Measuring periodic changes in the line-of-sight velocities of stars via spectroscopy (the “radial velocity technique”) is a well-established method to detect planets orbiting stars other than the Sun. As those distant stars orbit their system’s center of mass the radial velocity technique confirms that companions exist and allows for the measurement of fundamental parameters: companion masses, orbital characteristics, and, in some cases, aspects of atmospheric chemistry. Until recently Doppler spectrometers have been limited to detecting radial velocity signals of larger than one meter-per-second, a constraint that significantly hinders our discovery and characterization of small rocky worlds similar to our own. This is the motivation for developing instruments sensitive to extremely precise radial velocities (EPRVs, ??? < 1ms−1). This dissertation describes critical aspects of the development of one such spectrometer: the Palomar Radial Velocity Instrument (PARVI).Chapter 2 presents the characterization of the fine-guiding camera used in the fiber injection unit that couples light from Palomar’s extreme adaptive optics to the spectrograph’s single-mode fiber feed. Chapter 3 describes the data acquisition and data reduction pipelines for PARVI. It includes the methodology for acquiring data with a Teledyne H2RG array, the description of the wavelength calibration using a laser frequency comb, and the process for reducing the 2D echellogram down to a 1D spectrum. Chapter 4 reveals the discovery of a new and significant, polarization-dependent, instrument noise and a warning for those considering using single-mode fibers for high resolution spectroscopy. Chapter 5 contains the first results from PARVI commissioning data. This includes the detection of the Rossiter-Mclaughlin signal of the transiting planet HD 189733 b, and presence of water and carbon monoxide in the atmosphere of HD 189733 b via transmission spectroscopy.

We carried out a near-infrared radial velocity search for Jupiter-mass planets around 36 late M dwarfs. This survey was the first of its kind undertaken to monitor radial velocity variability of these faint dwarfs. For this unique survey we employed the 10-m Keck II on Mauna Kea in Hawaii. With a resolution of 20,000 on the near-infrared spectrograph, NIRSPEC, we monitored these stars over four epochs in 2007. In addition to the measurement of relative radial velocity we established physical properties of these stars. The physical properties of M dwarfs we determined included the identification of neutral atomic lines, the measurement of pseudo-equivalent widths, masses, surface gravity, effective temperature, absolute radial velocities, rotational velocities and rotation periods. The identification of neutral atomic lines was carried out using the Vienna Atomic line Database. We were able to confirm these lines that were previously identified. We also found that some of the lines observed in the K-type stars, such as Mg I though weak, still persist in late M dwarfs. Using the measurement of pseudo-equivalent widths (p-EW) of 13 neutral atomic lines, we have established relations between p-EW and spectral type. Such relations serve as a tool in determining the spectral type of an unknown dwarf star by means of measuring its p-EW. We employed the mass-luminosity relation to compute the masses of M dwarfs. Our calculations indicate these dwarfs to be in the range of 0.1 to 0.07 solar masses. This suggests that some of the late M dwarfs appear to be in the Brown dwarf regime. Assuming their radii of 0.1 solar radii, we calculated their surface gravity. The mean surface gravity is, log g = 5.38. Finally their effective temperature was determined by using the spectral-type iii temperature relationship. Our calculations show effective temperatures in the range of 3000 2300 K. Comparison of these values with models in literature show a good agreement. The absolute radial and rotational velocities of our targets were also calculated. Values of rotational velocities indicate that M dwarfs are, in general, slow rotators. Using our result and that from literature, we extended our study of rotational velocities to L dwarfs. Our observations show an increase in rotational velocities from late M to L dwarfs. We also find that the mean periods of M dwarfs are less than 10 hours. In order to improve our precision in measuring relative radial velocity (RV), we employed the use of deconvolution method. With this method we were able to ameliorate relative RV precision from 300 m/s to 200 m/s. This was a substantial improvement in our ability to detect gas-giant planets. However none of the 15 dwarfs we monitored indicate a presence of companions. This null result was then used to compute the upper limit to the binary frequency and close-in Jupiter mass planetary frequency. We find the binary frequency to be 11% while the planetary frequency was 1.20%.

The detection of low-mass extra-solar planets through radial-velocity searches is currently limited by the intrinsic magnetic activity of the host stars. The correlated noise that arises from their natural radial-velocity variability can easily mimic or conceal the orbital signals of super-Earth and Earth-mass extra-solar planets. I developed an intuitive and robust data analysis framework in which the activity-induced variations are modelled with a Gaussian process that has the frequency structure of the photometric variations of the star, thus allowing me to determine precise and reliable planetary masses. I applied this technique to three recently discovered planetary systems: CoRoT-7, Kepler-78 and Kepler-10. I determined the masses of the transiting super-Earth CoRoT-7b and the small Neptune CoRoT-7c to be 4.73 ± 0.95 M⊕ and 13.56 ± 1.08 M⊕, respectively. The density of CoRoT-7b is 6.61 ± 1.72 g.cm⁻³, which is compatible with a rocky composition. I carried out Bayesian model selection to assess the nature of a previously identified signal at 9 days, and found that it is best interpreted as stellar activity. Despite the high levels of activity of its host star, I determined the mass of the Earth-sized planet Kepler-78b to be 1.76 ± 0.18 M⊕. With a density of 6.2(+1.8:-1.4) g.cm⁻³, it is also a rocky planet. I found the masses of Kepler-10b and Kepler-10c to be 3.31 ± 0.32 M⊕ and 16.25 ± 3.66 M⊕, respectively. Their densities, of 6.4(+1.1:-0.7) g.cm⁻³ and 8.1 ± 1.8 g.cm⁻³, imply that they are both of rocky composition – even the 2 Earth-radius planet Kepler-10c! In parallel, I deepened our understanding of the physical origin of stellar radial-velocity variability through the study of the Sun, which is the only star whose surface can be imaged at high resolution. I found that the full-disc magnetic flux is an excellent proxy for activity-induced radial-velocity variations; this result may become key to breaking the activity barrier in coming years. I also found that in the case of CoRoT-7, the suppression of convective blueshift leads to radial-velocity variations with an rms of 1.82 m.s⁻¹, while the modulation induced by the presence of dark spots on the rotating stellar disc has an rms of 0.46 m.s⁻¹. For the Sun, I found these contributions to be 2.22 m.s⁻¹ and 0.14 m.s⁻¹, respectively. These results suggest that for slowly rotating stars, the suppression of convective blueshift is the dominant contributor to the activity-modulated radial-velocity signal, rather than the rotational Doppler shift of the flux blocked by starspots.