Torque Theory Research Articles

Early Evolution of Spin Direction in Dark Matter Halos and the Effect of the Surrounding Large-scale Tidal Field* *Thesis work conducted at Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Córdoba, Argentina. † † PhD Thesis directed by Manuel Merchán; PhD Degree awarded 2023 July 31.

It is usually assumed that the angular momentum (AM) of dark matter halos arises during the linear stages of structure formation, as a consequence of the coupling between the proto-haloes’ shape and the tidal field produced by their surrounding density perturbations. This approach, known as linear tidal torque theory (TTT), has been shown to make fairly good predictions about the mean evolution of both the AM amplitude and orientation up to approximately the time when the proto-haloes collapse. After this point, proto-haloes are increasingly affected by nonlinear processes that are not taken into account by the model. However, it has been seen in numerical simulations that, even at very early stages, the AM of proto-haloes is systematically reoriented toward perpendicularity with respect to the forming cosmic filaments, in contradiction with the fixed direction expected from the TTT. In this work we present a novel analytical approach that introduces an anisotropic scaling factor to the standard TTT equations, which allows the AM orientation to change in time, even during the linear regime. The amplitude and direction of this shift depend on the large scale tidal field around the forming proto-haloes. Our results significantly improve the predictions for the AM direction up to the time of protohalo collapse and, in some cases, even further in time.

Using Reluctance Torque Theory in Spoke Type Permanent Magnet Vernier Motors to Increase Average Torque

Using Reluctance Torque Theory in Spoke Type Permanent Magnet Vernier Motors to Increase Average Torque

Microscopic theory of spin-orbit torque and spin memory loss from interfacial spin-orbit coupling

Microscopic theory of spin-orbit torque and spin memory loss from interfacial spin-orbit coupling

B-fields and Dust in Interstellar Filaments Using Dust Polarization (BALLAD-POL). I. The Massive Filament G11.11–0.12 Observed by SOFIA/HAWC+

We report the first measurement of polarized thermal dust emission toward the entire infrared dark cloud G11.11−0.12 taken by the polarimeter SOFIA/HAWC+ at 214 μm. The obtained magnetic fields (B-fields) from the polarized emission of the early-stage and massive filament tend to be perpendicular to its spine. We produce a map of B-field strengths for the center region of the filament. The strengths vary in the range of 100–600 μG and are strongest along the filament's spine. The central region is sub-Alfvénic and mostly subcritical, meaning that B-fields dominate over turbulence and are strong enough to resist gravitational collapse. The alignment and properties of dust grains in the filament are studied using radiative torque (RAT) theory. We find the decrease of polarization degree P with emission intensity I, i.e., depolarization effect, of the form P ∝ I −α with α ∼ 0.8–0.9, implying a significant loss of grain alignment in the filament's spine. The depolarization can be explained by the decrease in RAT alignment efficiency toward the denser regions with weaker radiation field, which cannot be explained by B-field tangling. We study the effect of the enhanced magnetic relaxation by embedded iron inclusions on RAT alignment and find that the high polarization fraction P ∼ 20%–30% in the outer layer of the filament is potential evidence for the magnetically enhanced RAT alignment mechanism. This is the first time this effect is evaluated in a filament. Based on the polarization fraction and RAT alignment theory, we also find evidence for grain growth in the filament.

Direct Torque Control of Three Phase Induction Motors Concept and Principles

This paper thoroughly illustrates the Direct Torque Control (DTC) concept, principles and theory. It describes the dynamic behavior of a direct torque controlled three-phase induction motor. The complete analysis begins with a suitable mathematical model of the motor and the inverter circuit. It represents the DTC main parts and describes its operation. This paper also illustrates how the DTC can become a base for speed control schemes and the ability to switch between torque & speed control.

