# Non-thermal Sunyaev-Zel'dovich effect

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Exactly what is the non-thermal Sunyaev-Zel'dovich effect? From what I understand from reading several papers by Mark Birkinshaw and Sergio Colafrancesco, I get the rough idea that the non-thermal SZ effect has something to do with it being in the relativistic realm.

Papers by Sergio Colafrancesco:

Review by Mark Birkinshaw:

The Sunyaev-Zel'dovich effect

To clarify, I'm not referring to the kinematic SZ effect.

There appears to be a distinction by the authors between the SZ effect due to hot thermal electrons and relativistic electrons. I find the nomenclature ambiguous, as temperature is essentially kinetic energy on a smaller scale, so why would relativistic electrons that have more kinetic energy be 'non-thermal'?

Lastly, is the key distinction between them using a relativistic vs. a non-relativistic formulation?

The non-thermal S-Z effect is caused by inverse Compton scattering of the CMB photons from a non-thermal population of electrons - i.e. electrons that have high energies not because they are hot, but because they have been accelerated non-thermally. The usual mechanisms are accelerating by electromagnetic fields and the Lorentz force.

The rest-mass energy of an electron is 0.511 keV. In order to attain "relativistic energies" then the electrons must have kinetic energies similar to this or higher. The average kinetic energy of a particle due to its temperature is just $$3k_{B}T/2$$. If we equate this to 0.511 keV then the temperature required to have thermal relativistic electrons is $$T > 4 imes 10^{6}$$ K.

Gas at this temperature does exist in the intracluster medium of massive galaxy clusters. But in addition there are populations of non-thermal electrons that are accelerated to relativistic speeds for instance in the jets and radio-emitting lobes of active galaxies.

The distinction is important when studying the S-Z effect because the energy distributions of thermal and non-thermal populations can be quite different. Non-thermal populations are usually characterised by a power-law, whilst thermal electrons have a Maxwell-Boltzmann distribution. This results in a different inverse Comptonisation spectrum from electrons of the two populations that are often (usually) spatially unresolved. The non-thermal S-Z effect is essentially a contaminant that needs to be accounted for when using the thermal S-Z effect to investigate the structure and parameters of the intracluster gas and using the S-Z effect as a cosmological probe.

## Title: Polarization of the Sunyaev-Zel'dovich effect: relativistic imprint of thermal and non-thermal plasma

Inverse Compton (IC) scattering of the anisotropic CMB fluctuations off cosmic electron plasmas generates a polarization of the associated Sunyaev-Zel'dovich (SZ) effect. The polarized SZ effect has important applications in cosmology and in astrophysics of galaxy clusters. However, this signal has been studied so far mostly in the non-relativistic regime which is valid only in the very low electron temperature limit for a thermal electron population and, as such, has limited astrophysical applications. Partial attempts to extend this calculation to the IC scattering of a thermal electron plasma in the relativistic regime have been done but these cannot be applied to a more general or mildly relativistic electron distribution. In this paper we derive a general form of the SZ effect polarization that is valid in the full relativistic approach for both thermal and non-thermal electron plasmas, as well as for a generic combination of various electron population which can be co-spatially distributed in the environments of galaxy clusters or radiogalaxy lobes. We derive the spectral shape of the Stokes parameters induced by the IC scattering of every CMB multipole for both thermal and non-thermal electron populations, focussing in particular on the CMB quadrupole and octupole that provide the largestmore » detectable signals in cosmic structures (like galaxy clusters). We found that the CMB quadrupole induced Stoke parameter Q is always positive with a maximum amplitude at a frequency ≈ 216 GHz which increases non-linearly with increasing cluster temperature. On the contrary, the CMB octupole induced Q spectrum shows a cross-over frequency which depends on the cluster electron temperature in a linear way, while it shows a non-linear dependence on the minimum momentum p of a non-thermal power-law spectrum as well as a linear dependence on the power-law spectral index of the non-thermal electron population. We discuss some of the possibilities to disentangle the quadrupole-induced Q spectrum from the octupole-induced one which will allow to measure these important cosmological quantities through the SZ effect polarization at different cluster locations in the universe. We finally apply our model to the Bullet cluster and derive the visibility windows of the total, quandrupole-induced and octupole-induced Stoke parameter Q in the frequency ranges accessible to SKA, ALMA, MILLIMETRON and CORE++ experiments. « less

