Magnetic Equator Research Articles

Very local impact on the spectrum of cosmic-ray nuclei below 100 TeV

Recent measurements of primary and secondary CR spectra, their arrival directions, and our improved knowledge of the magnetic field geometry around the heliosphere allow us to set a bound on the distance beyond which a puzzling 10-TeV “bump” and certain related spectral features cannot originate. The sharpness of the spectral breaks associated with the bump, the abrupt change of the CR intensity across the local magnetic equator (90° pitch angle), and the similarity between the primary and secondary CR spectral patterns point to a local reacceleration of the bump particles out of the background CRs. We argue that, owing to a steep preexisting CR spectrum, a nearby shock may generate such a bump by boosting particle rigidity by a mere factor of ∼1.5 in the range below 50 TV. Reaccelerated particles below ∼0.5 TV are convected with the interstellar medium flow and do not reach the Sun. The particles above this rigidity then form the bump. This single universal process is responsible for the observed spectral features of all CR nuclei, primary and secondary, in the rigidity range below 100 TV. We propose that one viable candidate is the system of shocks associated with ∊ Eridani star at 3.2 pc of the Sun, which is well aligned with the direction of the local magnetic field. Other shocks, such as old supernova shells, may produce a similar effect. We provide a simple formula that reproduces the spectra of all CR species with only three parameters uniquely derived from the CR proton data. We show how our formalism predicts helium, boron, carbon, oxygen, and iron spectra, for which accurate data in GV-TV range exist. Our model thus unifies all the CR spectral features observed below 50 TV.

Revisiting the governing equations of a magnetic suspension of polar particles: From microhydrodynamics analysis to rheological response

In this review, we describe a formulation for the stress tensor of a monodisperse magnetic suspension of polarized neutrally buoyant spheroidal particles suspended in a non-magnetic liquid. A magnetic suspension affords a rare example of a material for which the stress tensor is non-symmetric. The present formulation is based on a microhydrodynamics description of a spherical particle suspended in a Newtonian fluid subjected to magnetic forces and torques. The magnetic suspension is considered statistically homogeneous and treated as being a homogeneous equivalent fluid. Under this condition, a volume average over all particles in the carrier fluid is used in order to obtain the magnetization equation evolution and the constitutive equation for the stress tensor of the magnetic suspension, in particular the magnetic stress contribution. The average effects on the homogeneous continuum fluid due to particle pressure, particle dipole, and the applied magnetic field on each particle are computed by our constitutive equation. In this approach, the particles are not considered force or torque free since their permanent magnetization allows them to experience the effects of an applied magnetic field. The calculated stress tension can be used for modeling common flows of symmetric or non-symmetric magnetic fluids flowing in arbitrary geometries and in rheological applications for determination of important properties such as the rotational viscosity of non-symmetric magnetic fluids. The final expression of the constitutive equation for the stress tensor based on a particle scale approach presents some difference as compared with current constitutive models proposed in the current literature. Our constitutive equation considers the effect of a magnetic particle pressure, the average particle stresslet contribution in terms of an effective viscosity, the average particle rotlet in terms of a rotational viscosity, and a configurational tensor associated with dipole–dipole interactions. In addition, we discuss the situation in which the dipole moment of the particle is not frozen on it which leads to the necessity of an internal balance of angular momentum in a fluid element to close the governing equations of the model. An extension of the model for emulsions of polar deformable droplets is also proposed.

Enhanced Efficiency of Solar Wind Electron Interaction with Whistlers Caused by Switchback-related Magnetic Dips

Through test particle simulations based on solar wind observations by the Parker Solar Probe (PSP) mission, we demonstrate that a magnetic gradient can significantly enhance the efficiency of scattering and energization of the strahl electrons by quasi-parallel whistlers, through the phase trapping effect due to the gyrosurfing mechanism. We identify quasi-linear and nonlinear regimes of these interactions for different combinations of wave amplitude (B w /B 0) and the strength of the magnetic field gradient with magnetic field depletion level (B h /B 0) as a proxy. Nonlinear effects are observed for B w /B 0 ≳ 10−3 and B h /B 0 ≳ 0.1. We estimated the extending of the resonant energy range due to the wave and the magnetic field gradient interplay and demonstrated that these mechanisms result in the broadening of the strahl electron pitch-angle distribution typically observed in situ. The combination of parallel whistlers collocated with a magnetic gradient is frequently observed by PSP in magnetic dips at the edges of magnetic switchbacks. Our results indicate that these mechanisms may be highly relevant for pitch-angle scattering of the strahl electrons and regulating the heat flux near the Sun at heliocentric distances of 30–45 R S . Specifically, core and halo electrons may experience a 10% increase in their initial energy, and the majority of strahl electrons may be scattered (by an average of 30°) into the hot and trapped plasma inside magnetic dips.

