EVIDENCE FOR ANOMALOUS DUST-CORRELATED EMISSION AT 8 GHz

Many observations have shown that there is diffuse dust-correlated emission at frequencies below 40 GHz where the thermal emission by dust grains is usually expected to be negligible. The effect was first seen at large angular scales in the COBE DMR data by Kogut et al. (1996), who attributed the phenomenon to the simple co-location of thermal dust and free–free emission. These observations were confirmed by ground-based measurements at finer angular scales (de Oliveira-Costa et al. 1997; Leitch et al. 1997). Soon thereafter, it was realized that the dust-correlated emission might in fact be due to microwave emission by spinning dust grains (Jones 1997; Draine & Lazarian 1998). In other words, where there is more thermally emitting dust radiating at frequencies ν  >  100 GHz, there would also be more spinning dust emitting near ν  ∼  20 GHz. Since then, the correlated diffuse emission has been seen at high and low Galactic latitudes (de Oliveira-Costa et al. 1998, 1999, 2004; Leitch et al. 2000; Mukherjee et al. 2001, 2002, 2003; Hamilton & Ganga 2001; Bennett et al. 2003; Banday et al. 2003; Lagache 2003; Finkbeiner 2004; Davies et al. 2006; Fernández-Cerezo et al. 2006; Boughn & Pober 2007; Hildebrandt et al. 2007; Dobler & Finkbeiner 2008a, 2008b; Dobler et al. 2009; Miville-Deschênes et al. 2008; Ysard et al. 2010; Kogut et al. 2011; Gold et al. 2011). At large angular scales, the Wilkinson Microwave Anisotropy Probe (WMAP; Bennett et al. 2003) suggested that this correlation could also be explained by variable-index synchrotron emission co-located with dusty star-forming regions. However, alternative and subsequent analyses gave more support to the spinning dust hypothesis and attributed the source of the correlation to a population of small spinning grains (de Oliveira-Costa et al. 2002; Lagache 2003; Ysard et al. 2010; Macellari et al. 2011).

Evidence for dust-correlated emission at microwave frequencies has also been reported in more compact regions (e.g., Finkbeiner et al. 2002, 2004; Watson et al. 2005; Battistelli et al. 2006; Casassus et al. 2006, 2008; Iglesias-Groth 2006; Dickinson et al. 2009; Scaife et al. 2009, 2010a, 2010b; Murphy et al. 2010; Tibbs et al. 2010; Planck Collaboration et al. 2011; Vidal et al. 2011; Castellanos et al. 2011; López-Caraballo et al. 2011). Most recently, the Planck satellite has shown in detail the presence of a non-power-law component. A new component of emission is clearly seen in the Perseus and ρ Ophiuchus regions (Planck Collaboration et al. 2011). The component is well modeled as spinning dust, although the range of gas temperatures is large.

It has long been realized that large area maps in the 5–20 GHz range would be ideal for separating free–free from variable-index synchrotron emission, spinning dust, or any other emission process. For diffuse sources, COSMOSOMAS (Hildebrandt et al. 2007) observed the sky between 11 and 17 GHz and identified a dust-correlated component, as did TENERIFE (de Oliveira-Costa et al. 1999) observing at 10 and 15 GHz. The ARCADE 2 experiment (Kogut et al. 2011) observed at 3, 8, and 10 GHz and also found evidence in support of a new component. Here, we show that Conklin's 1969 data (Conklin 1969a, 1969b) further improve constraints in this frequency range and at large angular scales.

Although spinning dust is currently the preferred single hypothesis for explaining the correlation, there are ∼10 free parameters in the spinning dust model (e.g., Ali-Haïmoud et al. 2009); and there could be multiple processes, including magnetized dust emission (Draine & Lazarian 1999), at work.

The rest of the paper is outlined as follows. We describe the observations in Section 2, discuss an interpretation of the observations in Section 3, and conclude in Section 4.

Conklin's observations took place on White Mountain in 1968 and 1969, using a coherent receiver at 8 GHz with an effective FWHM beam of θ_1/2 = 162. The radiometer Dicke switched at 37 Hz between two feeds with intrinsic beams of θ^H_1/2 = 145 pointed ±30° from the zenith along an E–W baseline. The data were averaged over four minutes, the entire apparatus was rotated 180° over one minute, data were averaged again for four more minutes, and finally the apparatus was rotated back to its original position. During each such 10 minute cycle, the temperature difference between the two feeds was recorded; Conklin reported the differences as "east"–"west." The 10 minute differences were then averaged with a 30 minute FWHM Gaussian function, effectively broadening the intrinsic beam profile to 162 along the scan direction. The data we use, shown in Figure 1 and reported in Table 1, come from a combination of the 1969 Nature paper and Conklin's PhD thesis, which included additional data. For this analysis, we use Conklin's reported data after subtracting the contribution from the now well-established dipole. The per-point error bars are deduced from the "probable error" reported in his thesis. They may be treated as independent. They are larger than the purely statistical error by a factor of 1.6.³

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The measurements were made at a single celestial circle at δ = 32° as indicated in Figure 2. The highest amplitude point at R.A.  ∼  300° comes from when the "E" beam crosses the Galactic plane at b = 0° and l = 695, and the "W" beam is out of the plane. The "E" beam again crosses the Galactic plane at l = 1764.

