The Pennsylvania State University

The Graduate School

Eberly College of Science

A SEARCH FOR PLANETS AROUND RED STARS

A Dissertation in

Astronomy and Astrophysics

by

Sara Gettel

c 2012 Sara Gettel !

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

December 2012 1 The dissertation of Sara Gettel was reviewed and approved by the following:

Alex Wolszczan Evan Pugh Professor of Astronomy and Astrophysics Dissertation Adviser Chair of Committee

Lawrence W. Ramsey Distinguished Senior Scholar & Professor of Astronomy and Astrophysics

John D. Mathews Professor of Electrical Engineering

Mercedes Richards Professor of Astronomy and Astrophysics

Kevin Luhman Associate Professor of Astronomy and Astrophysics

Jason T. Wright Assistant Professor of Astronomy and Astrophysics

Donald P. Schneider Professor of Astronomy and Astrophysics Head of the Department of Astronomy and Astrophysics

1 Signatures on file in the Graduate School. iii Abstract

Our knowledge of planets around other stars has expanded drastically in recent years, from a handful Jupiter-mass planets orbiting Sun-like stars, to encompass a wide range of planet masses and stellar host types. In this thesis, I review the development of radial velocity planet searches and present results from projects focusing on the detection of planets around two classes of red stars.

The first project is part of the Penn State - Toru´nPlanet Search (PTPS) for substellar companions to K giant stars using the Hobby-Eberly Telescope (HET). The results of this work include the discovery of planetary systems around five evolved stars.

These systems illustrate several of the differences between planet detection around giants and Solar-type stars, including increased masses and a lack of short period planets. One planet has a nearly six year orbit, the longest announced to date around a giant star, with an amplitude approaching the limits of detectability due to stellar ‘jitter’. Two more of these systems also show long-term radial velocity trends which are likely caused by the presence of an additional, more distant binary companion. The remaining two systems show increased radial velocity noise, typical of giant systems. Finally I show that, if the stellar jitter is caused by p-mode oscillations, the amplitude of this noise is anti-correlated with metallicity.

The second project focuses on the expansion of the current radial velocity calibra- tion methods to a new wavelength regime. The absorption cell technique is modified to use the telluric O2 and water vapor bands found between 6000-9000 A.˚ These features ∼ iv

1 have been found to be stable to 10 m s− and allow access to the increased red flux ∼ of low-mass and evolved stars. I carry out a mock planet search of six early M dwarfs that are known to be radial velocity stable, providing a recoverable null result. Measure- ments are also made of several telluric standards, to improve the characterization of the atmospheric conditions at the time of observation.

Radial velocities are measured by forward modeling the observations as a combi- nation of a best-fit model telluric spectrum and a deconvolved stellar template, convolved with a best-fit point-spread function (PSF). These measurements are tested using a small number of blocks and compared to analogous measurements made using the standard iodine calibration. This small sample of blocks is then extrapolated to the full wave-

1 length range, yielding a precision of 20 m s− for the iodine calibration and 30 m ∼ ∼ 1 s− for telluric calibration. These relatively modest precisions may be improved in the future both by improving portions of the PSF modeling and deconvolution algorithms, and by increasing the signal-to-noise ratio (S/N) of the observations. Nevertheless, it is reassuring to obtain relatively similar results with the two calibration methods and even with the present level of precision, telluric calibration would be able to detect a

Neptune-mass planet in the habitable zone of an M dwarf. v Table of Contents

List of Tables ...... vii

List of Figures ...... viii

Preface ...... x

Acknowledgments ...... xi

Chapter 1. Introduction ...... 1 1.1 RadialVelocityPlanetDetection ...... 1 1.1.1 Method ...... 1 1.1.2 Stellar Contamination ...... 5 1.1.3 Development ...... 7 1.1.4 Formation & Characteristics of the Exoplanet Population . . 9 1.2 Detecting Planets around Giant Stars ...... 13 1.2.1 Stellar Evolution ...... 14 1.2.2 Lack of Hot Jupiters ...... 16 1.2.3 Metallicity - Planet Frequency Correlation ...... 18 1.2.4 Stellar Mass - Planet Mass Correlation ...... 19 1.2.5 Stellar Variability ...... 20 1.3 Radial Velocity Measurements with Telluric Features ...... 22 1.3.1 Previous Work ...... 22 1.3.2 Detecting Planets around Low Mass Stars ...... 25 1.3.3 Radial Velocity Information Content ...... 26 1.3.4 Potential Uses of Telluric Calibration ...... 28 1.4 Outline ...... 29

Chapter 2. Penn State - Toru´nPlanet Search ...... 42 2.1 Overview ...... 42 2.2 Observations ...... 44 2.3 Measuring Stellar Parameters ...... 45 2.4 Measurements & Modeling of Radial Velocity Variations ...... 47 2.5 Bisector&PhotometryAnalysis ...... 49 2.6 ‘Fuzzy’Systems...... 50 2.6.1 HD 240237 ...... 51 2.6.2 HD 96127 ...... 52 2.6.3 Jitter - Metallicity Correlation ...... 54 2.7 LongPeriodSystems...... 56 2.7.1 HD 219415 ...... 56 2.7.2 Noise Floor ...... 58 2.8 SystemswithRamps...... 59 vi

2.8.1 BD+48 738 ...... 59 2.8.2 BD+20 274 ...... 61 2.8.3 Binary Companions ...... 63 2.9 UnresolvedSystems...... 65 2.9.1 HD 102103 ...... 65 2.10 HighlightsofthePTPSSurvey ...... 68

Chapter 3. Observations of Radial Velocity Stable M Dwarfs ...... 100 3.1 Targets ...... 101 3.2 Data Collection ...... 101 3.3 Data Reduction ...... 103 3.4 Wavelength Calibration with ThAr ...... 106

Chapter 4. Forward Modeling of Radial Velocity Measurements ...... 111 4.1 IodineTechnique ...... 111 4.1.1 Requirements for Precise Doppler Measurements ...... 111 4.1.2 Modeling the Observations ...... 113 4.1.3 Results with Iodine Calibration ...... 116 4.2 Modification of the Iodine Technique for Telluric Features ...... 118 4.3 ModelingTelluricSpectra ...... 119 4.4 GeneratingStellarTemplates ...... 121 4.5 Testing at 5900 A...... ˚ 122 4.6 Extrapolation to Other Bands ...... 124

Chapter 5. Summary & Future Prospects ...... 148 5.1 Summary ...... 148 5.1.1 Planets around Giant Stars ...... 148 5.1.2 Measuring Radial Velocities with Telluric Lines ...... 152

Bibliography ...... 155

Appendix. Permissions ...... 167 vii List of Tables

1.1 GiantStarswithPlanets...... 37

2.1 StellarParameters ...... 69 2.2 OrbitalParameters...... 70 2.3 Possible Orbital Solutions for HD 102103 ...... 70 2.4 Planet-Hosting Giants with Published RMS Values ...... 71 2.5 Relative Radial Velocity Measurements of HD 240237 ...... 72 2.6 Relative Radial Velocity Measurements of HD 96127 ...... 73 2.7 Relative Radial Velocity Measurements of HD 219415 ...... 74 2.8 Relative Radial Velocity Measurements of BD+48 738 ...... 75 2.9 Relative Radial Velocity Measurements of BD+20 274 ...... 76 2.10 Relative Radial Velocity Measurements of HD 102103 ...... 78

3.1 Radial Velocity Stable Targets ...... 108

4.1 PhotonLimitedVelocityPrecision ...... 143 viii List of Figures

1.1 RadialVelocityDiscoverySpace ...... 30 1.2 Starspot Contamination ...... 31 1.3 LineBisectorVariations ...... 32 1.4 Lack of Hot Jupiters around Giant Stars ...... 33 1.5 MetallicityDependenceofDwarfs&Giants ...... 34 1.6 MetallicityDependenceofGiants ...... 35 1.7 StellarMass-PlanetMassDependence ...... 36 1.8 R-band Atmospheric Transmission ...... 38 1.9 K&MDwarfFlux...... 39 1.10 Reflex Amplitude in the Habitable Zone ...... 40 1.11GiantStarFlux...... 41

2.1 HR Diagram of PTPS Targets ...... 81 2.2 Radial Velocity Measurements of HD 240237 ...... 82 2.3 Bisector & Photometry Measurements of HD 240237 ...... 83 2.4 Radial Velocity Measurements of HD 96127 ...... 84 2.5 Bisector & Photometry Measurements of HD 96127 ...... 85 2.6 StellarJitterv.Metallicity ...... 86 2.7 Radial Velocity Measurements of HD 219415 ...... 87 2.8 Bisector & Photometry Measurements of HD 219415 ...... 88 2.9 GiantStarDiscoverySpace ...... 89 2.10 Radial Velocity Measurements of BD+48 738 ...... 90 2 2.11 χ grid of BD+48 738 ...... 91 2.12 Bisector & Photometry Measurements of BD+48 738 ...... 92 2.13 Radial Velocity Measurements of BD+20 274 ...... 93 2.14 Bisector & Photometry Measurements of BD+20 274 ...... 94 2.15 Radial Velocity Measurements of HD 102103 ...... 95 2.16 Radial Velocity Measurements of HD 102103 ...... 96 2.17 Bisector & Photometry Measurements of HD 102103 ...... 97 2.18 Bisector & Photometry Measurements of HD 102103 ...... 98 2 2.19 χ grid of HD 102103 ...... 99

3.1 Sample Target and Telluric Standard Spectra ...... 108 3.2 Cross-DisperserRepeatability ...... 109 3.3 Cross-Disperser Repeatability with Consecutive Measurements . . . . . 110

4.1 SampleIodineBlock ...... 128 4.2 Iodine Radial Velocities of GJ 184 ...... 129 4.3 Iodine Radial Velocities of GJ 272 ...... 130 4.4 Iodine Radial Velocities of GJ 277.1 ...... 131 4.5 Iodine Radial Velocities of GJ 281 ...... 132 4.6 Iodine Radial Velocities of GJ 328 ...... 133 ix

