Assumption Of Spherical Symmetry Research Articles

Spherical shock waveform reconstruction by heterodyne interferometry.

The indirect measurement of shock waveforms by acousto-optic sensing requires a method to reconstruct the field from the projected data. Under the assumption of spherical symmetry, one approach is to reconstruct the field by the Abel inversion integral transform. When the acousto-optic sensing modality measures the change in optical phase difference time derivative, as for a heterodyne Mach-Zehnder interferometer, e.g., a laser Doppler vibrometer, the reconstructed field is the fluctuating refractive index time derivative. A technique is derived that reconstructs the fluctuating index directly by assuming plane wave propagation local to a probe beam. With synthetic data, this approach is compared to the Abel inversion integral transform and then applied to experimental data of laser-induced shockwaves. Time waveforms are reconstructed with greater accuracy except for the tail of the waveform that maps spatially to positions near a virtual origin. Furthermore, direct reconstruction of the fluctuating index field eliminates the required time integration and results in more accurate shock waveform peak values, rise times, and positive phase duration.

Bifurcation and dynamics of periodic solutions to the Rayleigh–Plesset equation: Theory and numerical simulation

In this paper, we study the oscillation of a gas-filled spherical bubble immersed in an infinite domain of incompressible liquid under the influence of a time-periodic acoustic field. The oscillation is described by the Rayleigh–Plesset equation, which is derived from the Navier–Stokes equation under the assumptions of spherical symmetry. Taking the initial radius R0, or the initial instantaneous partial pressure Pg0, of the gas-filled bubble as a parameter, we present a saddle–node bifurcation of periodic solutions to the Rayleigh–Plesset equation in the parameter space, provided the mean value of applied pressure is greater than the vapor pressure. Further, we show that the Rayleigh–Plesset equation has two classes of periodic solutions, as R0 (resp. Pg0) tends to +∞, the first class of solutions uniformly diverges to +∞ at the rate of R05 (resp. Pg05/2), while the second class converges to 0 at the rate of R0−5 (resp. Pg0−5/2). As for the case where the density of the liquid ρ is chosen as a parameter, we observe an interesting nonlinear phenomenon that, for some ρ, the Rayleigh–Plesset equation may possess four positive T-periodic solutions: two of them are stable, while the rest of them are unstable. This is quite different from the phenomenon that occurs when R0 (or Pg0) is chosen as a parameter.

Estimation and evaluation of hourly Meteorological Operational (MetOp) satellites' GPS receiver differential code biases (DCBs) with two different methods

Abstract. Differential code bias (DCB) is one of the Global Positioning System (GPS) errors, which typically affects the calculation of total electron content (TEC) and ionospheric modeling. In the past, DCB was normally estimated as a constant in 1 d, while DCB of a low Earth orbit (LEO) satellite GPS receiver may have large variations within 1 d due to complex space environments and highly dynamic orbit conditions. In this study, daily and hourly DCBs of Meteorological Operational (MetOp) satellites' GPS receivers are calculated and evaluated using the spherical harmonic function (SHF) and the local spherical symmetry (LSS) assumption. The results demonstrated that both approaches could obtain accurate and consistent DCB values. The estimated daily DCB standard deviation (SD) is within 0.1 ns in accordance with the LSS assumption, and it is numerically less than the standard deviation of the reference value provided by the Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC) Data Analysis and Archive Center (CDAAC). The average error's absolute value is within 0.2 ns with respect to the provided DCB reference value. As for the SHF method, the DCB's standard deviation is within 0.1 ns, which is also less than the standard deviation of the CDAAC reference value. The average error of the absolute value is within 0.2 ns. The estimated hourly DCB with LSS assumptions suggested that calculated results of MetOpA, MetOpB, and MetOpC are, respectively, 0.5 to 3.1 ns, −1.1 to 1.5 ns, and −1.3 to 0.7 ns. The root mean square error (RMSE) is less than 1.2 ns, and the SD is under 0.6 ns. According to the SHF method, the results of MetOpA, MetOpB, and MetOpC are 1 to 2.7 ns, −1 to 1 ns, and −1.3 to 0.6 ns, respectively. The RMSE is under 1.3 ns and the SD is less than 0.5 ns. The SD for solar active days is less than 0.43, 0.49, and 0.44 ns, respectively, with the LSS assumption, and the appropriate fluctuation ranges are 2.0, 2.2, and 2.2 ns. The variation ranges for the SHF method are 1.5, 1.2, and 1.2 ns, respectively, while the SD is under 0.28, 0.35, and 0.29 ns.

