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<jats:title>Abstract</jats:title> <jats:p>Galaxy morphology and its evolution over the cosmic epoch hold important clues for understanding the regulation of star formation (SF). However, studying the relationship between morphology and SF has been hindered by the availability of consistent data at different redshifts. Our sample, combining CANDELS (0.8 &lt; <jats:italic>z</jats:italic> &lt; 2.5) and the GALEX-SDSS-WISE Legacy Catalog (GSWLC; <jats:italic>z</jats:italic> ∼ 0), has physical parameters derived using consistent SED fitting with flexible dust attenuation laws. We adopt visual classifications from Kartaltepe et al. and expand them to <jats:italic>z</jats:italic> ∼ 0 using SDSS images matching the physical resolution of CANDELS rest-frame optical images and deep FUV GALEX images matching the physical resolution of the CANDELS rest-frame FUV images. Our main finding is that disks with SF clumps at <jats:italic>z</jats:italic> ∼ 0 make a similar fraction (∼15%) of star-forming galaxies as at <jats:italic>z</jats:italic> ∼ 2. The clumpy disk contribution to the SF budget peaks at <jats:italic>z</jats:italic> ∼ 1, rather than <jats:italic>z</jats:italic> ∼ 2, suggesting that the principal epoch of disk assembly continues to lower redshifts. Star-forming spheroids (“blue nuggets”), though less centrally concentrated than quenched spheroids, contribute significantly (∼15%) to the SF budget at <jats:italic>z</jats:italic> ∼ 1–2, suggesting that compaction precedes quenching. Among green valley and quiescent galaxies, the pure spheroid fraction drops after <jats:italic>z</jats:italic> ∼ 1, whereas spheroids with disks (S0-like) become dominant. Mergers at or nearing coalescence are enhanced in SFR relative to the main sequence at all redshifts by a factor of ∼2, but contribute ≲5% to the SF budget, with their contribution remaining small above the main sequence.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The recent discovery of high-redshift (<jats:italic>z</jats:italic> &gt; 6) supermassive black holes (SMBH) favors the formation of massive seed BHs in protogalaxies. One possible scenario is the formation of massive stars <jats:inline-formula> <jats:tex-math> <?CDATA $\simeq {10}^{3}\mbox{--}{10}^{4}\,{M}_{\odot }$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb463ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> via runaway stellar collisions in a dense cluster, leaving behind massive BHs without significant mass loss. We study the pulsational instability of massive stars with the zero-age main-sequence (ZAMS) mass <jats:inline-formula> <jats:tex-math> <?CDATA ${M}_{\mathrm{ZAMS}}/{M}_{\odot }=300\mbox{--}3000$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb463ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> and metallicity <jats:inline-formula> <jats:tex-math> <?CDATA $Z/{Z}_{\odot }=0\mbox{--}{10}^{-1}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb463ieqn3.gif" xlink:type="simple" /> </jats:inline-formula>, and discuss whether or not pulsation-driven mass loss prevents massive BH formation. In the MS phase, the pulsational instability excited by the <jats:italic>ϵ</jats:italic>-mechanism grows in <jats:inline-formula> <jats:tex-math> <?CDATA $\sim {10}^{3}\,\mathrm{yr}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb463ieqn4.gif" xlink:type="simple" /> </jats:inline-formula>. As the stellar mass and metallicity increase, the mass-loss rate increases to <jats:inline-formula> <jats:tex-math> <?CDATA $\lesssim {10}^{-3}\ {M}_{\odot }\,{\mathrm{yr}}^{-1}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb463ieqn5.gif" xlink:type="simple" /> </jats:inline-formula>. In the red supergiant (RSG) phase, the instability is excited by the <jats:italic>κ</jats:italic>-mechanism operating in the hydrogen ionization zone and grows more rapidly in <jats:inline-formula> <jats:tex-math> <?CDATA $\sim 10\,\mathrm{yr}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb463ieqn6.gif" xlink:type="simple" /> </jats:inline-formula>. The RSG mass-loss rate is almost independent of metallicity and distributes in the range of <jats:inline-formula> <jats:tex-math> <?CDATA $\sim {10}^{-3}\mbox{--}{10}^{-2}\ {M}_{\odot }\,{\mathrm{yr}}^{-1}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb463ieqn7.gif" xlink:type="simple" /> </jats:inline-formula>. Conducting stellar structure calculations including feedback due to pulsation-driven winds, we find that the stellar models of <jats:inline-formula> <jats:tex-math> <?CDATA ${M}_{\mathrm{ZAMS}}/{M}_{\odot }=300\mbox{--}3000$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb463ieqn8.gif" xlink:type="simple" /> </jats:inline-formula> can leave behind remnant BHs more massive than <jats:inline-formula> <jats:tex-math> <?CDATA $\sim 200\mbox{--}1200\ {M}_{\odot }$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb463ieqn9.gif" xlink:type="simple" /> </jats:inline-formula>. We conclude that massive merger products can seed monster SMBHs observed at <jats:italic>z</jats:italic> &gt; 6.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Massive, rapidly spinning magnetar remnants produced as a result of binary neutron-star (BNS) mergers may deposit a fraction of their energy into the surrounding kilonova ejecta, powering a synchrotron radio signal from the interaction of the ejecta with the circumburst medium. Here, we present 6.0 GHz Very Large Array (VLA) observations of nine, low-redshift short gamma-ray bursts (GRBs; <jats:italic>z</jats:italic> &lt; 0.5) on rest-frame timescales of ≈2.4–13.9 yr following the bursts. We place 3<jats:italic>σ</jats:italic> limits on radio continuum emission of <jats:italic>F</jats:italic> <jats:sub> <jats:italic>ν</jats:italic> </jats:sub> ≲ 6–20 <jats:italic>μ</jats:italic>Jy at the burst positions, or <jats:italic>L</jats:italic> <jats:sub> <jats:italic>ν</jats:italic> </jats:sub>  ≲  (0.6–8.3) × 10<jats:sup>28</jats:sup> erg s<jats:sup>−1</jats:sup> Hz<jats:sup>−1</jats:sup>. Comparing these limits with new light-curve modeling that properly incorporates relativistic effects, we obtain limits on the energy deposited into the ejecta of <jats:italic>E</jats:italic> <jats:sub>ej</jats:sub> ≲ (0.6–6.7) × 10<jats:sup>52</jats:sup> erg (<jats:inline-formula> <jats:tex-math> <?CDATA ${E}_{\mathrm{ej}}\lesssim (1.8\mbox{--}17.6)\times {10}^{52}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb407ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> erg) for an ejecta mass of 0.03 <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub> (0.1 <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub>). We present a uniform reanalysis of 27 short GRBs with 5.5–6.0 GHz observations, and find that ≳50% of short GRBs did not form stable magnetar remnants in their mergers. Assuming short GRBs are produced by BNS mergers drawn from the Galactic BNS population plus an additional component of high-mass GW194025-like mergers in a fraction <jats:italic>f</jats:italic> <jats:sub>GW190425</jats:sub> of cases, we place constraints on the maximum mass of a nonrotating neutron star (NS; Tolman–Oppenheimer–Volkoff mass; <jats:italic>M</jats:italic> <jats:sub>TOV</jats:sub>), finding <jats:inline-formula> <jats:tex-math> <?CDATA ${M}_{{\rm{T}}{\rm{O}}{\rm{V}}}\lesssim 2.23\,{M}_{\odot }$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb407ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> for <jats:italic>f</jats:italic> <jats:sub>GW190425</jats:sub> = 0.4; this limit increases for larger values of <jats:italic>f</jats:italic> <jats:sub>GW190425</jats:sub>. The detection (or lack thereof) of radio remnants in untargeted surveys such as the VLA Sky Survey (VLASS) could provide more stringent constraints on the fraction of mergers that produce stable remnants. If <jats:inline-formula> <jats:tex-math> <?CDATA $\gtrsim \,30\mbox{--}300$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb407ieqn3.gif" xlink:type="simple" /> </jats:inline-formula> radio remnants are discovered in VLASS, this suggests that short GRBs are a biased population of BNS mergers in terms of the stability of the remnants they produce.