4.7 Iodine Radial Velocities of GJ 353 ...... 134 4.8 SampleTelluricBlock ...... 135 4.9 TelluricModelingwithTERRASPEC ...... 136 4.10 Radial Velocities Measured with Telluric Features ...... 137 4.11 Radial Velocities Measured with Iodine Features ...... 137 4.12 Information Content of Telluric Spectrum with 1.0 cm PWV ...... 138 4.13 Information Content of Telluric Spectrum with 0.5 cm PWV ...... 139 4.14 Information Content of Iodine Spectrum ...... 140 4.15 Information Content of Solar Spectrum ...... 141 4.16 Information Content of M0 Spectrum ...... 142 4.17 Photon-limited Velocity Precision with Simulated Counts for Sun-like Star Using I2 Features ...... 144 4.18 Photon-limited Velocity Precision with Simulated Counts for M0 Dwarf Using I2 Features...... 144 4.19 Photon-limited Velocity Precision with Simulated Counts for M0 Dwarf UsingTelluricBandswith1.0cmPWV ...... 145 4.20 Photon-limited Velocity Precision with Simulated Counts for M0 Dwarf UsingTelluricBandswith0.5cmPWV ...... 145 4.21 Photon-limited Velocity Precision with Observed Counts for Sun-like Star Using I2 Features...... 146 4.22 Photon-limited Velocity Precision with Observed Counts for M0 Dwarf Using I2 Features...... 146 4.23 Photon-limited Velocity Precision with Observed Counts for M0 Dwarf UsingTelluricBandswith1.0cmPWV ...... 147 4.24 Photon-limited Velocity Precision with Observed Counts for M0 Dwarf UsingTelluricBandswith0.5cmPWV ...... 147 x Preface

The material in Chapter 2, except for Sections 2.1, 2.9 and 2.10, has been pub- lished in a substantially similar form as:

Substellar-Mass Companions to the K-Giants HD 240237, BD +48 738 and HD 96127 Gettel, S., Wolszczan, A., Niedzielski, A., Nowak, G., Adam´ow, M., Zieli´nski, P. & Ma- ciejewski, G., Astrophysical Journal, 745 (2012) 28

Planets around the K-Giants BD+20 274 and HD 219415 Gettel, S., Wolszczan, A., Niedzielski, A., Nowak, G., Adam´ow, M., Zieli´nski, P. & Ma- ciejewski, G., Astrophysical Journal, 756 (2012) 53 and this material is reproduced by permission of the AAS. Chapter 2 describes the detection of five planetary systems. The data reduction, radial velocity measurements, bisector and photometry measurements, and stellar char- acterization described therein were performed by my coauthors. I carried out the orbit fitting and all further analyses of the unique features of these systems, including charac- terization of the long period orbits and development of the jitter-metallicity correlation. xi Acknowledgments

I would like to thank my advisor Dr. Alex Wolszczan for giving me countless valuable opportunities, beginning with allowing me to work on these projects, and sup- porting me throughout the process. I would like to thank my PTPS collaborators Dr. Andrzej Niedzielski, Dr. Grzegorz Nowak, Monika Adam´ow, Pawel Zieli´nski and Gracjan Maciejewski for their timely assistance and many contributions to the K giant projects. I would like to thank Sharon Wang for teaching me to use her software. I would like to thank Dr. Chad Bender for help with TERRASPEC and for makingmeabetter observer. I would like to thank Dr. Jason Wright for much guidance, both on the science of planet hunting and on being a scientist. I would like to thank the Penn State Astron- omy & Astrophysics Department, the Penn State Center for Exoplanets and Habitable Worlds and NASA for financial support. I would like to thank the California Planet Search for the use of a Keck stellar template and Dr. John Johnson for the use of his radial velocity code. I would like to thank Dr. Grzegorz Pojmanski for the specialized lightcurve of HD 102103. I would like to thank my Dissertation Committee members for their patience and advice over the last few years. Finally, I would like to thank Reuben for having faith in me and my parents for tireless love and support.

This research has made use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at exoplanets.org. This research has made use of NASA’s Astrophysics Data System Bibliographic Services. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universi- ties for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. The HET is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universit¨at M¨unchen, and Georg-August-Universit¨atG¨ottingen. The HET is named in honor of its principal benefactors, William P. Hobby and Robert E. Eberly. The Center for Exoplan- ets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium. 1

Chapter 1

Introduction

Over the last twenty years, the detection of planets around other stars has changed from a theoretical possibility to a diverse and exciting field of study. Beginning with the discovery of companions to PSR B1257+12 (Wolszczan & Frail 1992) and 51 Pegasi

1 (Mayor & Queloz 1995), we now know of 518 stars hosting 640 confirmed planets .

These have been found through a variety of methods, including transit photometry, microlensing and more recently, direct observation. The radial velocity method was the first to be widely used and remains one of the most prolific, responsible for about two-thirds of currently known systems, which are shown in Figure 1.1.

1.1 Radial Velocity Planet Detection

1.1.1 Method

The radial velocity method detects planets indirectly, observing the reflex motion of the host star that is induced by a less massive companion along the line of sight. This motion can be detected spectroscopically, observing the small Doppler shifts of the star’s spectral lines due to its motion about the system barycenter.

Radial velocity measurements can determine five elements of a binary orbit: P , the orbital period, T , the time of periastron passage, e, the orbital eccentricity, ω,the

1 exoplanets.org (Wright et al. 2011) 2 longitude of periastron passage and a1, the stellar semimajor axis. The radial velocity of the star is then

2πa1sin(i) Vr(θ)= [cos(θ + ω)+e cos(ω)] (1.1) P √1 e2 · − where i is the orbital inclination and θ is the true anomaly of the star. The amplitude of the orbit is designated K. These are relative measurements, as the system typically has some net radial velocity, V0, with respect to Earth. Radial velocity measurements are made as a time series, Vr(t), requiring a transformation into θ

2π E e sin(E)= (t T ) (1.2) − · P −

1 2 θ 1+e / E tan = tan (1.3) !2" !1 e" ! 2 " − where E is the mean anomaly of the star. Assuming the mass of the star, m1 is known, a lower limit to the mass of the companion, m2 sin(i) can be calculated as

3 3 2 3/2 3 m2sin(i) (1 e ) K P 2 = − (1.4) (m1 + m2) 2πG

where typically m1 >> m2. For a fixed radial velocity precision, the signal will be stronger when the planet is more massive or has a shorter period.

It is not possible to determine inclination using radial velocity measurements alone, as we only measure motion in the direction of the line of sight. As a result, the true mass of the planet cannot be determined. However, Jorissen et al. (2001) 3 showed that the value of sin(i) is statistically likely to be near unity, assuming a random distribution of orbit orientations. The minimum mass of the planet, m2 sin(i)islikely to be accurate to within 15%.

The biggest challenge of the radial velocity method is that the stellar velocities must be measured with very high precision. The reflex motion of the Sun induced by

1 1 Jupiter is 13 m s− , while for Earth it is only 8cms− . The precision limit of the ∼ ∼ 1 best surveys is currently 1ms− . ∼ The non-relativistic Doppler equation is expressed as

∆λ V = r (1.5) λ c where λ is the reference wavelength at zero velocity, ∆λ is the observed wavelength shift and c is the speed of light. For optical wavelengths, the K value of Jupiter produces a

4 wavelength shift of ∆λ 10− A,˚ much less than the resolution of a typical spectrograph. ∼ As a result, it is necessary to statistically combine the Doppler shift of many lines across a stellar spectrum. The best targets for measuring radial velocities are cool stars

(F, G, K and M spectral types), which have numerous spectral lines. The amount of velocity information in a given line is determined by its slope, and can be measured as the change in the number of photons detected per pixel. Broad spectral lines therefore contain little radial velocity information and so rapidly rotating stars make difficult targets.

For precision radial velocity measurements, it is also necessary to accurately cal- ibrate wavelengths to detector pixels. This is challenging as small adjustments in the 4 spectrograph will cause the location of a given wavelength to change over time. These effects include pressure and temperature changes, as well as mechanical effects. Wave- length calibration is typically achieved in one of two ways, either by taking concurrent spectra of a emission lamp and the target star, or by observing the target through an absorption cell, superimposing the calibration spectrum on the target spectrum.

The emission lamp technique typically uses a Thorium-Argon (ThAr) arc lamp, with spectral features from 390 nm to 1.1 µm. Here, the calibration lamp and target star are observed through two separate fibers, ideally at the same time. A high degree of instrumental stability is required, as the two spectra have different optical paths and any changes to the spectrograph will affect them differently. The stellar spectra are then cross-correlated with a template, using a mask to select suitable lines. The cross-correlation function combines the radial velocity information in these lines and the radial velocity shift is measured as the change in the center of the cross-correlation profile. This technique has been used with great success by the Swiss planet hunting team using HARPS and its predecessors (Baranne et al. 1996; Mayor et al. 2003; Mayor

& Queloz 2012).

In the absorption cell technique, the target star is observed through a gas cell that is inserted into the optical path. Several different calibrators have been used, including hydrogen fluoride (HF), ammonia in the near infrared and most commonly, molecular iodine (I2) in the optical. The iodine spectrum consists of many sharp, stable lines between 505 and 620 nm. Though the wavelength range is less than for ThAr, the spectrum is much denser. As both the target and calibrator are observed with a single

fiber, the instrumental stability requirements are less stringent than with ThAr, though 5 it is still beneficial to keep the spectrograph at a constant temperature and pressure. A drawback to this method is the significant loss of throughput due to the absorption cell and the alteration of stellar line profiles due to blending. Radial velocities are determined by making a model of the observation using an intrinsic spectrum of the iodine cell and a template of the stellar spectrum made by observing the star without the gas cell. The radial velocity shift of the star with respect to the template is left as a free parameter and measured by iterative fitting. I use a variant on the absorption cell technique, which will be described in further detail in Section 4.1.

1.1.2 Stellar Contamination

Many stars undergo significant intrinsic radial velocity variations, due to such phenomena as non-radial pulsation, inhomogeneous convection or starspots. Spot activ- ity in particular is known to contaminate radial velocity surveys with false detections of planets. A notable example is the ‘hot Jupiter’ detected around HD 166435 that was later shown to be caused by a starspot (Queloz et al. 2001). Figure 1.2 illustrates the effect of a dark spot on a rotating star. A spot on the approaching (blueshifted) side of the star causes less light to be detected from that region. As we measure the integrated spectrum of the entire stellar disk, this is observable as light ‘missing’ from the blue side of the stellar line profile, generating a net redshift. As the star rotates, the spot crosses to the receding (redshifted) side of the star and this effect is reversed, causing light to be missing from the red side of the line profile and a net blueshift.

