Magnetic Flares Research Articles

Searching for pulsars, magnetars, and fast radio bursts in the sculptor galaxy using MeerKAT

Abstract The Sculptor Galaxy (NGC 253), located in the Southern Hemisphere, far off the Galactic Plane, has a relatively high star-formation rate of about 7 M⊙ yr−1 and hosts a young and bright stellar population, including several super star clusters and supernova remnants. It is also the first galaxy, apart from the Milky Way Galaxy to be associated with two giant magnetar flares. As such, it is a potential host of pulsars and/or fast radio bursts in the nearby Universe. The instantaneous sensitivity and multibeam sky coverage offered by MeerKAT therefore make it a favourable target. We searched for pulsars, radio-emitting magnetars, and fast radio bursts in NGC 253 as part of the TRAPUM large survey project with MeerKAT. We did not find any pulsars during a four-hour observation, and derive a flux density limit of 4.4 μJy at 1400 MHz, limiting the pseudo-luminosity of the brightest putative pulsar in this galaxy to 54 Jy kpc2. Assuming universality of pulsar populations between galaxies, we estimate that detecting a pulsar as bright as this limit requires NGC 253 to contain a pulsar population of ⪞20 000. We also did not detect any single pulses and our single pulse search flux density limit is 62 mJy at 1284 MHz. Our search is sensitive enough to have detected any fast radio bursts and radio emission similar to the brighter pulses seen from the magnetar SGR J1935+2154 if they had occurred during our observation.

GRB 180128A: A second magnetar giant flare candidate from the Sculptor Galaxy

Magnetars are slowly rotating neutron stars that possess the strongest magnetic fields known in the cosmos (1014 − 1015 G). They display a range of transient high-energy electromagnetic activity. The brightest and most energetic of these events are the gamma-ray bursts (GRBs) known as magnetar giant flares (MGFs), with isotropic energies Eiso ≈ 1044 − 1046 erg. Only seven MGF detections have been made to date: three unambiguous events occurred in our Galaxy and the Magellanic Clouds, and the other four MGF candidates are associated with nearby star-forming galaxies. As all seven identified MGFs are bright at Earth, additional weaker events likely remain unidentified in archival data. We conducted a search of the Fermi Gamma-ray Burst Monitor database for candidate extragalactic MGFs and, when possible, collected localization data from the Interplanetary Network (IPN) satellites. Our search yielded one convincing event, GRB 180128A. IPN localizes this burst within NGC 253, commonly known as the Sculptor Galaxy. The event is the second MGF in modern astronomy to be associated with this galaxy and the first time two bursts have been associated with a single galaxy outside our own. Here we detail the archival search criteria that uncovered this event and its spectral and temporal properties, which are consistent with expectations for a MGF. We also discuss the theoretical implications and finer burst structures resolved from various binning methods. Our analysis provides observational evidence of an eighth identified MGF.

Quasi-periodic oscillations in rotating and deformed space–times

ABSTRACT Quasi-periodic oscillation (QPOs) analysis is important for understanding the dynamical behaviour of many astrophysical objects during transient events such as gamma-ray bursts, solar flares, magnetar flares, and fast radio bursts. In this paper, we analyse QPO data in low-mass X-ray binary (LMXB) systems, using the Lense-Thirring, Kerr, and approximate Zipoy-Voorhees metrics. We demonstrate that the inclusion of spin and quadrupole parameters modifies the well-established results for the fundamental frequencies in the Schwarzschild space–time. We interpret the QPO data within the framework of the standard relativistic precession model, allowing us to infer the values of the mass, spin, and quadrupole parameters of neutron stars in LMXBs. We explore recent QPO data sets from eight distinct LMXBs, assess their optimal parameters, and compare our findings with results in the existing literature. Finally, we discuss the astrophysical implications of our findings.

Magnetar QPOs and Neutron Star Crust Elasticity

The crust region is a tiny fraction of neutron stars, but it has a variety of physical properties and plays an important role in astronomical observations. One of the properties characterizing the crust is elasticity. In this review, with the approach of asteroseismology, we systematically examine neutron star oscillations excited by crust elasticity, adopting the Cowling approximation. In particular, by identifying the quasi-periodic oscillations observed in magnetar flares with the torsional oscillations, we make a constraint on the nuclear saturation parameters. In addition, we also discuss how the shear and interface modes depend on the neutron star properties. Once one detects an additional signal associated with neutron star oscillations, one can obtain a more severe constraint on the saturation parameters and/or neutron star properties, which must be a qualitatively different constraint obtained from terrestrial experiments and help us to complementarily understand astrophysics and nuclear physics.

