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At least 397 records · Page 22

Axisymmetric hydrodynamics in numerical relativity: treating coordinate singularity, artificial heating and modeling MHD instabilities

Two-dimensional axisymmetric simulations of binary neutron star (BNS) merger remnant are a cheap alternative to 3D simulations. To maintain realism for secular timescales, simulations must avoid accumulated errors from drifts in conserved quantities and artificial heating, and they must model turbulent transport in a way that remains plausible throughout the evolution. It is also crucial to avoid numerical artifacts due to the polar coordinate axis singularity. Methods that behave well near the axis often break flux-conservative form of the hydrodynamic equations, resulting in significant drifts in conserved quantities. We present a flux-conservative scheme that maintains smoothness near the axis without sacrificing conservative formulation of the equations or incurring drifts in conserved global quantities. We compare the numerical performance of different treatments of the hydrodynamic equations when evolving a hypermassive neutron star resembling the remnant of a BNS merger. These simulations demonstrate that the new scheme combines the axis smoothness of non-conservative methods with the mass and angular momentum conservation of other conservative methods on $\sim 10^2$ ms timescales of viscous and neutrino-driven evolution. Because fluid profiles remain smooth in the remnant interior, it is possible to remove artificial heating by evolving the entropy density. We show how physical heating and cooling terms can be easily calculated from source terms of the conservative evolution variables and demonstrate our implementation. Finally, we discuss and implement improvements to the effective viscosity scheme to better model the effect of magnetohydrodynamic instabilities as the remnant evolves.

axisymmetry↗

The 2022 magneto-optics roadmap

Abstract Magneto-optical (MO) effects, viz. magnetically induced changes in light intensity or polarization upon reflection from or transmission through a magnetic sample, were discovered over a century and a half ago. Initially they played a crucially relevant role in unveiling the fundamentals of electromagnetism and quantum mechanics. A more broad-based relevance and wide-spread use of MO methods, however, remained quite limited until the 1960s due to a lack of suitable, reliable and easy-to-operate light sources. The advent of Laser technology and the availability of other novel light sources led to an enormous expansion of MO measurement techniques and applications that continues to this day (see section 1). The here-assembled roadmap article is intended to provide a meaningful survey over many of the most relevant recent developments, advances, and emerging research directions in a rather condensed form, so that readers can easily access a significant overview about this very dynamic research field. While light source technology and other experimental developments were crucial in the establishment of today’s magneto-optics, progress also relies on an ever-increasing theoretical understanding of MO effects from a quantum mechanical perspective (see section 2), as well as using electromagnetic theory and modelling approaches (see section 3) to enable quantitatively reliable predictions for ever more complex materials, metamaterials, and device geometries. The latest advances in established MO methodologies and especially the utilization of the MO Kerr effect (MOKE) are presented in sections 4 (MOKE spectroscopy), 5 (higher order MOKE effects), 6 (MOKE microscopy), 8 (high sensitivity MOKE), 9 (generalized MO ellipsometry), and 20 (Cotton–Mouton effect in two-dimensional materials). In addition, MO effects are now being investigated and utilized in spectral ranges, to which they originally seemed completely foreign, as those of synchrotron radiation x-rays (see section 14 on three-dimensional magnetic characterization and section 16 on light beams carrying orbital angular momentum) and, very recently, the terahertz (THz) regime (see section 18 on THz MOKE and section 19 on THz ellipsometry for electron paramagnetic resonance detection). Magneto-optics also demonstrates its strength in a unique way when combined with femtosecond laser pulses (see section 10 on ultrafast MOKE and section 15 on magneto-optics using x-ray free electron lasers), facilitating the very active field of time-resolved MO spectroscopy that enables investigations of phenomena like spin relaxation of non-equilibrium photoexcited carriers, transient modifications of ferromagnetic order, and photo-induced dynamic phase transitions, to name a few. Recent progress in nanoscience and nanotechnology, which is intimately linked to the achieved impressive ability to reliably fabricate materials and functional structures at the nanoscale, now enables the exploitation of strongly enhanced MO effects induced by light–matter interaction at the nanoscale (see section 12 on magnetoplasmonics and section 13 on MO metasurfaces). MO effects are also at the very heart of powerful magnetic characterization techniques like Brillouin light scattering and time-resolved pump-probe measurements for the study of spin waves (see section 7), their interactions with acoustic waves (see section 11), and ultra-sensitive magnetic field sensing applications based on nitrogen-vacancy centres in diamond (see section 17). Despite our best attempt to represent the field of magneto-optics accurately and do justice to all its novel developments and its diversity, the research area is so extensive and active that there remains great latitude in deciding what to include in an article of this sort, which in turn means that some areas might not be adequately represented here. However, we feel that the 20 sections that form this 2022 magneto-optics roadmap article, each written by experts in the field and addressing a specific subject on only two pages, provide an accurate snapshot of where this research field stands today. Correspondingly, it should act as a valuable reference point and guideline for emerging research directions in modern magneto-optics, as well as illustrate the directions this research field might take in the foreseeable future.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hyperfine and quadrupole interactions for Dy isotopes in DyPc 2 molecules

