Radial Action Research Articles

Scattering and Bound Observables for Spinning Particles in Kerr Spacetime with Generic Spin Orientations.

We derive the radial action of a spinning probe particle in Kerr spacetime from the worldline formalism in the first-order form, focusing on linear in spin effects. We then develop a novel covariant Dirac bracket formalism to compute the impulse and the spin kick directly from the radial action, generalizing some conjectural results in the literature and providing ready-to-use expressions for amplitude calculations with generic spin orientations. This allows, for the first time, to find new covariant expressions for scattering observables in the probe limit up to O(G^{6}s_{1}s_{2}^{4}). Finally, we use the action-angle representation to compute the fundamental frequencies for generic bound orbits, including the intrinsic spin precession, the periastron advance, and the precession of the orbital plane.

Investigating the vertical distribution of the disk as a function of radial action: Results from simulations

Previous research has established a relationship between radial action and scale height in Galactic disks, unveiling a correlation between radial and vertical heating. This finding poses a challenge to our existing comprehension of heating theories and consequently encodes crucial insights into the formation and heating history of Galactic disks. In this study, we perform N-body simulations with the aim of verifying the existence of this correlation between radial action and scale height, thereby enhancing our comprehension of the heating history of Galactic disks. We conducted a simulation featuring a disk embedded within a static dark matter halo potential, and systematically analyzed the correlation between radial action and scale height across every snapshot. Furthermore, we augmented this simulation by incorporating massive, long-lasting particles to examine their impact on the aforementioned relationship. We find that the relationship between radial action and scale height in our simulations can be described by the same functional form observed in previous work. Furthermore, the relationships derived from our simulations align well with those of the Galactic thin disk. However, they do not coincide with the inner thick disk but exhibit a rough correspondence with the outer thick disk, suggesting the possibility that additional heating mechanisms may be required to explain the inner thick disk. We also find that the mean radial action and scale height undergo rapid increases during the initial stages of the simulation, yet remain relatively unchanged as the disk evolves further. By tracing example particles, we uncover a correlation between radial and vertical heating in our simulation: as a particle in the disk gains or loses radial action, its vertical motion tends to oscillate on a more or less extended orbit, accompanied by a tendency to migrate outward or inward, respectively. The massive, long-lasting particles in our simulation contribute to disk heating by solely enhancing the rate of increase in scale height with radial action, while maintaining the functional form that describes the relationship between these two variables. We have successfully replicated the functional form previously reported in research, thereby confirming a correlation between radial and vertical heating. This achievement enhances our understanding of heating theories in galactic disks.

Amplitudes, supersymmetric black hole scattering at OG5, and loop integration

We compute the potential-graviton contribution to the scattering amplitude, the radial action, and the scattering angle of two extremal black holes in N = 8 supergravity at the fifth post-Minkowskian order and to next-to-leading order in a large mass expansion (first self-force order). Properties of classical unitarity cuts allow us to focus on the integration-by-parts reduction of planar integrals, while nonplanar integrals at this order are obtained from the planar ones by straightforward manipulations. We present the solution to the differential equations for all master integrals necessary to evaluate the classical scattering amplitudes of massive scalar particles at this order in all gravitational theories, in particular in N = 8 supergravity, and in general relativity. Despite the appearance of higher-weight generalized polylogarithms and elliptic functions in the solution to the differential equation for master integrals, the final supergravity answer is remarkably simple and contains only (harmonic) polylogarithmic functions up to weight 2. The systematic analysis of elliptic integrals discussed here, as well as the particular organization of boundary integrals in N = 8 observables are independent of supersymmetry and may have wider applications, including to aspects of collider physics.

