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At least 523 records · Page 29

SUNSPOT AND STARSPOT LIFETIMES IN A TURBULENT EROSION MODEL

Quantitative models of sunspot and starspot decay predict the timescale of magnetic diffusion and may yield important constraints in stellar dynamo models. Motivated by recent measurements of starspot lifetimes, we investigate the disintegration of a magnetic flux tube by nonlinear diffusion. Previous theoretical studies are extended by considering two physically motivated functional forms for the nonlinear diffusion coefficient D : an inverse power-law dependence D ∝ B {sup −ν} and a step-function dependence of D on the magnetic field magnitude B . Analytical self-similar solutions are presented for the power-law case, including solutions exhibiting “super fast” diffusion. For the step-function case, the heat-balance integral method yields approximate solutions, valid for moderately suppressed diffusion in the spot. The accuracy of the resulting solutions is confirmed numerically, using a method which provides an accurate description of long-time evolution by imposing boundary conditions at infinite distance from the spot. The new models may allow insight into the differences and similarities between sunspots and starspots.

79 ASTRONOMY AND ASTROPHYSICS↗

The Great Solar Active Region NOAA 12192: Helicity Transport, Filament Formation, and Impact on the Polar Field

The solar active region (AR), NOAA 12192, appeared in 2014 October as the largest AR in 24 years. Here we examine the counterintuitive nature of two diffusion-driven processes in the region: the role of helicity buildup in the formation of a major filament, and the relationship between the effects of supergranular diffusion and meridional flow on the AR and on the polar field. Quantitatively, calculations of current helicity and magnetic twist from Helioseismic and Magnetic Imager (HMI) vector magnetograms indicate that, though AR 12192 emerged with negative helicity, positive helicity from subsequent flux emergence, consistent with the hemispheric sign-preference of helicity, increased over time within large-scale, weak-field regions such as those near the polarity inversion line (PIL). Morphologically, Atmospheric Imaging Assembly observations of filament barbs, sigmoidal patterns, and bases of Fe xii stalks initially exhibited signatures of negative helicity, and the long filament that subsequently formed had a strong positive helicity consistent with the helicity buildup along the PIL. We find from full-disk HMI magnetograms that AR 12192's leading positive flux was initially closer to the equator but, owing either to the region’s magnetic surroundings or to its asymmetric flux density distribution, was transported poleward more quickly on average than its trailing negative flux, contrary to the canonical pattern of bipole flux transport. This behavior caused the AR to have a smaller effect on the polar fields than expected and enabled the formation of the very long neutral line where the filament formed.

79 ASTRONOMY AND ASTROPHYSICS↗

Empirical Constraints on the Origin of Fast Radio Bursts: Volumetric Rates and Host Galaxy Demographics as a Test of Millisecond Magnetar Connection

The localization of the repeating fast radio burst (FRB) 121102 to a low-metallicity dwarf galaxy at z = 0.193, and its association with a luminous quiescent radio source, suggests the possibility that FRBs originate from magnetars, formed by the unusual supernovae that occur in such galaxies. We investigate this possibility via a comparison of magnetar birth rates, the FRB volumetric rate, and host galaxy demographics. We calculate average volumetric rates of possible millisecond magnetar production channels, such as superluminous supernovae (SLSNe), long and short gamma-ray bursts (GRBs), and general magnetar production via core-collapse supernovae (CCSNe). For each channel, we also explore the expected host galaxy demographics using their known properties. We determine for the first time the number density of FRB emitters (the product of their volumetric birth rate and lifetime), R{sub FRB}τ≈10{sup 4} Gpc{sup −3}, assuming that FRBs are predominantly emitted from repetitive sources similar to FRB 121102 and adopting a beaming factor of 0.1. By comparing rates, we find that production via rare channels (SLSNe, GRBs) implies a typical FRB lifetime of ∼30–300 years, in good agreement with other lines of argument. The total energy emitted over this time is consistent with the available energy stored in the magnetic field. On the other hand, any relation to magnetars produced via normal CCSNe leads to a very short lifetime of ∼0.5 years, in conflict with both theory and observation. We demonstrate that due to the diverse host galaxy distributions of the different progenitor channels, many possible sources of FRB birth can be ruled out with ≲10 host galaxy identifications. Conversely, targeted searches of galaxies that have previously hosted decades-old SLSNe and GRBs may be a fruitful strategy for discovering new FRBs and related quiescent radio sources, and determining the nature of their progenitors.

