Changes between Version 5 and Version 6 of u/erica/CF_coldens

Timestamp:

01/19/15 14:55:00 (10 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/CF_coldens

@@ -5 +5 @@
 [[latex($\sum n_i dx = \bar{n} L_x$)]]
 
-which has the rather strange units of computational number density times computational length. We can not just assume that the resultant product will  have units of 1/computational length squared. Thus, we can not simply multiply our projected quantity by lscale^-2^ to get units of cm^-2^.
+which has the rather strange units of computational number density times computational length. We can not just assume that the resultant product will  have units of 1/computational length squared. This is because while nscale has units of 1/lscale^3^, it does not equal 1/lscale^3^,
 
-Instead, we should multiply it by lscale*nscale. This will give us the correct units for column density, when lscale and nscale are in cgs. 
+[[latex($nscale \neq lscale $)]] 
 
-For my specific data, my lscale is 1 pc, and my nscale is 1 (which just means it is in cgs by default). So the quantity the code gives for 'projected column density in computational units', can be thought of as being in pc/cm^3^. To convert this to 1/cm^2^, multiply by the conversion factor 1pc = 3.08567758 × 10^18^ cm.
+but in fact equals,
+
+[[latex($nscale = rhoscale/X $)]] 
+
+where X is the mean molecular weight.
+
+Therefore, 
+
+[[latex($n(cu)*l(cu) = \frac{n(cgs)}{nscale}* \frac{l(cgs)}{lscale} \neq \frac{n(cgs)*l(cgs)}{ lscale^{-2}} $)]] 
+
+This means that we can not simply multiply our projected quantity by lscale^-2^ to get units of cm^-2^. Instead, we should multiply it by lscale*nscale. This will give us the correct units for column density, when lscale and nscale are in cgs. 
+
+Note, for my setup, lscale is the number of cm in 1 pc, and my nscale is 1. This means that computational density and length can be thought of as being in units of cm^-3^ and pc. Thus the quantity the code gives for 'projected column density in computational units' is for all intents and purposes, in units of pc/cm^3^. To convert this to 1/cm^2^, multiply by the conversion factor 1pc = 3.08567758 × 10^18^ cm (which is of course equivalent to multiplying by nscale and lscale as stated above).