Constraining the Anomalous Microwave Emission Mechanism in the S140 Star-forming Region with Spectroscopic Observations between 4 and 8 GHz at the Green Bank Telescope

GBT is a fully steerable off-axis Gregorian reflecting antenna designed for observations below approximately 115 GHz. The prime focus of the parabolic primary mirror is directed into a receiver cabin using an elliptical secondary mirror. The C-band receiver we used for our observations is mounted in this receiver cabin. The unblocked aperture diameter is 100 m, so the beam size for our observations was between 1.8 and 2.8 arcmin, depending on frequency. The VEGAS back-end electronics used to measure the spectra are housed in a laboratory approximately 2 km from the telescope.

A schematic of the receiver and the digital spectrometer we used for this study is shown in Figure 1. The telescope first feeds a corrugated horn. An orthomode transducer (OMT) at the back of the horn splits the sky signals into two polarizations (polarization X and polarization Y). The two outputs of the OMT are routed to a cryogenic stage that is cooled to approximately 15 K. At this cryogenic stage, directional couplers are used to insert calibration signals from a noise diode. These calibration signals were switched on and off during our observations to help monitor time-dependent gain variations. The sky signals were then (i) amplified with a cryogenic low-noise amplifier, (ii) band-pass-filtered, (iii) amplified a second time with a room-temperature amplifier, (iv) mixed down in frequency, and (v) routed to the laboratory via optical fibers.

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In the laboratory, the signals were split into four banks: Banks A, B, C, and D. Each bank used its own hardware chain to measure the spectrum of that bank. For clarity, only one of the four spectrometer chains is shown in Figure 1. The spectral band for each bank is determined by mixing up the signal in that bank using a tunable local oscillator (LO) and then band-pass-filtering. The chosen LO frequency ultimately defines the spectral band. The passband of the filter is between 8.50 and 10.35 GHz. The signals were then mixed down using a fixed 10.5 GHz LO. At this stage, each bank has 1.85 GHz of bandwidth. The signals were then (i) amplified, (ii) low-pass-filtered to avoid aliasing (edge at 1.5 GHz), and (iii) sampled at 3 Gsps with an 8-bit analog-to-digital converter (ADC) that is connected to a Reconfigurable Open Architecture Computing Hardware 2 (ROACH2) board.³ The ROACH2 board uses a field-programmable gate array to compute the spectrum of the sampled data. Each bank has 16,384 raw spectral channels that are each 91.552 kHz wide. Spectra are integrated in the ROACH2, and one average spectrum is saved to disk every 40 ms. In the following sections, we use the term ADC count to refer to the power measurement in each filter bank channel. The spectral banks are defined in Table 1.

Our GBT observations were conducted in 2017 April and June. Ten total hours of mapping data were collected during observing sessions on April 5, April 10, and June 4. Eight total hours of polarization calibration data were collected on April 3 and June 3. We refer to these as Sessions 1 through 5 chronologically, so Sessions 1 and 4 are the polarization calibration sessions, and Sessions 2, 3, and 5 are the mapping sessions. At the beginning of each session, the system temperature was measured. For our five sessions, the mean system temperature was 19.5 ± 1 K.

We chose to use the "daisy" scan strategy available at GBT, which is typically used for MUSTANG mapping observations (Korngut et al. 2011). The daisy scan traces out three "petals" on the sky every 30 s (see Figure 2). Every 25 minutes, this scan strategy completes a full cycle densely covering both the innermost and the outermost portions of a nearly circular region. This approach works well with our mapmaking algorithm (see Section 3.3) because map pixels are revisited and sampled multiple times. Given that we want a densely sampled map, we scanned GBT close to the speed and acceleration limits of the telescope⁴ and were able to observe a nearly circular region 30 in diameter centered on G107.2+5.20. Our maximum scan speed was 21.6 arcmin s⁻¹, and the root mean squared (rms) speed was 10 arcmin s⁻¹. The scan pattern is calculated in an astronomical coordinate system to ensure the center is always on G107.2+5.20.

