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Publ. Astron. Soc. Aust., 1998, 15, 111­17
.

Cosmological Applications of H Surveys
David Valls­Gabaud1,2
UMR CNRS 7550, Observatoire de Strasbourg, 11 Rue de l'Universit´ 67000 Strasbourg, France e, Royal Greenwich Observatory, Madingley Road, Cambridge CB3 0EZ, UK dvg@astro.u-strasbg.fr Received 1997 November 15, accepted 1997 December 15
1

2

Abstract: We briefly review three main applications of H surveys in cosmology, namely: (1) the diffuse H emission as a tracer of the free­free foreground that contaminates the fluctuations in the cosmic microwave background radiation; (2) the H emission from galaxies as a measure of the formation rate of massive stars, both at low and high redshift; and (3) the diffuse H emission from ionised clouds as a constraint on the local ionising background radiation. Keywords: cosmology: CMBR fluctuations, ionising background radiation -- galaxies: star formation rate

1 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 an 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 free­free emission) have different spectral properties and spatial morphologies, and hence can be disentangled from the intrinsic, cosmological fluctuations. Figure 1 summarises 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 ma jor 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, N (E )dE E - dE , then the synchrotron spectrum of the ensemble is also a power law. The corresponding brightness temperature scales as Tb ( ) -(+3)/2 so that for a typical energy slope 2 · 5 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
Astronomical Society of Australia 1998

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 emission, 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). At the bottom of the `valley' of minimum foreground contamination, the free­free emission is the ma jor 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 free­free 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 free­free transition from Ei to Ej 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) d
ff

4 6 = 3 3hcm2 e

Z2 3

gff (ni ,nf ) v

dv , (1)

1323-3580/98/010111$05.00


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D. Valls­Gabaud

Figure 1--Comparison of the expected frequency dependence of foregrounds with the monopole, dipole, and quadrupole levels of the CMBR. The diffuse emission from dust dominates above 80 GHz, while synchrotron emission 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).

where ni,f = Z 2 Ry/Ei,f and h /Z 2 Ry = n-2 - n-2 . i f The total absorption cross section per ion and per electron is obtained by summing over all incident electron velocities, assuming a Maxwell­Boltzmann distribution, Ne (v )dv = 4Ne me 2kT
3 2

The thermal average is ( 2 ,u) =
0

g

ff

gff (ni (t),nf (t)) e-t dt ,

(4)

â v 2 exp so that ff = 4e6 3ch âT
-1/2

-me v 2kT
1 2

2

dv ,

(2)

2 3km Z 2g

3 e

ff

( 2 ,u)
3



.

(3)

where t = me v 2 /2kT , ni (t) = / t, nf (t) = /(u + 1 t) 2 , 2 = Z 2 Ry/k T and u = h /k T . 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 2â104 K, and a frequency range between 1 and 1000 GHz, that is 2 10 and u 0 · 01, the classical, small-angle, long-wavelength approximation is appropriate (see e.g. Novikov & Thorne 1973):


Cosmological Applications of H Surveys

113

g
ff

( ,u) = -
2

3 5 ln 4 2 u (5)

= 0 · 5513 ln T 1 · 5 /Z +9 · 75 ,

where = 1 · 781072... is Euler's constant. One can write this approximately as gff g0 T a b , and by noting that dgff /d = bgff / -0 · 5513/ , dgff /dT = agff /T = 0 · 82695/T , for Z = 1, g
ff

4·4

T 104 K

0 · 21

40 GHz

-0 · 14

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 temperature range from 5000 to 20,000 K, we get I (H)
CaseB

. (6)

=

9 · 41 â 10-8 T â EM cm-6 pc

-1 · 017 4

10-0 · s

029/T

4

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, was given by Hummer (1988) with a maximum relative error of 0 · 7%. Again, this new approximation is only valid above 10­40 GHz, given the likely temperature range. Since Bremsstrahlung emission is a purely collisional process, and hence in LTE, S = B , but stimulated emission must be taken into account for the final, thermally averaged absorption coefficient,


erg cm

-2 -1

sr

-1

(9) and I (H)
CaseA

=

6 · 36 â 10-8 T â EM cm-6 pc

-1 · 134 4

10

-0 · 038/T

4

erg cm

-2 -1

s

sr

-1

.

(10) A useful expression is then the brightness temperature of the free­free emission associated with the emission of one Rayleigh in H, assuming the same emission measure. Since Tb = 2 2 I /c2 , we have for Case B recombination Tb (µK) 0 14 · 0 T4 · IH (R)
317

=
ion

ff N

ion

N

e

1 - e-

h /kT

.

