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Papers for Wednesday, Jan 03 2024

Papers with local authors

David N. Hosking, David Wasserman, Steven C. Cowley

40 pages, 36 figures

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Paper 35 — arXiv:2401.01336
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Paper 35 — arXiv:2401.01336

Motivated by explosive releases of energy in fusion, space and astrophysical plasmas, we consider the nonlinear convective stability of stratified magnetohydrodynamic (MHD) equilibria in 2D. We demonstrate that, unlike the Schwarzschild criterion in hydrodynamics (``entropy must increase upwards for convective stability''), the so-called modified Schwarzschild criterion for 2D MHD (or for any kind of fluid dynamics with more than one source of pressure) guarantees only linear stability. As a result, in 2D MHD (unlike in hydrodynamics) there exist metastable equilibria that are unstable to nonlinear perturbations despite being stable to linear ones. We show that the minimum-energy configurations attainable by these atmospheres via non-diffusive reorganization can be determined by solving a combinatorial optimization problem. We find inter alia that these minimum-energy states are usually 2D, even when the original metastable equilibrium was 1D. We demonstrate with direct numerical simulations that these 2D states are fairly accurate predictors of the final state reached by laminar relaxation of metastable equilibria at small Reynolds number. To describe relaxation at large Reynolds number, we construct a statistical mechanical theory based on the maximization of Boltzmann's mixing entropy that is analogous to the Lynden-Bell statistical mechanics of self-gravitating systems and collisionless plasmas, and to the Robert-Sommeria-Miller (RSM) theory of 2D vortex turbulence. The minimum-energy states described above are, we show, the low-temperature limit of this theory. We demonstrate that the predictions of the statistical mechanics are in reasonable agreement with direct numerical simulations.

All other papers

(LISA Pathfinder Collaboration) M Armano, H Audley, J Baird, M Bassan, P Binetruy, M Born, D Bortoluzzi, E Castelli, A Cavalleri, A Cesarini, V Chiavegato, A M Cruise, D Dal Bosco, K Danzmann, M De Deus Silva, R De Rosa, L Di Fiore, I Diepholz, G Dixon, R Dolesi, L Ferraioli V Ferroni, E D Fitzsimons, M Freschi, L Gesa, D Giardini, F Gibert, R Giusteri, A Grado, C Grimani, J Grzymisch, I Harrison, M S Hartig, G Heinzel, M Hewitson, D Hollington, D Hoyland, M Hueller, H Inchauspé, O Jennrich, P Jetzer, B Johlander, N Karnesis, B Kaune, N Korsakova, C J Killow, L Liu, J A Lobo, J P López-Zaragoza, R Maarschalkerweerd, D Mance, V Martín, L Martin-Polo, F Martin-Porqueras, J Martino, P W McNamara, J Mendes, L Mendes, N Meshksar, J Moerschell, M Nofrarias, S Paczkowski, M Perreur-Lloyd, et al. (28 additional authors not shown)

Electrostatic force actuation is a key component of the system of geodesic reference test masses (TM) for the LISA orbiting gravitational wave observatory and in particular for performance at low frequencies, below 1 mHz, where the observatory sensitivity is limited by stray force noise. The system needs to apply forces of order 10$^{-9}$ N while limiting fluctuations in the measurement band to levels approaching 10$^{-15}$ N/Hz$^{1/2}$. We present here the LISA actuation system design, based on audio-frequency voltage carrier signals, and results of its in-flight performance test with the LISA Pathfinder test mission. In LISA, TM force actuation is used to align the otherwise free-falling TM to the spacecraft-mounted optical metrology system, without any forcing along the critical gravitational wave-sensitive interferometry axes. In LISA Pathfinder, on the other hand, the actuation was used also to stabilize the TM along the critical $x$ axis joining the two TM, with the commanded actuation force entering directly into the mission's main differential acceleration science observable. The mission allowed demonstration of the full compatibility of the electrostatic actuation system with the LISA observatory requirements, including dedicated measurement campaigns to amplify, isolate, and quantify the two main force noise contributions from the actuation system, from actuator gain noise and from low frequency ``in band'' voltage fluctuations. These campaigns have shown actuation force noise to be a relevant, but not dominant, noise source in LISA Pathfinder and have allowed performance projections for the conditions expected in the LISA mission.

John K. Webb, Chung-Chi Lee

10 pages, 13 figures. Submitted for publication

Searches for spacetime variations of fundamental constants have entered an era of unprecedented precision. New, high quality quasar spectra require increasingly refined analytic methods. In this article, a continuation in a series to establish robust and unbiased methodologies, we explore how convergence criteria in non-linear least squares optimisation impact on quasar absorption system measurements of the fine structure constant alpha. Given previous claims for high-precision constraints, we critically examine the veracity of a so-called ``blinding'' approach, in which alpha is fixed at the terrestrial value during the model building process, releasing it as a free parameter only after the ``final'' absorption system kinematic structure has been obtained. We show that this approach results in an extended flat canyon in chi squared-alpha space, such that convergence is unlikely to be reached, even after as many as 1000 iterations. The fix is straightforward: alpha must be treated as a free parameter from the earliest possible stages of absorption system model building. The implication of the results presented here is that all previous measurements that have used initially-fixed alpha should be reworked.

John K. Webb, Chung-Chi Lee, Dinko Milakovic, Victor V. Flambum, Vladimir A. Dzuba, Joao Magueijo

6 pages, 3 figures

We report unbiased AI measurements of the fine structure constant alpha in two proximate absorption regions in the spectrum of the quasar HE0515-4414. The data are high resolution, high signal to noise, and laser frequency comb calibrated, obtained using the ESPRESSO spectrograph on the VLT. The high quality of the data and proximity of the regions motivate a differential comparison, exploring the possibility of spatial variations of fundamental constants, as predicted in some theories. We show that if the magnesium isotopic relative abundances are terrestrial, the fine structure constants in these two systems differ at the 7-sigma level. A 3-sigma discrepancy between the two measurements persists even for the extreme non-terrestrial case of 100% ^{24}Mg, if shared by both systems. However, if Mg isotopic abundances take independent values in these two proximate systems, one terrestrial, the other with no heavy isotopes, both can be reconciled with a terrestrial alpha, and the discrepancy between the two measurements falls to 2-sigma. We discuss varying constant and varying isotope interpretations and resolutions to this conundrum for future high precision measurements.