This radial velocity signal is similar to that of a planet, with the key difference that orbital motion does not alter the spectral line profiles, as the presence of a planet 6 should not affect the photosphere of the star. Thus, it is important to monitor changes in the line profile. This is usually done by measuring the bisector of the line profile at several depths. Line bisectors are frequently characterized by the bisector velocity span

(BVS), or the difference between the top and bottom part of the bisector. If changes in the line bisector are correlated with radial velocity variations, as seen in Figure 1.3, the signal is likely due to stellar activity rather than a companion. Bisector changes due to a spot may be too small to detect, so it is important to consider other diagnostics as well.

Starspots are often found at two or three ‘active longitudes’ that persist in the same location, sometimes for years (Usoskin et al. 2005). Radial velocity variations caused by starspots will exhibit a period that is an integer fraction of the stellar rotation period, which can be calculated if the stellar radius and projected rotational velocity, V sin(i) are known. Unfortunately, most high-resolution spectrographs are not capable of

1 resolving rotational line broadening below V sin(i) of a few km s− , so for slowly rotating stars it is often only possible to measure a lower limit to the rotation period. As such, it is also useful to examine any available photometric time series of the target star to check for brightness variations consistent with the period of the radial velocity variations.

In addition to false detections, motions in the atmosphere of the target star can induce significant noise in the radial velocity measurements. Solar-type stars undergo acoustic oscillation modes and atmospheric granulation with timescales of order five minutes. This effect can be ameliorated by taking long exposures to average over the acoustic noise. 7

1.1.3 Development

Prior to the late 1970s, radial velocity measurements had a typical precision of 1 ∼ 1 km s− (Wilson 1953), two orders of magnitude larger than would be required to detect

Jupiter orbiting the Sun. These large errors were due to technological limitations, i.e., the difficulty of measuring a Doppler shift using photographic plates and guiding errors at the spectrograph slit. Significant advances were made over the following decades,

1 allowing for 3 m s− precision shortly after the first radial velocity planet detections

1 (Butler et al. 1996) and sub-1 m s− precision today (Mayor & Queloz 2012).

One of the first gas cell surveys was undertaken by Campbell & Walker (1979) using the Canada France Hawaii 3.6 m telescope. They used a hydrogen fluoride ab- sorption cell, chosen for its well-spaced, stable spectral lines. However, in addition to a wavelength range of only 100 A,˚ HF has the disadvantage of being highly corrosive

1 and toxic. Nevertheless, they were able to achieve precisions of 13 m s− for individual ∼ exposures and carried out an observing program of several main sequence and giant stars over the course of twelve years. Some of these stars showed hints of radial velocity vari- ations consistent with planet-mass companions, including Pollux and γ Cep (Campbell et al. 1988) which were eventually confirmed by other surveys. However, at the time it was not clear if the observed variations were due to a planet or simply stellar activity.

Around the same time, Mayor & Queloz began a radial velocity survey, using the

CORAVEL spectrograph on the Observatoire Haute-Provence 1 m telescope (Baranne

1 et al. 1979). They used the cross-correlation technique, with a precision of 250 m s− ∼ limited by the changing atmospheric conditions inside the spectrograph and the width 8 of the entry slit. The survey was intended to detect low-mass companions to solar-type stars and was able to verify the presence of the very low mass brown dwarf around HD

114762 detected by Latham et al. (1989). Baranne et al. (1996) later developed ELODIE, a spectrograph featuring several notable improvements that are now standard, including a CCD detector and an optical fiber feed to the spectrograph. The latter stabilizes the point-spread function (PSF) and decreases guiding and focus effects. Along with the introduction of simultaneous ThAr exposures, these developments improved the RV

1 precision to 15 m s− . The radial velocity survey with ELODIE began in 1994, focusing ∼ on 142 solar-type stars. By the end of the following year, they announced the detection of a half Jupiter-mass planet in a 4.2 day orbit around 51 Peg - the first exoplanet around a solar-type star (Mayor & Queloz 1995).

Marcy & Butler (1992) began the California Planet Search (CPS) by testing pre- cise Doppler measurements using the Hamilton spectrograph on the Lick 3 m telescope.

They used a temperature-controlled I2 gas cell to achieve an initial precision of 25 ∼ 1 ms− over the course of a year, though with increased throughput and much shorter observing time than the CFHT survey. As the iodine spectrum is much denser than HF, radial velocity measurements must be made by reconstructing the combined star+iodine spectrum, using an accurate model of the spectrograph’s PSF. Over the next few years they expanded the survey to use the Keck HIRES spectrograph and reached a consistent

1 precision of 3 m s− by carefully modeling the changes of the PSF as a function of wave- length and instrumental changes (Butler et al. 1996). The photon-weighted midpoint of the observations was also measured using a photometer, to correct for the topocentric velocity relative to the Solar System barycenter. They confirmed the detection of 51 Peg 9 b (Marcy & Butler 1995) and both planet-hunting teams have since carried out highly successful surveys around main sequence stars.

Many improvements have been made since those first planet detections. The

HARPS spectrograph (Mayor et al. 2003) introduced many instrumental modifications designed to increase RV stability, including vacuum operation, strict temperature control and the absence of moving parts. Careful calibration of changes in the ThAr lamp

1 over time and improvement of the image reduction led to a precision of <1ms− on bright stars (Pepe & Lovis 2008). The CPS team has improved itsmodelingprocedure, most notably by replacing the Jansson deconvolution algorithm used to create intrinsic stellar templates with a custom deconvolution algorithm (Howard et al. 2009). These

1 1 changes increased their precision to 1.5 m s− long term and <1ms− with binned ∼ measurements.

1.1.4 Formation & Characteristics of the Exoplanet Population

Prior to the detections of 51 Peg b in a very short orbit and 70 Vir b in an eccentric orbit (Marcy & Butler 1996), it was generally thought that all planetary systems would look like our own. Since then hundreds of planets have been detected, with a broad range of characteristics. Most detections have been made with the radial velocity or transit techniques, both of which provide well-characterized orbits, and we now have a robust sample with which to study the exoplanet population as a whole.

By the official IAU definition, the term ‘planet’ applies to ‘objects with true masses below the limiting mass for thermonuclear fusion of deuterium (currently calculated to be

13 Jupiter masses for objects of solar metallicity) that orbit stars or stellar remnants’, 10 no matter how they formed. Substellar objects more massive than 13 MJ are called brown dwarfs. This definition was intended to be temporary and is controversial, as there are no observable markers of deuterium burning. Instead, many in the scientific community have come to use formation mechanisms to distinguish between planets and brown dwarfs.

Brown dwarfs are thought to form like stars, directly from a contracting cloud of gas and dust. In contrast, in the standard core-accretion model, planets are created as a byproduct of star formation. As a protostellar cloud of gas and dust collapses, the conservation of angular momentum creates a flat disk of material. Particles in the disk collect into ‘planetesimals’ over several million years. In the outer portion of the disk where it is cool enough for ices to form, planetesimals reaching 10 M⊕ undergo runaway ∼ accretion of gas to form gaseous giant planets. Inside of the ‘ice line’, temperatures are too high for volatiles to condense and rocky planets are formed. This process is halted when the disk evaporates, after a lifetime of 1-10 Myr (Ida & Lin 2004).

The broad characteristics of the known exoplanet population support this theory, albeit with some modifications. The existence of ‘hot Jupiters’, giant planets with orbital periods of a few a days, was completely unexpected, as the high temperatures so close to the parent star should inhibit the formation of massive planets. This issue is resolved by allowing planets to migrate as they form. Models by Ida & Lin (2004), among others, suggest that during the accretion process, planets interact with the disk and so are able to migrate quickly over large distances. Migration stops when the disk is much less massive than the planet, allowing for a range of final semi-major axes encompassing both

Jupiter at 5 AU, and the abundance of planets with periods of 3days.Furtherevidence ∼ 11 for planetary migration comes from the several multi-Jupiter systems in mean-motion resonance, as planets are expected to form at arbitrary locations in the disk and these were likely captured into resonance as their orbits evolved (Marcy et al. 2001; Correia et al. 2009).

The orbital eccentricities of exoplanets range from about zero to >0.9, in con- trast to the nearly circular orbits of our own Solar System (Butler et al. 2006). The high-eccentricity planets were another surprise, as the standard formation model favors circular orbits. These eccentricities are likely caused by dynamical interactions in mul- tiplanet systems (Ford & Rasio 2008).

The frequency of gas giant planets is strongly dependent on the orbital period, increasing with log(P ) (Marcy et al. 2005; Udry & Santos 2007). The upper mass limit of these planets also increases with log(P ) (Udry et al. 2003). Both of these results are consistent with the classical core accretion model, as the amount of material at a given radius increases with distance from the star and so there is more material available to be accreted by a planet. Similarly, the core accretion model predicts that more massive stars will produce more massive planets, as there is more material in the disk with which to form planets. Statistical analyses of uniform samples bear this out (Lovis & Mayor 2007;

Johnson et al. 2010a), with very few Jupiter-mass planets detected around M dwarfs and giant stars evolved from F and A dwarfs hosting a disproportionate number of Jupiters, as well as brown dwarfs (Quirrenbach et al. 2011).

The metallicity of the host star is also strongly correlated with the frequency of giant planets, with this result observed in many early, unbiased studies (Santos et al.

2004b; Fischer & Valenti 2005) and directing planet search efforts to favor more metallic 12 stars. It is not yet clear whether this trend also holds for Neptune-mass planets, with early studies suggesting the absence of a correlation (Udry et al. 2006), but ambiguous results in more recent work (Mayor & Queloz 2012). In giant planets, this correlation results from the accretion process, with the observed stellar metallicity reflecting the initial metallicity of the protoplanetary disk and indicating a high dust-to-gas ratio. A dust-rich environment allows the planetary core to grow faster and makes it more likely to become massive enough to undergo runaway gas accretion before the disk evaporates.

The possible lack of a metallicity correlation in Neptunes may be real, as less massive planets do not accrete as much gas and so have more time in whichtobuilduptheir cores (Mordasini et al. 2012).

The observed planet mass distribution is consistent with this dichotomy in for- mation. A recent analysis of the HARPS planets with P>100 days (Mayor et al.