## Title: IMPACT OF CLUSTER PHYSICS ON THE SUNYAEV-ZEL'DOVICH POWER SPECTRUM

We use an analytic model to investigate the theoretical uncertainty on the thermal Sunyaev-Zel'dovich (SZ) power spectrum due to astrophysical uncertainties in the thermal structure of the intracluster medium. Our model accounts for star formation and energy feedback (from supernovae and active galactic nuclei) as well as radially dependent non-thermal pressure support due to random gas motions, the latter calibrated by recent hydrodynamical simulations. We compare the model against X-ray observations of low-redshift clusters, finding excellent agreement with observed pressure profiles. Varying the levels of feedback and non-thermal pressure support can significantly change both the amplitude and shape of the thermal SZ power spectrum. Increasing the feedback suppresses power at small angular scales, shifting the peak of the power spectrum to lower l. On the other hand, increasing the non-thermal pressure support has the opposite effect, significantly reducing power at large angular scales. In general, including non-thermal pressure at the level measured in simulations has a large effect on the power spectrum, reducing the amplitude by 50% at angular scales of a few arcminutes compared to a model without a non-thermal component. Our results demonstrate that measurements of the shape of the power spectrum can reveal useful information on importantmore » physical processes in groups and clusters, especially at high redshift where there exists little observational data. Comparing with the recent South Pole Telescope measurements of the small-scale cosmic microwave background power spectrum, we find our model reduces the tension between the values of measured from the SZ power spectrum and from cluster abundances. « less

## 1 INTRODUCTION

Galaxy clusters, as the largest gravitationally bound structures in the Universe, are important probes of cosmology and astrophysics. These massive systems imprint their signature on the cosmic microwave background (CMB) through both the thermal Sunyaev-Zel'dovich (tSZ) effect – in which ≲1 per cent of CMB photons passing through the centre of a massive cluster inverse-Compton scatter off electrons in the hot, ionized intracluster gas (Sunyaev & Zeldovich 1970, 1972 Birkinshaw 1999 Carlstrom, Holder & Reese 2002) – as well as the kinematic SZ effect (kSZ) in which the bulk motion of clusters imparts a Doppler shift to the CMB signal (Sunyaev & Zeldovich 1972, 1980). The kinematic and thermal SZ effects can also be thought of as first- and second-order terms of the same physical process: the scattering of photons with a Planck distribution on moving electrons. The first-order kSZ effect shifts but does not distort the CMB blackbody spectrum, whereas the second-order tSZ imparts spectral distortions. Because the thermal electron velocities within the cluster are much larger than its bulk velocity, the second-order effect dominates here: for typical cluster masses and velocities, the amplitude of the kSZ effect is an order of magnitude smaller than its thermal counterpart (e.g. Birkinshaw 1999).

The tSZ effect has been well characterized, both through its contribution to the CMB temperature power spectrum (see e.g. Das et al. 2014 George et al. 2015), and via measurements on individual clusters (e.g. Plagge et al. 2010 Bonamente et al. 2012 Planck Collaboration V 2013 Sayers et al. 2013a). The kSZ signal, however, has proved to be more elusive, both because of its smaller amplitude and its spectrum identical to that of primary CMB temperature fluctuations. While challenging to measure, the kSZ effect has great potential for constraining both astrophysical and cosmological models (see e.g. Rephaeli & Lahav 1991 Haehnelt & Tegmark 1996 Diaferio et al. 2005 Bhattacharya & Kosowsky 2007, 2008). From an astrophysical point of view, the kSZ signal can be used to probe so-called missing baryons (e.g. Hernández-Monteagudo et al. 2015 Schaan et al. 2016) – i.e. those baryons that reside in diffuse, highly ionized intergalactic media (see e.g. McGaugh 2008). Conversely, peculiar velocities estimated from the kSZ effect, together with external constraints on cluster astrophysics, provide independent measurements of the amplitude and growth rate of density perturbations. The latter in turn can be used to test models of dark energy, modified gravity (Keisler & Schmidt 2013 Ma & Zhao 2014 Mueller et al. 2015b Bianchini & Silvestri 2016) and massive neutrinos (Mueller et al. 2015a).

