How Polarized is Anomalous Microwave Emission?

Blog post written by Daniel Herman

 

Properly characterizing Galactic emission is vital to the future of Cosmic Microwave Background (CMB) science. Though synchrotron and thermal dust emission usually take front stage in polarization, anomalous microwave emission (AME) certainly cannot be discounted as a potential contaminant. Such an assumption could complicate future and current CMB studies. A preprint of this work can be found here.

Polarized emission within the Planck and WMAP frequency ranges. An AME spectrum that is 1 % polarized is also included.

Since the Penzias and Wilson experiment in the 1960s discovering the Cosmic Microwave Background (wiki page), cosmologists have been looking to make more detailed observations to reveal the secrets of the early universe. This led to a multitude of ground-based experiments (BICEP,  POLARBEAR, ACT, etc.), a handful of balloon experiments (BOOMERanG, SPIDER, etc.), and a series of satellite experiments (COBE, WMAP, Planck). As the observations became more and more sensitive, it became obvious that Galactic emission obscured our view of the primordial light, limiting the amount of cosmological information we could extract.

For many astrophysicists, this is a double-edged sword. This Galactic emission obscures our view of the early universe, but this also means that microwave observations contain a wealth of information about the interstellar medium, the dust, gas and magnetic fields in the Milky Way. Much of the emission detected by these experiments was expected from previous knowledge - dust grains warm up due to starlight, causing them to emit thermally in the microwave through the infrared - ionized gases cause free-free (Bremsstrahlung) emission - electrons trapped in magnetic fields cause synchrotron radiation. However, analysis of the COBE-DMR data led to a serendipitous discovery. There was a component of emission, lying in the 10-60 GHz range, that was not expected to be there. This caused astronomers to adopt the purely descriptive name anomalous microwave emission, often referred to simply as AME. Early analysis indicated that AME shared the morphology of the thermal dust emission in the 70-1000 GHz range. Astrophysicists theorized what could cause this anomalous component, and to date the most favored theory is that this emission is caused by tiny (<~1nm) dust grains spinning at a rate of billions of times per second, causing electric dipole emission. Again, this theory has a clear descriptive title - the spinning dust model.

Astrophysicists concerned about the nature of the interstellar medium have continued to investigate the predicted behaviors of such a model - what size would the dust have to be to spin so fast - what is its composition - what does the emission look like in different  environments - and importantly for today, how polarized do we expect this emission to be?

Modern measurements of the Cosmic Microwave Background are concerned with a multitude of fascinating phenomena, one of the most prominent being the detection of B-modes. B-modes are a type of polarization signature on the sky, and the detection of B-modes in the Cosmic Microwave Background would tell us about the nature of inflation - the theorized rapid expansion of the early universe. As such, it is vital that we are able to properly characterize the different emission mechanisms caused by our Galaxy in polarization. Having insufficient knowledge of polarized Galactic emission can give us a seriously misinformed view of the polarized signatures given to use by the early universe. Here enters AME. AME is expected to be polarized to a very low degree. However, studies have shown that if AME is polarized only at a 1% level, it can bias our estimates of the cosmological B-modes for current and future studies.

The Cosmic Microwave Background as derived by the BeyondPlanck analysis

The solution here seems easy! We have an idea of what the AME spectrum looks like given our measurements in total intensity. Let's just check to see how much polarized emission we see matching that spectrum. Things aren't so simple for a few reasons. First, it isn't clear how well we actually know the AME spectrum, especially over the full sky. Ali-Haïmoud et al. shows that we can have all sorts of different spectra for spinning dust in different environments. Second, if this emission is polarized, we do not expect it to be very polarized at all, meaning this signal we want to detect is very weak. Finally, we have our biggest obstacle. Polarized dust emission and polarized synchrotron emission look a lot like each other on the sky. This means it's difficult to distinguish between the two types of emission when solving our equations.

 

Polarized Dust Map
Map of polarized thermal dust emission from the Planck satellite.

 

Map of Polarized Synchrotron Emission
Map of polarized synchrotron emission from the Planck and WMAP satellites

In order to get what we really want here, an estimate of how polarized this AME might be, we mix a general approach called Gibbs sampling, with a novel approach which we'll describe in a second. Gibbs sampling is a sampling algorithm in which we solve a complex model by solving for each part of the model one step at a time. The goal of Gibbs sampling is to explore all possible solutions for our model parameters, allowing us to see not only what our best solution is, but also our uncertainty in that solution.