Structure formation heralds the era of deviation of the matter content of the Universe away from thermal equilibrium, so the gravitational contribution to entropy, in the form of Weyl curvature, must become active in order for the overall entropy of the Universe to remain increasing. The tidal and frame dragging sectors of the Weyl tensor must inevitably both be present in this dynamic environment, as they mutually induce each other. The frame dragging effect is able to impress vorticity onto the plasma current arising due to the mass disparity between electrons and protons, which in turn begets a magnetic field from none. We show that this gravity-driven magnetogenesis mechanism, besides being able to operate outside of galaxies, thus facilitate large coherence length scales, may be able to generate the field strength necessary to seed dynamo processes.

In this Master Thesis, we use a technique to shift and stack the X-Ray spectra of 1138 galaxy clusters from the eRASS-1 survey, totalling 430649 counts. In comparison with previous stacking techniques, the method presented here introduces proper normalization of the shifted redistribution matrix file (RMF), which allows to recover the physical temperature and metallicity of the stacked spectra. Using this technique, we can obtain constraints in the stacked spectra for the individual abundances of O, Ne, Mg, Si, Ar, Ca, and Fe. Additionally, we study the possible detection of the previously reported 3.5keV unidentified line emission; however, the residuals barely exceed $\pm 2 \sigma$ in the [3-4]keV range. On the other hand, although residuals in the [3.4-3.55]keV band are compatible with charge exchange emission from SXVI (bare sulphur ions), charge exchange emission from OVII at 0.56keV should also be present, since it is 200 orders of magnitude higher than charge emission from SXVI in the [3.4-3.55]keV band; however, it is unfortunately not detected.

The elusive polarized microwave signal from the Fermi bubbles is disentangled from the more extended polarized lobes, which similarly emanate from the Galactic plane but stretch farther west of the bubbles. The ~20% synchrotron polarization reveals magnetic fields preferentially parallel to the bubble edges, as expected downstream of a strong shock. The ~20% polarization of thermal dust emission is similarly oriented, constraining grain alignment in an extreme environment. We argue that the larger lobes arise from an older Galactic-center, likely supermassive black-hole, outburst.

Zhiyuan Ji, Christina C. Williams, Katherine A. Suess, Sandro Tacchella, Benjamin D. Johnson, Brant Robertson, Stacey Alberts, William M. Baker, Stefi Baum, Rachana Bhatawdekar, Nina Bonaventura, Kristan Boyett, Andrew J. Bunker, Stefano Carniani, Stephane Charlot, Zuyi Chen, Jacopo Chevallard, Emma Curtis-Lake, Francesco D'Eugenio, Anna de Graaff, Christa DeCoursey, Eiichi Egami, Daniel J. Eisenstein, Kevin Hainline, Ryan Hausen, Jakob M. Helton, Tobias J. Looser, Jianwei Lyu, Roberto Maiolino, Michael V. Maseda, Erica Nelson, George Rieke, Marcia Rieke, Hans-Walter Rix, Lester Sandles, Fengwu Sun, Hannah Übler, Christopher N. A. Willmer, Chris Willott, Joris Witstok

28 pages, 19 figures, submitted to ApJ

We present the UV-to-NIR size evolution of a sample of 161 quiescent galaxies (QGs) with $M_*>10^{10}M_\odot$ over $0.5<z<5$. With deep multi-band NIRCam images in GOODS-South from JADES, we measure the effective radii ($R_e$) of the galaxies at rest-frame 0.3, 0.5 and 1$\mu m$. On average, QGs are 45% (15%) more compact at rest-frame 1$\mu m$ than they are at 0.3$\mu m$ (0.5$\mu m$). Regardless of wavelengths, the $R_e$ of QGs strongly evolves with redshift, and this evolution depends on stellar mass. For lower-mass QGs with $M_*=10^{10}-10^{10.6}M_\odot$, the evolution follows $R_e\sim(1+z)^{-1.1}$, whereas it becomes steeper, following $R_e\sim(1+z)^{-1.7}$, for higher-mass QGs with $M_*>10^{10.6}M_\odot$. To constrain the physical mechanisms driving the apparent size evolution, we study the relationship between $R_e$ and the formation redshift ($z_{form}$) of QGs. For lower-mass QGs, this relationship is broadly consistent with $R_e\sim(1+z_{form})^{-1}$, in line with the expectation of the progenitor effect. For higher-mass QGs, the relationship between $R_e$ and $z_{form}$ depends on stellar age. Older QGs have a steeper relationship between $R_e$ and $z_{form}$ than that expected from the progenitor effect alone, suggesting that mergers and/or post-quenching continuous gas accretion drive additional size growth in very massive systems. We find that the $z>3$ QGs in our sample are very compact, with mass surface densities $\Sigma_e\gtrsim10^{10} M_\odot/\rm{kpc}^2$, and their $R_e$ are possibly even smaller than anticipated from the size evolution measured for lower-redshift QGs. Finally, we take a close look at the structure of GS-9209, one of the earliest confirmed massive QGs at $z_{spec}\sim4.7$. From UV to NIR, GS-9209 becomes increasingly compact, and its light profile becomes more spheroidal, showing that the color gradient is already present in this earliest massive QG.

Mikayla R. Huffman, Adam J. McKay, Anita L. Cochran

17 pages, 8 figures. To be published in The Planetary Science Journal

The study of cometary composition is important for understanding our solar system's early evolutionary processes. Carbon dioxide (CO2) is a common hypervolatile in comets that can drive activity but is more difficult to study than other hypervolatiles due to severe telluric absorption. CO2 can only be directly observed from space-borne assets. Therefore, a proxy is needed to measure CO2 abundances in comets using ground-based observations. The flux ratio of the [O I] 5577 A line to the sum of the [O I] 6300 A and [O I] 6364 A lines (hereafter referred to as the [O I] line ratio) has, with some success, been used in the past as such a proxy. We present an [O I] line ratio analysis of comet 45P/Honda-Mrkos-Pajdu\v{s}\'akov\'a (HMP), using data obtained with the Tull Coud\'e Spectrograph on the 2.7-meter Harlan J. Smith telescope at McDonald Observatory, taken from UT February 21-23, 2017 when the comet was at heliocentric distances of 1.12-1.15 AU. HMP is a hyperactive Jupiter family comet (JFC). Icy grains driven out by CO2 sublimation have been proposed as a driver of hyperactivity, but the CO2 abundance of HMP has not been measured. From our [O I] line ratio measurements, we find a CO2/H2O ratio for HMP of 22.9 +/- 1.4%. We compare the CO2/H2O ratios to the active fractions of the nine comets (including HMP) in the literature that have data for both values. We find no correlation. These findings imply that CO2 sublimation driving out icy grains is not the only factor influencing active fractions for cometary nuclei.

