# How to convert between surface density in JY/beam*KM/S / arcsec2 to mass surface density in Solar masses / pc2

I am interested in studying the gas kinematics of atomic hydrogen (21cm line) for a galaxy and have output I'd like to convert after assuming a model for my data using BBarolo.

Map units: unit = JY/BEAM*KM/S
Pixel area: 0.56250 arcs2
The Face On Surface Density (corrected for inclination) is 2.418e-02 unit/arcs2
The Mass Surface Density is 1.869 MSun/pc2


(The face on SD can be found by taking the Sum of the unit 4.859 JY/BEAM*KM/S divided by the number of pixels 106 and the pixel area 0.56250 arcs2. This value is then multiplied by cos(72.614 degrees) because the galaxy is inclined.)

What I don't understand is how the Face On Surface Density is converted to the mass surface density in Msun/pc2. The value reported is 1.869 Msun/pc2. Mass surface density is conserved so I am told I do not need the distance to determine this value (the distance to the galaxy is ~30.42 Mpc). I understand that it is conserved, but wouldn't I need the distance to figure out the physical area of a pixel in parsecs?

My goal is to figure out how the Mass surface density in Solar Masses per square parsec is calculated for a sanity check. The numbers seem reasonable but this conversion is not found in their paper or documentation. I should be able to recover this quantity myself.

If relevant, the beam is circular and 8 arcseconds.

• Using the parallax rule that two objects at a distance of 1pc separated by 1 arcsec will be 1 AU apart, then for your galaxy at 30.42 MPc an angle of 1 arcsec corresponds to a separation of 30,420,000 AU = ~147pc. The pixel area of 0.56250 arcs2 corresponds to a pixel width of 0.75 arcsec = 110pc. What are the units for the Face On Surface Density? In you code it just says 'unit/arcs2' Mar 25, 2022 at 22:50
• Units = JY/BEAM*KM/S Mar 25, 2022 at 22:54
• Ah okay yes I see. I've not managed to work it out myself, but you can find the formula for the conversion in the BBarolo code in the file 'Bbarolo-1.5//src/Tasks/ellprof.cpp', take a look at either line 505 or 799. The comment in the code says the formula is from 'Roberts75', maybe that's a reference you know? Mar 26, 2022 at 9:08
• Tanks for the tip. I found the formula but it isn't intuitive and I can't find a derivation of it. It can be found in this paper: arxiv.org/pdf/2110.01618.pdf (formula 2). The original publication seems to be inaccessible. I am stumped how you can go from given units to M_Sun/pc2. It would be nice to see the derivation, even if it is for a similar equation. Mar 28, 2022 at 0:28