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To convert our measurements into flux units, we calibrated using observations of 3C295. 3C295 is an unpolarized radio galaxy that has a power-law-with-curvature spectrum (Ott et al. 1994; Perley & Butler 2013). To mitigate the effects of any gain fluctuations, we switched the noise diode on and off at 25 Hz during all observations. With this approach, every other spectrum output by VEGAS was a measurement of the noise-diode spectrum. By comparing the noise-diode spectrum to the 3C295 spectrum, we calibrated the measured G107.2+5.20 spectra to the 3C295 calibration spectrum at every point in time during the observation session. To calibrate the noise diode into flux units, at the beginning and end of each observation session we pointed the antenna directly at 3C295 and collected data for two minutes. We then pointed 1° in R.A. away from 3C295 and collected two minutes of data. These on-source/off-source measurements yielded the desired calibration spectrum, which was measured relative to the background. Note that we assume that the on-source measurement includes a signal from 3C295 plus the unknown background, while the nearby off-source measurement includes only the background signal.

To measure the spectral flux density (SFD) of the AME region G107.2+5.2 and to inspect its morphology at different frequencies we compiled data from a range of observatories. A list of all the data sets used in our study is given in Table 2. Data-processing and unit conversions are required for each data set as described below.

For the radio observations we used the Canadian Galactic Plane Survey (CGPS) data (Taylor et al. 2003; Tung et al. 2017) at 408 MHz, as well as the Reich all sky survey at 1.420 GHz (Reich 1982; Reich & Reich 1986; Reich et al. 2001). The CGPS map was produced using Haslam data (Haslam et al. 1981, 1982; Remazeilles et al. 2015, 2016), which is widely used to trace synchrotron and optically thin free–free emission on 1° angular scales. The CGPS data⁵ have an arcminute resolution, which is useful for morphological comparisons. To convert from thermodynamic units to flux units we used the Rayleigh–Jeans approximation,

$$\begin{eqnarray}&&I=\displaystyle \frac{2{\nu }^{2}{k}_{B}}{{c}^{2}}{T}_{B}\times {{\rm{\Omega }}}_{p}\times {10}^{26},\end{eqnarray} \tag{ 1 }$$

where ν = 408 MHz for the CGPS data and 1.420 GHz for the Reich data, and Ω_p is the solid angle of a pixel in steradians. This conversion brings the maps into SFD units (Jy pixel⁻¹). The Reich data required a calibration correction factor of 1.55 to compensate for the full-beam to main-beam ratio, based on comparisons with bright calibrator sources (Reich & Reich 1988). We included an estimated 10% calibration uncertainty on all the radio data.

We used Planck observations for measurements between 30 and 857 GHz (Planck Collaboration et al. 2016b). To convert Planck data from K_CMB to spectral radiance we used the Planck unit conversion and color correction code available on the Planck Legacy Archive.⁶ Note that molecular CO lines have biased the 100 and 217 GHz Planck results, so these points are not included in the model fitting (see Section 4).

Far-infrared information was provided by IRIS (improved IRAS) and DIRBE data (Hauser et al. 1998; Miville-Deschênes & Lagache 2005). For our spectrum analysis we only used the DIRBE data up to 3 THz because of complexities from dust grain absorption and emission lines at higher frequencies. The IRIS data was used for morphological comparisons only (see the Appendix). We applied color corrections to the DIRBE data according to the DIRBE explanatory supplement (Hauser et al. 1998). For this analysis we did not use Haslam or WMAP (Bennett et al. 2013) data due to the low spatial resolutions of those data sets. However, we did check that our aperture photometry results using CGPS and Planck were consistent with the results using Haslam and WMAP.

Parts of the data sets are corrupted by radio frequency interference (RFI), transient signals, and instrumental artifacts. These spurious signals need to be removed before making maps. The transient signals and instrumental artifacts are excised by hand after inspection. To find RFI-corrupted spectral channels we search for high noise levels and non-Gaussianity using two statistics: the coefficient of variation and the spectral kurtosis (Nita & Gary 2010). The RFI removal techniques based on these statistics are described below.

The subscript ν denotes the frequency channel index and t denotes the time index. For example, ξ_ν,t is data in ADC counts in frequency channel ν at time t.