Hydrodynamic slender-body theory for local rotation at zero Reynolds number

Slender objects are commonplace in microscale flow problems, from soft deformable sensors to biological filaments such as flagella and cilia. Whilst much research has focussed on the local translational motion of these slender bodies, relatively little attention has been given to local rotation, even though it can be the dominant component of motion. In this study, we explore a classically motivated ansatz for the Stokes flow around a rotating slender body via superposed rotlet singularities, which leads us to pose an alternative ansatz that accounts for both translation and rotation. Through an asymptotic analysis that is supported by numerical examples, we determine the suitability of these flow ansatzes for capturing the fluid velocity at the surface of a slender body, assuming local axisymmetry of the object but allowing the cross-sectional radius to vary with arclength. In addition to formally justifying the presented slender-body ansatzes, this analysis reveals a markedly simple relation between the local angular velocity and the torque exerted on the body, which we term resistive torque theory. Though reminiscent of classical resistive force theories, this local relation is found to be algebraically accurate in the slender-body aspect ratio, even when translation is present, and is valid and required whenever local rotation contributes to the surface velocity at leading asymptotic order.

The Origin of the Relation Between Stellar Angular Momentum and Stellar Mass in Nearby Disk-dominated Galaxies

The IllustrisTNG simulations reproduce the observed scaling relation between the stellar specific angular momentum (sAM) j s and mass M s of central galaxies. We show that the local j s–M s relation develops at z ≲ 1 in disk-dominated galaxies. We provide a simple model that describes well such a connection between halos and galaxies. The index of 0.55 of the j s–M s relation comes from the product of the indices of the , , and j s ∝ j tot relations, where j tot and M tot are the overall sAM and mass of the halo, respectively. A non-negligible deviation from tidal torque theory, which predicts , should be included. This model further suggests that the stellar-to-halo mass ratio of disk galaxies increases monotonically following a nearly power-law function that is consistent with the latest dynamical measurements. Biased collapse, in which galaxies form from the inner and lower sAM portion of their parent halos, has a minor effect at low redshifts. The retention factor of angular momentum reaches ∼1 in disk galaxies with strong rotations, and it correlates inversely with the mass fraction of the spheroidal component, which partially explains the morphological dependence of the j s–M s relation.

Chirality-dependent spin-transfer torque and current-induced spin rotation in helimagnets

We have built a theory of the spin-transfer torque (STT) effect in a conductive chiral helical magnet (CHM). It is shown that the STT effect induced by a spin current flowing through CHM leads to the rotation of the CHM magnetization spiral around its axis. The frequency of such rotation of the CHM magnetization is found. The former is expressed in terms of the parameters of the quantum-exchange Hamiltonian that specifies helical magnetic ordering in a conductive crystal. We have showcased that both the direction of rotation of the CHM magnetization and the direction of changes in the shape of the magnetic spiral are determined by the electron flow direction and the chirality of the magnet. The theory developed accounts for the generation of an electromagnetic field when rotating the magnetic spiral in the CHM subjected to an electric current flowing through the helimagnet.

Quantum scattering theory of spin transfer torque, spin pumping, and fluctuations

Spin transfer torque and spin pumping are central reciprocal phenomena in spintronics. The author demonstrates a way to understand these effects within a quantum out-of-equilibrium path-integral model. At a finite temperature, frequency, or spin accumulation, the magnet also experiences fluctuating torques. In the quantum regime, transport coefficients related to electron shot noise caused by the discrete spin angular momentum of electrons govern the fluctuations at low temperatures. The results open a path for exploring low-temperature magnetization dynamics and spin caloritronics.

Correlating galaxy shapes and initial conditions: An observational study

Using data from the Sloan Digital Sky Survey we study correlations between directions of galaxy angular momenta determined from images of spiral galaxies and various observables derived from the reconstructed initial conditions. We find an apparent systematic effect consistent with galaxy-orientation-dependent selection function. After restricting our attention to the brightest half of the galaxies where this systematic effect is presumed to be absent, we find hints of excess/deficit correlation for two observables. Interestingly, tidal torque theory predicts excess/deficit correlation in exactly these two observables. After correcting for the redshift space distortions, the significance of these correlations drops below 3$\sigma$ threshold. We do not find any other systematic issues, but a thorough systematic analysis goes beyond the scope of this work.

