Abstract

A full-sky template map of the Galactic free–free foreground emission component is increasingly important for high-sensitivity cosmic microwave background (CMB) experiments. We use the recently published Hα data of both the northern and southern skies as the basis for such a template.

The first step is to correct the Hα maps for dust absorption using the 100-μm dust maps of Schlegel, Finkbeiner & Davis. We show that for a range of longitudes, the Galactic latitude distribution of absorption suggests that it is 33 per cent of the full extragalactic absorption. A reliable absorption-corrected Hα map can be produced for ∼95 per cent of the sky; the area for which a template cannot be recovered is the Galactic plane area |b| < 5°, l= 260°–0°–160° and some isolated dense dust clouds at intermediate latitudes.

The second step is to convert the dust-corrected Hα data into a predicted radio surface brightness. The free–free emission formula is revised to give an accurate expression (1 per cent) for the radio emission covering the frequency range 100 MHz–100 GHz and the electron temperature range 3000–20 000 K. The main uncertainty when applying this expression is the variation of electron temperature across the sky. The emission formula is verified in several extended H ii regions using data in the range 408–2326 MHz.

A full-sky free–free template map is presented at 30 GHz; the scaling to other frequencies is given. The Haslam et al. all-sky 408-MHz map of the sky can be corrected for this free–free component, which amounts to a ≈6 per cent correction at intermediate and high latitudes, to provide a pure synchrotron all-sky template. The implications for CMB experiments are discussed.

Introduction

Current cosmic microwave background (CMB) experiments are sensitive enough to measure the primordial fluctuations that have an amplitude in the range of ≈20–100 μK over the ℓ-range 10–2000, which corresponds to angular scales of ≈10°–10 arcmin (Hanany et al. 2000; Mauskopf et al. 2000; Padin et al. 2001; Halverson et al. 2002; Scott et al. 2003). The angular power spectrum of these fluctuations contains a wealth of cosmological information. One of the crucial factors in determining an accurate power spectrum of these fluctuations is understanding and removing the foreground contamination. The amplitude of the foreground signal depends on the frequency, the angular scale and the region of sky being observed. CMB foregrounds comprise point sources and diffuse Galactic foregrounds. Point sources are a particular problem at smaller angular scales (≲30 arcmin), while diffuse foreground structures become dominant on larger angular scales. Here we concentrate on the problem of diffuse Galactic foregrounds at frequencies below <100 GHz, a frequency range that is used in current and upcoming CMB experiments such as the MAP and Planck satellites.

Galactic foregrounds

The diffuse Galactic foreground has three (possibly four) components. (i) Synchrotron emission from relativistic electrons spiralling in the Galactic magnetic field dominates at frequencies below 1 GHz with a spectral index (T∝ν−β) of β≈ 2.7–3.2 (Davies, Watson & Gutiérrez 1996). It is traced by low-frequency surveys such as those of Haslam et al. (1982), Reich & Reich (1988) and Jonas, Baart & Nicolson (1998), where it is seen to extend well above the plane, e.g. the North Polar Spur which extends to Galactic latitude b≈ 80°. (ii) Free–free bremsstrahlung emission from thermal electrons has a flatter spectral index of β≈ 2.1. It is the dominant foreground at frequencies between ν= 10 and 100 GHz, where microwave CMB experiments operate (e.g. DASI, CBI, VSA, MAP, Planck). The optical Hα line is a good tracer of free–free emission, although it requires corrections for dust absorption. (iii) The vibrational emission from thermal dust is dominant at frequencies above ∼100 GHz. This is thermal emission from warm dust and is well traced at λ∼ 100 μm where it has its peak. (iv) An anomalous component has recently been discovered (Kogut et al. 1996; Leitch et al. 1997; de Oliveira-Costa et al. 1997, 1998, 1999, 2000, 2002; Finkbeiner et al. 2002). Draine & Lazarian (1998) proposed that this could be owing to spinning dust grains emitting in a 1–2 octave band centred at ∼20 GHz. It was first believed to be caused by free–free emission (Kogut et al. 1996), but this has been ruled out primarily by the lack of associated Hα emission.

The separation and quantifying of the individual CMB foreground components is a continuing challenge. Each component is of interest in its own right; its angular distribution and spectrum are basic parameters. They all contribute as foregrounds to the CMB and their removal is necessary to realize the full potential of current high-sensitivity CMB surveys where Cl values are to be measured to an accuracy of a few per cent. Such separations are best made using templates for each component. With the advent of the Hα survey, such a template is now available for each of the four proposed components. Although some approaches to separation of components are being made that reduce the assumptions concerning the template parameters (e.g. Baccigalupi et al. 2000; Vielva et al. 2001) they still face difficulties where the components are correlated. For example all the foregrounds are quasi-correlated as they increase strongly towards the Galactic plane. Also, the Hα and (spinning) dust emissions show considerable correlation over most of the sky (see Section 7); this was at the root of the original misunderstanding of the anomalous component. If one has a good free–free template as we derive here, the other three foreground components can be well characterized except possibly at the lowest Galactic latitudes.

Large area H; surveys

Extensive filamentary Hα emission regions, of galactic origin, were first found by Meaburn (1965, 1967) extending to high Galactic latitudes; Sivan (1974) demonstrated the wealth of Hα emission at low to intermediate latitudes but at a relatively low sensitivity of ≈15R; we note that 1 Rayleigh (R) ≡ 106/4π photon s−1 cm−2 sr−1≡ 2.41 × 107 erg s−1 cm−2 sr−1≡ 2.25 cm−6 pc for Te= 8000 K gas. Several large and very sensitive Hα surveys are now well under way. The most relevant surveys are listed in Table 1. In the northern sky covering declinations δ≥−30° the Wisconsin H Alpha Mapper project (WHAM) is the most sensitive Hα survey to-date, but is restricted to an angular resolution of ≈1° (Reynolds et al. 1998; Haffner 1999). The final sensitivity in each field is ≈0.05R and the data are calibrated to an accuracy conservatively estimated at 10 per cent. WHAM is a dual-etalon Fabry–Perot spectrometer with a velocity resolution of 12 km s−1. The spectra can be used to remove the geocoronal Hα emission from the Earth's upper atmosphere, which varies in strength from 2 to 13R; it is much brighter than the Galactic signals at high Galactic latitudes.

Table 1.

Current H± surveys relevant to CMB observations.

Table 1.

Current H± surveys relevant to CMB observations.

The ongoing Virginia Tech Spectral-line Survey (VTSS) is a complimentary narrow-band imaging survey of the northern sky covering δ≥−15° (Dennison, Simonetti & Topsana 1998). It has a resolution of 1.6 arcmin in each 10° diameter field, which will be good enough for almost all CMB experiments as most of the cosmological information is contained on scales between 10° and 10 arcmin. However, on larger angular scales, it will most likely be limited by the geocoronal emission that appears as a time-varying background signal of unknown level. Star residuals that have not been subtracted correctly can also be a problem. In combination with the WHAM survey, this survey will be a powerful tool.

The recently published (Gaustad et al. 2001) Southern H Alpha Sky Survey Atlas (SHASSA) covers the southern sky δ≤+15° at an angular resolution of 0.8 arcmin in each 13° field. The sensitivity reaches 2R limited by geocoronal emission and star residuals that have been partially removed by median filtering. Smoothing this survey to a resolution of 4 arcmin allows features of about 0.5R to be detected. The intensity calibration is accurate to about 9 per cent.

Two other Hα surveys are in progress. The Manchester Wide-Field Camera (MWFC) can observe Hα with a 32° field of view with 7-arcmin resolution (e.g. Boumis et al. 2001) and a sensitivity of ≈1R. This instrument is particularly sensitive to large-scale features (≳1°), which may be missed by cameras with smaller fields. We have recently observed several selected fields to look for diffuse Hα emission, both in the northern and southern hemispheres. The AAO/UK Schmidt Hα survey has high angular resolution (1 arcsec) but is restricted to the Galactic plane at relatively low sensitivity (Parker & Phillipps 1998) as given in Table 1.

This paper

In this paper we describe the steps taken to derive a free–free emission template from recently published Hα surveys. In Section 2 we determine the absorption of the Galactic Hα emission by dust based on the 100-μm dust template given by Schlegel, Finkbeiner & Davis (1998), hereafter SFD98; a statistical estimate is made of the relative distribution of the Hα emission and the dust in the line of sight. Section 3 summarizes the expressions required to convert the dust-corrected Hα emission into microwave emission at frequencies relevant to current CMB experiments. The uncertainties in the relation are evaluated. This relationship is tested in Section 4 using available radio surveys. The final free–free template is presented in Section 5. The 408-MHz all-sky map of Haslam et al. (1982) corrected for free–free emission is derived in Section 6; it is the best available synchrotron template. We discuss the implications of the new template for upcoming CMB experiments and for interstellar medium (ISM) studies in Section 7. The final conclusions of this work are given in Section 8.

