7. Hydrostatic Core Flashcards
Stages after fragmentation stops?
Formation of a protostar: first hydrostatic core
Shock fronts
Further collapse
Why does fragmentation stop?
Collapsing core becomes so dense that it becomes opaque to its own radiation
And can no longer efficiency radiate energy released during collapse
What happens when fragmentation stops?
Internal temp and therefore pressure increase
Eventually equilibrium is reached between internal pressure and gravity
Halting free fall collapse
What happens after free fall collapse is halted?
A hydrostatic core develops
Shock front develops at interface between core and envelope
How can infall velocity at shock front be approximated?
By free-fall velocity
Size of first hydrostatic core?
~ 5au
Structure of molecular cloud once hydrostatic core develops?
Centre: hydrostatic core, high T and P
Collapsing core and outer envelope surrounding - still being fed by accretion
What does the shock front do?
Feeds onto hydrostatic core but is no longer collapsing
How to derive free fall velocity of inflating material to hydrostatic core?
Equate KE to GPE
With a shock front at Rs, what happens to the KE of infalling material?
Most of KE converted to radiation (with certain accretion luminosity)
Where does accretion luminosity come from?
The KE from infalling material being converted into radiation at the shock front with accretion luminosity
Equation for accretion luminosity?
L_acc ~ 1/2Ṁ(v_ff)^2
~ GMṀ/Rs
Ṁ = mass infall / accretion rate
Why does accretion luminosity help to find embedded protostars in a molecular cloud?
Accretion luminosity is mostly absorbed by dust and re-radiated at IR wavelengths
Derive the density structure of infalling material to the hydrostatic core
See notes
Mass continuity equation?
Ṁ = 4π r^2 ρ v
ρ = density of material
v = free fall velocity
How does density of infalling matter to the hydrostatic core depend on radius?
ρ ∝ r^-3/2
When considering further collapse onto the hydrostatic core, what conditions are applied?
Adiabatic - no heat lost or gained from the system
What are the conditions for further collapse onto the hydrostatic core?
γ > 4/3 core is stable
γ <= 4/3 core is unstable (further collapse)
(γ = heat capacity ratio)
Why does γ > 4/3 mean core is stable?
MJ increases as T increases
Why does γ <= 4/3 mean core might collapse further?
MJ decreases as T increases - unstable
What relation relates hydrostatic core temperature to density?
T ∝ ρ^(γ-1)
What determines the ratio of specific heats at constant pressure to constant volume?
Number of degrees of freedom f, i.e., diatomic or monoatomic
When will γ be greater than 4/3?
For a diatomic molecule, monoatomic gas
What is the equation for γ?
γ = f + 2 / f
How many degrees of freedom for a diatomic molecule?
5; 3 translational, 2 rotational
How many degrees of freedom for a monoatomic gas?
3 translational only
Under high temp and pressure conditions of molecular hydrogen, what does gamma equal?
H2 dissociates into its constituent atoms
γ = 3+2/3 = 5/3
Is H2 stable under high temp and pressure conditions?
Yes, γ = 5/3 > 4/3
Does dissociation of dust and molecules affect stability?
Yes
Does dissociation of dust and molecules trigger second phase of collapse?
Yes
How is 2nd phase of collapse triggered?
H2 dissociation absorbs energy, that would otherwise provide pressure sufficient to maintain hydrostatic equilibrium
After the second collapse, when is hydrostatic equilibrium reestablished?
When core radius reaches 2 solar radii
When do we have dissociation of molecular hydrogen in the hydrostatic core?
T ~ 2000K and high pressures
After second collapse of the hydrostatic core, is it a star?
No - it is still a protostar
What happens after the second collapse?
Protostar accretes through first shock at first hydrostatic core - second shock front is established as the envelope continues to accrete infalling material
When do we have adiabatic conditions in the core?
When it becomes optically thick
When will hydrogen fusion occur?
After second hydrostatic core is establishing and temperature and pressure continues to increase at it accretes more material