Locally divergence-free well-balanced path-conservative central-upwind schemes for rotating shallow water MHD

We develop a new second-order flux globalization based path-conservative central-upwind (PCCU) scheme for rotating shallow water magnetohydrodynamic equations. The new scheme is designed not only to maintain the divergence-free constraint of the magnetic field at the discrete level but also to satisfy the well-balanced (WB) property by exactly preserving some physically relevant steady states of the underlying system. The locally divergence-free constraint of the magnetic field is enforced by following the method recently introduced in Chertock et al. (2024) [19]: we consider a Godunov-Powell modified version of the studied system, introduce additional equations by spatially differentiating the magnetic field equations, and modify the reconstruction procedures for magnetic field variables. The WB property is ensured by implementing a flux globalization approach within the PCCU scheme, leading to a method capable of preserving both still- and moving-water equilibria exactly. In addition to provably achieving both the WB and divergence-free properties, the new method is implemented on an unstaggered grid and does not require any (approximate) Riemann problem solvers. The performance of the proposed method is demonstrated in several numerical experiments that confirms robustness, a high resolution of obtained results, and a lack of spurious oscillations.

A simple physical model for simulation and design magneto-plethysmograph in application non-invasive hemoglobin measurement

The magneto-plethysmograph method is a combination of magnetic field and sensors used to detect changes in blood flow pulsation. However, to detect the magnetic properties of blood related to hemoglobin concentration, physical modeling and simulation are required. This approach involves designing simulations using magnetic field equations and magnetic susceptibility, where a permanent magnet is placed on the surface of blood vessels, and sensors based on giant magnetoresistance are placed at a distance r. The design originates from a simple approach involving the magnetization and detection of Fe atoms in hemoglobin. Parameters involved include the magnetic susceptibility of oxyhemoglobin and deoxyhemoglobin, with an external magnetic field exceeding 1 Tesla. From the physical modeling and simulation, graphs are obtained depicting the influence of hemoglobin concentration on the number of Fe atoms and its magnetization. This enables the design of non-invasive hemoglobin measurement sensor devices. The uniqueness of this simple physical model and simulation lies in its ability to produce specially designed device models for measuring hemoglobin concentration. This differs from other research focusing on blood flow pulse measurements; the results of this study provide new insights into the benefits of simple physics equations that can be developed for medical diagnostic research and device development.

Effect of hot isostatic pressing on microstructure and properties of cooled hot dip aluminum coating in magnetic field

The effect of hot isostatic pressing (HIP) on the microstructure and properties of hot dip aluminum coating cooled in a magnetic field was investigated in this study. In order to improve the microstructure and properties of magnetic dip aluminum coating, hot isostatic pressing technology was used for post-treatment. Initially, a traditional aluminum-impregnated coating was prepared on the surface of titanium alloy TA15, an alternating electromagnetic field was applied during the forming and solidification process of the coating. Finally, the coating was treated with hot isostatic pressing technology. Analyzed three different coatings of the microstructure and element distribution, and tested the microhardness of the coatings at various positions. The test results revealed that the TA15 titanium alloy hot-dip aluminum coatings obtained through the three different processes exhibited a gradient structure. Compared with the traditional hot-dipped aluminum air-cooled coating, when an appropriate intensity of alternating electromagnetic field was applied during the coating solidification process, the outer coating structure was enhanced, the number of holes was reduced, the microstructure density increased, and the number of cracks significantly decreased. The defects of the 800 °C hot isostatic magnetic cold and hot dip aluminum coating were repaired under high temperature and pressure, resulting in a uniform and fine microstructure. The comprehensive properties of the magnetic cold and hot dip aluminum coating on the surface of the titanium alloy were effectively enhanced through hot isostatic pressing.

