Fiber scrambling for precise radial velocities at Lick and Keck Observatories

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1 Fiber scrambling for precise radial velocities at Lick and Keck Observatories J.F.P. Spronck, D.A. Fischer, Z.A. Kaplan and C. Schwab, Department of Astronomy, Yale University, 260 Whitney Ave, New Haven, CT ABSTRACT The detection of Earth analogs with radial velocity requires extreme Doppler precision and long term stability. Variations in the illumination of the slit and of the spectrograph optics occur on time scales of seconds and minutes, primarily because of guiding, seeing and focusing. These variations yield differences in the instrumental profile (IP). In order to stabilize the IP, we designed a fiber feed for the Hamilton spectrograph at Lick and for HIRES at Keck. Here, we report all results obtained with these fiber scramblers. We also present the design of a new double scrambler/pupil slicer for HIRES at Keck. Keywords: Radial velocity, Optical fibers, Astronomical optics, Exoplanet detection 1. INTRODUCTION Since the discovery of the first exoplanet, 1 more than 700 planets have been found using the radial velocity method. Currently, state-of-the-art spectrometers, such as HARPS 2 on the 3.6-m telescope in La Silla and HIRES on Keck I, 3 typically achieve precisions of 1-3 m s 1. 4, 5 This only permits the detection of Super Earth or Neptune-mass planets in relatively short period orbits, or more massive Jupiter-like planets out to several AU. The Earth induces a reflex velocity of only 9 cm s 1 on the Sun, so the search for Earths requires Doppler precisions of about 10 cm s 1, corresponding to typical spectral line shifts across one ten-thousandth of a pixel. Further complicating the analysis, the periodicity of this shift occurs over time scales of months or years for the most interesting planets in the habitable zone. This requirement for a measurement precision of 10 cm s 1 leads to the demand for an instrument that exceeds the stability of current instruments by an order of magnitude. In order to reach the desired precision, we must reduce errors in the model of the instrumental profile, which cross-talk with our measurement of the Doppler shift. In many spectrographs, the starlight is coupled from the telescope to the instrument using a narrow slit. However, the slit illumination varies from observation to observation because of changes in seeing, focus, guiding errors or lack of atmospheric dispersion compensation. Changes in slit illumination affect the spectrum in two ways. Variations in slit illumination produce changes in the shape of the spectral lines since the spectral lines are direct images of the slit. Additionally, changes in slit illumination can result in changes in the illumination of the spectrograph optics. This will in turn introduce different aberrations, which will change the instrumental response. Mathematically, these two effects are modeled simultaneously by convolving the spectrum with the instrumental profile, also known as the spectral line spread function (SLSF), in such a way that any variability impedes our ability to recover Doppler shifts with the desired precision. If the SLSF were unchanging, variations in the final extracted spectrum would be dramatically reduced. Thus, instrumental profile stability has become a focus of current instrumentation work. Optical fibers provide an excellent way to reduce variability in the illumination of the spectrograph. The attribute of fibers that is particularly important today for high-precision Doppler measurements is the natural ability of optical fibers to scramble light 6 9 and produce a more uniform and constant output beam. Because light from the telescope must be efficiently coupled into the fiber, the fiber diameters must match the size of the seeing disk (typically microns), so multi-mode fibers are required. julpronck@gmail.com Ground-based and Airborne Instrumentation for Astronomy IV, edited by Ian S. McLean, Suzanne K. Ramsay, Hideki Takami, Proc. of SPIE Vol. 8446, 84468Z 2012 SPIE CCC code: X/12/$18 doi: / Proc. of SPIE Vol Z-1

