Stars as Laboratories for Fundamental Physics - MPP Theory Group

Units and Dimensions 581
In the astrophysical literature the cgs system of units is very popular
where magnetic fields are measured in Gauss (G). Confusingly, this
system happens to be an unrationalized one. Field strengths given in
Gauss can be translated into our rationalized natural units by virtue of
√
1 erg/cm
3
1 G →
= 1.953×10 −2 eV 2 = 0.502×10 8 cm −2 , (A.1)
4π
where I have converted erg and cm −1 into eV according to Tab. A.2.
The energy density of a magnetic field of strength 1 G is, therefore,
1
2 (1.953×10−2 eV 2 ) 2 = 1.908×10 −4 eV 4 = 3.979×10 −2 erg cm −3 =
(1/8π) erg cm −3 . For a further discussion of electromagnetic units see
Jackson (1975).
It is sometimes useful to measure very strong magnetic fields in
terms of a critical field strength B crit which is defined by the condition
that the quantum energy corresponding to the classical cyclotron frequency
¯h (eB/m e c) of an electron equals its rest energy m e c 2 so that in
natural units
B crit = m 2 e/e.
(A.2)
Note that the Lorentz force on an electron in this field is proportional
to eB crit so that the electron charge cancels. Hence, Eq. (A.2) is the
same in a rationalized or unrationalized system of units. In our rationalized
units e = √ 4πα = 0.303 so that B crit = (0.511 MeV) 2 /0.303 =
0.862×10 12 eV 2 which, with Eq. (A.1), corresponds to 4.413×10 13 G, in
accordance to what is found in the literature (Mészáros 1992).
Magnetic dipole moments of electrons and neutrinos are usually
discussed in terms of Bohr magnetons µ B ≡ e/2m e . For particle electric
dipole moments, on the other hand, one commonly uses 1 e cm as
a unit. The conversion is achieved by 1 e cm = (2m e cm) (e/2m e ) =
5.18×10 10 µ B .