Action and energy clustering of stellar streams in deforming Milky Way dark matter haloes

ABSTRACT We investigate the non-adiabatic effect of time-dependent deformations in the Milky Way (MW) halo potential on stellar streams. Specifically, we consider the MW’s response to the infall of the Large Magellanic Cloud (LMC) and how this impacts our ability to recover the spherically averaged MW mass profile from observation using stream actions. Previously, action clustering methods have only been applied to static or adiabatic MW systems to constrain the properties of the host system. We use a time-evolving MW–LMC simulation described by basis function expansions. We find that for streams with realistic observational uncertainties on shorter orbital periods and without close encounters with the LMC, e.g. GD-1, the radial action distribution is sufficiently clustered to locally recover the spherical MW mass profile across the stream radial range within a $2\sigma$ confidence interval determined using a Fisher information approach. For streams with longer orbital periods and close encounters with the LMC, e.g. Orphan–Chenab (OC), the radial action distribution disperses as the MW halo has deformed non-adiabatically. Hence, for OC streams generated in potentials that include an MW halo with any deformations, action clustering methods will fail to recover the spherical mass profile within a $2\sigma$ uncertainty. Finally, we investigate whether the clustering of stream energies can provide similar constraints. Surprisingly, we find for OC-like streams, the recovered spherically averaged mass profiles demonstrate less sensitivity to the time-dependent deformations in the potential.

Normative Data and Quantile Regression Analysis of the Sural-to-Radial Nerve Amplitude Ratio.

The aim of this study was to establish normative data for the sural-to-radial nerve amplitude ratio (SRAR) and develop a quantile regression model for individualized cutoff values. A cohort of 68 healthy individuals (36 female participants) aged 20 to 59 years was recruited. Sensory nerve conduction studies were conducted to measure sural and radial sensory nerve action potential amplitudes. Quantile regression analysis was used to determine the fifth percentile of SRAR after adjusting for age, sex, and other demographic variables. This study found significant differences in body height and weight between the sexes, with radial sensory nerve action potential being higher in female participants. The sural-to-radial nerve amplitude ratio was negatively correlated with age (r = -0.3, p = 0.007) and showed significant sex differences. The final regression equation, SRAR = 0.519 - 0.006 × age + 0.046 × sex (1 = male, 0 = female), was developed for the fifth percentile cutoff, accounting for age and sex. This study establishes normative SRAR data and introduces a novel quantile regression approach to determine individualized cutoff values. Age and sex are critical factors for SRAR variation, necessitating tailored diagnostic criteria for neuropathy assessment. This model enhances diagnostic accuracy and potentially reduces misdiagnosis in clinical settings. Further research is recommended to validate the clinical applicability of SRAR across different types of neuropathies.

Local in Time Conservative Binary Dynamics at Fourth Post-Minkowskian Order.

Leveraging scattering information to describe binary systems in generic orbits requires identifying local and nonlocal in time tail effects. We report here the derivation of the universal (nonspinning) local in time conservative dynamics at fourth post-Minkowskian order, i.e., O(G^{4}). This is achtieved by computing the nonlocal-in-time contribution to the deflection angle, and removing it from the full conservative value in [C. Dlapa et al., Phys. Rev. Lett. 128, 161104 (2022).PRLTAO0031-900710.1103/PhysRevLett.128.161104; C. Dlapa et al., Phys. Rev. Lett. 130, 101401 (2023).PRLTAO0031-900710.1103/PhysRevLett.130.101401]. Unlike the total result, the integration problem involves two scales-velocity and mass ratio-and features multiple polylogarithms, complete elliptic and iterated elliptic integrals, notably in the mass ratio. We reconstruct the local radial action, center-of-mass momentum and Hamiltonian, as well as the exact logarithmic-dependent part(s), all valid for generic orbits. We incorporate the remaining nonlocal terms for ellipticlike motion to sixth post-Newtonian order. The combined Hamiltonian is in perfect agreement in the overlap with the post-Newtonian state of the art. The results presented here provide the most accurate description of gravitationally bound binaries harnessing scattering data to date, readily applicable to waveform modeling.

Conservative scattering of Reissner-Nordström black holes at third post-Minkowskian order

Using a recently developed effective field theory formalism for extreme mass ratios arXiv:2308.14832, we present a calculation of charged black hole scattering at third post-Minkowskian order. The charges and masses are kept arbitrary, and the result interpolates from the scattering of Schwarzschild to extremal charged black holes, and beyond to charged particles in electrodynamics — agreeing with previously reported results in all such limits. The computation of the radial action is neatly organized in powers of the mass ratio. The probe (0SF) contributions are readily computed by direct integration of the radial momentum, and we use the effective field theory to compute the subleading (1SF) contributions via background-field Feynman rules supplemented by an operator encoding recoil of the background. Together these contributions completely determine the conservative physics at order OG3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({G}^3\\right) $$\\end{document}.