2011) indicates a bimodal distribution, with a gap between 40-60 M⊕ where any existing planets should be detectable. Below this gap is the emerging population of planets with masses ranging from Neptune-sized to a few times the mass of the Earth. While we have only been able to detect such small planets over the last several years, beginning with Santos et al. (2004a) and Butler et al. (2004), a few trends can be seen among the population of Neptunes and Super-Earths. Unlike systems with multiple Jupiters, multi- planet systems with several low-mass planets are not resonant (Mayor et al. 2009). They also show a smaller range of eccentricity values, with a maximum of e 0.45 (Mayor ∼ et al. 2011), suggesting that low-mass planets are not subject to dynamical interactions in the way that Jupiters are. Current formation models predict that giants make up 13 only 10% of all planets (Alibert et al. 2011), suggesting many more planets will be ∼ discovered in the near future.

1.2 Detecting Planets around Giant Stars

Although the majority of planets searches to date have focused on FGKM dwarfs, planets have been found around stars in a wide variety of evolutionary states, includ- ing neutron stars (Konacki & Wolszczan 2003), subdwarfs (Silvotti et al. 2007), giants

(Niedzielski et al. 2007), subgiants (Johnson et al. 2007) and young stars (Kraus & Ire- land 2012). Given the unexpected diversity of planets around main sequence stars, it is important to study planetary systems in a broad range of evolutionary states, to ensure that we have a complete picture of planet formation and evolution. To this end, there are a number of surveys looking for planets around giant stars. Giants are particularly valuable, as they allow us a glimpse of planetary systems that are otherwise difficult to observe with radial velocities. While a few planets have been found around A & F dwarfs

(Galland et al. 2005), main sequence stars with spectral types earlier than mid-late F make poor targets for a Doppler search, as their spectra have sparse features that are rotationally broadened. As a result, we have little direct information about the popu- lation of planets around stars with masses larger than 1.5 M#. As these stars evolve ∼ offthe main sequence and into giants, their atmospheres cool and form many narrow spectral lines, making them accessible to radial velocity planet searches.

Walker et al. (1989) and Hatzes & Cochran (1993) found preliminary indications of a substellar companion to K giant β Gem (Pollux) that was later confirmed (Hatzes et al. 2006). The first solid detections of planets around giants were HD 104985 (Sato 14 et al. 2003), from a survey of 300 stars at the Okayama Astrophysical Observatory and

HD11977 (Setiawan et al. 2005), from a survey with FEROS on the ESO 2.2 m. Several surveys are underway at other telescopes, including TLS (D¨ollinger et al. 2007), HARPS

(Lovis & Mayor 2007) and Lick (Quirrenbach et al. 2011). Johnson et al. (2007) is leading a successful search for planets around subgiant stars, though for this work I am only focusing on giants. Our own Penn State-Toru´nPlanet Search using HET began in 2004 and remains the largest to date, with 900 targets (Niedzielski et al. 2007). Altogether, ∼ there are now 40 known planets orbiting giant stars and their characteristics are listed ∼ in Table 1.1.

1.2.1 Stellar Evolution

The following description of stellar evolution is largely based on the textbook by

Carroll & Ostlie (2006). Stars spend the vast majority of their lifetimes on the ‘main sequence’ (MS), generating the light we see by fusing hydrogen into helium in their cores. At this stage, a star is in hydrostatic equilibrium, with the gravitational force on the material in the star balanced by the pressure gradient caused by gas, radiation and sometimes electron degeneracy pressure. Eventually, the hydrogen in the core is depleted and the internal structure of the star adjusts. While a shell of hydrogen continues to burn, the core of the star contracts, causing the core temperature to rise and the star to become more luminous. At the same time, the outer layers of the star expand and become cooler. This is visible on the Hertzsprung-Russell diagram as the star moving offthe main sequence onto the subgiant branch, becoming brighter and redder. 15

As the stellar atmosphere cools, its photospheric opacity increases. This creates a convection layer near the surface that deepens over time, transporting energy to the surface more efficiently. This makes the star rapidly brighten, ascending the red giant branch (RGB). Meanwhile, the core continues to contract until the tip of the RGB, when it becomes dense and hot enough to fuse helium into carbon and oxygen. This new energy source causes both the core and the hydrogen-burning shell around it to expand, cooling it and decreasing its energy output. As a result, the star abruptly becomes fainter and its envelope contracts, descending the RGB.

This process then essentially repeats itself, with helium replacing hydrogen, though on a much shorter timescale. The stellar core fuses helium on the horizontal branch, anal- ogous to the main sequence, until the helium is depleted. Once again, the core contracts and the star brightens and cools, ascending the asymptotic giant branch (AGB). Stellar evolution beyond this point is heavily dependent on the initial mass of the star. Here

I only consider stars less massive than 8 M#, which are incapable of fusing heavier el- ements. AGB stars undergo rapid mass loss, eventually shedding their envelopes and leaving q hot carbon-oxygen core, which slowly cools to become a white dwarf star.

The evolutionary tracks ascending and descending the red giant branch, and as- cending the asymptotic giant branch all occur in approximately the same region of the

HR diagram, known as the red giant clump. It is difficult to observationally distinguish the evolutionary stage of a clump giant due to this overlap, though most are thought to be burning helium in their cores, i.e. post-RGB (Kunitomo et al. 2011). 16

1.2.2 Lack of Hot Jupiters

As the number of planets orbiting giant stars has grown, it has become apparent that there are a few significant differences between the population of planets around dwarfs and the planets around giants. To begin, there is a complete absence of hot

Jupiters, unlike the many found around main sequence stars. With the exception of one close planet around a subgiant (Johnson et al. 2010b), there no planets interior to 0.6 ∼ AU around evolved stars (Johnson et al. 2007; Sato et al. 2008a), as shown in Figure 1.4.

The current record holders are a 5.9 MJ planet around HD 102272 at 0.61 AU found by

Niedzielski et al. (2009a) and a 3.4 MJ planet around HD 32518 at 0.59 AU found by

D¨ollinger et al. (2009).

The mechanism behind the absence of close planets is not yet known, and it is possible that either planets do not form close to more massive stars or that planets do form interior to 0.6 AU, but they are lost as the host star evolves. Another, less explored possibility is that closer planets do exist around giant stars, but that the typical sampling of their orbits has been sufficiently infrequent and uneven that their signals are not yet detectable.

Two competing effects can alter a planet’s orbit as its host evolves. As a star ascends the red giant branch, it undergoes some mass loss, decreasing its gravitational pull. As a result, its planets will drift outward into new orbits. At the same time, the stellar envelope expands and any planets in sufficiently tight orbits will be engulfed. Early studies disagree whether Earth will survive our Sun’s red giant phase, with Goldstein

(1987) predicting that Earth will be engulfed and lose too much momentum to survive 17 once the Sun’s atmosphere shrinks. Conversely, Sackmann et al. (1993) calculated that due to stellar mass loss, all planets but Mercury will be pushed outward and survive.

More recent studies have expanded this question to cover a range of stellar masses, with mixed results. Sato et al. (2008a) find that mass loss on the RGB is negligible and

2-3 M# stars are capable of engulfing planets within 0.5 AU. However, most other sources

find that the maximum radii of giants are too small to account for the absence of planets

(Johnson et al. 2007; Currie 2009). More detailed models by Villaver & Livio (2009)

find that tidal interactions are strong enough to cause planets within a mass-dependent critical radius to decay and be consumed, accounting for the observed absence. A similar analysis by Kunitomo et al. (2011) compares tidal interaction models to individual planet detections, finding that each is near or beyond the critical radius of their stars. They also find that for stars more massive than 2.1 M#, the planets are far beyond the survival limit, indicating that there may be other mechanisms at work.

It is also possible that the protoplanetary disks of massive stars simply do not produce close planets. The disk lifetimes may be shorter due to higher accretion rates

(Muzerolle et al. 2005). Formation models for F stars (Burkert & Ida 2007) and heavier

(Currie 2009) suggest that the disks dissipate before planets are able to migrate near the central stars. However it is also not established that planets are able to migrate in disks undergoing significant accretion. A larger sample of known planets around giants will be needed to resolve this issue. 18

1.2.3 Metallicity - Planet Frequency Correlation

It is well established (Santos et al. 2004b; Fischer & Valenti 2005) that main sequence planet hosts are more likely to be metal rich than non-hosting stars. This is in agreement with the core accretion model of planet formation, which predicts that planets form more readily in high-metallicity environments. In contrast, many studies have found that planet-hosting giant stars are not metallicity enhanced relative to the

Sun (Hatzes 2008; Zieli´nski et al. 2010; Ghezzi et al. 2010; D¨ollinger et al. 2011), as shown in Figure 1.5. These results remain controversial, with a study by Hekker & Mel´endez

(2007) finding that planet-hosting giants are 0.1 dex more metallic than giants without ∼ planets, and a similar analysis by Pasquini et al. (2008) finding no difference between the two populations, as shown in Figure 1.6.

One possible explanation for the difference between dwarfs with planets and giants with planets is that the metallicity-planet frequency correlation seen in dwarfs is due to the ‘pollution’ of a dwarf’s atmosphere by its planets (Pasquini et al. 2007). Late in the planet formation process, metal-rich material may be accreted onto the surface of the star, causing a metallicity enhancement only in the outer layers. As the star evolves and develops a deeper convective envelope this metal rich material is diluted, lowering the observed metallicity. According to this model, the deepening convection zones of planet- hosting subgiants should cause a similar, though less pronounced decrease in metallicity.

However, Ghezzi et al. (2010) find that the metallicities of subgiants with planets are similar to the metallicities of dwarfs with planets. The core-accretion model provides an alternative explanation, that the larger disks of intermediate mass stars have higher 19 surface densities, making it easier to form giant planets even around less metallic stars

(Ida & Lin 2005).

1.2.4 Stellar Mass - Planet Mass Correlation

Following the above argument, the core-accretion model also predicts that for a fixed metallicity, higher mass stars are more likely to form Jupiter-mass planets than lower mass stars. This prediction has been borne out by the known population of planets around giants (D¨ollinger et al. 2011; Bowler et al. 2010; Hatzes 2008). The most influ- ential studies by Johnson et al. (2007) and Lovis & Mayor (2007) compare the detection rate of planets with a>2.5 AU and Mp sin(i) > 0.8 MJ and 5 MJ , respectively, around

M dwarfs, solar-like stars, and intermediate mass stars. The amplitude of a star’s reflex

2 3 velocity scales as K M − / , making it easier to detect a planet of a given mass and ∼ ∗ period around a lower mass star. Nevertheless, both analyses find that giant planets are most likely to be found around intermediate mass stars and least likely to be found around M dwarfs.