Correction of Hα for Dust Absorption

The Galactic distribution of absorption

It is clear that the use of Hα surveys as a template for free–free emission will be jeopardized in the Galactic plane where visual absorption is typically 1 mag kpc−1 in the local arms and where the total absorption to the Galactic Centre is ≈20 mag. At intermediate latitudes the absorption broadly follows a cosecant law with a vertical slab half-thickness of 0.1–0.2 blue magnitudes. Such a cosecant law was widely used in extragalactic astronomy. In order to take account of the known structure in the obscuration, the line integral of H i combined with a factor derived from the Shane–Wirtanen galaxy counts was introduced by Burstein & Heiles (1978). This procedure took account of the possibility that the gas-to-dust ratio might not be constant and the fact that not all hydrogen is in the neutral atomic form. The Burstein–Heiles approach is limited by the angular resolution of H i all-sky surveys, which is currently ∼30 arcmin.

A new approach that provides a resolution of 6.1 arcmin and has a complete all-sky coverage is offered by SFD98 who use far infrared data from the COBE-DIRBE and IRAS satellites. This combination of data at a range of FIR wavelengths enabled a good zero level to be established, an adequate removal of zodiacal light and a more effective destriping than previously. Also, by comparing the DIRBE 240-μm and IRAS 100-μm results to derive a dust temperature, an estimate could be made of the dust column density, DT, measured in units of MJy sr−1, in terms of a 100-μm surface brightness at a fixed temperature of 18.2 K. This correction to a fixed temperature can only be made on the angular scale of the DIRBE observations, namely graphic, and consequently is not strictly true on the 6.1-arcmin scale of the DT dust maps. The dust temperatures are typically in the range 17–21 K, which corresponds to a correction of up to a factor of ∼5 in the dust column density (see SFD98).

Derivation of a Hα absorption template

We will adopt the DT dust template as the indicator of dust absorption. This then requires a conversion factor to estimate the absorption at 656.3 nm, the Hα wavelength. SFD98 use the (BV) colours of some 470 galaxies at a wide range of Galactic coordinates to derive a best-fitting correlation with the DT value at the position of each galaxy. They find the E(BV) colour can be estimated from DT with the expression E(BV) = (0.0184 ± 0.0014) DT mag and claim that the reddening estimated in this way has a standard deviation of 16 per cent at any given position.

In order to estimate the absorption at the Hα wavelength we use the parametric extinction curve for optical wavelengths given by O'Donnell (1994) and find the Galactic absorption at Hα to be A(Hα) = 0.81A(V). Assuming the dust is characterized by a reddening value RV=A(V)/E(BV) = 3.1, this leads to an absorption at Hα of  

(1)
formula
where DT is in units MJy sr−1. The values given in table 6 of SFD98 are 6 per cent higher than this, corresponding to a higher value of RV.

A range of reddening laws, characterized by different values of RV, are found in different directions in the Galaxy. The different laws are thought to derive from different grain chemistry and size distributions. Values of RV range from 2.5 to 5, with the higher values often in denser dust clouds. A value of 3.1 is widely adopted as representative of the diffuse ISM in directions away from dense dust clouds. However, it should be emphasized that this is only an average value and that any line of sight will have a scatter about this value. Putting all of these statistical factors together we consider that the relationship between A(Hα) and DT is accurate to about 20 per cent.

The absorption of Galactic Hα

The expression given in the preceding section applies to absorption of extragalactic objects at optical wavelengths. Here we are considering Galactic Hα emission, which is mixed with the dust. At first sight it might be argued that since the dust and gas are uniformly mixed, then the ionized gas and the dust would also be uniformly mixed. The correlation between gas and dust will be discussed further in Section 7. The major part of the Hα seen from our position in the Galaxy is the result of ionization by the UV radiation field from young stars embedded in the dust plus the contribution from nearby regions of localized recent star formation. Such regions include the Gould Belt system, which reaches to Galactic latitudes of 40° or more.

We seek a first-order absorption formula for correction of the Hα emission based on the dust distribution given by SFD98. If the ionized gas were uniformly mixed with the dust then the average absorption would be half the extragalactic value given in Section 2.2 on the assumption that the dust absorption is optically thin (say ≤0.5 mag). We define fd, the effective dust fraction in the line of sight actually absorbing the Hα so that the actual absorption of Hα is given by fd×A(Hα), where A(Hα) is the full extragalactic absorption. For example, uniform mixing of ionized gas and dust corresponds to fd= 0.5. There would be a systematic modification of this value if the z-distribution of the dust and the ionized gas were not the same. An example would be the ionization produced by the interstellar radiation field propagating away from the plane and ionizing the ‘under’-side of the gas clouds that were themselves optically thick to the UV ionizing radiation. This would lead to a narrower z-distribution of Hα emission than dust, which is assumed to be well mixed with the gas, and to a reduced value of fd.

We are now in the position to test the uniform mixing hypothesis by comparing at low and intermediate latitudes the z-distribution of neutral gas (H i), ionized gas (Hα) and dust.

Galactic latitude scans

By plotting the Hα dependence on Galactic latitude b, and comparing this with the unabsorbed gas indicators of H i and FIR dust (DT), we can estimate the Hα absorption as a function of b and determine a best-fitting value of fd, the effective dust fraction producing absorption.

For neutral H i gas we use the 1420-MHz Leiden–Dwingeloo northern sky survey (Hartmann & Burton 1997), Hα data from the WHAM survey and the SFD98 100-μm DT map to trace the dust. Each map was resampled on to a Galactic coordinate grid and smoothed to a resolution of 1°. Along each 1°-wide latitude strip, the values are averaged over a range of longitudes to give a representative value for that latitude. Fig. 1 shows the latitude dependence of the gas and dust in the region l= 30°–60°. Both the H i gas and 100-μm dust follow similar cosecant-law trends. Assuming a homogeneous slab of material viewed at different latitudes b, the column density along a line of sight is expected to follow a cosecant law when viewed from the central plane:  

(2)
formula
where A0 is an offset and A1 is the amplitude of the cosecant law. This is indeed found to be the case, with deviations occurring owing to large concentrations of emitting material such as extended H ii regions and features such as the Local System (Gould Belt). The region l= 30°–60° is one of the ‘cleaner’ regions of the plane where no large structures exist. This region includes our own spiral arm and the Sagittarius arm; here the dust emission on the Galactic ridge reaches an average of 500 MJy sr−1 corresponding to A(Hα) = 23 mag for an extragalactic object. At intermediate and high latitudes (|b| > 15°), DT is ≲8 MJy sr−1 and the Hα absorption is therefore small.

Figure 1.

Galactic latitude scans for the longitude range l= 30°–60°. (a) H i from Leiden–Dwingeloo survey data. (b) Dust emissivity at 100 μ m from the SFD98 DT template. (c) Hα data from the WHAM survey. In (c) the Hα data corrected for dust absorption (fd= 0.33) are shown as filled circles while the uncorrected data are open circles. The best-fitting cosecant law is shown for each distribution (see the text). Note the logarithmic scale on the vertical axes.

Figure 1.

Galactic latitude scans for the longitude range l= 30°–60°. (a) H i from Leiden–Dwingeloo survey data. (b) Dust emissivity at 100 μ m from the SFD98 DT template. (c) Hα data from the WHAM survey. In (c) the Hα data corrected for dust absorption (fd= 0.33) are shown as filled circles while the uncorrected data are open circles. The best-fitting cosecant law is shown for each distribution (see the text). Note the logarithmic scale on the vertical axes.

The best-fitting cosecant law is a good match to the H i and dust distributions as shown in Fig. 1. This figure also shows that the Hα intensity is greatly attenuated at low latitudes (|b| < 15°) owing to the increased dust absorption nearer to the plane. Note also that there is a significant offset A0; this corresponds to the Sun being in a local ‘hole’. The A0/A1 values suggest that there is a ∼30–50 per cent deficit in the local slab density. If one adopts equation (1) as the model for Hα absorption we can correct the Hα emission, adopting a value of fd as discussed in Section 2.3. We can then determine a value for fd by correcting the Hα latitude distribution for absorption, so that it matches that of the gas and dust distributions shown in Fig. 1. By varying fd we find the best-fitting value is given by fd= 0.33+0.10−0.15. The fit was made by deriving the cosecant law using data at |b| > 20° and fitting fd to this cosecant law over |b|= 5°–15°. For |b| < 5°, the absorption is likely to be >1 mag and therefore any derived value for fd becomes unreliable. The value fd= 0.33 derived here is representative of the solar neighbourhood of our Galaxy within a few kiloparsecs. Other longitudes gave similar results, although the cosecant fitting is difficult owing to local structures such as the Gould Belt system and other bright extended H ii regions. Further information on the value of fd is obtained from the study of the radio free–free emission from several nearby H ii complexes given in Section 4.