The first detection of the kSZ signal was reported in (Hand et al. 2012, H12 henceforth), using high-resolution CMB data from the Atacama Cosmology Telescope (ACT Swetz et al. 2011) in conjunction with the Baryon Oscillation Spectroscopic Survey (BOSS) spectroscopic catalogue (Ahn et al. 2012). To isolate the kSZ signal, H12 applied a differential (or pairwise) statistical approach, which we also adopt in this paper. H12 rejected the null hypothesis of zero kSZ signal with a p value of 0.002. Subsequently, the Planck collaboration (Planck Collaboration XXXVII 2016) used the Central Galaxy Catalog derived from the Sloan Digital Sky Survey (Abazajian et al. 2009) to report 1.8–2.5σ evidence for the pairwise kSZ signal with a template fit. Other recent detections (∼3σ) of the kSZ signal have been obtained via cross-correlation of CMB maps with velocity fields reconstructed from galaxy density fields (Planck Collaboration XXXVII 2016 Schaan et al. 2016) see also Li et al. ( 2014) for a demonstration of this method using simulations. Indirect evidence for a kSZ component in the CMB power spectrum was also seen in power spectrum measurements from the South Pole Telescope (SPT George et al. 2015). Lastly, the kSZ signal has been measured locally for one individual cluster by Sayers et al. ( 2013b).

In this work, we measure the pairwise kSZ signal by combining a catalogue of galaxy clusters derived from the Dark Energy Survey (DES The Dark Energy Survey Collaboration 2005, Dark Energy Survey Collaboration et al. 2016) Year 1 data with a CMB temperature map from the 2500 deg 2 South Pole Telescope Sunyaev-Zel'dovich (SPT-SZ) Survey. Our paper is organized as follows: in Section 2 we briefly review the kSZ effect and the theory of pairwise velocities, and derive an analytic template for the pairwise kSZ effect. Section 3 introduces the two input data sets from DES and SPT and in Section 4 we detail the analysis methods. In Section 5, we briefly describe the new suite of realistic high-resolution kSZ simulations by Flender et al. ( 2016) and validate the pairwise kSZ template and the analysis methods on these simulations. We proceed by showing our main results and comparing them both to analytic theory and the expectation from simulations in Section 6. The various checks and different null tests that we perform to demonstrate the robustness of our results against systematic uncertainties are described in Section 7. Finally, we discuss the implications of our detection for cluster astrophysics in Section 8.

Unless otherwise specified, we use the Planck 2015 TT+TE+EE+lowP cosmological parameters, i.e. the Hubble parameter H0 = 67.3 km s −1 Mpc −1 , cold dark matter density Ωch 2 = 0.1198, baryon density Ωbh 2 = 0.022 25, current root mean square (rms) of the linear matter fluctuations on scales of 8 h −1 Mpc, σ8 = 0.831, and spectral index of the primordial scalar fluctuations ns = 0.9645 (Planck Collaboration XIII 2015), to compute theoretical predictions and to translate redshifts into distances.

## First Science from Planck

It’s been quite a long wait for results to emerge from the Planck satellite, which was launched in May 2009, but today the first science results have at last been released. These aren’t to do with the cosmological aspects of the mission – those will have to wait another two years – but things we cosmologists tend to think of as “foregrounds”, although they are of great astrophysical interest in themselves.

For an overview, with lots of pretty pictures, see the European Space Agency’s Planck site and the UK Planck outreach site you can also watch this morning’s press briefing in full here.