Spin Alignment of Dark Matter Halos: Fast Halos

Abstract We investigate the spin alignment of dark matter halos by considering a mechanism somewhat similar to tidal locking; we dub it tidal-locking theory (TLT). While tidal torque theory (TTT) is responsible for the initial angular momentum of dark matter halos, TLT explains the angular momentum evolution during nonlinear ages. Our previous work showed that close encounters between halos could drastically change their angular momentum. This paper argues that TLT predicts partial alignment between the speed and spin direction for large high-speed halos. To examine this prediction, we use IllustrisTNG simulations and look for the alignment of the halos’ rotation axes. We find that the excess probability of alignment between spin and speed is about 10% at z = 0 for the large fast halos with velocities larger than twice the median. This spin–speed alignment weakens at z = 1 and disappears at z = 4. We also show that TTT predicts that the spin of a halo tends to be aligned with the middle eigendirection of the tidal tensor. Moreover, we find that the halos at z = 10 are preferentially aligned with the middle eigendirection of the tidal tensor with an excess probability of 15%. We show that TTT fails to predict the correct alignment at z = 0, while it works almost flawlessly at z = 10. These findings confirm that at earlier redshifts, during which mergers and fly-bys are rare, TTT works well, but after enough time, when fly-bys have occurred, the spin of the halos tends to align with speed for high-speed halos, due to the TLT effect.

An Online Parameter Estimation Using Current Injection with Intelligent Current-Loop Control for IPMSM Drives

An online parameter estimation methodology using the d-axis current injection, which can estimate the distorted voltage of the current-controlled voltage source inverter (CCVSI), the varying dq-axis inductances, and the rotor flux, is proposed in this study for interior permanent magnet synchronous motor (IPMSM) drives in the constant torque region. First, a d-axis current injection-based parameter estimation methodology considering the nonlinearity of a CCVSI is proposed. Then, during current injection, a simple linear model is developed to model the cross- and self-saturation of the dq-axis inductances. Since the d-axis unsaturated inductance is difficult to obtain by merely using the recursive least square (RLS) method, a novel tuning method for the d-axis unsaturated inductance is proposed by using the theory of the maximum torque per ampere (MTPA) with the combination of the RLS method. Moreover, to improve the bandwidth of the current loop, an intelligent proportional-integral-derivative (PID) neural network controller with improved online learning algorithm is adopted to replace the traditional PI controller. The estimated the dq-axis inductances and the rotor flux are adopted in the decoupled control of the current loops. Finally, the experimental results at various operating conditions of the IPMSM in the constant torque region are given.

Fast state detection in F1-ATPase rotation enhanced by theory of mixed states and external torque

During brief 120° transitions between long catalytic dwells, single F1-ATPase molecules exhibit angular jumps that vary with rotation angles. Using the angular jump profile enables the detection of fast states in the mechano-chemical scheme of the enzyme, states that are difficult to capture from single-molecule trajectories due to the fluctuations of the imaging nanoprobe. In a previous work, a short-lived, three occupancy state was postulated from a multi-state, probabilistic theory to explain the mean angular jump profile. An assumption in the theory was that the ‘mixing’ of chemical states is negligible during jumps. In a mixing event, two subsequent angular positions recorded by the imaging apparatus belong to two different chemical states of the motor enzyme due to fast reactions within a recording frame. In this paper, we provide an enhanced method for the detection of fast states. On one hand, we show using Langevin simulations that state mixing leads to faster mean angular jump, shifting up the profile. Consequently, the improved method provides a correction to the angular position and lifetime of the postulated three-occupancy metastable state. On the other hand, we show that when F1-ATPase is subject to torques opposing rotation in hydrolysis direction, the torques shift down the dwell angles without affecting the angle-dependent reaction rates. The torques improve detection capability for the fast state by increasing dwell times which is made evident by the flattening of the mean angular jump profile within 40°–60° from the catalytic dwell. In the three-occupancy state release of ADP occurs in concert with the binding of ATP to a different site in the F1-ATPase. Similarly, in the full ATP synthase when torques are created by the proton gradient in the FO region, the release of the product ATP is presumably accelerated by the binding of ADP to a different site in the F1 domain.

