Long- and short-pulse limits

Ram pressure stripping of galaxies: The long- and short-pulse limits
Joachim Köppen Kiel September 2017

Some brief explanations

This utility allows the user to estimate the consequences of ram pressure stripping on the gas disk of a galaxy:
Is the ram pressure pulse longer than the period for vertical oscillations in the galactic disk (typically 100 Myr), one may treat the problem by a quasi-static argument (Gunn & Gott, 1972): gas is removed from the disk, if the ram pressure exceeds the maximum of the vertical restoring force. This may also be called the long-pulse limit, and the result depends on the maximum ram pressure.
If, on the other hand, the pulse is much shorter, it depends the amount of momentum deposited in the gas element whether the gas can escape. This is called the short-pulse limit, and the outcome depends on the time-integrated ram pressure

How much gas is removed from a given galaxy as the result of a certain ram pressure history, is uniquely characterized by these two parameters, if the ram pressure is a pulse with e.g. a Lorentzian time-profile.
The solution is best shown in the plane spanned by time-integrated ram pressure vΣ and maximum ram pressure p_max. This utility allows the user to explore this diagram. We use a simplified model for the galaxy, where the rotation speed is used as an approximate description of the galaxy's gravitational potential.
- For a given galaxy and a specified deficiency (i.e. stripped mass fraction) the vΣ-p_max diagram marks the long-pulse limit with a black line, the short-pulse limit with a blue line, and the red curve as the interpolating curve between the two limits. The red dot marks the intersection of the two limits. The green line indicates the relation between vΣ and p_max for a Lorentzian pulse with the specified pulse duration.
- For the long-pulse limit the relations between the maximum ram pressure value and the parameters for the outcome: stripping radius, lost mass fraction, deficiency are shown.
- Likewise, for the short-pulse limit the dependence of the outcome parameters on the time-integrated ram pressure are displayed.

The galaxy is specified by these parameters:
(Green background indicates current input fields)

rotation speed: as spiral galaxies usually a rotation speed which remains constant width distance from the centre, this single value suffices to characterize the gravitational potential.
exponential disk profile: specifies the type of profile for the surface density in the gas disk. The other option is a Kuzmin profile.
gas disk radius: is the initial outer radius of the gas disk.
gas radial scale: is the parameter for the disk profile.
cent.surf.density: specifies of shows the gas surface density at the galactic centre ...
gas mass: gives or specifies the total gas mass. A click on this field allows to enter data here, as indicated by the green background.

The maximum restoring force in the criterion of Gunn & Gott is well approximated by one half of the centrifugal force. Hence the ram pressure needed to remove gas from radius r in the long-pulse limit can be written as p = Σ_gas(r) v²_rot / 2r
The escape speed is assumed to be 1.41.. times the circular speed. This simplifcation allows to write the value of the time-integrated ram pressure needed to remove gas from radius r in the short-pulse limit as: (vΣ)_ICM = Σ_gas(r) v_rot

The display is controlled by:

X, Y: chose the abscissa and the ordinate among:
- maximum ram pressure
- time integrated ram pressure AKA (vΣ)_ICM
- gas mass fraction: the fraction of the inital mass that remains.
- deficiency = log10(initial mass/remaining mass).
- stripping radius = the outer radius of the remaining gas disk.
wipe&plot: clear the plot area and draws the last curve in red. Changing any parameter value (and hitting the Enter key) will overplot the new curve in red.
overplot: after changing any parameter value, these button will overplot the new curve in the corresponding colour.