Thermal performance analysis of oriented MHD convective flow and entropy production of hybrid nanofluids in a cavity induced by semicircles at different radii ratios

AbstractThe current study numerically treats the magnetic field impacts on the natural convection flow and entropy generation in a square cavity filled with hybrid nanofluid and induced by two isothermally heated semicircles at the bottom and left walls of the cavity. The cavity is filled by hybrid nanofluid (titanium oxide/silver‐water) and oriented under different inclination angles with the applied magnetic field. The simulations in this study were executed via a home‐made code written in the FORTRAN programing language. The numerical methodology considered to solve the coupled equations of continuity, momentum, energy, and entropy generation equations with the associated boundary conditions is the finite volume method and the full multigrid acceleration. Various wake parameters are considered in this research study, namely, the inclination angle of the cavity (α), the magnetic field inclination (γ), the Hartmann number (Ha), the Rayleigh number (Ra), the volume fraction of the hybrid nanofluid (ϕ) and the internal semicircles radii ratio (β). The major findings issued from the impact of these parameters on the fluid flow and heat transfer characteristics reveal that heat transfer and entropy generation are a decreasing function of the Hartmann parameter. Moreover, the total entropy generation is intensified by 85.23% from Ra = 103 to Ra = 106 for Ha = 10, by 85.818% for Ha = 50 and 83.813% for Ha = 100. Besides, the flow magnitude is found decreasing with increasing the radii ratio β of the semicircles. It is also found that optimal heat transfer rates deducted from the variation of average Nusselt number versus Ra for different volume fractions of the hybrid nanoparticles are obtained for the extreme values of the pertinent parameters (β = 1, ϕ = 8%, Ra = 106). Hence, the present work offers a useful tool and a parametric study for the research community and engineers on the design and optimization of thermal management systems used in a variety of industrial applications, such as heat exchangers, nuclear reactors, and energy systems.

Energy‐based PINNs for solving coupled field problems: Concepts and application to the multi‐objective optimal design of an induction heater

AbstractPhysics‐informed neural networks (PINNs) are neural networks (NNs) that directly encode model equations, like Partial Differential Equations (PDEs), in the network itself. While most of the PINN algorithms in the literature minimize the local residual of the governing equations, there are energy‐based approaches that take a different path by minimizing the variational energy of the model. It is shown that in the case of the steady thermal equation weakly coupled to magnetic equation, the energy‐based approach displays multiple advantages compared to the standard residual‐based PINN: it is more computationally efficient, it requires a lower order of derivatives to compute, and it involves less hyperparameters. The analyzed benchmark problems are the single‐ and multi‐objective optimal design of an inductor for the controlled heating of a graphite plate. The optimized device is designed by involving a multi‐physics problem: a time‐harmonic magnetic problem and a steady thermal problem. For the former, a deep neural network solving the direct problem is supervisedly trained on Finite Element Analysis (FEA) data. In turn, the solution of the latter relies on a hypernetwork that takes as input the inductor geometry parameters and outputs the model weights of an energy‐based PINN (or ePINN). Eventually, the ePINN predicts the temperature field within the graphite plate.

Magnetic field effects on double diffusion of four sloshing fins in a nanofluid-occupied cavity

ABSTRACT This article offers a novel study on the impacts of magnetic field and Soret-Dufour numbers on the thermosolutal convection of sloshing four fins on the wall sides of a square cavity occupied by a nanofluid. The incompressible condition of smoothed particle hydrodynamics (SPH) entitled ISPH method simulated sloshing four fins inside a nanofluid flow contained by a square cavity. The scales of pertinent parameters are fin length 0.05 ≤ L Fin ≤ 0.3 , Dufour number 0 ≤ Du ≤ 1 , a magnetic field inclination angle 30 ∘ ≤ γ ≤ 90 ∘ , Soret number 0 ≤ Sr ≤ 2 , Hartmann number 10 ≤ Ha ≤ 50 , Rayleigh number 10 4 ≤ Ra ≤ 10 7 , and nanoparticle parameter 0 ≤ ϕ ≤ 0.2 . The simulations of the ISPH method indicated the significant role of the fin’s length in enhancing the nanofluid alterations and transmission of thermal/solutal convection inside a cavity. Besides, the Rayleigh number has a great influence on improving nanofluid velocity and power of temperature/concentration. The Soret/Dufour numbers are successful in boosting the nanofluid speed as well as heat and mass transport, while the Hartmann number and nanoparticles parameter are effective in reducing the nanofluid movements.