Scattering amplitudes for self-force

The self-force expansion allows the study of deviations from geodesic motion due to the emission of radiation and its consequent back-reaction. We investigate this scheme within the on-shell framework of semiclassical scattering amplitudes for particles emitting photons or gravitons on a static, spherically symmetric background. We first present the exact scalar two-point amplitudes for Coulomb and Schwarzschild, from which one can extract classical observables such as the change in momentum due to geodesic motion. We then present, for the first time, the three-point semiclassical amplitudes for a scalar emitting a photon in Coulomb and a graviton on linearised Schwarzschild, outlining how the latter calculation can be generalized to the fully non-linear Schwarzschild metric. Our results are proper resummations of perturbative amplitudes in vacuum but, notably, are expressed in terms of Hamilton’s principal function for the backgrounds, rather than the radial action.

2D chemical evolution models

Context. According to observations and numerical simulations, the Milky Way could exhibit several spiral-arm modes of various pattern speeds, with the slower patterns located at larger galactocentric distances. Aims. Our aim is to quantify the effects of the spiral arms on the azimuthal variations in the chemical abundances of oxygen and iron and for the first time of neutron-capture elements (europium and barium) in the Galactic disc. We assume a model based on multiple spiral-arm modes with different pattern speeds. The resulting model is an updated version of previous 2D chemical evolution models. Methods. We apply new analytical prescriptions for the spiral arms in a 2D Galactic disc chemical evolution model, exploring the possibility that the spiral structure is formed by the overlap of chunks with different pattern speeds and spatial extent. Results. The predicted azimuthal variations in abundance gradients are dependent on the considered chemical element. Elements synthesised on short timescales (i.e. oxygen and europium in this study) exhibit larger abundance fluctuations. Moreover, for progenitors with short lifetimes, the chemical elements returned to the ISM perfectly trace the star formation perturbed by the passage of the spiral arms. The map of the star formation rate (SFR) predicted by our chemical evolution model with multiple patterns of spiral arms presents arcs and arms compatible with those revealed by multiple tracers (young upper-main sequence stars, Cepheids, and the distribution of stars with low radial actions). Finally, our model predictions are in good agreement with the azimuthal variations that emerged from the analysis of Gaia DR3 GSP-Spec [M/H] abundance ratios, if at most recent times the pattern speeds match the Galactic rotational curve at all radii. Conclusions. We provide an updated version of a 2D chemical evolution model capable of tracing the azimuthal density variations created by the presence of multiple spiral patterns. We show that elements synthesised on short timescales exhibit larger abundance fluctuations.

Exploring Asymmetric Substructures of the Outer Disk Based on the Conjugate Angle of the Radial Action

We use the conjugate angle of radial action (θ R ), the best representation of the orbital phase, to explore the “midplane,” “north branch,” “south branch,” and “Monoceros area” disk structures that were previously revealed in the LAMOST K giants. The former three substructures, identified by their 3D kinematical distributions, have been shown to be projections of the phase space spiral (resulting from nonequilibrium phase mixing). In this work, we find that all of these substructures associated with the phase spiral show high aggregation in conjugate angle phase space, indicating that the clumping in conjugate angle space is a feature of ongoing, incomplete phase mixing. We do not find the Z–V Z phase spiral located in the “Monoceros area,” but we do find a very highly concentrated substructure in the quadrant of conjugate angle space with the orbital phase from the apocenter to the guiding radius. The existence of the clump in conjugate angle space provides a complementary way to connect the “Monoceros area” with the direct response to a perturbation from a significant gravitationally interactive event. Using test particle simulations, we show that these features are analogous to disturbances caused by the impact of the last passage of the Sagittarius dwarf spheroidal galaxy.

