unit module: behavior of Gauss units

I am having some problem using the astropy unit module, in particular with the Gauss units (magnetic flux density). Let me remind you that Gauss is a cgs unit: 1 Gauss =1 cm^(-1/2) g^(1/2) s^(-1).

Here is what I get when I define a B value:_

from astropy import units as u
B = 1*u.Gauss
print(B)
#1.0 G
print( B.cgs )
#1.0 G

…it looks like the G units are correctly assumed cgs. Now I want to estimate the energy per particle, so I need to square and divide by the density:

n_e = 100 * u.cm**(-3)

E_mag = B**2/n_e  # forget about 4pi factors...
print(E_mag)
# 0.01 cm3 G2

which is correct, but units should realy be g cm2 / s2… I guess it really likes using G! But just to be check

print(E_mag.decompose())
1e-16 kg2 m3 / (A2 s4)

which is in MKS… Strange, for something that is defined in cos (Gauss is cgs; corresponding MKS unit is Tesla).

Problems start if I add this energy density to another energy density, say the kinetic energy of a proton at 100km/s, given by:

from astropy.constants import m_p
m_h = m_p.cgs
v_0 = (100 * u.kilometer/u.second).cgs
E_kin = 1/2. * m_h * v_0**2
print(E_kin)
#8.363108885e-11 cm2 g / s2

in cgs units, as expected. But if I add the two energies I get a dimensional error

print(E_kin + E_mag)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/Users/robberto/anaconda/lib/python2.7/site-packages/astropy/units/quantity.py", line 295, in __array_prepare__
    converters, result_unit = UFUNC_HELPERS[function](function, *units)
  File "/Users/robberto/anaconda/lib/python2.7/site-packages/astropy/units/quantity_helper.py",  line 290, in helper_twoarg_invariant
    return get_converters_and_unit(f, unit1, unit2)
  File "/Users/robberto/anaconda/lib/python2.7/site-packages/astropy/units/quantity_helper.py",  line 284, in get_converters_and_unit
    .format(f.__name__))
astropy.units.core.UnitConversionError: Can only apply 'add' function to quantities with compatible dimensions

Again, If I decompose

print(E_kin.decompose())
#8.363108885e-18 kg m2 / s2
print(E_mag.decompose())
#1e-16 kg2 m3 / (A2 s4)

I see that I am stuck with the Gauss behaving as a MKS unit. This seems to be an error, or at least a feature that is not well documented.

[jzuhone]

Hi all,

This issue was pointed out to me and I wanted to comment on it from the perspective of someone who has gotten bit by this same issue in a different context. I’m one of the yt developers and we have a similar symbolic units system to AstroPy, and last year I implemented a system for translating betweek different unit systems (e.g., MKS, cgs, imperial, etc.).

It is true that numerically speaking 1 G = 1.0e-4 T. However, they are actually not in the same dimensions, because the MKS unit system has current as a fundamental dimension and Tesla are defined in terms of it. cgs units do not have current:

1 G = 1 g^0.5 / (cm^0.5 ^ s) 1 T = 1 kg / (A * s^2)

I admittedly am not an expert in how the AstroPy unit code works, but I have used it and I suspect that what’s happened here is that G has been defined in terms of T which means that it gets reduced to the second dimensional form above instead of the first. Strictly speaking, for symbolic unit systems like this G should not be formulated in terms of T if you want to keep the base dimensions consistent with their usual definitions.

For more information on how we handled this in yt, see the following document:

http://ytep.readthedocs.io/en/latest/YTEPs/YTEP-0028.html#special-handling-for-magnetic-fields

I’m not sure if this helps, but if it does that would be great.

[mhvk]

closing in favour of #4359 - really, the user has to have a way to tell they are working in (one of the) cgs systems