79 ASTRONOMY AND ASTROPHYSICS↗

Plasmoid Instability in Forming Current Sheets

The plasmoid instability has revolutionized our understanding of magnetic reconnection in astrophysical environments. By preventing the formation of highly elongated reconnection layers, it is crucial in enabling the rapid energy conversion rates that are characteristic of many astrophysical phenomena. Most previous studies have focused on Sweet–Parker current sheets, which are unattainable in typical astrophysical systems. Here we derive a general set of scaling laws for the plasmoid instability in resistive and visco-resistive current sheets that evolve over time. Our method relies on a principle of least time that enables us to determine the properties of the reconnecting current sheet (aspect ratio and elapsed time) and the plasmoid instability (growth rate, wavenumber, inner layer width) at the end of the linear phase. After this phase the reconnecting current sheet is disrupted and fast reconnection can occur. The scaling laws of the plasmoid instability are not simple power laws, and they depend on the Lundquist number (S), the magnetic Prandtl number (P m ), the noise of the system (${\psi }_{0}$), the characteristic rate of current sheet evolution ($1/\tau $), and the thinning process. We also demonstrate that previous scalings are inapplicable to the vast majority of astrophysical systems. Furthermore, we explore the implications of the new scaling relations in astrophysical systems such as the solar corona and the interstellar medium. In both of these systems, we show that our scaling laws yield values for the growth rate, wavenumber, and aspect ratio that are much smaller than the Sweet–Parker–based scalings.

Sun: flares↗

Magnetar Broadband X-Ray Spectra Correlated with Magnetic Fields: Suzaku Archive of SGRs and AXPs Combined with NuSTAR, Swift, and RXTE

The 1–70 keV persistent spectra of 15 magnetars, observed with Suzaku from 2006 to 2013, were studied as a complete sample. Combined with early NuSTAR observations of four hard X-ray emitters, nine objects showed a hard power-law emission dominating at ≳10 keV with the 15–60 keV flux of ∼1–11×10{sup −11} erg s{sup −1} cm{sup −2}. The hard X-ray luminosity L{sub h}, relative to that of a soft-thermal surface radiation L{sub s}, tends to become higher toward younger and strongly magnetized objects. Their hardness ratio, updated from a previous study and defined as ξ=L{sub h}/L{sub s}, is correlated with the measured spin-down rate P-dot as ξ=0.62×( P-dot /10{sup −11}ss{sup −1}){sup 0.72}, corresponding to positive and negative correlations with the dipole field strength B{sub d} (ξ∝B{sub d}{sup 1.41}) and the characteristic age τ{sub c} (ξ∝τ{sub c}{sup −0.68}), respectively. Among our sample, five transients were observed during X-ray outbursts, and the results are compared with their long-term 1–10 keV flux decays monitored with Swift/XRT and RXTE/PCA. Fading curves of three bright outbursts are approximated by an empirical formula used in the seismology, showing a ∼10–40 day plateau phase. Transients show the maximum luminosities of L{sub s} ∼ 10{sup 35} erg s{sup −1}, which are comparable to those of persistently bright ones, and fade back to ≲10{sup 32} erg s{sup −1}. Spectral properties are discussed in the framework of the magnetar hypothesis.

79 ASTRONOMY AND ASTROPHYSICS↗

Measuring Filament Orientation: A New Quantitative, Local Approach

The relative orientation between filamentary structures in molecular clouds and the ambient magnetic field provides insight into filament formation and stability. To calculate the relative orientation, a measurement of filament orientation is first required. We propose a new method to calculate the orientation of the one-pixel-wide filament skeleton that is output by filament identification algorithms such as filfinder. We derive the local filament orientation from the direction of the intensity gradient in the skeleton image using the Sobel filter and a few simple post-processing steps. We call this the “Sobel-gradient method.” The resulting filament orientation map can be compared quantitatively on a local scale with the magnetic field orientation map to then find the relative orientation of the filament with respect to the magnetic field at each point along the filament. It can also be used for constructing radial profiles for filament width fitting. The proposed method facilitates automation in analyses of filament skeletons, which is imperative in this era of “big data.”.