Self-induced spin-orbit torques in metallic ferromagnets

We present a phenomenological theory of spin-orbit torques in a metallic ferromagnet with spin-relaxing boundaries. The model is rooted in the coupled diffusion of charge and spin in the bulk of the ferromagnet, where we account for the anomalous Hall effects as well as the anisotropic magnetoresistance in the corresponding constitutive relations for both charge and spin sectors. The diffusion equations are supplemented with suitable boundary conditions reflecting the spin-sink capacity of the environment. In inversion-asymmetric heterostructures, the uncompensated spin accumulation exerts a dissipative torque on the order parameter, giving rise to a current-dependent linewidth in the ferromagnetic resonance with a characteristic angular dependence. We compare our model to recent spin-torque ferromagnetic resonance measurements, illustrating how rich self-induced spin-torque phenomenology can arise even in simple magnetic structures.

The Effect of the Angular Momentum in the Formation and Evolution of Low Surface Brightness Galaxies

Abstract Using observed data from the literature, we compare in one single publication the angular momentum (AM) of low surface brightness galaxies (LSBGs), with that of high surface brightness galaxies (HSBGs), a comparison that either is currently spread across many unconnected references, or simply does not exist. Partly because of the subject, this has received little attention outside the realm of simulations. We use previous results of the stellar specific AM j * from the SPARC database containing Spitzer 3.6 μm photometry and accurate H i rotation curves from Lelli et al. using a sample of 38 LSBGs and 82 HSBGs. We do this with the objective of comparing both galaxy populations, finding that LSBGs are higher in the Fall relation by about 0.174 dex. Additionally, we apply and test different masses and formation models to estimate the spin parameter λ, which quantifies the rotation obtained from the tidal torque theory, finding no clear evidence of a difference in the spin of LSBGs and HSBGs under a classic disk formation model that assumes the ratio (f j ) between j * and the specific AM of the halo is ∼1. In another respect, by using the biased collapse model, where f j depends on the star formation efficiency, it was found that LSBGs clearly show higher spin values, having an average spin of ∼2 times the average spin of HSBGs. This latter result is consistent with those obtained from simulations by Dalcanton et al.

Dynamical Tidal Locking Theory: A New Source of the Spin of Dark Matter Halos

Abstract We revisit the question of what mechanism is responsible for the spins of halos of dark matter. The answer to this question is of high importance for modeling galaxy intrinsic alignment, which can potentially contaminate current and future lensing data. In particular, we show that when the dark matter halos pass nearly each other in dense environments—namely halo assemblies—they swing and spin each other via exerting mutual tidal torques. We show that this has a significant contribution to the spin of dark matter halos comparable to that calculated by the so-called tidal torque theory. We use the results of the state-of-the-art simulation of Illutris to check the prediction of this theory against the simulation data.

