Hypothetical low-mass particles, such as axions, provide a compelling explanation for the dark matter in the universe. Such particles are expected to emerge abundantly from the hot interior of stars. To test this prediction, the CERN Axion Solar Telescope (CAST) uses a 9 T refurbished Large Hadron Collider test magnet directed towards the Sun. In the strong magnetic field, solar axions can be converted to X-ray photons which can be recorded by X-ray detectors. In the 2013–2015 run, thanks to low-background detectors and a new X-ray telescope, the signal-to-noise ratio was increased by about a factor of three. Here, we report the best limit on the axion–photon coupling strength (0.66 × 10−10 GeV−1 at 95% confidence level) set by CAST, which now reaches similar levels to the most restrictive astrophysical bounds.
At a glance
Advancing the low-energy frontier is a key endeavour in the worldwide quest for particle physics beyond the standard model and in the effort to identify dark matter1, 2. Nearly massless pseudoscalar bosons, often generically called axions, are particularly promising because they appear in many extensions of the standard model. They can be dark matter in the form of classical field oscillations that were excited in the early universe, notably by the re-alignment mechanism3. One particularly well motivated case is the quantum chromodynamics (QCD) axion, the eponym for all such particles. The existence of this new low-mass boson follows from the Peccei–Quinn mechanism as an explanation why QCD is perfectly time-reversal invariant within current experimental precision3.
Axions were often termed ‘invisible’ because of their extremely feeble interactions, yet they are the target of a fast-growing international landscape of experiments. Numerous existing and foreseen projects assume that axions are the galactic dark matter and use a variety of techniques that are sensitive to different interaction channels and optimal in different mass ranges4. Independently of the dark-matter assumption, one can search for new forces mediated by these low-mass bosons5 or the back-reaction on spinning black holes (superradiance)6. Stellar energy-loss arguments provide restrictive limits that can guide experimental efforts, and in some cases may even suggest new loss channels3, 7, 8.
The least model-dependent search strategies use the production and detection of axions and similar particles by their generic two-photon coupling. It is given by the vertex , where a is the axion field, F the electromagnetic field-strength tensor, and gaγ a coupling constant of dimension (energy)−1. Notice that we use natural units with ℏ = c = kB = 1. This vertex enables the decay a γγ, the Primakoff production in stars—that is, the γ a scattering in the Coulomb fields of charged particles in the stellar plasma—and the coherent conversion a ↔ γ in laboratory or astrophysical B-fields9, 10.
The helioscope concept, in particular, uses a dipole magnet directed at the Sun to convert axions to X-rays (see Fig. 1 for a sketch). Solar axions emerge from many thermal processes, depending on their model-dependent interaction channels. We specifically consider axion production by Primakoff scattering of thermal photons deep in the Sun, a process that depends on the same coupling constant, gaγ, which is also used for detection.
Since 2003, the CERN Axion Solar Telescope (CAST) has explored the ma–gaγ parameter space with this approach (more details to be given below). The black solid line in Fig. 2 is the envelope of all previous CAST results. The low-mass part ma ≲ 0.02 eV corresponds to the first phase 2003–2004 using evacuated magnet bores11, 12. The a γ conversion probability in a homogeneous B field over a distance L is
where q = ma2/2E is the a–γ momentum transfer in vacuum. For L = 9.26 m and energies of a few keV, coherence is lost for ma ≳ 0.02 eV, explaining the loss of sensitivity for larger ma.
Later, CAST has explored this higher-mass range by filling the conversion pipes with 4He (refs 13,14) and 3He (refs 15,16) at variable pressure settings to provide photons with a refractive mass, and in this way match the a and γ momenta. The sensitivity is smaller because, at each pressure setting, data were typically taken for a few hours only. Despite this limitation, CAST has reached realistic QCD axion models and has superseded previous solar axion searches using the helioscope17 and Bragg scattering technique18, 19. (For a more complete list of previous solar axion constraints see ref. 1.) The CAST data were also interpreted in terms of other assumed axion production channels in the Sun20, 21, 22. Moreover, CAST constraints on other low-mass bosons include chameleons23 and hidden photons24.
During this long experimental programme, CAST has used a variety of detection systems at both magnet ends, including a multiwire time projection chamber25, several Micromegas detectors26, a low-noise charged coupled device attached to a spare X-ray telescope (XRT) from the ABRIXAS X-ray mission27, a γ-ray calorimeter21, and a silicon drift detector23.
In the latest data-taking campaign (2013–2015), CAST has returned to evacuated pipes, with an improvement in the sensitivity to solar axions of about a factor of three in signal-to-noise ratio over a decade ago, thanks to the development of novel detection systems—notably new Micromegas detectors with lower background levels, as well as a new XRT built specifically for axion searches. These developments are also part of the activities to define the detection technologies suitable for the proposed much larger next-generation axion helioscope IAXO28. We here report the results of this effort in CAST.