Adam M. Ritchey (Eureka Scientific), S. R. Federman (Univ. of Toledo), David L. Lambert (Univ. of Texas at Austin)

14 pages, 14 figures, submitted to MNRAS

We present the results of a sensitive search for high-velocity gas in interstellar absorption lines associated with the Cygnus Loop supernova remnant (SNR). We examine high-resolution, high signal-to-noise ratio optical spectra of six stars in the Cygnus Loop region with distances greater than ~700 pc. All stars show low-velocity Na I and Ca II absorption. However, only one star, HD 198301, exhibits high-velocity Ca II absorption components, at velocities of +62, +82, and +96 km/s. The distance to this star of ~870 pc helps to constrain the distance to the receding edge of the Cygnus Loop's expanding shock front. One of our targets, HD 335334, was previously thought to exhibit high positive and high negative velocity interstellar Na I and Ca II absorption. This was one factor leading Fesen et al. to derive a distance to the Cygnus Loop of 725 pc. However, we find that HD 335334 is in fact a double-line spectroscopic binary and shows no evidence of high-velocity interstellar absorption. As such, the distance to HD 335334 cannot be used to constrain the distance to the Cygnus Loop. Our detection of Ca II absorption approaching 100 km/s toward HD 198301 is the first conclusive detection of high-velocity absorption from a low ionization species associated with the Cygnus Loop SNR. A large jump in the Na I column density toward BD+31 4218, a star located beyond the northwestern boundary of the Cygnus Loop, helps to constrain the distance to a large molecular cloud complex with which the Cygnus Loop is evidently interacting.

Cold, neutral interstellar gas, the reservoir for star formation, is traced through the absorption of the 21-centimetre continuum radiation by neutral hydrogen (HI). Although detected in one hundred cases in the host galaxies of distant radio sources, only recently have column densities approaching the maximum value observed in Lyman-alpha absorption systems been found. Here we explore the implications these have for the hypothesis that the detection rate of HI absorption is dominated by photo-ionisation from the active galactic nucleus (AGN). We find, with the addition all of the current searches for HI absorption at z > 0.1, a strong correlation between the HI absorption strength and the ionising photon rate, with the maximum value at which HI is detected remaining close to the theoretical value in which all of the neutral gas would be ionised in a large spiral galaxy (Q = 2.9e56 ionising photons/s). We also rule out other effects (excitation by the radio continuum and changing gas properties) as the dominant cause for the decrease in the detection rate with redshift. Furthermore, from the maximum theoretical column density we find that the five high column density systems have spin temperatures close to those of the Milky Way (T < 300 K), whereas, from our model of a gaseous galactic disk, the HI detection at Q= 2.9e56 per s yields T~10 000 K, consistent with the gas being highly ionised.

Asca Miyamoto, Yasuharu Sugawara, Yoshitomo Maeda, Manabu Ishida, Kenji Hamaguchi, Christopher M. P. Russell, Anthony F. J. Moffat

16 pages, 9 figures, Accepted for publication in MNRAS

We analyse $\textit{XMM-Newton}$ RGS spectra of Wolf-Rayet (WR) 140, an archetype long-period eccentric WR+O colliding wind binary. We evaluate the spectra of O and Fe emission lines and find that the plasmas emitting these lines have the largest approaching velocities with the largest velocity dispersions between phases 0.935 and 0.968 where the inferior conjunction of the O star occurs. This behaviour is the same as that of the Ne line-emission plasma presented in our previous paper. We perform diagnosis of electron number density $n_{\rm e}$ using He-like triplet lines of O and Ne-like Fe-L lines. The former results in a conservative upper limit of $n_{\rm e} \lesssim 10^{10}$-10$^{12}$ cm$^{-3}$ on the O line-emission site, while the latter can not impose any constraint on the Fe line-emission site because of statistical limitations. We calculate the line-of-sight velocity and its dispersion separately along the shock cone. By comparing the observed and calculated line-of-sight velocities, we update the distance of the Ne line-emission site from the stagnation point. By assuming radiative cooling of the Ne line-emission plasma using the observed temperature and the local stellar wind density, we estimate the line-emission site extends along the shock cone by at most $\pm$58 per cent (phase 0.816) of the distance from the stagnation point. In this framework, excess of the observed velocity dispersion over the calculated one is ascribed to turbulence in the hot-shocked plasma at earlier orbital phases of 0.816, 0.912, and 0.935, with the largest velocity dispersion of 340-630 km s$^{-1}$ at phase 0.912.

Zhiwei Chen (NAOC), Youjun Lu (NAOC), Yunfeng Chen (UCAS)

11 pages, 6 figures, accepted for publication in ApJ

More than one hundred tidal disruption events (TDEs) have been detected at multi-bands, which can be viewed as extreme laboratories to investigate the accretion physics and gravity in the immediate vicinity of massive black holes (MBHs). Future transient surveys are expected to detect several tens of thousands of TDEs, among which a small fraction may be strongly gravitationally lensed by intervening galaxies. In this paper, we statistically etsimate the detection rate of lensed TDEs, with dependence on the limiting magnitude of the transient all-sky surveys searching for them. We find that the requisite limiting magnitude for an all-sky transient survey to observe at least $1$ yr$^{-1}$ is $\gtrsim 21.3$, $21.2$, and $21.5$ mag in the u-, g-, and z-bands, respectively. If the limiting magnitude of the all-sky survey can reach $\sim 25-26$ mag in the u-, g-, and z-bands, the detection rate can be upto about several tens to hundreds per year. The discovery and identification of the first image of the lensed TDE can be taken as an early-warning of the second and other subsequent images, which may enable detailed monitoring of the pre-peak photometry and spectroscopy evolution of the TDE. The additional early-stage information may help to constrain the dynamical and radiation processes involving in the TDEs.