(7)

The final intensity is then 8e6 I = 3 3c â
ion

2 3km
2

1 2

3 e ff

1- 1e T2

h /kT

10

+0 · 029/T

4

Zg

(Z, , T ) Ne N

ion

.

(8)

At long wavelengths, the stimulated emission correction dominates, 1 - e-h /kT h /k T , 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) indicates that most of the He has to be neutral. However, new observations detect the line (Rand 1997; Greenawalt, Walterbos & Braun 1997; Martin & Kennicutt 1997 Reynolds et al. 1998, present issue p. 14) 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

â 1+0 · 08

HeII nHe He 0 · 08

Z2 g

ff (, 2 10

T)

,

(11) where 10 is the frequency in units of 10 GHz, and nHe 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 µm and DIRBE 240 µm 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


114

D. Valls­Gabaud

Figure 2--Predicted brightness temperature of the free­free 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 emission 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.

& 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 subtracted with high accuracy. Alternatively, one could use Fabry­Perot observations to separate this line from the diffuse H emission. A collaboration between the Strasbourg and Marseilles observatories, using 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) where 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. Above 100 GHz, the emission is dominated by cold dust, and the IRAS 100 µm and DIRBE 240 µm 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. 1996a,b), and the comparison

of the Saskatoon maps with IRAS also presents 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 Figure 1). A recent alternative has been suggested by Draine & 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). 2 Star Formation Rate of Massive Stars The proportionality between the emission measure and the intensity of the Balmer H emission provides an estimate of the total number of ionising photons emitted, and hence on the number of massive, hot stars that produced them. This has become the standard technique to infer not only the star formation rate but also the initial mass function (IMF) of massive stars. The total number of ionising photons in a stellar population of age t, with an IMF (m), and with a history of SFR given by (t), can be expressed as


Cosmological Applications of H Surveys

115

Figure 3--Sample Fabry­Perot scans for 25 South Pole fields observed by the Strasbourg­Marseille collaboration. Note the very small residual levels between the geocoronal H and sky OH 6568 · 77, 6568 · 78 ° lines. A

mup

(TAMS)

N

Ly-c

(t) =
meff

dm
0

(t - ) (m) âN
Ly-c

NLy-c 1056 s-1

= 3·1 â

M yr-

1 66

(m, )d , (12)

-0 1· 0 · 1 - 1 · 5mup · 66 +8 · 6mup m-0 · 35 - m-0 · 35 low up

. (13)

where NLy-c (m, ) is the number of ionising photons emitted by stars of mass m at time , and the effective lifetime extends from the ZAMS to the terminal age main sequence (TAMS). Note that the effective cutoff mass meff is given by the IMF-weighted Ly­c production rate, and is about 10 M . The reason for this is that the dependence of the number of emitted ionising photons with temperature (mass) is extremely steep: going from 20,000 K to 35,000 K increases the Ly­c flux density by 4 orders of magnitude. This sharp cutoff, weighted by the IMF, makes sure that no stars below about 10 M contribute to the final ionising flux. This implies that estimates of the ionising flux give a direct constraint on the IMF of stars above 10 M , but says nothing on the IMF below that mass. Using the recent models from Schaerer & De Koter (1997), which incorporate for the first time stellar interiors with realistic stellar atmospheres, we obtain for a Salpeter IMF

The existence of mlow in the equation above is only the consequence of the assumption of continuity (a la Salpeter) of the IMF below 10 solar ` masses. Under standard (case B) recombination conditions, the ratio /L(H) is approximately +2 2 · 2-1 · 5 â 10-8 M yr-1 L-1 , for a wide range of ·5 IMF slopes. However, estimating the flux of ionising photons from the H emission has several problems: (1) the ionisation conditions for the opacity in the Lyman continuum (clumpy ISM, escape fraction, diffuse emission); (2) dust corrections (at wavelengths below 912 ° dust tends to absorb rather than to A scatter); (3) contamination by the [NII] 6583 line (variable, and usually not resolved from H); (4) evolution of the stellar populations (which may produce an underlying absorption H line); and (5) contamination of the H line by nonthermal processes (presence of AGN-like activity).