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After subtracting up to a 10 mK Galactic contribution by extrapolating the 404 MHz Pauliny-Toth & Shakeshaft map (Pauliny-Toth & Shakeshaft 1962) to 8 GHz, Conklin reported a preliminary measurement of the dipole with amplitude 1.6  ±  0.8 mK in the direction α = 13 h. After Conklin's 1969 PhD thesis, this became 2.3  ±  0.9 mK in the direction α = 11 h as reported at the IAU 44 symposium (Conklin 1972). Though the error bars include an estimate for a ±0.1 uncertainty in the Galactic index (the statistical uncertainty was ≈0.02 mK), there were lingering doubts about the extrapolation (Webster 1974). Neglecting the correction for Earth's motion, the WMAP dipole (3.358  ±  0.017 mK in direction α = 11.19h at δ = −690 for the full sky) has an amplitude of 2.83 mK at δ = 32°, in excellent agreement.

2.1. Calibration and Beam Characteristics

We compare Conklin's data to that from Haslam et al. (Haslam et al. 1981, 1982) at 0.408 GHz; Reich and Reich (Reich 1982; Reich & Reich 1986; Reich et al. 2001)⁴ at 1.42 GHz; WMAP at 23, 33, 44, 60, and 94 GHz (Jarosik et al. 2011); and the Finkbeiner et al. (1999) map model 8 extrapolated to 94 GHz (hereafter FDS99). We adopt calibration errors of 7%, 4%, and 2% for Haslam, Reich & Reich, and WMAP, respectively. The statistical errors are negligible compared to the uncertainty on Conklin's observations. We convolve the multi-frequency maps to the same 162 resolution and extract differenced measurements at δ = 32° to compare to the Conklin data, shown in Figure 4. We do not account for the asymmetry in the Conklin effective beam, but test that varying the beam size by 2° has a negligible effect on conclusions. In all of our fits the calibration uncertainties dominate the statistical uncertainties.

We initially compare the emission, I, at ν₀ = 8 GHz to the WMAP K-band emission (ν = 23 GHz), using a two parameter model,

$$\begin{equation} I(\nu _0,\hat{n}) = I(\nu,\hat{n})(\nu _0/\nu)^\beta + A. \end{equation} \tag{ 1 }$$

We fit for the index, β, and offset, A, finding a marginalized limit of β = −1.7  ±  0.1, with best-fit χ² = 64.5 (reduced χ² = 1.33). Because WMAP and Conklin are not observing the same mixture of foreground components, the high χ² is not surprising. Figure 3 shows the marginalized distribution for the spectral index of the model. We include calibration error and the possible 6% calibration bias due to beam uncertainty. The index is incompatible with free–free emission (β = −2.15), synchrotron emission −3  <  β  < − 2.7, or a "breaking" synchrotron index (e.g., Banday & Wolfendale 1991). Additionally, the WMAP best-fitting maximum entropy model, excluding a spinning dust component, overpredicts the emission at 8 GHz by a factor of two. We conclude that there must exist another component of foreground emission which has lower emission at 8 GHz than at 23 GHz.

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To determine the scaling between Conklin's data and each of the data sets in the range 0.4–94 GHz, we fit I(ν) = s(ν)I(ν₀) + A(ν). Figure 4 shows how the intensity measured at each frequency, I(ν), compared to the scaled Conklin data, s(ν)I(ν₀) + A(ν). The estimated scaling factors are reported in Table 2, with the goodness of fit. The closest fit is obtained between 8 GHz and the WMAP K band because these are the closest in the logarithm of the observation frequency. A simple power-law extrapolation is a poor fit for more widely spaced frequencies as multiple components contribute to the emission. Figure 5 shows the frequency dependence of the estimated scaling factors s(ν) after multiplying by the rms of Conklin's data.

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We find the same general trend, that Conklin's data are significantly lower than expected based on a free–free or synchrotron power-law extrapolation from WMAP's 23 GHz channel, by fitting to the l = 176° or l = 695 Galaxy crossings, to the rms of each data set, or to the peak-to-peak amplitude as a function of frequency. The fit is dominated by the Galactic crossing regions.