The value of fd derived in this section is not consistent with uniform mixing of ionized gas and dust, which requires fd= 0.5. However, there is a large uncertainty in fd and it is expected that fd will vary significantly across the sky. However, as a first-order approach, we will adopt the value fd= 0.33 when estimating the free–free template in Section 5. This lower value is indicative of non-uniform ionization; for example, a region of cloud is ionized by the interstellar radiation field, which is in a narrower Galactic layer of O and B stars.

The Hα absorption template

Using equation (1) we can convert the DT dust map to an absorption map, which can be applied to the Hα intensity I, using  

(3)
formula
The value of fd is taken to be 0.33. The absorption template to be applied to Galactic Hα and smoothed to a resolution of 1° is shown in Fig. 2.

Figure 2.

The absorption template to be applied to the Galactic Hα emission. This assumes an absorbing dust-fraction of fd= 0.33, as derived in Section 2.4, and the total extragalactic value A(Hα) given in equation (1). Linear grey-scale and contours show absorption in magnitudes. Contours are given at 0.05 (dot-dashed), 0.1, 0.2, 0.3, 0.4, 0.5 and 0.7 mag. Absorption above 1 mag is black on the grey-scale.

Figure 2.

The absorption template to be applied to the Galactic Hα emission. This assumes an absorbing dust-fraction of fd= 0.33, as derived in Section 2.4, and the total extragalactic value A(Hα) given in equation (1). Linear grey-scale and contours show absorption in magnitudes. Contours are given at 0.05 (dot-dashed), 0.1, 0.2, 0.3, 0.4, 0.5 and 0.7 mag. Absorption above 1 mag is black on the grey-scale.

The template clearly shows that the absorption of Hα by dust is modest – less than 0.2 mag (20 per cent correction) for most of the sky. Beyond |b|≳ 50°, it is less than 0.05 mag (5 per cent correction). At |b|≲ 5°, the absorption increases beyond 1 mag for much of the Galactic plane. Individual dust clouds can have>1 mag of absorption at intermediate latitudes. For a major portion of the sky the dust correction clearly needs to be taken into account. For example, a correction of more than 50 per cent is required in a limited area of the sky such as the Gould Belt system.

It is interesting to note that the absorption can be low (<0.5 mag) close to the Galactic plane in the longitude range 160° < l < 260°. These regions may be useful in testing the dust absorption and Hα templates at low latitudes. However, for the remainder of the Galactic plane (|b| < 5°) the absorption is too great to make any reasonable estimate of Hα emission.

The uncertainty in deriving the Hα absorption from the dust using equation (1) is considered to be 20 per cent (see Section 2.2). A second factor in the uncertainty is the relative distribution of gas (Hα) and dust in the line of sight (fd). Near the Galactic plane where there are many clouds/features in the line of sight, our value of fd= 0.33 is realistic, while at higher latitudes where there are only a few clouds in the line of sight, the uncertainty (in a smaller total absorption) is greater. If we adopt a 20 per cent uncertainty in fd and combine it with a 20 per cent error in equation (1), we obtain a total uncertainty of 30 per cent in the correction to the Hα intensity for dust absorption. Thus if there is an Hα absorption [fd×A(Hα)] of 1.0 mag, the 30 per cent uncertainty in the multiplying factor required to give the estimate of the true Hα intensity is 2.5±0.7. However, for a total absorption of 0.2 mag the multiplying factor is 1.20 ± 0.07. This illustrates the higher fractional accuracy of estimating the Hα intensity at lower levels of absorption. In summary, the absorption of Hα can be estimated up to a limit of ∼1 mag; this corresponds to DT= 65 MJy sr−1 for fd= 0.33 and is shown in black in Fig. 2.

Conversion of Hα to Free-Free Continuum Emission

The ionized interstellar medium generates both radio free–free continuum and Hα emission. Ionized hydrogen alone is responsible for the Hα emission while ionized hydrogen and helium produce the radio continuum. Both the optical and radio emission are functions of electron temperature, Te. A relationship between the two can be determined under certain assumptions. We will derive this relationship and give an estimate of the uncertainties that come from the theory and from the variation in the electron temperature at different locations within the Galaxy.

Hα emission

The Balmer line emission from ionized interstellar gas is well understood; a clear discussion is given by Osterbrock (1989). However, the Hα line intensity depends upon whether the emitting medium is optically thick (case B) or optically thin (case A) to the ionizing Lyman continuum. In the H ii regions and nebulae studied using Hα it is believed that case B applies (Osterbrock 1989). Knowing the emission coefficients for both cases A and B for Hβ and using the Balmer decrements (Hummer & Storey 1987), the Hα emission can be readily calculated for the temperature range 5000–20 000 K both for cases A and B. Fig. 3 shows the Hα intensity per unit emission measure graphic for Te= 5000, 10 000, 20 000 K for both cases A and B.

Figure 3.

Hα emission per unit emission measure as a function of Te for case A (optically thin to Lyman photons) and case B (optically thick to Lyman photons) for ne= 102 cm−3. The circles represent the values calculated by theory given by Hummer & Storey (1987). The curves are the expressions given by Valls-Gabaud (1998); case B is given in equation (4).

Figure 3.

Hα emission per unit emission measure as a function of Te for case A (optically thin to Lyman photons) and case B (optically thick to Lyman photons) for ne= 102 cm−3. The circles represent the values calculated by theory given by Hummer & Storey (1987). The curves are the expressions given by Valls-Gabaud (1998); case B is given in equation (4).

The emission coefficients are generally accepted to be accurate to ≈1 per cent (Pengelly 1964; Hummer & Storey 1987). For case B, the intensity varies very weakly with number density, amounting to a few per cent over two orders of magnitude in density. The values shown in Fig. 3 are for a density (ne= 102 cm−3) gas. Case A gives ≈30 per cent lower intensity than case B over the likely temperature range.

The situation for intermediate and high latitudes appears to favour case B with the following arguments. For case B to apply, the optical depth τ, to Lyman continuum photons (λ≲ 900 Å) must be greater than unity in the emitting region. Pottasch (1983) gives the mean free path of Lyman continuum photons as ≈0.052 n−1H pc, corresponding to an optical depth relation τ= 19.2 nHl, where l is the path-length in parsecs. For a typical H ii region in the Galactic plane nenH= 102–106 cm−3 on typical scales of 1–10 pc and case B conditions are clearly satisfied with τ≈ 103–1010. At intermediate latitudes faint Hα features with EM ∼ 1 cm−6 pc can be identified with scale sizes of ∼10–100 pc. The corresponding ne is 0.1–0.3 cm−3. The optical depth to Lyman continuum in these low-density regions is then 1–30, still satisfying the case B conditions.

A useful and accurate expression for the Hα intensity based on data from Hummer & Storey (1987) is given by Valls-Gabaud (1998) for case B in units of erg cm−2 s−1 sr−1:  

(4)
formula
where T4 is the electron temperature in units of 104 K. This is plotted as a continuous curve along with the equivalent curve for case A in Fig. 3, which shows that the agreement of equation (4) with theory is better than 1 per cent over the temperature range 5000–20 000 K.

Radio continuum emission

The free–free radio continuum emission for an ionized gas at Te < 550 000 K and in local thermal equilibrium (LTE) is well described in terms of a volume emissivity in units of erg cm−3 s−1 Hz−1 (Oster 1961):  

(5)
formula
where graphic is the velocity-averaged Gaunt factor. The Gaunt factor comprises all the terms by which the quantum mechanical expressions differ from the classical ones. The evaluation of the Gaunt factor has been refined over recent years since the work of Scheuer (1960) and Oster (1961) for a range of frequencies and temperatures. Karzas & Latter (1961) have given definitive expressions for graphic. Hummer (1988) has used these expressions to obtain an accurate analytical expansion for graphic in terms of a two-dimensional Chebyshev fit covering a wide range of frequencies and temperatures. Table 2 lists accurate Gaunt factors (accurate to 0.7 per cent) derived from Hummer (1988) for a range of frequencies and temperatures relevant to CMB studies.

Table 2.

Gaunt factors for relevant frequencies and electron temperatures calculated from Hummer (1988) and accurate to 0.7 per cent.

Table 2.

Gaunt factors for relevant frequencies and electron temperatures calculated from Hummer (1988) and accurate to 0.7 per cent.

We now summarize the present situation for the frequencies (0.4–100 GHz) covered by the observations analysed here and the observing range of the low-frequency instrument (LFI) on the Planck Surveyor satellite. The free–free spectral index βff is a slow function of frequency and electron temperature (Bennett et al. 1992) as shown in Fig. 4. Over a wide range in frequencies this can lead to a significant discrepancy in the predicted radio emission if this is not accounted for. One should therefore still use the accurate formalism given by Oster (1961) who derives the optical depth for free–free emission as  

(6)
formula
The approximation given by Altenhoff et al. (1960) is often used:  
(7)
formula
For low frequencies (≲1 GHz) the error in this expression is of the order a few per cent but increases to 5–20 per cent for frequencies above 10 GHz. Mezger & Henderson (1967) define a factor a(T, ν), the ratio between the two formulae, as  
(8)
formula

Figure 4.