2 We have designed optical fiber feeds for the Hamilton spectrograph at Lick Observatory 10, 11 and for HIRES at Keck Observatory 11 that stabilize the illumination of the spectrographs and the SLSF. In this paper, we present the results obtained with these fiber scramblers. We show dramatic improvement in instrumental profile stability. In Section 2, we present the results obtained at Lick Observatory. We show the instrumental profile stability when using the regular slit and the fiber feed. In Section 3, we present the results obtained with a double scrambler. The tests performed on HIRES at Keck Observatory are presented in Section 4. Finally, in Section 5, we present the design of a new fiber scrambler for Keck, that makes use of double scrambling and pupil slicing for improved scrambling and resolution. 2. COMPARISON BETWEEN SLIT AND FIBER USING THE HAMILTON SPECTROGRAPH AT LICK OBSERVATORY In August 2010, extensive tests were carried out to quantify the improvement in instrumental profile stability brought by the fiber scrambler 10 and to identify the remaining sources of error. Observations of stars with known constant radial velocities were made on two consecutive nights. The weather and seeing conditions were nearly identical for both nights. The fiber scrambler was installed for the first night, and the regular observing slit (640 µm wide) was used on the second night. On both nights, an iodine cell was used. As starlight passes through the cell, the molecular iodine imposes thousands of absorption lines in the stellar spectrum. The SLSF is determined by modeling the narrow iodine lines in the spectrum. We use a high resolution (R 1,000,000) spectrum of our iodine cell with SNR 1000, obtained with a Fourier Transform Spectrograph (FTS) at the EMSL division of the Pacific Northwest National Laboratory. This FTS iodine spectrum is convolved with the model SLSF description that gives a best fit to our observations. Our SLSF model consists of 17 Gaussians (1 central main Gaussian and 8 outer ones on each side). Although there are some asymmetries in the wings of the SLSF, we are, in this test, merely interested in the SLSF stability. This can simply be studied by fitting a single Gaussian to the SLSF model. The SLSF must be modeled for small wavelength segments of the echelle spectrum to account for 2-D spatial variations. We fitted a Gaussian to it for each of the spatial regions on the CCD and calculated the average fullwidth half maximum (FWHM) of the Gaussian across the entire detector (only in the iodine region). In reality, the time variation of the FWHM will also be spatially dependent. In other words, the SLSF corresponding to different wavelength segments will have different time behaviors. However, for simplicity, we only considered here spatially-averaged data. Fig. 1 depicts the evolution of the average FWHM for the slit observations (blue squares) and for the fiber observations (red filled circles) through time. The time-dependence variation of the SLSF for the slit observations (blue squares) is quite dramatic. For both nights, the same sequence of observations were taken: a set of B stars, 50 observations of the velocity standard star HD , a second set of B stars, 50 observations of the velocity standard star HD and a third set of B stars. The smooth functional dependence on time for slit observations strongly suggests that the dominant factor in the SLSF variation is the changing illumination of the slit due to monotonic changes in seeing or tracking through different hour angles (which induces systematic errors due to the lack of atmospheric dispersion correction). Through the night, seeing was recorded and there seem to be very little correlation between seeing and the SLSF variations. Also, we refocused the telescope every few observations. This leaves atmospheric dispersion as main culprit for these variations. The peak-to-valley (PTV) amplitude of the variation is about 8% throughout the night. Fig. 1 also shows significant improvement in instrumental profile stability due to the fiber scrambler (red solid dots). However, there is still a slight linear (upward) trend in the fiber data (1%-2% PTV), indicative of incomplete scrambling with the fiber. After removing the linear trend, the residual fluctuation is of the order of 1% PTV. Proc. of SPIE Vol Z-2