For each 5 minute data segment, we calculated the coefficient of variation in each spectral channel, which is the the inverse signal-to-noise ratio (NSR_ν). This statistic finds spectral channels with persistently high noise levels. We define the mean and the standard deviation in time per channel as

$$\begin{eqnarray}&&{\mu }_{\nu }=\langle {\xi }_{\nu ,t}{\rangle }_{t},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{\sigma }_{\nu }=\sqrt{{\langle {({\xi }_{\nu ,t}-{\mu }_{\nu })}^{2}\rangle }_{t}},\end{eqnarray} \tag{ 3 }$$

therefore

$$\begin{eqnarray}&&{\mathrm{NSR}}_{\nu }=\displaystyle \frac{{\sigma }_{\nu }}{{\mu }_{\nu }}.\end{eqnarray} \tag{ 4 }$$

We masked channels with NSR_ν greater than 7.5 times the median absolute deviation of the NSR_ν. We empirically chose this cutoff level because it corresponds to approximately 5σ and effectively detects outliers. In addition, we calculated the spectral kurtosis (or the fourth standardized moment),

$$\begin{eqnarray}&&{K}_{\nu }=\displaystyle \frac{{\langle {({\xi }_{\nu ,t}-{\mu }_{\nu })}^{4}\rangle }_{t}}{{\langle {({\xi }_{\nu ,t}-{\mu }_{\nu })}^{2}\rangle }_{t}^{2}}.\end{eqnarray} \tag{ 5 }$$

This statistic finds channels with non-Gaussian noise properties. Again, we mask spectral channels with K_ν greater than 7.5 times the median absolute deviation of K_ν.

Finally, we only used the selected bandwidth that is listed in Table 1 for each bank because at the spectral bank edges the band-pass filters in the receiver (see Figure 1) attenuate the sky signals and the gain is low. In total, for Banks A, B, and C in Session 5, 0.7% of the bandwidth-selected data was excised because of RFI contamination, 2% was excised because of transient signals, and 7% was excised because of instrumental artifacts. The signal-to-noise ratio (S/N) for Bank D was low so the data in this bank were ultimately unusable.

To convert the mapping data from ADC units to spectral radiance (Jy sr⁻¹), we first calibrate the noise diode using the point source 3C295 and then calibrate the mapping data using the noise diode (see Section 2.2). The point-source observations take place at the beginning and end of the observing sessions, and they allow us to convert the data to Janskys. The noise diode is flashed at 25 Hz during both the point source and the mapping observations, so the noise diode is used as a calibration signal to track gain stability. The assumptions are the noise-diode spectrum is stable in time and the gain is linear as a function of signal brightness over the observing session.

In this subsection, we now define x as calibration data while pointing away from 3C295 (off-source), y as calibration data while pointing at 3C295 (on-source), and z as mapping data, scanning G107.2+5.2. We use the superscripts on or off to denote whether the noise diode is on or off. For example, ${x}_{\nu ,t}^{\mathrm{on}}$ is off-source calibration data at time t for channel ν while the noise diode is on. We calculated the average noise diode level in a spectral channel as

$$\begin{eqnarray}&&{D}_{\nu }=\langle {x}_{\nu ,t}^{\mathrm{on}}-{x}_{\nu ,t}^{\mathrm{off}}{\rangle }_{t},\end{eqnarray} \tag{ 6 }$$

which has units of ADC counts. We computed the average source level in a spectral channel as

$$\begin{eqnarray}&&{S}_{\nu }=\langle {y}_{\nu ,t}^{\mathrm{off}}-{x}_{\nu ,t}^{\mathrm{off}}{\rangle }_{t},\end{eqnarray} \tag{ 7 }$$

which also has units of ADC counts. Both D_ν and S_ν were averaged over two minutes, which was the total duration of the point-source calibration observations. The noise-diode signal was calibrated using the known SFD of 3C295 (Perley & Butler 2013) in the following way:

$$\begin{eqnarray}&&{P}_{\nu }=\displaystyle \frac{{I}_{\nu }}{{S}_{\nu }}{D}_{\nu }.\end{eqnarray} \tag{ 8 }$$

Here, P_ν is the calibrated noise-diode signal in units of Janskys (see Figure 3) and I_ν is the SFD of 3C295. We then used P_ν to calibrate the mapping data z into Janskys.