Hong Bae Ann, Mira Seo

12 pages, 13 figures, submitted to MNRAS

We present the mean star formation histories (SFHs) of 148 dwarf lenticular galaxies (dS0s) derived from SDSS spectra. The SFHs of dS0s are characterized by multiple bursts of star formation, including an initial burst at a lookback time of $\sim14$ Gyr for most galaxies. Stars formed during the first star-forming phase which ends at a lookback time of 6.3 Gyr primarily consist of old, metal-poor (Z=0.0004) stars , contributing to $\sim60\%$ of the stellar mass and $\sim30\%$ of the luminosity. The almost absence of extremely metal poor (Z=0.0001) stars seems to be due to pre-enrichment during the re-ionization era. Star formation gradually decreases during this initial period. In contrast, during the second period of star formation, there is an increase in star formation activity, peaking at a lookback time of 2.5 Gyr before declining again. Most moderately old stellar populations with intermediate metallicity were formed during this phase. We observe a strong dependence of SFHs on the mass and u-r color of dS0 galaxies but no significant dependence on morphological properties such as the presence or absence of outer spiral arms and nucleation. The star formation history of dS0 galaxies shares many similarities with that of dE galaxies, and many of them are believed to have originated from late-type galaxies.

Xuqiang Dong, Cong Li, Huihai He

13 pages, 13 figures

The full array of the Large High Altitude Air Shower Observatory (LHAASO) has been in operation since July 2021. For its kilometer-square array (KM2A), we have optimized the selection criteria for very high and ultra-high energy $\gamma$-rays, using the data collected from August 2021 to August 2022, resulting in an improvement on significance of about 15$\%$ compared with previous cuts. With the implementation of these new selection criteria, the angular resolution is also significantly improved by approximately 10$\%$ at tens of TeV. Other aspects of the full KM2A array performance, such as the pointing error are also calibrated using the Crab Nebula. The resulting energy spectrum of the Crab Nebula in the energy range of 10-1000 TeV can be well fitted by a log-parabola model, which is consistent with the previous results from LHAASO and other experiments.

Yu-Wei Lin, Cossas K.-W. Wu, Chih-Teng Ling, Tomotsugu Goto, Seong Jin Kim, Ece Kilerci, Tetsuya Hashimoto, Po-Ya Wang, Simon C.-C. Ho, Tiger Yu-Yang Hsiao, Bjorn Jasper R. Raquel, Yuri Uno

12 pages, 20 figures, 4 tables. Accepted by MNRAS. A summary video is at this https URL &ab_channel=NTHUCosmology

It has been an unanswered question how many dusty galaxies have been undetected from the state-of-the-art observational surveys. JWST enables us to detect faint IR galaxies that have prominent polycyclic aromatic hydrocarbon (PAH) features in the mid-IR wavelengths. PAH is a valuable tracer of star formation and dust properties in the mid-infrared wavelength. The JWST Cosmic Evolution Early Release Science (CEERS) fields provide us with wavelength coverage from 7.7 to 21 $\mu$m using six photometric bands of the mid-infrared instrument (MIRI). We have identified galaxies dominated by mid-IR emission from PAHs, termed PAH galaxies. From our multi-band photometry catalogue, we selected ten PAH galaxies displaying high flux ratios of $\log(S_{15}/S_{10}) > 0.8$. The SED fitting analysis indicates that these galaxies are star-forming galaxies with total IR luminosities of $10^{10}$ $\sim$ $10^{11.5}$ $L_{\odot}$ at z $\sim 1$. The morphology of PAH galaxies does not show any clear signatures of major merging or interaction within the MIRI resolution. The majority of them are on the star-formation main sequence at $z \sim 1$. Our result demonstrates that JWST can detect PAH emissions from normal star-forming galaxies at $z \sim 1$, in addition to ultra-luminous infrared galaxies (ULIRGs) or luminous infrared galaxies (LIRGs).

Atila Poro, S. Javad Jafarzadeh, Roghaye Harzandjadidi, Mohammad Madani, Elnaz Bozorgzadeh, Esfandiar Jahangiri, Ahmad Sarostad, Ailar Alizadehsabegh, Maryam Hadizadeh, Mohammad EsmaeiliVakilabadi

Accepted by the RAA journal

The Gaia DR3 parallax approach was used to estimate the absolute parameters of 2375 Delta Scuti stars from the ASAS catalog. The selected stars have a variety of observational characteristics, with a higher than 80% probability of being Delta Scuti stars. We have displayed all the stars in the Hertzsprung-Russell (H-R) diagram along with the Delta Scuti instability strip, the Zero Age Main Sequence (ZAMS), and the Terminal-Age Main Sequence (TAMS). Then, we determined which fundamental and overtone modes each star belongs to using pulsation constant (Q) calculations. In addition, we evaluated the parameters in the Q calculation equation using three machine learning methods, which showed that surface gravity and temperature have the greatest effect on its calculation. The Period-Luminosity (P-L) relationship of the Delta Scuti stars was also revisited. Eventually, using least squares linear regression, we made four linear fits for fundamental and overtone modes and updated their relationships.

Konstantinos Karampelas, Tom Van Doorsselaere

6 pages, 5 figures

Aims. We studied the manifestation of decayless oscillations in 3D simulations of coronal loops, driven by random motions. Methods. Using the PLUTO code, we ran magnetohydrodynamic (MHD) simulations of a straight gravitationally stratified flux tube, with its footpoints embedded in chromospheric plasma. We consider transverse waves drivers with a horizontally polarised red noise power-law spectrum. Results. Our broadband drivers lead to the excitation of standing waves with frequencies equal to the fundamental standing kink mode and its harmonics. These standing kink oscillations have non-decaying amplitudes, and spectra that depend on the characteristics of the loops, with the latter amplifying the resonant frequencies from the drivers. We thus report for the first time in 3D simulations the manifestation of decayless oscillations from broadband drivers. The spatial and temporal evolution of our oscillation spectra reveals the manifestation of a half harmonic, which exhibits half the frequency of the identified fundamental mode with a similar spatial profile. Our results suggest that this mode is related to the presence of the transition region in our model and could be interpreted as being the equivalent to the fundamental mode of standing sound waves driven on pipes closed at one end. Conclusions. The potential existence of this half harmonic has important implications for coronal seismology, since misinterpreting it for the fundamental mode of the system can lead to false estimations of the average kink speed profile along oscillating loops. Finally, its detection could potentially give us a tool for distinguishing between different excitation and driving mechanisms of decayless oscillations in observations.