Search for Gravitational-wave Transients Associated with Magnetar Bursts in Advanced LIGO and Advanced Virgo Data from the Third Observing Run

Gravitational waves are expected to be produced from neutron star oscillations associated with magnetar giant flares and short bursts. We present the results of a search for short-duration (milliseconds to seconds) and long-duration (∼100 s) transient gravitational waves from 13 magnetar short bursts observed during Advanced LIGO, Advanced Virgo, and KAGRA’s third observation run. These 13 bursts come from two magnetars, SGR 1935+2154 and Swift J1818.0−1607. We also include three other electromagnetic burst events detected by Fermi-GBM which were identified as likely coming from one or more magnetars, but they have no association with a known magnetar. No magnetar giant flares were detected during the analysis period. We find no evidence of gravitational waves associated with any of these 16 bursts. We place upper limits on the rss of the integrated incident gravitational-wave strain that reach 3.6 × 10−23 /Hz at 100 Hz for the short-duration search and 1.1 × 10−22 /Hz at 450 Hz for the long-duration search. For a ringdown signal at 1590 Hz targeted by the short-duration search the limit is set to 2.3 × 10−22 /Hz . Using the estimated distance to each magnetar, we derive upper limits on the emitted gravitational-wave energy of 1.5 × 1044 erg (1.0 × 1044 erg) for SGR 1935+2154 and 9.4 × 1043 erg (1.3 × 1044 erg) for Swift J1818.0−1607, for the short-duration (long-duration) search. Assuming isotropic emission of electromagnetic radiation of the burst fluences, we constrain the ratio of gravitational-wave energy to electromagnetic energy for bursts from SGR 1935+2154 with the available fluence information. The lowest of these ratios is 4.5 × 103.

A magnetar giant flare in the nearby starburst galaxy M82.

Magnetar giant flares are rare explosive events releasing up to 1047 erg in gamma rays in less than 1 second from young neutron stars with magnetic fields up to 1015-16 G (refs. 1,2). Only three such flares have been seen from magnetars in our Galaxy3,4 and in the Large Magellanic Cloud5 in roughly 50 years. This small sample can be enlarged by the discovery of extragalactic events, as for a fraction of a second giant flares reach luminosities above 1046 erg s-1, which makes them visible up to a few tens of megaparsecs. However, at these distances they are difficult to distinguish from short gamma-ray bursts (GRBs); much more distant and energetic (1050-53 erg) events, originating in compact binary mergers6. A few short GRBs have been proposed7-11, with different amounts of confidence, as candidate giant magnetar flares in nearby galaxies. Here we report observations of GRB 231115A, positionally coincident with the starburst galaxy M82 (ref. 12). Its spectral properties, along with the length of the burst, the limits on its X-ray and optical counterparts obtained within a few hours, and the lack of a gravitational wave signal, unambiguously qualify this burst as a giant flare from a magnetar in M82.

LISA and LISA-like mission test-mass charging for gamma-ray burst detection

Cubic gold-platinum test-masses (TMs) play the role of free-falling geodesic reference and interferometer end mirrors of the future Laser Interferometer Space Antenna (LISA) observatory for low-frequency gravitational wave detection in space. A similar arrangement has been proposed for the Chinese missions Taiji and TianQin and for the LISA follow-on missions such as ALIA and BBO. The TMs are charged by high-energy particles and photons. The deposited charge couples with stray electric fields surrounding the TMs thus inducing spurious forces that limit the sensitivity of the mission mainly at low frequencies. The TM charging was measured in space in 2016-2017 with LISA Pathfinder (LPF), meant for the testing of the LISA instrumentation. Unfortunately, during the time LPF remained in orbit, no solar energetic particle events or major astrophysical phenomena were observed. We aim at estimating the LISA TM charging attributable to long, short gamma-ray bursts (GRBs) and magnetar flares in comparison to that of charged particles of galactic and solar origin. The contribution of these major astrophysical phenomena to the LISA TM charging is discussed here for the first time. The results found here can be extended to LISA-like missions. The response of the radiation monitors hosted on the three LISA S/C is also evaluated. We show that long, intense extragalactic GRBs and galactic magnetar flares at kpc distances can be detected and monitored through a sudden change from positive to negative charging of the TMs and an increase of the TM charging noise. This is a unique signature since both galactic and solar particles charge positively the LISA TMs. This peculiar behavior of the TM charging would allow monitoring the whole dynamics of GRBs. The suggestion reported in the literature, about the detection of long GRBs and gravitational waves from the same sources, in principle, may apply to LISA and other LISA-like missions since the increase of the TM charging noise during these extreme transient phenomena is estimated to remain below the mission sensitivity while particle detectors are expected to saturate.