Neutrino flavor conversion, advection, and collisions: Toward the full solution

At high densities in compact astrophysical sources, the coherent forward scattering of neutrinos onto each other is responsible for making the flavor evolution non-linear. Under the assumption of spherical symmetry, we present the first simulations tracking flavor transformation in the presence of neutrino-neutrino forward scattering, neutral and charged current collisions with the matter background, as well as neutrino advection. We find that, although flavor equipartition could be one of the solutions, it is not a generic outcome, as often postulated in the literature. Intriguingly, the strong interplay between flavor conversion, collisions, and advection leads to a spread of flavor conversion across the neutrino angular distributions and neighboring spatial regions. Our simulations show that slow and fast flavor transformation can occur simultaneously. In the light of this, looking for crossings in the electron neutrino lepton number as a diagnostic tool of the occurrence of flavor transformation in the high-density regime is a limiting method.

Modeling acoustic emissions and shock formation of cavitation bubbles

Despite significant progress in understanding and foretelling pressure-driven bubble dynamics, models that faithfully predict the emitted acoustic waves and the associated shock formation of oscillating or collapsing bubbles have received comparably little attention. We propose a numerical framework using a Lagrangian wave tracking approach to model the acoustic emissions of pressure-driven bubbles based on the Kirkwood–Bethe hypothesis and under the assumption of spherical symmetry. This modeling approach is agnostic to the equation of the state of the liquid and enables the accurate prediction of pressure and velocity in the vicinity of pressure-driven bubbles, including the formation and attenuation of shock fronts. We validate and test this new numerical framework by comparison with solutions of the full Navier–Stokes equations and by considering a laser-induced cavitation bubble as well as pressure-driven microbubbles in excitation regimes relevant to sonoluminescence and medical ultrasound, including different equations of state for the liquid. A detailed analysis of the bubble-induced flow field as a function of the radial coordinate r demonstrates that the flow velocity u is dominated by acoustic contributions during a strong bubble collapse and, hence, decays predominantly with u∝r−1, contrary to the frequently postulated decay with u∝r−2 in an incompressible fluid.

Dimensional reduction of a poromechanical cardiac model for myocardial perfusion studies

In this paper, we adapt a previously developed poromechanical formulation to model the perfusion of myocardium during a cardiac cycle. First, a complete model is derived in 3D. Then, we perform a dimensional reduction under the assumption of spherical symmetry and propose a numerical algorithm that enables us to perform simulations of the myocardial perfusion throughout the cardiac cycle. These simulations illustrate the use of the proposed model to represent various physiological and pathological scenarios, specifically the vasodilation in the coronary network (to reproduce the standard clinical assessment of myocardial perfusion and perfusion reserve), the stenosis of a large coronary artery, an increased vascular resistance in the microcirculation (microvascular disease) and the consequences of inotropic activation (increased myocardial contractility) particularly at the level of the systolic flow impediment. Our results show that the model gives promising qualitative reproductions of complex physiological phenomena. This paves the way for future quantitative studies using clinical or experimental data.

Cosmological simulations of self-interacting Bose-Einstein condensate dark matter

Fully 3D cosmological simulations of scalar field dark matter with self-interactions, also known as Bose-Einstein condensate dark matter, are performed using a set of effective hydrodynamic equations. These are derived from the non-linear Schrödinger equation by performing a smoothing operation over scales larger than the de Broglie wavelength, but smaller than the self-interaction Jeans’ length. The dynamics on the de Broglie scale become an effective thermal energy in the hydrodynamic approximation, which is assumed to be subdominant in the initial conditions, but become important as structures collapse and the fluid is shock-heated. The halos that form have Navarro-Frenk-White envelopes, while the centers are cored due to the fluid pressures (thermal + self-interaction), confirming the features found by Dawoodbhoy et al. (2021, MNRAS, 506, 2418) using 1D simulations under the assumption of spherical symmetry. The core radii are largely determined by the self-interaction Jeans’ length, even though the effective thermal energy eventually dominates over the self-interaction energy everywhere, a result that is insensitive to the initial ratio of thermal energy to interaction energy, provided it is sufficiently small to not affect the linear and weakly non-linear regimes. Scaling relations for the simulated population of halos are compared to Milky Way dwarf spheroidals and nearby galaxies, assuming a Burkert halo profile, and are found to not match, although they conform better with observations compared to fuzzy dark matter-only simulations.