The local free–free spectral index as a function of frequency and electron temperature; given by equation (3) of Bennett et al. (1992). The curves from top to bottom are for temperatures Te= (2, 4, 6, 8 (heavy), 10, 12, 14, 16, 18, 20) × 103 K.

Figure 4.

The local free–free spectral index as a function of frequency and electron temperature; given by equation (3) of Bennett et al. (1992). The curves from top to bottom are for temperatures Te= (2, 4, 6, 8 (heavy), 10, 12, 14, 16, 18, 20) × 103 K.

Table 3 gives accurate values of a based on equation (8) for a range of temperatures and frequencies. The a factor is convenient in that it allows a simple formula to be written down using a single spectral index and temperature dependence that are modified by the Gaunt factor.

Table 3.

The factor a = τc (Oster)/τc (AMWW) for relevant frequencies and temperatures using equation (8)

Table 3.

The factor a = τc (Oster)/τc (AMWW) for relevant frequencies and temperatures using equation (8)

The brightness temperature Tb is given by  

(9)
formula
For the frequencies relevant to CMB observations and the diffuse interstellar medium discussed here, the optically thin assumption is valid. At 1 GHz only the brightest H ii regions in the Galaxy are optically thick (EM ≥ 106 cm−6 pc) while the Galactic ridge has τ∼ 10−3 (EM ≥ 103 cm−6 pc ≈ 500R) estimated for Te= 7000 K.

Finally, the brightness temperature in kelvin can now be written as  

(10)
formula
where the factor (1 + 0.08) is the contribution from the fraction of He atoms, all of which are assumed to be singly ionized; a is given by equation (8).

Electron temperatures in Galactic H ii regions

Optical determinations of electron temperatures in H ii regions using forbidden line ratios give values in the range 5000–20 000 K with a mean value of ≈8000 K (Reynolds 1985). These determinations refer to the solar neighbourhood within 1 or 2 kpc of the Sun.

Electron temperature determinations using extensive radio recombination line (RRL) data probe the greater part of the Galaxy and show a clear temperature gradient as a function of galactocentric radius. The results of Shaver et al. (1983) for 67 H ii regions show a clear gradient in temperature increasing with galactocentric radius from 5000 K at 4 kpc to 9000 K at 12 kpc. This is owing to the decreasing metallicity at larger radii (Panagia 1979). There is a spread of approximately 1000 K at a particular radius. The local value at R0= 8.5 kpc is Te= 7000 K and will be adopted as the typical value in the absence of other information.

Expected radio emission from H± maps

The relationship between radio emission and Hα emission can now be calculated using equations (4) and (10), in units of mK/R as  

(11)
formula
where T4 is the electron temperature in units of 104 K. The conversion factors for relevant frequencies are given in Table 4 for Te= 7000 K. Fig. 5 shows (Tffb/I2GHz over the frequency range 100 MHz–100 GHz for Te= 4000, 7000, 10 000 and 15 000 K. The increase in (negative) slope with frequency is owing to the effect of a arising from the Gaunt factor dependence. The variation in Tffb at a given frequency corresponds to a factor of ∼2.4 between 4000 and 15 000 K.

Table 4.

Free-free brightness temperatures per unit Rayleigh for a range of frequencies assuming Te = 7000 K.

Table 4.

Free-free brightness temperatures per unit Rayleigh for a range of frequencies assuming Te = 7000 K.

Figure 5.

Ratio of radio brightness temperature to Hα intensity multiplied by ν2GHz as a function of frequency. Curves are for T= 4000, 7000 (heavy), 10 000 and 15 000 K, which is the likely temperature range corresponding to a factor ∼2.4 in the ratio. The curvature in each curve reflects the frequency dependence of the Gaunt factor.

Figure 5.

Ratio of radio brightness temperature to Hα intensity multiplied by ν2GHz as a function of frequency. Curves are for T= 4000, 7000 (heavy), 10 000 and 15 000 K, which is the likely temperature range corresponding to a factor ∼2.4 in the ratio. The curvature in each curve reflects the frequency dependence of the Gaunt factor.

It is of interest to compare our equation (11) with recent expressions given in the literature. Reynolds & Haffner (2002) give Tffb/I= 7.4ν−2.1430μK/R at Te= 8000 K. Our value at 30 GHz and 8000 K would be 17 per cent lower at 6.35 μK/R. This difference may be attributed to the 17 per cent overestimate of the Gaunt factor in equation (6) of Valls-Gabaud (1998), which are used by Reynolds & Haffner (2002). We have resolved this difference with help from David Valls-Gabaud (private communication). The coefficient in his equation (6) should be 3.96 and not 4.4; furthermore, a typographical error in his equation (11) gave the exponent of T4 as 0.317 instead of 0.517. He agrees with the calculations of the Gaunt factors in Section 3.2. His new calculations also agree well with our equation (11). equation (4), also from Valls-Gabaud (1998), is not affected.

The uncertainty in predicting the radio free–free emission from the Hα emission as given in equation (11) arises mainly from the uncertainty in the electron temperature. The ±1000 K uncertainty in the adopted solar neighbourhood value of 7000 K is an upper limit to the scatter of H ii region temperatures since it includes some measurement errors. The corresponding error in equation (11) is 10 per cent. The other possible uncertainty is in whether case A or case B applies in the lower-density regions at intermediate and high Galactic latitudes of interest to CMB studies. For the reasons given in Section 3.1, we will adopt the generally assumed position that case B is correct and take the associated error in equation (4) to be 1 per cent. However, in the unlikely event that case A were to apply, the value of Tb/I given in equation (11) would be increased by 30 per cent. Uncertainties in equation (4) and in the ionized helium-to-hydrogen ratio in equation (10) are only a few per cent. We consider that the overall uncertainty in applying equation (11) to be ∼10 per cent for a large sample of the sky, assuming case B applies.

Observational Tests of the Hα to Free–Free Relation

We now make an observational test of equation (11), which predicts the free–free radio emission for a given Hα intensity. In practice, the diffuse free–free emission is mixed with synchrotron emission so the free–free component must be identified and separated. The free–free emission can be identified in two ways. First, by its associated radio recombination line emission and secondly, by its free–free spectrum using multifrequency observations. Furthermore, a comparison between the radio and Hα will lead to an estimate of the Hα absorption by dust; this can be compared with A(Hα) given by equation (1) to give a value of the absorbing factor of dust fd in front of the Hα.

Radio recombination lines

One advantage of using radio recombination lines (RRLs) is that the ratio of the line temperature to the continuum temperature can be used to derive an electron temperature Te for the H ii emission, which can be substituted in equation (11) to give the radio emission expected from the observed Hα emission. Two extended regions of Hα emission, which are sufficiently bright to have been studied in RRLs are Barnard's Arc and the Gum Nebula.

Barnard's Arc

Barnard's Arc is an ionization-bounded H ii region at 460 pc photoionized by the Orion I OB star association (Reynolds & Ogden 1979). At radio frequencies Barnard's Arc has a thermal spectral index (Davies 1963). Gaylard (1984) describes RRL observations at 2.272 GHz at three positions in the Arc. The radio data were converted from antenna to brightness temperatures using the factor 1.5 used by Gaylard (1984). The Hα observations from SHASSA and the DT dust map were smoothed to 20-arcmin resolution for this study. Table 5 gives the observed brightness temperature Tb, Te and T, the brightness temperature expected from the observed Hα intensity I, uncorrected for absorption using Te values also given in Table 5. The small (<10 per cent) errors in the radio data for the three positions in Barnard's Arc, indicate that the calculated fd values are accurate to about ±0.15 and are therefore consistent with no or little absorption (fd∼ 0) in all three positions. No absorption would be expected if the Hα-emitting gas were nearer than the dust, in this nearby (<500 pc) Gould Belt feature.

Table 5.

Comparison of the observed brightness temperature Tb from RRL data with the predicted brightness temperature THa from Ha data using equation (11). The first three positions are in Barnard's Arc (Gaylard 1984) and the next three are in the Gum Nebula (Woermann et al. 2000). Using the dust column density DT and electron temperature Te, the fraction of ƒd dust causing absorption of Ha emission is calculated for each observation.

Table 5.

Comparison of the observed brightness temperature Tb from RRL data with the predicted brightness temperature THa from Ha data using equation (11). The first three positions are in Barnard's Arc (Gaylard 1984) and the next three are in the Gum Nebula (Woermann et al. 2000). Using the dust column density DT and electron temperature Te, the fraction of ƒd dust causing absorption of Ha emission is calculated for each observation.

