By Ken Van Tilburg and Tim Wiser

Indirect searches for dark matter look for high-energy photons from either decays  or collisions of dark matter particles in astrophysical locations.  If such signals are ever confirmed, they may be the first to shed light (so to speak!) on the possible nongravitational interactions and properties of dark matter.  Over the past few years, several anomalies have appeared in the data collected by experiments searching for these kinds of signals.  However, no conclusive signal of dark matter has yet emerged, partially because there are not many other experimental “handles” to confirm the source of the signal, besides the observed photon energy spectrum, and there is always a danger that instrumental or astrophysical backgrounds are underestimated in the observed spectrum.  

In an effort to get beyond these limitations, in the recent arXiv preprint “Towards a Bullet-proof test for indirect signals of dark matter” we and our collaborators propose powerful and robust methods using spatial information based on gravitational lensing maps of merging galaxy clusters to test observed photon excesses for a dark matter origin.

The Long-Elusive Dark Matter

Scientists have long been convinced that the majority of the matter in our universe is some sort of “stuff” that no human, telescope, or detector has ever directly observed (e.g. through seeing it interact with normal matter, or emit photons).  But we are very sure this “dark matter” must be real: there is a vast amount of evidence for its existence through its gravitational effects on astrophysical and cosmological scales, and that there is about six times as much of it by mass as there is of the normal matter which we are composed of and interact with continuously.  

One spectacular piece of evidence that lent strong credence to the idea that most of the matter in our universe is composed of dark matter came from observations of the “Bullet Cluster” in 2006 (which was discussed by Marusa Bradac in this recent KIPAC blogpost).  In this system, two massive clusters of galaxies are in the process of colliding, with some components of them passing through one another.  This leads to the bulk of the gravitating matter being physically separated from the visible matter - which in these systems is primarily the “intracluster medium”: the hot but tenuous gas between the galaxies in these big conglomerations.  This feature was discovered by comparing gravitational lensing maps with X-ray observations, which are both seen in the figure below.

Above is shown the mass distribution (contours) measured by weak gravitational lensing and the glowing intracluster medium (colors) measured by X-ray emission, in the Bullet Cluster. The separation of the mass (which is primarily dark matter) from the intracluster medium (most of the normal matter) provides a way to distinguish possible signals of dark matter from astrophysical backgrounds.

Since the first discovery of the clear separation of mass peaks in the Bullet Cluster, evidence of merging events has been found in many more clusters, including the nearby Coma Cluster (shown above, with colors and contours representing the same as in the Bullet Cluster figure).

Seeing the Light: searching for nongravitational signals of dark matter

The hunt for the nongravitational interactions of dark matter is one of the most important experimental endeavors in experimental physics, since a positive detection would uncover many properties (such as mass, interaction strength, velocity and density distributions in our galaxy, and more) of the particles that make up the large majority of the mass in our Universe. Previous posts in this blog have discussed some of the experiments in the “direct detection” class that have participation from researchers at KIPAC, e.g. here in xenon and here in silicon and germanium.  

A wholly different class of experiments, which are collectively known as “indirect detection” experiments, search for high-energy photons produced in decays or annihilations of the dark matter particles.  Some of the most sensitive indirect detection experiments aim to detect high-energy photons (X-rays and gamma rays) coming from the center of our Milky Way Galaxy, from nearby “dwarf spheroidal” galaxies, or from galaxy clusters. In this effort, the experimental challenge is to tease out small, unaccounted-for photon excesses from other astrophysical and instrumental backgrounds.  To confirm an excess as evidence of dark matter, one has to be absolutely sure all backgrounds are taken into account correctly.  Generally speaking, this is exceedingly difficult.

How to test an indirect photon signal for a dark matter origin

When does a positive signal constitute a dark matter discovery?  In our recent paper, we show that one can construct a robust statistical test of a potential X-ray or gamma ray signal by observing a merging galaxy cluster, and rule out or provide stronger evidence for a dark matter explanation of its origin with high statistical significance.  Going back to the above picture of the Bullet Cluster, we exploit the expected difference in spatial distributions of the dark matter (the signal) and the hot intracluster medium (which is usually the main background, as this hot gas emits in the X-ray band).  If an excess is a true signal, the additional photons will be spatially correlated with the DM distribution and not with the spatial distribution of the main background source. The key feature of our proposal is the fact that both alternatives have spatial distributions which have been measured - the dark matter distribution by gravitational lensing, and the intracluster medium by its X-ray emission.