As a corollary, the Jupiters found around giants may be more massive than those around solar-type stars. Several brown dwarf-mass companions have recently been de- tected within a few AU of intermediate mass stars (Liu et al. 2008; Omiya et al. 2009), including the system found by Quirrenbach et al. (2011) consisting of two brown dwarfs in near 6:1 resonance, suggestive of migration in a protoplanetary disk. In contrast, <1% of dwarf stars have brown dwarf companions within 1000 AU (Grether & Lineweaver ∼ 2006). This lack of brown dwarfs relative to both stellar and planetary companions is 20 known as the ‘brown dwarf desert’ and may be caused by the migration or ejection of brown dwarfs, or by separate formation mechanisms for different companion masses.

Omiya et al. (2009) find that all brown dwarf mass companions are found around giant stars of >2.7 M#. They also find that less massive planets are not detected around

2.4 - 4 M# stars, suggesting that the masses of substellar companions may scale with stellar mass, as shown in Figure 1.7. The core-accretion model predicts that giant planet formation peaks around 3 M# stars due to the increasing distance of the ice line with ∼ stellar temperature (Kennedy & Kenyon 2008). Both of these predictions require more planet detections around stars with massive MS progenitors to be tested.

Massive stars are thought to have more massive disks (Natta et al. 2000), provid- ing more material for nascent planetary cores to accrete. However, these brown dwarf companions or ‘super-planets’ may require a more exotic formation scenario, such as disk instability, in which a sufficiently massive protoplanetary disk fragments into clumps that quickly condense into substellar companions (Mayer et al. 2002). In either scenario, these brown dwarfs may form more like planets than like small stars.

1.2.5 Stellar Variability

G and K giants are known to have intrinsic radial velocity variations, with ampli-

1 1 tudes of 20 m s− for earlier spectral types, increasing to 50 m s− for later spectral ∼ ∼ types. These are thought to be caused by pressure (acoustic) or p-mode oscillations, similar to those found in the sun, which have been observed in giant stars by many studies (Hatzes & Cochran 1994; Hatzes & Zechmeister 2007; Frandsen et al. 2002; De

Ridder et al. 2009), most recently with the CoRoT and Kepler satellites (Barban et al. 21

2010; Baudin et al. 2011; Hekker et al. 2011; Ciardi et al. 2011). P -mode oscillations are excited by turbulent convection near the stellar surface and are quasi-periodic, with periods of hours to days in giants and mode lifetimes of tens of days. These oscillation timescales are much longer than those seen in dwarfs and it is impractical to integrate

RV observations long enough to average over the variability. Most surveys have an ob- serving cadence greater than a few days, so the oscillations appear as excess noise or stellar ‘jitter’, making it more difficult to detect low amplitude RV signals.

Hekker et al. (2006), among others, find that while all K giants show radial velocity

1 variations of a few m s− , only giants redder than B V = 1.2 have variations greater − 1 than 20 m s− and that the minimum oscillation amplitude increases toward redder stars.

Hatzes & Cochran (1998) predict that due to the low surface gravity of giant stars, it is more difficult to slow a moving packet of gas, resulting in larger oscillation amplitudes.

Hekker et al. (2008) confirm this theory, finding a strong inverse correlation between log(g) and the amplitude of non-periodic RV oscillations. They also find that some giants show periodic variability, and that these stars have higher jitter than expected for their log(g) values. This suggests that these stars may have detectable planets in addition to their intrinsic RV signals.

Rotational modulation due to starspots can also cause radial velocity variations, as discussed in Section 1.1.2. This is a concern for giant star planet surveys, as the rotational periods of giants can reach several hundreds of days, similar to the long periods of their planets. There has been extensive research into spot activity on the Sun and similar stars, indicating dark, cool patches with strong magnetic fields that can persist for years. These spots are often found in pairs at ‘active longitude’ bands on opposite 22 sides of the star, developing and fading at different latitudes within the bands over time

(Usoskin et al. 2005). The understanding of starspots on giants is more limited, and the increased depth of the convection zone may cause different spot characteristics. However,

Gray & Brown (2006) observe rotational modulation of the line bisectors in Arcturus, likely caused by the presence of two or three active longitudes similar to those observed in dwarf stars. Recent studies with CoRoT (Gondoin et al. 2009) of multiple F, G & K giants find that spot coverage increases with decreasing rotation period and increasing depth of the convection zone, leading to peak coverage at around spectral type K1.

There are several ways to test for starspot contamination, including checking for photometric variations and monitoring inversion in the Ca II H and K lines, an indicator of stellar activity. The presence of a starspot also distorts spectral line profiles, causing

RV variations and bisector changes with the same periodicity. Simulations by Hatzes

(2002) and others can be used to predict the amplitude of this variability and limit false planet detections.

1.3 Radial Velocity Measurements with Telluric Features

1.3.1 Previous Work

The idea of using telluric lines as a wavelength standard is an old one. Griffin

(1973) first suggested the use of the water vapor (H2O) and molecular oxygen (O2) bands in the red end of the optical spectrum. Telluric lines have several advantages over emission lamps, most notably that the target and calibration spectrum both have the same optical path. This greatly reduces errors in wavelength caused by temperature 23 and pressure drifts, as well as mechanical shifts. Atmospheric spectra are also naturally imposed during an observation, requiring no equipment and being absorption spectra, are affected by the instrumental profile in a similar fashion to the stellar spectra.

Griffin (1973) note several limiting factors to measuring precise radial velocities with telluric lines. One is that superimposing the calibration lines on the target causes some mutual line blending, altering the shape of those lines, though this is true of any absorption medium. More importantly, telluric lines are inherently unstable due to changes in the atmosphere. Telluric water vapor lines are formed in the lower 2km ∼ of the atmosphere and their strength is dependent on the amount of precipitable water vapor along the line of sight, which can change considerably in less than an hour. The amount of molecular oxygen in the atmosphere is approximately constant over time, though the oxygen lines form over a much larger scale height, 8km.Theupper ∼ atmosphere is subject to strong winds, which result in a net Doppler shift if there is a component along the line of sight. The oxygen lines are also asymmetric due to pressure shifts throughout the layers of the atmosphere, and their shape changes with airmass.

Throughout the 1980s there were several observational studies done on the sta- bility of O2 lines. Each used a small number ( 10) of telluric and stellar lines, care- ∼ fully selected to avoid blends and measured individual line positions. Smith (1982) and

Cochran (1988) each looked for stellar oscillations in Arcturus using the O2 γ band as a

1 1 calibrator and reported a precision of 7ms− and 15 m s− , respectively. Balthasar ∼ ∼ et al. (1982) considered the effect of wind displacement, comparing observations of the same region to line models made using radiosonde wind measurements. They measured

1 a precision of 3 m s− over the course of a day given sufficient wind data and anticipated 24

1 15 m s− without corrections. Caccin et al. (1985) studied the line asymmetries due to ∼ pressure shifts, as a function of observatory height and zenith distance, and found that

1 large changes in air mass cause line shape changes up to 10 m s− . They also modeled

1 wind effects, finding line shifts of <10 m s− and noted the ambiguity in determining an exact position for asymmetric lines.

Telluric lines fell out of favor due to the success of the iodine cell, though there has been renewed interest in recent years. Gray & Brown (2006) took the novel approach of using the water lines at 9350 A˚ formed by the atmosphere inside their coud´espec- ∼ trograph and an order-sorting filter to alternate between target and calibration orders.

This allows for more thorough knowledge of temperature and pressure conditions than can be obtained with the Earth’s atmosphere, but taking sequential images decreases

−1 the precision to 25 m s . Blake et al. (2007, 2010) use the NIR CH4 absorption band ∼ as a radial velocity standard in a search for planets around late M and L dwarfs. They forward model the observations in manner similar to the iodine technique, using models to create the intrinsic stellar spectrum and calibration spectrum, and attain a precision

−1 of 100-300 m s . Figueira et al. (2010) measure the stability of O2 lines in comparison to the standard HARPS ThAr technique, cross-correlating observations of a few bright stars with an O2 mask. They find that the line bisector changes are correlated with air

1 mass and are correctable with simple models, yielding a short term precision of 2 m s−

1 and a precision of 10 m s− over six years. ∼ 25

1.3.2 Detecting Planets around Low Mass Stars

There is widespread interest in detecting Earth-like planets, both to understand the full diversity of planetary systems and as an end in itself. While RV precision has greatly improved in recent decades, current technology is not yet able to reach the 10 ∼ 1 cm s− precision necessary to detect an Earth-mass planet in the habitable zone of a solar-type star. Many surveys are now directed to low mass stars (Howard et al. 2009;

2 3 O’Toole et al. 2009; Lovis et al. 2006), taking advantage of the K M − / increase ∼ ∗ in signal with decreasing host mass. Masses down to 2 M⊕ have now been detected ∼ around several stars (Pepe et al. 2011).

M dwarf systems are of great interest to astrobiology, as their their habitable zones are much closer to the star than 1 AU (Kasting & Catling 2003; Kaltenegger & Sasselov ∼ 2011). Here I use the conventional definition of a habitable zone, a circumstellar annulus where a planet with an atmosphere can sustain liquid water on a solid surface. The decreased luminosity places M dwarf habitable zones at 0.1-0.3 AU, giving any Earth- ∼ like planets in the region a larger RV signal than the Earth imposes on the Sun. Low mass stars are also much more populous than Sun-like stars, with M dwarfs accounting for 75% of the local Solar neighborhood and K dwarfs about three times as populous as

G dwarfs (Henry et al. 2006). The population of very low mass stars and brown dwarfs is not yet well characterized, but the mass function appears to peak around 0.1-0.3 M#

(Da Rio et al. 2012). This makes low mass stars one of the most important populations for a survey, as they may comprise the majority of planet hosts. 26

Spectral types through about M4 are feasible targets for the traditional optical surveys. Less massive stars are too faint, producing most of their light in the NIR.