SDSS-IV MaNGA: 3D spin alignment of spiral and S0 galaxies

ABSTRACT We investigate the 3D spin alignment of galaxies with respect to the large-scale filaments using the MaNGA survey. The cosmic web is reconstructed from the Sloan Digital Sky Survey using disperse and the 3D spins of MaNGA galaxies are estimated using the thin disc approximation with integral field spectroscopy kinematics. Late-type spiral galaxies are found to have their spins parallel to the closest filament’s axis. The alignment signal is found to be dominated by low-mass spirals. Spins of S0-type galaxies tend to be oriented preferentially in perpendicular direction with respect to the filament’s axis. This orthogonal orientation is found to be dominated by S0s that show a notable misalignment between their kinematic components of stellar and ionized gas velocity fields and/or by low-mass S0s with lower rotation support compared to their high-mass counterparts. Qualitatively similar results are obtained when splitting galaxies based on the degree of ordered stellar rotation, such that galaxies with high spin magnitude have their spin aligned, and those with low spin magnitude in perpendicular direction to the filaments. In the context of conditional tidal torque theory, these findings suggest that galaxies’ spins retain memory of their larger scale environment. In agreement with measurements from hydrodynamical cosmological simulations, the measured signal at low redshift is weak, yet statistically significant. The dependence of the spin-filament orientation of galaxies on their stellar mass, morphology, and kinematics highlights the importance of sample selection to detect the signal.

Spin mode reconstruction in Lagrangian space

Galaxy angular momentum directions (spins) are observable, well described by the Lagrangian tidal torque theory, and proposed to probe the primordial universe. They trace the spins of dark matter halos, and are indicators of protohalos properties in Lagrangian space. We define a Lagrangian spin parameter and tidal twist parameters and quantify their influence on the spin conservation and predictability in the spin mode reconstruction in $N$-body simulations. We conclude that protohalos in a more tidal twisting environments are preferentially more rotation-supported, and more likely to conserve their spin direction through the cosmic evolution. These tidal environments and spin magnitudes are predictable by a density reconstruction in Lagrangian space, and such predictions can improve the correlation between galaxy spins and the initial conditions in the study of constraining the primordial universe by spin mode reconstruction.

Interstellar Extinction, Polarization, and Grain Alignment in the Sh 2-185 (IC 59 and IC 63) Region

Abstract Optical and infrared continuum polarization from the interstellar medium is driven by radiative processes aligning the grains with the magnetic field. While a quantitative, predictive theory of radiative alignment torques (RATs) exists and has been extensively tested, several parameters of the theory remain to be fully constrained. In a recent paper, Medan & Andersson showed that the polarization efficiency (and therefore grain alignment efficiency) at different locations in the wall of the Local Bubble (LB) could be modeled as proportional to the integrated light intensity from the surrounding stars and OB associations. Here we probe that relationship at high radiation field intensities by studying the extinction and polarization in the two reflection nebulae IC 59 and IC 63 in the Sh 2-185 H ii region, illuminated by the B0 IV star γ Cassiopeia. We combine archival visual polarimetry with new seven-band photometry in the Vilnius system, to derive the polarization efficiency from the material. We find that the same linear relationship seen in the LB wall also applies to the Sh 2-185 region, strengthening the conclusion from the earlier study.

Deviations from tidal torque theory: Evolution of the halo spin–filament alignment

ABSTRACT The alignment between halo spins and the cosmic web is still poorly understood despite being a widely studied topic. Here, we study this alignment within the context of tidal torque theory (TTT) and deviations from it. To this end, we analyse the evolution of the shape and spin direction of proto-haloes, i.e. of all the volume elements associated to a z = 0 halo, with respect to the present-day filaments. We find that the major axis of proto-haloes undergoes a major change, from being strongly perpendicular to the filament spine in the initial conditions, to being preferentially aligned at the present time. In comparison, the spin orientation shows only a mild evolution: it starts slightly parallel to the filament spine, but the subsequent evolution, up to z ∼ 1, gradually changes its orientation to preferentially perpendicular. In order to analyse these signals in the TTT framework, we split the haloes according to their net spin growth with respect to the median TTT expectation, finding a clear correlation with the spin–filament alignment. At the present time, haloes whose spin grew the most are the ones most perpendicular to the filament spine, while haloes whose spin grew below the median TTT expectation are typically more aligned. The dependence of spin directions on net spin growth is already present in the initial conditions, and gets further modified by late-time, z < 2, evolution. Also, spin directions mildly deviate from the TTT predictions even at high redshift, indicating the need for extensions to the model.