The Gum Nebula

The Gum Nebula is a diffuse emission region centred on (l, b) = (258°,−2°) (Gum 1952). It is a complex at a distance of 500 pc containing both free–free and synchrotron features, which are probably the consequence of supernova activity (Duncan et al. 1996; Reynosa & Dubner 1997). The RRL data from Woermann, Gaylard Otrupcek (2000) for Hα features within the complex taken with 20-arcmin resolution are compared with the Hα and dust data as in Section 4.1.1 and are given in Table 5. The data tabulated are for the three strongest Hα features in the Gum Nebula. There is a large spread in fd values from −1.4 to +1.0. The large error bars on the radio data (Tb, Te) correspond to an error of approximately ±0.6 to ±1.0 in the derived fd values for the three Gum nebula positions. Little can be deduced concerning the value of fd without better radio data; negative values have no physical meaning except that the Hα prediction is larger than is measured in the radio band.

Multifrequency scans across Hα features

An alternative method of identifying and measuring the radio free–free emission from an Hα feature is to use multifrequency scans across it to separate the free–free from the underlying synchrotron emission. The brightest features of Barnard's Arc are ideal since they lie some 20° from the Galactic plane where the background synchrotron emission is weak and relatively smooth. We have used the 408-MHz map of Haslam et al. (1982) in the destriped form given by Davies et al. (1996) and the 2326-MHz map of Jonas et al. (1998) to make three Galactic longitude scans across the Barnard Arc feature at b=−18°,−20° and −22° centred on l∼ 212°. These are illustrated in Fig. 6 along with the corresponding Hα scans from WHAM data; all data are at a resolution of 1°. The amplitudes of the best-fitting Gaussians to the feature centred on each Hα position are given in Table 6. Values of fd are estimated as in Section 4.1 for Te= 7000 K (the average local value) and Te= 5100 K (the weighted average of Te from Table 5). The derived fd values are accurate to about ±0.1 to ±0.2 and are significantly negative when Te= 7000 K is assumed, indicating that the radio emission is greater than expected from the Hα brightness with no foreground absorption. However, when the average measured value of Te(5100 K) is used, the derived fd values are consistent with no absorption (fd= 0). This clearly shows the importance of having accurate electron temperatures. In this case, the lower electron temperature corresponds to a ∼25 per cent reduction in T. A further consideration is the full-beam to main-beam correction (see Sections 6 and 7), which can lead to a factor of ∼1.5 for objects comparable in size to the beam. For Barnard's Arc, which is extended (∼5°) in one direction and graphic in the perpendicular direction, the correction is likely to be the square root of this factor (∼1.2). This further correction would lead to a slightly positive (∼0.2) value for fd.

Figure 6.

408 and 2326 MHz scans across Barnard's Arc at constant b=−18° (left), −20° (middle) and −22° (right). The top panels show the 408-MHz scan and the prediction from Hα; both WHAM and SHASSA are shown for each. WHAM is the dotted line and SHASSA is the dashed line. The best-fitting Gaussian plus a linear baseline is shown as a heavy line; WHAM is the heavier line and SHASSA is the lighter line. The middle panels show 2326-MHz data and the same predictions as above for Hα. The bottom panel is the scan for DT (SFD98).

Figure 6.

408 and 2326 MHz scans across Barnard's Arc at constant b=−18° (left), −20° (middle) and −22° (right). The top panels show the 408-MHz scan and the prediction from Hα; both WHAM and SHASSA are shown for each. WHAM is the dotted line and SHASSA is the dashed line. The best-fitting Gaussian plus a linear baseline is shown as a heavy line; WHAM is the heavier line and SHASSA is the lighter line. The middle panels show 2326-MHz data and the same predictions as above for Hα. The bottom panel is the scan for DT (SFD98).

Table 6.

Comparison of the observed radio brightness temperature Tb with the prediction from Ha data, THa, for three scans across Barnard's Arc at frequencies of 408 and 2326 MHz. The Ha intensity IHa and dust column density DT are also listed. The expected brightness temperature THa and the associated dust fraction actually absorbing ƒd are calculated for Te= 7000 K (columns 7 and 8), and for Te= 5100 K (columns 9 and 10) (see the text).

Table 6.

Comparison of the observed radio brightness temperature Tb with the prediction from Ha data, THa, for three scans across Barnard's Arc at frequencies of 408 and 2326 MHz. The Ha intensity IHa and dust column density DT are also listed. The expected brightness temperature THa and the associated dust fraction actually absorbing ƒd are calculated for Te= 7000 K (columns 7 and 8), and for Te= 5100 K (columns 9 and 10) (see the text).

Identifying Hα morphology in radio maps

The morphology of extended bright Hα regions can be identified in the low-frequency continuum maps even in the presence of significant synchrotron emission. By subtracting a template from the radio continuum maps proportional to the Hα intensity, it is possible to estimate the amplitude of the free–free emission. A first-order approach is illustrated for the Orion region in Fig. 7. The 408, 2326 MHz, WHAM Hα and the DT dust maps are first smoothed to 1° resolution. Different amplitudes of the free–free emission expected from the Hα maps are subtracted from the radio maps until the correlation with the Hα maps disappears from the radio maps; we are left with the synchrotron features only. Then using the absorption expected from the DT dust map, an estimate is made of fd for the field. In this case, assuming a nominal electron temperature of Te= 7000 K, both the λ-Orionis nebula (l, b) ≈ (195°, −11°) and Barnard's Arc give fd=−0.2 ± 0.1, suggesting no dust absorption. The error bars are estimated by comparing maps with different amounts of Hα. As shown in Section 4.2, the effect of a lower average temperature for these regions and/or the full-beam to main-beam correction, may bring the Hα estimate in agreement with the radio data (fd≥ 0).

Figure 7.

Morphology of the free–free component in the Orion region. (a) Hα data from WHAM clearly shows Barnard's Arc and λ-Orionis. (b) 2326-MHz data from Jonas et al. (1998) showing a similar morphology. (c) 100-μ m DT map from SFD98 shows some correlation but not a one-to-one correlation. Panels (d, e, f) show the 2326-MHz map with varying levels (1.0, 0.7 and 0.4 multiplied by the conversions given in Table 4) of free–free emission subtracted as predicted by the Hα data. Panels (g, h, i) are the same for the 408-MHz map from Haslam et al. (1982). The electron temperature is assumed to be Te= 7000 K. The best subtraction occurs when the factor is ∼0.7. Note that no correction has been made for dust in this illustration and that the full-beam brightness temperature correction has not been applied (see the text).

Figure 7.

Morphology of the free–free component in the Orion region. (a) Hα data from WHAM clearly shows Barnard's Arc and λ-Orionis. (b) 2326-MHz data from Jonas et al. (1998) showing a similar morphology. (c) 100-μ m DT map from SFD98 shows some correlation but not a one-to-one correlation. Panels (d, e, f) show the 2326-MHz map with varying levels (1.0, 0.7 and 0.4 multiplied by the conversions given in Table 4) of free–free emission subtracted as predicted by the Hα data. Panels (g, h, i) are the same for the 408-MHz map from Haslam et al. (1982). The electron temperature is assumed to be Te= 7000 K. The best subtraction occurs when the factor is ∼0.7. Note that no correction has been made for dust in this illustration and that the full-beam brightness temperature correction has not been applied (see the text).

A similar study was made of the Gum Nebula, where fd was found to be −0.2 ± 0.2, and the Ophiuchus H ii region l≈ (0°)–(20°), b≈ (+15°)–(+30°), where fd= 0 ± 0.2. The increased error in the estimate is a result of the complexity of the emission across each region. In general, the Hα predictions assuming Te= 7000 K are correct when a factor of 0.7–1.0 is included in the Hα estimates (Fig. 7).

In summary, the raw Hα predictions in these selected regions are slightly too large to fit the current low-frequency data by up to ∼30 per cent. This may be accounted for by lower than average electron temperatures (probably the case in some parts of the Orion region), which will vary the conversion factor from Hα to radio continuum by up to ∼30 per cent within a temperature range of 5000–10 000 K. The full-beam to main-beam correction may also be a significant correction; up to 50 per cent, but ∼20–30 per cent in elongated structures. The resulting fd values for these regions are consistent with little or no absorption (fd∼ 0). This might be expected since these regions are at relatively high Galactic latitudes (|b| > 10°) and therefore nearby objects in which the geometry of the ionization, as seen from the Sun's position in the Galactic plane, produces ionization on the near side of the gas/dust clouds.

The Best-Estimate Free–Free Template

We are now in a position to move from the observed Hα maps of the northern and southern skies to produce a full-sky dust-corrected Hα map at an angular resolution of 1°. Then, using equation (11) we can derive all-sky free–free maps except in areas near the Galactic plane where the predicted dust absorption becomes uncertain.