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Let ${z}_{\nu ,t}^{\mathrm{on}}$ and ${z}_{\nu ,t}^{\mathrm{off}}$ be the mapping data at time t and frequency channel ν with the noise diode on and off, respectively. We calculated the inverse receiver gain

$$\begin{eqnarray}&&{G}_{\nu }=\displaystyle \frac{{P}_{\nu }}{\langle {z}_{\nu ,t}^{\mathrm{on}}-{z}_{\nu ,t}^{\mathrm{off}}{\rangle }_{t}},\end{eqnarray} \tag{ 9 }$$

which has units of Janskys per ADC count. G_ν was calculated for every 5 minute data segment. When making maps of diffuse sky signals we divide the data by the beam solid angle,

$$\begin{eqnarray}&&{{\rm{\Omega }}}_{\nu }=\displaystyle \frac{\pi }{4\mathrm{log}2}\,{\mathrm{FWHM}}_{\nu }^{2}.\end{eqnarray} \tag{ 10 }$$

Here, ${\mathrm{FWHM}}_{\nu }$ is the beam FWHM at the frequency channel ν and we assume a Gaussian beam profile. The FWHM values for the center frequencies of the four Banks are given in Table 1. The calibrated time-ordered mapping data were then calculated as

$$\begin{eqnarray}&&{d}_{t}={\left\langle \displaystyle \frac{{G}_{\nu }{z}_{\nu ,t}^{\mathrm{off}}}{{{\rm{\Omega }}}_{\nu }}\right\rangle }_{\nu },\end{eqnarray} \tag{ 11 }$$

which have units of spectral radiance (Jy sr⁻¹). The average is taken over the selected bandwidth in a given spectral bank (see Table 1) after data selection (see Section 3.1).

Variations in the gain and system temperature of a receiver result in a form of correlated noise that is often referred to as 1/f noise. To separate the sky signal from the 1/f noise we implemented a form of the destriping mapmaking method as described in Delabrouille (1998) and Sutton et al. (2009, 2010). The aim of the destriping mapmaking method is to solve for the 1/f noise in the time-ordered data as a series of linear offsets. To do this the time-ordered data from a receiver system is defined as

$$\begin{eqnarray}&&{\boldsymbol{d}}={\boldsymbol{P}}\,{\boldsymbol{m}}+{\boldsymbol{F}}\,{\boldsymbol{a}}+{{\boldsymbol{n}}}_{w},\end{eqnarray} \tag{ 12 }$$

where ${\boldsymbol{m}}$ is the map vector of the true sky signal, ${\boldsymbol{P}}$ is the pointing matrix that transforms pixel locations on the sky into time positions in the data stream, ${\boldsymbol{Fa}}$ describes the 1/f noise linear offsets, and ${{\boldsymbol{n}}}_{w}$ is the white noise vector. For our GBT data, the ${\boldsymbol{d}}$ is populated with d_t, which is the calibrated time-ordered data for a spectral bank given in Equation (11).

Solving for the amplitudes of the 1/f noise linear offsets (${\boldsymbol{a}}$) requires minimizing

$$\begin{eqnarray}&&{\chi }^{2}={({\boldsymbol{d}}-{\boldsymbol{P}}{\boldsymbol{m}}-{\boldsymbol{F}}{\boldsymbol{a}})}^{{\rm{T}}}{{\boldsymbol{N}}}^{-1}({\boldsymbol{d}}-{\boldsymbol{P}}\,{\boldsymbol{m}}-{\boldsymbol{F}}\,{\boldsymbol{a}}),\end{eqnarray} \tag{ 13 }$$

where N is a diagonal matrix describing the receiver white noise. By minimizing derivatives of Equation (13) with respect to the sky signal ${\boldsymbol{m}}$ and 1/f noise amplitude ${\boldsymbol{a}}$, it is possible to derive the following maximum-likelihood estimate for the amplitudes

$$\begin{eqnarray}&&\hat{{\boldsymbol{a}}}={({{\boldsymbol{F}}}^{{\rm{T}}}{{\boldsymbol{Z}}}^{{\rm{T}}}{{\boldsymbol{N}}}^{-1}{\boldsymbol{Z}}{\boldsymbol{F}})}^{-1}{{\boldsymbol{F}}}^{{\rm{T}}}\,{{\boldsymbol{Z}}}^{{\rm{T}}}\,{{\boldsymbol{N}}}^{-1}\,{\boldsymbol{Z}}\,{\boldsymbol{d}}.\end{eqnarray} \tag{ 14 }$$