Michele Piana, Federico Benvenuto, Anna Maria Massone, Cristina Campi, Sabrina Guastavino, Francesco Marchetti, Paolo Massa, Emma Perracchione, Anna Volpara

AI-FLARES (Artificial Intelligence for the Analysis of Solar Flares Data) is a research project funded by the Agenzia Spaziale Italiana and by the Istituto Nazionale di Astrofisica within the framework of the ``Attivit\`a di Studio per la Comunit\`a Scientifica Nazionale Sole, Sistema Solare ed Esopianeti'' program. The topic addressed by this project was the development and use of computational methods for the analysis of remote sensing space data associated to solar flare emission. This paper overviews the main results obtained by the project, with specific focus on solar flare forecasting, reconstruction of morphologies of the flaring sources, and interpretation of acceleration mechanisms triggered by solar flares.

Jesús Maíz Apellániz

38 pages, 15 figures. To appear in the edition of the Central European Astrophysical Bulletin dedicated to the proceedings of the Hvar Stellar Meeting 2023

Extinction is the elephant in the room that almost everyone tries to avoid when analyzing optical/IR data: astronomers tend to find a quick fix for it that the referee will accept, but that does not mean such a solution is correct or even optimal. In this contribution I address three important issues related to extinction that are commonly ignored and present current and future solutions for them: [1] Extinction produces non-linear photometric effects, [2] the extinction law changes between sightlines, and [3] not all families of extinction laws have the same accuracy.

Shocks are often invoked as heating mechanisms in astrophysical systems, with both adiabatic compression and dissipative heating that leading to temperature increases. Whilst shocks are reasonably well understood for ideal magnetohydrodynamic (MHD) systems, in many astrophysical plasmas, radiation is an important phenomena, which can allow energy to leave the system. As such, energy becomes non-conservative which can fundamentally change the behaviour of shocks. The energy emitted through optically-thin radiation post-shock can exceed the thermal energy increase, resulting in shocks that reduce the temperature of the medium, i.e., cooling shocks that have a net decrease in temperature across the interface. In this paper, semi-analytical solutions for radiative shocks are derived to demonstrate that both cooling (temperature decreasing) and heating (temperature increasing) shock solutions are possible in radiative MHD. Numerical simulations of magnetic reconnection with optically-thin radiative losses also yield both heating and cooling shocks in roughly equal abundances. The detected cooling shocks feature a significantly lower pressure jump across the shock than their heating counterparts. The compression at the shock front leads to locally-enhanced radiative losses, resulting in significant cooling within a few grid cells in the upstream and downstream directions. The presence of temperature-reducing (cooling) shocks is critical in determining the thermal evolution, and heating or cooling, across a wealth of radiative astrophysical plasmas.

Mark Taylor

4 pages, 1 figure; to appear in proceedings of ADASS XXXIII

TOPCAT is a desktop GUI tool for working with tabular data such as source catalogues. Among other capabilities it provides a rich set of visualisation options suitable for interactive exploration of large datasets. The latest release introduces a Corner Plot window which displays a grid of linked scatter-plot-like and histogram-like plots for all pair and single combinations from a supplied list of coordinates.

Plasmoid-mediated reconnection plays a fundamental role in different solar atmospheric phenomena. Numerical reproduction of this process is therefore essential for developing robust solar models. Our goal is to assess plasmoid-mediated reconnection across various numerical resistivity models in order to investigate how plasmoid numbers and reconnection rates depend on the Lundquist number. We used the Bifrost code to drive magnetic reconnection in a 2D coronal fan-spine topology, carrying out a parametric study of several experiments with different numerical resolution and resistivity models. We employed three anomalous resistivity models: (1) the original hyper-diffusion from Bifrost, (2) a resistivity proportional to current density, and (3) a resistivity quadratically proportional to electron drift velocity. For comparisons, experiments with uniform resistivity were also run. Plasmoid-mediated reconnection is obtained in most of the experiments. With uniform resistivity, increasing the resolution reveals higher plasmoid frequency with weaker scaling to the Lundquist number, obtaining 7.9-12 plasmoids per minute for $S_L\in[1.8 \times 10^4, 2.6\times 10^5]$ with a scaling of $S_L^{0.210}$ in the highest-resolution resistivity cases, transcending into Petschek reconnection in the high-$S_L$ limit and Sweet-Parker reconnection in the low-$S_L$ limit. Anomalous resistivity leads to similar results even with lower resolution. The drift-velocity-dependent resistivity excellently reproduces Petschek reconnection for any Lundquist number, and similar results are seen with resistivity proportional to current-density. Among the different resistivity models applied on the given numerical resolution, the hyper-diffusion model reproduced plasmoid characteristics in closest resemblance to those obtained with uniform resistivity at a significantly higher resolution.

The high resolution rovibronic line list of MgH+ molecular cation are presented in our work. The potential energy curves are calculated by the method of multireference configuration interaction plus Davidson correction (MRCI+Q) and spin-orbit coupling (SOC) effect. Spectroscopy constants are fitted and the results are in good agreement with the experiment, ensuring the accuracy of the electronic structure. On account of potential energy curves and transition dipole moments, the Franck - Condon factors and Einstein coefficients of transition are obtained. These calculations are used to obtain an accurate partition functions and line list for the molecule. Using the data obtained from the ab initio calculation, the absorption cross-sections under different temperatures and pressures were simulated. Our work could provide some theoretical insights into solar and cold planet spectrum.

Óscar Rodríguez, Giovanni F. Gronchi, Giulio Baù, Robert Jedicke

We present a new procedure to identify observations of known objects in large data sets of unlinked detections. It begins with a Keplerian integrals method that allows us to link two tracklets, computing preliminary orbits, even when the tracklets are separated in time by a few years. In the second step, we represent the results in a `graph' where the tracklets are the nodes and the preliminary orbits are the edges. Then, acceptable `3-cycles' are identified and a least squares orbit is computed for each of them. Finally, we construct sequences of $n \geq 4$ tracklets by searching through the orbits of nearby 3-cycles and attempting to attribute the remaining tracklets. We calculate the technique's efficiency at identifying unknown objects using real detections that attempt to mimic key parameters of the Minor Planet Center's Isolated Tracklet File (ITF) and then apply the procedure to the ITF to identify tens of thousands of new objects.

