A characterization of the diffuse Galactic emissions in the anti-center of the Galaxy

Using the Archeops and WMAP data we perform a study of the anti-center Galactic diffuse emissions - thermal dust, synchrotron, free-free and anomalous emission - at degree scales. The high frequency data are used to infer the thermal dust electromagnetic spectrum and spatial distribution allowing us to precisely subtract this component at lower frequencies. After subtraction of the thermal dust component a mixture of standard synchrotron and free-free emissions does not account for the residuals at these low frequencies. Including the all-sky 408 MHz Haslam data we find evidences for anomalous emission with a spectral index of 2.5 in TRJ units. However, we are not able to conclude regarding the nature of this anomalous emission in this region. For the purpose, data between 408 MHz and 20 GHz covering the same sky region are needed.


I. INTRODUCTION
The anomalous microwave emission (AME in the following), is an important contributor of the Galactic diffuse emissions in the range from 20 to 60 GHz. It was first observed by (de Oliveira-Costa et al., 1997; Kogut et al., 1996) and then identified by (Leitch et al., 1997) as free-free emission from electrons with temperature, Te > 10 6 K. Draine & Lazarian (1998a) argued that AME may result from electric dipole radiation due to small rotating grains, the so-called spinning dust. Models of the spinning dust emission (Draine & Lazarian, 1998b) show an electromagnetic spectra peaking at around 20-50 GHz being able to reproduce the observations (Finkbeiner, 2003 Correlation between microwave and infrared maps, mainly dominated by dust thermal emission (Désert et al., 1990) Independently, Bennett et al. (2003) proposed an alternative explanation of AME based on flat-spectrum synchrotron emission associated to star-forming regions to explain part of the WMAP first-year observations. This hypothesis seems to be disagreement with results from de Oliveira-Costa et al. We propose here to study the Galactic diffuse emissions in the Galactic plane, particularly focusing on the anti-center region. The observational data, from 408 MHz to 3000 GHz, used for this study are presented in Section II. Section III discusses in details the contribution of the diffuse Galactic thermal dust emission using the high frequency data. In Section IV we consider a simple free-free and canonical synchrotron emission model for the thermal dust subtracted microwave data. The possible contribution from anomalous emission is discussed in Section V. We draw conclusions in Section VI.

II. MICROWAVE AND MILLIMETER OBSERVATIONS
We describe in this section the data used for the analysis presented in this paper. As we are interested in the Galactic diffuse emission we consider only large coverage sky surveys in the radio, microwave, millimeter and infrared domain including the 408 MHz all-sky survey and the WMAP ARCHEOPS and IRAS data.

MHz all-sky survey
In the radio domain, the 408MHz all-sky continuum survey (Haslam et al. (1982)) at a resolution of of 0.85 degrees, is a good tracer of the synchrotron emission. In particular, we use

WMAP
In order to estimate the diffuse Galactic emission at microwave frequencies we used the maps in temperature using the K, Ka, Q, V and W band maps of the WMAP mission of its 7-years WMAP citephinshaw09. In particular, we used the co-added maps available on the the Lambda web site, also smoothed down to a resolution of 1 degree and downgraded to N side = 64. Uncertainties in the WMAP data were computed assuming a uncorrelated anisotropic noise as described in (Hinshaw et al., 2009). The variance per pixel at the working resolution was computed using the variance of a single hit and the number of hits per pixels.

IRAS
In the infrared, we have used the new generation of the IRAS data (InfraRed Astronomical Satellite) at 100 and 60 µm (3000 and 5000 GHz). This release of the IRAS data is called IRIS (Improved Reprocessing of the IRAS data)(Miville-Deschênes, 2005) and has been built with a better destroying, a better subtraction of the zodiacal light and a calibration and a zero level compatible with the far infrared instrument, FIRAS, of COBE. The IRIS maps were also smoothed down to a resolution of one degree and downgraded to N side = 64.
In order to avoid the contamination from the CMB at intermediate frequencies, 30-200 GHz, we have restricted our study to the Galactic plane where the Galactic emissions dominate over the cosmological CMB emission. In practice, we selected those regions in the Archeops 353 GHz map with intensity above 3000

III. DIFFUSE GALACTIC THERMAL DUST EMISSION
We first study the electromagnetic and spatial properties of the thermal dust diffuse Galactic emission. In order to model the intensity of the thermal dust emission, we use a simple grey body spectrum of the form where β d is the spectral index of the thermal dust emission and T d is the dust temperature.
We used the ARCHEOPS and IRIS 100 µm maps to characterize the dust thermal emission model. We fitted the data to the model pixel by pixel using as free parameters I0, β d and T d , and the following likelihood function where D p ν and M p ν correspond to the data and model at the pixel p within the mask and for the observation frequency ν (= 143, 217, 353, 545 and 3000 GHz). σ p ν is the 1-σ error bar associated to D p ν . β d and T d were explored using an uniformly spaced grid as defined in Table II)  In Figure 1 we present maps of the dust temperature and spectral index within the considered mask. We also show the statistical uncertainties on these parameters. As expected the errors increase significantly on the edges of the maps. These noisy pixels will be excluded from the analysis hereafter. We can also notice that in the inner regions the statistical errors are significantly smaller than the observed dispersion for the two parameters. We observe that the mean dust temperature is 20.0 K with 2.1 K dispersion, while the mean instrumental uncertainties are of the order of 1 K. In the same way, the mean dust spectral index is 1.40 with a dispersion of 0.25, and the mean instrumental uncertainties of the order of 0.1.   scope of this study and does not have any consequence in the following study. Table I (Finkbeiner, 2003). We started from a map at resolution N side = 512 and downgraded it, as the other maps, at a resolution of N side = 64.