Several new NIR spectrographs and calibration techniques are being developed to better utilize this flux and reach the lowest mass stars (Mahadevan et al. 2010; Osterman et al. 2011; Bean et al. 2010; Erskine et al. 2011). Meanwhile the spectral regime in between the iodine region and the NIR, approximately the R-band, is easily observed with current technology, though the means to calibrate this wavelength range with a sufficient precision are limited. Making the R-band accessible to radial velocity surveys would allow the use of more of the spectral energy distribution of low mass stars than is accessible with iodine.

1.3.3 Radial Velocity Information Content

There are numerous atmospheric absorption features in between 5800-8800 A,˚ mostly consisting of H2O at 5900, 6500, 7300 and 7900-8400 A,˚ as well as the O2 γ ∼ band at 6300 A,˚ B band at 6900 A˚ and A band at 7600 A,˚ as shown in Figure 1.8.

Individual bands have been used to calibrate radial velocities (Smith 1982; Cochran

1988), though never the entire region. Taken together, the R-band telluric features provide similar bandwidth to the iodine cell, though spread over about three times the spectral range. It may not be possible to use all lines for any given epoch, as the water line strengths vary over time and portions of the O2 A band are likely to be saturated.

Bouchy et al. (2001) defined a quantitative measure of the radial velocity infor- mation content, Q, that is flux independent. Radial velocity shifts are measured as the sum of changes in the intensity recorded at each pixel, so spectra with many sharp 27 features will produce the largest signal. They find that Q values increase with increas- ing resolution and toward redder spectral types. The information content also degrades with increasing V sin(i) values, as the spectral lines are first broadened at low rotational

1 velocity values, then blend together for V sin(i) 10 km s− and greater. ∼ Bouchy et al. (2001) also find that Q values decrease toward longer wavelengths, though this effect should be mitigated with increased flux. Low mass dwarfs produce most of their light in the optical red to NIR, with K5 dwarfs peaking around 6300 A,˚

M0 dwarfs around 7600 A˚ and M6 dwarfs around 10300 A˚ (Jones et al. 2005; Pavlenko et al. 2006), as shown in Figure 1.9. Simulations by Jones (2006) indicate that M dwarf spectra in the 0.5-0.7 µm region have enough spectral information content to measure precision RVs, with comparable precision to individual NIR bands measured for slowly rotating early to mid-M dwarfs. More recent simulations by Reiners et al. (2010) give similar results. It is worth noting that the lowest errors in the earlier study were obtained by combining the entire NIR region, suggesting that it would be beneficial to expand the spectral region available for RV surveys.

Historically, M dwarfs have been less appealing targets for radial velocity mea- surements, both due to their faintness in the optical and their increased activity rates.

Though their starspot activity is not well understood, M dwarfs are observed to flare on timescales of about half an hour, producing a forest of strong emission lines (Fuhrmeister et al. 2008). Reiners (2009) find that while large flares can produce radial velocity shifts

1 of several hundred m s− , these events are easily detected by monitoring Hα emission.

1 Smaller flare events produce RV scatter of 10-20 m s− , or less if prominent emission lines are avoided. Stellar activity is also correlated with rotational velocity (Noyes et al. 28

1984) and M dwarfs have longer spindown times due to their decreased mass (Mohanty

& Basri 2003). Jenkins et al. (2009) measured rotational velocity values for 56 M dwarfs and observe that a significant fraction of stars with spectral types M6 and earlier have

1 V sin(i) < 10 m s− , making them feasible radial velocity targets.

1.3.4 Potential Uses of Telluric Calibration

There are several potential applications of R-band telluric line calibration, in- cluding a planet search around K and M dwarfs. Studies of R-band telluric lines have

1 consistently measured a radial velocity stability of 10 m s− or better (Figueira et al. ∼ 2010; Balthasar et al. 1982), a precision sufficient to detect a Neptune-mass planet in the habitable zone of an M dwarf, as shown in Figure 1.10. Ida & Lin (2005) predict that Neptunes should be common around M dwarfs and there are a growing number of such detections (Butler et al. 2004; Bonfils et al. 2005, 2011). Indeed, several low mass stars have multiple planetary companions (Rivera et al. 2010; Forveille et al. 2011), suggesting that a Neptune detected by a telluric survey would be a good candidate for further observation with higher precision work.

The ideal targets for a telluric radial velocity survey are stars that have more

flux in R-band than the iodine region and that also have a moderate amount of intrinsic

1 noise, such that a precision higher than 10 m s− would not be fully utilized. Flaring ∼ M dwarfs are one such example, and K giant stars also have increased red flux, as shown

1 in Figure 1.11, as well as 20 m s− RV jitter. Faint K and M stars, such as those in ∼ clusters, are also interesting targets as they may have less arduous integration times in redder light. 29

In addition, telluric calibration can add radial velocity capabilities to any high- resolution optical spectrograph, without the need for additional equipment. This could be a valuable tool for studying binary stars and other topics where observing time on the most competitive telescopes is unnecessary.

It can also be advantageous to use iodine and telluric calibration in tandem, either to increase the available spectral range or to compare results between V and R-band.

Reiners et al. (2010) predict that the RV signal caused by a starspot will decrease toward redder light. In contrast, orbital motion should show no such wavelength dependence, providing another test for false detections.

1.4 Outline

In this thesis I investigate two aspects of radial velocity planet searches around red stars. Chapter 2 focuses on an ongoing search for planets around G & K giant stars.

I characterize six individual planetary systems and discuss their traits in the context of the broader field of planet-hosting giants. Chapters 3 and 4 focus on the development of a new radial velocity measurement technique using the telluric lines in the R-band.

In Chapter 3, I describe how the observations were collected and reduced. In Chapter

4, I describe the new technique and preliminary results. In Chapter 5, I summarize the results of my work and present some suggestions for future work. 30

Fig. 1.1 The discovery space of RV-discovered planets. While the majority of planets are 1 M ,massesdowntoafewM⊕ are now detectable. Figure created by Exoplanets.org ∼ J 31

Fig. 1.2 Schematic diagram of the change in the line profile (left) caused by the motion of a starspot across the stellar disk (right). The line centroid and measured radial velocity are also altered, potentially causing false planet detections. Reprinted from New Astronomy Reviews, 52, N. C. Santos, Extra-solar Planets: Detection Methods and Results, 154, 2008, with permission from Elsevier. 32

Fig. 1.3 Line bisectors for HD 166435 for two sets of spectra selected at opposite phases of the radial velocity cycle caused by the presence of a starspot. The hatched line illustrates the mean bisector computed by averaging over all phases. Credit: D. Queloz et al., A&A, 379, 279, 2001, reproduced with permission c ESO. ! 33

Fig. 1.4 The planets detected by radial velocities around stars with M∗ < 1.5 M# (black circles), primarily dwarfs, and the planets detected around stars with M∗ > 1.5 M# (red dots), primarily evolved stars. There are no known planets around evolved stars within 0.6 AU with the exception of HD 102956 b at 0.08 AU, orbiting a subgiant. 34

Fig. 1.5 Top: Metallicity distributions obtained for planet-hosting dwarfs (black solid line) and giants (red dotted line). All abundance results in these distributions were de- rived homogeneously. Bottom: Metallicity distributions for planet-hosting dwarfs (black solid line; same as top panel), and all giant star hosting giant planets known to date (blue dashed line). The metallicities for those planet-hosting giants not analyzed by Ghezzi et al. (2010) were taken as the average of the iron abundance values found in the literature. Figure from Ghezzi et al. (2010), reproduced by the permission of the AAS. 35

star planet

Fig. 1.6 Age-metallicity relationship for giants with and without planets, either from the FEROS and Tautenburg surveys or from literature, showingnodifferenceinthe metallicity distributions. Credit: L. Pasquini et al., A&A, 473, 979, 2007, reproduced with permission c ESO. ! 36

Fig. 1.7 Primary star masses versus masses of substellar companions orbiting within 3 AU, including solar-mass stars (open triangles), subgiants and giants (filled circles), and intermediate mass dwarfs (open circles). New detections by Omiya et al. (2011) are shown as stars. Solid lines indicate the detection limits for the mass of companions orbiting at 3 AU, corresponding to three times of typical radial velocity jitters σ of 5 −1 −1 ms for solar-mass stars (0.7 M# solar mass stars and intermediate-mass evolved stars, respectively. Two regions devoid of substellar companions are denoted by (a) and (b). Reprinted with permission from Omiya et al., 2011, in American Institute of Physics Conference Series, Vol. 1331, American Institute of Physics Conference Series, ed. S. Schuh, H. Drechsel, & U. Heber, 122129. Copyright 2011, American Institute of Physics. 37