79 ASTRONOMY AND ASTROPHYSICS↗

Magnetic Navigation for GPS-Denied Airborne Applications

Most current flight systems are dependent on GPS for navigation. Recently, however, navigation in GPS-denied environments has become an area of intensive research. Additional navigation sensor data can be obtained from visual observations (stars or terrain), inertial measurement units, radar, measurements of the local magnetic field, or perhaps even gravity. Absolute and relative positioning via magnetic field measurements have been shown to be viable in many applications including ground navigation, low altitude aircraft flight, and spaceflight. There is greater variability in the magnetic field over shorter distances when flying at low altitude and in ground applications, leading to more accurate positioning. However, ground-based magnetic navigation is often heavily influenced by man-made structures, especially in urban environments. This is not the case for airborne magnetic navigation since the influence of buildings, roads, etc. is negligible for typical aircraft altitudes. For absolute magnetic navigation, the positioning accuracy decreases as altitude increases for a given vehicle velocity, but the observed time variability in the field can be reclaimed by traveling faster through the field. Thus, navigation accuracy becomes a balance of speed and altitude since the higher altitude can be counterbalanced by higher velocity. To understand these effects quantitatively, we explored various techniques to aid a simulated inertial measurement unit with magnetic information. Using a technique known as two-dimensional magnetic map matching, we simulated the performance of airborne magnetic navigation at fixed speed while varying the altitude, flight direction, magnetometer data collection time, reference magnetic map bias error, and type of trajectory (over land or over ocean).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The JCMT BISTRO Survey: The Magnetic Field Strength in the Orion A Filament

We determine the magnetic field strength in the OMC 1 region of the Orion A filament via a new implementation of the Chandrasekhar–Fermi method using observations performed as part of the James Clerk Maxwell Telescope (JCMT) B-Fields In Star-forming Region Observations (BISTRO) survey with the POL-2 instrument. We combine BISTRO data with archival SCUBA-2 and HARP observations to find a plane-of-sky magnetic field strength in OMC 1 of B{sub pos}=6.6±4.7 mG, where δB{sub pos}=4.7 mG represents a predominantly systematic uncertainty. We develop a new method for measuring angular dispersion, analogous to unsharp masking. We find a magnetic energy density of ∼1.7×10{sup −7} J m{sup −3} in OMC 1, comparable both to the gravitational potential energy density of OMC 1 (∼10{sup −7} J m{sup −3}) and to the energy density in the Orion BN/KL outflow (∼10{sup −7} J m{sup −3}). We find that neither the Alfvén velocity in OMC 1 nor the velocity of the super-Alfvénic outflow ejecta is sufficiently large for the BN/KL outflow to have caused large-scale distortion of the local magnetic field in the ∼500 yr lifetime of the outflow. Hence, we propose that the hourglass field morphology in OMC 1 is caused by the distortion of a primordial cylindrically symmetric magnetic field by the gravitational fragmentation of the filament and/or the gravitational interaction of the BN/KL and S clumps. We find that OMC 1 is currently in or near magnetically supported equilibrium, and that the current large-scale morphology of the BN/KL outflow is regulated by the geometry of the magnetic field in OMC 1, and not vice versa.

79 ASTRONOMY AND ASTROPHYSICS↗

Kiloparsec-scale simulations of star formation in disk galaxies. III. Structure and dynamics of filaments and clumps in giant molecular clouds

We present hydrodynamic simulations of self-gravitating dense gas in a galactic disk, exploring scales ranging from 1 kpc down to ∼0.1 pc. Our primary goal is to understand how dense filaments form in giant molecular clouds (GMCs). These structures, often observed as infrared dark clouds (IRDCs) in the Galactic plane, are thought to be the precursors to massive stars and star clusters, so their formation may be the rate-limiting step controlling global star formation rates in galactic systems as described by the Kennicutt–Schmidt relation. Our study follows on from Van Loo et al., which carried out simulations to 0.5 pc resolution and examined global aspects of the formation of dense gas clumps and the resulting star formation rate. Here, using our higher resolution, we examine the detailed structural, kinematic, and dynamical properties of dense filaments and clumps, including mass surface density (Σ) probability distribution functions, filament mass per unit length and its dispersion, lateral Σ profiles, filament fragmentation, filament velocity gradients and infall, and degree of filament and clump virialization. Where possible, these properties are compared to observations of IRDCs. By many metrics, especially too large mass fractions of high Σ>1 g cm{sup −2} material, too high mass per unit length dispersion due to dense clump formation, too high velocity gradients, and too high velocity dispersion for a given mass per unit length, the simulated filaments differ from observed IRDCs. We thus conclude that IRDCs do not form from global fast collapse of GMCs. Rather, we expect that IRDC formation and collapse are slowed significantly by the influence of dynamically important magnetic fields, which may thus play a crucial role in regulating galactic star formation rates.

