Maximum-likelihood astrometric geometry calibration of interferometric telescopes: application to the Very Small Array

Interferometers require accurate determination of the array configuration in order to produce reliable observations. A method is presented for finding the maximum-likelihood estimate of the telescope geometry, and of other instrumental parameters, astrometrically from the visibility timelines obtained from observations of celestial calibrator sources. The method copes systematically with complicated and unconventional antenna and array geometries, with electronic bandpasses that are different for each antenna radiometer, and with low signal-to-noise ratios for the calibrators. The technique automatically focusses on the geometry errors that are most significant for astronomical observation. We apply this method to observations made with the Very Small Array and constrain some 450 telescope parameters, such as the antenna positions, effective observing frequencies and correlator amplitudes and phase shifts; this requires only ~ 1 h of CPU time on a typical workstation.Comment: 9 pages, 8 figures, submitted to MNRA

Searching for non-Gaussianity in the VSA data

We have tested Very Small Array (VSA) observations of three regions of sky for the presence of non-Gaussianity, using high-order cumulants, Minkowski functionals, a wavelet-based test and a Bayesian joint power spectrum/non-Gaussianity analysis. We find the data from two regions to be consistent with Gaussianity. In the third region, we obtain a 96.7% detection of non-Gaussianity using the wavelet test. We perform simulations to characterise the tests, and conclude that this is consistent with expected residual point source contamination. There is therefore no evidence that this detection is of cosmological origin. Our simulations show that the tests would be sensitive to any residual point sources above the data's source subtraction level of 20 mJy. The tests are also sensitive to cosmic string networks at an rms fluctuation level of $105 \mu K$ (i.e. equivalent to the best-fit observed value). They are not sensitive to string-induced fluctuations if an equal rms of Gaussian CDM fluctuations is added, thereby reducing the fluctuations due to the strings network to $74 \mu K$ rms . We especially highlight the usefulness of non-Gaussianity testing in eliminating systematic effects from our data.Comment: Minor corrections; accepted for publication to MNRA

High sensitivity measurements of the CMB power spectrum with the extended Very Small Array

We present deep Ka-band ($\nu \approx 33$ GHz) observations of the CMB made with the extended Very Small Array (VSA). This configuration produces a naturally weighted synthesized FWHM beamwidth of $\sim 11$ arcmin which covers an $\ell$-range of 300 to 1500. On these scales, foreground extragalactic sources can be a major source of contamination to the CMB anisotropy. This problem has been alleviated by identifying sources at 15 GHz with the Ryle Telescope and then monitoring these sources at 33 GHz using a single baseline interferometer co-located with the VSA. Sources with flux densities \gtsim 20 mJy at 33 GHz are subtracted from the data. In addition, we calculate a statistical correction for the small residual contribution from weaker sources that are below the detection limit of the survey. The CMB power spectrum corrected for Galactic foregrounds and extragalactic point sources is presented. A total $\ell$-range of 150-1500 is achieved by combining the complete extended array data with earlier VSA data in a compact configuration. Our resolution of $\Delta \ell \approx 60$ allows the first 3 acoustic peaks to be clearly delineated. The is achieved by using mosaiced observations in 7 regions covering a total area of 82 sq. degrees. There is good agreement with WMAP data up to $\ell=700$ where WMAP data run out of resolution. For higher $\ell$-values out to $\ell = 1500$, the agreement in power spectrum amplitudes with other experiments is also very good despite differences in frequency and observing technique.Comment: 16 pages. Accepted in MNRAS (minor revisions

First results from the Very Small Array -- I. Observational methods

The Very Small Array (VSA) is a synthesis telescope designed to image faint structures in the cosmic microwave background on degree and sub-degree angular scales. The VSA has key differences from other CMB interferometers with the result that different systematic errors are expected. We have tested the operation of the VSA with a variety of blank-field and calibrator observations and cross-checked its calibration scale against independent measurements. We find that systematic effects can be suppressed below the thermal noise level in long observations; the overall calibration accuracy of the flux density scale is 3.5 percent and is limited by the external absolute calibration scale.Comment: 9 pages, 10 figures, MNRAS in press (Minor revisions

