Fiber-optic Improved Next generation Doppler Search for Exo-Earths
With support from the Planetary Society we are designing a fiber scrambler with the aim of achieving higher Doppler precision. The advantage of the optical fiber is that it scrambles the starlight and therefore stabilizes the slit and pupil illumination of the spectrometer. This improves our ability to model the instrumental point spread function (described below). At Lick Observatory, this instrument is mounted behind the slit of the Hamilton spectrograph. The first light results from this project were presented by Julien Spronck at the SPIE meeting and proceedings were submitted in "Fiber-stabilized PSF for sub-m/s Doppler precision at Lick Observatory."
With the dramatic improvement in PSF stability, we were prompted to build a prototype at Keck Observatory. However, the space constraints forced Julien Spronck to design an ingenious "matchbox" size version of the Lick Fiber scrambler.
The following plot shows how one of the model PSF parameters varied for observations of a velocity-stable star, HD26965. The first 147 measurements (shown as black dots) were made between August 2004 and September 2010 and show variability with an RMS of 0.15. On the night of Sept 29th, we used a fiber to obtain a series of 25 observations (shown as red dots) and the PSF model is extremely stable with an RMS of about 0.01. This stability is important to improving velocity precision so that we can observe smaller planets. As a control, we removed the fiber on the following night and took 25 observations (with comparable weather and seeing) through the slit (shown as black dots to the right of the red dots). The PSF model again varies strongly. This demonstration of PSF stability with the fiber is exactly what we hoped to achieve.
Our measurement of the Doppler shift, delta lambda = lambda * vel / c, is carried out with forward modeling of our spectra. Our model includes wavelength zero point, dispersion, continuum offset, Doppler shift and 17 additional free parameters that describe the PSF model for ~700 2-Angstrom chunks of the spectrum. We multiply the true intrinsic stellar spectrum (ISS) by the (shifted) FTS iodine spectrum and convolve this product by a PSF description. The best chi-squared fit to the observations allows us to derive the Doppler shift.
The PSF comes from two sources: (1) the optics and pupil illumination pattern in the spectrometer and (2) the slit illumination function. The PSF may change through the night with temperature and pressure changes in HIRES on hour time scales and from changing pupil and slit illumination on time scales of seconds. If the PSF model is wrong, covariance with the wavelength solution can result in errors in the radial velocity measurement. Furthermore, to obtain the ISS, we deconvolve the stellar “template” spectrum (taken without iodine) using a PSF obtained from a spectrum of the iodine cell illuminated by a featureless B-star, which has a different PSF than that of the template. If the slit and pupil illumination were more stable, then we could (1) constrain the PSF model to physically reasonable values and (2) obtain a more accurate deconvolved ISS.