Small Frequency Separations Research Articles

Simplifying asteroseismic analysis of solar-like oscillators

Context. The asteroseismic analysis of stellar power density spectra is often computationally expensive. The models used in the analysis may require several dozen parameters to accurately describe features in the spectra caused by the oscillation modes and surface granulation. Many of these parameters are often highly correlated, making the parameter space difficult to quickly and accurately sample. They are, however, all dependent on a much smaller set of parameters, namely the fundamental stellar properties. Aims. We aim to leverage this to develop a method for simplifying the process of sampling the model parameter space for the asteroseismic analysis of solar-like oscillators, with an emphasis on mode identification. Methods. Using a large set of previous observations, we applied principal component analysis to the sample covariance matrix to select a new basis on which to sample the model parameters. Selecting the subset of basis vectors that explains the majority of the sample variance, we then redefined the model parameter prior probability density distributions in terms of a smaller set of latent parameters. Results. We are able to reduce the dimensionality of the sampled parameter space by a factor of two to three. The number of latent parameters needed to accurately model the stellar oscillation spectra cannot be determined exactly but is likely only between four and six. Using two latent parameters, the method is able to produce models that describe the bulk features of the oscillation spectrum, while including more latent parameters allows for a frequency precision better than ≈10% of the small frequency separation for a given target. Conclusions. We find that sampling a lower-rank latent parameter space still allows for accurate mode identification and parameter estimation on solar-like oscillators over a wide range of evolutionary stages. This allows for the potential to increase the complexity of spectrum models without a corresponding increase in computational expense.

Observation of ionospheric Alfven resonator with double spectral resonance structures at low latitude station, Shillong (dipole L=1.08)

Spectral Resonance Structures (SRS) of Ionospheric Alfven Resonator (IAR) are investigated by analysing the magnetic field data of a high sampling frequency induction coil magnetometer, installed at a low latitude Indian station, Shillong(25.56^circ N, 91.86^circ E, dipole L=1.08 ). One of the distinguishing features of IAR resonance structure observed at this latitude is the excitation of two spectral resonance structures simultaneously, one with a small frequency separation and the other with a large frequency separation of subsequent harmonics. The seasonal variation shows that the occurrence of double SRS is more favoured during winter, where, out of the total IAR events observed during winter, about 47% show clear signatures of double SRS and no double SRS are observed during summer. We have examined the altitudinal variation of refractive index using IRI 2016 model to understand the role of local ionospheric conditions in the formation of double spectral resonance structures. Our study reveals that the excitation of double SRS is related to the E-region to F-region variability of refractive index of the ionosphere. We also report that the double spectral resonance structures at Shillong are always observed only in the {B}_{x} component of the magnetic field variation.Graphical

Dual-band broadside-coupled based BPF with improved performance

This paper presents a unique structure of a dual-band microstrip bandpass filter (BPF) that works at 1.25 GHz, 1.9 GHz for global positioning systems (GPS) and TV broadcast auxiliary service applications, respectively. The proposed BPF provides compactness, small fractional bandwidth (FBW), small frequency separation, and low IL. The prospective filter is constructed employing broadside-coupling techniques to achieve low insertion loss (IL). The feeding structure is accomplished utilizing a 50 Ω co-planar waveguide (CPW) scheme due to its low loss characteristics. The small 3-dB FBW is accomplished by inserting four transmission zeros (TZs). The size of the overall structure, including I/O transmission lines, is 34.9 × 23.5 mm2. The measured and simulated results fit well with each other and show an IL of 0.77 dB and 0.5 dB, and FBW of 7.6% and 8.4% at 1.25 GHz and 1.9 GHz, respectively.

Frequency Superresolution with Spectrotemporal Shaping of Photons

Quantum sensing and metrology promise useful insights and alternative techniques to surpass the measurement limits of a classical framework. Significant improvement has been made in the areas of imaging, positioning, timing, interferometry, communication, and information processing through quantum detection and estimation techniques. In this Letter, we focus on the application of quantum information for spectral measurements. Specifically, we study the quantum limit to resolve two spectral modes with small frequency separation. We show that frequency superresolution can be achieved with spectrotemporal shaping of input fields before detection. Through a numerical optimization algorithm, we design the apparatus for spectrotemporal shaping based on phase modulation and dispersion engineering. This scheme can achieve performance close to the quantum limit with minimum resources, showing the robustness for experimental implementation and real-world applications.