A repository of all 25 science papers can be found here and there’ll no doubt be a deluge of them on the arXiv tomorrow.

A few of my Cardiff colleagues are currently in Paris living it up at the junket working hard at the serious scientific conference at which these results are being discussed. I, on the other hand, not being one of the in-crowd, am back here in Cardiff, only have a short window in between meetings, project vivas and postgraduate lectures to comment on the new data. I’m also sure there’ll be a huge amount of interest in the professional media and in the blogosphere for some time to come. I’ll therefore just mention a couple of things that struck me immediately as I went quickly through the papers while I was eating my sandwich the following was cobbled together from the associated ESA press release.

The first concerns the so-called ‘anomalous microwave emission’ (aka Foreground X) , which is a diffuse glow most strongly associated with the dense, dusty regions of our Galaxy. Its origin has been a puzzle for decades, but data collected by Planck seem to confirm the theory that it comes from rapidly spinning dust grains. Identifying the source of this emission will help Planck scientists remove foreground contamination which much greater precision, enabling them to construct much cleaner maps of the cosmic microwave background and thus, among other things, perhaps clarify the nature of the various apparent anomalies present in current cosmological data sets.

Here’s a nice composite image of a region of anomalous emission, alongside individual maps derived from low-frequency radio observations as well as two of the Planck channels (left).

Credits: ESA/Planck Collaboration

The colour composite of the Rho Ophiuchus molecular cloud highlights the correlation between the anomalous microwave emission, most likely due to miniature spinning dust grains observed at 30 GHz (shown here in red), and the thermal dust emission, observed at 857 GHz (shown here in green). The complex structure of knots and filaments, visible in this cloud of gas and dust, represents striking evidence for the ongoing processes of star formation. The composite image (right) is based on three individual maps (left) taken at 0.4 GHz from Haslam et al. (1982) and at 30 GHz and 857 GHz by Planck, respectively. The size of the image is about 5 degrees on a side, which is about 10 times the apparent diameter of the full Moon.

The second of the many other exciting results presented today that I wanted to mention is a release of new data on clusters of galaxies – the largest structures in the Universe, each containing hundreds or even thousands of galaxies. Owing to the Sunyaev-Zel’dovich Effect these show up in the Planck data as compact regions of lower temperature in the cosmic microwave background. By surveying the whole sky, Planck stands the best chance of finding the most massive examples of these clusters. They are rare and their number is a sensitive probe of the kind of Universe we live in, how fast it is expanding, and how much matter it contains.

Credits: ESA/Planck Collaboration XMM-Newton image: ESA

This image shows one of the newly discovered superclusters of galaxies, PLCK G214.6+37.0, detected by Planck and confirmed by XMM-Newton. This is the first supercluster to be discovered through its Sunyaev-Zel’dovich effect. The effect is the name for the cluster’s silhouette against the cosmic microwave background radiation. Combined with other observations, the Sunyaev-Zel’dovich effect allows astronomers to measure properties such as the temperature and density of the cluster’s hot gas where the galaxies are embedded. The right panel shows the X-ray image of the supercluster obtained with XMM-Newton, which reveals that three galaxy clusters comprise this supercluster. The bright orange blob in the left panel shows the Sunyaev-Zel’dovich image of the supercluster, obtained by Planck. The X-ray contours are also superimposed on the Planck image.

UPDATES: For other early perspectives on the early release results, see the blogs of Andrew Jaffe and Stuart Lowe as usual, Jonathan Amos has done a very quick and well-written news piece for the BBC.