Energy Conversion in the Dip Region Preceding Dipolarization Front

AbstractDipolarization fronts (DFs), characterized by sharp increases in the northward magnetic field and usually preceded by magnetic dips, are suggested to play an important role in energy conversion and transport in the magnetotail. It has been documented that strong energy conversion typically develops right at the fronts. Here we present spacecraft observations of electron‐scale energy conversion (EEC) developed inside the dip region ahead of a DF, by using high‐cadence data from the Magnetospheric Multiscale Mission. The EEC, with magnitude comparable to that at the front, is primarily driven by ion current and electron‐scale electric field. The electric field inside the dip is provided by electrostatic waves fed by lower hybrid drift instability, which experiences temporal decaying. Such decaying leads to nonhomogeneity of EEC along the dawn‐dusk direction. These results, uncovering a new channel for DF‐driven energy conversion, can provide important insights into understanding energy transport in the magnetotail.

Empirical Model of the Lowest Cutoff Altitude of Global Hiss Near Magnetic Equator

Empirical Model of the Lowest Cutoff Altitude of Global Hiss Near Magnetic Equator

Generation and Impacts of Whistler‐Mode Waves During Energetic Electron Injections in Jupiter's Outer Radiation Belt

AbstractEnergetic particle injections are commonly observed in Jupiter's magnetosphere and have important impacts on the radiation belts. We evaluate the roles of electron injections in the dynamics of whistler‐mode waves and relativistic electrons using Juno measurements and wave‐particle interaction modeling. The Juno spacecraft observed injected electron flux bursts at energies up to 300 keV at M shell ∼11 near the magnetic equator during perijove‐31. The electron injections are related to chorus wave bursts at 0.05–0.5 fce frequencies, where fce is the electron gyrofrequency. The electron pitch angle distributions are anisotropic, peaking near 90° pitch angle, and the fluxes are high during injections. We calculate the whistler‐mode wave growth rates using the observed electron distributions and linear theory. The frequency spectrum of the wave growth rate is consistent with that of the observed chorus magnetic intensity, suggesting that the observed electron injections provide free energy to generate whistler‐mode chorus waves. We further use quasilinear theory to model the impacts of chorus waves on 0.1–10 MeV electrons. Our modeling shows that the chorus waves could cause the pitch angle scattering loss of electrons at <1 MeV energies and accelerate relativistic electrons at multiple MeV energies in Jupiter's outer radiation belt. The electron injections also provide an important seed population at several hundred keV energies to support the acceleration to higher energies. Our wave‐particle interaction modeling demonstrates the energy flow from the electron injections to the relativistic electron population through the medium of whistler‐mode waves in Jupiter's outer radiation belt.

On the Factors Controlling the Relationship Between Type of Pulsating Aurora and Energy of Pulsating Auroral Electrons: Simultaneous Observations by Arase Satellite, Ground‐Based All‐Sky Imagers and EISCAT Radar

AbstractPulsating Aurora (PsA) is one of the major classes of diffuse aurora associated with precipitation of a few to a few tens of keV electrons from the magnetosphere. Recent studies suggested that, during PsA, more energetic (i.e., sub‐relativistic/relativistic) electrons precipitate into the ionosphere at the same time. Those electrons are considered to be scattered at the higher latitude part of the magnetosphere by whistler‐mode chorus waves propagating away from the magnetic equator. However, there have been no actual cases of simultaneous observations of precipitating electrons causing PsA (PsA electrons) and chorus waves propagating toward higher latitudes; thus, we still do not quite well understand under what conditions PsA electrons become harder and precipitate to lower altitudes. To address this question, we have investigated an extended interval of PsA on 12 January 2021, during which simultaneous observations with the Arase satellite, ground‐based all‐sky imagers and the European Incoherent SCATter (EISCAT) radar were conducted. We found that, when the PsA shape became patchy, the PsA electron energy increased and Arase detected intense chorus waves at magnetic latitudes above 20°, indicating the propagation of chorus waves up to higher latitudes along the field line. A direct comparison between the irregularities of the magnetospheric electron density and the emission intensity of PsA patches at the footprint of the satellite suggests that the PsA morphology and the energy of PsA electrons are determined by the presence of “magnetospheric density ducts,” which allow chorus waves to travel to higher latitudes and thereby precipitate more energetic electrons.