Two symmetric four-wave mixing signals generated in a medium with anomalous refractive index

We report experimental and theoretical results of two symmetrical signals of degenerate four-wave mixing generated in rubidium vapor. Both nonlinear signals are induced by two almost copropagating laser beams, with and wave-vectors, and detected simultaneously in the and directions. In each direction, we observe a single peak when the two beams are tuned on the closed transition 85Rb 5S 1/2(F = 3) → 5P 3/2(F = 4). The excitation spectra reveal a small frequency separation between the two peaks, which is explained when propagation effects are taken into account. Furthermore, our theoretical analysis shows that a correct description of the frequency position of each peak is achieved with a variable refractive index for both lasers, in which the scanning laser experiences an anomalous window in the refractive index near resonance.

Small cap decouplings

We develop a toolbox for proving decouplings into boxes with diameter smaller than the canonical scale. As an application of this new technique, we solve three problems for which earlier methods have failed. We start by verifying the small cap decoupling for the parabola. Then we find sharp estimates for exponential sums with small frequency separation on the moment curve in $$\mathbb {R}^3$$ . This part of the work relies on recent improved Kakeya-type estimates for planar tubes, as well as on new multilinear incidence bounds for plates and planks. We also combine our method with the recent advance on the reverse square function estimate, in order to prove small cap decoupling into square-like caps for the two dimensional cone. The Appendix by Roger Heath-Brown contains an application of the new exponential sum estimates for the moment curve, to the Riemann zeta-function.

Relevance of the small frequency separation for asteroseismic stellar age, mass, and radius

Aims. We performed a theoretical analysis aimed at quantifying the relevance of the small frequency separation δν in determining stellar ages, masses, and radii. We aimed to establish a minimum uncertainty on these quantities for low-mass stars across different evolutionary stages of the main sequence and to evaluate the biases that come from some systematic differences between the stellar model grid adopted for the recovery and the observed stars. Methods. We adopted the Stellar CharactEristics Pisa Estimation gRid (SCEPtER) pipeline for low-mass stars, [0.7, 1.05] M⊙, from the zero-age main sequence (ZAMS) to the central hydrogen depletion. For each model in the grid, we computed oscillation frequencies. Synthetic stars were generated and reconstructed based on different assumptions about the relative precision in the δν parameter (namely 5% and 2%). The quantification of the systematic errors arising from a possible mismatch between synthetic stars and the recovery grid was performed by generating stars from synthetic grids of stellar models with different initial helium abundance and microscopic diffusion efficiency. The results obtained without δν as an observable are included for comparison. Results. The investigation highlighted and confirmed the improvement in the age estimates when δν is available, which has already been reported in the literature. While the biases were negligible, the statistical error affecting age estimates was strongly dependent on the stellar evolutionary phase. The error is at its maximum at ZAMS and it decreases to about 11% and 6% (δν known at 5% and 2% level, respectively) when stars reach the 30% of their evolutionary MS lifetime. The usefulness of small frequency separation in improving age estimates vanishes in the last 20% of the MS. The availability of δν in the fit for mass and radius estimates provided an effect that was nearly identical to its effect on age, assuming an observational uncertainty of 5%. As a departure, with respect to age estimates, no benefit was detected for mass and radius determinations from a reduction of the observational error in δν to 2%. The age variability attributed to differences in the initial helium abundance resulted in negligible results owing to compensation effects that have already been discussed in previous works. On the other hand, the current uncertainty in the initial helium abundance leads to a greater bias (2% and 1% level) in mass and radius estimates whenever δν is in the observational pool. This result, together with the presence of further unexplored uncertainty sources, suggest that precision in the derived stellar quantities below these thresholds may possibly be overoptimistic. The impact of microscopic diffusion was investigated by adopting a grid of models for the recovery which totally neglected the process. The availability of the small frequency separation resulted in biases lower than 5% and 2% for observational errors of 5% and 2%, respectively. The estimates of mass and radius showed again a greater distortion when δν is included among the observables. These biases are at the level of 1%, confirming that threshold as a minimum realistic uncertainty on the derived stellar quantities. Finally, we compared the estimates by the SCEPtER pipeline for 13 Kepler asteroseismic LEGACY sample stars with those given by six different pipelines from literature. This procedure demonstrated a fair agreement for the results. The comparison suggests that a realistic approach to the determination of the error on the estimated parameters consists of approximately doubling the error in the recovered stellar characteristics from a single pipeline. Overall, on the LEGACY sample data, we obtained a multi-pipeline precision of about 4.4%, 1.7%, and 11% on the estimated masses, radii, and ages, respectively.