3 i69: Fiber run i70: Slit run 1.02 FWHM of the SLSF Time (in hours) Figure 1. Average FWHM of a Gaussian fit to the SLSF for all observations during Night 1 using the fiber (red filled circles) and Night 2 using the slit (blue squares). 3. RESULTS WITH A DOUBLE SCRAMBLER USING THE HAMILTON SPECTROGRAPH AT LICK OBSERVATORY In August 2010, a double scrambler 12, 13 was designed and built (see Fig. 2 (a)). In this double scrambler, a ball-lens injects the far-field 12 of the fiber into a second fiber. The light from the second fiber is then sent to the spectrograph. Because of time constraints, the double scrambler was not optimized and as a consequence, the throughput when used in the Hamilton spectrograph was rather low (15% compared to the slit as opposed to 65% with one fiber only). This low throughput was mainly due to misalignments and the lack of mechanical adjustments. The double scrambler test consisted in taking alternative sets of five B-star observations with the regular fiber scrambler (one fiber only) and with the double scrambler throughout the same night. For each observation, we calculated the SLSF for each region of the CCD and fitted it with a Gaussian. We then calculated the average FWHM of the fit across the entire detector (only in the iodine region). Fig. 2 (b) depicts the evolution of the average FWHM for the single fiber observations (red solid line) and for the double scrambler observations (green dashed line) through the night. Different symbols correspond to different sets of B stars. Even though the scale is different from Fig. 1, we can still see a linear trend in the fiber data (in red solid line) in Fig. 2 (b), indicating imperfect fiber scrambling. In this case, the amplitude of the variation is about 3%. The SLSF obtained with the double scrambler is significantly more stable throughout the night, with no significant (above errors) systematic trend. Instrumental noise can be broken down into two main components: errors due to coupling of the light to the instrument (varying fiber illumination due to guiding, tracking, seeing, focusing and lack of atmospheric dispersion compensation) and environmental instability (mechanical, temperature or pressure). The double scrambler results prove that coupling errors are the dominant source of instrumental noise on short time scales (throughout a night). Residual fluctuations in the double scrambler data from observation to observation have an amplitude of 1%, which is large for precise radial velocities. The source for these fluctuations has not yet been identified but possible culprits include modal noise in the fiber (since the fiber was not agitated to reduce modal noise), photon noise and modeling errors. We do not expect the environmental instability to be responsible for residual fluctuations because of the short time scale of the variability. If these fluctuations are not real, then our errors in modeling the SLSF represent a significant error source for precise radial velocity measurements. In particular, errors in the centroid of the SLSF will cross talk with the wavelength dispersion and introduce errors in our Doppler measurements. Also, errors in the asymmetry of the lines will be directly translated into radial velocity Proc. of SPIE Vol Z-3

4 shifts. The trends depicted in Fig. 2 (b) for the fiber without scrambling are likely to produce systematic velocity errors that average out much more slowly than random errors. (a) Average FWHM of the SLSF Fiber Double Scrambler Time (in hours) (b) Figure 2. (Left) Schematic design of the double scrambler. (Right) Average FWHM of a Gaussian fit to the SLSF for B- star observations taken with the fiber (red solid line) and with the double scrambler (green dashed line). All observations were taken during the same night alternating with the fiber and with the double scrambler. 4. FIBER SCRAMBLER AT KECK During the last week of September 2010, we repeated the tests performed at Lick Observatory at the Keck I telescope using the HIRES spectrograph. The larger aperture telescope at Keck helped to keep the exposure times short so that a large data set could be acquired and so that barycentric errors were minimized. We designed and built a prototype fiber scrambler with a 200-micron 20-m Polymicro fiber. During this test, a single fiber was used. Note that, when using the HIRES spectrograph, atmospheric dispersion is compensated. We collected data on two nights; on September 30, 2010, we used the fiber scrambler and on October 1, 2010, we obtained a similar set of data with the usual slit. On both nights, we collected sets of 25 observations for the standard stars HD and HD For each observation, we use a Levenberg-Marquardt algorithm to model the SLSF. The SLSF model consists of 1 central Gaussian and 16 narrow Gaussians to model the wings of the SLSF. Fig. 3 depicts one of these SLSF parameters (one of the Gaussians in the wing) for all existing observations of HD (left) and HD (right). The blue squares and triangles correspond to slit Proc. of SPIE Vol Z-4

