physical unit of AnyRazorThinDiskPotential

[sugar-joh]

Hi Dr.Jo Bovy:
I am using trying to get the rotation curve of thin disk with different surface density distribution and keep the total disk mass fixed. I wonder how I can get the physical velocity as a function of radius. I try to add unit to 'amp', but get 'amp= parameter of AnyAxisymmetricRazorThinDiskPotential should have units of None, but has units of surface density instead'.

Best,
Johnson

[jobovy]

Hi!

The easiest way to get unitful output is to set the ro and vo unit conversion parameters:

diskpot = AnyAxisymmetricRazorThinDiskPotential(surfdens=lambda R: 1.5*numpy.exp(-R/0.5),ro=8.,vo=220.)

where ro is the length-scale in kpc (8 kpc is the default) and vo is the velocity scale in km/s (220 km/s. by default). Note that the surfdens function can return astropy Quantities and take as input R as an astropy Quantity as well. In that case, it doesn't matter what you set for ro and vo, because it's just used to convert to and from internal units.

[sugar-joh]

Hi Dr.Jo Bovy:
Thank you for your reply. I have specified the units in the surfdens function which should give me physical units, but I am having trouble reconciling the following two expressions. These potentials give circular velocities that differ by two orders of magnitude. In principle, they should produce identical results, right? I also tried setting ro = 1, but the discrepancy persists.

expdisk = RazorThinExponentialDiskPotential(amp=1e10*u.Msun/u.kpc**2, hr=1*u.kpc)
diskpot = AnyAxisymmetricRazorThinDiskPotential(surfdens=lambda R: np.exp(-R/(1*u.kpc))*u.Msun/u.kpc**2, amp=1e10) 

Best,
Johnson

[jobovy]

The confusing thing here is that having surfdens return a Quantity does not make diskpot return outputs as Quantities. It probably should. But now you can do as I suggested before

expdisk = RazorThinExponentialDiskPotential(amp=1e10*u.Msun/u.kpc**2, hr=1*u.kpc)
diskpot = AnyAxisymmetricRazorThinDiskPotential(surfdens=lambda R: np.exp(-R/(1*u.kpc))*u.Msun/u.kpc**2, amp=1e10,ro=8.,vo=220.)

and the circular velocities match, e.g.

print(expdisk.vcirc(6*u.kpc),diskpot.vcirc(6*u.kpc))