Simple Triple-Mode Dual-Polarized Dipole Antenna With Small Frequency Separation Ratio

A triple-mode dual-polarized dipole antenna topology with a very small frequency separation ratio is proposed. The antenna has a simple structure with a very low manufacturing cost while maintaining a good performance. A conventional dipole is fed by a feeding network also acting as a radiator to generate a second resonant mode. A shorted conductor loaded to the dipole is used to excite a third resonant mode. It is shown that the three modes can be tuned in order to cover different sets of applications. By fusing the two higher resonances, an antenna with a lower band and a very wide higher band can be obtained. Two orthogonal linear polarizations are achieved by integrating two of the aforementioned topologies. The conceptual structure is prototyped and measured. The realized antenna has a lower band of 2.38–2.54 GHz and a higher band of 3.11–4.15 GHz. Its electrical size is 0.8 × 0.8 λ2, with a profile of 0.27 λ ( λ is the wavelength in free space at 2.4 GHz). The mutual coupling between the two ports is below -20 dB, which is quite beneficial for the diversity performance in multiple-input–multiple-output (MIMO) systems.

Acoustic modes of pulsating axion stars: Nonradial oscillations

We compute the lowest frequency nonradial oscillation modes of dilute axion stars. The effective potential that enters into the Schrödinger-like equation, several associated eigenfunctions and the large as well as the small frequency separations are shown as well.

K2 observations of the rapidly oscillating Ap star 33 Lib (HD 137949): new frequencies and unique non-linear interactions

We present the analysis of K2 short cadence data of the rapidly oscillating Ap (roAp) star, 33 Librae (HD 137949). The precision afforded to the K2 data allow us to identify at least 11 pulsation modes in this star, compared to the three previously reported. Reoccurring separations between these modes leads us to suggest a large frequency separation, $\Delta\nu$, of 78.9 $\mu$Hz, twice that reported in the literature. Other frequency separations we detect may represent the small frequency separation, $\delta\nu$, but this is inconclusive at this stage due to magnetic perturbation of the frequencies. Due to the highly non-linear pulsation in 33 Lib, we identify harmonics to four times the principal frequency. Furthermore, we note a unique occurrence of non-linear interactions of the 11 identified modes. The frequency separations of the modes around the principal frequency are replicated around the first harmonic, with some interaction with the second harmonic also. Such a phenomenon has not been seen in roAp stars before. With revised stellar parameters, linear non-adiabatic modelling of 33 Lib shows that the pulsations are not greater than the acoustic cutoff frequency, and that the $\kappa$-mechanism can excite the observed modes. Our observations are consistent with 33 Lib having a rotation period much larger than 88 d as presented in the literature.

Probing Convective Mixing in Stellar Interiors with α Centauri A and B

AbstractThe bright nearby binary α Centauri constitutes an excellent laboratory for testing stellar evolution models. The mass, radius, and luminosity of α Cen A and B are known to better than 1% accuracy thanks to recent interferometric and adaptive optical observations, and p-mode oscillations have been observed in both stars. We present new stellar models which fit simultaneously the classical and seismic observations, with particular emphasis on the convective mixing length parameter MLT – the adaptivity of which is necessary to fit the models to observations. The oscillation data provide an important constraint on the models, as the small frequency separation is sensitive to the composition gradient in the core of the stars, while the large frequency separation constrains the mean density of the stars, providing an independent check on the mass and radius.

Effect of electromagnetic dipole dark matter on energy transport in the solar interior

In recent years, a revised set of solar abundances has led to a discrepancy in the sound-speed profile between helioseismology and theoretical solar models. Conventional solutions require additional mechanisms for energy transport within the Sun. Vincent et al. have recently suggested that dark matter with a momentum or velocity dependent cross section could provide a solution. In this work, we consider three models of dark matter with such cross sections and their effect on the stellar structure. In particular, the three models incorporate dark matter particles interacting through an electromagnetic dipole moment: an electric dipole, a magnetic dipole or an anapole. Each model is implemented in the DarkStec stellar evolution program, which incorporates the effects of dark matter capture and heat transport within the solar interior. We show that dark matter with an anapole moment of ∼ 1 GeV−2 or magnetic dipole moment of ∼ 10−3μp can improve the sound-speed profile, small frequency separations and convective zone radius with respect to the Standard Solar Model. However, the required dipole moments are strongly excluded by direct detection experiments.

