Spectrocopy with the 21cm Hydrogen Line

Joachim Köppen Strasbourg 2010

The 21 cm radio line of hydrogen was predicted from quantum mechanical considerations by H.C. van de Hulst in 1944. The ground state of the hydrogen atom is split up in two states due to the interaction of the spins of the electron and the proton in the nucleus: If the spins are parallel to each other, the energy of the system is slightly higher than when the spins are oriented anti-parallel. The energy difference corresponds to a frequency of 1420.405751786(30) MHz (for radio astronomy 1420.406 MHz is quite sufficient) or a wavelength of about 21cm. Everytime a hydrogen atom makes a transition from the higher to the lower state, it emits a radio wave at that frequency. The presence of this line emission from the neutral hydrogen gas in our Milky Way galaxy was first detected in 1951 by Ewen and Purcell of Havard University.

The intensity of the emission depends on the number of hydrogen atoms encountered along the line of sight:

N_H [1/cm²]= 1.8224(3) E+18 *(T_spin [K]) * INT( t(v) dv[km/s]
where N_H is the column density of H atoms, T_spin is the spin temperature which describes the equilibrium populations of the two energy levels, and t(v) is the optical depth as a function of radial velocity v which in general is defined as
t = -ln (1 - T_L/(T_spin -T_BG)
where T_L is the observed line brightness temperature and T_BG the background temperature ... (this text is not final ... and we won't need these details for the analysis of our observations ;-)

Hydrogen is the most abundant element in the universe, and the clouds of interstellar gas from which stars are born, consist essentially of hydrogen atoms, because of their rather low temperatures of less than 100 K. About 10 percent in mass of our own Galaxy is in the form of interstellar gas, most of which is located in a thin disk, which rotates around the Galactic Centre, along with the stars.

Since the presence of a spectral line, whose true frequency is known, permits to measure the movements of the gas clouds via the Doppler effect, the 21 cm line has been of immense value to study the motions of gas in our own galaxy as well as in other galaxies. These investigations started in the 1950s and lead to the discovery that the Milky Way is indeed a spiral galaxy. The spiral arms can be detected and the Galactic rotation can be measured with radio telescopes as small as the ESA-Haystack instrument.

If one points the telescope towards a position in the Galactic Plane, one may obtain a raw spectrum like this:

On top of the noise background from the receiver - at about 1200 cts in power ('cts' for 'counts': the numerical values of the uncalibrated measure for power used and displayed by our software) - one finds the galactic emission features near 1420.4 MHz. This is not a single sharp line, but the emission is spread out over about 500 kHz, having several "bumps". Because the emission of hydrogen atoms in an interstellar cloud occurs at the true frequency of 1420.406 MHz, the measured frequency allows us to infer on the radial velocity of that bunch of atoms. There are two processes which affect this apparent velocity: In this manner, the observed profile of the emission feature is the composite of all contributions. In the spectrum above we may distinguish two main bumps and smaller one on the high frequency side. The main features have a width of about 100 kHz, which corresponds to 20 km/s. This is wider than we could expect for the thermal motions in cool clouds, so it is the larger motions of individual clouds that produces one such a feature. As the features are well separated, we see here several groups of interstellar gas clouds moving in a systematic way: Thus the gas is organized in several spiral arms.

We notice that the important information is in the spectral feature, and not in the height of the background. For any analysis, we shall substract this background. We may do so, because the signal here is mostly the noise produced in the receiver itself. There can be external noise from electronic pollution by all sorts of electronic and electric apparatus from the neighbourhood, also some continuum emission from the galaxy and the earth atmosphere. In the spectrum above, the background increases slightly with frequency. Thus, it is reasonable to assume that it increases linearly with frequency, and to define a straight line, the baseline (the straight blue line in the plot above), and consider for analysis the observed flux minus this baseline. If one had more information of the spectrum far away from the feature, one could even correct for a nonlinear background.

When the data have been subtracted by the background, one integrates the excess emission by the feature over all frequencies, and gets the total flux of the spectral feature ... which can be modeled or compared with models for the total emission.

We can try to interpret the observed profile in a more detailed way. We assume that the emission comes from a number of components, each being described by a gaussian emission profile from a large number of clouds; each component may have a different average radial velocity (i.e. frequency), a different height (because of the number of clouds making the component), and a different width (because of the variation of speeds of individual clouds). If one plays with these parameters for a sufficient number of components, one may try to match the observed profile of the feature. Here is an example of a quick, manual fit involving 10 components:

The red dots show the observed data, the blue curve is the sum of all contributions whose individual profiles are shown in black thin lines. This plot also shows the spectrum as a function of radial velocity.

The feature close to 0 km/s has rather steep sides. Therefore one needs two narrow components instead of a single broader one. This gives a upper limit to the widths of the components: we had to use 35 kHz which corresponds to 7.3 km/s. This gives us the dispersion for the speeds of individual clouds. And it implies that the 0 km/s feature is probably really two overlapping features, while the broad feature near -50 km/s may be the superposition of three components.

This shows that with a more careful analysis, quite a few things can be extracted from the data. Obviously, one has to be aware that such a fitting method may have its limits and problems, such as the uniqueness of the solutions ...

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last update: Feb. 2010 J.Köppen