Estimating Maximum Power from Wind Turbines with a Simple Newtonian Approach

Action mechanics showing torques result from rates of variation in impulsive action motivated a new method to estimate maximum power from wind turbines. Newton’s third law of equality of action and reaction provides a strictly causal mechanism of wind power from the deflection of wind momentum by twice its angle (θ) of incidence on rotor blades. The transverse reaction needed to conserve deflected wind momentum provides the turning moment for turbine rotation. Action mechanics integrates impulsive wind action on turbine blades as differing torques (ʃmrvdθ/dt ≡ mv2 ) exerted on rotor surfaces at each radius. Windward torque (Tw) is estimated from rotor dimensions, the angle of wind incidence and radial action of wind impulses on the blade surfaces (also ʃmrvdθ/dt ≡ mv2). A leeward torque (Tb) is exerted as back reaction on turbine blades parallel to the plane of rotation of the blade. Net torque is then converted to potential power (Tw - Tb)Ω by the angular velocity (Ω) of the turbine rotors, a function of tip speed ratio to wind speed. Better predictions of limits to wind power can be made, by including control of optimal wind angle and blade length. An analysis of the equivalence of deflected air momentum on turbine blades or air foils for aircraft reveals that even the lifting action on air foils can be explained by the normal reaction to the momentum in an air stream, also deflected by an angle twice that (2θ) of incidence. Release of vortical field energy from laminar flow of air in winds as heat is predicted in turbulent wakes, possibly affecting achievement of maximum power output by wind farms. Significant heat release by downwind turbulence from vortical energy requires their careful location. Diligence demands that use of windfarms as sources of renewable energy should minimize any environmental impacts, such as drying of landscapes.

Conceptual design of the DTT in-vessel equatorial coils

For the next generation fusion devices, the presence of in-vessel coils is fundamental to deal with elongated plasmas and alternative configurations, highly performant, yet critically sensitive to the vertical unstable mode. A pair of equatorial in-vessel coils connected in anti-series is sufficient to deal with the vertical control problem. In case of independent equatorial coils, they can also be used to produce a fast radial control action able to preserve plasma facing components during fast plasma transients. The main criticality of independent in-vessel coils is related to the induced current during disruptive events, making the coils extremely vulnerable due to overcurrents and mechanical stress. In this paper, we present the solution proposed for the conceptual design of the in-vessel equatorial coils for the Divertor Tokamak Test fusion device. This solution is able to guarantee radial and vertical control performance and robustness in case of disruption. Simulations are provided to show the efficiency of the design in case of disruptions and the effectiveness of the closed-loop control actions.

Binary dynamics from worldline QFT for scalar QED

We investigate the worldline quantum field theory (WQFT) formalism for scalar QED and observe that a generating function emerges from WQFT, from which the scattering angle ensues. This generating function bears important similarities to the radial action in that it requires no consideration of exponentiation of lower-order contributions. We demonstrate the computations of this generating function and the resulting scattering angle of a binary system coupled to an electromagnetic field up to the third order in the post-Minkowskian expansion.

Vertical motion in the Galactic disc: unwinding the snail

ABSTRACTThe distribution of stars in the Milky Way disc shows a spiral structure − the snail − in the space of velocity and position normal to the Galactic mid-plane. The snail appears as straight lines in the vertical frequency−vertical phase plane when effects from sample selection are removed. Their slope has the dimension of inverse time, with the simplest interpretation being the inverse age of the snail. Here, we devise and fit a simple model in which the spiral starts as a lopsided perturbation from steady state, that winds up into the present-day morphology. The winding occurs because the vertical frequency decreases with vertical action. We use data from stars in Gaia EDR3 that have measured radial velocities, pruned by simple distance and photometric selection functions. We divide the data into boxels of dynamical invariants (radial action, angular momentum); our model fits the data well in many of the boxels. The model parameters have physical interpretations: one, A, is a perturbation amplitude, and one, t, is interpretable in the simplest models as the time since the event that caused the snail. We find trends relating the strength and age to angular momentum: (i) the amplitude A is small at low angular momentum (${\lt 1\, 600{\,}kpc\ km\ s}^{-1}$ or guiding-centre radius $\lt 7.3\,$kpc) and over a factor of three larger, with strong variations, in the outer disc; (ii) there is no single well-defined perturbation time, with t varying between 0.2 and 0.6 Gyr. Residuals between the data and the model display systematic trends, implying that the data call for more complex models.