## Non-thermal Sunyaev-Zel'dovich effect - Astronomy

We discuss non-Gaussian effects associated with the local large-scale structure contributions to the cosmic microwave background (CMB) anisotropies through the thermal Sunyaev-Zel’dovich (SZ) effect. The non-Gaussianities associated with the SZ effect arise from the existence of a significant four-point correlation function in large scale pressure fluctuations. Using the pressure trispectrum calculated under the recently popular halo model, we discuss the full covariance of the SZ thermal power spectrum. We use this full covariance matrix to study the astrophysical uses of the SZ effect and discuss the extent to which gas properties can be derived from a measurement of the SZ power spectrum. With the SZ thermal effect separated in temperature fluctuations using its frequency information, the kinetic SZ effect, also known as the Ostriker-Vishniac effect, is expected to dominate the CMB temperature fluctuations at small angular scales. This effect arises from the baryon modulation of the first order Doppler effect resulting from the relative motion of scatterers. The presence of the SZ kinetic effect can be determined through a cross-correlation between the SZ thermal and a CMB map at small scales. Since the SZ kinetic effect is second order, however, contributions to such a cross-correlation arise to lower order in the form of a three-point correlation function, or a bispectrum in Fourier space. We suggest an additional statistic that can be used to study the correlation between pressure traced by the SZ thermal effect and the baryons traced by the SZ kinetic effect involving the cross-power spectrum constructed through squared temperatures instead of the usual temperature itself. Through a signal-to-noise calculation, we show that future small angular scale multifrequency CMB experiments, sensitive to multipoles of a few thousand, will be able to measure the cross-correlation of SZ thermal and SZ kinetic effects through a temperature squared power spectrum.

#### Authors & Affiliations

• * Present address: Division of Physics, Mathematics and Astronomy, California Institute of Technology, MS 130-33, Pasadena, California 91125. Email address: [email protected]

#### References (Subscription Required)

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Figure 9 SZE-determined distances versus redshift. The theoretical angular diameter distance relation is plotted for three different cosmologies, assuming H0 = 60 km s −1 Mpc −1 . ΩM = 0.3, ΩΛ = 0.7 (solid line), ΩM = 0.3, ΩΛ = 0 (dashed line), and ΩM = 1.0, ΩΛ = 0 (dot-dashed line). The clusters are beginning to trace out the angular diameter distance relation. References: (1) Reese et al. 2002 (2) Pointecouteau et al. 2001 (3) Mauskopf et al. 2000a (4) Reese et al. 2000 (5) Patel et al. 2000 (6) Grainge et al. 2000 (7) Saunders et al. 2000 (8) Andreani et al. 1999 (9) Komatsu et al. 1999 (10) Mason et al. 2001, Mason 1999, Myers et al. 1997 (11) Lamarre et al. 1998 (12) Tsuboi et al. 1998 (13) Hughes & Birkinshaw 1998 (14) Holzapfel et al. 1997 (15) Birkinshaw & Hughes 1994 (16) Birkinshaw et al. 1991.

Figure 10 Limits on ΩM from SZE-measured cluster gas fractions (Grego et al. 2001). Upper limit on the total matter density, ΩM ≤ ΩB/(fB h70) (solid line) and its associated 68% confidence region (dotted lines) as a function of cosmology with ΩΛ ≡ 1 − ΩM. The intercept between the upper dotted line and the dashed line ΩM = ΩB/(fB h70) gives the upper limit to ΩM at 68% confidence. The dot-dashed line shows the total matter density when the baryon fraction includes an estimate of the contribution from baryons in galaxies and those lost during cluster formation. The intercept of the dot-dashed line and the dashed line gives the best estimate of ΩM ∼ 0.25, assuming a flat universe with h = 0.7.

## Abstract

AbstractThe Sunyaev-Zel'dovich effect (SZE) provides a unique way to map the large-scale structure of the universe as traced by massive clusters of galaxies. As a spectral distortion of the cosmic microwave background, the SZE is insensitive to the redshift of the galaxy cluster, making it well-suited for studies of clusters at all redshifts, and especially at reasonably high redshifts (z > 1) where the abundance of clusters is critically dependent on the underlying cosmology. Recent high signal-to-noise detections of the SZE have enabled interesting constraints on the Hubble constant and on the matter density of the universe using small samples of galaxy clusters. Upcoming SZE surveys are expected to find hundreds to thousands of new galaxy clusters, with a mass selection function that is remarkably uniform with redshift. In this review we provide an overview of the SZE and its use for cosmological studies, with emphasis on the cosmology that can, in principle, be extracted from SZE survey yields. We discuss the observational and theoretical challenges that must be met before precise cosmological constraints can be extracted from the survey yields.