Experiment and data taking
CAST has utilized an LHC prototype dipole magnet29 (magnetic field B ~ 9 T, length L = 9.26 m) with two parallel straight pipes (cross-sectional area S = 2 × 14.5 cm2). The magnet is mounted on a movable platform (±8° vertical and ±40° horizontal movement), allowing it to follow the Sun for about 1.5 h both at sunrise and sunset during the whole year. The pointing accuracy of the system is monitored to be well below 10% of the solar radius, both by periodic geometric surveys, as well as, twice per year, by filming the Sun with an optical telescope and camera attached to the magnet, and whose optical axis has been set parallel to it. The effect of refraction in the atmosphere, relevant for photons, but not for axions, is properly taken into account. At both ends of the magnet, different X-ray detectors have been searching for photons coming from axion conversion inside the magnet when it is pointing to the Sun. During non-tracking time, calibrations are performed and detectors record background data.
The data presented here were taken with three detection systems. On the sunset (SS) side of the magnet, two gas-based low-background detectors (SS1 and SS2) read by Micromegas planes30, were directly connected to each of the magnet pipes. On the sunrise (SR) side of the magnet, an improved Micromegas detector was situated at the focal plane of the new XRT. The detectors were small gaseous time projection chambers of 3 cm drift and were filled with a 1.4 bar argon–2% isobutane mixture. Their cathodes were 4-μm-thick mylar windows that face the magnet pipe vacuum and hold the pressure difference while being transparent to X-rays. The detector parts were built with carefully selected low-radioactivity materials, and surrounded by passive (copper and lead) and active (5-cm-thick plastic scintillators) shielding. The Micromegas readouts were built with the microbulk technique31, out of copper and kapton, and were patterned with 500 μm pixels interconnected in the x and y directions32. These design choices are the outcome of a long-standing effort to understand and reduce background sources in these detectors33, 34. This effort has led to the best background levels (~10−6 keV −1 cm−2 s−1) ever obtained in CAST.
The XRT installed in the SR system was a telescope (of focal length 1.5 m) that follows a cone-approximation Wolter I design. It is comprised of thermally formed glass substrates deposited with Pt/C multilayers to enhance X-ray reflectivity in the 0.5–10 keV band. The techniques and infrastructure used in fabricating the CAST XRT were originally developed35 to make the two hard X-ray telescopes that are flying on NASA’s NuSTAR satellite36. The optical prescription and multilayer coatings were optimized when considering factors including: the physical constraints of the CAST experiment; the predicted axion spectrum; and the quantum efficiency of the Micromegas detector37. The point spread function (PSF) and effective area (that is, throughput) of the XRT were calibrated at the PANTER X-ray test facility at MPE in Munich in July 2016. These calibration data were incorporated into Monte Carlo geometric ray-trace simulations to determine the expected two-dimensional (2D) distribution of solar axion-induced photons, which is shown in Fig. 3. Although there is a slight energy dependence on the PSF (the XRT focuses better at higher X-ray energy), more than 50% of the flux is always concentrated in an area of a few mm2, effectively reducing the background to levels down to ~0.003 counts h−1. In addition, the combined XRT and detector system was regularly calibrated in CAST using an X-ray source placed ~12 m away from the optics (at the SS side of the magnet). One such calibration is shown in Fig. 3, together with the expected 2D distribution from the ray-trace simulation. These contours are different from the ones expected from axion-induced photons (shown in Fig. 3) due to the different angular size and distance of the source. The agreement between data and simulations confirms our good understanding of the optics performance. This is the first time an XRT has been designed and built specifically for axion physics and operated together with a Micromegas detector at its focal point34. This experience is particularly valuable to develop a next-generation scaled-up helioscope.
Our results correspond to 1,132.6 h × detector of data taken in axion-sensitive conditions (that is, magnet powered and pointing to the Sun) with the aforementioned detectors in 2013, 2014 and 2015. In 2013, only SS detectors were operative, while in 2014 and 2015 both the SS detectors and the new SR system, installed in CAST in September 2014, took data. The data are divided in sets as shown in Table 1, according to detector and the year of the data-taking campaign. The 2015 SS detectors data are further divided into three sets (E, F, G and H, I, J for SS1 and SS2 detectors respectively) due to an accidental variation in the detector configuration: one of the muon vetoes remained inoperative for about one month, leading to a different background rate during that period. Background levels are defined independently for every data set using data acquired during non-tracking periods. These data typically have ~10 times more exposure than tracking data, and consequently background levels have ~3 times smaller statistical error bars. Data shown in the tables and figures always refer to levels after processing. Raw data from the Micromegas detectors undergo an offline filtering process, detailed elsewhere32, based on topological information of the event (for example, number of ionization clusters recorded in the chamber, or longitudinal and transversal spread of the signal), to keep only signal-like (that is, X-ray-like) events. The effect of this filtering on raw background levels at low energies is about a factor of 100, while the signal efficiency stays at 60–70%, depending on the event energy, as determined experimentally by careful calibrations with an X-ray tube at different representative energies38. In addition, an anti-coincidence condition with the external plastic muon vetoes is applied, leading to an additional rejection factor of ~2 (see Fig. 3).