Nuclear spin levels play a vital role in understanding magnetization dynamics and implementation and control of quantum bits in lanthanide-based single-molecule magnets. We investigate the hyperfine and nuclear quadrupole interactions for 161 Dy and 163 Dy nuclei in anionic DyPc 2 (Pc=phthalocyanine) single-molecule magnets, using multiconfigurational ab initio methods (beyond density-functional theory) including spin–orbit interaction. The two isotopes of Dy are chosen because the others have zero nuclear spin. Both isotopes have the nuclear spin I =5/2, although the magnitude and sign of the nuclear magnetic moment differ from each other. The large energy gap between the electronic ground and first-excited Kramers doublets, allows us to map the microscopic hyperfine and quadrupole interaction Hamiltonian onto an effective Hamiltonian with an electronic pseudo-spin that corresponds to the ground Kramers doublet. Our ab initio calculations illustrate that the coupling between the nuclear spin and electronic orbital angular momentum contributes the most to the hyperfine interaction and that both the hyperfine and nuclear quadrupole interactions for 161 Dy and 163 Dy nuclei are much smaller than those for the 159 Tb nucleus in TbPc 2 single-molecule magnets. The calculated separations of the electronic-nuclear levels are comparable to experimental data reported for 163 DyPc 2 . We demonstrate that hyperfine interaction for the Dy Kramers ion leads to tunnel splitting (or quantum tunneling of magnetization) at zero field. This effect does not occur for TbPc 2 single-molecule magnets. The magnetic field values of the avoided level crossings for 161 DyPc 2 and 163 DyPc 2 are found to be noticeably different, which can be observed from the experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Magnetic fluctuations and the spin–orbit interaction in Mott insulating CoO

Motivated by the presence of an unquenched orbital angular momentum in CoO, a team at Chalk River, including a recently hired research officer Roger Cowley, performed the first inelastic neutron scattering experiments on the classic Mott insulator. Despite identifying two magnon modes at the zone boundary, the team was unable to parameterise the low energy magnetic excitation spectrum below TN using conventional pseudo-bosonic approaches, instead achieving only qualitative agreement. It would not be for another 40 years that Roger, now at Oxford and motivated by the discovery of the high-Tc cuprate superconductors, would make another attempt at the parameterisation of the magnetic excitation spectrum that had previously alluded him at the start of his career. Upon his return to CoO, Roger found a system embroiled in controversy, with some of its most fundamental parameters still remaining undetermined. Faced with such a formidable task, Roger performed a series of inelastic neutron scattering experiments in the early 2010s on both CoO and a magnetically dilute structural analogue Mg 0.97 Co 0.03 O. These experiments would prove instrumental in the determination of both single-ion and cooperative magnetic parameters for CoO. Both these sets of parameters would eventually be used in a spin–orbit exciton model, developed by his longtime friend and collaborator Bill Buyers, to successfully parameterise the complex spectrum that both measured at Chalk River almost 50 years prior. The story of CoO is of one that has come full circle, one filled with both spectacular failures and intermittent, yet profound, little victories.

