Regular vs. classical M\"obius transformations of the quaternionic unit ball

The regular fractional transformations of the extended quaternionic space have been recently introduced as variants of the classical linear fractional transformations. These variants have the advantage of being included in the class of slice regular functions, introduced by Gentili and Struppa in 2006, so that they can be studied with the useful tools available in this theory. We first consider their general properties, then focus on the regular M\"obius transformations of the quaternionic unit ball B, comparing the latter with their classical analogs. In particular we study the relation between the regular M\"obius transformations and the Poincar\'e metric of B, which is preserved by the classical M\"obius transformations. Furthermore, we announce a result that is a quaternionic analog of the Schwarz-Pick lemma.Comment: 14 page

The Scintillating Tail of Comet C/2020 F3 (Neowise)

Context. The occultation of a radio source by the plasma tail of a comet can be used to probe structure and dynamics in the tail. Such occultations are rare, and the occurrence of scintillation, due to small-scale density variations in the tail, remains somewhat controversial. Aims. A detailed observation taken with the Low-Frequency Array (LOFAR) of a serendipitous occultation of the compact radio source 3C196 by the plasma tail of comet C/2020 F3 (Neowise) is presented. 3C196 tracked almost perpendicularly behind the tail, providing a unique profile cut only a short distance downstream from the cometary nucleus itself. Methods. Interplanetary scintillation (IPS) is observed as the rapid variation of the intensity received of a compact radio source due to density variations in the solar wind. IPS in the signal received from 3C196 was observed for five hours, covering the full transit behind the plasma tail of comet C/2020 F3 (Neowise) on 16 July 2020, and allowing an assessment of the solar wind in which the comet and its tail are embedded. Results. The results reveal a sudden and strong enhancement in scintillation which is unequivocally attributable to the plasma tail. The strongest scintillation is associated with the tail boundaries, weaker scintillation is seen within the tail, and previously-unreported periodic variations in scintillation are noted, possibly associated with individual filaments of plasma. Furthermore, contributions from the solar wind and comet tail are separated to measure a sharp decrease in the velocity of material within the tail, suggesting a steep velocity shear resulting in strong turbulence along the tail boundaryComment: Accepted for publication in Astronomy and Astrophysics, 8 pages, 9 figure

LOFAR observations of the quiet solar corona

The quiet solar corona emits meter-wave thermal bremsstrahlung. Coronal radio emission can only propagate above that radius, $R_\omega$, where the local plasma frequency eqals the observing frequency. The radio interferometer LOw Frequency ARray (LOFAR) observes in its low band (10 -- 90 MHz) solar radio emission originating from the middle and upper corona. We present the first solar aperture synthesis imaging observations in the low band of LOFAR in 12 frequencies each separated by 5 MHz. From each of these radio maps we infer $R_\omega$, and a scale height temperature, $T$. These results can be combined into coronal density and temperature profiles. We derived radial intensity profiles from the radio images. We focus on polar directions with simpler, radial magnetic field structure. Intensity profiles were modeled by ray-tracing simulations, following wave paths through the refractive solar corona, and including free-free emission and absorption. We fitted model profiles to observations with $R_\omega$ and $T$ as fitting parameters. In the low corona, $R_\omega < 1.5$ solar radii, we find high scale height temperatures up to 2.2e6 K, much more than the brightness temperatures usually found there. But if all $R_\omega$ values are combined into a density profile, this profile can be fitted by a hydrostatic model with the same temperature, thereby confirming this with two independent methods. The density profile deviates from the hydrostatic model above 1.5 solar radii, indicating the transition into the solar wind. These results demonstrate what information can be gleaned from solar low-frequency radio images. The scale height temperatures we find are not only higher than brightness temperatures, but also than temperatures derived from coronograph or EUV data. Future observations will provide continuous frequency coverage, eliminating the need for local hydrostatic density models

LOFAR tied-array imaging and spectroscopy of solar S bursts

Context. The Sun is an active source of radio emission that is often associated with energetic phenomena ranging from nanoflares to coronal mass ejections (CMEs). At low radio frequencies (&lt;100 MHz), numerous millisecond duration radio bursts have been reported, such as radio spikes or solar S bursts (where S stands for short). To date, these have neither been studied extensively nor imaged because of the instrumental limitations of previous radio telescopes. Aims. Here, LOw Frequency ARray (LOFAR) observations were used to study the spectral and spatial characteristics of a multitude of S bursts, as well as their origin and possible emission mechanisms. Methods. We used 170 simultaneous tied-array beams for spectroscopy and imaging of S bursts. Since S bursts have short timescales and fine frequency structures, high cadence (~50 ms) tied-array images were used instead of standard interferometric imaging, that is currently limited to one image per second. Results. On 9 July 2013, over 3000 S bursts were observed over a time period of ~8 h. S bursts were found to appear as groups of short-lived (&lt;1 s) and narrow-bandwidth (~2.5 MHz) features, the majority drifting at ~3.5 MHz s-1 and a wide range of circular polarisation degrees (2−8 times more polarised than the accompanying Type III bursts). Extrapolation of the photospheric magnetic field using the potential field source surface (PFSS) model suggests that S bursts are associated with a trans-equatorial loop system that connects an active region in the southern hemisphere to a bipolar region of plage in the northern hemisphere. Conclusions. We have identified polarised, short-lived solar radio bursts that have never been imaged before. They are observed at a height and frequency range where plasma emission is the dominant emission mechanism, however, they possess some of the characteristics of electron-cyclotron maser emission