The energy range of interest (RoI) is set between 2 and 7 keV, the band that contains most of the expected signal. The low-energy bound is safely above the effective energy threshold of the detectors (which are around ~1 and ~1.5 keV, respectively for SR and SS detectors), and the high-energy bound prevents contamination from the prominent ~8 keV Cu fluorescence peak observed in the background. The measured tracking and background levels, integrated in this RoI, are presented in Table 1 for each of the data sets. Figure 4 shows the spectral distribution of all SS data sets. The background spectra of the two SR data sets are shown in Fig. 5. In these latter plots, data from all the detector area—also outside the signal spot—are included to increase the statistics of the spectra; however, only data from the spot area are used to define the background in the analysis. These measured background levels are primarily attributed to cosmic muon-induced secondaries that are not properly tagged (the muon veto coverage of the shielding is not complete due to spatial constraints of the CAST setups) as well as a remaining environmental γ-induced background population that reaches the detector despite the shielding, probably associated with the small solid angle facing the magnet that is not possible to shield. This insight is corroborated by the ~3 keV Ar and ~8 keV Cu fluorescence peaks observed in the background spectra (better seen in the SR plot of Fig. 5, due to the better energy resolution of this detector), and will be the basis of future improvements of the detector33.
Figure 3 shows the 2D distribution of detected events, both in background and tracking data, in the SR detector, superimposed on the region where the signal is expected. The background level in the signal area could be estimated using the data outside the spot or the data in the spot in non-tracking periods. This second method is preferable, as the background level shows a slight increase at the centre of the detector (attributed to the detector and shielding geometry). When normalized to the 290 h of tracking data available (data sets K and L in Table 1) only 1.02 ± 0.22 (2.13 ± 0.47) background counts are expected in the 95% (99%) signal-enclosing focal spot region, where errors indicate 1-σ intervals. The tracking data reveal 3 (4) observed counts inside such regions. Their measured energies are 3.05, 2.86, 2.94 and 2.56 keV.
Data analysis and results
where RT is the expected number of counts from the axion-to-photon conversion in all data sets, integrated over the tracking exposure time and energy of interest. The sum is over each of the n detected counts in the energy RoI during the tracking time, for an expected rate R(Ei, di, xi) as a function of the energy Ei, data set di, and detector coordinates xi of the event i, and given by the expression
where B(E, d) is the background level for data set d, considered constant in time and xi within the data set. S(E, d, x) is the expected rate from axion conversion in the detector of data set d given by
Here, ϵ(d, E, x) is the detector response for data set d, and includes both the E-dependent detector efficiency (both hardware and software), and for the SR system also the E-dependent optics throughput and the expected signal distribution over x due to the optics PSF shown in Fig. 3. For the SS detector there is no such dependency and ϵ(d, E, x) = ϵ(d, E).
Finally, dΦa/dE is the differential solar axion flux, which can be parameterized by the expression12
with g10 = gaγ/(10−10 GeV−1) and energy E in keV. The axion-to-photon conversion probability Pa→γ was given in equation (1).
By numerically maximizing a best-fit value g10, min4 is obtained. This value is compatible with the absence of a signal in the entire axion mass range, and thus an upper limit on gaγ is extracted, by integrating the Bayesian posterior probability density function (PDF) from zero up to 95% of the total PDF area, using a flat prior in g104 for positive values, and zero for the unphysical negative ones. The computed upper limit for several values of ma is displayed in red in Fig. 2.
For mass values below ma ≲ 0.02 eV, the mass independent best-fit value is g10, min4 = (−0.06−0.07+0.10), where the errors indicate 1-σ intervals. The upper limit in this mass range constitutes our main result:
This constraint considers only statistical fluctuations in the tracking data. Other potentially important systematic effects would include uncertainties in input parameters such as the magnet length and strength, the background levels, the tracking accuracy, the optical alignment of the SR system, and the theoretical uncertainty of the expected signal. All these contributions have been estimated to be negligible in the final result, which is dominated by the statistical error of the low-counting observation. Overall systematic effects are well below 10% of the quoted result. It is worth noting that the observation of the SR counts represents a statistical fluctuation that slightly worsens the final result with respect to the expected sensitivity (defined as the average exclusion of an ensemble of possible statistical outcomes under the background-only hypothesis), estimated as g10, average ≲ 0.64.