36 MATERIALS SCIENCE↗

Hardware, methodology and applications of 2 + D backscatter Mössbauer spectroscopy with simultaneous x-ray and γ-ray detection

Abstract A unique method is presented for the acquisition and analysis of 57 Fe backscatter Mössbauer spectra with simultaneous detection of the resonant 14.4 keV γ -rays and the characteristic 6.4 keV x-rays, using a custom-built multi-parameter analyser constructed on the basis of commercial analogue to digital converters and high-speed digital latches. The system allows for the simultaneous registration of Doppler-modulation velocities and photon energies, with up to 4096 and 8192 digital channels respectively. This arrangement is in contrast to most related systems, which detect at a single narrow energy window per detector. Samples of arbitrary atomic structure, morphology and surface topography can be studied without altering the setup or the analysis procedure, provided that the samples are at least micrometre sized. The hardware and software that are used to acquire data with minimal dead time are described and the custom and self-contained methods for post-measurement energy discrimination, background correction and velocity-axis folding are discussed. The data are fit using a general Hamiltonian model for the nuclear energy levels of 57 Fe and a quantum mechanical description of the angular momentum coupling is utilised, with consideration of the crystalline and chemical disorder of the sample under examination. Three examples of distinct magnetic systems, with thicknesses ranging from 5 μ m to 6 mm, that were studied using this method are presented, these are: an amorphous CoFeB-based ribbon with ultra-soft coercivity for high-frequency applications, magnetically hard Nd-Fe-B thick films on Si substrates, examined in both as-deposited and annealed states, and a sample from the nickel-rich iron meteorite NWA 6259 that contains the atomically ordered, elevated coercivity, L 1 0 phase of FeNi, tetrataenite. The wide applicability and usefulness of this method is thus demonstrated on three distinct sample morphologies that required little to no surface preparation prior to examination.

Engineering↗

Orbit-modulated transport and sources in time-dependent plasmas

The orbit-modulation framework for steady-state ion-orbit boundary fluxes is reformulated to apply to time-dependent plasmas. The new formulation can quantify the extent to which orbit fluxes are affected by the time dependence of the distribution function, and may be applied both to time-dependent physical scenarios and to computationally expensive simulations that are unable to reach a true steady state. As the system tends to a time-independent state, the orbit-loss fluxes approach their steady-state values, which are determined entirely by upstream transport (turbulent and collisional) and upstream sources and sinks. This result holds for the fluxes of any moments that are expressible in terms of the invariants that determine the orbits, including parallel toroidal angular momentum.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Accurate CI-MBPT calculation of radiative lifetimes and transition probabilities of neutral lanthanum (La I) odd states with J = 3/2

In this work, an accurate calculation of radiative lifetimes and transition probabilities of the first 21 odd states with a total angular momentum J = 3/2 was performed for La I using configuration-interaction many-body perturbation theory (CI-MBPT). A technique to obtain correct transition amplitudes was devised for pairs of states with substantial mixing that improved the theoretical accuracy. The results were compared to known experimental and theoretical data for the considered transitions. It has been shown that the transition data calculated with CI-MBPT and with corrections for pairs of mixed states are in good agreement with the latest experimental data of Den Hartog et al, 2015 J. Phys. B: At. Mol. Phys. 48, 155 001, better than other theoretical results. The transition data can find many applications in astrophysics, and the CI-MBPT formalism with mixing correction is applicable to other atoms similar to or more complex than La I.

36 MATERIALS SCIENCE↗

The spatial wavefunction of half-integer spins

Within a nonrelativistic framework, spin is generally included as an intrinsic angular momentum. It is proposed here that consistent results can be obtained with a spatial wavefunction of an oriented complex exponential ${e}^{\mp {\boldsymbol{i}}\hat{{\bf{a}}}\varphi }$, where the bivector ${\boldsymbol{i}}\hat{{\bf{a}}}$ is written in terms of the pseudoscalar i = e x e y e z and the axis of rotation given by the unit vector $\hat{{\bf{a}}}$, which is generally an (effective) magnetic field direction (this can also be written as ${e}^{\mp i{\boldsymbol{\sigma }}\cdot \hat{{\bf{a}}}\varphi }$ in terms of the Pauli vector σ). The wavefunction is a multivector and not a complex scalar. The signs in the exponential correspond to the two directions of rotation around the axis. The transformation properties of these wavefunctions are given by the Pauli spinors. Finally, spin can be viewed as a zero-point rotation arising from the noncommutativity of the momentum and the vector potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Rotating cosmologies: classical and quantum

Here, we revisit spatially flat, anisotropic cosmologies within the framework of mini-superspace. Putting special emphasis on the symmetries of the mini-superspace action and on the associated conservation laws, we unveil a new class of rotating cosmologies driven by solid matter. Their rotating is physical, in that it is characterized in an invariant way in terms of a conserved angular momentum. Along the way, we confirm the results of Bartolo et al. regarding the slow decay of anisotropies for solid inflation. We then use our minisuperspace approach as a laboratory to address certain puzzles of quantum cosmology — among these, how to characterize the spacetime symmetries of a quantum state at the level of the wavefunction of the universe. For the case of a solid driven cosmology, this question seems better defined than in more standard cases. Other questions remain unanswered, though; in particular, the general question of how to operate a minisuperspace-like truncation of degrees of freedom that is consistent at the quantum level.