Acoustic black hole analogy to analyze nonlinear acoustic wave dynamics in accelerating flow fields

We present a physical model and a numerical method based on a space- and time-dependent Galilean-type coordinate transformation to simulate acoustic waves in the presence of an accelerating background flow field with sonic transition. Kinematically, the coordinate transformation is designed so as to maintain the well-posedness of the transformed wave equation, which is solved in a fixed computational domain using standard finite differences. Considering an acoustic black hole analogy, we analyze the nonlinear dynamics of acoustic waves in a stationary but non-uniformly accelerating flow field under the assumption of spherical symmetry. The choice of the acoustic black hole analogy is motivated by the fact that the steady-state spherical sonic horizon allows us to parameterize the wave-flow configuration in terms of a Helmholtz number He=c2/(λagh), which is expressed as a function of the speed of sound c, the emitted wavelength λa, and the flow acceleration at the sonic horizon, that is, the acoustic surface gravity gh. The results of the numerical simulations show that He describes geometrically similar sets of wave characteristics for different combinations of gh and λa. However, we also observe nonlinear variations of the wave amplitude along the wave characteristics, which are attributed to nonlinear Doppler modulations. It appears that these amplitude modulations depend on the acceleration of the flow field and can, therefore, differ for geometrically similar characteristics.

Cavitation in a soft porous material.

We study the collapse and expansion of a cavitation bubble in a deformable porous medium. We develop a continuum-scale model that couples compressible fluid flow in the pore network with the elastic response of a solid skeleton. Under the assumption of spherical symmetry, our model can be reduced to an ordinary differential equationthat extends the Rayleigh-Plesset equationto bubbles in soft porous media. The extended Rayleigh-Plesset equationreveals that finite-size effects lead to the breakdown of the universal scaling relation between bubble radius and time that holds in the infinite-size limit. Our data indicate that the deformability of the porous medium slows down the collapse and expansion processes, a result with important consequences for wide-ranging phenomena, from drug delivery to spore dispersion.

Deprojection of X-ray data in galaxy clusters: confronting simulations with observations

ABSTRACT Numerical simulations with varying realism indicate an emergent principle−multiphase condensation and large cavity power occur when the ratio of the cooling time to the free-fall time (tcool/tff) falls below a threshold value close to 10. Observations indeed show cool-core signatures when this ratio falls below 20–30, but the prevalence of cores with tcool/tff ratio below 10 is rare as compared to simulations. In X-ray observations, we obtain projected spectra from which we have to infer radial gas density and temperature profiles. Using idealized models of X-ray cavities and multiphase gas in the core and 3D hydro jet-ICM simulations, we quantify the biases introduced by deprojection based on the assumption of spherical symmetry in determining tcool/tff. We show that while the used methods are able to recover the tcool/tff ratio for relaxed clusters, they have an uncertainty of a factor of 2−3 in systems containing large cavities (≳ 20 kpc). We also show that the mass estimates from these methods, in the absence of X-ray spectra close to the virial radius, suffer from a degeneracy between the virial mass (M200) and the concentration parameter (c) in the form of M200c2 ≈ constant. Additionally, the lack of soft-X-ray (≲ 0.5 keV) coverage and poor spatial resolution makes us overestimate min(tcool/tff) by a factor of few in clusters with min(tcool/tff) ≲ 5. This bias can largely explain the lack of cool-core clusters with min(tcool/tff) ≲ 5.

