scholarly journals On the rotational velocity of Sirius A

2020 ◽  
Vol 499 (1) ◽  
pp. 1126-1139
Author(s):  
Yoichi Takeda
Keyword(s):  
Fourier Transform ◽  
Temperature Sensitivity ◽  
Profile Analysis ◽  
Rotational Velocity ◽  
Rotation Velocity ◽  
Spectral Lines ◽  
Surface Chemical ◽  
Model Calculations ◽  
The Fourier Transform ◽  
Chemical Peculiarity

ABSTRACT With an aim of getting information on the equatorial rotation velocity (ve) of Sirius A separated from the inclination effect (sin i), a detailed profile analysis based on the Fourier transform technique was carried out for a large number of spectral lines, while explicitly taking into account the line-by-line differences in the centre–limb behaviours and the gravity darkening effect (which depend on the physical properties of each line) based on model calculations. The simulations showed that how the first-zero frequencies (q1) of Fourier transform amplitudes depends on ve is essentially determined by the temperature-sensitivity parameter (K) differing from line to line, and that Fe i lines (especially those of very weak ones) are more sensitive to ve than Fe ii lines. The following conclusions were drawn by comparing the theoretical and observed q1 values for many Fe i and Fe ii lines: (1) The projected rotational velocity (vesin i) for Sirius A is fairly well established at 16.3(±0.1) km s−1 by requiring that both Fe i and Fe ii lines yield consistent results. (2) Although precise separation of ve and i is difficult, ve is concluded to be in the range of $16 \le v_{\rm e} \lesssim$ 30–40 km s−1, which corresponds to $25^{\circ } \lesssim i \le 90^{\circ }$. Accordingly, Sirius A is an intrinsically slow rotator for an A-type star, being consistent with its surface chemical peculiarity.

scholarly journals On the detection of stellar differential rotation based on the Fourier transform of spectral line profiles

2019 ◽  
Vol 72 (1) ◽  
Author(s):  
Yoichi Takeda
Keyword(s):  
Fourier Transform ◽  
Spectral Line ◽  
Differential Rotation ◽  
Fourier Transforms ◽  
Rotational Velocity ◽  
Model Atmosphere ◽  
Strict Sense ◽  
Line Profiles ◽  
Classical Formulation ◽  
The Fourier Transform

Abstract It is known that stellar differential rotation can be detected by analyzing the Fourier transform of spectral line profiles, since the ratio of the first and second zero frequencies is a useful indicator. This approach essentially relies on the conventional formulation that the observed flux profile is expressible as a convolution of the rotational broadening function and the intrinsic profile, which implicitly assumes that the local intensity profile does not change over the disk. Although this postulation is unrealistic in the strict sense, how the result is affected by this approximation is still unclear. With the aim of examining this problem, flux profiles of several test lines (showing different center-to-limb variations) were simulated using a model atmosphere corresponding to a mid-F dwarf by integrating the intensity profiles for various combinations of vesin i (projected rotational velocity), α (differential degree), and i (inclination angle), and their Fourier transforms were computed to check whether the zeros are detected at the predicted positions or not. For this comparison a large grid of standard rotational broadening functions and their transforms/zeros were also calculated. It turned out that the situation depends critically on vesin i: In the case of vesin i ≳ 20 km s−1, where rotational broadening is predominant over other line broadening velocities (typically several km s−1), the first/second zeros of the transform are confirmed almost at the expected positions. In contrast, deviations begin to appear as vesin i is lowered, and the zero features of the transform are totally different from those expected at vesin i as low as ∼10 km s−1, which means that the classical formulation is no longer valid. Accordingly, while the zero-frequency approach is safely applicable to studying differential rotation in the former broader-line case, it would be difficult to practice for the latter sharp-line case.

Spectral Line Narrowing by Use of the Theoretical Impulse Response

1997 ◽  
Vol 51 (2) ◽  
pp. 188-200 ◽  
Author(s):  
Pekka E. Saarinen
Keyword(s):  
Fourier Transform ◽  
Linear Prediction ◽  
Spectral Lines ◽  
High Signal ◽  
Line Shapes ◽  
Line Narrowing ◽  
The Fourier Transform ◽  
Spectral Line Narrowing ◽  
Made In ◽  
Prediction Strategy