In order to estimate the contribution of the diffuse galactic free-free emission, which is expected to be important at the WMAP bands, we use the Extinction-Corrected Halpha Foreground Template (Hα) map built by Finkbeiner (2003). This map was computed using data from the Virginia Tech Spectral line Survey (VTSS), for the North and of data from the Southern H-Alpha Sky Survey Atlas (SHASSA) for the South sky. Correction factors are applied to take into account dust absorption
(4)

Thus the intensity of the free-free emission ( in mKRJ ) is given as a function of the intensity of the H-α emission (in Rayleighs) by
We have extrapolated this free-free emission template at each of the WMAP frequencies assuming that the electromagnetic spectrum of the free-free emission is well represented by a power law of the form ν β f f (Bennett et al., 2003) We set a standard value for the electronic temperature at 8000 K, following (Otte et al., 2002). The values of the spectral index obtained at the WMAP frequencies assuming these hypothesis are given in Table III.
In order to model the synchrotron contribution we used the 408 MHz all-sky continuum survey as a template map. We extrapolated it at all the considered frequencies assuming a power law like electromagnetic spectrum in antenna temperature with fix spectral index that we set to -2.7 (Bennett et al., 2003). Table ?? we present the rms of the residuals after subtraction of the Galactic thermal dust, synchrotron and free-free emission models. These residuals are significant: up to 90 % of the original emission (first column of the table). We have observed both point like and diffuse structures in these residuals. The former are more probably related to uncertainties in the modeling of the free-free emission. By contrast, the extra diffuse emission is most probably related to anomalous emission. This hypothesis is considered in the following section.

V. STUDY OF THE ANOMALOUS EMISSION
In the previous section we concluded that the observed emission in the range from 23 to 94 GHz can not be explained only by the combination of the canonical Galactic diffuse emission: thermal dust, soft synchrotron and free-free. Indeed, we have observed that in some compact regions there seems to be extra freefree emission with respect to the predictions from the Hα template . Furthermore, the diffuse emission is underestimated in general indicating either an extra component or a softer synchrotron component. In order to investigate these two problems we have considered a two component model composed of free-free and anomalous emissions in addition to diffuse thermal dust emission. We assume that the free-free and the anomalous emissions follow a simple power-law model such that where Mν are the observed maps in KRJ units at the frequency ν after subtraction of the contribution from thermal dust. Finally, we consider 4 free parameters in the model: the normalization coefficients Async and A f f , the spectral index βs of the anomalous component and the free electron temperature (??). To simplify the fitting procedures we vary βs and Te in the ranges shown in Table IV. Notice that we have not explicitly consider the canonical synchrotron emission in this model. Indeed, our so called anomalous component will be a mixture of real anomalous emission and canonical synchrotron emission. We fit this two-component model to the dust subtracted WMAP maps and to the 408 MHz map for which the thermal dust emission is negligible. As discussed before, the uncertainties on the WMAP data have been calculated assuming anisotropic white noise on the maps. We compute the variance r pixel using the variance per single observation provided on the LAMBDA website and maps of the number of hit counts. For the 408 MHz map we assume 10 % uncertainties as discussed in Section II. It is important to notice that an alternative three component component model (including free-free, canonical synchrotron and anomalous emission) would imply at least 6 free parameters to be fitted on only 6 sky maps. That is why we have chosen to consider a two-component model only.
From the results of the fit we observe that the anomalous emission seems to dominate the diffuse component at 1 GHz while the free-free emission seems to be mainly located in few compact regions. In Figure 4 we present the map of the reconstructed spectral index for the anomalous emission, βs. We observe that the anomalous emission seems to be well represented by a power-law with average spectra index of -2.5. Similar results have been found by Bennett

VI. SUMMARY AND CONCLUSIONS
We have presented in this paper a detailed analysis of the Galactic diffuse emissions at the Galactic anti center in the frequency range from 23 to 545 GHz. We have shown that a simple grey-body model can be used to describe the thermal dust emission in the frequency range from 100 to 3000 GHz. We find a mean temperature of 20 K with an intrinsic dispersion of 2.1 K and a spectral index of 1.4 with intrinsic dispersion of 0.25. These values are significantly larger and lower than expected from canonical models of the dust emission, T dust ∼ 17 K and β dust = 1. although as they fixed the spectral index to 1.8 they obtain a lower temperature of 14 K. We have performed a similar analysis fixing β dust = 1.8 and we have also obtained lower dust temperatures. At high frequencies (above 3000 GHz) extra hot thermal dust emission from small dust grains is needed to account for the observations (Désert et al., 1990). The former dust model have been used to extrapolate the thermal dust emission to microwave frequencies from 23 to 100 GHz. After subtraction of the thermal dust emission we have shown that the microwave data can not be simply explained by a combination of free-free and canonical synchrotron emission. A more detailed analysis including AME has shown that the latter can be well approximated by a power-law of average spectral index −2.5 in KRJ units. This anomalous emission seems to dominate the diffuse emission at microwave frequencies while free-free emission seems to be located in few compact regions. Indeed, we have found that outside those regions the data required electron temperature has not physically meaningful.
The spectral index found for the anomalous emission is consistent with hard synchrotron emission (Bennett et al., 2003;Hinshaw et al., 2007). However, we can not formally conclude on this as our analysis did not include data in the 1 to 20 GHz that would help discriminating this hypothesis from spinning dust emission Draine & Lazarian (1998a)