Predicting analytically stripped and re-accreted mass fraction - - PowerPoint PPT Presentation

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Jul 31, 2023 194 likes •363 views

Predicting analytically stripped and re-accreted mass fraction Joachim Kppen A gas parcel in the galactic disk potential Restoring force Gunn & Gott criterion = force acting slowly escape potential Restoring force What happens

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Predicting ‘analytically’ stripped and re-accreted mass fraction

Joachim Köppen

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A gas parcel in the galactic disk

potential Restoring force

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Gunn & Gott criterion

potential Restoring force = force acting slowly escape

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What happens after a short force pulse?

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Taking RPS as a collision

Momentum balance

ΣISM * vAFTER = ΣICM * vICM

Stripping if

vAFTER > vESC

Works well to explain stripped mass

fractions in Pavel’s SPH models

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How to predict the re-accretable fraction?

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Simulations with test particle models

stripped (ETOTAL > 0) kicked above 1 kpc unmoved At time of max. pressure

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Remember the ballistic galvanometer?

If an undamped harmonic oscillator is

kicked by a pulse shorter than its natural period, it will oscillate with an amplitude which is proportional to the time-integrated force i.e. the momentum transferred to it. NB: The amplitude is independent of the form of the pulse.

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Period of vertical oscillations

Pavel’s « standard » run 10 Myr

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Let’s apply it to face-on RPS

Equation of motion

d(ΣISMv)/dt = ρICM (vICM-v)² - ΣISM dΦ/dz

Solution: (a) during the kick (z = v = 0)

ΣISMvAFTER = ρICM vICM² Δt

Solution: (b) after the kick (Force=0; v = vAFTER)

d(ΣISMv)/dt = - ΣISM dΦ/dz  (harmonic) oscillation with amplitude corresponding to initial kick …

the important parameter:

ρICM vICM² Δt = vICM (ρICM vICM Δt) = vICM ΣICM

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Given the speed after the kick

… and the potential, we can compute how

high above the disk the gas packet can move

… and hence we can predict which parts
f the disk will be displaced by some

minimum height, say 1 kpc

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We get

stripped kicked above 1kpc but not stripped R [kpc] stays in disk

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Compare with Pavel’s SPH models

Not all kicked matter really reaches above 1 kpc …

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… while other matter is displaced Depending on the initial vertical velocity some kicked matter remains unmoved

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Summary

Momentum transfer determines the fate of

a gas parcel

The primary parameter is the column

density ΣICM of the accumulated ICM

For the reaccreted fraction we can give
nly an upper limit
For slow stripping, the efficiency of