3D Magnetic Free Energy and Flaring Activity Using 83 Major Solar Flares

In this Letter, we examine the relationship between 3D magnetic free energy (MFE) and flaring activity using 83 major solar flares (M-class and X-class) in nine solar active regions (ARs). For this, we use 998 nonlinear force-free field extrapolations compiled by the “Institute for Space-Earth Environmental Research Database” at Nagoya University. These ARs produced at least three major flares with distinct rising and peak phases of 3D MFE. For each phase, the solar flare occurrence rate (FOR) is calculated as a ratio of the number of flares to the duration. The major results from this study are summarized as follows. First, there is no clear linear correlation (CC = 0.15) between 3D MFE and flare peak flux. Second, the FOR (3.4 day−1) of the rising phase is a little higher than that (3.1 day−1) of the peak phase, depending on AR. Third, for several flares, there are noticeable decreases in 3D MFE, which correspond to the typical energy of a major flare (about 1032 erg). Fourth, it is interesting to note that there are noticeable enhancements in FORs at several local maxima of 3D MFE, which may be associated with flux emergence and/or shearing motions. Fifth, the flare index rates, which are defined as the summation of flaring activity divided by the duration, of rising and peak phases are 151 day−1 and 314 day−1, respectively. Our results imply that the traditional and simple “storage and release” model does not apply to flare activities, and the random perturbation may be important for triggering flares.

Investigation of Nonequilibrium Ionization Plasma during a Giant Flare of UX Arietis Triggered with MAXI and Observed with NICER

We detected a giant X-ray flare from the RS CVn–type binary star UX Ari using the Monitor of All-sky X-ray Image on 2020 August 17 and started a series of Neutron star Interior Composition Explorer observations 89 minutes later. For a week, the entire duration of the flare was covered with 32 snapshot observations including the rising phase. The X-ray luminosity reached 2 × 1033 erg s−1, and the entire energy release was ∼1038 erg in the 0.5–8.0 keV band. X-ray spectra characterized by continuum emission with lines of Fe xxv Heα and Fe xxvi Lyα were obtained. We found that the temperature peaks before the flux does, which suggests that the period of plasma formation in the magnetic flare loop was captured. Using the continuum information (temperature, flux, and their delay time), we estimated the flare loop size to be ∼3 × 1011 cm and the peak electron density to be ∼4 × 1010 cm−3. Furthermore, using the line ratio of Fe xxv and Fe xxvi, we investigated any potential indications of deviation from collisional ionization equilibrium (CIE). The X-ray spectra were consistent with CIE plasma throughout the flare, but the possibility of an ionizing plasma away from CIE was not rejected in the flux rising phase.

Photometric Variability of Low Mass Stars and Brown Dwarfs in IC 348 and Taurus Star-Forming Regions

Low-mass stars belonging to the M spectral type are the most numerous stars in our Galaxy, amounting to about two-thirds in number, and are found at the bottom of the main sequence in the H-R diagram. Photometric studies of low-mass stars, including brown dwarfs (Bds), provide several important evolutions of their atmosphere, magnetic flares and chromospheric activity. This paper highlights a few interesting results from our optical I-band observations of 2MASS J03435638+3209591 in the young star-forming IC 348 region and three BDs in Taurus star-forming regions using ground-based telescopes as well as a space-based telescope. We estimated the fast periodicities in the range of 1.5 to 3 hours in Taurus BDs. Furthermore, using the long-term photometry from the Transiting Exoplanet Survey Satellite (TESS), we have conducted a time-resolved variability analysis of CFHT-BD-Tau 4. The periodogram analysis of TESS data reveals an orbital period of ∼ 3 days. We found two flare events in TESS sector 43 data for this BD and estimated the flared energies as 4.59×1035 erg and 2.64×1036 erg, which sit in the superflare range.

