### Question about calculating the Baryonic Tully Fisher Relation Julia Falcone
• 18 Jul '19

Hi Dylan,

I am trying to recreate the Baryonic Tully Fisher Relation for my research, which I know has been done using data from the simulation. I was wondering whether you had any insight as to how the circular velocity for the data was obtained, because my own attempts have given me a relation which deviates a bit from the BTFR. I would assume that the calculation for a given subhalo (all of which are at z=0) is as follows:

`M_bary = (subhalo['massinrad_stars'] + subhalo['massinrad_gas'])*1e10` (obtain baryonic mass, convert to Msun)
`M_tot = subhalo['massinrad'] * 1e10` (multiply total mass by 1e10 to get Msun)
`R_tot = subhalo['halfmassrad']*2` (multiply half mass radius by 2 to get full mass radius in kpc)
`G = G.to(u.kpc / u.Msun * (u.km/u.s)**2).value` (conversion of G to applicable units)
`V_circ = np.sqrt(G * M_tot / R_tot)` (circular velocity formula)

and from there I have M_bary and V_circ to graph. To the best of your knowledge, do these calculations seem like the reasonable way to find the desired quantities? I would appreciate any guidance, since I'm not sure where I might have made a mistake or if there's a better way to do this. Thank you very much!

Julia Dylan Nelson
• 19 Jul '19

Hi Julia,

We had a quick presentation of this e.g. in the original Illustris simulation in Vogelsberger+ (2014) Fig 23. Some of the choices involved are described therein.

If you want to compare to an observed BTFR, then there are many additional details one could consider. Namely, how (and where, and in what phase) is each property of the observed galaxies measured, and how best to recreate such a measurement from the simulation side.

The options you propose are a good 0th order estimate, but are quite theory-oriented, so I wouldn't necessarily anticipate that they should correspond to a given observational measurement. Julia Falcone
• 19 Jul '19

Hi Dylan,

Thank you very much for your response! I'll be sure to consider these other factors in my work.

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