Characterizing the spatial pattern of solar supergranulation using the bispectrum

Context. The spatial power spectrum of supergranulation does not fully characterize the underlying physics of turbulent convection. For example, it does not describe the non-Gaussianity in the horizontal flow divergence. Aims. Our aim is to statistically characterize the spatial pattern of solar supergranulation beyond the power spectrum. The next-order statistic is the bispectrum. It measures correlations of three Fourier components and is related to the nonlinearities in the underlying physics. It also characterizes how a skewness in the dataset is generated by the coupling of three Fourier components. Methods. We estimated the bispectrum of supergranular horizontal surface divergence maps that were obtained using local correlation tracking (LCT) and time-distance helioseismology (TD) from one year of data from the helioseismic and magnetic imager on-board the solar dynamics observatory starting in May 2010. Results. We find significantly nonzero and consistent estimates for the bispectrum using LCT and TD. The strongest nonlinearity is present when the three coupling wave vectors are at the supergranular scale. These are the same wave vectors that are present in regular hexagons, which have been used in analytical studies of solar convection. At these Fourier components, the bispectrum is positive, consistent with the positive skewness in the data and consistent with supergranules preferentially consisting of outflows surrounded by a network of inflows. We use the bispectral estimates to generate synthetic divergence maps that are very similar to the data. This is done by a model that consists of a Gaussian term and a weaker quadratic nonlinear component. Using this method, we estimate the fraction of the variance in the divergence maps from the nonlinear component to be of the order of 4–6%. Conclusions. We propose that bispectral analysis is useful for understanding the dynamics of solar turbulent convection, for example for comparing observations and numerical models of supergranular flows. This analysis may also be useful to generate synthetic flow fields.

Spatial power spectra of dust across the Local Group: No constraint on disc scale height

ABSTRACT We analyse the 1D spatial power spectra of dust surface density and mid to far-infrared emission at $24\!-\!500\, \mu$m in the LMC, SMC, M31, and M33. By forward-modelling the point spread function (PSF) on the power spectrum, we find that nearly all power spectra have a single power-law and point source component. A broken power-law model is only favoured for the LMC 24 μm MIPS power spectrum and is due to intense dust heating in 30 Doradus. We also test for local power spectrum variations by splitting the LMC and SMC maps into 820 pc boxes. We find significant variations in the power-law index with no strong evidence for breaks. The lack of a ubiquitous break suggests that the spatial power spectrum does not constrain the disc scale height. This contradicts claims of a break where the turbulent motion changes from 3D to 2D. The power spectrum indices in the LMC, SMC, and M31 are similar (2.0–2.5). M33 has a flatter power spectrum (1.3), similar to more distant spiral galaxies with a centrally-concentrated H2 distribution. We compare the power spectra of H i, CO, and dust in M31 and M33, and find that H i power spectra are consistently flatter than CO power spectra. These results cast doubt on the idea that the spatial power spectrum traces large scale turbulent motion in nearby galaxies. Instead, we find that the spatial power spectrum is influenced by (1) the PSF on scales below ∼3 times the FWHM, (2) bright compact regions (30 Doradus), and (3) the global morphology of the tracer (an exponential CO disc).

Detecting baryon acoustic oscillations in dark matter from kinematic weak lensing surveys

We investigate the feasibility of extracting baryon acoustic oscillations (BAO) from cosmic shear tomography. We particularly focus on the BAO scale precision that can be achieved by future spectroscopy-based, kinematic weak lensing (KWL) surveys in comparison to the traditional photometry-based weak lensing surveys. We simulate cosmic shear tomography data of such surveys with a few simple assumptions to focus on the BAO information, extract the spatial power spectrum, and constrain the recovered BAO feature. Due to the small shape noise and the shape of the lensing kernel, we find that a Dark Energy Task Force Stage IV version of such KWL survey can detect the BAO feature in dark matter by 3σ and measure the BAO scale at the precision level of 4 per cent, while it will be difficult to detect the feature in photometry-based weak lensing surveys. With a more optimistic assumption, a KWL-Stage IV could achieve a ${\sim } 2{{\ \rm per\ cent}}$ BAO scale measurement with 4.9σ confidence. A built-in spectroscopic galaxy survey within such KWL survey will allow cross-correlation between galaxies and cosmic shear, which will tighten the constraint beyond the lower limit we present in this paper and therefore possibly allow a detection of the BAO scale bias between galaxies and dark matter.

Spatial power spectrum of the photospheric magnetic field during solar minimum

Context. During solar minima the spatial power spectrum of the photospheric magnetic field is dominated by the low-degree zonal (axisymmetric; m = 0) harmonic components, reflecting the large polar coronal holes of unipolar magnetic field. However, measuring polar fields is difficult because of the unequal visibility of the two poles during most of the year and the small line-of-sight component of the roughly radial field at high solar latitudes. Aims. In this paper we derive the spatial power spectrum of the photospheric magnetic field in terms of the harmonic coefficients of the radial component (Br) as well as in terms of the harmonic coefficients of the internal potential (known as Gauss coefficients). We calculate the zonal spatial power spectrum using Mount Wilson Observatory synoptic maps from 1995–1996, during the solar minimum between solar cycles 22 and 23, and investigate how filling or not filling the polar data gaps affects the zonal harmonic coefficients. Methods. We eliminated the vantage point effect by removing the highest 5° of the measured magnetic field and calculating the latitudinal profile of the zonal median field over the two years, which ensured equal latitudinal data coverage of both solar hemispheres. We then derived the zonal harmonic coefficients using this latitudinal profile of Br. Results. We find that when the polar data gaps are left unfilled, a strong artificial power above l = 8 is produced. Only the first five zonal harmonic coefficients can be considered reliable in this case. Therefore polar filling is essential to obtain a realistic spatial power spectrum. Filling the polar gap with a constant (non-zero) value yields zonal harmonics that are reliable up to l = 9. We find that the zonal octupole component contributes most to the total spatial power, more than the zonal dipole, even during the solar minimum conditions. This difference is seen more clearly in the case of polar filling. We also prove that the asymmetry of the polar fields during this solar minimum is statistically significant. Conclusions. Our results emphasize the importance of filling the polar data gaps in order to obtain a correct estimate of the spatial power spectrum of the photospheric field. This helps in estimating the reliability of polar fields and the large-scale structure in synoptic maps of different origin. Our results also verify the asymmetric nature of the polar fields, which is important for the heliospheric magnetic field and for solar dynamo modeling.

In-Depth Exploration of Signal Self-Cancellation Phenomenon to Achieve DOA Estimation of Underwater Acoustic Sources

In the ocean environment, the minimum variance distortionless response beamformer usually has the problem of signal self-cancellation, that is, the acoustic signal of interest is erroneously suppressed as interference. By exploring the useful information behind the signal self-cancellation phenomenon, a high-precision direction estimation method for underwater acoustic sources is proposed. First, a pseudo spatial power spectrum is obtained by performing unit circle mapping on the beam response in the direction interval. Second, the online calculation process is given for reducing the computational complexity. The computer simulation results show that the proposed algorithm can obtain satisfactory direction estimation accuracy under the conditions of low intensity of acoustic source, strong interference and noise, and less array snapshot data.