(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to infer the observed star formation efficiency of the Kennicutt Schimdt law starting from a volumetric SF law.

The KS law is a relationship between gas and stellar surface density that we can approximate as:

[itex]\frac{d\Sigma_*}{dt}=A\Sigma_{gas}^{1.5}[/itex]

Where [itex]A[/itex] is the efficiency and its values is roughly 2.5e-4 when [itex]\frac{d\Sigma_*}{dt}[/itex] is measured in [itex]M_\odot kpc^{-2} yr^{-1}[/itex] and [itex]\Sigma_{gas}[/itex] in [itex] M_\odot pc^{-2}[/itex].

Now the problem is I want to derive this efficiency starting from this formula

[itex]\frac{d\rho_*}{dt}=B\frac{\rho_{gas}}{t_{ff}}[/itex]

where [itex] {t_{ff}}[/itex] is the free-falling time and is equal to

[itex] {t_{ff}}=\sqrt{\frac{3}{32\pi G \rho_{gas}}}[/itex]

I need to compute B and then convert it in the same units of the Kennicutt Schimdt law.

2. The attempt at a solution

Since the Kennicutt law involes surface density I have multiplied both sides of the volumetric equation by a characteristic scale length [itex]\Delta x[/itex].

Therefore B should be equal to:

[itex]\sqrt{\frac{32\pi G}{3}} \Delta x[/itex]

The things is I had to convert this number from cgs units to the units in which the Kennicutt law is given but I don't get the same order of magnitude. Can you help me?

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# Difficult units conversion

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