In this paper we use the Cramer-Rao lower uncertainty bound to estimate the maximum precision that could be achieved on the joint simultaneous (or 2D) estimation of photometry and astrometry of a point source measured by a linear CCD detector array.
We develop exact expressions for the Fisher matrix elements required to compute the Cramer-Rao bound in the case of a source with a Gaussian light profile. From these expressions we predict the behavior of the Cramer-Rao astrometric and photometric precision as a function of the signal and the noise of the observations, and compare them to actual observations - finding a good correspondence between them. We show that the astrometric Cramer-Rao bound goes as $(S/N)^{-1}$ (similar to the photometric bound) but, additionally, we find that this bound is quite sensitive to the value of the background - suppressing the background can greatly enhance the astrometric accuracy. We present a systematic analysis of the elements of the Fisher matrix in the case when the detector adequately samples the source (oversampling regime), leading to closed-form analytical expressions for the Cramer-Rao bound. We show that, in this regime, the joint parametric determination of photometry and astrometry for the source become decoupled from each other, and furthermore, it is possible to write down expressions (approximate to first order in the small quantities F/B or B/F) for the expected minimum uncertainty in flux and position. These expressions are shown to be quite resilient to the oversampling condition, and become thus very valuable benchmark tools to estimate the approximate behavior of the maximum photometric and astrometric precision attainable under pre-specified observing conditions and detector properties.
We present the first entirely ground-based astrometric determination of the proper motion for the Fornax Local Group Dwarf Spheroidal satellite galaxy of the Milky Way, using CCD data acquired with the ESO 3.5 m NTT telescope at La Silla Observatory
in Chile. Our unweighted mean from five Quasar fields in the background of Fornax, used as fiducial reference points, leads to $mu_alpha cos delta=0.62 pm 0.16$ $masy$, and $mu_delta=-0.53 pm 0.15$ $masy$. A detailed comparison with all previous measurements of this quantity seems to imply that there is still no convincing convergence to a single value, perhaps indicating the existence of unnacounted systematic effects in (some of) these measurements. From all available proper motion and radial velocity measurements for Fornax, we compute Fornaxs orbital parameters and their uncertainty using a realistic Galactic potential and a Monte Carlo simulation. Properties of the derived orbits are then compared to main star formation episodes in the history of Fornax. All published proper motion values imply that Fornax has recently (200-300 Myr ago) approached perigalacticon at a distance of $sim$150 kpc. However, the derived period exhibits a large scatter, as does the apogalacticon. Our orbit, being the most energetic, implies a very large apogalactic distance of $sim 950$ kpc. If this were the case, then Fornax would be a representative of an hypervelocity MW satellite in late infall.