Óscar Rodríguez, Giovanni F. Gronchi, Giulio Baù, Robert Jedicke

We investigate the behaviour of two recent methods for the computation of preliminary orbits. These methods are based on the conservation laws of Kepler's problem, and enable the linkage of very short arcs of optical observations even when they are separated in time by a few years. Our analysis is performed using both synthetic and real data of 822 main belt asteroids. The differences between computed and true orbital elements have been analysed for the true linkages, as well as the occurrence of alternative solutions. Some metrics have been introduced to quantify the results, with the aim of discarding as many of the false linkages as possible and keeping the vast majority of true ones. These numerical experiments provide thresholds for the metrics which take advantage of the knowledge of the \emph{ground truth}: the values of these thresholds can be used in normal operation mode, when we do not know the correct values of the orbital elements and whether the linkages are true or false.

M. Elyajouri, N. Ysard, A. Abergel, E. Habart, L. Verstraete, A. Jones, M. Juvela, T. Schirmer, R. Meshaka, E. Dartois, J. Lebourlot, G. Rouille, T. Onaka, E. Peeters, O. Berne, F. Alarcon, J. Bernard-Salas, M. Buragohain, J. Cami, A. Canin, R. Chown, K. Demyk, K. Gordon, O. Kannavou, M. Kirsanova, S. Madden, R. Paladini, Y. Pendleton, F. Salama, I. Schroetter, A. Sidhu, M. Rollig, B. Trahin, D. Van De Putte

18 pages, 11 figures, accepted for publication in A&A

We study the emission of dust grains within the Orion Bar - a well-known, highly far-UV (FUV)-irradiated PDR. The Orion Bar because of its edge-on geometry provides an exceptional benchmark for characterizing dust evolution and the associated driving processes under varying physical conditions. Our goal is to constrain the local properties of dust by comparing its emission to models. Taking advantage of the recent JWST PDRs4All data, we follow the dust emission as traced by JWST NIRCam (at 3.35 and 4.8 micron) and MIRI (at 7.7, 11.3, 15.0, and 25.5 micron), along with NIRSpec and MRS spectroscopic observations. First, we constrain the minimum size and hydrogen content of carbon nano-grains from a comparison between the observed dust emission spectra and the predictions of the THEMIS dust model coupled to the numerical code DustEM. Using this dust model, we then perform 3D radiative transfer simulations of dust emission with the SOC code and compare to data obtained along well chosen profiles across the Orion Bar. The JWST data allows us, for the first time, to spatially resolve the steep variation of dust emission at the illuminated edge of the Orion Bar PDR. By considering a dust model with carbonaceous nano-grains and submicronic coated silicate grains, we derive unprecedented constraints on the properties of across the Orion Bar. To explain the observed emission profiles with our simulations, we find that the nano-grains must be strongly depleted with an abundance (relative to the gas) 15 times less than in the diffuse ISM. The NIRSpec and MRS spectroscopic observations reveal variations in the hydrogenation of the carbon nano-grains. The lowest hydrogenation levels are found in the vicinity of the illuminating stars suggesting photo-processing while more hydrogenated nano-grains are found in the cold and dense molecular region, potentially indicative of larger grains.

Accretion-powered X-ray pulsars offer a unique opportunity to study physics under extreme conditions. To fully exploit this potential, the interrelated problems of modelling radiative transport and the dynamical structure of the accretion flow must, however, be solved. This task is challenging both from a theoretical and observational point of view and is further complicated by a lack of direct correspondence between the properties of emission emerging from the neutron star and observed far away from it. In general, a mixture of emission from both poles of the neutron star viewed from different angles is indeed observed at some or even all phases of the pulse cycle. It is essential, therefore, to reconstruct the contributions of each pole to the observed flux in order to test and refine models describing the formation of the spectra and pulse profiles of X-ray pulsars. In this paper we propose a novel data-driven approach to address this problem using the pulse-to-pulse variability in the observed flux, and demonstrate its application to RXTE observations of the bright persistent X-ray pulsar Cen X-3. We then discuss the comparison of our results with previous work attempting to solve the same problem and how they can be qualitatively interpreted in the framework of a toy model describing emission from the poles of a neutron star.

Alex Doner, Mihaly Horanyi, Fran Bagenal, Pontus Brandt, Will Grundy, Carey Lisse, Joel Parker, Andrew R. Poppe, Kelsi N. Singer, S. Alan Stern, Anne Verbiscer

9 pages, 5 figures, accepted for publication in APJL

The NASA New Horizons Venetia Burney Student Dust Counter (SDC) measures dust particle impacts along the spacecraft's flight path for grains with mass $\ge$ $10^{-12}$ g, mapping out their spatial density distribution. We present the latest SDC dust density, size distribution, and flux measurements through 55 au and compare them to numerical model predictions. Kuiper Belt Objects (KBOs) are thought to be the dominant source of interplanetary dust particles (IDP) in the outer solar system due to both collisions between KBOs, and their continual bombardment by interstellar dust particles (ISD). Continued measurements through 55 au show higher than model-predicted dust fluxes as New Horizons approaches the putative outer edge of the Kuiper Belt (KB). We discuss potential explanations for the growing deviation: radiation pressure stretches the dust distribution to further heliocentric distances than its parent body distribution; icy dust grains undergo photo-sputtering that rapidly increases their response to radiation pressure forces and pushes them further away from the sun; and the distribution of KBOs may extend much further than existing observations suggest. Ongoing SDC measurements at even larger heliocentric distances will continue to constrain the contributions of dust production in the KB. Continued SDC measurements remain crucial for understanding the Kuiper Belt and the interpretation of observations of dust disks around other stars.

Timothy N. Parsons, Raman K. Prinja, Matheus Bernini-Peron, Alex W. Fullerton, Derck L. Massa, Lidia M. Oskinova, Daniel Pauli, Andreas A.C. Sander, Matthew J. Rickard

18 pages plus Appendices, 9 figures plus 37 figures in Appendices. Accepted by MNRAS

Accurate determination of mass-loss rates from massive stars is important to understanding stellar and galactic evolution and enrichment of the interstellar medium. Large-scale structure and variability in stellar winds have significant effects on mass-loss rates. Time-series observations provide direct quantification of such variability. Observations of this nature are available for some Galactic early supergiant stars but not yet for stars in lower metallicity environments such as the Magellanic Clouds. We utilise ultraviolet spectra from the Hubble Space Telescope ULLYSES program to demonstrate that the presence of structure in stellar winds of supergiant stars at low metallicities may be discerned from single-epoch spectra. We find evidence that, for given stellar luminosities and mean stellar wind optical depths, structure is more prevalent at higher metallicities. We confirm, at Large Magellanic Cloud (0.5 Z_solar), Small Magellanic Cloud (0.2 Z_solar) and lower (0.14 -- 0.1 Z_solar) metallicities, earlier Galactic results that there does not appear to be correlation between the degree of structure in stellar winds of massive stars and stellar effective temperature. Similar lack of correlation is found with regard to terminal velocity of stellar winds. Additional and revised values for radial velocities of stars and terminal velocities of stellar winds are presented. Direct evidence of temporal variability, on timescales of several days, in stellar wind at low metallicity is found. We illustrate that narrow absorption components in wind-formed profiles of Galactic OB stellar spectra remain common in early B supergiant spectra at low metallicities, providing means for better constraining hot, massive star mass-loss rates.