X-Ray, Near-ultraviolet, and Optical Flares Produced by Colliding Magnetospheres in the Young High-eccentricity Binary DQ Tau

DQ Tau is a unique young high-eccentricity binary system that exhibits regular magnetic reconnection flares and pulsed accretion near periastron. We conducted NuSTAR, Swift, and Chandra observations during the 2022 July 30 periastron to characterize X-ray, near-ultraviolet (NUV), and optical flaring emissions. Our findings confirm the presence of X-ray superflares accompanied by substantial NUV and optical flares, consistent with previous discoveries of periastron flares in 2010 and 2021. These observations, supported by new evidence, strongly establish the magnetosphere collision mechanism as the primary driver of magnetic energy release during DQ Tau’s periastron flares. The energetics of the observed X-ray superflares remain consistent across the three periastra, indicating recurring energy sources during each passage, surpassing the capabilities of single stars. The observed flaring across multiple bands supports the Adams et al. model for magnetosphere interaction in eccentric binaries. Evidence from modeling and past and current observations suggests that both the millimeter/X-ray periastron flares and, tentatively, the magnetic-reconnection-related components of the optical/NUV emissions conform to the classical solar/stellar nonthermal thick-target model, except for the distinctive magnetic energy source. However, our NuSTAR observations suffered from high background levels, hindering the detection of anticipated nonthermal hard X-rays. Furthermore, we report the serendipitous discovery of X-ray superflares occurring away from periastron, potentially associated with interacting magnetospheres. The current study is part of a broader multiwavelength campaign, which plans to investigate the influence of DQ Tau’s stellar radiation on gas-phase ion chemistry within its circumbinary disk.

The Role of Magnetic Shear in Reconnection-driven Flare Energy Release

Using observations from the Solar Dynamics Observatory’s Atmosphere Imaging Assembly and the Ramaty High Energy Solar Spectroscopic Imager, we present novel measurements of the shear of post-reconnection flare loops (PRFLs) in SOL20141218T21:40 and study its evolution with respect to magnetic reconnection and flare emission. Two quasi-parallel ribbons form adjacent to the magnetic polarity inversion line (PIL), spreading in time first parallel to the PIL and then mostly in a perpendicular direction. We measure the magnetic reconnection rate from the ribbon evolution, and also the shear angle of a large number of PRFLs observed in extreme ultraviolet passbands (≲1 MK). For the first time, the shear angle measurements are conducted using several complementary techniques allowing for cross validation of the results. In this flare, the total reconnection rate is much enhanced before a sharp increase in the hard X-ray emission, and the median shear decreases from 60°–70° to 20°, on a timescale of 10 minutes. We find a correlation between the shear-modulated total reconnection rate and the nonthermal electron flux. These results confirm the strong-to-weak shear evolution suggested in previous observational studies and reproduced in numerical models, and also confirm that, in this flare, reconnection is not an efficient producer of energetic nonthermal electrons during the first 10 minutes when the strongly sheared PRFLs are formed. We conclude that an intermediate shear angle, ≤40°, is needed for efficient particle acceleration via reconnection, and we propose a theoretical interpretation.

An Evenly Spaced LSST Cadence for Rapidly Variable Stars

Abstract Stars exhibit a bewildering variety of rapidly variable behaviors ranging from explosive magnetic flares to stochastically changing accretion to periodic pulsations or rotation. The principal Rubin Observatory Legacy Survey of Space and Time (LSST) surveys will have cadences too sparse and irregular to capture many of these phenomena. We propose here an LSST microsurvey to observe a single Galactic field, rich in unobscured stars, in a continuous sequence of 30 s exposures for one long winter night in a single photometric band. The result will be a unique data set of ∼1 million regularly spaced stellar light curves. The light curves will constitute a comprehensive collection of late-type stellar flaring, but also other classes like short-period binary systems and cataclysmic variables, young stellar objects, and ultrashort-period exoplanets. An unknown variety of anomalous solar system, Galactic, and extragalactic variables and transients may also be present. A powerful array of statistical procedures can be applied to individual light curves from the long-standing fields of time series analysis, signal processing, and econometrics. Dozens of “features” describing the variability can be extracted and the ensemble of light curves can be subject to advanced machine-learning clustering procedures. This will give a unique, authoritative, objective taxonomy of the rapidly variable sky derived from identically cadenced light curves. This microsurvey is best performed early in the Rubin Observatory program, and the results can inform the wider community on the best approaches to variable star identification and classification from the sparse, irregular cadences that dominate the planned surveys.