Fourier transform spectroscopy is nowadays able to produce spectra with extremely high signal-to-noise ratios, and thus extremely high information content. Unfortunately, this information is partially lost because of a lack of sufficiently effective line-narrowing methods to resolve overlapping spectral lines. A novel, and very promising, approach to the problem is the LOMEP line-narrowing method, based on consecutive linear prediction; the line narrowing is carried out in the signal domain by extrapolating the Fourier transform of the spectrum. However, LOMEP is not yet optimal. For example, it does not make use of the information contained in the output line shapes to correct the errors made in linear prediction. In fact, that procedure would not even be possible by using the prediction strategy adopted by LOMEP. Therefore it is possible to considerably improve the method by including the information contained in the distortions of the output spectral lines. In this paper a new method of line narrowing is presented, based on progressive improvement of the prediction until the output is free from distortions. The method is very easy to use and does not require a profound understanding of the underlying mathematics.

scholarly journals Direct recovery of interfacial topography from coherent X-ray reflectivity: model calculations for a 1D interface

2020 ◽  
Vol 76 (4) ◽  
pp. 458-467
Author(s):  
Paul Fenter
Keyword(s):  
Fourier Transform ◽  
Momentum Transfer ◽  
Second Order ◽  
Model Calculations ◽  
Scattering Intensity ◽  
X Ray ◽  
Patterson Function ◽  
Scattering Factor ◽  
The Fourier Transform

The use of coherent X-ray reflectivity to recover interfacial topography is described using model calculations for a 1D interface. The results reveal that the illuminated topography can be recovered directly from the measured reflected intensities. This is achieved through an analysis of the Patterson function, the Fourier transform of the scattering intensity (as a function of lateral momentum transfer, Q //, at fixed vertical momentum transfer, Q z ). Specifically, a second-order Patterson function is defined that reveals the discrete set of separations and contrast factors (i.e. the product of changes in the effective scattering factor) associated with discontinuities in the effective interfacial topography. It is shown that the topography is significantly overdetermined by the measurements, and an algorithm is described that recovers the actual topography through a deterministic sorting of this information.

scholarly journals The Berkeley Program on Molecules of Astrophysical Interest

1994 ◽  
Vol 146 ◽  
pp. 397-411
Author(s):  
Sumner P. Davis
Keyword(s):  
Fourier Transform ◽  
Spectral Lines ◽  
Carbon Clusters ◽  
Molecular Spectra ◽  
Fourier Transform Spectrometer ◽  
Excitation Energies ◽  
Astrophysical Interest ◽  
Computer Codes ◽  
The Fourier Transform ◽  
Systematic Program

A systematic program of laboratory analyses of selected molecular spectra of astrophysical interest started in 1958 and continues to the present time. The program includes production of spectral atlases, tabulations of spectral lines, analyses, calculations of excitation energies and molecular parameters, measurements of radiative lifetimes, and determinations of transition strengths. Work has been completed or is in progress on the spectra of ArH+, C2, carbon clusters, CN, CS, CaCl, CaH, CaS, FeD, FeH, HgH, HgD, InI, LaO, LaS, OD, OH, SH, Si2, SiC2, TiCl, TiO, TiO+, VO, YS, ZrCl, ZrO, and ZrS. The basic needs for astronomically useful data have not changed, but laboratory and analysis methods have become more sophisticated in order to cope with ever greater demands for consistency, accuracy, and breadth of information. The Fourier transform spectrometer and computer codes for analyses have enhanced our ability to satisfy some of these demands.

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

Determination of starch crystallinity with the Fourier-transform terahertz spectrometer

2021 ◽  
Vol 262 ◽  
pp. 117928
Author(s):  
Shusaku Nakajima ◽  
Shuhei Horiuchi ◽  
Akifumi Ikehata ◽  
Yuichi Ogawa
Keyword(s):  
Fourier Transform ◽  
The Fourier Transform ◽  
Starch Crystallinity

Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lung-Hui Chen
Keyword(s):  
Fourier Transform ◽  
Entire Function ◽  
Convex Hull ◽  
Scattering Theory ◽  
Phase Retrieval ◽  
Indicator Function ◽  
Band Limited ◽  
The Fourier Transform ◽  
Complex Valued ◽  
Spectral Invariant

Abstract In this paper, we discuss how to partially determine the Fourier transform F ⁢ ( z ) = ∫ - 1 1 f ⁢ ( t ) ⁢ e i ⁢ z ⁢ t ⁢ 𝑑 t , z ∈ ℂ , F(z)=\int_{-1}^{1}f(t)e^{izt}\,dt,\quad z\in\mathbb{C}, given the data | F ⁢ ( z ) | {\lvert F(z)\rvert} or arg ⁡ F ⁢ ( z ) {\arg F(z)} for z ∈ ℝ {z\in\mathbb{R}} . Initially, we assume [ - 1 , 1 ] {[-1,1]} to be the convex hull of the support of the signal f. We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F ⁢ ( z ) {F(z)} . Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness. We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform. We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

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