79 ASTRONOMY AND ASTROPHYSICS↗

Dimensionless parameter scaling of intrinsic torque in C-Mod enhanced confinement plasmas

A dimensionless parameter dependence study of intrinsic torque has been performed on a database of H- and I-mode plasmas from the Alcator C-Mod tokamak. Here, the torque was determined by comparing intrinsic angular momentum density profiles just before and just after L–H and L–I transitions. The intrinsic torque has been found to scale as ${\beta }_{N}^{ 1.5}\enspace {\rho }_{{\ast}}^{-1.0}\enspace {\nu }_{{\ast}}^{0.1}$, with the parameter ranges 0.3 $\leqslant$ β N $\leqslant$ 1.5, 0.004 $\leqslant$ ρ* $\leqslant$ 0.011 and 0.04 $\leqslant$ ν * $\leqslant$ 0.9. Comparison with results from JET and DIII-D suggests that the intrinsic torque should be normalized by some measure of the device size. Depending upon this normalization, the estimated total intrinsic torques for ITER, SPARC and ARC are ~20, ~4 and ~8 Nm, respectively.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Drift orbit islands of energetic particles due to 3D fields in ITER

In this study, we report a comparative study of the orbit islands formed by the guiding center drift motion of test energetic particles (EPs), including both high-energy deuterium ions and fusion-born α-particles, with respect to the magnetic islands formed by tracing the field lines, for an ITER plasma representing the 15 MA baseline scenario. The particle drift orbit is modified by the presence of static resonant magnetic perturbations (RMPs) of different toroidal mode numbers n (n = 1 and 3 in this study), forming orbit islands in the Poincaré plane by passing EPs. The key findings are as follows. (i) With an n = 1 RMP field, the size of the orbit islands combined with the total RMP field, including the plasma response, is about three times smaller than that obtained by assuming the corresponding vacuum field. (ii) The orbit island size is not sensitive to the EP energy, and is comparable to those of the magnetic islands. (iii) Passing EPs with outward radial orbital drift form orbit islands that shift inward with respect to the corresponding magnetic islands, and vice versa. This radial shift, ΔΨ, measured in the normalized equilibrium poloidal flux, is quantified as ΔΨ ≃ 0.03X for the ITER baseline plasma and assuming n = 1 RMPs, with $X\equiv {(M/{M}_{\mathrm{p}})}^{1/2}{(E[\mathrm{M}\mathrm{e}\mathrm{V}])}^{1/2}{Z}^{-1}$, where M is the particle mass, Mp is the proton mass, E is the particle energy, and Z is the particle charge number. (iv) Trapped EPs do not form drift orbit islands, even in the presence of the 3D fields produced by the 90 kAt ELM control coil current in ITER, and thus possess good confinement properties. Nevertheless, the deformation of the trapped particle drift orbits in the Poincaré plane shows that the canonical toroidal angular momentum of EPs is no longer conserved in the presence of the RMP fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simulation study of fast ion losses associated with the rotating n = 1 resonant magnetic perturbations in KSTAR

In this work we describe a simulation framework for testing the fast ion loss mechanism associated with the experimentally observed beam ion losses when an externally applied toroidally rotating perturbed magnetic field is used to control edge localized modes in the KSTAR tokamak. The simulations reproduce the key qualitative features of neutral beam injection (NBI) ion detection by a fast ion loss detector. The NBI ion losses in the simulation mainly occur for passing particles due to orbit stochastization, which is caused by orbit resonance with the 3D field perturbations. The relative toroidal angle of NBI ion deposition to the orbit island determines the radial path of the particles between confinement or loss. The fast ion loss quantity depends on the toroidal angle rotation of the 3D field with respect to the beam deposition position. The averaged transport of toroidal canonical angular momentum reveals that linear and nonlinear resonance of the NBI ions within the 3D field are the main factors determining fast ion transport and loss.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Invariant regimes of Spencer scaling law for magnetic compression of rotating FRC plasma