A, Benoit-Lévy (1 and 3), K. Kotera (2 and 3 and 4), M. Tueros (5 and 6) ((1) Université Paris-Saclay, (2) Sorbonne Université et CNRS, (3) Pennsylvania State University, (4) Vrije Universiteit Brussel, (5) CONICET, (6) Universidad Nacional de La Plata)

Submitted to JINST

The deployment of several large scale arrays is envisioned to study astroparticles at ultra-high energies. In order to circumvent the heavy computational costs of exploring and optimizing their layouts, we have developed a pruning method. It consists in i) running a set of microscopic simulations and interpolate them over a dense, regularly spaced array of detection units, and ii) pruning the unnecessary units out of the layout, in order to obtain the shower footprint on a newly shaped layout. This method offers flexibility to test various layout parameters, instrumental constraints, and physical inputs, with a drastic reduction in the required CPU time. The method can be universally applied to optimize arrays of any size, and using any detection techniques. For demonstration, we apply the pruning tool to radio antenna layouts, which allows us to discuss the interplay between the energy and inclination of air-showers on the size of the radio footprint and the intensity of the signal on the ground. Some rule-of-thumb conclusions that can be drawn for this specific case are: i) a hexagonal geometry is more efficient than a triangular geometry, ii) the detection efficiency of the array is stable to changes in the spacing between radio antennas around 1000m step size, iii) for a given number of antennas, adding a granular infill on top of a coarse hexagonal array is more efficient than instrumenting the full array with a less dense spacing.

Shobha Kumari, Sabyasachi Pal

Accepted for publication in the Monthly Notices of the Royal Astronomical Society

We identify an extended diffuse radio emission (J1507+3013) around an elliptical galaxy from the Very Large Array (VLA) Faint Images of Radio Sky at Twenty-cm (FIRST) survey. J1507+3013 possesses a morphology similar to the recently identified circular, low-surface-brightness, edge-brightened radio sources commonly known as odd radio circles (ORCs). Such diffuse emissions, as reported in the current paper, are also found in mini haloes and fossil radio galaxies, but the results presented in the current paper do not match the properties of mini haloes or fossil radio galaxies. The extended emission observed in J1507+3013 around an elliptical galaxy is a very rare class of diffuse emission which is unlike any previously known classes of diffuse emission. The extended diffuse emission of J1507+3013 is also detected in LOFAR at 144 MHz. J1507+3013 is hosted by an optical galaxy near the geometrical centre of the structure with a photometric redshift of $z=0.079$. The physical extent of J1507+3013 is approximately 68 kpc, with a peak-to-peak angular size of 44 arcsec. J1507+3013 shows significantly higher flux densities compared to previously discovered ORCs. The spectral index of J1507+3013 varies between -0.90 and -1.4 in different regions of the diffused structure, which is comparable to previously discovered ORCs but less steep than mini halos and fossil radio galaxies. If we consider J1507+3013 as a candidate ORC, then this would be the closest and most luminous ORC discovered so far. This paper describes the radio, spectral, and optical/IR properties of J1507+3013 to study the nature of this source.

We propose a model of a twisted accretion disc around a Kerr black hole interacting with a secondary black hole of a smaller mass on an inclined eccentric orbit. We use parameters of the system, which may be appropriate for the so-called 'precessing massive' model of OJ 287. We calculate expressions for torque exerted on the disc by the secondary and a contribution of the secondary to the apsidal precession of disc elements by a double averaging procedure over the periods of the secondary and the disc elements. These expressions are used at all scales of interest, including the ones inside the binary orbit. We calculate numerically the evolution of the disc tilt and twist assuming a flat initial configuration. We consider the disc aspect ratio $h/r=10^{-3}$, a rather large viscosity parameter $\alpha=0.1$ and several values of the primary rotational parameter, $\chi$. We find that, after a few periods of Lense-Thirring precession of the orbit, the disc relaxes to a quasi-stationary configuration in the precessing frame with a non-trivial distribution of the disc inclination angle, $\beta$, over the radial scale. We propose an analytic model for this configuration. We show that the presence of the twisted disc leads to multiple crossings of the disc by the secondary per one orbital period, with time periods between the crossings being different from the flat disc model. Our results should be taken into account in the modelling of OJ 287. They can also be applied to similar sources.

Scott G. Call (1), Eric G. Hintz (1), Steve Ardern (2), Victoria Scowcroft (2), Timothy D. Morrell (1) ((1) Brigham Young University, (2) University of Bath)

4 pages, 4 figures

We present time-series near-infrared (NIR) spectra for the classical Cepheid, CP Cephei, from the Astrophysical Research Consortium 3.5-m telescope and NIR spectrograph, TripleSpec, at Apache Point Observatory, NM, USA. Spectral observations were made at three points on the ascending portion of the visible phase diagram for the star. Carbon monoxide (CO) was detected in absorption in the 2.3-micron band head for each observation. We observed that the equivalent width of the 3-1 transition of the CO band head decreased by half from our first observation to the second, or slightly over one day out of the 17.867-day period. Our third observation occurred 54 days after the first (slightly over three periods for the star) and showed similar CO levels to the first observation, suggesting that the CO is in the stellar atmosphere and varies with pulsation.