Table 1.1. Giant Stars with Planets

Name M!/M! R!/R! m sin(i)/MJ a(AU) P (d) e [Fe/H] Reference BD +20 274 0.8 17.3 4.2 1.3 578.2 0.21 -0.46 Gettel et al. (2012a) BD +20 2457 b 2.8 49 22.67 1.45 379.63 0.15 -1.0 Niedzielski et al. (2009b) BD +20 2457 c 2.8 49 13.17 2.01 621.99 0.18 -1.0 Niedzielski et al. (2009b) BD +48 738 0.74 11 0.81 0.95 389.9 0.23 -0.2 Gettel et al. (2012b) HD 1690 1.09 16.7 6.1 1.3 533 0.64 -0.32 Moutou et al. (2011) HD 11977 1.9 10.2 6.5 1.9 1420 0.40 -0.21 Setiawan et al. (2005) HD 13189 3.5 50 14 1.8 471 0.27 -0.59 Hatzes et al. (2005) HD 17028 5.5 – 8.6 1.6 463 0.09 +0.22 PTPS HD 17092 2.3 10.9 4.6 1.3 360 0.17 +0.18 Niedzielski et al. (2007) HD 32518 1.13 10 3.35 0.6 157.54 0.01 -0.15 D¨ollinger et al. (2009) HD 81688 2.1 13 2.69 0.81 184.02 0 -0.36 Sato et al. (2008a) HD 96127 0.91 20 4.0 1.42 647.30 0.29 -0.24 Gettel et al. (2012b) HD 102272 b 1.9 10 5.9 0.6 127.6 0.05 -0.26 Niedzielski et al. (2009a) HD 102272 c 1.9 10 2.6 1.6 520 0.05 -0.26 Niedzielski et al. (2009a) HD 104985 1.6 11 6.5 0.78 199.5 0.03 -0.35 Sato et al. (2003) HD 119445 3.9 20 37.6 1.71 410.2 0.082 0.04 Omiya et al. (2009) HD 139357 1.35 12 10.08 2.35 1125.7 0.1 -0.13 D¨ollinger et al.(2009) HD 145457 1.9 10 2.9 0.76 176.30 0.11 -0.14 Sato et al. (2010) HD 173416 2 13 2.72 1.16 323.6 0.21 -0.22 Liu et al. (2009) HD 180314 2.6 9 22 1.4 396.03 0.26 0.20 Sato et al. (2010) HD 219415 1.0 2.9 1.0 3.2 2093.3 0.40 -0.04 Gettel et al. (2012a) HD 240210 1.25 11 7.29 1.33 501.75 0.15 -0.18 Niedzielski et al. (2009b) HD 240237 1.69 20 5.6 1.96 746.05 0.37 -0.26 Gettel et al. (2012b) NGC 2423 No 3 2.4 – 10.6 2.1 714.3 0.21 +0.14 Lovis & Mayor (2007) NGC 4349 No 127 3.9 – 19.8 2.38 677.8 0.19 – Lovis & Mayor (2007) α Ari 1.5 13.9 1.8 1.2 380.8 0.25 -0.25 Lee et al. (2011) β Gem 1.7 8.4 2.7 1.7 590 0.02 +0.19 Hatzes & Cochran (1993) γ Leo A 1.23 40 8.82 1.19 428.5 0.14 -0.49 Han et al. (2010) * Tau 2.7 13.7 7.6 1.93 595 0.15 +0.17 Satoetal.(2007) * CrB 1.7 21 6.7 1.3 417.9 0.11 -0.09 Lee et al. (2012) ι Dra 1.05 12.9 8.9 1.3 536 0.7 +0.03 Sato et al. (2007) ν Oph b 2.7 – 22.3 – 530 0.13 – Quirrenbach et al. (2011) ν Oph c 2.7 – 24.5 – 3169 0.18 – Quirrenbach et al. (2011) ξ Aql 2.2 12 2.81 0.68 136.75 0 -0.21 Sato et al. (2008a) 4UMa 1.23 18.1 7.1 0.87 269 0.43 -0.25 D¨ollingeretal.(2007) 11 Com 2.7 19 19.4 1.29 326.03 0.231 -0.35 Liu et al. (2008) 11 Umi 1.8 24 11.09 1.53 516.22 0.08 0.04 D¨ollinger et al. (2009) 14 And 2.2 11 4.68 0.82 185.84 0 -0.24 Sato et al. (2008b) 18 Del 2.3 9 10.21 2.58 993.3 0.08 -0.05 Sato et al. (2008a) 42 Dra 0.98 22 3.89 1.19 479.1 0.38 -0.46 D¨ollinger et al. (2009) 81 Cet 2.4 11 5.34 2.54 952.7 0.21 -0.06 Sato et al. (2008b) 38

Fig. 1.8 Atmospheric transmission for the R-band region, including several strong H2O bands (5900, 6500, 7300, 7900-8400 A)˚ and O2 bands (6300, 6900, 7600 A).˚ 39

Fig. 1.9 Flux as a function of wavelength for representative models of K2, K5, M0 and M3 dwarfs, in order of decreasing maximum flux. 40

Fig. 1.10 RV reflex amplitude as a function of separation for planets around host stars of 1.0 M# (dashed line), 0.3 M# (dotted line) and 0.1 M# (solid line). The yellow shaded 1 region indicates the habitable zone for M dwarfs. 10 m s− is our expected precision. 41

Fig. 1.11 Flux as a function of wavelength for a representative giant starmodel. 42

Chapter 2

Penn State - Toru´nPlanet Search

2.1 Overview

The Penn State - Toru´nPlanet Search is one of the most successful planet surveys targeting giant stars. Of the 40 systems with low-mass companions detected to date, ∼ 9 have come from our survey (Niedzielski et al. 2007, 2009a,b; Gettel et al. 2012a,b).

Notable results include a planet orbiting HD 219415 at 3.2 AU, the furthest yet found around a giant, and a planet orbiting HD 102272 at 0.6 AU, near the minimum orbital radii predicted by theory (Kunitomo et al. 2011; Villaver 2011).

The first tens of target stars were identified as part of the astrometric reference star selection program related to a search for terrestrial-mass planets with the Space

Interferometry Mission (Gelino et al. 2005; Niedzielski et al. 2005). These stars were ob-

1 served to exhibit RV variations greater than 50 m s− , disqualifying them as astrometric standards, but raising the possibility of substellar companions.

The full target list of 900 stars consists of giants, subgiants and dwarfs as shown ∼ in Figure 2.1. The majority of these stars are either clump giants or post-MS stars evolving toward the clump. This diversity of objects was chosen to provide access to a broad range of evolutionary states, though the primary focus to date has been GK giants.

Each target is brighter than V = 12, to ensure reaching S/N 150 in a single 900 s ≥ ≤ 43 exposure and to have declinations of 11◦ <δ<72◦, accessible by the Hobby-Eberly − Telescope (HET; Ramsey et al. 1998).

To date 330 stars, most of which are giants, have been flagged as candidates, as they show an approximately planetary/substellar-mass companion range of RV variations

1 ( 50-2500 m s− ). In addition to the published detections, about 40 of these targets ∼± have nearly enough observations to be modeled reliably.

Most of our candidates fall into one of four general types: the‘fuzzy’systemsin which the effects that are intrinsic to the star determine the effective RV precision, the

‘easy’ systems with a single, clean periodicity indicating a giant planet or brown dwarf - mass companion to the star in a circular or mildly eccentric orbit, the ‘weavers’ with a possible second, low-amplitude periodicity, whose precise determination clearly requires more observations, and the ‘ramp climbers’, for which a long-term, large RV trend must be fitted out of the data to obtain acceptable Keplerian models of the orbits. These are candidates for multiple systems or stellar-mass companions.

In this chapter I describe six of our systems, all but one of which are published detections. The standard data reduction, radial velocity measurements and stellar char- acterization for these objects were performed by members of the PTPS team, while I modeled the orbits and carried out data analyses tailored to the unique features of each system. Between them, these stars illustrate the features and challenges of radial velocity planet detection particular to giants. The most of the content of this chapter has been published in the Astrophysical Journal as Gettel et al. (2012a,b). 44

2.2 Observations

Observations began in January 2004 and are ongoing. They were made with HET equipped with the High-Resolution Spectrograph (HRS; Tull 1998). The HET is a fixed- truss telescope consisting of 91 hexagonal, 1 m diameter, spherical figure mirrors, with a maximum effective aperture of 9.2 m. The truss is tilted at 35◦ zenith distance, covering a declination range of 11◦ <δ<72◦. The telescope is operated in queue-scheduled − mode (Shetrone et al. 2007), making it particularly well-suited for large surveys, in which a high efficiency of usage of the telescope time must be combinedwithflexible,quick access to make time-critical followup measurements.

1 The HRS has been designed to ensure a RV measurement precision of 3ms− ≤ for stars brighter than V = 10. The spectrograph was used in the R = 60,000 resolution mode with the gas cell (I2) inserted in front of the spectrograph slit, and it was fed with a 2” fiber. The 316g5936 cross-disperser configuration was used, generating spectra that consist of 46 echelle orders recorded on the blue CCD chip (407.6-592 nm) and 24 orders on the red one (602-783.8 nm). 17 orders, covering the 505-592 nm range of the I2 cell spectrum were used for RV measurements. In practice, a measurement precision of 5-10

1 ms− is typical for a single observation.

The observing strategy for each target is to begin with 2 or 3 exposures about

1 1-2 months apart, to check for RV variability of greater than 30-50 m s− and less than

1 1kms− . These limits are greater than the typical radial velocity ‘jitter’ intrinsic to ∼ giants and select against stars with likely binary companions. Stars meeting these criteria 45 are scheduled for more frequent observations and if the RV variability is confirmed, it becomes part of the high-priority target list.

The observing procedure follows the standard method for precision radial velocity measurements with an iodine cell, as outlined in Marcy & Butler (1992). Most observa- tions consist of a 5-10 minute exposure of the target star taken through the iodine cell.

A calibration image is also made at the beginning or end of the night, to track small changes in the instrumental PSF, with the gas cell illuminated by the flatfield lamp. For at least one epoch a high S/N observation will be made of the target star without the iodine cell, in addition to and directly before or after the normal star+iodine exposure.

This star-only observation is used to generate a stellar ‘template’ as described in Section

4.1, by deconvolving the PSF.

The data reduction is performed using standard IRAF scripts (Tody 1993), with a preliminary wavelength calibration made using a ThAr lamp. For observations made prior to 2006, when the red CCD was replaced, an additional correction is made to remove the significant fringing effects in the red images.

2.3 Measuring Stellar Parameters

The atmospheric parameters of these stars were determined as part of an extensive study of the PTPS targets described in the forthcoming paper by Zielinski et al. (2012,

Z12). Here, we give a brief description of the methodology employed in that work.

Measurements of Teff , log(g), and [Fe/H] were based on the spectroscopic method of Takeda et al. (2002, 2005a), in which the Fe I and Fe II lines are analyzed assuming 46 local thermodynamic equilibrium. We used equivalent width measurements of 190 non- blended, strong FeI and 15 FeII lines per star which resulted in the mean uncertainties of 13 K, 0.05 dex, and 0.07 dex for Teff , log(g), and [Fe/H], respectively. Except for

[Fe/H], these uncertainties represent numerical errors intrinsic to the iterative procedures of Takeda et al. (2005a,b). The actual uncertainties are likely to be 2-3 times larger.

Uncertainties of the [Fe/H] measurements were computed as standard deviations of the mean Fe I and Fe II abundances and are thus more realistic.

Since the Hipparcos parallaxes of our stars are either unavailable or very uncertain, only rough estimates of their masses and radii could be made. Initial estimates of stellar luminosities were derived from the MV values resulting from the empirical calibrations of Straizys & Kuriliene (1981). The intrinsic color indices,(B V )0, and bolometric − corrections, BCV, were calculated from the empirical calibrations of Alonso et al. (1999).

Stellar masses and ages were estimated by comparing positions of these stars in

[log(L/L#), log(g), log(Teff )] space with the theoretical evolutionary tracks of Girardi et al. (2000) and Salasnich et al. (2000) for the closest respective values of metallicity.