In this instance we have three things we want to solve for - what does the synchrotron emission (\(A_S\)) look like morphologically? How does that emission change as a function of frequency (\(\beta_S\))? And finally, how much dust-like emission (\(A_{\mathrm{AME}}\)) is there at each frequency ? Using Gibbs sampling we would solve for \(A_S\) (given some values for \(\beta_S \) and \(A_{\mathrm{AME}}\)), then \(\beta_S \) (given \(A_S\) and \(A_{\mathrm{AME}}\)), and finally \(A_{\mathrm{AME}}\) (given \(A_S\) and \(\beta_S \)). We then go back to the first step and repeat! This method is very effective in general, but when two of the quantities we're solving for are hard to distinguish from one another, this method slows down, becoming less efficient.

This is where our novel approach comes into play. In our Gibbs sampling scheme, we adjust our equations to solve for both \(A_S\) and \(A_{\mathrm{AME}}\) at the same time. This allows us to explore the distribution of the AME and synchrotron more efficiently. 

25 samples of the sky components \(A_S\) and \(A_{\mathrm{AME}}\) in the Stokes polarization parameters \(Q\) and \(U\).

Additionally, fitting for \(\beta_S \) is not a trivial venture. The data we currently have access to does not do a fantastic job at constraining the value of this parameter, as is the topic of another BeyondPlanck study (BeyondPlanck XIV). Because of this we need to inform our fit by instituting a prior. A prior is a distribution of values which are used to bring in external/previous information to help us make a better fit. A repetition of our analysis is done for a suite of priors, as we will see later.

A small, but important note here. Seeing as we don't know if AME is actually polarized, we don't know how it looks on the sky in polarization. Here we assume that polarized AME has the exact same morphology as polarized thermal dust emission. Going all the way back to the discovery of AME, and the first spinning dust models, we see that this assumption is well motivated (Draine & Lazarian 1998). With polarized thermal dust emission as a template, we just fit a single value for \(A_{\mathrm{AME}}\) at each observational frequency.

In this work, we make our model fit to each of the WMAP and Planck observations in the 20-70 GHz range, as this is exactly where we expect to be able to detect AME. Instead of using previously published Planck sky maps in our frequency range, we utilize brand new data products from the BeyondPlanck collaboration (beyondplanck.science). BeyondPlanck takes a Gibbs sampling approach to creating sky maps of the Planck Low Frequency Instrument data maps, taking into account uncertainties in a whole host of instrumental systematics. With BeyondPlanck, we have many different realizations of what we think the Planck instrument actually observed. These different realizations are used here, allowing us to take uncertainties in the instrument into account when estimating the amount of polarized AME in the Galaxy. This is an exciting new approach to Galactic emission modelling in the microwave sky.

Now that we have fit our data model, we have to answer our main questions: Is AME polarized? If so, how polarized? What is the uncertainty in our results?

We take results of the AME spectrum from earlier full sky analysis in total sky intensity (Planck 2015 X) as a frequency template to compare to. With this, we create some mock spectra - how strong would this emission be if the AME is 1 % polarized? 2 % polarized? 5 % polarized?

 

Potential AME polarization spectra, and the results of our \(A_{\mathrm{AME}}\) fit

By creating potential polarized AME spectra, we can again make more fits! We can fit the results of our analysis to these spectra to determine what the most likely polarization fraction is, and how confident we are in our result. This fit will give us an answer in terms of a distribution, called the posterior. As we talked about earlier, we had to institute a prior for \(\beta_S\), and as it turns out, our results vary depending on our prior, as we see here!

Results of our polarization fraction distribution (y-axis) as a function of the prior (x-axis).

Overall, we have clearly constrained the polarization fraction to under 3.5% regardless of our prior on \(\beta_S\). We also see that for most of our prior range, the polarization fraction of AME is below about 0.6 %. As \(\beta_S\) goes closer to zero, we see a slight polarization fraction, and if we use \(\beta_S \)=-3.0, AME looks like it is polarized at about the 2.5 % level, and clearly polarized within in the confidence interval (CI). 

How does this tie into our two areas of interest, namely the CMB polarization, and the dust physics? The big take away here is that we can confidently say that with our current data we cannot make any tighter constraints on how polarized AME is. An exciting conclusion is that even though we cannot set super tight constraints, our results agree with the theory of spinning dust emission - if the emission is polarized, it's not very strong. However, we will need better data to help constrain this even further for future CMB analysis. New data on the horizon will help clear up this picture, hopefully making us more confident about our ability to clean up microwave data sets from our polarized Galaxy.

 

 

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Thanks for reading! If you're interested in reading the preprint of this work, you can find the paper here. A huge thanks to Jeff Wilkerson for catalyzing my interest in astronomy, Brandon Hensley for the multi-layered support and motivation, Ingunn Wehus  and Hans Kristian Eriksen for pushing me to take on this project, and take the path of greatest resistance to learn the most I could, and Duncan Watts and Eirik Gjerløw for helping me debug and problem solve my way to resolution. Work like this does not happen in a closed box.

By Daniel Herman
Published Jan. 31, 2022 2:36 PM - Last modified Jan. 31, 2022 3:12 PM