The LOFAR Global Sky Model (GSM) will be an all-sky database of some 100 million objects, with flux & polarization measurements in the 20-200 MHz range. The primary function of the GSM is to support LOFAR calibration and data reduction. The GSM is expected to provide a model of all sufficiently bright sources in any given field, having enough detail and precision to calibrate and subtract these sources and yield residual images of the faint background. The GSM is expected to be continuously updated and refined during LOFAR operation in a ``closed loop'' of sorts. The GSM is also a valuable stand-alone data product that can be made compatible with the VO.
The instrumental characteristics of LOFAR pose large challenges to GSM design, some of them unique even in the field of very large catalogs. Besides sheer size, this includes highly complex source models (thus making for a very non-uniform database structure), stringent performance requirements for operational use, the need to update source models operationally, and various data management issues. This paper will focus on some of these challenges, discuss our approaches to dealing with them, and present a prototype GSM being developed for the LOFAR Pilot Selfcal System (PSS).
LOFAR is a a large, distributed radio telescope being designed by an international consortium (ASTRON, ATNF, MIT Haystack, NRL). Some architectural features of the current design are:
The unique instrumental characteristics of LOFAR pose new challenges to calibration. This has led us to formulate a requirement for a Global Sky Model (GSM):
The self-calibration algorithm employed in radio astronomy is simple in essence, but extremely difficult in the details. The basic selfcal iteration step consists of predicting the sky, applying instrumental effects, and comparing the results with observed data. The current record for dynamic range with selfcal is , achieved at the WSRT (de Bruin 1996). The LOFAR design target is . A proof of concept study will be carried out using WSRT data, which can potentially yield , given a sophisticated enough calibration approach.
One of the main limiting factors in the dynamic range of selfcal is accuracy of the predict step. An accurate predict requires a sufficiently complex and flexible flux source representation, and a complex enough Measurement Equation (Hamaker, Bregman & Sault 1996).
LOFAR (and other future instruments such as the Square Kilometer Array) requires us to take the next step. This includes more sophisticated source models, in particular spatially extended sources, as well as time and frequency variability of all source parameters.
Operationally, the GSM software must support the following life cycle:
The question of data representation has emerged as one of the central issues of GSM design. This representation must be flexible enough to capture sufficient detail for calibration and imaging. Because of the GSM-calibration-GSM ``closed loop'', the notion of parametrized sources must be explicitly supported by the GSM itself. Thus, what is really required is a non-uniform and extensible source representation.
MeqTrees (Measurement Equation Trees) are a mechanism being developed in the LOFAR Pilot Selfcal System (PSS). A MeqTree1 corresponds to a mathematical expression. The leaf nodes represent parameters and data sources, while nodes down the tree represent derived expressions, such as the predicted visibility of a source in a given direction.
A MeqTree can recursively evaluate its expression, and estimate partial derivatives w.r.t. specific parameters. Thus, a MeqTree can be employed to iteratively solve an equation for a set of parameters. All parameters in the tree ( MeqParms) are polynomials (and in the future, possibly other smooth functions) of frequency and time, so the actual solvables are the individual polynomial coefficients.
Since any mathematical equation can be represented in tree form, PSS-4 (the current development cycle of PSS) should be able to solve for arbitrary measurement equations. Operationally, trees are constructed from a scripting layer, while a fast C++ kernel to evaluate and solve them. In PSS-4, the scripting is provided by the Glish language of AIPS++; support for other languages (primarily Python) will be added in future cycles.
MeqTrees provide a perfect answer to the issue of GSM data representation. To predict the sky, we need to be able to predict the visibility contribution of each source for a given baseline and pointing direction. This, however, may need to be computed differently for different types of sources. By representing a source (or rather, the components of a source, such as the Stokes flux) as a MeqTree, we reap a number of benefits:
Of course, this approach also incurs a number of trade-offs:
An initial version of the LOFAR GSM (GSM-0), is being developed as part of the PSS-4 cycle. This is meant as proof-of-concept implementation, thus we have set the following modest goals:
de Bruin, G. 1996, in High-Sensitivity Radio Astronomy, ed. D. Jackson, 233
Hamaker, J.P., Bregman, J.D., Sault, R.J. 1996, A&AS, 117, 137