Abstract The scaling laws for the magnetic compression of a toroidally rotating field reversed configuration (FRC) have been investigated in this work. The magnetohydrodynamics (MHD) simulations of the magnetic compression on rotating FRCs employing the NIMROD code (Sovinec et al 2004 J. Comput. Phys. 195 355), are compared with the Spencer’s one-dimensional (1D) theory (Spencer et al 1983 Phys. Fluids 26 1564) for a wide range of initial flow speeds and profiles. The toroidal flow can influence the scalings directly through the alteration of the compressional work as also evidenced in the 1D adiabatic model, and indirectly by reshaping the initial equilibrium. However, in comparison to the static initial FRC equilibrium cases, the pressure and the radius scalings remain invariant for the magnetic compression ratio B w 2 / B w 1 up to 6 in presence of the initial equilibrium flow, suggesting a broader applicable regime of the Spencer scaling law for FRC magnetic compression. The invariant scaling has been proven a natural consequence of the conservation of angular momentum of both fluid and magnetic field during the dynamic compression process.

Ma, Yiming↗

Magnetism and spin dynamics in room-temperature van der Waals magnet Fe 5 GeTe 2

Two-dimensional van der Waals (vdWs) materials have gathered a lot of attention recently. However, the majority of these materials have Curie temperatures that are well below room temperature, making it challenging to incorporate them into device applications. In this work, we synthesized a room-temperature vdW magnetic crystal Fe 5 GeTe 2 with a Curie temperature T c = 332 K, and studied its magnetic properties by vibrating sample magnetometry (VSM) and broadband ferromagnetic resonance (FMR) spectroscopy. The experiments were performed with external magnetic fields applied along the c -axis (H∥ c ) and the ab -plane (H∥ ab ), with temperatures ranging from 300 to 10 K. We have found a sizable Landé g -factor difference between the H∥ c and H∥ ab cases. In both cases, the Landé g -factor values deviated from g = 2. This indicates contribution of orbital angular momentum to the magnetic moment. The FMR measurements reveal that Fe 5 GeTe 2 has a damping constant comparable to Permalloy. With reducing temperature, the linewidth was broadened. Together with the VSM data, our measurements indicate that Fe 5 GeTe 2 transitions from ferromagnetic to ferrimagnetic at lower temperatures. Our experiments highlight key information regarding the magnetic state and spin scattering processes in Fe 5 GeTe 2 , which promote the understanding of magnetism in Fe 5 GeTe 2 , leading to implementations of Fe 5 GeTe 2 based room-temperature spintronic devices.

36 MATERIALS SCIENCE↗

Origin of spin–orbit misalignments: the microblazar V4641 Sgr

ABSTRACT Of the known microquasars, V4641 Sgr boasts the most severe lower limit (>52°) on the misalignment angle between the relativistic jet axis and the binary orbital angular momentum. Assuming the jet and black hole spin axes coincide, we attempt to explain the origin of this extreme spin–orbit misalignment with a natal kick model, whereby an aligned binary system becomes misaligned by a supernova kick imparted to the newborn black hole. The model inputs are the kick velocity distribution, which we measure customized to V4641 Sgr, and the immediate pre/post-supernova binary system parameters. Using a grid of binary stellar evolution models, we determine post-supernova configurations that evolve to become consistent with V4641 Sgr today and obtain the corresponding pre-supernova configurations by using standard prescriptions for common envelope evolution. Using each of these potential progenitor system parameter sets as inputs, we find that a natal kick struggles to explain the origin of the V4641 Sgr spin–orbit misalignment. Consequently, we conclude that evolutionary pathways involving a standard common envelope phase followed by a supernova kick are highly unlikely for V4641 Sgr. An alternative interpretation is that the jet axis does not reliably trace the black hole spin axis. Our results raise concerns about compact object merger statistics gleaned from binary population synthesis models, which rely on unverified prescriptions for common envelope evolution and natal kicks. We also challenge the spin–orbit alignment assumption routinely invoked to measure black hole spin magnitudes.