A seismic and gravitationally bound double star observed byKepler

Context. Solar-like oscillations have been observed by Kepler and CoRoT in many solar-type stars, thereby providing a way to probe stars using asteroseismology.Aims. The derivation of stellar parameters has usually been done with single stars. The aim of the paper is to derive the stellar parameters of a double-star system (HIP 93511), for which an interferometric orbit has been observed along with asteroseismic measurements.Methods. We used a time series of nearly two years of data for the double star to detect the two oscillation-mode envelopes that appear in the power spectrum. Using a new scaling relation based on luminosity, we derived the radius and mass of each star. We derived the age of each star using two proxies: one based upon the large frequency separation and a new one based upon the small frequency separation. Using stellar modelling, the mode frequencies allowed us to derive the radius, the mass, and the age of each component. In addition, speckle interferometry performed since 2006 has enabled us to recover the orbit of the system and the total mass of the system.Results. From the determination of the orbit, the total mass of the system is 2.34-0.33+0.45 M⊙. The total seismic mass using scaling relations is 2.47 ± 0.07 M⊙. The seismic age derived using the new proxy based upon the small frequency separation is 3.5 ± 0.3 Gyr. Based on stellar modelling, the mean common age of the system is 2.7–3.9 Gyr. The mean total seismic mass of the system is 2.34–2.53 M⊙ consistent with what we determined independently with the orbit. The stellar models provide the mean radius, mass, and age of the stars as RA = 1.82−1.87R⊙, MA = 1.25−1.39 M⊙, AgeA = 2.6–3.5 Gyr; RB = 1.22−1.25 R⊙, MB = 1.08−1.14 M⊙, AgeB = 3.35–4.21 Gyr. The models provide two sets of values for Star A: [1.25–1.27] M⊙ and [1.34–1.39] M⊙. We detect a convective core in Star A, while Star B does not have any. For the metallicity of the binary system of Z ≈ 0.02, we set the limit between stars having a convective core in the range [1.14–1.25] M⊙.

Generalised form factor dark matter in the Sun

We study the effects of energy transport in the Sun by asymmetric dark matter with momentum and velocity-dependent interactions, with an eye to solving the decade-old Solar Abundance Problem. We study effective theories where the dark matter-nucleon scattering cross-section goes as vrel2n and q2n with n = −1, 0, 1 or 2, where vrel is the dark matter-nucleon relative velocity and q is the momentum exchanged in the collision. Such cross-sections can arise generically as leading terms from the most basic nonstandard DM-quark operators. We employ a high-precision solar simulation code to study the impact on solar neutrino rates, the sound speed profile, convective zone depth, surface helium abundance and small frequency separations. We find that the majority of models that improve agreement with the observed sound speed profile and depth of the convection zone also reduce neutrino fluxes beyond the level that can be reasonably accommodated by measurement and theory errors. However, a few specific points in parameter space yield a significant overall improvement. A 3–5 GeV DM particle with σSI ∝ q2 is particularly appealing, yielding more than a 6σ improvement with respect to standard solar models, while being allowed by direct detection and collider limits. We provide full analytical capture expressions for q- and vrel-dependent scattering, as well as complete likelihood tables for all models.

Determination of fundamental asteroseismic parameters using the Hilbert transform

Context. Solar-like oscillations exhibit a regular pattern of frequencies. This pattern is dominated by the small and large frequency separations between modes. The accurate determination of these parameters is of great interest, because they give information about e.g. the evolutionary state and the mass of a star. Aims. We want to develop a robust method to determine the large and small frequency separations for time series with low signal-tonoise ratio. For this purpose, we analyse a time series of the Sun from the GOLF instrument aboard SOHO and a time series of the star KIC 5184732 from the NASA Kepler satellite by employing a combination of Fourier and Hilbert transform. Methods. We use the analytic signal of filtered stellar oscillation time series to compute the signal envelope. Spectral analysis of the signal envelope then reveals frequency differences of dominant modes in the periodogram of the stellar time series. Results. With the described method the large frequency separation $\Delta\nu$ can be extracted from the envelope spectrum even for data of poor signal-to-noise ratio. A modification of the method allows for an overview of the regularities in the periodogram of the time series.