One possible application: testing the “3.55 keV line”

One concrete example where merging galaxy clusters can help identify dark matter is the so-called “3.55 keV line,” a recently discovered excess of X-rays seen in many sources, including galaxy clusters. The excess has been confirmed by multiple groups in observations of multiple sources, e.g. here, here, and here, but it remains to be seen if it is truly a signal of dark matter. It might be a sign of one type of dark matter, a “sterile neutrino,” as it decays into a regular neutrino and an X-ray photon, or it could be a normal X-ray emission line from the intracluster medium that is stronger than expected as argued here.

We advocate searching for the 3.55 keV line in a merging cluster, where the dark matter and intracluster medium are in different places. Unfortunately, the Bullet Cluster is just too far away to see the 3.55 keV line - even if it is being emitted, it would be too dim for us to observe.Fortunately, recent gravitational lensing studies of one of our nearest cosmic “neighbors,”  the Coma Cluster, have revealed that it is undergoing a merger event of its own. Of course “neighborliness” is relative, as Coma is about 330 million light years away (!), but still, Coma is over ten times closer than the Bullet Cluster and nearly as massive.  Thus, by the inverse square law, it is roughly a hundred times brighter and an excellent place to look for X-rays. In fact, the 3.55 keV line has already been seen at high significance (more than "4 sigma," and this blog piece explains more what this term means) in a combination of data from Coma and two other sources.

In our paper, we propose a “test statistic” - a number calculated from the positions of detected photons - to evaluate which source of X-rays is more likely. In a nutshell, X-ray photons that come from areas of the cluster with more dark matter than normal matter add to the test statistic, while photons that come from normal-matter-rich regions subtract from it. Therefore, the larger the value of the test statistic you end up with, the more likely the signal is really dark matter.  

Due to statistical fluctuations, there is some uncertainty in the value of the test statistic (which we label “Λ” in the figure below).  Under some mild assumptions, it has a Gaussian (bell-shaped) probability distribution - but with a different average value depending on whether the 3.55 keV line is from dark matter or plasma. The figure below illustrates how our test statistic Λ works for a hypothetical 5 sigma detection of the 3.55 keV line in Coma. 

This figure shows the probability distributions for our test statistic Λ in a scenario where the 3.55 keV line is seen at 5 sigma in the Coma Cluster. (This level of significance should be achievable in the near future with some additional observation time, but our method can be applied now to data that already exists; the peaks will just be closer together than shown above.) The blue curve is the distribution for Λ if the excess originates from the normal matter of the intracluster medium - in this case, the most likely values of Λ are near zero. If the excess is dark matter, Λ should follow the red curve, where the most likely values are around 2.3.

The value of Λ calculated from data can then tell us which scenario is more likely: if it comes out near zero, it is more likely to be ordinary matter, but if it comes out near 2.3 it is more likely to be dark matter. The width of these peaks (labelled 󝜎) is a property of the Coma Cluster itself, but the separation between the peaks depends on how strong the signal is. A larger signal moves the peaks apart, making it easier to tell the difference between dark matter and ordinary matter.

Since we are not experts in the intricacies of X-ray telescope data analysis, we do not check to see if the existing data from the Coma Cluster favors dark matter or an intracluster medium emission line.  Nevertheless, even without a detailed analysis, we can say how powerful our test statistic will be. It turns out that the strength of our test - how far apart the bell curves are in the figure above - depends only on two things: how strong the signal is, and how separated the dark matter is from the intracluster medium in the merging cluster.  This degree of separation is something we can calculate easily, without a detailed analysis, and for the Coma Cluster we find that the two peaks in the distribution of Λ are separated by N*0.68 sigma. N is the size of the signal, measured in sigma, and 0.68 is a number that comes from the geometry of the dark matter and intracluster medium. Our above plot assumed a robust signal of N=5 sigma, so the peaks are separated by 3.4 sigma. A smaller excess, say N=3 sigma, would give rise to a separation of 2 sigma, which is still quite good: in that case, the value of Λ calculated from data could support or disfavor a dark matter explanation with a 95% confidence level.

Summary and Tantalizing Future Prospects

To summarize, we have constructed a robust procedure to check whether any tentative X-ray or gamma ray signal from a merging galaxy cluster has a dark matter origin.  All one needs is a gravitational lensing map of sufficient quality, and the angular resolution to distinguish the substructure of the merging cluster. 

In the figure below, we plot the angular resolution of various telescopes as a function of photon energy, and show that many X-ray and gamma-ray instruments have a resolution sharp enough to see sufficient detail in the Coma and Bullet Clusters.  With the advent of new, more powerful telescopes such as the gamma-ray observatory CTA, and the rapid discovery rate of merging events in nearby galaxy clusters, we hope our techniques will help to disentangle potential new dark matter signals from astrophysical backgrounds.

For further reading: In our paper, we also develop two additional procedures: one that can better test signals from possible dark matter annihilation channels, and the other to aid in extracting weak signals above background.