We study the equilibrium configurations of relativistic Neutron Stars(NS) with a polytropic model in a $f(R,T)=R+2\lambda T+\xi T^{2}$ gravity.We investigate the neutron star properties and their dependence on $\lambda$ and $\xi$ corresponding to different central densities ($\rho_c$) of the NS. For $\lambda = 0,-1,-3,-5$ with $\xi=0$ and $\rho_c=1.5\times10^{18}~\rm{kg~m^{-3}}$, we find the maximum mass of the NS as $M = 1.06 M_\odot$, $1.19 M_\odot$ $1.61 M_\odot$ and $2.47~M_\odot$ corresponding to the radius($R$) $10.409$ km, $10.737$ km, $11.461$ km and $12.119$ km. This higher value of NS mass can be compared with gravitational wave data(GW170817). For given $\lambda =-6$ and $\xi = 0$, we find that as $\rho_c$ increases from $\rho_c=1.1 to 1.6 \times 10^{18}~\rm{kg~m^{-3}}$, the maximum mass of the NS decreases from $4.19 M_\odot$ to $3.23 M_\odot$ while it's radius $R$ decreases $13.86 \rm{km}$ to $11.54 \rm{km}$. With the fixed value of $\xi = 10^{-27}$ and $\lambda = 0,-1,-3,-5$, we find the maximum mass $M =1.06 M_\odot$,$1.34 M_\odot$,$1.89 M_\odot$ and $3.39~M_\odot$ corresponding to the radius $R = 10.409$ km, $10.843$ km, $11.549$ km and $11.680$ km. respectively. Taking our observational constraints i.e. GW170817 (BNS Merger) mass - radius data, observed pulsars PSRJ1614-2230, PSRJ0348+0432 maximum mass - radius data; we found that posterior distribution plot of mass $\&$ radius gives good result and the corner plot of modified gravity parameters $\lambda$ and $\xi$ are giving very good posterior results. So, for a range of values of $\lambda$ with $\xi=0 (\neq 0)$, we found that the mass $M$ and the radius $R$ of the NS lie within the range given by the GW170817 gravitational wave data given by LIGO, Pulsars $\&$ Millisecond Pulsars data and the NICER (Neutron star Interior Composition ExploreR) mass-radius data given by NASA.

We study analytically the superradiant instability properties of the hydrodynamic vortex model, an asymptotically flat acoustic geometry which, like the spinning Kerr black-hole spacetime, possesses an effective ergoregion. In particular, we derive a compact analytical formula for the complex resonant frequencies that characterize the long-wavelength dynamics of sound modes in this physically interesting acoustic spacetime.

Takahiro S. Yamamoto, Ryoto Inui, Yuichiro Tada, Shuichiro Yokoyama

13 pages, 10 figures

The subsolar mass primordial black hole (PBH) attracts attention as robust evidence of its primordial origin against the astrophysical black hole. Not only with themselves, PBHs can also form binaries with ordinary astrophysical objects, catching them by gravitational wave (GW) bremsstrahlung. We discuss the detectability of the inspiral GWs from binaries consisting of a PBH and a white dwarf (WD) by using space-borne gravitational wave interferometers like DECIGO. The conservative assessment shows the expected event number in three years by DECIGO is $\mathcal{O}(10^{-6})$ for $M_\mathrm{PBH} \sim 0.1M_\odot$. Possible enhancement mechanisms of WD-PBH binary formation may amplify this event rate. We discuss how large enhancement associated with WDs is required to detect WD-PBH merger events without violating the existing constraints on the PBH-PBH merger by the ground-based detector.

Nicholas Speeney, Emanuele Berti, Vitor Cardoso, Andrea Maselli

11 pages, 5 figures, 1 table

We develop a numerical approach to compute polar parity perturbations within fully relativistic models of black hole systems embedded in generic, spherically symmetric, anisotropic fluids. We apply this framework to study gravitational wave generation and propagation from extreme mass-ratio inspirals in the presence of several astrophysically relevant dark matter models, namely the Hernquist, Navarro-Frenk-White, and Einasto profiles. We also study dark matter spike profiles obtained from a fully relativistic calculation of the adiabatic growth of a BH within the Hernquist profile, and provide a closed-form analytic fit of these profiles. Our analysis completes prior numerical work in the axial sector, yielding a fully numerical pipeline to study black hole environmental effects. We study the dependence of the fluxes on the DM halo mass and compactness. We find that, unlike the axial case, polar fluxes are not adequately described by simple gravitational-redshift effects, thus offering an exciting avenue for the study of black hole environments with gravitational waves.

Stochastic gravitational-wave (GW) background (SGWB) contains information about the early Universe and astrophysical processes. The recent evidence of SGWB by pulsar timing arrays in the nanohertz band is a breakthrough in the GW astronomy. For ground-based GW detectors, while unfortunately in data analysis the SGWB can be masked by loud GW events from compact binary coalescences (CBCs). Assuming a next-generation ground-based GW detector network, we investigate the potential for detecting the astrophysical and cosmological SGWB with non-CBC origins by subtracting recovered foreground signals of loud CBC events. As an extension of the studies by Sachdev et al. (2020) and Zhou et al. (2023), we incorporate aligned spin parameters in our waveform model. Because of the inclusion of spins, we obtain significantly more pessimistic results than the previous work, where the residual energy density of foreground is even larger than the original background. The degeneracy between the spin parameters and symmetric mass ratio is strong in the parameter estimation process and it contributes most to the imperfect foreground subtraction. Our results have important implications for assessing the detectability of SGWB from non-CBC origins for ground-based GW detectors.

Sahar Safari, Mehran Dehpour, Saeed Abbaslu, Siamak Sadat Gousheh

22 pages, 3 figures

One of the major challenges in particle physics and cosmology is understanding why there is an asymmetry between matter and antimatter in the Universe. One possible explanation for this phenomenon is thermal leptogenesis, which involves the addition of at least two right-handed neutrinos (RHNs) to the standard model. Another possible explanation is baryogenesis through the hypermagnetic fields which involves the ${\rm U}_Y(1)$ anomaly and helical hypermagnetic fields in the early Universe. In this paper, after reviewing the thermal leptogenesis and baryogenesis through the ${\rm U}_Y(1)$ anomaly, we investigate the simplest model that combines these two scenarios and explore the parameter space for optimal results. Our results show that the combined scenario permits a specific region of parameter space that is not covered by either one separately. In fact, the minimum required mass scale of the RHN and strength of initial hypermagnetic helicity are reduced by one order of magnitude in our model. Moreover, we find that in the combined scenario, leptogenesis and baryogenesis through the ${\rm U}_Y(1)$ anomaly can either amplify or reduce the effect of each other, i.e., the generated asymmetry, depending on the sign of the helical hypermagnetic fields. Finally, we show the surprising result that a drastic amplification can occur even when the initial abundance of RHN is its equilibrium value for leptogenesis.