The final solar axion run of CAST has provided the new constraint of equation (6) on the axion–photon coupling strength for ma ≲ 0.02 eV . It is shown in the wider ma–gaγ landscape in Fig. 6. In particular, axions and photons can also interconvert in astrophysical B fields that tend to be much weaker than in CAST, but extend over much larger distances. For example, the non-observation of γ rays contemporaneous with the SN 1987A neutrino signal provides a limit g10 ≲ 0.053 for ma ≲ 0.44 neV (ref. 39). This conversion effect could be important also for other astrophysical and cosmological sources, especially for the propagation of TeV γ rays and as an explanation for the soft X-ray excess in galaxy clusters (for a recent review see ref. 40). In the very low mass domain, propagation experiments for laser beams in magnetic fields have also explored the gaγ–ma parameter space41, 42.
Helioscopes using the Bragg technique can reach larger axion masses than CAST because the electric fields in the crystals are inhomogeneous on much smaller scales. Yet because of their limited size, even the best case shown in Fig. 6 from DAMA19 is not competitive. In the future, CUORE may reach values of gaγ comparable to the CAST 3He limits near ma ~ 1 eV, but extended to larger masses43.
However, QCD axions in this parameter range would thermalize in the early universe and provide a hot dark-matter fraction. Cosmology provides a constraint corresponding to ma < 0.86 eV (vertical dashed red line in Fig. 6), which in the future may reach ma < 0.15 eV (ref. 44). Therefore, exploring beyond the 1 eV mass range is relevant only for those axion-like particles which, unlike QCD axions, do not thermalize efficiently.
Solar axion searches usually assume that the axion flux is only a small perturbation of the Sun. Actually for g10 ≳ 20 axion losses are so large that one cannot construct self-consistent solar models45. Moreover, the measured solar neutrino flux and helioseismology require g10 < 4.1 at 3σ confidence46 (dashed blue line in Fig. 6), implying that CAST is the only solar axion search that has gone beyond this recent limit.
A sensitivity comparable to the new CAST limit derives from traditional stellar energy-loss arguments. In particular, Primakoff losses accelerate the helium-burning phase of horizontal branch (HB) stars, reducing their number count relative to low-mass red giants, R = NHB/NRGB, in globular clusters (see dashed line labelled ‘HB’ in Fig. 6). The most recent analysis finds g10 < 0.66 (95% CL) and actually a mild preference for g10 ~ 0.4, although a detailed budget of systematic uncertainties is not currently available7.
Solar axion searches beyond CAST, and at the same time beyond the HB star limit as a benchmark, require a new effort on a much larger scale, for example the proposed helioscope IAXO28. For small masses, new regions in the gaγ–ma will be explored with the upcoming ALPS-II laser propagation experiment at DESY47, by higher-statistics TeV γ-ray observations, or the γ-ray signal from a future galactic supernova40. Beyond the gaγ–ma parameter space, many attractive detection opportunities are pursued worldwide, notably under the assumption that axions are the cosmic dark matter4.
After finishing its solar axion programme in 2015, CAST itself has turned to a broad physics programme at the low-energy frontier. In particular, this includes KWISP, a sensitive force detector, and an InGrid detector, both in search of solar chameleons, as well as CAST-CAPP and RADES, implementing long-aspect-ratio microwave cavities in the CAST magnet to search for dark-matter axions around ma ~ 20 μeV (ref. 48).
Whichever of the many new developments worldwide will lead to the detection of axions or similar particles in the gaγ–ma parameter space, our new CAST result will remain the benchmark for many years to come and guide future explorations.
Data availability. The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
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We thank CERN for hosting the experiment and for technical support to operate the magnet and cryogenics. We thank V. Burwitz, G. Hartner of the MPE PANTER X-ray test facility for providing the opportunity to calibrate the X-ray telescope and for assistance in collecting and analysing the characterization data. We acknowledge support from NSERC (Canada), MSE (Croatia) and Croatian Science Foundation under the project IP-2014-09-3720, CEA (France), BMBF (Germany) under the grant numbers 05 CC2EEA/9 and 05 CC1RD1/0, DFG (Germany) under grant numbers HO 1400/7-1 and EXC-153, GSRT (Greece), NSRF: Heracleitus II, RFFR (Russia), the Spanish Ministry of Economy and Competitiveness (MINECO) under Grants No. FPA2011-24058 and No. FPA2013-41085-P (grants partially funded by the European Regional Development Fund, ERDF/FEDER), the European Research Council (ERC) under grant ERC-2009-StG-240054 (T-REX), Turkish Atomic Energy Authority (TAEK), NSF (USA) under Award No. 0239812, NASA under the grant number NAG5-10842, and IBS (Korea) with code IBS-R017-D1-2017-a00. Part of this work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.