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We present optical, radio, and X-ray observations of SN 2020bvc (=ASASSN-20bs, ZTF 20aalxlis), a nearby (<jats:inline-formula> <jats:tex-math> <?CDATA $z=0.0252;$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>z</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.0252</mml:mn> <mml:mo>;</mml:mo> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaba630ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> <jats:italic>d</jats:italic> = 114 Mpc) broad-line (BL) Type Ic supernova (SN) and the first double-peaked Ic-BL discovered without a gamma-ray burst (GRB) trigger. Our observations show that SN 2020bvc shares several properties in common with the Ic-BL SN 2006aj, which was associated with the low-luminosity gamma-ray burst (LLGRB) 060218. First, the 10 GHz radio luminosity (<jats:inline-formula> <jats:tex-math> <?CDATA ${L}_{\mathrm{radio}}\approx {10}^{37}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>radio</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≈</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>37</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em" /> <mml:mi>erg</mml:mi> <mml:mspace width="0.25em" /> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaba630ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>) is brighter than ordinary core-collapse SNe but fainter than LLGRB SNe such as SN 1998bw (associated with LLGRB 980425). We model our VLA observations (spanning 13–43 days) as synchrotron emission from a mildly relativistic (<jats:italic>v</jats:italic> ≳ 0.3<jats:italic>c</jats:italic>) forward shock. Second, with Swift and Chandra, we detect X-ray emission (<jats:italic>L</jats:italic> <jats:sub> <jats:italic>X</jats:italic> </jats:sub> ≈ 10<jats:sup>41</jats:sup> erg <jats:inline-formula> <jats:tex-math> <?CDATA ${{\rm{s}}}^{-1}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaba630ieqn3.gif" xlink:type="simple" /> </jats:inline-formula>) that is not naturally explained as inverse Compton emission or part of the same synchrotron spectrum as the radio emission. Third, high-cadence (6× night<jats:sup>–1</jats:sup>) data from the Zwicky Transient Facility (ZTF) show a double-peaked optical light curve, the first peak from shock cooling of extended low-mass material (mass <jats:inline-formula> <jats:tex-math> <?CDATA ${M}_{e}\lt {10}^{-2}\,{M}_{\odot }$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em" /> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaba630ieqn4.gif" xlink:type="simple" /> </jats:inline-formula> at radius <jats:italic>R</jats:italic> <jats:sub> <jats:italic>e</jats:italic> </jats:sub> &gt; 10<jats:sup>12</jats:sup> cm) and the second peak from the radioactive decay of <jats:inline-formula> <jats:tex-math> <?CDATA ${}^{56}\mathrm{Ni}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow /> <mml:mrow> <mml:mn>56</mml:mn> </mml:mrow> </mml:msup> <mml:mi>Ni</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaba630ieqn5.gif" xlink:type="simple" /> </jats:inline-formula>. SN 2020bvc is the first double-peaked Ic-BL SN discovered without a GRB trigger, so it is noteworthy that it shows X-ray and radio emission similar to LLGRB SNe. For four of the five other nearby (<jats:italic>z</jats:italic> ≲ 0.05) Ic-BL SNe with ZTF high-cadence data, we rule out a first peak like that seen in SN 2006aj and SN 2020bvc, i.e., that lasts ≈1 day and reaches a peak luminosity <jats:italic>M</jats:italic> ≈ −18. Follow-up X-ray and radio observations of Ic-BL SNe with well-sampled early optical light curves will establish whether double-peaked optical light curves are indeed predictive of LLGRB-like X-ray and radio emission.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Previous work utilizing NASA’s High-resolution Coronal Imager (Hi-C 2.1) 172 Å observations revealed that, even at the increased spatial scales available in the dataset, there may be evidence for coronal structures that are still not fully resolved. In this follow-up study, cross-section slices of coronal strands are taken across the Hi-C 2.1 field of view. Following previous loop-width studies, the background emission is removed to isolate the coronal strands. The resulting intensity variations are reproduced by simultaneously fitting multiple Gaussian profiles using a nonlinear least-squares curve-fitting method. In total, 183 Gaussian profiles are examined for possible structures that are hinted at in the data. The full width at half maximum is determined for each Gaussian, which are then collated and analyzed. The most frequent structural widths are ≈450–575 km with 47% of the strand widths beneath NASA’s Solar Dynamics Observatory Atmospheric Imaging Assembly (AIA) resolving scale (600–1000 km). Only 17% reside beneath an AIA pixel width (435 km) with just 6% of the strands at the Hi-C 2.1 resolving scale (≈220–340 km). These results suggest that non-Gaussian shaped cross-sectional emission profiles observed by Hi-C 2.1 are the result of multiple strands along the integrated line of sight that can be resolved, rather than being the result of even finer sub-resolution elements.