Full-sky Hα map corrected for dust absorption

We obtain a full-sky Hα map using the northern WHAM Hα data at 1° resolution and the higher angular resolution Southern SHASSA Hα data. The Hα map produced from WHAM data was made by interpolating the irregularly spaced data grid using the Interactive Data Language (IDL) routines triangulate and trigrid, which are based on Delauney triangulation, as suggested by the WHAM team (L. M. Haffner, private communication). The median filtered, continuum subtracted composite SHASSA map was used as given by the SHASSA team (J. E. Gaustad, private communication). Where the maps overlap, the WHAM map is used because of its higher sensitivity and better zero-level certainty, except for declinations < −15°, where SHASSA data are preferred. The observed maps are regridded on to an oversampled Cartesian Galactic coordinate grid and smoothed to 1° resolution. We then use the DT map of 100-μm dust emission to correct for dust absorption at each point on the Hα map according to equation (1). The fraction of the dust fd lying in front of the Hα is taken to be 0.33 as shown in Section 2.4 and discussed in Section 4.

Fig. 8 shows a colour representation of the dust-corrected full-sky Hα map in Mollweide projection. Regions where the dust absorption correction is greater than 1.0 mag are shown as grey; Hα data become unreliable in these regions. The Local System (Gould's Belt) is clearly seen beneath the plane at l∼ 180° and above the plane at l∼ 0°, reaching to |b|∼ 30° or more.

Figure 8.

Full-sky dust-corrected Hα map in Mollweide projection. The map has been repixelated into the healpix representation (Górski, Hivon & Wandelt 1999). The colour scale has been histogram-equalized. Longitude l= 0° is in the centre and increasing to the left. Units are log(R). The composite map uses data from the WHAM survey (north) and the SHASSA survey (south) smoothed to a resolution of 1°. Data from WHAM is used in regions where data overlap for declinations > −15°. The data are corrected for dust extinction up to a 1 mag of absorption assuming fd= 0.33 derived in Section 2.4. Absorption above 1 mag is masked off as grey and depicts regions where the true Hα absorption is uncertain. Baseline uncertainties are evident at high Galactic latitudes.

Figure 8.

Full-sky dust-corrected Hα map in Mollweide projection. The map has been repixelated into the healpix representation (Górski, Hivon & Wandelt 1999). The colour scale has been histogram-equalized. Longitude l= 0° is in the centre and increasing to the left. Units are log(R). The composite map uses data from the WHAM survey (north) and the SHASSA survey (south) smoothed to a resolution of 1°. Data from WHAM is used in regions where data overlap for declinations > −15°. The data are corrected for dust extinction up to a 1 mag of absorption assuming fd= 0.33 derived in Section 2.4. Absorption above 1 mag is masked off as grey and depicts regions where the true Hα absorption is uncertain. Baseline uncertainties are evident at high Galactic latitudes.

It should be remembered that both the WHAM and SHASSA surveys are in the early stages of analysis and further revisions are anticipated. Baseline effects are still visible in the data as presented in Fig. 8. For example, the WHAM data cannot accurately subtract the geocoronal emission near the ecliptic pole [(l, b) ≈ (96°, 30°)], while the SHASSA data have artefacts owing to the varying geocoronal emission in each 13 × 13 deg2 field, which results in a residual power on these scales in the region near [(l, b) ≈ (320°, −45°]. The typical level of these baseline variations are ≲1R.

A free–free all-sky template

We can now use Fig. 8 to produce an all-sky free–free template at any radio frequency using equation (11). For illustration we generate the template for 30 GHz, a frequency that is widely used for CMB studies such as the space projects MAP and Planck and the ground-based arrays CBI, DASI and VSA. In applying equation (11) we have taken Te= 7000 K, the appropriate value for the region of Galaxy sampled by the Hα maps at |b|≳ 10°. At 30 GHz, Tb= 5.83 μK/R (Table 4).

The all-sky template for 30-GHz free–free emission is shown in Fig. 9. The amplitude of the free–free signal is <10 μK for |b| > 30° at most Galactic longitudes, although in the Local System Tb can be as large as 100 μK. At higher frequencies the free–free emission falls as ν−2.15 and accordingly at 70–100 GHz, where foreground contamination of the CMB is least, the Tb values will be 5–10 times less than shown in Fig. 9. At these frequencies free–free and vibrational dust emission are the dominant foregrounds. Only the Galactic ridge (|b| < 5°–10°) and isolated regions such as Orion have Tb > 10–20 μK at frequencies of 70–100 GHz.

Figure 9.

Free–free brightness temperature template at 30 GHz with 1° resolution. Grey-scale is logarithmic from 5 to 1000 μ K. Regions where the template is unreliable are masked white. Contours are given at 5 (dot-dashed), 10, 20, 40, 100, 200 and 500 μ K.

Figure 9.

Free–free brightness temperature template at 30 GHz with 1° resolution. Grey-scale is logarithmic from 5 to 1000 μ K. Regions where the template is unreliable are masked white. Contours are given at 5 (dot-dashed), 10, 20, 40, 100, 200 and 500 μ K.

We discuss the contribution of free–free emission to the CMB foregrounds in Section 7.3.

AN IMPROVED LOW-FREQUENCY TEMPLATE

The 408-MHz all-sky map (Haslam et al. 1982) made at graphic resolution is widely used as a template for the Galactic synchrotron foreground. Our present study allows us to correct this map for free–free emission at 408 MHz to obtain a clean synchrotron template. The free–free correction is estimated from the dust-corrected Hα template of Fig. 8 using Tb= 51.2 mK/R as given by equation (11) and Table 4 with Te= 7000 K.

Over much of the sky the free–free features are weaker than the synchrotron features at 408 MHz. However, in regions such as the Local System at intermediate latitudes and the Gum Nebula at lower latitudes, the free–free features can be brighter than the synchrotron features. This is demonstrated in the Orion region in Fig. 7 where significant free–free emission is seen at both 408 and 2326 MHz. In such regions the correction is clearly important.

To estimate the level at which free–free emission is present at 408 MHz, the rms fluctuation of the 408-MHz map smoothed to 1° resolution, are compared with that given by the free–free template map. Table 7 gives the results for different Galactic latitude cuts. The estimate of free–free contamination suggests that at high Galactic latitude (|b| > 40°), away from bright Hα features, the free–free component is a few per cent compared with the synchrotron component. At lower latitudes, the fraction increases to ∼10 per cent. The all-sky value will be considerably underestimated since the corrections for dust absorption near the Galactic plane (|b| < 5°) are uncertain. These estimates agree well with previous best estimates of the ratio of synchrotron and free–free emission. For example, the 10-, 15- and 33-GHz Tenerife experiments combined with the 5-GHz Jodrell Bank interferometer show that the synchrotron and free–free components at intermediate latitudes are approximately equal at ∼10 GHz (Jones et al. 2001). Assuming spectral indices of −3.0 and −2.1 for the synchrotron and free–free, respectively, the ratio at 408 MHz extrapolated from 10 GHz predicts ∼6 per cent of 408-MHz emission is in the form of free–free emission, in good agreement with the Hα values given in Table 7.

Table 7.

Comparison of the rms fluctuations at 1° resolution of 408-MHz data and the free-free template for different Galactic latitude cuts. The all-sky value will be a lower limit since the corrections for dust are uncertain near the Galactic plane (ǀbǀ < 5°).

Table 7.

Comparison of the rms fluctuations at 1° resolution of 408-MHz data and the free-free template for different Galactic latitude cuts. The all-sky value will be a lower limit since the corrections for dust are uncertain near the Galactic plane (ǀbǀ < 5°).

Higher-frequency maps will necessarily have higher fractions of free–free emission. The widely used maps at 1420 MHz (Reich & Reich 1988) and 2326 MHz (Jonas et al. 1998) are used for estimating the Galactic contribution at higher frequencies. Using the estimate of 6 per cent at 408 MHz, the free–free fluctuations at 1420 MHz will contribute ≈15 per cent compared with the synchrotron component at intermediate latitudes, while at 2326 MHz this increases to ≈24 per cent. By correcting the 408-MHz map for free–free emission, a better synchrotron map can be made. This is particularly important for cross-correlation analyses, which assume that the templates are not correlated.

With Hα data alone it is not possible to construct a free–free correction template at lower Galactic latitudes. Fig. 8 shows regions along the Galactic plane where the dust absorption is too large to estimate an accurate dust-free Hα intensity. We plan to use multifrequency maps of the Galactic plane to separate the free–free and synchrotron components at low latitudes. The narrow free–free latitude distribution along the plane has a peak brightness at 408 MHz, which varies from 40 to 80 per cent that of the broader synchrotron distribution at l= 10° to 50° (Large, Mathewson & Haslam 1961). Accordingly, the correction of the 408-MHz map for free–free emission is important at low latitudes.

