Interferometric Visibility of a Scintillating Source: Statistics at the Nyquist Limit

We derive the distribution of interferometric visibility for a source exhibiting strong diffractive scintillation, with particular attention to spectral resolution at or near the Nyquist limit. We also account for arbitrary temporal averaging, intrinsic variability within the averaging time, and the possibility of spatially-extended source emission. We demonstrate that the interplay between scintillation and self-noise induces several remarkable features, such as a broad "skirt" in the visibility distribution. Our results facilitate the interpretation of interferometric observations of pulsars at meter and decimeter wavelengths.Comment: 14 Pages, 5 Figures, accepted for publication in Ap

Theory and Simulations of Refractive Substructure in Resolved Scatter-Broadened Images

At radio wavelengths, scattering in the interstellar medium distorts the appearance of astronomical sources. Averaged over a scattering ensemble, the result is a blurred image of the source. However, Narayan & Goodman (1989) and Goodman & Narayan (1989) showed that for an incomplete average, scattering introduces refractive substructure in the image of a point source that is both persistent and wideband. We show that this substructure is quenched but not smoothed by an extended source. As a result, when the scatter-broadening is comparable to or exceeds the unscattered source size, the scattering can introduce spurious compact features into images. In addition, we derive efficient strategies to numerically compute realistic scattered images, and we present characteristic examples from simulations. Our results show that refractive substructure is an important consideration for ongoing missions at the highest angular resolutions, and we discuss specific implications for RadioAstron and the Event Horizon Telescope.Comment: Equation numbering in appendix now matches published version. Two minor typos correcte

Size of the Vela Pulsar's Emission Region at 18 cm Wavelength

We present measurements of the linear diameter of the emission region of the Vela pulsar at observing wavelength lambda=18 cm. We infer the diameter as a function of pulse phase from the distribution of visibility on the Mopra-Tidbinbilla baseline. As we demonstrate, in the presence of strong scintillation, finite size of the emission region produces a characteristic W-shaped signature in the projection of the visibility distribution onto the real axis. This modification involves heightened probability density near the mean amplitude, decreased probability to either side, and a return to the zero-size distribution beyond. We observe this signature with high statistical significance, as compared with the best-fitting zero-size model, in many regions of pulse phase. We find that the equivalent full width at half maximum of the pulsar's emission region decreases from more than 400 km early in the pulse to near zero at the peak of the pulse, and then increases again to approximately 800 km near the trailing edge. We discuss possible systematic effects, and compare our work with previous results

Optimal Correlation Estimators for Quantized Signals

Using a maximum-likelihood criterion, we derive optimal correlation strategies for signals with and without digitization. We assume that the signals are drawn from zero-mean Gaussian distributions, as is expected in radio-astronomical applications, and we present correlation estimators both with and without a priori knowledge of the signal variances. We demonstrate that traditional estimators of correlation, which rely on averaging products, exhibit large and paradoxical noise when the correlation is strong. However, we also show that these estimators are fully optimal in the limit of vanishing correlation. We calculate the bias and noise in each of these estimators and discuss their suitability for implementation in modern digital correlators.Comment: 8 Pages, 3 Figures, Submitted to Ap

On the Ionisation of Warm Opaque Interstellar Clouds and the Intercloud Medium

In this paper we use a number of observations to construct an integrated picture of the ionisation in the interiors of quiescent warm opaque interstellar clouds and in the intercloud medium (ICM) outside dense HII regions and hot dilute bubbles. Our main conclusion is that within $\sim$ 1kpc of the sun the ionisation rate of hydrogen per unit volume in both the interiors of such clouds and in the ICM is independent of the local density of neutral hydrogen, and varies with position by less than $\sim$ 20 per cent. These conclusions strongly favour the decaying neutrino hypothesis for the ionisation of the interstellar medium in these regions. Our analysis is based on a variety of observations, of which the most remarkable is the discovery by Spitzer and Fitzpatrick (1993) that, in the four slowly moving clouds along the line of sight to the halo star HD93521, the column densities of both SII and CII$^*$, which individually range over a factor $\sim$4, are proportional to the column density of HI to within $\sim$20 per cent. This proportionality is used to show that the free electrons exciting the CII to CII$^*$ are located mainly in the interiors of the clouds, rather than in their skins, despite the large opacity of the clouds to Lyman continuum radiation. The same conclusion also follows more unambiguously from the low value of the H$\alpha$ flux in this direction which was found by Reynolds (1996) in unpublished observations. These results are then used, in conjunction with observations of three pulsar parallaxes and dispersion measures, and with data on HeI, NII and OI line emissions, to constrain the ionisation of H, He, N and O and the flux of Lyman continuum photons from O stars in the ICM.Comment: 16 pages, no figures, Latex fil

The Multi-Component Nature of the Vela Pulsar Nonthermal X-ray Spectrum

We report on our analysis of a 274 ks observation of the Vela pulsar with the Rossi X-Ray Timing Explorer (RXTE). The double-peaked, pulsed emission at 2 - 30 keV, which we had previously detected during a 93 ks observation, is confirmed with much improved statistics. There is now clear evidence, both in the spectrum and the light curve, that the emission in the RXTE band is a blend of two separate non-thermal components. The spectrum of the harder component connects smoothly with the OSSE, COMPTEL and EGRET spectrum and the peaks in the light curve are in phase coincidence with those of the high-energy light curve. The spectrum of the softer component is consistent with an extrapolation to the pulsed optical flux, and the second RXTE pulse is in phase coincidence with the second optical peak. In addition, we see a peak in the 2-8 keV RXTE pulse profile at the radio phase.Comment: 12 pages, 3 figures, accepted for publication in Astrophysical Journa

Effects of Intermittent Emission: Noise Inventory for Scintillating Pulsar B0834+06

We compare signal and noise for observations of the scintillating pulsar B0834+06, using very-long baseline interferometry and a single-dish spectrometer. Comparisons between instruments and with models suggest that amplitude variations of the pulsar strongly affect the amount and distribution of self-noise. We show that noise follows a quadratic polynomial with flux density, in spectral observations. Constant coefficients, indicative of background noise, agree well with expectation; whereas second-order coefficients, indicative of self-noise, are about 3 times values expected for a pulsar with constant on-pulse flux density. We show that variations in flux density during the 10-sec integration account for the discrepancy. In the secondary spectrum, about 97% of spectral power lies within the pulsar's typical scintillation bandwidth and timescale; an extended scintillation arc contains about 3%. For a pulsar with constant on-pulse flux density, noise in the dynamic spectrum will appear as a uniformly-distributed background in the secondary spectrum. We find that this uniform noise background contains 95% of noise in the dynamic spectrum for interferometric observations; but only 35% of noise in the dynamic spectrum for single-dish observations. Receiver and sky dominate noise for our interferometric observations, whereas self-noise dominates for single-dish. We suggest that intermittent emission by the pulsar, on timescales < 300 microseconds, concentrates self-noise near the origin in the secondary spectrum, by correlating noise over the dynamic spectrum. We suggest that intermittency sets fundamental limits on pulsar astrometry or timing. Accounting of noise may provide means for detection of intermittent sources, when effects of propagation are unknown or impractical to invert.Comment: 38 pages, 10 figure