To find a physical model that fits Conklin's observations in addition to the Haslam et al., Reich & Reich, and WMAP data we perform a simultaneous fit to s(ν) in the range 0.4–94 GHz. The model includes free–free, synchrotron, thermal dust, and spinning dust. We test the improvement in χ² as we add a spinning dust component, using the model of Ali-Haïmoud et al. (2009). As free parameters, we take the total hydrogen number density n_H and the gas temperature T, assuming that a single density and temperature can be used to model the global emission. For the other parameters, we use the values given by Ali-Haïmoud et al. (2009) in their sample spectrum and nominal parameters in Weingartner & Draine (2001) their Table 1, line 7. Best fits are obtained with n_H = 20 cm⁻³ and T = 300 K. The values of these parameters, however, would be affected by more refined models of the emission process (e.g., B. T. Draine 2011, private communication via L. A. Page). For the thermal dust emission, we consider two models: one in which the thermal dust amplitude is constrained by the FDS99 model and one in which the amplitude is allowed to vary (hereafter referred to as "free dust"). The results are not significantly different, so we report only the "free dust" results.⁵

Model 1. First, we fit s(ν) with synchrotron, free–free, and thermal dust emission:

$$\begin{equation} M_1(\nu) = a_0\nu ^{a_1} + a_2\nu ^{-2.15}+ a_3\nu ^{1.7}, \end{equation} \tag{ 2 }$$

where $a_0\nu ^{a_1}$ represents synchrotron emission with spectral index a₁ and amplitude a₀, a₂ν^−2.15 represents free–free emission, and a₃ν^1.7 represents thermal dust emission with fixed spectral index. The fit parameters a₀, a₂, and a₃ are required to be positive, and the synchrotron spectral index a₁ is varied in the range −3.5  <  a₁ < − 2. The probability distribution for the four parameters is estimated using Markov Chain Monte Carlo sampling methods. The best-fitting synchrotron index and χ² are reported in Table 3; the model is a poor fit to the data with χ²/dof = 49.9/4.

Model 2. We then include an additional spinning dust component:

$$\begin{equation} M_2(\nu) = a_0\nu ^{a_1} + a_2\nu ^{-2.15} + a_3\nu ^{1.7}+ a_4D_s(\nu), \end{equation} \tag{ 3 }$$

where D_s(ν) represents the spinning dust emission template from Ali-Haïmoud et al. (2009) described above, with amplitude a₄. Adding the spinning dust improves the goodness of fit by Δχ² = 31, indicating a strong preference for this additional component.

This model is physically reasonable for a single pixel or direction on the sky. Generally, the relative amplitudes and frequency dependence of the synchrotron, spinning dust, and thermal dust components vary spatially. In our case, the model assumes that the relative foreground intensity over the region of sky observed by Conklin may be quantified by a single scaling factor s(ν). This is likely oversimplified, but the fit is good. It is noteworthy that the amplitude of the best-fit synchrotron spectrum at WMAP's 23 GHz band is low compared to the free–free and spinning dust, contributing only ∼10% of the anisotropy, although the best-fit synchrotron spectral index, β ≈ − 3.00, is reasonable. One must keep in mind that with so little data the parameter degeneracies are large, and a more realistic model of the relative contribution of the foreground components would allow for spatially varying amplitude ratios. For example, Macellari et al. (2011) estimate ∼1/3 of the all-sky intensity anisotropy to be synchrotron at 23 GHz.

Anisotropy in the diffuse microwave emission at 8 GHz, originally measured by Conklin in 1969 to estimate the cosmic microwave background (CMB) dipole, now sheds light on Galactic emission. The observed signal is consistent with synchrotron, free–free, and spinning dust emission from the Galaxy. In combination with multi-frequency observations, the 8 GHz data strongly disfavor an emission model with no anomalous dust component, assumed to be rapidly rotating polycyclic aromatic hydrocarbon grains. The presence of this additional diffuse component is consistent with observations by ARCADE-2, COSMOSOMAS, and the TENERIFE experiment, and with targeted measurements of dusty regions in the Galaxy. Accurate characterization of the Galactic foregrounds in intensity and polarization is important for extracting cosmological information from the CMB, and will be vital for constraining inflationary models via the large-scale polarization signal. Upcoming low-frequency observations, for example from the C-BASS experiment at 5 GHz (King et al. 2010), will shed further light on the diffuse anomalous dust behavior and allow its properties to be better established.

We gratefully acknowledge the support of the U.S. NSF through award PHY-0355328. We also thank Ned Conklin, Angelica de Oliveira-Costa, Clive Dickinson, Bruce Draine, Ben Gold, Al Kogut, David Spergel, and Ed Wollack for their comments on an earlier draft. This research has made use of NASA's Astrophysics Data System Bibliographic Services. We acknowledge use of the HEALPix package and Lambda. We thank Angelica de Oliveira-Costa for helpful comments and assistance with the Reich & Reich data.