45 research outputs found
A linearized approach to radial velocity extraction
High-precision radial velocity (RV) measurements are crucial for exoplanet
detection and characterisation. Efforts to achieve ~10 cm/s precision have been
made over the recent decades, with significant advancements in instrumentation,
data reduction techniques, and statistical inference methods. However, despite
these efforts, RV precision is currently limited to ~50 cm/s. This value
exceeds state-of-the-art spectrographs' expected instrumental noise floor and
is mainly attributed to RV signals induced by stellar variability. In this
work, we propose a factorisation method to overcome this limitation. The
factorisation is particularly suitable for controlling the effect of localised
changes in the stellar emission profile, assuming some smooth function of a few
astrophysical parameters governs them. We use short-time Fourier transforms
(STFT) to infer the RV in a procedure equivalent to least-squares minimisation
in the wavelength domain and demonstrate the effectiveness of our method in
treating arbitrary temperature fluctuations on the star's surface. The proposed
prescription can be naturally generalised to account for other effects, either
intrinsic to the star, such as magnetic fields, or extrinsic to it, such as
telluric contamination. As a proof-of-concept, we empirically derive a set of
factorisation terms describing the Solar centre-to-limb variation and apply
them to a set of realistic SOAP-GPU spectral simulations. We discuss the
method's capability to mitigate variability-induced RV signals and its
potential extensions to serve as a tomographic tool.Comment: 14 pages, 9 figures. Accepted for publication in MNRA
How to COAAD Images. II. A Coaddition Image that is Optimal for Any Purpose in the Background-dominated Noise Limit
Image coaddition is one of the most basic operations that astronomers perform. In Paper I, we presented the optimal ways to coadd images in order to detect faint sources and to perform flux measurements under the assumption that the noise is approximately Gaussian. Here, we build on these results and derive from first principles a coaddition technique that is optimal for any hypothesis testing and measurement (e.g., source detection, flux or shape measurements, and star/galaxy separation), in the background-noise-dominated case. This method has several important properties. The pixels of the resulting coadded image are uncorrelated. This image preserves all the information (from the original individual images) on all spatial frequencies. Any hypothesis testing or measurement that can be done on all the individual images simultaneously, can be done on the coadded image without any loss of information. The PSF of this image is typically as narrow, or narrower than the PSF of the best image in the ensemble. Moreover, this image is practically indistinguishable from a regular single image, meaning that any code that measures any property on a regular astronomical image can be applied to it unchanged. In particular, the optimal source detection statistic derived in Paper I is reproduced by matched filtering this image with its own PSF. This coaddition process, which we call proper coaddition, can be understood as the maximum signal-to-noise ratio measurement of the Fourier transform of the image, weighted in such a way that the noise in the entire Fourier domain is of equal variance. This method has important implications for multi-epoch seeing-limited deep surveys, weak lensing galaxy shape measurements, and diffraction-limited imaging via speckle observations. The last topic will be covered in depth in future papers. We provide an implementation of this algorithm in MATLAB