6. Fragmentation Flashcards
How do we know another process must occur to form solar mass (and lower) stars?
Jeans mass for a typical dense core is 5 solar masses
So there must be another process that means collapse occurs at lower solar masses
Under what condition will the Jeans mass decrease as density increases?
If core temperature remains constant during the initial stages of the collapse
Equation for cooling time of a molecular cloud?
t_cool = u / Λ
where
u = 3/2nkT thermal energy
Λ = rate of loss of thermal energy
Why are molecular clouds (~10K) warmer than the Cosmic Microwave Background (2.7K)?
There must be a heating process - Cosmic-ray heating
Why is the ionisation fraction in molecular clouds > 0?
Cosmic-ray proton scatters inelastically with H2 (ionising it)
What do cosmic rays consist of?
Mostly relativistic (v ~ c) protons, with a mix of heavy elements and electrons
[all particles are charged so subject to magnetic deflection]
How are cosmic rays produced?
Particle acceleration within the magnetised shocks created by supernova remnants
How do cosmic rays provide heat?
Cosmic-ray proton scatters inelastically, ionising H2
Secondary electron collides with another H2 = dissociation
[e- + H2 -> H + H + e-]
Resulting 2 H molecules have higher KE, colliding with other molecules and creating heating mechanism
What type of collisions are involved with hydrogen and cosmic-ray protons?
Inelastic
How does dissociation relate to the heating mechanics within a molecular cloud?
An electron dissociates a H2 molecule, so 4.5eV goes into KE of the 2 H atoms
Why do cosmic-ray protons behave different to other protons (H+) in the gas?
They are relativistic so much higher energy
Equation for heat deposition in a molecular cloud per unit volume?
Γcr(H2) = ζ(H2)n(H2)ΔE(H2)
where
ζ = ionisation rate
n = number density
ΔE = energy deposition
Typical ionisation rate?
(1-10)e17 s^-1
What is meant by ionisation rate?
Probability per unit time of ionisation
Why do we have an equilibrium temperature of around 10K in a typical molecular cloud?
Cosmic-ray heating is balanced by cooling
Net energy provided by a single 10MeV proton?
ΔE(H2) ~ 7eV (very small)
What is the main cooling mechanism in molecular clouds?
CO rotational emission
How is energy removed and transferred to radiation in a molecular cloud?
CO is easily excited in low temperature gas; it will spontaneously decay, emitting photons as radiation and removing KE
What does rate of loss of thermal energy ΛCO depend on?
Number density of CO molecules in the cloud, the energy of the transition, and the optical depth of the emitted lines
ΛCO value in a typical cloud?
10e-23 J/s/m^3
Is cooling rate sensitive to temperature?
Yes
How does cooling time compare to free fall time at the same density?
Free fall time is longer than cooling time by 2 orders of magnitude
Why do we compare cooling time and free fall time?
Cooling time is shorter than free fall time, therefore cooling time is fast enough that the cloud can maintain an isothermal temperature
How does density affect ratio of cooling time to free fall time?
Higher density: cooling time wrt free fall time is faster
Why can we say that the molecular gas stays isothermal during collapse?
Cooling time is fast compared to free fall time
(despite some cosmic-ray heating)
What implication does cooling time being fast compared to free fall time have on Jeans mass?
Means initial collapse of cloud is isothermal (removing T dependence)
Therefore MJ decreases (since MJ prop to n^-1/2)
But initial cloud MJ doesn’t decrease, instead subunits within cloud reach MJ for that given density
When we say MJ decreases in isothermal collapse, what does this mean specifically?
The initial MJ of the cloud doesn’t decrease, instead subunits within cloud reach MJ for that given density (fragmentation)
How does fragmentation occur?
A single entity reaches MJ and begins to collapse
Cloud cools sufficiently so collapse is isothermal
As density increases in subunits within the cloud, these reach MJ for that given density and fragments collapse
What are the stages of collapse of molecular clouds into stars?
Large cloud begins to collapse as it becomes sufficiently dense
Fragmentation: Localised regions collapse
When fragment collapses independently without further disruption, forms protostar
What halts fragmentation?
When cloud becomes optically thick and cannot cool efficiently
[Once opaque a fragment radiates almost as a black body]
Why must a cloud remain optically thin for it to remain isothermal?
If cloud becomes optically thick, it can no longer cool efficiently i.e., cannot radiate GPE released during collapse
What effect does a cloud being optically thick have on Jeans Mass?
Since it is no longer isothermal, T increases does MJ
Why does optical depth τ increase during fragmentation?
τ ∝ n^1/2 for constant T
So τ increases as density increases
Derive the dependency of mass (at which the fragment becomes opaque) on temperature
See notes
Once a fragment is opaque, what assumption can be used?
It will radiate almost as a black body
Therefore rate of energy lost due to radiation = rate in gain in GPE
How does minimum fragment mass depend on temperature?
M prop to T^1/4
For a typical molecular cloud (T~10K, µ = 2.4), what is the mass of the smallest fragment?
M ~ 0.002 solar masses
How is minimum fragment mass estimated?
Equating rate of energy lost via radiation with that gained in GPE