Neuropathy due to bi-allelic SH3TC2 variants: genotype-phenotype correlation and natural history.

Recessive SH3TC2 variants cause Charcot-Marie-Tooth disease type 4C (CMT4C). CMT4C is typically a sensorimotor demyelinating polyneuropathy, marked by early onset spinal deformities, but its clinical characteristics and severity are quite variable. Clear relationships between pathogenic variants and the spectrum of disease manifestations are to date lacking. Gene replacement therapy has been shown to ameliorate the phenotype in a mouse model of CMT4C, emphasizing the need for natural history studies to inform clinical trial readiness. Data, including both genetic information and clinical characteristics, were compiled from the longitudinal, prospective dataset of the Inherited Neuropathy Consortium, a member of the Rare Diseases Clinical Research Network (INC-RDCRN). The Charcot Marie Tooth Neuropathy Score (CMTNS), Examination Score (CMTES) and the Rasch-weighted CMTES (CMTES-R) were used to describe symptoms, neurological examinations and neurophysiological characteristics. Standardized response means were calculated at yearly intervals and a mixed model for repeated measures was used to estimate the change in CMTES and CMTES-R over time. Fifty-six individuals (59% female), median age 27 years (range 2-67 years) with homozygous or compound heterozygous variants in SH3TC2 were identified, including 34 unique variants, 14 of which have not previously been published. Twenty-eight participants had longitudinal data available. While there was no significant difference in the CMTES in those with protein truncating versus non-protein truncating variants, there were significant differences in the mean ulnar nerve compound muscle action potential amplitude, the mean radial sensory nerve action potential amplitude, and in the prevalence of scoliosis, suggesting the possibility of a milder phenotype in individuals with one or two non-protein-truncating variants. Overall, the mean value of the CMTES was 13, reflecting moderate clinical severity. There was a high rate of scoliosis (81%), scoliosis surgery (36%), and walking difficulty (94%) among study participants. The CMTES and CMTES-R appeared moderately responsive to change over extended follow-up, demonstrating a standardized response mean of 0.81 standard deviation units or 0.71 standard deviation units, respectively, over 3 years. Our analysis represents the largest cross-sectional and only longitudinal study to date, of the clinical phenotype of both adults and children with CMT4C. With the promise of upcoming genetic treatments, these data will further define the natural history of the disease and inform study design in preparation for clinical trials.

Spiral-like features in the disc revealed by Gaia DR3 radial actions

Context. The so-called action variables are specific functions of the positions and velocities that remain constant along the stellar orbit. The astrometry provided by Gaia Early Data Release 3 (EDR3), combined with the velocities inferred from the Radial Velocity Spectrograph (RVS) spectra of Gaia DR3, allows for the estimation of these actions for the largest volume of stars to date. Aims. We explore such actions with the aim of locating structures in the Galactic disc. Methods. We computed the actions and the orbital parameters of the Gaia DR3 stars, assuming an axisymmetric model for the Milky Way. Using Gaia DR3 photometric data, we also selected a subset of giant stars with better astrometry as a control sample. Results. We find that the maps of the percentiles of the radial action JR reveal arc-like segments. We found a high JR region centered at R ≈ 10.5 kpc of 1 kpc width, as well as three arc-shape regions dominated by circular orbits at inner radii. We also identified the spiral arms in the overdensities of the giant population. Conclusions. For Galactic coordinates (X, Y, Z), we find good agreement with the literature in the innermost region for the Scutum-Sagittarius spiral arms. At larger radii, the low JR structure tracks the Local arm at negative X, while for the Perseus arm, the agreement is restricted to the X < 2 kpc region, with a displacement with respect to the literature at more negative longitudes. We detected a high JR area at a Galactocentric radii of ∼10.5 kpc, consistent with some estimations of the Outer Lindblad Resonance location. We conclude that the pattern in the dynamics of the old stars is consistent in several places with the spatial distribution of the spiral arms traced by young populations, with small potential contributions from the moving groups.

