What is the universe made out of? In grade school, most students learn about atoms, then electrons, protons and neutrons. As it turns out, protons and neutrons are made up of even smaller components called quarks. Quarks, however, are only one subset of a whole system of fundamental particles described by the Standard Model of particle physics. The Standard Model is an extremely useful theory that describes the multitude of particles that make up our universe and how they interact with each other. The Standard Model includes particles you’ve probably heard of, like the photon, and some you might not have, like the tau neutrino. The Standard Model does very well at explaining much of what particle physicists have observed over the years, but there are some problems with it—indications that the particles and interactions described in the theory do not account for all of the matter in the universe. This extra matter is known as “dark matter”.
My research with Professor Kerstin Perez this past summer, to be continued as my senior thesis in physics this year, focused on learning how to search for dark matter with a high-energy x-ray satellite telescope called NuSTAR. NuSTAR is the first focusing telescope in its energy range, meaning that it has much better spatial resolution in that range than any other instrument. For this reason, it may be a promising tool for searches for dark matter.
An illustration from nasa.gov of the NuSTAR satellite telescope, launched in 2012.
Dark matter accounts for over eighty percent of the matter in the universe, but nobody knows exactly what it is. It is so difficult to study because it interacts extremely weakly with light. Direct evidence for its existence comes mostly from its gravitational effects on normal matter, such as the speed of galaxy rotation and gravitational lensing (or bending) of light. Nobody has so far been able to figure out the actual characteristics of the particles that make up dark matter. Particle physicists have put forth a variety of theories, each one attempting to fix a “hole” in the Standard Model. Among the more popular theoretical particles are WIMPs (Weakly Interacting Massive Particles), axions, and sterile neutrinos. My research this summer centers mainly on the sterile neutrino, a theorized type of neutrino that interacts only via gravity, not gravity and the weak force as do other types of neutrinos. Why is the sterile neutrino interesting for my research? As it turns out, even though all theorized dark matter particles interact very weakly with light, some might occasionally decay to produce photons that can be detected with a telescope. When a sterile neutrino decays, it releases a “normal” neutrino along with a photon of energy equal to half the mass of the sterile neutrino (remember Einstein’s E=mc2 equation, which states that energy and mass are essentially interchangeable). The range of possible photon energies from sterile neutrino decay falls within the span energies that NuSTAR can observe, making sterile neutrinos a potentially promising target of study using NuSTAR.
The way this type of dark matter search works is by looking for peaks in spectral data that might correspond to photons from dark matter particle decay. NuSTAR points at some object in space (like a galaxy), collects photons coming from that object, and sorts them by energy. One can observe the output as an image of the light source, or as a graph of energy versus photon counts called a spectrum. Using a spectral analysis tool from NASA called XSPEC, one can fit a model of all the components of the spectrum that are well-understood, i.e. blackbody radiation, atomic transitions lines, etc. If there is a peak in the data above these components that cannot be explained by anything known, there is a chance it can be explained by dark matter.
Of course, despite the multitude of teams of scientists working on such searches, no definitively significant dark matter spectral peaks have been discovered. It is quite likely, then, that despite NuSTAR’s excellent spectral resolution and high energy range, my project will not produce concrete evidence of dark matter particle discovery. But do not despair, for useful results can still be produced from a dark matter search that comes up empty. What a null result can do is rule out certain characteristics of dark matter particles. Particle physicists would like to know the mass and mixing angle—the strength of interaction between a dark matter particle and normal matter that defines how likely a sterile neutrino is to decay into a photon/neutrino pair—of dark matter particles. Using spectral data, I can say, if a sterile neutrino has this combination of mass and mixing angle, I will see it as a peak in the spectrum. If I do not, it must not have these characteristics.
Over the summer, I produced a detailed procedure for finding mixing angle constraints for a given dark matter mass, and used simulations and sample data to find tentative estimates of NuSTAR’s capabilities in this sort of dark matter search for a few promising observation targets. I will try to summarize the procedure without getting overly technical. Once spectral data is obtained—this can be real data or simulated data from a tool like SciSim, a simulator developed for the XMM Newton X-ray observatory—find a model to fit the data using NASA’s XSPEC tool. Next, calculate the total dark matter mass in the field of view of the telescope observation. For my mass/mixing angle estimates looking at the Milky Way center, I did this by integrating a Milky Way dark matter density function found in a 2010 paper from a team led by Alexey Boyarsky. For targets farther away from Earth, I looked up the dark matter density of the object and multiplied by the area of the NuSTAR observation at that object. Next, select a few sterile neutrino masses for which to calculate mixing angle limits. Remember, the photons that correspond to sterile neutrino decay have half the energy of the sterile neutrino. Using the model found for the spectral data, determine the maximum possible flux (related to the photon counts at a certain energy) for each sterile neutrino mass using XSPEC. For the most conservative estimates of mixing angle, just say that the dark matter flux is the flux of the model in XSPEC. Next, calculate the maximum decay rate to photons given each sterile neutrino mass and maximum flux. For this step, I used an equation from the same Boyarsky et. al. paper that contained the dark matter density function. From the decay rate, one can calculate the mixing angle using another formula in a 2006 paper written by Boyarsky et. al. Once each chosen possible sterile neutrino mass is matched with a mixing angle, the results can be compared to existing mass/mixing angle limits from previous experiments.
I ran through this process for a few different potential sources. These sources included the Milky Way center, a galaxy called M31 (also known as Andromeda), and the dwarf spheroidal galaxy Fornax. These sources were chosen for their high dark matter content and well-understood background spectra, among other factors.
An image of the M31 galaxy from messier.seds.org.
Over the course of the summer, as I learned more about NuSTAR’s instrumental background spectrum and about the potential dark matter observation targets, I came up with mass/mixing angle limits that were increasingly more accurate to NuSTAR’s capabilities. By the end of my 10 weeks of research, I had this plot:
My calculated mass/mixing angle limits, overlayed as colored points on a figure taken from Boyarsky et al., 2013, only barely improve on previously discovered limits, if at all. My process for finding these limits, however, was quite conservative, as I explained earlier. A promising next step in my research could be to use maximum dark matter flux values that are, say, related to the error bars on the spectral model’s flux instead of just being the value of the flux from the model. This would make the flux estimates much smaller, and thus make the mixing angle limits smaller as well. In this way, with the help of NuSTAR data, my research could potentially break new ground on mass/mixing angle limits for sterile neutrinos.