Here, we have made the substitution

$$\begin{eqnarray}&&{\boldsymbol{Z}}={\boldsymbol{I}}-{\boldsymbol{P}}{({{\boldsymbol{P}}}^{{\rm{T}}}{{\boldsymbol{N}}}^{-1}{\boldsymbol{P}})}^{-1}{\boldsymbol{P}}\,{{\boldsymbol{N}}}^{-1}.\end{eqnarray} \tag{ 15 }$$

Once the 1/f noise amplitudes have been computed the, 1/f noise can be subtracted in the time domain, and the sky map becomes

$$\begin{eqnarray}&&\hat{{\boldsymbol{m}}}={({{\boldsymbol{P}}}^{{\rm{T}}}{{\boldsymbol{N}}}^{-1}{\boldsymbol{P}})}^{-1}{{\boldsymbol{P}}}^{{\rm{T}}}\,{{\boldsymbol{N}}}^{-1}({\boldsymbol{d}}-{\boldsymbol{F}}\,{\boldsymbol{a}}),\end{eqnarray} \tag{ 16 }$$

which is a noise-weighted histogram of the data.

For our GBT observations a linear offset length of 1 s was chosen, which removes 1/f noise on scales larger than 10'. The noise weights for each data point were calculated by subtracting neighboring pairs of data and taking the running rms within 2 s chunks of the auto-subtracted data. The destriped sky maps and the associated uncertainty-per-pixel maps for Bank A, B, and C are shown in Figure 4.

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We used aperture photometry (Planck Collaboration et al. 2014; Génova-Santos et al. 2017) to measure the SFD (Jy) of the AME region centered on G107.2+5.2. This analysis used 17 total maps including our GBT maps and maps from CGPS, Reich, Planck, and DIRBE (see Table 2). This aperture photometry procedure involves five key steps.

First, we removed a spatial gradient and smoothed all the maps in the study to a common resolution of 40' by convolving the maps with a two-dimensional Gaussian with

$$\begin{eqnarray}&&\mathrm{FWHM}=\sqrt{{({40}^{{\prime} })}^{2}-{{\rm{\Theta }}}^{2}},\end{eqnarray} \tag{ 17 }$$

where Θ is the beam FWHM of each data set. The common 40' resolution is set by DIRBE, which has the largest beam of all of the data sets used in this study. The beam sizes are given in Table 2.

Second, we integrated the spectral radiance over the solid angle of a map pixel Ω_p to convert the units to Jy pixel⁻¹. For our GBT maps,

$$\begin{eqnarray}&&{{\rm{\Omega }}}_{p}={s}_{p}^{2},\end{eqnarray} \tag{ 18 }$$

where s_p = 1' is the length of the side of each square pixel in the map.

Third, the map offsets needed to be subtracted because the aperture photometry technique references a common zero-point among all the maps. We determined this zero-point by calculating the median value of all the pixels in an annulus with an inner radius of 60' and an outer radius of 80' centered on G107.2+5.2. We found the results do not strongly depend on the precise annulus dimensions as long as it is away from the aperture and within the boundaries of our maps (see Figure 5).

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Fourth, we summed all the pixels inside a circular aperture with a radius of 45' centered on G107.2+5.2 to get the SFD of the AME region. The aperture radius we chose is well matched to the map resolution after smoothing.

Fifth, we estimated the uncertainty in the aperture SFD by computing the standard deviation of the pixel values in the annulus and propagating this uncertainty through to each pixel within the aperture. See Equations (4) and (5) in Génova-Santos et al. (2015). An additional systematic error for the GBT data was estimated using jackknife tests of the mapping data taken on different days. We found a 10% variation from this jackknife test and included this as a systematic uncertainty (see Table 3). A breakdown of the statistical and systematic uncertainty of the SFD measurements from our GBT maps is listed in Table 3.

The SFD values from all maps computed with this aperture photometry technique are listed in Table 2 and plotted in Figures 6 and 7. All of the maps and the smoothed versions of the maps are shown in Figures 10–12.

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4.1.1. Free–Free

4.1.2. Thermal Dust

4.1.3. CMB

4.1.4. Spinning Dust

4.1.5. Other

Our GBT maps show diffuse emission inside the photometry aperture, which extends out to approximately 45' away from G107.2+5.2 (see Figure 4). This diffuse emission spatially correlates very well visually with the high-resolution CGPS data at 408 MHz. Inside the photometry aperture we see the star-forming region S140, a diffuse cloud centered on G107.2+5.2 (hereafter the cloud), and one bright radio point source. Outside the photometry aperture, we also detected three additional bright radio point sources and several other point sources with low S/N.