79 ASTRONOMY AND ASTROPHYSICS↗

High-energy neutrino emission from magnetized jets of rapidly rotating protomagnetars

ABSTRACT Relativistic jets originating from protomagnetar central engines can lead to long duration gamma-ray bursts (GRBs) and are considered potential sources of ultra-high-energy cosmic rays and secondary neutrinos. We explore the propagation of such jets through a broad range of progenitors, from stars which have shed their envelopes to supergiants which have not. We use a semi-analytical spin-down model for the strongly magnetized and rapidly rotating protoneutron star (PNS) to investigate the role of central engine properties such as the surface dipole field strength, initial rotation period, and jet opening angle on the interactions and dynamical evolution of the jet-cocoon system. With this model, we determine the properties of the relativistic jet, the mildly relativistic cocoon, and the collimation shock in terms of system parameters such as the time-dependent jet luminosity, injection angle, and density profile of the stellar medium. We also analyse the criteria for a successful jet breakout, the maximum energy that can be deposited into the cocoon by the relativistic jet, and structural stability of the magnetized outflow relative to local instabilities. Lastly, we compute the high-energy neutrino emission as these magnetized outflows burrow through their progenitors. Precursor neutrinos from successful GRB jets are unlikely to be detected by IceCube, which is consistent with the results of previous works. On the other hand, we find that high-energy neutrinos may be produced for extended progenitors like blue and red supergiants, and we estimate the detectability of neutrinos with next generation detectors such as IceCube-Gen2.

Astronomy & Astrophysics↗

Gravitational waves from rotating neutron stars: Current limits and prospects

Rotating neutron stars that emit continuous gravitational waves are among promising targets of the LIGO and Virgo detectors: sufficiently large non-axisymmetrie deformation w.r.t. the axis of rotation of a star generates a time-varying mass-quadrupole moment and henceforth gravitational wave emission. The departure from an axisymmetrie shape may be caused by the internal magnetic field and/or elastic stresses in the crust/core. If detected, it will provide novel insight into the presently obscured details of the interior neutron-star structure. This talk presents basic types of searches for such signals: from targeted searches from known pulsars to all-sky wide parameter searches for unknown objects. Selected methods used in the data analysis and to calculate the upper limits on the gravitational waves in the initial phase of LIGO and Virgo projects are briefly described. Observational results of LIGO and Virgo collaborations include “beating” the spin-down limit for the Crab and Vela pulsars [7, 11], search for a coherent signal from the direction of the Cas A supernova remnant [5], as well as the Galactic center [1], SN1987A and the Sco-X1 binary with the cross-correlation method [6], and the all-sky searches for signals of unknown position and frequency [2, 4, 8].

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Multidimensional Simulations of Core Convection

The cores of main sequence intermediate- and high-mass stars are convective. Mixing at the radiative–convective boundary, waves excited by the convection, and magnetic fields generated by convective dynamos all influence the main sequence and post-main sequence evolution of these stars. These effects must be understood to accurately model the structure and evolution of intermediate- and high-mass stars. Unfortunately, there are many challenges in simulating core convection due to the wide range of temporal and spatial scales, as well as many important physics effects. In this review, we describe the latest numerical strategies to address these challenges. We then describe the latest state-of-the-art simulations of core convection, summarizing their main findings. These simulations have led to important insights into many of the processes associated with core convection. Two outstanding problems with multidimensional simulations are, 1. it is not always straightforward to extrapolate from simulation parameters to the parameters of real stars; and 2. simulations using different methods sometimes appear to arrive at contradictory results. To address these issues, next generation simulations of core convection must address how their results depend on stellar luminosity, dimensionality, and turbulence intensity. Furthermore, code comparison projects will be essential to establish robust parameterizations that will become the new standard in stellar modeling.