Avalanches and the Distribution of Reconnection Events in Magnetized Circumstellar Disks

Cosmic rays produced by young stellar objects can potentially alter the ionization structure, heating budget, chemical composition, and accretion activity in circumstellar disks. The inner edges of these disks are truncated by strong magnetic fields, which can reconnect and produce flaring activity that accelerates cosmic radiation. The resulting cosmic rays can provide a source of ionization and produce spallation reactions that alter the composition of planetesimals. These reconnection and particle acceleration processes are analogous to the physical processes that produce flaring in and the heating of stellar coronae. Flaring events on the surface of the Sun exhibit a power-law distribution of energy, reminiscent of those measured for earthquakes and avalanches. Numerical lattice reconnection models are capable of reproducing the observed power-law behavior of solar flares under the paradigm of self-organized criticality. One interpretation of these experiments is that the solar corona maintains a nonlinear attractor—or “critical”—state by balancing energy input via braided magnetic fields and output via reconnection events. Motivated by these results, we generalize the lattice reconnection formalism for applications in the truncation region of magnetized disks. Our numerical experiments demonstrate that these nonlinear dynamical systems are capable of both attaining and maintaining criticality in the presence of Keplerian shear and other complications. The resulting power-law spectrum of flare energies in the equilibrium attractor state is found to be nearly universal in magnetized disks. This finding indicates that magnetic reconnection and flaring in the inner regions of circumstellar disks occur in a manner similar to the activity on stellar surfaces. These results, in turn, have ramifications for the spallation-driven injection of radionuclides in planetesimals, disk ionization, and the subsequent planetary formation process.

Multiwavelength afterglow emission from bursts associated with magnetar flares and fast radio bursts

ABSTRACT Magnetars have been considered as progenitors of magnetar giant flares (MGFs) and fast radio bursts (FRBs). We present detailed studies on afterglow emissions caused by bursts that occur in their wind nebulae and surrounding baryonic ejecta. In particular, following the bursts-in-bubble model, we analytically and numerically calculate spectra and light curves of such afterglow emission. We scan parameter space for the detectability of radio signals, and find that a burst with ∼1045 erg is detectable with the Very Large Array or other next-generation radio facilities. The detection of multiwavelength afterglow emission from MGFs and/or FRBs is of great significance for their localization and revealing their progenitors, and we estimate the number of detectable afterglow events.

Detection of Quasi-periodic Oscillations in SGR 150228213

The detection of quasi-periodic oscillations (QPOs) in magnetar giant flares (GFs) has brought a new perspective to studies of the mechanism of magnetar bursts. Due to the scarcity of GFs, searching for QPOs in magnetar short bursts is reasonable. Here we report the detection of a narrow QPO at approximately 110 Hz and a wide QPO at approximately 60 Hz in the short magnetar burst SGR 150228213, with a confidence level of 3.35σ. This burst was initially attributed to 4U 0142+61 by Fermi/GBM on location, but we have not detected such QPOs in other bursts from this magnetar. We also found that there was a repeating fast radio burst associated with SGR 150228213 on location. Finally, we discuss the possible origins of SGR 150228213.

Expectations for fast radio bursts in neutron star–massive star binaries

Context. Recent observations of a small sample of repeating fast radio bursts (FRBs) have revealed a periodicity in their bursting activity that suggests a binary origin for the modulation. Aims. We set out to explore the scenario where a subset of repeating FRBs originates in binary systems that host a highly energetic neutron star and a massive companion star, akin to γ-ray binaries and young high-mass X-ray binaries. Methods. In this scenario, we infer observables, compare them with current observational constraints, and make predictions for future observations. Firstly, we specifically focused on the host galaxy properties and binary formation rates. Subsequently, we investigated the expected evolution of the rotation and dispersion measure in this scenario, the predicted birth site offsets, and the origin of the persistent radio emission observed in a subset of these systems. Results. The host galaxies for repeating FRBs favour the formation of neutron star–massive star binary systems, but any conclusive evidence will require future discoveries and localisations of FRBs. The birth rate of high-mass X-ray binaries, used as a proxy for all considered binaries, significantly exceeds the estimated rate of FRBs, which can be explained if only a small subset of these systems produce FRBs. We show that, under simple assumptions, we can reproduce the dispersion measure and rotation measure evolution that is seen in a subset of repeating FRBs. We also discuss the possibility of detecting a persistent radio source associated with the FRB due to an intra-binary shock between the companion star wind and either the pulsar wind or giant magnetar flares. The observed long-term luminosity stability of the persistent radio sources is most consistent with a giant flare-powered scenario. However, this explanation is highly dependent on the magnetic field properties of the neutron star. Conclusions. With these explorations, we provide a framework to discuss future FRB observations in the context of neutron star–massive star binary scenarios. We conclude that more localisations and observations of repeaters will be necessary to conclusively determine or rule out a connection between (repeating) FRBs and such binaries.

