Section 2

Question 1

What are the assumptions for Virial equation?

Answer 1

Cloud is spherical
Cloud is isothermal
hydrostatic equilibrium (self-gravity and thermal pressure)

Question 2

When is a star in hydrostatic equilibrium?

Answer 2

The outward pressure force on the shell will be equal to the force of gravity acting on the shell

Question 3

What is omega in the Virial equation?

Answer 3

The total gravitational energy of the cloud

Question 4

What is the equation of thermal energy?

Answer 4

u = 3/2kT = 3/2 P

(for an ideal monatomic gas)

Question 5

What is U in the Virial equation?

Answer 5

The total thermal energy content of the cloud

Question 6

What is the Virial equation?

Answer 6

It is used to determine the criterion for cloud collapse supported by thermal pressure alone
3V_cP_s = 2U + Ω

Question 7

When the collapse criterion is simplified, what does this do the Virial equation?

Answer 7

constant density
constant pressure
zero external (surface) pressure

2U + Ω = 0

Question 8

What is Ω?

Answer 8

-3/5 G(M_c)^2 /R_c

Question 9

When is a cloud stable?

Answer 9

When 2U = - Ω

Question 10

When does pressure win and what happens to the cloud?

Answer 10

When 2U > - Ω
dispersion of cloud

Question 11

When does gravity win and what happens to the cloud?

Answer 11

When 2U < - Ω
contraction of cloud

Question 12

What is μmH?

Answer 12

The mean molecular mass of the gas
where mH ≃ 1.67 × 10^−27 kg (the average mass m in units of the mass of a hydrogen atom)

Question 13

What is the Jeans Mass?

Answer 13

The critical mass above which gravity dominates and below it the pressure force dominates
(using the case of contraction of virial equation to derive it)

Question 14

What are the typical values for a dense core?

Answer 14

T = 10K
n = 10^10 m^-3
μ = 2.4

Question 15

What is μ?

Answer 15

The mean molecular weight

Question 16

What is the equation for mass density?

Answer 16

ρ = nμmH

n = number density
μ = mean molecular weight
mH = mass of a hydrogen atom

Question 17

For a typical dense cloud, what is the Jeans Mass and what does it indicate?

Answer 17

5 solar masses

Where to look for star formation: cold, dense regions of ISM i.e molecular clouds

Question 18

If a cloud collapses as a whole what happens?

Answer 18

The total mass Mc stays CONSTANT
the density increases

Question 19

What happens initially when a cloud collapses as a whole?

Answer 19

It remains isothermal
the gravitational potential energy that is released is radiated away
Gravity will increasingly dominate over the pressure as pressure force is proportional to the inverse of the radius

Question 20

When will a cloud supported only by thermal pressure collapse?

Answer 20

If it’s mass exceeds the Jeans Mass

Question 21

What happens in an isothermal collapse?

Answer 21

Gravity dominates over pressure

Question 22

What is the free fall time?

Answer 22

The time it would take for a star to collapse to a point if there was no outward pressure to counteract gravity

Estimated by assuming acceleration is constant (t proportional to ρ^-1/2)

(it is independent of initial radius of cloud)

Question 23

What is the free fall time proportional to?

Answer 23

n^-1/2

Question 24

What is the free fall time for the formation of a 5 solar masses star?

Answer 24

3 x 10^5 years

Question 25

When is free fall time longer?

Answer 25

For less dense regions and shorter for denser regions