## The First-Ever Detection of the Kinematic Sunyaev-Zel’dovich Effect

Title: Detection of Galaxy Cluster Motions with the Kinematic Sunyaev-Zel’dovich E ffect
Authors: Nick Hand, the Atacama Cosmology Telescope, and the Baryon Oscillation Spectroscopic Survey (58 co-authors)
First Author’s Institution: Department of Astronomy, University of California Berkeley

Today I have the privilege of presenting to you a paper that not only describes the first detection of a cosmic effect that was theorized some forty years ago (as if that wasn’t enough), but was also first-authored by one of Astrobites’s very own: Nick Hand. Nick first began this work, which describes the first detection of the motion of distant galaxy clusters via the kinematic Sunyaev-Zel’dovich effect, as part of his senior thesis at Princeton University.

OK, so now that I’ve given away the punch line, let’s take a few steps back. What in the world is the kinematic Sunyaev-Zel’dovich effect? You may have guessed from the word “kinematic” that motion is somehow involved. However, if you faltered at that point, never fear, the name of the effect isn’t meant to be incredibly informative. Rashid Sunyaev and Yakov Zel’dovich are/were brilliant theorists who in the late sixties/early seventies decided to tackle a specific scientific question: what happens to Cosmic Microwave Background photons when they pass through a massive galaxy cluster on their way to Earth?

The CMB (left) and solar (right) spectra. In comparison, the CMB is MUCH closer to a perfect blackbody.

As you may recall, the Cosmic Microwave Background (CMB) is the remnant of the radiation which was released when the hydrogen in the Universe first became neutral (known as “recombination“) some 13.7 billion years ago (only about 300,000 years after the big bang!). Although initially very hot, this radiation has cooled though cosmic time, such that we now observe it to be a nearly uniform blackbody at a temperature of 2.7 Kelvin. And when I say nearly uniform, I mean it. In introductory level astrophysics courses we often like to say the spectrum of the Sun is essentially a blackbody. However, the CMB puts the Sun – or any other star – to shame (see Figure 1): the Planck satellite measured the CMB to be a uniform blackbody to one part in 100,000. It really is the closest thing to a perfect blackbody astronomers have ever observed.

However, nothing is truly perfect there are anisotropies in the CMB (places where it is distinctly not uniform), and these anisotropies can tell us quite a bit about the Universe. Perhaps the most well known anisotropies in the CMB are those on a relatively large scale (first mapped in detail by WMAP), which are caused by effects such as the size of the horizon at the time of recombination, and matter density fluctuations in the early Universe. However, these are not the ONLY anisotropies present in the CMB, which finally brings us back to Sunyaev and Zel’dovich. It turns out that when CMB photons pass through a large galaxy cluster on their way to Earth the result is that the CMB radiation field is distorted in the direction of the cluster.

Figure 2: Example of how the various SZ change the spectra of the CMB. Black Dashed line: the orginalCMB black body, scaled down by a factor of 0.0005. Blue line: the thermal effect. You can see it shifts photons from low to high frequency. Red Line: The kinematic effect (much smaller).

