Cosmological Applications of H Surveys

Diffuse H emission and CMBR fluctuations

With the advent of dedicated satellites that will make precision measures of the fluctuations of the Cosmic Microwave Background Radiation (CMBR) over the whole sky, the next decades will see the attempt to measure the cosmological parameters from these fluctuations with high precision, provided some hypotheses are made (nature of the dark matter, history of the reionisation, etc). Although the present data are encouraging (see Lineweaver et al. 1997), one of the main limitations will come from our ignorance of the properties of the different contaminating foregrounds. Besides the contamination by galaxies, however, the known Galactic foregrounds (dust, synchrotron and free-free emission) have different spectral properties and spatial morphologies, and hence can be disentangled from the intrinsic, cosmological fluctuations. Figure 1 summarizes the expected behaviour of these foregrounds and compares them with the levels of the monopole, dipole and quadrupole moments. Clearly, at the quadrupole level the foregrounds are a major contamination.

Below 10 GHz, the Galactic diffuse emission is dominated by the synchrotron emission from relativistic cosmic rays interacting with Galactic magnetic fields. If the energy distribution of the electron population is a power law, , then the synchrotron spectrum of the ensemble is also a power law. The corresponding brightness temperature scales as so that for a typical energy slope for electrons between 2 and 15 GeV (corresponding to radiation between 408 MHz and 10 GHz) the spectral slope is approximately -2.7. The actual distribution on the sky depends of course on the distribution of the magnetic field, as well as the electron density along the line of sight. For instance, near the Galactic centre, the spectral indices cover the range -2.2 to -1.9 (Yusef-Zadeh 1989), and so even though steep spectra may be associated with synchrotron, flatter energy distributions may be more ambiguous. Currently the only way to quantify the contribution of the synchrotron emission is using the maps at 408 MHz (Haslam et al. 1982) or 1.42 GHz (Reich & Reich 1988), but their angular resolution is too coarse for the smaller angular scales we are interested in. Extrapolation at both smaller scales and higher frequencies is tricky (e.g. Platania et al. 1997 for a steepening of the spectrum).

  
Figure 1: Comparison of the expected frequency dependence of foregrounds with the monopole, dipole, and quadrupole levels of the CMBR. The diffuse emision from dust dominates above 80 GHz, while synchrotron dominates below 20 GHz. The Bremsstrahlung is likely to contaminate the fluctuations observed between 20 and 80 GHz. The dashed vertical lines indicate the channels used in the DMR experiment on COBE (31.5, 53 and 90 GHz).

  
Figure 2: Predicted brightness temperature of the free-free emission associated with the emission of 1 Rayleigh in Balmer , assuming a common emission measure. (a) Brightness temperature for several gas temperatures, (b) Spectral slope of the Bremsstrahlung with two different approximations for the thermal average of the Gaunt factor : long wavelength (dotted lines), Hummer (1988) bi-dimensional Chebyshev fit (same lines as panel (a)). The small discontinuities are due to the transition between the two approximations.

At the bottom of the 'valley' of minimum foreground contamination, the free-free emission is the major contribution, and is the least known. Because the Balmer H line originates from the same recombinations of ionised gas as the Bremsstrahlung emission, one could use an all-sky H survey to trace the free-free contamination. Since there is much confusion in the present literature concerning the precise relation between the H and the Bremsstrahlung emissions (mainly due to different underlying approximations), we derive here accurate expressions. These are important because we are looking for fluctuations in the residuals, rather than simple proportions.

The absorption cross-section for a free-free transition from to for an ion of charge Z by an electron with initial velocity v is given by the classical (Kramers) cross-section times a Gaunt cofactor (e.g. Oster 1961)

where and . The total absorption cross section per ion and per electron is obtained by summing over all incident electron velocities, assuming a Maxwell-Boltzmann distribution

so that

The thermal average is

where , , , and .

The crux of the problem is the evaluation of the Gaunt factor, for which several approximations exist, depending upon the regime where the electron-ion collisions take place. For temperatures below 2 10 K, and a frequency range between 1 and 1,000 GHz, that is and , the classical, small-angle, long wavelength approximation is appropriate (see, e.g., Novikov & Thorne 1973)

where is Euler's constant. One can write this approximately as , and by noting that , , for Z=1,

But in fact the 'effective' spectral slope changes from about -0.08 at 1 GHz to -0.18 at 1000 GHz, and in any case these expressions give errors up to 20% at the high frequency range. A more convenient approximation, based on a bi-dimensional Chebyshev fit is given by Hummer (1988) with a maximum relative error of 0.7%. Again, this new approximation is only valid above 10-40 GHz, given the likely temperature range.

