80 research outputs found

    Feasibility study of parameter estimation of random sampling jitter using the bispectrum

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    An actual sampling process can be modeled as a random process, which consists of the regular (uniform) deterministic sampling process plus an error in the sampling times which constitutes a zero-mean noise (the jitter). In this paper we discuss the problem of estimating the jitter process. By assuming that the jitter process is an i.i.d. one, with standard deviation that is small compared to the regular sampling time, we show that the variance of the jitter process can be estimated from the n th order spectrum of the sampled data, n =2, 3, i.e., the jitter variance can be extracted from the 2nd-order spectrum or the 3rd-order spectrum (the bispectrum) of the sampled data, provided the continuous signal spectrum is known. However when the signal skewness exceeds a certain level, the potential performance of the bispectrum-based estimation is better than that of the spectrum-based estimation. Moreover, the former can also provide jitter variance estimates when the continuous signal spectrum is unknown while the latter cannot. This suggests that the bispectrum of the sampled data is potentially better for estimating any parameter of the sampling jitter process, once the signal skewness is sufficiently large.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43577/1/34_2005_Article_BF01183740.pd

    A suboptimal estimator of the sampling jitter variance using the bispectrum

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    We consider the problem of estimating parameters of an irregular sampling process defined as a uniform sampling process in which the deviations from the nominal sampling times constitute a random IID process (jitter). Emphasis is placed on estimating the variance of the jitter, based on observation of samples taken from a continuous band-limited third-order stationary process. We derive an estimation procedure which uses the bispectrum estimates of a process with a priori known bispectrum. Derivation of the generalized likelihood ratio in the bispectral domain, leads to a statistic with which a bispectrum-based maximum likelihood estimation can be done. We propose a suboptimal estimator, and show that it is asymptotically unbiased and consistent. The dependence of the estimator's performance on the data length and the skewness is studied for a specific example. The estimator's variance is compared to the bispectrum-based Cramer-Rao bound (BCRB), and is shown to approach it for sufficiently large data length or skewness. Computer simulations verify the effectiveness of the proposed estimation method for small jitter.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31464/1/0000386.pd

    Infrared Spectro-Interferometry of Massive Stars : Disks, Winds, Outflows, and Stellar Multiplicity