Faraday rotation measure variations of repeating fast radio burst sources

ABSTRACT Recently, some fast radio burst (FRB) repeaters were reported to exhibit complex, diverse variations of Faraday rotation measures (RMs), which implies that they are surrounded by an inhomogeneous, dynamically evolving, magnetized environment. We systematically investigate some possible astrophysical processes that may cause RM variations of an FRB repeater. The processes include (1) a supernova remnant (SNR) with a fluctuating medium; (2) a binary system with stellar winds from a massive/giant star companion or stellar flares from a low-mass star companion; (3) a pair plasma medium from a neutron star (including pulsar winds, pulsar wind nebulae, and magnetar flares); (4) outflows from a massive black hole. For the SNR scenario, a large relative RM variation within a few years requires that the SNR is young with a thin and local anisotropic shell, or the size of dense gas clouds in interstellar/circumstellar medium around the SNR is extremely small. If the RM variation is caused by the companion medium in a binary system, it is more likely from the stellar winds of a massive/giant star companion. The RM variation contributed by stellar flares from a low-mass star is disfavored, because this scenario predicts an extremely large relative RM variation during a short period of time. The scenarios invoking a pair plasma from a neutron star can be ruled out due to their extremely low RM contributions. Outflows from a massive black hole could provide a large RM variation if the FRB source is in the vicinity of the black hole.

Direct emission of strong radio pulses during magnetar flares

ABSTRACT The emission of intense radio pulses by flaring magnetars is investigated. Small-scale current gradients can be imprinted into a strongly magnetized outflow by the same processes that source fireball radiation in the closed magnetosphere. This structure arises from a combination of crustal yielding, internal tearing, and turbulent cascade. We consider the quasi-linear development of weak, small-scale currents as (i) they are stretched out and frozen by relativistic expansion, and then (ii) pass through a shock. In particular, we derive the amplitudes of the ordinary and fast waves that emerge downstream of a relativistically magnetized shock in response to a mode that is frozen into the upstream flow (a frozen Alfvén wave or entropy wave). An upstream mode with comoving wavelength exceeding the skin depth can linearly convert to a secondary mode propagating above the plasma frequency. A simple and accurate treatment of shocks with extreme magnetization is developed, and the formation of internal shocks in the outflow from a bursting, rotating magnetar is outlined. The emission process described here does not require a strong shock or cool e± pairs (in contrast with the electromagnetic maser shock instability). In some cases, a high-frequency wave is reflected back to the observer, but with a minuscule amplitude that makes it subdominant to other emission channels. The dominant secondary electromagnetic mode is superluminal at emission, is subject to weak induced scattering within the outflow, and can reach the observer in the radio band.

Neutron star inner crust: reduction of shear modulus by nuclei finite size effect

ABSTRACT The elasticity of neutron star crust is important for adequate interpretation of observations. To describe elastic properties one should rely on theoretical models. The most widely used is Coulomb crystal model (system of point-like charges on neutralizing uniform background), in some works it is corrected for electron screening. These models neglect finite size of nuclei. This approximation is well justified except for the innermost crustal layers, where nuclei size becomes comparable with the inter-nuclear spacing. Still, even in those dense layers it seems reasonable to apply the Coulomb crystal result, if one assumes that nuclei are spherically symmetric: Coulomb interaction between them should be the same as interaction between point-like charges. This argument is indeed correct; however, as we point here, shear of crustal lattice generates (microscopic) quadrupole electrostatic potential in a vicinity of lattice cites, which induces deformation on the nuclei. We analyse this problem analytically within compressible liquid drop model. In particular, for ground state crust composition the effective shear modulus is reduced for a factor of $1-u^{5/3}/(2+3\, u-4\, u^{1/3})$, where u is the ratio of the nuclei volume to the volume of the cell. This result is universal, i.e. it does not depend on the applied nucleon interaction model within applied approach. For the innermost layers of inner crust u ∼ 0.2 leading to reduction of the shear modulus by $\sim 25{{\ \rm per\ cent}}$, which can be important for correct interpretation of quasi-periodic oscillations in the tails of magnetar flares.