Investigating the vertical distribution of the disk as a function of radial action

Aims. As heating processes can broaden the distributions of radial actions and the vertical distributions of the Galactic disks, we investigate the vertical distribution of the Galactic disks as a function of radial action based on Apache Point Observatory Galactic Evolution Experiment (APOGEE) and Gaia data in order to deepen our understanding of the formation and heating history of the Galactic disks. Methods. The vertical distributions of the thin and thick Galactic disks defined in the chemical plane were fitted with a simple exponential function with a free parameter of scale height in different radial action ranges. Therefore, we were able to analyze the scale height as a function of radial action for different disk populations. Results. We find that the distributions of radial action for both the thin and thick disks can be approximately described by pseudo-isothermal distributions, which give a statistical measurement for the temperature of the disk as indicated by the mean radial action of the star sample. Estimations of the scale heights in different radial action ranges for these pseudo-isothermal distributions of the disks seem to show fixed relationships between radial action JR and scale height h. We describe these relationships with a two-parameter function of h = √(JR/a)+b, where a and b are free parameters. When testing with a three-parameter function of h = α√(JR/a)+b, we find that this two-parameter function describes the thin disk well, but we note the function should be used with care for the thick disk. When comparing the best-fit relationships between the inner and outer disk for both of the thin and thick disks, we find that the relationships are nearly the same for the thin disks but are different for the thick disks. The inner thick disk shows a nearly flattened relationship, while the outer thick disk presents a gradually increasing relationship. This work highlights an alternative way to unveil the heating history of the disks by investigating the relationship between scale height and radial action, as these relationships encode the formation and heating history of the Galactic disks.

Orbits and action changes during star-clump encounters responsible for the origin of exponential discs in dwarf galaxies

ABSTRACT Previous studies found that stellar scattering by massive clumps can lead to the formation of exponential profiles in galaxy discs, but details on how a star is moved around have not been fully explained. We use a gadget-2 simulation where an exponential profile forms from an initially Gaussian disc in about 4 Gyr for a low-mass galaxy like a dwarf irregular. We find that nearly all large angular momentum changes of stars are caused by star-clump encounters with the closest approach less than 0.5 kpc. During star-clump encounters, stars may increase their random motions, resulting in an increase in the average radial and vertical actions of the whole stellar population. The angular momentum change and the radial action change of an individual star are influenced by the direction from which the star approaches a clump. A star initially at a higher galactic radius relative to the scattering clump usually gets pulled inwards and loses its angular momentum during the encounter, and one at a lower radius tends to shift outwards and gains angular momentum. The increase in the radial action is the largest if a star encounters a clump from the azimuthal direction, and is the smallest from a radial approach. The angular momentum change due to encounters has an inward bias when the clump profile has a steep radial decline, and a shallow decline can make the bias outwards. The stellar profile evolution towards an exponential seems to occur regardless of the direction of the bias.

Engineering and Structural Assessment for the Design of the DTT Central Solenoid

The “Divertor Tokamak Test” (DTT) is an experimental fusion reactor being built in Frascati (IT) in the framework of the European Fusion Roadmap. The DTT Central Solenoid, used to drive the current in the magnetically coupled plasma, comprises six Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn layer-wound independently energized modules. Each module is made of three sub-modules: High Field (HF), Medium Field (MF) and Low Field (LF) grades. To meet all goals of the DTT scientific program, a variety of plasma scenarios have been designed. These cause intense and heterogeneous loading conditions for the CS stack; from the mechanical point of view, each module is subjected to a vertical expansion or compression and to a huge radial action, whereas the current variations cause relevant heat loads due to AC losses, with impact on the coil temperature margin. In this work, the engineering study on the current design and the analyses on the module windings are presented.

Scalar QED as a toy model for higher-order effects in classical gravitational scattering

Quantum Electrodynamics (QED) serves as a useful toy model for classical observables in gravitational two-body systems with reduced complexity due to the linearity of QED. We investigate scattering observables in scalar QED at the sixth order in the charges (two-loop order) in a classical regime analogous to the post-Minkowskian expansion in General Relativity. We employ modern scattering amplitude tools and extract classical observables by both eikonal methods and the formalism of Kosower, Maybee, and O’Connell (KMOC). In addition, we provide a simplified approach to extracting the radial action beyond the conservative sector.