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    Interferometry is the ultimate technology for overcoming the limitations which diffraction and the atmosphere-induced seeing impose on the resolution achievable with ground-based telescopes. The latest generation of long-baseline interferometric instruments (in particular VLTI/AMBER and VLTI/MIDI), combines the high spatial resolution (typically a few milliarcseconds) with spectroscopic capabilities, allowing one to characterize the geometry of a continuum-emitting region over a wide spectral range or to spatially resolve the emitting region of Doppler-broadened spectral lines in many velocity channels. One branch of astrophysics which might particularly benefit from these advances in technology is the study of massive (O-B type) stars. In order to characterize these stars and their companions and to study accretion and outflow processes in their vicinity with unprecedented angular resolution, we have performed interferometric studies on four key objects, representing the still most enigmatic evolutionary phases of massive stars; namely the pre-main-sequence (MWC 147, NGC 7538 IRS1, Theta 1 C) and the post-main-sequence phase (Eta Carinae). MWC 147: As indicated by its strong infrared excess, this young Herbig Be star (B6-type) is still associated with residual material from its formation; maybe arranged in a circumstellar disk. In order to investigate the geometry of the material, we combined, for the first time, long-baseline spectro-interferometric observations at near- (NIR) and mid-infrared (MIR) wavelengths (using VLTI/AMBER, VLTI/MIDI, and archival PTI data). Fitting analytic models to the obtained interferometric data revealed a significant elongation of the continuum-emitting region. For a physical interpretation, we modeled the geometry of the dust distribution using 2-D radiative transfer simulations of Keplerian disks with and without a puffed-up inner rim, simultaneously fitting the wavelength-dependent visibilities and the SED, which we complemented with archival Spitzer/IRS spectra. Surprisingly, we found that passive disk models, which can reproduce the SED well, are in strong conflict with the interferometric data. However, when including emission from an optically thick inner gaseous disk, good quantitative agreement was found for all observables, suggesting that MWC 147 harbours a still actively accreting disk. NGC 7538 IRS1/2: NGC 7538 IRS1 is a high-mass (O7-type) protostar with a CO outflow, an associated ultracompact H II region, and a linear methanol maser structure, which might trace a Keplerian-rotating circumstellar disk. We investigated the NIR morphology of the source with unprecedented resolution using NIR bispectrum speckle interferometry obtained at the BTA 6 m and the MMT 6.5 m telescopes. Our high-dynamic range images show fan-shaped outflow structures, in which we detected 18 stars and several blobs of diffuse emission. Complementary archival Spitzer/IRAC images were used to relate the detected structures with the outflow at larger scales. We found a misalignment of various outflow axes and interpreted this in the context of a disk precession model, also using molecular hydrodynamic simulations. As a possible triggering mechanism, we identified non-coplanar tidal interaction of an (yet undiscovered) close companion with the circumbinary disk. Finally, our observations resolved the nearby massive protostar NGC 7538 IRS2 as a close binary with a separation of 195 mas, finding indications for shock interaction between the outflows from IRS1 and IRS2. Theta 1 Orionis C/D: Located in the Orion Trapezium Cluster, Theta 1 C is one of the youngest and nearest high-mass (O5-O7) stars. The star is also known to be a close binary system. We traced the orbital motion from 1997.8 to 2004.8 using visual and NIR bispectrum speckle interferometry at the BTA 6 m telescope. In 2005.9, we obtained first IOTA long-baseline interferometry on the Theta 1 C system, allowing us to derive preliminary solutions for the dynamical orbit and the dynamical mass. Taking the measured flux ratio and the derived location in the HR-diagram into account, we estimated the spectral types and masses of Theta 1 C1 and C2 to be O5.5 (M=34.0 M_sun) and O9.5 (M=15.5 M_sun), respectively. Thus, the companion C2 appears to be much more massive than previously thought, suggesting strong wind-wind interaction during the periastron passage, which we predict for epoch 2007.5 with a small physical separation of only approx. 1.5 AU. From the IOTA data on Theta 1 C, we reconstructed the first optical aperture synthesis image of a young star. We also obtained IOTA data for Theta 1 D, which appears resolved, perhaps indicating the presence of a close, faint companion. Eta Carinae: Using VLTI/AMBER, we performed the first NIR spectro-interferometry of the Luminous Blue Variable (LBV) Eta Car, simultaneously obtaining high spatial and spectral resolutions (R=1,500 and 12,000). The measured wavelength-dependent visibilities, differential phases, and closure phases were used to constrain the geometry of the continuum-emitting region, as well as the Br Gamma 2.166 micron and He I 2.059 micron line-emitting region. We compared the measured visibilities with predictions of the radiative transfer model of Hillier et al. (2001), finding good agreement. For the interpretation of the non-zero differential and closure phases measured within the Br Gamma line, we present a simple geometric model of an inclined, latitude-dependent wind zone. Thus, our observations support theoretical models of anisotropic winds from fast-rotating, luminous hot stars with enhanced high-velocity mass loss near the polar regions. In the He I line, we measured non-zero phases as well, indicating asymmetries in the brightness distribution, which we discuss in the context of wind-wind interaction between Eta Car and its hypothetical hot binary companion. Using simulations, we examined the possibility to directly detect this companion in future observations. Besides these astrophysical results of my dissertation, I present work related to methodological and technical aspects of infrared interferometry. The principles of a data reduction software developed for IOTA/IONIC3 and a pipeline for VLTI/AMBER are discussed. Furthermore, I summarize comparative studies which aim to evaluate the performance of different image reconstruction algorithms in order to explore the prospects and limitations of optical aperture synthesis imaging

    Planck 2013 results. XXIII. Isotropy and statistics of the CMB

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    The two fundamental assumptions of the standard cosmological model – that the initial fluctuations are statistically isotropic and Gaussian – are rigorously tested using maps of the cosmic microwave background (CMB) anisotropy from the Planck satellite. The detailed results are based on studies of four independent estimates of the CMB that are compared to simulations using a fiducial ΛCDM model and incorporating essential aspects of the Planck measurement process. Deviations from isotropy have been found and demonstrated to be robust against component separation algorithm, mask choice, and frequency dependence. Many of these anomalies were previously observed in the WMAP data, and are now confirmed at similar levels of significance (about 3σ). However, we find little evidence of non-Gaussianity, with the exception of a few statistical signatures that seem to be associated with specific anomalies. In particular, we find that the quadrupole-octopole alignment is also connected to a low observed variance in the CMB signal. A power asymmetry is now found to persist on scales corresponding to about ℓ = 600 and can be described in the low-ℓ regime by a phenomenological dipole modulation model. However, any primordial power asymmetry is strongly scale-dependent and does not extend toarbitrarily small angular scales. Finally, it is plausible that some of these features may be reflected in the angular power spectrum of the data, which shows a deficit of power on similar scales. Indeed, when the power spectra of two hemispheres defined by a preferred direction are considered separately, one shows evidence of a deficit in power, while its opposite contains oscillations between odd and even modes that may be related to the parity violation and phase correlations also detected in the data. Although these analyses represent a step forward in building an understanding of the anomalies, a satisfactory explanation based on physically motivated models is still lacking

    Observations of variability of TeV gamma-ray blazars

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    The boom in ground-based gamma-ray astronomy since the beginning of the 21st century has enabled a new probe of the universe using very-high-energy photons. The Very Energetic Radiation Imaging Telescope Array System (VERITAS) is an array of four 12-m imaging Cherenkov telescopes that is sensitive to gamma rays in the energy range between ~100 GeV and ~30 TeV
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