Some History of Dark Matter
In 1933, Cal Tech astronomer Fritz Zwicky was studying a small group of seven galaxies in the Coma Cluster. His objective was to calculate the total mass of this cluster by studying the speed of rotation of these seven galaxies. By using Newton laws, he calculated their individual masses and the total mass of the cluster, and then compared it with the mass calculated from the amount of light emitted by the cluster. Zwicky was surprised to find that the speeds observed in the Coma Cluster were much higher than expected. In fact, the mass that came from his calculations was 400 times larger than was estimated by the luminosity of the cluster!
The same phenomenon was again observed in 1936 by Sinclair Smith who was making an almost identical analysis of the Virgo Cluster’s total mass. Smith found that the mass of the Virgo Cluster was 200 times the estimate given from the study of their luminosity. These are the first two observations that led astronomers to postulate the existence of “Dark Matter” to explain this discrepancy. These observations then lay dormant for nearly half a century until other scientists started to examine the work of Zwicky and Smith to explain their own observations that showed the same unexplained discrepancy.
An Introduction to Dark Matter
Today there are many theories and predictions among scientists to describe the universe and its contents. Attempting to solve the dilemma of whether dark matter exists and, if so, what it consists of is of great importance to the scientific world. By definition dark matter emits no electromagnetic radiation but must have a large cumulative mass, since its presence is inferred solely through its gravitational effects on visible (luminous) matter. It is now widely believed that dark matter does, indeed, exist and the standard model of cosmology anticipates that dark matter accounts for > 90% of all matter in the Universe. The overall matter-energy density of the Universe has been found to have large proportions of dark matter (23%) and dark energy (72%) (WMAP), which is consistent with the standard cosmological model.
There are several pieces of observational evidence for dark matter in our Universe. Gravitational lensing (see figure below: Hubble Deep Field) and the unexpected rotational curves of spiral galaxies (see figure below: Rotational velocity curve) are among these observations that point to there being so-called “missing mass” throughout the Universe. Recent results from WMAP give us our most accurate value for the total mass in the Universe and how it is divided between different types of matter and energy.
These pieces of observational evidence lead to the idea of a dark matter halo approximated as a sphere surrounding the visible galaxy with a density distribution proportional to the radius squared, and contributing circa 90% of the galactic mass. The favoured dark matter candidate at present is the Weakly Interacting Massive Particle (WIMP). The WIMP halo is what all dark matter experiments are attempting to observe.
WIMPs are expected to form a halo in and around the visible constituents of our Galaxy, the Milky Way. Since the Sun and, therefore, the Solar System is in motion around the centre of the Galaxy, it is expected that the Earth should experience a so-called ‘WIMP wind’ that is detectable as fluctuations in the magnitude and direction of a WIMP signal. All dark matter detectors with sufficient target mass, directional or otherwise, are capable of noticing an annual modulation due to the Earth’s orbit around the Sun as the Sun orbits the galactic centre (see figure below: Annual modulation).
Only directional dark matter detectors such as the DRIFT detector, however, have the ability to observe fluctuations in the direction of incoming WIMPs throughout a 24 hour period (see figure below: Daily fluctuation). Illustration of annual modulation in a WIMP signal. The solar system is ~ 8.5 kpc from the galactic centre and is travelling around it at ~ 220 km / s. The Earth’s orbit around the Sun is inclined at 60 degrees to the galactic plane and the Earth’s spin axis is 23.5 degrees from its orbital plane. This leads to a `WIMP wind’ that means the WIMP flux observed by a static detector on Earth will not be isotropic, but will be peaked in the direction in which the Earth is travelling. This subsequently causes the nuclear recoil flux, due to WIMP-nucleon scattering, to be anisotropic also, although less so than the WIMP flux since scattering does not always happen with a full head-on contact between particles. A detector that can accurately reconstruct track information and produce directional data can observe the changes in signal flux over particular periods of time. For example, a laboratory located at a similar latitude to that at Boulby mine should observe a direction change in the signal from downward to Southward and back again during a sidereal day. The signal coordinates can then be transformed from the laboratory frame to galactic coordinates, which removes the effects of the Earth’s rotation, and hence determine whether the signal is of galactic origin, which is expected of a WIMP signal, or not.
The nuclear recoils that must be observed for dark matter detection are of energies less than 100 keV. Dark matter experiments therefore need detectors with a good (low) energy threshold to be able to detect these recoils accurately. Directional dark matter detectors then also need to be able to demonstrate a correlation of these recoil signals and their anisotropy with what is expected due to the Earth’s rotation. It is this recognition of patterns within the recoil flux and direction that allow directional detectors to identify any signal as galactic in origin, as it must be to be due to WIMP interactions. Directional detectors have the capability to then probe further into the structure and dynamics of the WIMP halo and distinguish between different halo models proposed from theory. This is a very powerful opportunity for directional dark matter detection to produce a definite and indisputable result.
Setting WIMP limits
Dark matter experiments attempt to confine the properties that can be assigned to WIMPs by detecting no events over as long a period of time as possible. These confines can be found since it is known that if WIMPs exist with particular characteristics they would be observed by the detector. Since no events are observed, it can be stated to a good level of confidence that WIMPs with these characteristics do not exist.
It is also possible to set limits on these parameters even when events are observed, as long as they are consistent with what is expected from backgrounds that cannot be removed. The parameter space that experiments are most interested in for comparison of results is the WIMP-nucleon cross-section as a function of WIMP mass, and this is what is plotted when illustrating the sensitivity reached by a dark matter experiment. The important things to be considered when trying to achieve the best possible sensitivity from a WIMP search experiment are the energy threshold, target mass, spin-dependency and the discrimination capabilities.
The energy threshold must be as low as possible, in order that the WIMP interactions, which are expected to produce nuclear recoils of < few keV energies, can be detected. The target mass should be high, since larger target nuclei have a higher probability of interaction and a higher target mass means more target nuclei, which raises the interaction probability further, and with a predicted WIMP interaction rate of about 1 per day per kg of target mass it is important that the target mass be as large as possible and the detector runs for as long a time as possible to achieve the best results. Nuclei with an overall non-zero spin, i.e. a nucleus with an odd number of neutrons and/or protons, have a scattering cross-section with WIMPs that is proportional to the spin value J. The cross-section for nuclei with zero spin is simply proportional to the mass number, A.
The ability to discriminate WIMP-induced nuclear recoils from any other events in a detector is vital. This is done using knowledge of the differences in the ionization, scintillation and/or thermal energy deposition in a detector produced by background events compared to those of WIMP-like events. There are essentially two types of discrimination attainable by detectors, statistical discrimination, where not all events are distinguishable, and absolute, or event-by-event, discrimination, where all events and interactions can be distinguished. To aid this, it is also imperative that sources of backgrounds, such as uranium and thorium contamination in materials is kept to a minimum through the use of radiopure materials in constructing the detector and shielding, e.g. hydrogen-rich materials to thermalise neutrons from U and Th, and an overburden of rock to suppress the cosmic ray-induced backgrounds. Once all these items have been taken into consideration and the best possible sensitivity has been achieved, data from the experiment is analysed and the resulting energy spectrum of nuclear recoils is examined to determine any peak that is not simply what is expected from background events. If the observed rate is consistent with that expected from background sources an upper limit on the WIMP-nucleon cross-section can be set.
There are many dark matter searches being executed worldwide. The current best dark matter limits have been set by CDMS-II and NaIAD (UKDMC) for spin-independent and spin-dependent cross-sections, respectively.