3.1. Zeeman splitting

In order to measure large scale magnetic fields, one of the first effects coming to mind, is the Zeeman effect. The energy levels of an hydrogen atom in the background of a magnetic field are not degenerate. The presence of a magnetic field produces a well known splitting of the spectral lines:

(3.2)

where _|| denotes the uniform component of the magnetic field along the line of sight. From the estimate of the splitting, the magnetic field intensity can be deduced. Indeed this technique is the one commonly employed in order to measure the magnetic field of the sun [22]. The most common element in the interstellar medium is neutral hydrogen, emitting the celebrated 21-cm line (corresponding to a frequency of 1420 MHz). If a magnetic field of µ G strength is present in the interstellar medium, according to Eq. (3.2), an induced splitting, _Z ~ 3 Hz, can be estimated. Zeeman splitting of the 21-cm line generates two oppositely circular polarized spectral lines whose apparent splitting is however sub-leading if compared to the Doppler broadening. In fact, the atoms and molecules in the interstellar medium are subjected to thermal motion and the amount of induced Doppler broadening is roughly given by

(3.3)

where v_th is the thermal velocity (T / m)^1/2 where m is the mass of the atom or molecule. The amount of Doppler broadening is _Dop ~ 30 kHz which is much larger than the Zeeman splitting which should be eventually detected. Zeeman splitting of molecules and recombination lines should however be detectable if the magnetic field strength gets larger with the density. Indeed in the interstellar medium there are molecules with an unpaired electron spin. From Eq. (3.2) it is clear that a detectable Zeeman splitting (i.e. comparable or possibly larger than the Doppler broadening) can be generically obtained for magnetic fields where _|| 10^-3 G, i.e. magnetic fields of the order of the m G. Molecules with an unpaired electron spin include OH, CN, CH and some other. In the past, for instance, magnetic fields have been estimated in OH clouds (see [12] and references therein). Magnetic fields of the order of 10 m G have been detected in interstellar H₂O maser clumps (with typical densities (10¹⁰ cm^-3)) [23]. More recently attempts of measuring magnetic fields in CN have been reported [24]. The possible caveat with this type of estimates is that the measurements can only be very local: the above mentioned molecules are much less common than neutral hydrogen and are localized in specific regions of the interstellar medium. In spite of this caveat, Zeeman splitting measurements can provide reliable informations on the local direction of the magnetic field. This determination is important in order to understand the possible origin of the magnetic field. This aspect will be discussed, in more detail, when describing the magnetic field of the Milky Way.