The other factor in constructing a template at 1° resolution from the low-frequency radio maps is the effect of the main-beam to full-beam ratio (∼1.5) on angular scales of a few degrees; we note that the brightness temperature scale of the published maps is on the full-beam scale (∼5°–10°). The result is that temperatures on the main-beam scale (∼1°) should be multiplied by a factor of ∼1.5 to bring them to the correct brightness temperature scale. This procedure has been considered in Sections 4 .2 and 4.3 and clearly needs to be taken into account for accurate free–free and synchrotron predictions. This scale dependence on the true brightness temperature has been noted before (e.g. Jonas et al. 1998) and is currently under review when applying it to existing full-sky maps.

Discussion

Precision of the free–free template

The Hα intensities given by WHAM and SHASSA have quoted calibration accuracies of 10 and 9 per cent, respectively. The corresponding zero-level uncertainties are approximately 0.2 and 0.5 R. The accuracy is likely to be improved as these surveys are refined. The largest uncertainty in the Hα intensity is in the dust absorption correction as discussed in Section 2. At intermediate and higher Galactic latitudes where fd×A≤ 0.2 mag, the error in the corrected I is ≤5 per cent; this error increases to ∼30 per cent, where fd×A is 1 mag nearer the Galactic plane.

On converting the dust-corrected I to Tb, the free–free brightness temperature, a further uncertainty is introduced by the spread in Te, the electron temperature, in the local region of the Galaxy covered by the Hα maps. For Te= 7000 ± 1000 K, the Tb uncertainty is ±10 per cent as derived from equation (11). As far as the emission theory used in Section 3 is concerned, we believe that the Gaunt factor and the analytical relations given are accurate to 1–2 per cent. It is assumed throughout that the Hα emission is given by the case B emission formulae; the observed radio Tb values are consistent with this assumption.

The contribution to other templates

A radio-independent method of determining a free–free template has a significant benefit in establishing the other Galactic foreground templates for CMB studies. We have already shown in Section 6 that an improved synchrotron template can be derived from the 408-MHz map by correcting for the known free–free emission. This method breaks down for the small area along the Galactic plane where the dust absorption of the Hα becomes too high; other methods of determining the free–free emission are available here.

Spinning dust radiating in the region 10–40 GHz is proposed as a Galactic foreground (Draine & Lazarian 1998); observations appear to confirm this scenario (Kogut et al. 1996; Leitch et al. 1997; de Oliveira-Costa et al. 1997, 1998, 1999, 2000, 2002; Finkbeiner et al. 2002). A strong confirmation of the presence of spinning dust radio emission correlated with the SFD98 dust template requires a clean separation of the free–free component beforehand. This is important because the dust and Hα are generally thought of as being correlated. An example of a region of the Galaxy where the correlation is relatively strong is l= (90°–120°), b= (20°–40°). This is illustrated in Fig. 10(a), which shows the correlation between Hα and (DT) from SFD98 at 1° resolution. The relation between I and DT for the region in Orion l= (180°–210°), b= (−20° to −40°) is given in Fig. 10(b), where it is seen that the correlation is less strong. The distribution of Hα and dust for the Orion region is shown in Fig. 11. The situation is clearly complex on the scale of 1° as would be expected for a star-forming region and underscores the necessity of removing the free–free emission before investigating spinning dust.

Figure 10.

Correlation plots between Hα and dust at a resolution of 1° for two regions (a) l= (90°–120°), b= (20°–40°) and (b) l= (180°–210°), b= (−20° to −40°). There is an overall positive correlation with considerable scatter. The Orion region (b) is brighter and shows a much larger scatter. The Pearson's correlation coefficients are 0.59 and 0.22, respectively.

Figure 10.

Correlation plots between Hα and dust at a resolution of 1° for two regions (a) l= (90°–120°), b= (20°–40°) and (b) l= (180°–210°), b= (−20° to −40°). There is an overall positive correlation with considerable scatter. The Orion region (b) is brighter and shows a much larger scatter. The Pearson's correlation coefficients are 0.59 and 0.22, respectively.

Figure 11.

Correlations between Hα and dust in the Orion region. (a) Hα data from WHAM shown as a logarithmic grey-scale from 3 to 380R and contoured at 5 (dot-dashed), 10, 20, 30, 40, 70, 100, 150 and 200 R. (b) 100-μ m data from SFD98 depicting the dust in a logarithmic grey-scale from 0.1 to 200 MJy sr−1 and contoured at 3 (dot-dashed), 5, 7, 10, 15, 20, 25, 30, 35, 40, 50, 70 and 100 MJy sr−1. There is an overall correlation between Hα and dust but it is not one-to-one.

Figure 11.

Correlations between Hα and dust in the Orion region. (a) Hα data from WHAM shown as a logarithmic grey-scale from 3 to 380R and contoured at 5 (dot-dashed), 10, 20, 30, 40, 70, 100, 150 and 200 R. (b) 100-μ m data from SFD98 depicting the dust in a logarithmic grey-scale from 0.1 to 200 MJy sr−1 and contoured at 3 (dot-dashed), 5, 7, 10, 15, 20, 25, 30, 35, 40, 50, 70 and 100 MJy sr−1. There is an overall correlation between Hα and dust but it is not one-to-one.

Free–free contribution to the CMB foregrounds

We will now estimate the free–free contribution to the CMB foregrounds at ∼30 GHz. If not subtracted from the data, the foreground signal will add in quadrature to the CMB signal in the power spectrum since they will be uncorrelated on the sky. The free–free template allows statistical estimates to be made of the free–free component on angular scales ≳1° compared with the primordial CMB fluctuations. At angular scales of 1° (ℓ≈ 200), the CMB has rms fluctuations of ≈75 μK, falling to ≈30 μK at smaller and larger angular scales. Over a large portion of the higher-latitude sky (|b| > 40°), the average contribution of free–free emission is ≈9 μK at 30 GHz on scales of 1°. This amounts to a 1 per cent increase in the power spectrum at ℓ= 200. However, individual regions may be contaminated at a much higher level depending on their position. At higher frequencies (∼70–100 GHz), the free–free contribution will be ≲1 μK and will be negligible at high latitudes.

We can also compare the estimates for specific regions of the sky where CMB observations have been made. The VSA has observed three regions of the sky measuring angular scales of graphic(ℓ≈ 150–900) covering a total area of 101 deg2 at a frequency of 34 GHz (Taylor et al. 2003). The contamination from free–free emission using the free–free template is estimated to give an rms temperature of 0.6–0.8 μK at the 1° scale and hence the free–free contamination is negligible in these selected regions.

The North Celestial Pole (NCP) region has been studied by the Saskatoon group (Wollack et al. 1997). The Saskatoon data show an anomalous component, which cannot be explained on conventional grounds. Using the free–free template, the rms variations are ≈3.4 μK in a 15°-diameter circle centred on the NCP on smoothing the Hα map to a resolution of graphic and assuming a conversion factor of ≈7 μK/R. Simonetti, Dennison & Topsana (1996) use their Hα data to estimate an upper limit of 4.6 μK at 27.5 GHz in this region. These values of ∼4 μK can be compared with the ≈40 μK rms variations in the Saskatoon data. It therefore seems clear that the anomalous emission is not in the form of free–free emission from gas at Te∼ 10 000 K. The current view is that it may be caused by spinning dust emission as proposed by Draine & Lazarian (1998).

Conclusions

The recent publication of Hα surveys covering the majority of the sky has provided a breakthrough in obtaining a free–free Galactic foreground template of importance for CMB and ISM studies. Having derived the free–free template it is then possible to determine a better synchrotron template and to make real progress in constructing a spinning dust template. The free–free template has many other applications, which include a re-analysis of the COBE-DMR data (Banday et al. 2003) and a free–free power spectrum analysis (Dickinson et al., in preparation).

We can look forward to an improved all-sky free–free template at higher resolution than the 1° used in the present work. A combination of the high-resolution (arcmin-scale) narrow-band filter surveys such as SHASSA and VTSS combined with the high-sensitivity Fabry–Perot survey at a 1° scale would be ideal. At lower Galactic latitudes where the dust absorption of the Hα emission is significant, multifrequency continuum surveys should be able to separate the strong synchrotron and free–free components. Recombination line surveys such as those being undertaken with HIPASS in the south (Barnes et al. 2001) and HIJASS in the north (Kilborn 2002) will provide a confirmation of the low-latitude free–free template and distinguish it from spinning dust, which will have a very similar latitude distribution. The recombination line data will also lead to a kinematic two-dimensional picture of the ionized gas distribution in the Galaxy using kinematic distances since they contain velocity information.