116

D. Valls­Gabaud

Each of these caveats would deserve a section by itself, but we will comment here only on the first one, which has implications for the next section. Oey & Kennicutt (1997) compared H fluxes with predicted Ly­c fluxes and found that a significant fraction (up to 51%) could leak from HII regions, providing a bath of ionising photons in the WIM. The origin of these Ly­c photons could either be from the leakage in HII regions or from field massive stars. The first interpretation is favoured by Ferguson et al. (1996a, b), although Patel & Wilson (1995a, b) argue that the number of OB stars detected in the field is more than enough to ionise the WIM. In any case, the failure to take into account the diffuse H emission underestimates the true SFR by factors between about 3 and an order of magnitude. In the case of an ensemble of galaxies, there is, in addition, the problem of the completeness of the sample, and of the temporal evolution of the emission line due to the evolving stellar populations on cosmological timescales. Despite these caveats, useful constraints can be obtained on the luminosity density at H (assuming that the observations are sensitive enough to low fluxes that the luminosity density converges). For instance, Tresse & Maddox (1997) obtained a luminosity density of 3 · 16â1039 erg s-1 Mpc-3 at z 0 · 2 using the CFRS sample, which is substantially larger than the local value. For higher redshifts the sensitivity in the near IR is much lower, and the current limits (van der Werf, in preparation) are about 1 · 56â1039 erg s-1 Mpc-3 at z 2 · 25, much lower than the (lower) limits obtained from the HDF survey. 3 Local Ionising Background Radiation From the studies of the WIM in our Galaxy and in nearby galaxies, it appears likely that a substantial fraction of ionising photons could escape from galaxies. Although at first surprising, the high escape fraction may be due to the patchy, clumpy nature nature of the ISM, fractal (Elmegreen 1997) or otherwise. Disk photons reach the Reynolds layer. Within the inner 60 kpc or so, the detection of diffuse H in the Magellanic Stream (Weiner & Williams 1996) implies that a large fraction of galactic ionising photons reach that distance (BlandHawthorn & Maloney 1998), while in nearby dwarf galaxies the large number of expanding cavities which may be fully ionised certainly allows a large fraction of ionising photons to escape from these low-opacity regions (e.g. Puche et al. 1992; Puche & Westpfahl 1994). An obvious test is to take integrated spectra of these galaxies at wavelengths around 912 ° This has been attempted with HUT A. on a few nearby starburst galaxies, with apparently negative results (Leitherer et al. 1995). However, the inclusion of the Galactic absorption, important for the low-redshift galaxies studied, increased the

escaping fraction, and lower limits ranging from 3% to 57% are allowed (Hurwitz, Jelinsky & van Dyke Dixon 1997). If many ionising photons escape from galaxies, they will contribute significantly to the ionising background radiation, which is usually thought to be dominated by quasars. Yet locally quasars contribute much less than 10% to the luminosity density in the B and U bands. Could galaxies dominate the background, at least locally? Again the proportionality between the emission measure, the number of recombinations and the H emission give a useful constraint on the local ionising background, as first pointed out by Sunyaev (1969). Assuming that the H is optically thin, the ionising photon flux is


ion =
L

J d h (14)

4tot I (H) A , = (H) h Atot

where tot and (H) are the total recombination coefficient and the H emission rate respectively, and the aspect ratio of pro jected to total area, A /Atot , goes from 1/2 for a two-sided slab to 1/4 for a sphere. This expression actually assumes that the ionisation comes only from one side, the general expression for the ionisation from both sides not having been solved yet. The observations of isolated extragalactic clouds (e.g. Stocke et al. 1991; Vogel et al. 1995) provide limits of about 3â104 ionising photons s-1 cm-2 , which becomes a limit on the ionising background at the Lyman limit of JL < 8 â 10-23 erg s-1 cm-2 Hz-1 sr-1 , assuming a slope of 1 · 4 for the background, typical for quasars. These values also assume case B recombination. However, as shown elsewhere (Valls­Gabaud & Vernet 1998), galaxies are the main component of the ionising background, and their soft spectra are consistent with the pattern of ionisation traced by Si IV, Si III, C IV, C III observed at z > 3. The consequence of this model is that at low redshift the background is also very soft, with an effective slope of the order of 3 or more. This relaxes the constraint on the amplitude of the background, since J = JL L
-

= JL =

h

ion

.