In most contexts when you hear the term “Sunyaev-Zel’dovich effect” (for instance this, this and this astrobite) the authors are specifically referring to the “thermal” Sunyaev-Zel’dovich effect. In this case, CMB photons are Compton scattered off of hot (hence, thermal) electrons in the center of the galaxy cluster. The result of this process is to “shift” some of the CMB photons from lower frequencies to higher frequencies, and the effect was first detected in the 1980s. However, around the same time Sunyaev and Zel’dovich also predicted another effect: if the galaxy cluster were moving (with respect to the rest frame of the CMB) then this bulk motion would also cause scatterings of CMB photons. In this case, the entire blackbody curve is shifted such that the temperature of the CMB appears different in the direction of the cluster. THIS is the kinematic Sunyaev-Zel’dovitch effect, essentially just the Doppler shift of the photon frequency, caused by the motion of the cluster. The magnitude of the effect is proportional to both the line-of-sight velocity and mass of electrons in the galaxy. Unfortunately, for a large galaxy cluster, the kinematic SZ effect is predicted to be on the order of 20 times weaker than the thermal SZ effect (which is already relatively small – see Figure 2). Thus, when looking at individual galaxy clusters, scientists have thus far only been able to put upper limits on the distortions due to the kinematic SZ effect, simply due to the difficulty of observing such a weak signal.

So how did the authors get around this? They did something which is quite simple in concept, but also ingenious (and certainly not simple in application): they stopped trying to look at individual galaxy clusters. Instead, the authors combined information for literally thousands of clusters by utilizing information from two large survey telescopes: the Baryon Oscillation Spectroscopic Survey (BOSS, part of the Sloan Digital Sky Survey III) and the Atacama Cosmology Telescope (ACT). BOSS has mapped the three-dimensional locations of hundreds of thousands of ‘luminous galaxies’, which are known to often be found in massive galaxy clusters. Thus, the BOSS data set provides the locations of potentially thousands of massive galaxy clusters. The authors have selected the 7,500 brightest of these galaxies that fall within the ACT data region. They then went to the data from ACT (which maps the CMB at several microwave frequencies), stacked and averaged the data in the direction of the galaxies selected from BOSS in a particular way and were able to detect a non-negligible temperature shift in the region around the brightest galaxy clusters compared to the background. However, this shift is due to the thermal SZ effect, which is always negative for the frequencies at which the ACT data was taken. This cannot be done for the kinematic SZ effect, however, because the sign of the distortion depends on the on the sign of the peculiar velocity of the galaxy cluster, and galaxy clusters are just as likely to be moving towards us as away from us. Hence, when directly averaging together the signal from thousands of galaxies, the signal from the kinematic SZ effect goes to zero.

So what do the authors do instead? One of the real advantages of the kinematic Sunyaev-Zel’dovich effect is that it depends on the peculiar velocity of a galaxy cluster (i.e., it does NOT depend on the velocity of the cluster due to the expansion of the universe), and thus should offer us information on gravitational forces pulling on the clusters (which relates to the formation of structure in the universe). To assess this, the authors computed something referred to as the mean pairwise momentum of their set of 7500 galaxy clusters. This is essentially a measurement of how much, on average, galaxy clusters are moving either towards or away from one other. If all of the galaxy clusters have truly random peculiar motions, this value should be zero. However, from our current theories of structure formation and gravity, we expect massive galaxy clusters to be moving towards one another, on average.

Figure 3: Results showing the motion of galaxies via the kinematic SZ effect (see text)

Figure 3 shows the results from this analysis. The top panel shows the mean pairwise momentum calculated from this data set (red) as a function of comoving separation (i.e., neglecting the expansion of the universe) of the galaxy clusters, and the expected values based on numerical simulations (bold black line). The red points clearly deviate from zero, at a statistically significant level of 3.8 sigma. The bottom panel shows the results for the same analysis, applied to random positions in the ACT map as opposed to the known locations of galaxy clusters. The fact that these points do essentially average to zero gives added credence to the idea that the signal shown in the top panel is real. Thus, this represents the first detection of the motion of galaxy clusters via the kinematic Sunyaev-Zel’dovich effect.

This discovery truly is a very important first step in opening up a new means of investigation in physical cosmology. Once it is possible to make more precise measurements of the kinematic S-Z effect, the velocity information it provides will be able to give us additional constraints on the various gravitational forces acting on structures in the universe, such as dark matter and dark energy.

If you are interested in a more technical description of the kinematic S-Z effect, check out this link. (Also have a look at the press release put out by Princeton University here).