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Register a new userOn the detection of stellar differential rotation based on the Fourier transform of spectral line profiles
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Yoichi Takeda
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It is known that stellar differential rotation can be detected by analyzing the Fourier transform of spectral line profiles, since the ratio of the 1st- and 2nd-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 broadning function and the intrinsic profile, which implicitly assumes that the local intensity profile does not change over disk. Although this postulation is unrealistic in the strict sense, how the result is affected by this approximation is still unclear. In order to examine this problem, profiles of several lines (showing different center-limb variations) were simulated using a model atmosphere corresponding to a mid-F dwarf by integrating intensity profiles for various combinations of vsini (rot. velocity), alpha (diff. degree), and i (inc. angle), and their Fourier transforms were computed to check whether zeros are detected at the predicted positions or not. For this comparison purpose, a large grid of standard rotational broadening functions and their transforms/zeros were also calculated. It turned out that the situation criticaly depends on vsini: In case of vsini>~20km/s where rotational broadening is predominant over other line broadening velocities (typically several km/s), the 1st/2nd zeros of the transform are confirmed almost at the expected positions. In contrast, deviations begin to appear as vsini is lowered, and the zero features of the transform are totally different from the expectation at vsini as low as ~10km/s, which means that the classical formulation is no more 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.
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While it is known that the sharp-line star Vega (vsini ~ 20km/s) is actually a rapid rotator seen nearly pole-on with low i (< 10 deg), no consensus has yet been accomplished regarding its intrinsic rotational velocity (v_e), for which rather different values have been reported so far. Methodologically, detailed analysis of spectral line profiles is useful for this purpose, since they reflect more or less the v_e-dependent gravitational darkening effect. However, direct comparison of observed and theoretically simulated line profiles is not necessarily effective in practice, where the solution is sensitively affected by various conditions and the scope for combining many lines is lacking. In this study, determination of Vegas v_e was attempted based on an alternative approach making use of the first zero (q_1) of the Fourier transform of each line profile, which depends upon K (temperature sensitivity parameter differing from line to line) and v_e. It turned out that v_e and vsini could be separately established by comparing the observed q_1^obs and calculated q_1^cal values for a number of lines of different K. Actually, independent analysis applied to two line sets (49 Fe I lines and 41 Fe II lines) yielded results reasonably consistent with each other. The final parameters of Vegas rotation were concluded as vsini = 21.6 (+/- 0.3) km/s, v_e = 195 (+/- 15) km/s, and i = 6.4 (+/- 0.5) deg.
(abridged) Context: Solar-like differential rotation is characterized by a rapidly rotating equator and slower poles. However, theoretical models and numerical simulations can result in a slower equator and faster poles when the rotation is slow. Aims: We study the critical rotational influence under which differential rotation flips from solar-like (fast equator, slow poles) to an anti-solar one (slow equator, fast poles). We estimate the non-diffusive ($Lambda$ effect) and diffusive (turbulent viscosity) contributions to the Reynolds stress. Methods: We present the results of three-dimensional numerical simulations of mildly turbulent convection in spherical wedge geometry. Here we apply a fully compressible setup which would suffer from a prohibitive time step constraint if the real solar luminosity was used. We regulate the convective velocities by varying the amount of heat transported by thermal conduction, turbulent diffusion, and resolved convection. Results: Increasing the efficiency of resolved convection leads to a reduction of the rotational influence on the flow and a sharp transition from solar-like to anti-solar differential rotation for Coriolis numbers around 1.3. We confirm the recent finding of a large-scale flow bistability: contrasted with running the models from an initial condition with unprescribed differential rotation, the initialization of the model with certain kind of rotation profile sustains the solution over a wider parameter range. Conclusions: Our results may have implications for real stars that start their lives as rapid rotators implying solar-like rotation in the early main-sequence evolution. As they slow down, they might be able to retain solar-like rotation for lower Coriolis numbers before switching to anti-solar rotation. This could partially explain the puzzling findings of anti-solar rotation profiles for models in the solar parameter regime.
Observations of Sun-like stars over the last half-century have improved our understanding of how magnetic dynamos, like that responsible for the 11-year solar cycle, change with rotation, mass and age. Here we show for the first time how metallicity can affect a stellar dynamo. Using the most complete set of observations of a stellar cycle ever obtained for a Sun-like star, we show how the solar analog HD 173701 exhibits solar-like differential rotation and a 7.4-year activity cycle. While the duration of the cycle is comparable to that generated by the solar dynamo, the amplitude of the brightness variability is substantially stronger. The only significant difference between HD 173701 and the Sun is its metallicity, which is twice the solar value. Therefore, this provides a unique opportunity to study the effect of the higher metallicity on the dynamo acting in this star and to obtain a comprehensive understanding of the physical mechanisms responsible for the observed photometric variability. The observations can be explained by the higher metallicity of the star, which is predicted to foster a deeper outer convection zone and a higher facular contrast, resulting in stronger variability.
Study of general purpose computation by GPU (Graphics Processing Unit) can improve the image processing capability of micro-computer system. This paper studies the parallelism of the different stages of decimation in time radix 2 FFT algorithm, designs the butterfly and scramble kernels and implements 2D FFT on GPU. The experiment result demonstrates the validity and advantage over general CPU, especially in the condition of large input size. The approach can also be generalized to other transforms alike.
The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational complexity of $O(N)$ and $O(N log N)$, respectively, where $N$ is the number of samples in the signal space. We have recently proposed a sparse Fourier transform based on the Fourier projection-slice theorem (FPS-SFT), which applies to multidimensional signals that are sparse in the frequency domain. FPS-SFT achieves sample complexity of $O(K)$ and computational complexity of $O(K log K)$ for a multidimensional, $K$-sparse signal. While FPS-SFT considers the ideal scenario, i.e., exactly sparse data that contains on-grid frequencies, in this paper, by extending FPS-SFT into a robust version (RFPS-SFT), we emphasize on addressing noisy signals that contain off-grid frequencies; such signals arise from radar applications. This is achieved by employing a windowing technique and a voting-based frequency decoding procedure; the former reduces the frequency leakage of the off-grid frequencies below the noise level to preserve the sparsity of the signal, while the latter significantly lowers the frequency localization error stemming from the noise. The performance of the proposed method is demonstrated both theoretically and numerically.
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