The diffuse emission centered on G107.2+5.2 appears in all of the maps from 408 MHz up to 100 GHz. This seems to indicate that this emission is diffuse free–free and possibly AME near 30 GHz. Above 100 GHz, the diffuse signal in this region is faint when compared with the signal from S140. This seems to indicate that S140 contributes the majority of the thermal dust emission that appears in the measured spectrum. Since S140 appears all the way down to 408 MHz, this seems to indicate that it contains a range of signals because thermal dust emission should be negligible below 70 GHz and effectively zero below 10 GHz (see Figure 7).

The spectrum shows a clear deviation from a simple model consisting of only optically thin free–free emission and thermal dust emission near 30 GHz, indicating there is AME somewhere in the region defined by our photometry aperture. The AME could be either in S140 or in the cloud or both. Given the varied angular resolutions of all of the data in this study—in particular the coarse resolution at 28 GHz—it is difficult to say which case is correct. Our GBT measurements near 5 GHz suggest the signal from the cloud is predominantly optically thin free–free emission. Therefore, viable AME models must rapidly rise above approximately 5 GHz, peak near 30 GHz, and then remain sub dominant to thermal dust emission above 100 GHz. Models based on both the spinning dust signal and the UCH ii signal match this description. However, this new information puts a tighter constraint on the angular size and emission measure of viable UCH ii AME scenarios.

Fitting the combined model with the UCH ii AME component to the observed spectrum results in a best-fit emission measure of ${5.27}_{-1.5}^{+2.5}\times {10}^{8}\,{\mathrm{cm}}^{-6}\,\mathrm{pc}$ and an angular size of ${2.49}_{-0.44}^{+0.47}$ arcsec. Given that S140 is 910 pc away, the angular size from the fit corresponds to an H ii region with a physical extent of ${1.01}_{-0.20}^{+0.21}\times {10}^{-2}$ pc. Note that a UCH ii region of this size and emission measure might be better classified as a hyper-compact H ii region (Murphy et al. 2010). High-resolution, interferometric measurements of S140 at 15 GHz from AMI did indeed reveal a rising spectrum but did not conclusively resolve any UCH ii regions and the AMI collaboration concluded the AME signal is likely from spinning dust (Perrott et al. 2013). Our spectrum fit suggests that, if it is present, we have enough sensitivity to see the UCH ii signal in our GBT maps, however our maps do not conclusively show compact discrete sources in the the cloud. Therefore, if the AME signal is from UCH ii emission in the cloud, then it seems there must be multiple UCH ii sources that together look like the single diffuse region we detected.

The combined model with the spinning dust AME component also explains the AME excess. The best-fit model gives a spinning dust peak frequency of 30.9 ± 1.4 GHz, with a peak amplitude of ${15.2}_{-1.7}^{+1.8}$ Jy. Spinning dust should correlate well with thermal dust emission. The spinning dust AME signal could be from S140, where there is obviously a significant amount of thermal dust emission, or it could be from the cloud, or both. However, the Planck maps show that any thermal dust emission in the cloud is small. Therefore, if the AME is from spinning dust it seems likely that it is coming from S140. The resulting emission at 28 GHz is then both spinning dust emission emanating from around S140 and optically thin free–free emission from the diffuse cloud present at 28 GHz. The comparatively low angular resolution of the 28 GHz map results in the bright region over both S140 and the cloud as seen in Figure 10.

To estimate the relative goodness-of-fit between the two models we calculated the Akaike Information Criteria (Akaike 1974; AIC),

$$\begin{eqnarray}&&\mathrm{AIC}=2k-2\mathrm{ln}(\hat{{ \mathcal L }}),\end{eqnarray} \tag{ 19 }$$

where k is the number of model parameters (7 in both cases) and $\hat{{ \mathcal L }}$ is the maximum value of the likelihood function. The AIC is an estimate of information loss and is used to select between two models, but does not reveal information on the absolute quality of the models. We found for the spinning dust model AIC = 54 and for the UCH ii model AIC = 70. The AIC relative likelihood estimated that the UCH ii model is 0.04% as likely as the spinning dust model to minimize the information loss and therefore strongly favors the spinning dust model.