Stellar Structure and Evolution

draw an HR diagram and label parts and scales along axes

formula for luminosity of a star

L = 4𝝅R²𝝈T⁴

what do spectral linewidths tell us about a star’s luminosity, density, and pressure?

• narrower lines - typically brighter supergiant stars, lower density and lower pressure. energy levels undisturbed

• broader lines - typically less bright main sequence stars, higher density and pressure, many collisions within the star’s gas

what is the mass luminosity relation for average main sequence star?

L = M⁴ or M^3.5

how can we estimate the age of a cluster?

fitting stellar evolutionary models and observing where its MS turnoff point is - the lower the turn off point the older the cluster is (less MS stars present)

how can we determine the distance to a cluster?

main sequence fitting techniques (detailed description in lecture 1 slides)

illustrate the differences between globular and open clusters

open clusters:

• distributed in the galactic disc

• Population I stars - metal rich

• younger - slightly older stars

• lower stellar density - more spread out

globular clusters:

• around galactic halo and nucleus

• Population II stars - metal poor

• very old

• high stellar density - stars are close together

what is stellar structure generally governed by?

mass, age, and initial chemical composition

mass equation

dM(r)/dr = 4𝜋r²𝜌(r)

• derived by mass, volume, density relationship!

define hydrostatic equilibrium

the balance between inward gravitational forces and outward pressure forces

equation of hydrostatic equilibrium - with the aid of a diagram

dP(r)/dr = -GM𝜌 / r²

• essentially equating pressure gradient (force) with gravitational force

dynamic timescale - definition and equation

dynamic timescale:

• timescale over which a star responds to deviations in hydrostatic equilibrium

• time it would take for a star to completely collapse if pressure forces were removed

t_dyn = √2R³ / GM

equation of state + its components

• this is basically just the equation of gas pressure!

P = 𝜌k_BT / 𝜇m_o = 𝜌k_BT / 𝑚

• 𝜇 = mean molecular weight (amu)

• 𝑚 = average mass of particle in gas

• m_o = amu conversion

where are the convective and radiative zones located in:

• >1.5 solar mass stars

• 0.5-1.5 solar mass stars

• >1.5 solar mass

radiative zones are in outer layers, while the inner parts are convective

• 0.5-1.5 solar mass

convective zones in outer layers, radiative inside

what are four sources of opacity/ absorption and re-emission that occur within a star?

• electron scattering - photon is deflected off of a free electron, resulting in a change of photon’s wavelength as its momentum is disturbed

• free-free - free electron absorbs energy from incident photon, or photon is emitted as electron is accelerated/change in direction. electron remains free

• bound-free - “photoionization”; bound electron absorbs photon, freeing it from its bound state

• bound-bound - bound electron absorbs a photon but it only works to push it up to an excited state within its potential well.

energy generation equation? simple derivation and diagram used?

dL(r)/dr = 4𝜋r²𝜌(r)𝜀(r)

from energy generation = M(r)𝜀(r) using mass equation

what is virial theorem?

2U + 𝛺 = 0

showing that for balance systems that two times the thermal kinetic energy is equal to the negative gravitational potential energy. system in equilibrium.

thermal timescale

the timescale through which thermal energy is able to supply a star’s luminosity. shocking, it can’t for very long, since nuclear energy is the main source for a star’s luminosity!

t_th=GM_*² / 2R_*L

what are the two main methods of burning hydrogen in a star?

Proton-proton chain (PP-I) and the CNO cycle both take 4 hydrogen atoms, and results in helium-4 and some energy

describe the steps of the proton-proton I chain.

what is the Russell-Vogt theorem?

if a star is in hydrostatic equilibrium, deriving all of it’s energy from nuclear reactions, therefore it’s structure can be completely and uniquely determined by it’s mass, and the distribution of chemical elements throughout its interior. (this explains the existence and structure of the main sequence!)