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