Possible indication of momentum-dependent asymmetric dark matter in the sun.

Broad disagreement persists between helioseismological observables and predictions of solar models computed with the latest surface abundances. Here we show that most of these problems can be solved by the presence of asymmetric dark matter coupling to nucleons as the square of the momentum q exchanged in the collision. We compute neutrino fluxes, small frequency separations, surface helium abundances, sound speed profiles, and convective zone depths for a number of models, showing more than a 6σ preference for q^{2} models over others, and over the standard solar model. The preferred mass (3GeV) and reference dark matter-nucleon cross section (10^{-37} cm^{2} at q_{0}=40 MeV) are within the region of parameter space allowed by both direct detection and collider searches.

Stellar acoustic radii, mean densities, and ages from seismic inversion techniques

Context. Determining stellar characteristics such as the radius, the mass or the age is crucial when studying stellar evolution, exoplanetary systems or characterising stellar populations in the Galaxy. Asteroseismology is the golden path to accurately obtain these characteristics. In this context, a key question is how to make these methods less model-dependant. Aims. Building on the work of Reese et al. (2012), we wish to extend the SOLA inversion technique to new stellar global characteristics in addition to the mean density. The goal is to provide a general framework in which to estimate these characteristics as accurately as possible in low mass main sequence stars. Methods. First, we describe our framework and discuss the reliability of the inversion technique and the possible sources of error.We then apply this methodology to the acoustic radius, an age indicator based on the sound speed derivative and the mean density and compare it to estimates based on the average large and small frequency separations. These inversions are carried out for several test cases which include: various metallicities, different mixing-lengths, non-adiabatic effects and turbulent pressure. Results. We observe that the SOLA method yields accurate results in all test cases whereas results based on the large and small frequency separations are less accurate and more sensitive to surface effects and structural differences in the models. If we include the surface corrections of Kjeldsen et al. (2008), we obtain results of comparable accuracy for the mean density. Overall, the mean density and acoustic radius inversions are more robust than the inversions for the age indicator. Moreover, the current approach is limited to relatively young stars with radiative cores. Increasing the number of observed frequencies improves the reliability and accuracy of the method.

Stellar acoustic radii and ages from seismic inversion techniques

Determining stellar characteristics such as the radius, mass or age is crucial and asteroseismology is currently the most promising tool to provide these results accurately. We extend the SOLA inversion technique to new global characteristics in addition to the mean density [2] and apply our methodology to the acoustic radius and an age indicator based on the sound speed derivative. The results from SOLA inversions are compared with estimates based on the small and large frequency separations for several test cases. We show that SOLA inversions yield more accurate results than other techniques which are more sensitive to surface effects.

Asteroseismic stellar activity relations

In asteroseismology an important diagnostic of the evolutionary status of a star is the small frequency separation which is sensitive to the gradient of the mean molecular weight in the stellar interior. It is thus interesting to discuss the classical age-activity relations in terms of this quantity. Moreover, as the photospheric magnetic field tends to suppress the amplitudes of acoustic oscillations, it is important to quantify the importance of this effect by considering various activity indicators. We propose a new class of age-activity relations that connects the Mt. Wilson $S$ index and the average scatter in the light curve with the small frequency separation and the amplitude of the p-mode oscillations. We used a Bayesian inference to compute the posterior probability of various empirical laws for a sample of 19 solar-like active stars observed by the Kepler telescope. We demonstrate the presence of a clear correlation between the Mt. Wilson $S$ index and the relative age of the stars as indicated by the small frequency separation, as well as an anti-correlation between the $S$ index and the oscillation amplitudes. We argue that the average activity level of the stars shows a stronger correlation with the small frequency separation than with the absolute age that is often considered in the literature. The phenomenological laws discovered in this paper have the potential to become new important diagnostics to link stellar evolution theory with the dynamics of global magnetic fields. In particular we argue that the relation between the Mt. Wilson $S$ index and the oscillation amplitudes is in good agreement with the findings of direct numerical simulations of magneto-convection.

Precise and accurate interpolated stellar oscillation frequencies on the main sequence

AbstractHigh-quality data from space-based observatories present an opportunity to fit stellar models to observations of individually-identified oscillation frequencies, not just the large and small frequency separations. But such fits require the evaluation of a large number of accurate stellar models, which remains expensive. Here, we show that global-mode oscillation frequencies interpolated in a grid of stellar models are precise and accurate, at least in the neighbourhood of a solar model.