Calculation of β -decay half-lives within a Skyrme-Hartree-Fock-Bogoliubov energy density functional with the proton-neutron quasiparticle random-phase approximation and isoscalar pairing strengths optimized by a Bayesian method

Background: For data on radioactive nuclei, $\ensuremath{\beta}$ decay provides some of the most important information, applicable to various fields. However, some $\ensuremath{\beta}$-decay data are not available due to experimental difficulties. For this reason, theoretically calculated results have been embedded in the data on radioactive nuclear $\ensuremath{\beta}$ decay to compensate for the missing information.Purpose: It is necessary to treat various nuclear correlations as precisely as possible for theoretical $\ensuremath{\beta}$-decay calculations. In particular, the pairing correlation is one of the most important factors for reproducing $\ensuremath{\beta}$-decay half-lives correctly. Therefore, we first study the effect of zero- and finite-range isovector pairings on half-lives. Second, we investigate the isoscalar pairing strengths, which are determined through experimental data of half-lives. Finally, we predict the isoscalar pairing strengths and half-lives of neutron-rich nuclei.Methods: To calculate the $\ensuremath{\beta}$-decay half-lives, a proton-neutron quasiparticle random-phase approximation on top of a Skryme energy density functional is applied with an assumption of spherical symmetry. The half-lives are calculated by including the allowed and first-forbidden transitions. The isoscalar pairing strength is estimated by a Bayesian neural network (BNN). We verify the predicted isoscalar pairing strengths by preparing the training data and test data.Results: It was confirmed that the finite-range isovector pairing ensures that the $\ensuremath{\beta}$-decay half-lives are insensitive to the model space, while the zero-range one is largely dependent on it. The half-lives calculated with the BNN isoscalar pairing strengths reproduced most of the experimental data, although those of highly deformed nuclei were underestimated. We also studied the predictive performance on new experimental data that were not used for the BNN training and found that they were reproduced well.Conclusions: Our study demonstrates that the isoscalar pairing strengths determined by the BNN can reproduce experimental data with the same accuracy as other theoretical works. To achieve a more precise prediction, the nuclear deformation is important.

Assessment of ZTD Derived from COSMIC Occultation Data with ECWMF, Radiosondes, and GNSS.

Global Navigation Satellite System (GNSS) signals generate slant tropospheric delays when they pass through the atmosphere, which is recognized as the main source of error in many spatial geodetic applications. The zenith tropospheric delay (ZTD) derived from radio occultation data is of great significance to atmospheric research and meteorology and needs to be assessed in the use of precision positioning. Based on the atmPrf, sonPrf, and echPrf data from the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) Data Analysis and Archiving Center (CDAAC) from 1 January to 31 December 2008 and 2012, we obtained the ZTDs of the radio occultation data (occZTD) and the corresponding radiosonde (sonZTD) and ECWMF data (echZTD). The ZTDs derived from ground-based global positioning system (GPS) observations from the International GNSS Service (IGS) were corrected to the lowest tangent point height of the matched radio occultation profile by the barometric height formula (gnsZTD). The statistical results show that the absolute values of the bias between occZTD and echZTD, sonZTD, or gnsZTD are less than 5 mm, and the standard deviations are approximately 20 mm or less, indicating that occZTD had significant accuracy in the GNSS positioning model even when the local spherical symmetry assumption error was introduced when the Abel inversion algorithm was used to obtain the refractive index profile of atmPrf. The effects of the horizontal/vertical matching resolution and the variation in the station height/latitude on the biases of occZTD and gnsZTD were analyzed. The results can be used to quantify the performance of radio occultation data for tropospheric delay error correction in dynamic high-precision positioning.

Comparison of COSMIC and COSMIC-2 Radio Occultation Refractivity and Bending Angle Uncertainties in August 2006 and 2021

We compare the random error statistics (uncertainties) of COSMIC (Constellation Observing System for Meteorology, Ionosphere and Climate, C1) and COSMIC-2 (C2) radio occultation (RO) bending angles and refractivities for the months of August 2006 and 2021 over the tropics and subtropics using the three-cornered hat method. The uncertainty profiles are similar for the two RO missions in the troposphere. However, a higher percentage of C2 profiles reach close to the surface in the moisture-rich tropics, an advantage of the higher signal-to-noise ratio (SNR) in C2. C2 uses signals from both GPS (Global Positioning System) and GLONASS Global Navigation System Satellites (GNSS). The GPS occultations show smaller uncertainties in the stratosphere and lower mesosphere (30–60 km) than the GLONASS occultations, a result of more accurate GPS clocks. Therefore, C2 (GPS) uncertainties are smaller than C1 uncertainties between 30–60 km while the C2 (GLONASS) uncertainties are larger than those of C1. The uncertainty profiles vary with latitude at all levels. We find that horizontal gradients in temperature and water vapor, and therefore refractivity, are the major cause of uncertainties in the tropopause region and troposphere through the violation of the assumption of spherical symmetry in the retrieval of bending angles and refractivity.