LOFAR tied-array imaging of Type III solar radio bursts

Context. The Sun is an active source of radio emission which is often associated with energetic phenomena such as solar flares and coronal mass ejections (CMEs). At low radio frequencies (< 100 MHz), the Sun has not been imaged extensively because of

Neutrino astronomy with the MACRO detector

High energy gamma ray astronomy is now a well established field and several sources have been discovered in the region from a few GeV up to several TeV. If sources involving hadronic processes exist, the production of photons would be accompanied by neutrinos too. Other possible neutrino sources could be related to the annihilation of WIMPs at the center of galaxies with black holes. We present the results of a search for point-like sources using 1100 upward-going muons produced by neutrino interactions in the rock below and inside the MACRO detector in the underground Gran Sasso Laboratory. These data show no evidence for a possible neutrino point-like source or for possible correlations between gamma ray bursts and neutrinos. They have been used to set flux upper limits for candidate point-like sources which are in the range 10^-14-10^-15 cm-2 s-1.Comment: 37 pages, 15 figures, replacement due to a typo in tab. 6, AASLaTex, submitted to Ap

New MACRO results on atmospheric neutrino oscillations

The final results of the MACRO experiment on atmospheric neutrino oscillations are presented and discussed. The data concern different event topologies with average neutrino energies of ~3 and ~50 GeV. Multiple Coulomb Scattering of the high energy muons in absorbers was used to estimate the neutrino energy of each event. The angular distributions, the L/E_nu distribution, the particle ratios and the absolute fluxes all favour nu_mu --> nu_tau oscillations with maximal mixing and Delta m^2 =0.0023 eV^2. A discussion is made on the Monte Carlos used for the atmospheric neutrino flux. Some results on neutrino astrophysics are also briefly discussed.Comment: Invited Paper at the NANP03 Int. Conf., Dubna, 200

Search for massive rare particles with MACRO

Massive rare particles have been searched for in the penetrating cosmic radiation using the MACRO apparatus at the Gran Sasso National Laboratories. Liquid scintillators, streamer tubes and nuclear track detectors have been used to search for magnetic monopoles (MMs). Based on no observation of such signals, stringent flux limits are established for MMs as slow as a few 10^(-5)c. The methods based on the scintillator and on the nuclear track subdetectors were also applied to search for nuclearites. Preliminary results of the searches for charged Q-balls are also presented.Comment: 20 pages, 9 EPS figures included with epsfi

The Observation of Up-going Charged Particles Produced by High Energy Muons in Underground Detectors

An experimental study of the production of up-going charged particles in inelastic interactions of down-going underground muons is reported, using data obtained from the MACRO detector at the Gran Sasso Laboratory. In a sample of 12.2 10^6 single muons, corresponding to a detector livetime of 1.55 y, 243 events are observed having an up-going particle associated with a down-going muon. These events are analysed to determine the range and emission angle distributions of the up-going particle, corrected for detection and reconstruction efficiency. Measurements of the muon neutrino flux by underground detectors are often based on the observation of through-going and stopping muons produced in $\nu_\mu$ interactions in the rock below the detector. Up-going particles produced by an undetected down-going muon are a potential background source in these measurements. The implications of this background for neutrino studies using MACRO are discussed.Comment: 18 pages, 9 figures. Accepted by Astrop. Physic

Observation of the Shadowing of Cosmic Rays by the Moon using a Deep Underground Detector

Using data collected by the MACRO experiment during the years 1989-1996, we show evidence for the shadow of the moon in the underground cosmic ray flux with a significance of 3.6 sigma. This detection of the shadowing effect is the first by an underground detector. A maximum-likelihood analysis is used to determine that the angular resolution of the apparatus is 0.9+/-0.3 degrees. These results demonstrate MACRO's capabilities as a muon telescope by confirming its absolute pointing ability and quantifying its angular resolution.Comment: 14 pages, 8 figures Submitted to Phys. Rev.