Symmetric Gaussian Model Research Articles

The Intrinsic Structure of Sagittarius A* at 1.3 cm and 7 mm

Abstract Sagittarius A* (Sgr A*), the Galactic Center supermassive black hole (SMBH), is one of the best targets in which to resolve the innermost region of an SMBH with very long baseline interferometry (VLBI). In this study, we have carried out observations toward Sgr A* at 1.349 cm (22.223 GHz) and 6.950 mm (43.135 GHz) with the East Asian VLBI Network, as a part of the multiwavelength campaign of the Event Horizon Telescope (EHT) in 2017 April. To mitigate scattering effects, the physically motivated scattering kernel model from Psaltis et al. (2018) and the scattering parameters from Johnson et al. (2018) have been applied. As a result, a single, symmetric Gaussian model well describes the intrinsic structure of Sgr A* at both wavelengths. From closure amplitudes, the major-axis sizes are ∼704 ± 102 μas (axial ratio ∼ 1.19 − 0.19 + 0.24 ) and ∼300 ± 25 μas (axial ratio ∼1.28 ± 0.2) at 1.349 cm and 6.95 mm, respectively. Together with a quasi-simultaneous observation at 3.5 mm (86 GHz) by Issaoun et al. (2019), we show that the intrinsic size scales with observing wavelength as a power law, with an index ∼1.2 ± 0.2. Our results also provide estimates of the size and compact flux density at 1.3 mm, which can be incorporated into the analysis of the EHT observations. In terms of the origin of radio emission, we have compared the intrinsic structures with the accretion flow scenario, especially the radiatively inefficient accretion flow based on the Keplerian shell model. With this, we show that a nonthermal electron population is necessary to reproduce the source sizes.

New CCD astrometric observations of the five major uranian satellites using Gaia DR1 in 2014–2016

710 CCD frames, observed by 1–m telescope at Yunnan Observatory over 15 nights, have been reduced to derive new precise positions of the five Uranian major satellites (Ariel, Umbriel, Titania, Oberon and Miranda). In the pixel positional measurement of the faint satellites near Uranus, a halo removal procedure similar to that of Veiga et al. (Veiga and Vieira Martins, 1995) was carried out. After that we adopted a two-dimensional symmetric Gaussian model with as high as a third order polynomial to deliver the pixel positions of the concerned satellites. Lastly, the positions of satellites were measured with reference stars from Gaia DR1. The theoretical positions of Uranian satellites were retrieved from the Jet Propulsion Laboratory (JPL) Horizons System that includes the satellite ephemeris ura111, while the position of Uranus was from DE431. We also compared our observations with different satellite ephemerides from the Institut de Mcanique Cleste et de Calcul des phmrides (IMCCE). When Gaia DR1 is used for the reference star catalogue and meanwhile satellites ephemeris is obtained from JPL, our results show that the absolute values of the mean (O-C) (observed minus computed) residuals are not greater than 0.020 arcsec in both right ascension and declination for the five satellites. The positional precision is better than 0.030 arcsec for the four greatest Uranian satellites and 0.050 arcsec for Miranda in each direction.

Percentage points of LRC for testing equality of covariance matrices under intraclass correlation structure

ABSTRACTThe exact null distribution of the likelihood ratio test statistic for testing equality of covariance matrices of q compound symmetric Gaussian models (bivariate or trivariate) has been obtained and percentage points for q ⩽ 5 have been computed. The inverse Mellin transform and calculus of residues have been used to derive these results.

THE SPATIALLY RESOLVED Hα-EMITTING WIND STRUCTURE OF P CYGNI

High spatial resolution observations of the H\alpha-emitting wind structure associated with the Luminous Blue Variable star P Cygni were obtained with the Navy Prototype Optical Interferometer (NPOI). These observations represent the most comprehensive interferometric data set on P Cyg to date. We demonstrate how the apparent size of the H\alpha-emitting region of the wind structure of P Cyg compares between the 2005, 2007 and 2008 observing seasons and how this relates to the H\alpha line spectroscopy. Using the data sets from 2005, 2007 and 2008 observing seasons, we fit a circularly symmetric Gaussian model to the interferometric signature from the H\alpha-emitting wind structure of P Cyg. Based on our results we conclude that the radial extent of the H\alpha-emitting wind structure around P Cyg is stable at the 10% level. We also show how the radial distribution of the H\alpha flux from the wind structure deviates from a Gaussian shape, whereas a two-component Gaussian model is sufficient to fully describe the H\alpha-emitting region around P Cyg.

Distribution of the likelihood ratio statistic for testing homogeneity of covariance matrices of completely symmetric Gaussian models

In this article the distribution of the likelihood ratio test statistic for testing equality of covariance matrices of completely symmetric Gaussian models has been derived in beta series. Comparison of results with the exact results has also been done.

Study on the short-term characteristics of the wind field in Keelung, Taiwan

Short-term characteristics of the wind field and temperature measured in Keelung, Taiwan were studied. The fluctuating components of measured wind speeds and the temperature were fitted with statistical models found in the literature. In general, the distributions of the fluctuating components are skewed, having more pronounced peaks as compared with the symmetric Gaussian model. The Edgeworth's type A Gram–Charlier series expansion was found to be more adequate in describing the statistical properties of the winds. Spectra of the turbulent wind fluctuations are found to follow the − 5 3 -power law at the high-frequency tail. The spectra of the temperature, on the other hand, are usually flat in this region, resembling that of the white noise.