Stable Hydrogen-burning Limits in Rapidly Rotating Very Low Mass Objects

We present novel effects of uniform rapid stellar rotation on the minimum mass of stable hydrogen burning in very low mass stars, using an analytic model and relaxing the assumption of spherical symmetry. We obtain an analytic formula for the minimum mass of hydrogen burning as a function of the angular speed of stellar rotation. Further, we show the existence of a maximum mass of stable hydrogen burning in such stars, which is purely an artifact of rapid rotation. The existence of this extremum in mass results in a minimum admissible value of the stellar rotation period of ∼22 minutes, below which a very low mass object does not reach the main sequence, within the ambit of our model. For a given angular speed, we predict a mass range beyond which such an object will not evolve into a main-sequence star.

Non-parametric spherical Jeans mass estimation with B-splines

ABSTRACTSpherical Jeans modelling is widely used to estimate mass profiles of systems from star clusters to galactic stellar haloes to clusters of galaxies. It derives the cumulative mass profile, M(<r), from kinematics of tracers of the potential under the assumptions of spherical symmetry and dynamical equilibrium. We consider the application of Jeans modelling to mapping the dark matter distribution in the outer reaches of the Milky Way using field halo stars. We present a novel non-parametric routine for solving the spherical Jeans equation by fitting B-splines to the velocity and density profiles of halo stars. While most implementations assume parametric forms for these profiles, B-splines provide non-parametric fitting curves with analytical derivatives. Our routine recovers the mass profiles of equilibrium systems with flattened haloes or a stellar disc and bulge excellently (${\lesssim} 10{{\ \rm per\ cent}}$ error at most radii). Tests with non-equilibrium, Milky Way-like galaxies from the Latte suite of the Feedback In Realistic Environments model 2 (FIRE-2) simulations perform quite well (${\lesssim} 15{{\ \rm per\ cent}}$ error for r$\lesssim$ 100 kpc). We also create observationally motivated data sets for the Latte suite by imposing selection functions and errors on phase-space coordinates characteristic of Gaia and the Dark Energy Spectroscopic Instrument (DESI) Milky Way Survey. The resulting imprecise and incomplete data require us to introduce a Markov chain Monte Carlo (MCMC)-based subroutine to obtain deconvolved density and velocity dispersion profiles from the tracer population. With these observational effects taken into account, the accuracy of the Jeans mass estimate remains at the level 20 per cent or better.

Radiation hydrodynamics modelling of kilonovae withSNEC

ABSTRACTWe develop a method to compute synthetic kilonova light curves that combine numerical relativity simulations of neutron star mergers and the SNEC radiation–hydrodynamics code. We describe our implementation of initial and boundary conditions, r-process heating, and opacities for kilonova simulations. We validate our approach by carefully checking that energy conservation is satisfied and by comparing the SNEC results with those of two semi-analytic light-curve models. We apply our code to the calculation of colour light curves for three binaries having different mass ratios (equal and unequal mass) and different merger outcome (short-lived and long-lived remnants). We study the sensitivity of our results to hydrodynamic effects, nuclear physics uncertainties in the heating rates, and duration of the merger simulations. We find that hydrodynamics effects are typically negligible and that homologous expansion is a good approximation in most cases. However, pressure forces can amplify the impact of uncertainties in the radioactive heating rates. We also study the impact of shocks possibly launched into the outflows by a relativistic jet. None of our models match AT2017gfo, the kilonova in GW170817. This points to possible deficiencies in our merger simulations and kilonova models that neglect non-LTE effects and possible additional energy injection from the merger remnant and to the need to go beyond the assumption of spherical symmetry adopted in this work.

