. Deuterium burning starts increasing T when it stops the protostar arrives on the Hayashi track.

Question 84

What is the Hayashi forbidden zone?

Answer 84

Where no solutions in H.E exist for a fully convective star

Question 85

How does a protostar leave the Hayashi track?

Answer 85

If a star has a high enough mass and develops a radiative core it will leave the Hayashi track.

Question 86

How long does it take for the triple alpha process to occur?

Answer 86

In starts with M < 2-3 M☉ the process initiates in a matter of minutes or hours. The reaction quickly spreads due to the behaviour of the electron degenerate gas.

Question 87

Describe fragmentation.

Answer 87

Stellar masses are much greater than their estimate for jeans mass so the cloud fragments into smaller bits. As the cloud shrinks it further collapses until stable clouds until clouds with M < MJ are reached.

Question 88

Where does initial collapse occur?

Answer 88

On the free fall timescale.

Question 89

Describe stability in the adiabatic regime.

Answer 89

If a cloud has p > pj it will collapse, if p = pj collapse will halt and for p < pj the cloud expands.

Question 90

Describe Pre-MS evolutionary tracks for high mass stars.

Answer 90

High mass stars develop a radiative core. High temperatures and low opacity prevent convection. The protostar has a Henyey track.

Question 91

Describe Core He burning in high mass stars.

Answer 91

If the core exceeds the S-C mass the core contracts. Depending on the core mass it may become hot enough for He burning which proceeds via the triple alpha process.

Question 92

What is photodisintegration?

Answer 92

When the gamma ray photons produced in nuclear reactions have sufficient energy to destroy heavy nuclei.

Question 93

How does the iron core collapse proceed in different regions?

Answer 93

In the inner part the core collapses homologously whereas in the outer core it collapses in freefall. This causes density to increase trapping neutrinos in the inner core. Eventually neutrons become degenerate forming a nearly rigid core.

Question 94

Describe the Tolman-Oppenheimer-Volkoff limit.

Answer 94

For a adiabatic index of 4/3 no stable solution is possible and the remnant collapses directly to a black hole. This occurs at the T-O-V mass limit.

Question 95

Describe neutrinos during the iron core collapse.

Answer 95

Initially most PE lost during the collapse is converted into the KE of neutrinos. The neutrinos are temporarily trapped behind the shock wave of the collapsing core. As the shock wave propagates into less dense regions the neutrinos can stream out, leading to a neutrino burst.