79 ASTRONOMY AND ASTROPHYSICS↗

Further Evidence of Modified Spin-down in Sun-like Stars: Pileups in the Temperature–Period Distribution

We combine stellar surface rotation periods determined from NASA's Kepler mission with spectroscopic temperatures to demonstrate the existence of pileups at the long-period and short-period edges of the temperature–period distribution for main-sequence stars with temperatures exceeding ~5500 K. The long-period pileup is well described by a curve of constant Rossby number, with a critical value of Ro crit ≲ Ro ⊙ . The long-period pileup was predicted by van Saders et al. as a consequence of weakened magnetic braking, in which wind-driven angular momentum losses cease once stars reach a critical Rossby number. Stars in the long-period pileup are found to have a wide range of ages (~2–6 Gyr), meaning that, along the pileup, rotation period is strongly predictive of a star's surface temperature but weakly predictive of its age. The short-period pileup, which is also well described by a curve of constant Rossby number, is not a prediction of the weakened magnetic braking hypothesis but may instead be related to a phase of slowed surface spin-down due to core-envelope coupling. The same mechanism was proposed by Curtis et al. to explain the overlapping rotation sequences of low-mass members of differently aged open clusters. The relative dearth of stars with intermediate rotation periods between the short- and long-period pileups is also well described by a curve of constant Rossby number, which aligns with the period gap initially discovered by McQuillan et al. in M-type stars. These observations provide further support for the hypothesis that the period gap is due to stellar astrophysics, rather than a nonuniform star formation history in the Kepler field.

79 ASTRONOMY AND ASTROPHYSICS↗

Relativistic Magnetic Reconnection in Astrophysical Plasmas: A Powerful Mechanism of Nonthermal Emission

Magnetic reconnection—a fundamental plasma physics process, where magnetic field lines of opposite polarity annihilate—is invoked in astrophysical plasmas as a powerful mechanism of nonthermal particle acceleration, able to explain fast-evolving, bright high-energy flares. Near black holes and neutron stars, reconnection occurs in the relativistic regime, in which the mean magnetic energy per particle exceeds the rest mass energy. This review reports recent advances in our understanding of the kinetic physics of relativistic reconnection (RR): ▪ Kinetic simulations have elucidated the physics of plasma heating and nonthermal particle acceleration in RR. ▪ The physics of radiative RR, with its self-consistent interplay between photons and reconnection-accelerated particles—a peculiarity of luminous, high-energy astrophysical sources—is the new frontier of research. ▪ RR plays a key role in global models of high-energy sources, in terms of both global-scale layers and reconnection sites generated as a by-product of local magnetohydrodynamic instabilities. We summarize themes of active investigation and future directions, emphasizing the role of upcoming observational capabilities, laboratory experiments, and new computational tools.

acceleration of particles↗

New Low-mass Eclipsing Binary Systems in Praesepe Discovered by K2

We present the discovery and characterization of four low-mass (M<0.6 M{sub ⊙}) eclipsing binary (EB) systems in the sub-Gyr old Praesepe open cluster using Kepler/K2 time series photometry and Keck/HIRES spectroscopy. We present a new Gaussian process EB model, GP–EBOP, as well as a method of simultaneously determining effective temperatures and distances for EBs. Three of the reported systems (AD 3814, AD 2615 and AD 1508) are detached and double-lined, and precise solutions are presented for the first two. We determine masses and radii to 1%–3% precision for AD 3814 and to 5%–6% for AD 2615. Together with effective temperatures determined to ∼50 K precision, we test the PARSEC v1.2 and BHAC15 stellar evolution models. Our EB parameters are more consistent with the PARSEC models, primarily because the BHAC15 temperature scale is hotter than our data over the mid-M-dwarf mass range probed. Both ADs 3814 and 2615, which have orbital periods of 6.0 and 11.6 days, are circularized but not synchronized. This suggests that either synchronization proceeds more slowly in fully convective stars than the theory of equilibrium tides predicts, or magnetic braking is currently playing a more important role than tidal forces in the spin evolution of these binaries. The fourth system (AD 3116) comprises a brown dwarf transiting a mid-M-dwarf, which is the first such system discovered in a sub-Gyr open cluster. Finally, these new discoveries increase the number of characterized EBs in sub-Gyr open clusters by 20% (40%) below M<1.5 M {sub ⊙} (M<0.6 M {sub ⊙}).