Short-range disorder of Si and Ti in the tetrahedral double-chain unit of synthetic Ti-bearing potassium-richterite

Ti-rich potassium-richterite samples were synthesized at 900°C and 1 kbar PH20 and characterized by Fourier-transform infrared spectroscopy (FTIR) and Rietveld structure refinement. The infrared spectrum of end-member Ti-free potassium-richterite shows a main band at 3734 cm-I assigned to an OH anion bonded to three octahedral Mg cations and directed toward K at the A site facing a tetrahedral ring of composition Si6. When Ti is introduced into the structure, two new overlapping components appear in the infrared spectrum. Using a symmetric Gaussian model, they can be resolved into two single bands at 3711 and 3698 cm-I. These two bands are assigned to OH groups facing rings of tetrahedra with compositions SisTi and Si4Ti2, respectively. Their intensities are linearly related to the Rietveld-refined Ti content at T2 up to 0.8 apfu (atoms per formula unit). The analysis of relative band intensities indicates short-range disorder of Si and Ti over the T2 sites. tensities and to derive the short-range order associated with Si-Ti substitution at the T2 sites in the structure. This work required development of an accurate and physically consistent model for depicting the absorption band shape and for the spectrum-fitting procedure. The situation in the present study is almost ideal: Because the samples were previously characterized by a variety of techniques, and both the location and amount ofTi present in the phase are known, the spectrum-fitting procedure can be optimized. INTRODUCTION In the OH-stretching region of OH-bearing minerals, the measured infrared absorptions are not usually single bands but consist of overlapping components that must be resolved for use in quantitative interpretation. In the past, there has been much infrared spectroscopy done on natural amphiboles (Strens 1966; Burns and Strens 1966; Burns and Greaves 1971), but the method fell into disuse owing to the difficulties involved. Specifically, most natural amphiboles are chemically complex, which introduces too many sources of uncertainty into the spectrum-resolution procedure. However, IR analysis of well characEXPERIMENTAL METHODS terized, compositionally simple, synthetic solid-solutions The amphiboles studied here are those synthesized at is more tractable and provides an ideal situation for ex900°C and 1 kbar PH20by Della Ventura et al. (1991). amining the behavior of OH absorption bands in terms Description of the synthesis conditions and characterizaof multiplicity, position, shape, and intensity. tion methods may be found in Mottana et al. (1990), In the last few years, we have devoted much effort to Della Ventura et al. (1991), and Paris et al. (1993). Along this approach. By experimentally producing selected catthe join between potassium-richterite and the Ti endion substitutions at single structural sites in amphiboles, member of potassium-richterite, a single-phase amphibands can be associated with specific substitutions at parbole was obtained for compositions up to 0.6 apfu of Ti ticular crystallographic sites. These efforts have allowed in the system; for higher Ti contents, minor amounts of us to make progress in understanding some crystal-chemadditional Ti-bearing phases were observed (Della Venical aspects of the clino-amphibole structure (Robert et tura et al. 1991). Only the single-phase experimental al. 1989; Della Ventura and Robert 1990; Della Ventura products (i.e., those with a nominal content up to 0.6 Ti et al. 1991, 1993a; Hawthorne et al. 1993). The evolution apfu in the amphibole) were used for structure refinement ofIR spectra in the OH-stretching region along the Si-Ti by the Rietveld method, with final RB<a88 values in the join for potassium-richterite has been briefly considered range 4-6%. Full details of the XRD data collection and in previous works (Della Ventura and Robert 1988; Della refinement procedures may be found in Della Ventura et Ventura et al. 1991, 1993a). Here we propose a model to al. (1993a, 1993b). Detailed discussion of the Rietveld quantify the Si-Ti substitution from measured band inresults is beyond the scope of the present paper. We merely 0003-004X/96/0 102-0056$05.00 56 DELLA VENTURA ET AL.: Si AND Ti DISORDER IN RICHTERlTE note that, for all samples, the refined tetrahedral site occupancies are coincident (within 20-)with the nominal values. For the FTIR data collection, samples were prepared as KBr pellets using the procedure of Robert et al. (1989). Spectra in the range 4000-3000 cm-I were recorded on a Perkin-Elmer model1760 spectrometer equipped with a DTGS detector and a KBr beam splitter and operating at a nominal resolution of I cm-I. Low-temperature spectra were collected on a Bruker IFSl13V spectrophotometer equipped with a nitrogen-cooled cryostat.

On testing structure of mean vector of compound symmetric gaussian model

In this paper the moments of the likelihood ratio statistic for testing the structure of mean vector of a compound symmetric Gaussian model, have been derived by using the orthogonal transformation of variables. Then the distribution of the test statistic is studied.

NONNULL DISTRIBUTION OF LRC FOR TESTING HOMOGENEITY OF COVARIANCE MATRICES OF COMPLETELY SYMMETRIC GAUSSIAN MODELS

&#x0D; &#x0D; &#x0D; The nonnull moments of the likelihood ratio statistic for testing equality of covariance matrices of completely symmetric Gaussian models are obta.ined in terms of the Lauricella's hypergeometric functions and also in terms of zonal polynomials. Then the nonnull asymptotic distribution of the statistic is derived under certain alternatives for unequal samples. &#x0D; &#x0D; &#x0D;