Combination of Ferromagnetic and Antiferromagnetic Features in Heisenberg Ferrimagnets

We investigate the thermodynamic properties of Heisenberg ferrimagnetic mixed-spin chains both numerically and analytically with particular emphasis on the combination of ferromagnetic and antiferromagnetic features. Employing a new density-matrix renormalization-group technique as well as a quantum Monte Carlo method, we reveal the overall thermal behavior: At very low temperatures, the specific heat and the magnetic susceptibility times temperature behave like $T^{1/2}$ and $T^{-1}$, respectively, whereas at intermediate temperatures, they exhibit a Schottky-like peak and a minimum, respectively. Developing the modified spin-wave theory, we complement the numerical findings and give a precise estimate of the low-temperature behavior.Comment: 9 pages, 9 postscript figures, RevTe

Estimating the bispectrum of the Very Small Array data

We estimate the bispectrum of the Very Small Array data from the compact and extended configuration observations released in December 2002, and compare our results to those obtained from Gaussian simulations. There is a slight excess of large bispectrum values for two individual fields, but this does not appear when the fields are combined. Given our expected level of residual point sources, we do not expect these to be the source of the discrepancy. Using the compact configuration data, we put an upper limit of 5400 on the value of f_NL, the non-linear coupling parameter, at 95 per cent confidence. We test our bispectrum estimator using non-Gaussian simulations with a known bispectrum, and recover the input values.Comment: 17 pages, 16 figures, replaced with version accepted by MNRAS. Primordial bispectrum recalculated and figure 11 change

Cosmological parameter estimation using Very Small Array data out to l=1500

We estimate cosmological parameters using data obtained by the Very Small Array (VSA) in its extended configuration, in conjunction with a variety of other CMB data and external priors. Within the flat $\Lambda$CDM model, we find that the inclusion of high resolution data from the VSA modifies the limits on the cosmological parameters as compared to those suggested by WMAP alone, while still remaining compatible with their estimates. We find that $\Omega_{\rm b}h^2=0.0234^{+0.0012}_{-0.0014}$, $\Omega_{\rm dm}h^2=0.111^{+0.014}_{-0.016}$, $h=0.73^{+0.09}_{-0.05}$, $n_{\rm S}=0.97^{+0.06}_{-0.03}$, $10^{10}A_{\rm S}=23^{+7}_{-3}$ and $\tau=0.14^{+0.14}_{-0.07}$ for WMAP and VSA when no external prior is included.On extending the model to include a running spectral index of density fluctuations, we find that the inclusion of VSA data leads to a negative running at a level of more than 95% confidence ($n_{\rm run}=-0.069\pm 0.032$), something which is not significantly changed by the inclusion of a stringent prior on the Hubble constant. Inclusion of prior information from the 2dF galaxy redshift survey reduces the significance of the result by constraining the value of $\Omega_{\rm m}$. We discuss the veracity of this result in the context of various systematic effects and also a broken spectral index model. We also constrain the fraction of neutrinos and find that $f_{\nu}< 0.087$ at 95% confidence which corresponds to $m_\nu<0.32{\rm eV}$ when all neutrino masses are the equal. Finally, we consider the global best fit within a general cosmological model with 12 parameters and find consistency with other analyses available in the literature. The evidence for $n_{\rm run}<0$ is only marginal within this model

First results from the Very Small Array -- III. The CMB power spectrum

We present the power spectrum of the fluctuations in the cosmic microwave background detected by the Very Small Array (VSA) in its first season of observations in its compact configuration. We find clear detections of first and second acoustic peaks at l~200 and l~550, plus detection of power on scales up to l=800. The VSA power spectrum is in very good agreement with the results of the Boomerang, Dasi and Maxima telescopes despite the differing potential systematic errors.Comment: 10 pages, 6 figure, MNRAS in press. (Minor revisions - accepted 17 December 2002