79 ASTRONOMY AND ASTROPHYSICS↗

The evolution of carbon-polluted white dwarfs at low effective temperatures

Taking advantage of the Gaia Data Release 2, recent studies have revisited the evolution of carbon-polluted white dwarfs (DQs) across a large range of effective temperatures. These analyses have clearly confirmed the existence of two distinct DQ evolutionary sequences: one with normal-mass white dwarfs and one with heavily polluted and generally more massive objects. The first sequence is thought to result from the dredge-up of carbon from the core, while the second could at least partially be made of descendants of hot DQs. However, the evolution of carbon-polluted white dwarfs below 6500 K remains unexplored, mainly due to the theoretical difficulties associated with modelling their dense atmospheres. In this work, we present a detailed star-by-star analysis of cool carbon-polluted white dwarfs. Our recently improved atmosphere models allow us to obtain good fits to most objects, including very cool DQpec white dwarfs with strongly shifted C2 molecular bands. We show herein that cool carbon-polluted white dwarfs keep following the two distinct evolutionary tracks previously identified at higher temperatures. We also find that most DQ white dwarfs transform into DQpec when their photospheric densities exceed ${\approx}0.15\, {\textrm{g\,cm}}^{-3}$. However, we identify stars for which the DQ→DQpec transition occurs at lower photospheric densities, possibly due to the presence of a strong magnetic field.

79 ASTRONOMY AND ASTROPHYSICS↗

What Sets the Star Formation Rate of Molecular Clouds? The Density Distribution as a Fingerprint of Compression and Expansion Rates

We use a suite of 3D simulations of star-forming molecular clouds, with and without stellar feedback, magnetic fields, and driven turbulence, to study the compression and expansion rates of the gas as functions of density. We show that, around the mean density, supersonic turbulence promotes rough equilibrium between the amounts of compressing and expanding gas, consistent with continuous gas cycling between high- and low-density states. We find that the inclusion of protostellar jets produces rapidly expanding and compressing low-density gas. We find that the gas mass flux peaks at the transition between the lognormal and power-law forms of the density probability distribution function (PDF). This is consistent with the transition density tracking the post-shock density, which promotes an enhancement of mass at this density (i.e., shock compression and filament formation). At high densities, the gas dynamics are dominated by self-gravity: the compression rate in all of our runs matches the rate of the run with only gravity, suggesting that processes other than self-gravity have little effect at these densities. The net gas mass flux becomes constant at a density below the sink formation threshold, where it equals the star formation rate. The density at which the net gas mass flux equals the star formation rate is one order of magnitude lower than our sink threshold density, corresponds to the formation of the second power-law tail in the density PDF, and sets the overall star formation rates of these simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

Electric field screening with backflow at pulsar polar cap

Recent γ-ray observations suggest that particle acceleration occurs at the outer region of the pulsar magnetosphere. The magnetic field lines in the outer acceleration region (OAR) are connected to the neutron star surface (NSS). If copious electron–positron pairs are produced near the NSS, such pairs flow into the OAR and screen the electric field there. To activate the OAR, the electromagnetic cascade due to the electric field near the NSS should be suppressed. However, since a return current is expected along the field lines through the OAR, the outflow extracted from the NSS alone cannot screen the electric field just above the NSS. In this paper, we analytically and numerically study the electric field screening at the NSS, taking into account the effects of the backflowing particles from the OAR. In certain limited cases, the electric field is screened without significant pair cascade if only ultra-relativistic particles (γ≫1) flow back to the NSS. On the other hand, if electron–positron pairs with a significant number density and mildly relativistic temperature, expected to distribute in a wide region of the magnetosphere, flow back to the NSS, these particles adjust the current and charge densities so that the electric field can be screened without pair cascade. We obtain the condition needed for the number density of particles to screen the electric field at the NSS. We also find that in the ion-extracted case from the NSS, bunches of particles are ejected to the outer region quasi-periodically, which is a possible mechanism of observed radio emission.

79 ASTRONOMY AND ASTROPHYSICS↗