Interaction of a singular surface with a strong shock in the interstellar gas clouds

We investigate the interaction between a singular surface and a strong shock in the self-gravitating interstellar gas clouds with the assumption of spherical symmetry. Using the method of the Lie group of transformations, a particular solution of the flow variables and the cooling–heating function for an infinitely strong shock is obtained. This paper explores an application of the singular surface theory in the evolution of an acceleration wave front propagating through an unperturbed medium. We discuss the formation of an acceleration, considering the cases of compression and expansion waves. The influence of the cooling–heating function on a shock formation is explained. The results of a collision between a strong shock and an acceleration wave are discussed using the Lax evolutionary conditions. doi:10.1017/S1446181121000328

Higher order interface conditions for piezoelectric spherical hollow composites: asymptotic approach and transfer matrix homogenization method

The paper describes the mechanical behavior of composites made of piezoelectric spheres in perfect or imperfect contact. The imperfect contact is achieved by interposing piezoelectric thin adhesive layers between the spheres. First, using asymptotic analysis, transmission conditions of imperfect interface equivalent to the behavior of piezoelectric adhesive layers are obtained at order 0 and 1. These transmission conditions are calculated for ”hard” adhesives, i.e. adhesive materials whose electromechanical constants do not rescale with their thickness. Next, under the assumption of spherical symmetry, the transmission conditions are condensed to a general law of imperfect contact, able to simultaneously describe different contact regimes: piezoelectric hard (order 0 and 1) and soft (or spring-type, order 0 and 1) interface conditions, the perfect continuity conditions, and the piezoelectric rigid (Gurtin–Murdoch or membrane-type) conditions. Lastly, following Bufler’s approach, the homogenization problem of a spherical hollow piezoelectric assembly is solved, extending the classical transfer matrix method to take into account the presence of thin adhesive layers described using the proposed transmission conditions of imperfect contact. A simple numerical example is provided, illustrating the correctness and effectiveness of the homogenization approach in describing the electromechanical behavior of spherical piezoelectric assemblies.

Systematical studies of theE1photon strength functions combining the Skyrme-Hartree-Fock-Bogoliubov plus quasiparticle random-phase approximation model and experimental giant dipole resonance properties

Valuable theoretical predictions of nuclear dipole excitations in the whole nuclear chart are of great interest for different applications, including in particular nuclear astrophysics. We present here the systematic study of the electric-dipole $(E1)$ photon strength functions combining the microscopic Hartree-Fock-Bogoliubov plus quasiparticle random-phase approximation (HFB $+$ QRPA) model and the parametrizations constrained by the available experimental giant dipole resonance (GDR) data. For about 10 000 nuclei with $8\ensuremath{\le}\mathrm{Z}\ensuremath{\le}124$ lying between the proton and the neutron drip-lines on nuclear chart, the particle-hole (ph) strength distributions are computed using the HFB + QRPA model under the assumption of spherical symmetry and making use of the BSk27 Skyrme effective interaction derived from the most accurate HFB mass model (HFB-27) so far achieved. Large-scale calculations of the BSk27 + QRPA $E1$ photon strength functions are performed in the framework of a specific folding procedure describing the damping of nuclear collective motion empirically. In particular, three phenomenological improvements are considered in this folding procedure. First, two interference factors are introduced and adjusted to reproduce at best the available experimental GDR data. Second, an empirical expression accounting for the deformation effect is applied to describe the peak splitting of the strength function. Third, the width of the strength function is corrected by a temperature-dependent term, which effectively increases the deexcitation photon strength function at low energy. The theoretical $E1$ photon strength functions as well as the extracted GDR peaks and widths are comprehensively compared with available experimental data. A relatively good agreement with data indicates the reliability of the present calculations. Eventually, the astrophysical rates of $(n,\ensuremath{\gamma})$ reactions for all the 10 000 nuclei with $8\ensuremath{\le}Z\ensuremath{\le}124$ lying between the proton and the neutron drip lines are estimated using the present $E1$ photon strength functions. The resulting reaction rates are compared with the previous BSk7 + QRPA results as well as the Gogny-HFB + QRPA predictions based on the D1M interaction.

Impact of inhomogeneities on slowly rolling quintessence: implications for the local variations of the fine-structure constant

We study how the evolution of a dark energy quintessence fluid is modified by the presence of a matter inhomogeneity. To do so, we study linear perturbations of a flat FLRW background containing dust and a slowly rolling scalar field. Under the assumptions of spherical symmetry and a static density contrast, i.e. , we obtain simple analytical solutions for perturbations in the matter and dark energy-dominated epochs. As a consequence, we show that perturbations of the scalar field, if a coupling à la Bekenstein is assumed, trigger a spatial dependence of the fine-structure ‘constant’ which then varies as Δα ∝ 1/r. We finally highlight that such variations can be constrained with spectroscopic observations of stars from within our galaxy, therefore offering a new probe of the nature of dark renergy.