Since Bremsstrahlung is a purely collisional process, and hence in LTE, , but stimulated emission must be taken into account for the final, thermally averaged absorption coefficient

The final intensity is then

At long wavelengths, the stimulated emission correction dominates, and the exponential in the previous equation becomes unity (as would be obtained by substituting the Rayleigh-Jeans approximation for the source function). Since under normal photoionisation conditions the dominant ions will be HII and HeII, sharing the same Z=1, the Gaunt factor comes out of the sum. The emission measure contributed by Helium is most uncertain. The upper limits on the emission of the HeI 5876 recombination line (Reynolds & Tufte, 1995) indicated that most of the He had to be neutral. However, new observations detect the line (Rand 1997, Greenawalt et al. 1997, Martin & Kennicutt 1997, Reynolds this volume) indicating not only that HeII is clearly present, but also that He could perhaps be fully ionised, although further measures are required. What is really needed to quantify the Bremsstrahlung emission is the measure of ionisation degree in the diffuse ISM along the different lines of sight, via the detection of several metal lines sensitive to temperature and density.

The Balmer emission is also proportional to the emission measure, since it is a fraction of the total number of recombinations. It also depends on whether the Lyman continuum is optically thin (case A) or not (case B). Fitting the emission coefficients for H given by Brocklehurst (1972) and Martin (1988), and the Balmer decrement H/H for the range in temperatures from 5,000 K to 20,000 K, we get

and

A useful expression is then the brightness temperature of the free-free emission associated with the emission of one Rayleigh in H assuming the same emission measure. Since , we have for Case B recombination

where is the frequency in units of 10 GHz, and is the abundance of Helium by number (see Figure 2). The usefulness of this technique is limited by at least two factors. First, the dust present along the line of sight will decrease the H surface brightness. Correlations between the IRAS 100 m and DIRBE 240 m maps could help to explain possible partial correlations between these maps and the diffuse H emission. Second, the temperature could be much higher, and so decrease the number of optical recombinations to undetectable levels, and at the same time increase the contribution from helium to the Bremsstrahlung emission. Despite these caveats, there have been a few attempts to measure the fluctuations in the H brightness in the North Celestial Pole (Simonetti, Dennison & Topasna 1996, Gaustad, McCullough & Van Buren 1996). The limitation of these narrow bandpass filter observations is that most of the signal comes in fact from the geocoronal emission, which needs to be substracted with high accuracy. Alternatively, one could use Fabry-Perot observations to separate this line from the diffuse H emission. A collaboration between the Strasbourg and Marseilles observatories used the CIGALE interferometer at La Silla observed some of the fields measured by the CMBR South Pole experiment (Schuster et al. 1991, Gundersen et al. 1994) were an excess temperature was reported. Figure 3 presents some of the scans, and shows that very little diffuse emission (less than 0.2 Rayleigh) is present between the geocoronal H line and the night sky OH line. These small residuals cannot explain the anomalous component seen in several experiments, provided the assumptions made above in relating H and Bremsstrahlung apply.

  
Figure 3: Sample Fabry-Perot scans for 25 South Pole fields observed by the Strasbourg-Marseille collaboration. Note the very small residual levels between the geocoronal H and sky OH 6568.77, 6568.78 Å lines.

Above 100 GHz, the emission is dominated by cold dust, and the IRAS 100 m and DIRBE 240 m maps are useful indicators of the expected contamination level. recent analysis of the COBE/DMR data shows a significant correlation between the CMBR fluctuations and the DIRBE maps in the North Polar spur area (Kogut et al., 1996), and the comparison of the Saskatoon maps with IRAS also present some correlation (De Oliveira-Costa et al. 1997, Leitch et al. 1997). This is all the more surprising because the frequencies selected, around 40 GHz, should be more sensitive to the Bremsstrahlung emission than to the dust foreground (see Fig. 1). A recent alternative has been suggested by Draine and Lazarian (1997) where spinning dust grains would produce a significant emission up to 10 GHz, but given the patchy nature of the WIM, it is unlikely that the correlation extends on all scales (see also Gutierrez de la Cruz et al. 1995, McCullough 1997, Kogut 1997, Kowitt et al. 1997).

© Copyright Astronomical Society of Australia 1997