Large-scale Linear Magnetic Holes with Magnetic Mirror Properties in Hybrid Simulations of Solar Wind Turbulence

Magnetic holes (MHs) are coherent magnetic field dips whose size ranges from fluid to kinetic scale, ubiquitously observed in the heliosphere and in planetary environments. Despite the long-standing effort in interpreting the abundance of observations, the origin and properties of MHs are still debated. In this Letter, we investigate the interplay between plasma turbulence and MHs, using a 2D hybrid simulation initialized with solar wind parameters. We show that fully developed turbulence exhibits localized elongated magnetic depressions, whose properties are consistent with linear MHs frequently encountered in space. The observed MHs develop self-consistently from the initial magnetic field perturbations by trapping hot ions with large pitch angles. Ion trapping produces an enhanced perpendicular temperature anisotropy that makes MHs stable for hundreds of ion gyroperiods, despite the surrounding turbulence. We introduce a new quantity, based on local magnetic field and ion temperature values, to measure the efficiency of ion trapping, with potential applications to the detection of MHs in satellite measurements. We complement this method by analyzing the ion velocity distribution functions inside MHs. Our diagnostics reveal the presence of trapped gyrotropic ion populations, whose velocity distribution is consistent with a loss cone, as expected for the motion of particles inside a magnetic mirror. Our results have potential implications for the theoretical and numerical modeling of MHs.

Localizing the non-thermal X-ray emission of PSR J2229+6114 from its multi-wavelength pulse profiles

Context. Pulsars are detected over the whole electromagnetic spectrum, from radio wavelengths up to very high energies, in the GeV-TeV range. While the radio emission site for young pulsars is well constrained to occur at altitudes about several percent of the light-cylinder radius and γ-ray emission is believed to be produced in the striped wind, outside the light cylinder, the non-thermal X-ray production site remains unknown. Aims. The aim of this Letter is to localize the non-thermal X-ray emission region based on a multi-wavelength pulse profile fitting for PSR J2229+6114, which stands as a particularly good candidate given its high X-ray brightness. Methods. Based on the geometry deduced from the joint radio and γ-ray pulse profiles, we fixed the magnetic axis inclination angle and the line-of-sight (LoS) inclination angle. However, we left the region of X-ray emission unlocalized, setting it somewhere between the surface and the light cylinder. We localized this region and its extension by fitting the X-ray pulse profile as observed by the NICER, NuSTAR, and RXTE telescopes in the ranges of 2–7 keV, 3–10 keV, and 9.4–22.4 keV, respectively. Results. We constrained the non-thermal X-ray emission to arise from altitudes between 0.2 rL and 0.55 rL where rL is the light-cylinder radius. The magnetic obliquity is approximately α ≈ 45° −50° and the LoS inclination angle is ζ ≈ 32° −48°. Conclusions. This Letter is among the first works to offer a tight constraint on the location of non-thermal X-ray emission from pulsars. We plan to apply this procedure to several other promising candidates to confirm this new result.

Isochronous bifurcations of magnetic islands in tokamaks

On a rational magnetic surface, an isochronous bifurcation transforms one island chain into another chain with the same winding number. This transformation has been the subject of recent studies in tokamak plasmas. Namely, visco-resistive magnetohydrodynamic simulations of NSTX-U and DIII-D plasmas showed the onset of bifurcations with new magnetic isochronous islands for two competing helical perturbations on the same rational magnetic surface. To investigate these bifurcations, we use a cylindrical plasma model, with first-order correction for toroidicity, subject to externally applied magnetic perturbations, generated by a pair of resonant helical windings (RHWs) on the external wall and superposed to a helical current sheet (HCS) located on a rational plasma surface. We numerically integrate the magnetic field line equation and show that isochronous islands emerge when the perturbation created by the HCS increases. We present examples of such bifurcations on primary and secondary magnetic surfaces for different RHW configurations.

Quasi‐Diurnal Lunar Tide O1 in Ionospheric Total Electron Content at Solar Minimum

AbstractFor the first time, characteristics of the geographical and seasonal distribution of the quasi‐diurnal lunar O1 tide were derived from a time series of ionospheric total electron content (TEC) maps provided by International Global Navigation Satellite System Service (IGS). The data analysis is focused on solar minimum in 2008 and 2009 where disturbing influences of geomagnetic and solar activity were minimal. We found that the magnitude of the O1 tide is as strong as the “dominant” semidiurnal lunar M2 tide. Relative amplitudes of 10% and larger are observed in some regions for the O1 component in TEC. The O1 component is particularly strong in northern hemispheric winter over the west coast of South America. There, two maxima occur which are northward and southward of the magnetic equator in the Equatorial Ionization Anomaly (EIA) crest regions. Following Yamazaki et al. (2017, https://doi.org/10.1002/2017ja024601), it might be assumed that a longitudinal anomaly of ionospheric conductivities in the Peruvian sector leads to a stronger modulation of the equatorial electrojet by the lunar tides. Electrodynamic lifting of plasma and transport to the EIA crests may explain the variations of the O1 component in TEC. Contrary to many studies, we find the O1 component (period 25.82 hr) more important than the M1 component (period 24.84 hr, a lunar day). We show that the geographical distribution of the O1 component is totally different from that of the M1 component which is smaller. The seasonal variation of O1 shows maximal amplitudes in northern hemispheric winter and minimal amplitudes in southern hemispheric winter.