Acknowledgments

CD acknowledges a PPARC research grant. WHAM is funded by the National Science Foundation (NSF). The Southern H-Alpha Sky Survey Atlas (SHASSA) is supported by the National Science Foundation. We thank the WHAM/SHASSA teams for making their surveys available and answering our queries. We also thank David Valls-Gabaud for verifying the calculation of the Gaunt factor.

References

Altenhoff
W.
Mezger
P.G.
Wendker
H.
Westerhout
G.
,
1960
,
Veröff. Sternwärte Bonn, No 59
 ,
48
Baccigalupi
C.
et al
,
2000
,
MNRAS
 ,
318
,
769
Banday
A.J.
Dickinson
C.
Davies
R.D.
Davis
R.J.
Górski
K.M.
,
2003
,
MNRAS
 , submitted
Barnes
D.G.
et al
,
2001
,
MNRAS
 ,
322
,
486
Bennett
C.L.
et al
,
1992
,
ApJ
 ,
396
,
L7
Boumis
P.
Dickinson
C.
Meaburn
J.
Goudis
C.D.
Christopoulou
P.E.
López
J.A.
Bryce
M.
Redman
M.P.
,
2001
,
MNRAS
 ,
320
,
61
Burstein
D.
Heiles
C.
,
1978
,
ApJ
 ,
225
,
40
Davies
R.D.
,
1963
,
Observatory
 ,
83
,
172
Davies
R.D.
Watson
R.A.
Gutiérrez
C.M.
,
1996
,
MNRAS
 ,
278
,
925
de Oliveira-Costa
A.
Kogut
A.
Devlin
M.J.
Netterfield
C.B.
Page
L.A.
Wollack
E.J.
,
1997
,
ApJ
 ,
482
,
L17
de Oliveira-Costa
A.
Tegmark
M.
Page
L.M.
Boughn
S.P.
,
1998
,
ApJ
 ,
509
,
L9
de Oliveira-Costa
A.
Tegmark
M.
Gutiérrez
C.M.
Jones
A.W.
Davies
R.D.
Lasenby
A.N.
Rebolo
R.
Watson
R.A.
,
1999
,
ApJ
 ,
527
,
L9
de Oliveira-Costa
A.
et al
,
2000
,
ApJ
 ,
542
,
L5
de Oliveira-Costa
A.
et al
,
2002
,
ApJ
 ,
567
,
363
Dennison
B.
Simonetti
J.H.
Topsana
G.A.
,
1998
,
Publ. Astron. Soc. Aust.
 ,
15
,
147
Draine
B.T.
Lazarian
A.
,
1998
,
ApJ
 ,
494
,
L19
Duncan
A.R.
Stewart
R.T.
Haynes
R.F.
Jones
K.L.
,
1996
,
MNRAS
 ,
280
,
252
Finkbeiner
D.P.
Schlegel
D.J.
Frank
C.
Heiles
C.
,
2002
,
ApJ
 ,
566
,
898
Gaustad
J.E.
McCullough
P.R.
Rosing
W.R.
Buren
D.V.
,
2001
,
PASP
 ,
113
,
1326
Gaylard
M.J.
,
1984
,
MNRAS
 ,
211
,
149
Górski
K.M.
Hivon
E.
Wandelt
B.D.
,
1999
, in
Banday
A.J.
Sheth
R.S.
Da Costa
L.
, eds,
Proc. MPA/ESO Cosmology Conf. Evolution of Large-Scale Structure
 , p.
37
Gum
C.S.
,
1952
,
Observatory
 ,
72
,
151
Haffner
L.M.
,
1999
,
PhD thesis
 ,
Univ. Wisconsin
Halverson
N.W.
et al
,
2002
,
ApJ
 ,
568
,
38
Hanany
S.
et al
,
2000
,
ApJ
 ,
545
,
L5
Hartmann
D.
Burton
W.B.
,
1997
,
Atlas of Galactic Neutral Hydrogen
 .
Cambridge Univ. Press
,
Cambridge
Haslam
C.G.T.
Salter
C.J.
Stoffel
H.
Wilson
W.
,
1982
,
A&AS
 ,
47
,
1
Hummer
D.G.
,
1988
,
ApJ
 ,
327
,
477
Hummer
D.G.
Storey
P.J.
,
1987
,
MNRAS
 ,
224
,
801
Jonas
J.L.
Baart
E.E.
Nicolson
G.D.
,
1998
,
MNRAS
 ,
297
,
977
Jones
A.W.
Davis
R.J.
Wilkinson
A.
Giardino
G.
Melhuish
S.J.
Asareh
H.
Davies
R.D.
Lasenby
A.N.
,
2001
,
MNRAS
 ,
327
,
545
Karzas
W.J.
Latter
R.
,
1961
,
ApJS
 ,
6
,
167
Kilborn
V.A.
,
2003
, in
Taylor
A.R.
Landecker
T.L.
Willis
A.G.
, eds,
ASP Conf. Ser. Vol. 276, Seeing through the Dust. Astron. Soc. Pac.
 , San Francisco, in press
Kogut
A.
Banday
A.J.
Bennett
C.L.
Górski
K.M.
Hinshaw
G.
Smoot
G.F.
Wright
E.L.
,
1996
,
ApJ
 ,
464
,
L5
Large
M.I.
Mathewson
D.S.
Haslam
C.G.T.
,
1961
,
MNRAS
 ,
123
,
123
Leitch
E.M.
Readhead
A.C.S.
Pearson
T.J.
Myers
S.T.
,
1997
,
ApJ
 ,
486
,
L23
Mauskopf
P.D.
et al
,
2000
,
ApJ
 ,
536
,
L59
Meaburn
J.
,
1965
,
Nat
 ,
208
,
575
Meaburn
J.
,
1967
,
Z. Astrophys.
 ,
65
,
93
Mezger
P.G.
Henderson
A.P.
,
1967
,
ApJ
 ,
147
,
471
O'Donnell
J.E.
,
1994
,
ApJ
 ,
422
,
158
Oster
L.
,
1961
,
Rev. Mod. Phys.
 ,
33
,
525
Osterbrock
D.E.
,
1989
,
Astrophysics of Gaseous Nebulae and Active Galactic Nuclei
 .
Univ. Science Books
,
Mill Valley
Padin
S.
et al
,
2001
,
ApJ
 ,
549
,
L1
Panagia
N.
,
1979
,
Mem. Soc. Astron. Ital.
 ,
50
,
79
Parker
Q.A.
Phillipps
S.
,
1998
,
Publ. Astron. Soc. Aust.
 ,
15
,
28
Pengelly
R.M.
,
1964
,
MNRAS
 ,
127
,
145
Pottasch
S.R.
,
1983
,
Planetary Nebulae
 .
Reidel
,
Dordrecht
, p.
285
Reich
P.
Reich
W.
,
1988
,
A&AS
 ,
74
,
7
Reynolds
R.J.
,
1985
,
ApJ
 ,
294
,
256
Reynolds
R.J.
Haffner
L.M.
,
2002
, in
Lasenby
A.N.
,
Wilkinson
A.
, eds,
Proc. IAU Symp. 201
 ,
PASP
,
in press
Reynolds
R.J.
Ogden
P.M.
,
1979
,
ApJ
 ,
229
,
942
Reynolds
R.J.
Tufte
S.L.
Haffner
L.M.
Jaehnig
K.P.
Percival
J.P.
,
1998
,
Publ. Astron. Soc. Aust.
 ,
15
,
14
Reynosa
E.M.
Dubner
G.M.
,
1997
,
A&AS
 ,
123
,
31
Scheuer
P.A.G.
,
1960
,
MNRAS
 ,
120
,
231
Schlegel
D.J.
Finkbeiner
D.P.
Davis
M.
,
1998
,
ApJ
 ,
500
,
525
(SFD98)
Scott
P.F.
et al
,
2003
,
MNRAS
 , in press
Shaver
P.A.
McGee
R.X.
Newton
L.M.
Danks
A.C.
Pottasch
S.R.
,
1983
,
MNRAS
 ,
204
,
53
Simonetti
J.H.
Dennison
B.
Topsana
G.A.
,
1996
,
ApJ
 ,
458
,
L1
Sivan
J.P.
,
1974
,
A&AS
 ,
16
,
163
Taylor
A.C.
et al
,
2003
,
MNRAS
 , in press
Valls-Gabaud
D.
,
1998
,
Publ. Astron. Soc. Aust.
 ,
15
,
111
Vielva
P.
Barreiro
R.B.
Hobson
M.P.
Martínez-González
E.
Lasenby
A.N.
Sanz
J.L.
Toffolatti
L.
,
2001
,
MNRAS
 ,
328
,
1
Woermann
B.
Gaylard
M.J.
Otrupcek
R.
,
2000
,
MNRAS
 ,
315
,
241
Wollack
E.J.
Devlin
M.J.
Jarosik
N.
Netterfield
C.B.
Page
L.
Wilkinson
D.
,
1997
,
ApJ
 ,
476
,
440