5 observations and exhibit an RMS scatter of for HD 32147, while the fiber observations for the same star (red filled circles) exhibit a dramatically reduced RMS scatter of , demonstrating a factor of 15 improvement in the SLSF stability. The blue triangles correspond to the set of 25 slit observations taken on October 1, Note that, even though only one SLSF parameter is depicted in Fig. 3, other SLSF parameters show similar behavior. These results clearly show that the fiber stabilizes the SLSF, which is crucial for extreme Doppler precisions. SLSF Parameter # Observation number Fiber: 09/30 Slit: 10/01 Slit: all obs. SLSF Parameter # Fiber: 09/30 Slit: 10/01 Slit: all obs Observation number (a) (b) Figure 3. SLSF parameter for all observations of HD (left) and HD (right). Blue squares correspond to slit observations, red dots correspond to fiber observations taken on September 30, 2010, while the blue triangles correspond to sli observations taken on October 1st, DESIGN OF A NEXT GENERATION FIBER SCRAMBLER AT KECK Despite the improvements in SLSF stability with the Keck fiber scrambler, we have not measured improvement in radial velocity precision. We believe this is due to a loss in resolution and SNR with the fiber during that experiment. The low throughput of the fiber scrambler is mainly due to tight tolerances of the design and the small size of all optics involved, which made the alignment very tricky. In order to recover resolution and SNR, we have designed a new fiber scrambler for Keck. In this new design, we pick off the light coming from the telescope and send it into a 200-micron octagonal fiber for better 11, 14 scrambling. Light from the octagonal fiber is sent into a second fiber with the help of a double scrambler. This double scrambler injects the far-field of the octagonal fiber into the second fiber. Additionally, we use a pupil slicer (modified Bowen-Walraven design) to slice the pupil into two half moons to increase the resolution. To take advantage of the increase in resolution while minimizing the light losses, the second fiber is a 100 x 400 µm rectangular fiber. Light from the rectangular fiber is then re-directed towards the spectrograph, which will see a uniformly-lit rectangular fiber, similar to a slit but with extremely stable illumination. We have modeled this double scrambler/pupil slicer using Zemax. Fig. 4 depicts the calculated ray distribution in the plane of the entrance face of the rectangular fiber. The rectangle represents the rectangular fiber. With this model, we estimate that 98% of the rays will enter the rectangular fiber. This does not take into account losses on the various optical surfaces (lenses, mirrors, fibers). However, we have measured the throughput of the double scrambler (without the pupil slicer) to be 98%. Each of the octagonal fiber and the rectangular fiber have a transmission of 90%. If we take into account the throughput of the slicer (assumed to be 90%) and the pick-off and re-imaging optics, we hope to have an overal throughput of about 60% and a resolution of about 80, 000 (as opposed to 40, 000 and a throughput of 40% in the previous version). 6. CONCLUSIONS To summarize, in order to measure spectral line shifts smaller than one ten-thousandth of a pixel and stable for many months, we must reduce errors in our instrumental profile or SLSF, which cross-talks with our measurement Proc. of SPIE Vol Z-5

6 98.1% Figure 4. Zemax footprint diagram in the plane of the entrance face of the rectangular fiber. of the Doppler shift. The instrumental noise can be broken down in coupling errors (slit or fiber illumination) and environmental instability. In this paper, we have shown dramatic improvement in SLSF stability (a factor 10 or more) using a fiber scrambler. These results show that coupling errors are the dominant source of instrumental noise at Lick and Keck observatories. At Lick, we show that double scrambler observations have a more stable SLSF than fiber observations by a factor 3. These have a more stable SLSF than slit observations by a factor 10. The double scrambler data still has residual RMS scatter. The source of this has not yet been identified but is likely to be modal noise, photon noise or modeling errors. We do not expect that the residual scatter can be caused by environmental effects due to the random nature of the variability. At Keck, we demonstrated a factor 15 improvement in SLSF stability using the fiber scrambler. However, we have not measured an improvement in radial velocity precision, most probably due to a loss of resolution and SNR. We designed a new fiber scrambler for Keck, that makes use of a double scrambler and a pupil slicer for improved throughput, resolution and scrambling. ACKNOWLEDGMENTS We acknowledge the support of the Planetary Society, who made possible the development and installation of the fiber feeds at Lick and Keck observatories. The authors would like to thank all staff at Lick and Keck observatories who have helped many times in the implementation of these fiber scramblers. In particular, we are grateful to Scott Dahm and Grant Hill for their very appreciated help. We are also grateful to Kelsey Clubb for helping with the observing runs. DAF acknowledges research support from NSF grant AST and NASA grant NNX08AF42G. The authors wish to recognize and acknowledge the very signicant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. REFERENCES 1. M. Mayor and D. Queloz, A jupiter-mass companion to a solar-type star, Nature 378, pp , M. Mayor, F. Pepe, D. Queloz, F. Bouchy, G. Rupprecht, G. Lo Curto, G. Avila, W. Benz, J.-L. Bertaux, X. Bonfils, T. Dall, H. Dekker, B. Delabre, W. Eckert, M. Fleury, A. Gilliotte, D. Gojak, J. C. Guzman, Proc. of SPIE Vol Z-6

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