79 ASTRONOMY AND ASTROPHYSICS↗

SDSS-IV MaNGA: The kinematic-morphology of galaxies on the mass versus star-formation relation in different environments

ABSTRACT We study the link between the kinematic-morphology of galaxies, as inferred from integral-field stellar kinematics, and their relation between mass and star formation rate. Our sample consists of ∼3200 galaxies with integral-field spectroscopic data from the MaNGA survey (Mapping Nearby Galaxies at Apache Point Observatory) with available determinations of their effective stellar angular momentum within the half-light radius $\lambda _{R_e}$. We find that for star-forming galaxies, namely along the star formation main sequence (SFMS), the $\lambda _{R_e}$ values remain large and almost unchanged over about two orders of magnitude in stellar mass, with the exception of the lowest masses $\mathcal {M}_{\star }\lesssim 2\times 10^{9} \, \mathcal {M}_{\odot }$, where $\lambda _{R_e}$ slightly decreases. The SFMS is dominated by spiral galaxies with small bulges. Below the SFMS, but above the characteristic stellar mass $\mathcal {M}_{\rm crit}\approx 2\times 10^{11} \, \mathcal {M}_{\odot }$, there is a sharp decrease in $\lambda _{R_e}$ with decreasing star formation rate (SFR): massive galaxies well below the SFMS are mainly slow-rotator early-type galaxies, namely genuinely spheroidal galaxies without discs. Below the SFMS and below $\mathcal {M}_{\rm crit}$ the decrease of $\lambda _{R_e}$ with decreasing SFR becomes modest or nearly absent: low-mass galaxies well below the SFMS, are fast-rotator early-type galaxies, and contain fast-rotating stellar discs like their star-forming counterparts. We also find a small but clear environmental dependence for the massive galaxies: in the mass range $10^{10.9}\!-\!10^{11.5} \, \mathcal {M}_{\odot }$, galaxies in rich groups or denser regions or classified as central galaxies have lower values of $\lambda _{R_e}$. While no environmental dependence is found for galaxies of lower mass. We discuss how the above results can be understood as due to the different star formation and mass assembly histories of galaxies with varying mass.

Wang, Bitao↗

The effect of non-linear mutual friction on pulsar glitch sizes and rise times

ABSTRACT Observations of pulsar glitches have the potential to provide constraints on the dynamics of the high density interior of neutron stars. However, to do so, realistic glitch models must be constructed and compared to the data. We take a step towards this goal by testing non-linear models for the mutual friction force, which is responsible for the exchange of angular momentum between the neutron superfluid and the observable normal component in a glitch. In particular, we consider a non-linear dependence of the drag force on the relative velocity between superfluid vortices and the normal component, in which the contributions of both kelvin and phonon excitations are included. This non-linear model produces qualitatively new features, and is able to reproduce the observed bimodal distribution of glitch sizes in the pulsar population. The model also suggests that the differences in size distributions in individual pulsars may be due to the glitches being triggered in regions with different pinning strengths, as stronger pinning leads to higher vortex velocities and a qualitatively different mutual friction coupling with respect to the weak pinning case. Glitches in pulsars that appear to glitch quasi-periodically with similar sizes may thus be due to the same mechanisms as smaller events in pulsars that have no preferred glitch size, but simply originate in stronger pinning regions, possibly in the core of the star.

79 ASTRONOMY AND ASTROPHYSICS↗

Chemical enrichment and radial migration in the Galactic disc – the origin of the [αFe] double sequence

The ([α/Fe], [Fe/H]) distribution of Milky Way stars shows at least two distinct sequences, which have traditionally been associated with the thin and thick disc components. The abundance distribution varies systematically with location R and |z| across the Galaxy. We reproduce this using an analytical chemodynamical model that includes the effects of radial migration and kinematic heating. Unlike some earlier models, our scheme does not require a distinct thick disc component emerging from a separate evolutionary path. The proposed model has a continuous star formation history and a continuous age velocity dispersion relation. Moreover, [α/Fe] is constant for stellar ages less than 8 Gyr, but increases sharply for older stars over a time-scale of 1.5 Gyr. The gap between the two sequences is due to this sharp transition. We show that the high-[α/Fe] sequence at the low-metallicity end is simply a pile-up of old stars, but towards the high-metallicity end, the age progressively decreases and stars have small birth radii. Our model successfully explains the uniformity of the locus of the high-[α/Fe] sequence across different locations. The low-[α/Fe] sequence contains stars with different birth radii that owes its existence to radial migration. For the low-[α/Fe] stars, angular momentum is anticorrelated with [Fe/H], while the opposite is true for high-[α/Fe] stars. We show that the later trend can be explained by the increase of circular velocity with time. If radial migration is not included, the model fails to generate the double sequence and instead shows only a single sequence. Our simple scheme has major advantages over earlier chemodynamical models, as we show.

79 ASTRONOMY AND ASTROPHYSICS↗