STUDY ON AUTOMATED DETECTION OF EQUATORIAL PLASMA BUBBLES EPB

A processing application has been developed to detect and characterize localized plasma decreases: Equatorial plasma bubbles. The algorithm used is based on an automated search for negative STEC variations during a GPS satellite passage. First, an example of detection is shown. The method used has been applied to available data from seven (7) stations in West Africa, and the results over several years of measurements are presented. A study of spatial behavior was also carried out. The results show that the location of EPB bubbles depends on magnetic position. Bubbles are more present near the position of the North and South Equatorial Anomaly (EIA) ridges, but exist near the magnetic equator. Beyond 30° of inclination, bubbles are rarely present. The study of EPB characteristics also revealed durations mostly between 10 and 25 min, and maximum depths between 5 and 25 TECU.

Seasonal–Longitudinal Variability of Equatorial Plasma Bubbles Observed by FormoSat-7/Constellation Observing System for Meteorology Ionosphere and Climate II and Relevant to the Rayleigh–Taylor Instability

The FormoSat-7/Constellation Observing System for Meteorology, Ionosphere, and Climate II (FS7/COSMIC2) program has acquired over three hundred thousand equatorial plasma bubble (EPB) observations from 2019 to 2023 in the equatorial and near low-latitude regions. The huge FS7/COSMIC2 database offers an opportunity to perform statistical inspections of the proposed hypothesis on seasonal versus longitudinal variability of EPB occurrence rates relevant to the Rayleigh–Taylor (R-T) instability. The detected EPBs are distributed along the magnetic equator with a half width of ~20° in geomagnetic latitude. The obtained EPB occurrence rates in local time (LT) rose rapidly after sunsets, and could be deconstructed into two overlapped Gaussian distributions resembling a major peak around 23:00 LT and a minor peak around 20:20 LT. The two groups of Gaussian-distributed EPBs in LT were classified as first- and second-type EPBs, which could be caused by different mechanisms such as sporadic E (Es) instabilities and pre-reversal enhancement (PRE) fields. The obtained seasonal–longitudinal distributions of both types of EPBs presented two diffused traces of high occurrence rates, which happened near the days and longitudes when and where the angle between the two lines of magnetic declination and solar terminator at the magnetic equator was equal to zero. Finally, we analyzed the climatological and seasonal–longitudinal variability of EPB occurrences and compared the results with the physical R-T instability model controlled by Es instabilities and/or PRE fields.

Curvature of the chiral phase transition line from the magnetic equation of state of ( 2+1 )-flavor QCD

We analyze the dependence of the chiral phase transition temperature on baryon number and strangeness chemical potentials by calculating the leading order curvature coefficients in the light and strange quark flavor basis as well as in the conserved charge (B, S) basis. Making use of scaling properties of the magnetic equation of state (MEoS) and including diagonal as well as off-diagonal contributions in the expansion of the energylike scaling variable that enters the parametrization of the MEoS, allows to explore the variation of Tc(μB,μS)=Tc(1−(κ2Bμ^B2+κ2Sμ^S2+2κ11BSμ^Bμ^S)) along different lines in the (μB,μS) plane. On lattices with fixed cutoff in units of temperature, aT=1/8, we find κ2B=0.015(1), κ2S=0.0124(5) and κ11BS=−0.0050(7). We show that the chemical potential dependence along the line of vanishing strangeness chemical potential is about 10% larger than along the strangeness neutral line. The latter differs only by about 3% from the curvature on a line of vanishing strange quark chemical potential, μs=0. We also show that close to the chiral limit the strange quark mass contributes like an energylike variable in scaling relations for pseudocritical temperatures. The chiral phase transition temperature decreases with decreasing strange quark mass, Tc(ms)=Tc(msphy)(1−0.097(2)(ms−msphys)/msphy+O((Δms)2). Published by the American Physical Society 2024