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Cooling white dwarfs (WDs) can yield accurate ages when theoretical cooling models fully account for the physics of the dense plasma of WD interiors. We use <jats:monospace>MESA</jats:monospace> to investigate cooling models for a set of massive and ultramassive WDs (0.9–1.3 <jats:inline-formula> <jats:tex-math> <?CDATA ${M}_{\odot }$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb5a5ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>) for which previous models have failed to match kinematic age indicators based on Gaia DR2. We find that the WDs in this population can be explained as C/O cores experiencing unexpectedly rapid <jats:sup>22</jats:sup>Ne sedimentation in the strongly liquid interior just prior to crystallization. We propose that this rapid sedimentation is due to the formation of solid clusters of <jats:sup>22</jats:sup>Ne in the liquid C/O background plasma. We show that these heavier solid clusters sink faster than individual <jats:sup>22</jats:sup>Ne ions and enhance the sedimentation heating rate enough to dramatically slow WD cooling. <jats:monospace>MESA</jats:monospace> models including our prescription for cluster formation and sedimentation experience cooling delays of ≈4 Gyr on the WD <jats:italic>Q</jats:italic> branch, alleviating tension between cooling ages and kinematic ages. This same model then predicts cooling delays coinciding with crystallization of 6 Gyr or more in lower-mass WDs (0.6–0.8 <jats:inline-formula> <jats:tex-math> <?CDATA ${M}_{\odot }$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb5a5ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>). Such delays are compatible with, and perhaps required by, observations of WD populations in the local 100 pc WD sample and the open cluster NGC 6791. These results motivate new investigations of the physics of strongly coupled C/O/Ne plasma mixtures in the strongly liquid state near crystallization and tests through comparisons with observed WD cooling.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Motivated by prior remote observations of a transition from striated solar coronal structures to more isotropic “flocculated” fluctuations, we propose that the dynamics of the inner solar wind just outside the Alfvén critical zone, and in the vicinity of the first <jats:inline-formula> <jats:tex-math> <?CDATA $\beta =1$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjabb594ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> surface, is powered by the relative velocities of adjacent coronal magnetic flux tubes. We suggest that large-amplitude flow contrasts are magnetically constrained at lower altitude but shear-driven dynamics are triggered as such constraints are released above the Alfvén critical zone, as suggested by global magnetohydrodynamic (MHD) simulations that include self-consistent turbulence transport. We argue that this dynamical evolution accounts for features observed by Parker Solar Probe (PSP) near initial perihelia, including magnetic “switchbacks,” and large transverse velocities that are partially corotational and saturate near the local Alfvén speed. Large-scale magnetic increments are more longitudinal than latitudinal, a state unlikely to originate in or below the lower corona. We attribute this to preferentially longitudinal velocity shear from varying degrees of corotation. Supporting evidence includes comparison with a high Mach number three-dimensional compressible MHD simulation of nonlinear shear-driven turbulence, reproducing several observed diagnostics, including characteristic distributions of fluctuations that are qualitatively similar to PSP observations near the first perihelion. The concurrence of evidence from remote sensing observations, in situ measurements, and both global and local simulations supports the idea that the dynamics just above the Alfvén critical zone boost low-frequency plasma turbulence to the level routinely observed throughout the explored solar system.