(15)

Then the limit becomes JL < 5 · 6 â 10-22 erg s-1 cm-2 Hz-1 sr-1 for case A recombination, which is more appropriate. Deharveng et al. (1997) obtained strong upper limits on the escape fraction using the H luminosity density at z = 0, but assuming a background dominated by quasars. With a galaxy-dominated background, the present limits are consistent with an average escaping fraction larger


Cosmological Applications of H Surveys

117

than 30%. The model predicts that the local background must be very soft, and hence can be falsified because low ionisation stages must prevail over high ionisation species in isolated extragalactic clouds. Acknowledgments It is a pleasure to thank my collaborators on these topics, and particularly J. Bartlett, P. Amram, M. Marcelin and J. Vernet for letting me mention some of our recent results here. I thank R. Reynolds, S. Nossal and D. Schaerer for interesting discussions. I am grateful to the organisers for financial support and to Prof. B. McAdam and his family for their friendly hospitality.
Bland-Hawthorn, J., & Maloney, P. 1998, ApJ, in press Brocklehurst, M. 1972, MNRAS, 157, 211 De Oliveira-Costa, A., et al. 1997, ApJ, 482, L17 Deharveng, J. M., Fa¨ isse, S., Milliard, B., & LeBrun, V. 1997, A&A, 325, 1259 Draine, B. T., & Lazarian, A. 1997, ApJ, submitted Elmegreen, B. G. 1997, ApJ, 477, 196 Ferguson, A. M. N, Wyse, R. F. G., Gallagher, J. S., & Hunter, D. A. 1996a, AJ, 111, 2265 Ferguson, A. M. N, Wyse, R. F. G., & Gallagher, J. S. 1996b, AJ, 112, 2567 Gaustad, J. E., McCullough, P. R., & Van Buren, D. 1996, PASP, 108, 351 Greenawalt, B., Walterbos, R. A. M., & Braun, R. 1997, ApJ, 483, 666 Gundersen, J. O., et al. 1995, ApJ, 443, L57 Gutierrez de la Cruz, C. M., et al. 1995, ApJ, 442, 10 Haslam, C. G. T., Salter, C. J., Stoffel, H., & Wilson, W. E. 1982, A&AS, 47, 1 Hummer, D. G. 1988, ApJ, 327, 477 Hurwitz, M., Jelinsky, P., & van Dyke Dixon, W. 1997, ApJ, 481, L31

Kogut, A. 1997, AJ, 114, 1127 Kogut, A., et al. 1996a, ApJ, 460, 1 Kogut, A., et al. 1996b, ApJ, 464, L5 Kowitt, M. S., et al. 1996, ApJ, 482, 17 Leitch, E. M., Readhead, A. C. S., Pearson, T. J., & Myers, S. T. 1997, ApJ, 486, L23 Leitherer, C., et al. 1995, ApJ, 454, L19 Lineweaver, C. H., Barbosa, D., Blanchard, A., & Bartlett, J. G. 1997, A&A, 322, 365 Martin, C. L., & Kennicutt, R. C. 1997, ApJ, 483, 698 Martin, P. G. 1988, ApJS, 66, 125 McCullough, P. R. 1997, AJ, 113, 2186 Novikov, I. D., & Thorne, K. S. 1973, in Black Holes, ed. C. DeWitt & B. S. DeWitt (New York: Gordon & Breach), p. 343 Oey, M. S., & Kennicutt, R. C. 1997, MNRAS, 291, 827 Oster, L. 1961, Rev. Mod. Phys., 33, 525 Patel, K., & Wilson, C. D. 1995a, ApJ, 451, 607 Patel, K., & Wilson, C. D. 1995b, ApJ, 453, 162 Platania, P., et al. 1997, ApJ, submitted (astro-ph 9707252) Puche, D., et al. 1992, AJ, 103, 1841 Puche, D., & Westpfahl, D. 1994, in ESO/OHP Workshop on Dwarf Galaxies, ed. G. Meylan & P. Prugniel (Garching: ESO), p. 273 Rand, R. J. 1997, ApJ, 474, 129 Reich, P., & Reich, W. 1988, A&AS, 74, 7 Reynolds, R. J., & Tufte, S. L. 1993, ApJ, 439, L17 Reynolds, R. J., Tufte, S. L., Haffner, L. M., Jaehnig, K., & Percival, J. W. 1998, PASA, 15, 14 Schaerer, D., & De Koter, A. 1997, A&A, 322, 598 Schuster, J., et al. 1993, ApJ, 412, L47 Simonetti, J. H., Dennison, B., & Topasna, G. A. 1996, ApJ, 458, L1 Stocke, J. T., et al. 1991, ApJ, 374, 72 Sunyaev, R. 1969, ApJ Lett., 3, 33 Tresse, L., & Maddox, S. J. 1997, ApJ, in press Vogel, S. N., et al. 1995, ApJ, 441, 162 Valls-Gabaud, D., & Vernet, J. 1998, MNRAS, submitted Weiner, B. J., & Williams, T. B. 1996, AJ, 111, 1156 Yusef-Zadeh, F. 1989, in The Center of the Galaxy, ed. M. Morris (Dordrecht: Kluwer), p. 243