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>High-resolution (1″ × 2″) Atacama Large Millimeter Array CO(2−1) observations of the ram pressure stripped galaxy NGC 4402 in the Virgo cluster show some of the clearest evidence yet for the impacts of ram pressure on the molecular interstellar medium (ISM) of a galaxy. The eastern side of the galaxy at <jats:italic>r</jats:italic> ∼ 4.5 kpc, upon which ram pressure is incident, has a large (width ∼1 kpc, height ∼1 kpc above the disk midplane) extraplanar plume of molecular gas and dust. Molecular gas in the plume region shows distinct noncircular motions in the direction of the ram pressure; the kinematic offset of up to 60 km s<jats:sup>−1</jats:sup> is consistent with acceleration by ram pressure. We also detect a small amount of gas in clouds below the plume that are spatially and kinematically distinct from the surrounding medium, and appear to be decoupled from the stripped ISM. We propose that diffuse molecular gas is directly stripped but giant molecular cloud (GMC) density gas is not directly stripped, and so decouples from lower density stripped gas. However, GMCs become effectively stripped on short timescales. We also find morphological and kinematic signatures of ram pressure compression of molecular gas in a region of intense star formation on the leading side at <jats:italic>r</jats:italic> ∼ 3.5 kpc. We propose that the compressed and stripped zones represent different evolutionary stages of the ram pressure interaction, and that feedback from star formation in the compressed zone facilitates the effective stripping of GMCs by making the gas cycle rapidly to a lower density diffuse state.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Radiative torques (RATs) or mechanical torques acting on irregular grains can induce the alignment of dust grains in respect to the alignment axis (AA), which can be either the direction of the magnetic field or the direction of the radiation. We show that carbonaceous grains can be aligned with their axes both parallel and perpendicular to the AA, and we explore the conditions where the particular mode of alignment takes place. We identify a new process of alignment of charged carbonaceous grains in a turbulent, magnetized interstellar medium with respect to an electric field. This field acts on grains accelerated in a turbulent medium and gyrorotating about a magnetic field. The electric field can also arise from the temporal variations of the magnetic field strength in turbulent, compressible media. The direction of the electric field is perpendicular to the magnetic field, and the carbonaceous grains precess in the electric field because of their electric moments. If this precession is faster than Larmor precession in the magnetic field, the alignment of such grains is with their long axes parallel to the magnetic field. We explore the parameter space for which the new mechanism aligns grains with long axes parallel to the magnetic field. We compare this mechanism with another process that provides the same type of alignment, namely, the RAT alignment of grains with insufficiently fast internal relaxation. We describe the conditions for which the particular mode of carbonaceous grain alignment is realized and discuss what information can be obtained by measuring the resulting polarization.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The linear magnetohydrodynamic stability of a shielding magnetic flux rope with a surface current under coronal solar conditions is analyzed in the framework of an energy principle. The equation describing the potential energy change induced by disturbances of the equilibrium was derived. It has been shown that the surface reverse current shielding the azimuthal component of the magnetic field lines outside a flux rope stabilizes the development of kink- and flute-type instabilities in the long-wavelength limit independently of the cross-sectional radial profile of current density. Kink modes are the most unstable ones as their generation requires less energy than other modes. Based on the obtained dispersion relation for kink oscillations, we proposed a new expression for the determination of magnetic field components of the twisted loop.</jats:p>