Stellar mass estimates derived from this modeling process were then used to adopt the

final values of luminosity. Stellar radii and the associated uncertainties were computed using the spectroscopic values of Teff and adopted luminosities.

Obviously, uncertainties affecting the position of a star in the parameter space determine the corresponding errors in mass estimates. As the values of Teff and log(g) are relatively well determined, the largest uncertainties are contributed by stellar luminosity or parallax. As a useful benchmark, the mean uncertainty in stellar mass estimates for 47 over 300 Red Clump giants analyzed in Z12 using the above approach amounts to about

0.3 M#.

The stellar rotation velocities were estimated by means of the Benz & Mayor

(1984) cross-correlation method. The cross-correlation functions were computed as de- scribed by Nowak et al. (2010) with the template profiles cleaned of the blended lines.

Given the estimates of stellar radii, the derived rotation velocity limits were used to ap- proximate the stellar rotation periods. The parameters of the six stars are summarized in Table 2.1.

2.4 Measurements & Modeling of Radial Velocity Variations

RVs were measured using the standard I2 cell calibration technique (Butler et al.

1996). A model spectrum was constructed from a high-resolution Fourier transform spectrometer (FTS) I2 spectrum and a high signal-to-noise stellar spectrum measured without the I2 cell. Doppler shifts were derived from least-squares fits of model spectra to stellar spectra with the imprinted I2 absorption lines. Typical S/N for each epoch was 200, as measured at the peak of the blaze function at 5936 A.˚ The RV for each ∼ epoch was derived as a mean value of 391 independent measurements from the 17 usable echelle orders, each divided into 23, 4-5 A˚ blocks, with a typical, intrinsic uncertainty of

1 6-10 m s− at 1σ level over all blocks (Nowak 2012, in preparation). This RV precision level made it quite sufficient to use the Stumpff(1980) algorithm to refer the measured

RVs to the Solar System barycenter.

The RV measurements of each star were modeled in terms of the standard, six- parameter Keplerian orbits, as shown in Figures 2.2, 2.4, 2.7, 2.10, 2.13, 2.15 and 2.16. 48

Least-squares fits to the data were performed using the Levenberg-Marquardt algorithm

(Press et al. 1992). Errors in the best-fit orbital parameters were estimated from the parameter covariance matrix. These parameters are listed in Table 2.2 for each of the five

1 published stars. The estimated 7ms− errors in RV measurements were evidently too ∼ small to account for the actual measured post-fit rms residuals. As outlined in Chapter 1, giant stars are subject to atmospheric fluctuations, and radial and non-radial pulsations that may manifest themselves as an excess RV variability. In particular, the p-mode oscillations, typically occurring on the timescales of hours to days, are usually heavily under-sampled in the RV surveys of giants and can account for a significant fraction of the observed post-fit RV noise (Hekker et al. 2006). A rough estimate of such variations can be made using the scaling relation of Kjeldsen & Bedding (1995), which relates the amplitude of p-mode oscillations to the mass, M, and the luminosity, L, of the star:

L/L# vosc = (23.4 1.4) (2.1) M/M# ±

−1 where the amplitude, vosc is in cm s .

The statistical significance of each detection was assessed by calculating false alarm probabilities (FAP) using the RV scrambling method (Wright et al. 2007, and references therein). FAPs for HD 240237, HD 96127, and HD 219415 were calculated for the null hypothesis that the planetary signal can be adequately accounted for by noise.

Two FAP values each were calculated for BD+48 738, BD+20 274 and HD 102103, first for the null hypothesis that the RV ramp can be treated as a linear trend plus noise, then 49 for the null hypothesis that it can be modeled as a fraction of a long-period, circular orbit and noise.

2.5 Bisector & Photometry Analysis

Photometry and line bisector analysis, which are efficient stellar activity indica- tors, have been routinely used to verify the authenticity of planet detections by means of the RV method (e.g. Queloz et al. 2001). In particular, as simultaneous photometric data are typically not available for our targets, it is useful to correlate the time vari- ability of line bisectors and RVs, in order to obtain additional information on a possible contribution of stellar activity to the observed RV behavior. For example, even for slow rotators like the K giants discussed here, a stellar spot only a few percent in size could introduce potentially detectable line profile variations (Hatzes 2002).

Although a correlation between line bisectors and RVs does provide evidence that intrinsic stellar processes contribute part or all of the observed RV variability, many sources of jitter cannot be readily identified in a bisector analysis. This is because the bisector changes may be too small to measure distinctly from the apparent RV shift or they are indistinguishable from temporal changes in the spectrograph line spread

1 function. In addition, for these stars the instrumental profile width of 5 km s− is comparable to the rotational line broadening (Table 2.1), which restricts the diagnostic value of line bisector analysis. Consequently, the lack of such a correlation is a necessary but not a sufficient condition for demonstrating that measured RV variations are of a planetary origin. Additional information, such as a distinctly Keplerian shape of the

RV curve (Frink et al. 2002; Zechmeister et al. 2008) or a strict persistence of the RV 50 periodicity over many cycles (Quirrenbach et al. 2011), is necessary to fully verify such detections.

In order to investigate the possible contribution of stellar jitter to the observed RV periodicities, we have examined the existing photometry data in search for any periodic light variations, and performed a thorough analysis of time variations in line bisector velocity span (BVS) for each of the stars discussed below. Bisector curvature values

(BC) were measured for some of the PTPS targets, including three of these stars, but were found not to provide more information than can be obtained with BVS measure- ments. The BVSs and BCs were measured using the cross-correlation method proposed by Mart´ınez Fiorenzano et al. (2005) and applied to our data as described in Nowak et al. (2010). For each star and each spectrum used to measure RVs at all the observing epochs, cross-correlation functions were computed from 1000 line profiles with the I2 ∼ lines removed from the spectra. The time series for these parameters and the photomet- ric data folded at the observed RV periods for these stars are shown in Figures 2.3, 2.5,

2.8, 2.12, 2.14, 2.17 and 2.18.

In addition, assuming that the scatter seen in the photometry data is solely due to a rotating spot, we have used it to estimate the corresponding amplitude of RV and

BVS variations as in Hatzes (2002).

2.6 ‘Fuzzy’ Systems

The RV variations over a wide range of timescales and amplitudes observed in giant stars can be caused by a variety of phenomena, including orbital dynamics, pro- cesses intrinsic to the star such as stellar oscillations or spot activity coupled with stellar 51 rotation, and other effects that may still await identification. Studies by Hekker et al.

(2006, 2008) demonstrate that one can make a statistical distinction between the stellar and non-stellar origin of RV variations in giants by correlating them with stellar prop- erties, such as the B V color and surface gravity. Here, we show two examples of − such variability in the K2 giants HD 240237 and HD 96127. Also, using the empirically established dependencies between the effective temperature, Teff , and the B V color −

(Alonso et al. 1999), and Teff and surface gravity, log(g), (Hekker & Mel´endez 2007) we investigate the intrinsic RV variability in a sample of K giants with planets in terms of stellar metallicity, [Fe/H], and find a suggestive anti-correlation between [Fe/H] and the observed stellar jitter.

2.6.1 HD 240237

RVs of HD 240237 (BD+57 2714, HIP 114840) are listed in Table 2.5. They were measured at 40 epochs over a period of 1930 days from July 2004 to October 2009.

The S/N values ranged from 161 to 450. The exposure time was selected according to actual weather conditions and ranged between 184 and 900 s. The estimated mean RV

1 uncertainty for this star was 7 m s− .

Radial velocity variations of HD 240237 over a 5 year period are shown in Figure

2.2, together with the best-fit model of a Keplerian orbit. The post-fit residuals are

1 characterized by the rms value of 36 m s− and the FAP for this signal is <0.01%.

The observed RV variations point to an orbiting companion, which moves in a 746 day, eccentric orbit, with a semi-major axis of 1.9 AU, and has a minimum mass of m2 52 sin(i) = 5.3 MJ for the assumed stellar mass of 1.7 M#. For randomly oriented orbital inclinations, there is a 90% probability that the companion is planet-mass. ∼ 1 The post-fit residuals for this model exhibit a large, 36 m s− rms noise. Assuming that this RV jitter is due to solar-like oscillations, the Kjeldsen-Bedding relation predicts

1 an even larger amplitude of 45 m s− for this star. To account for these variations, ∼ 1 we have quadratically added 35 m s− to the RV measurement uncertainties before performing the least-squares fit of the orbit.

The longest time span photometry available for this star comes from 120 Hipparcos measurements (Perryman & ESA 1997), made between MJD 47884 and 49042. These data give a mean magnitude of the star of V =8.30 0.02. There are also 15 epochs of ± photometric observations of this star available from the Northern Sky Variability Survey

(Wo´zniak et al. 2004). Neither of these data sets exhibits periodic brightness variations.

The mean values of the BVS and the BC for this star are 136.6 51.4 and 29.9 47.3 ± ± 1 ms− . No correlations between the RV variations and those of the BVS and BC were found, with the respective correlation coefficients of r = -0.15 for the BVS and r = -0.06 for the BC.

2.6.2 HD 96127

RVs of HD 96127 (BD+45 1892) were measured at 50 epochs over a period of 1840 days from January 2004 to February 2009 (Table 2.6). The S/N for these measurements ranged from 80 to 494. The exposure time was selected according to actual weather conditions and ranged between 72 and 1200 s. The estimated mean RV uncertainty for

1 this star was 6 m s− . 53

The radial velocity variations of HD 96127 over a 5 year period are shown in Figure

2.4, together with the best-fit model of a Keplerian orbit. As with HD 240237, the post-

1 fit residuals show a large, 50 m s− rms RV jitter, comparable to the Kjeldsen-Bedding

1 amplitude estimate of 45 m s− . To account for these variations, we have quadratically

1 added 45 m s− to the RV measurement uncertainties. The best-fit parameters indicate a planet candidate with a minimum mass of 4 MJ , and a 647 day, 1.42 AU, moderately eccentric orbit. The FAP for this signal is <0.01%.

Because this star is relatively bright, the only photometry available for it is from

100 Hipparcos measurements (Perryman & ESA 1997), made between MJD 47892 and

48933. The mean magnitude of the star calculated from these data is V =7.43 0.01. ± In addition, the time series exhibits a marginal (2σ), 25.2 0.05 day periodicity with the ± peak-to-peak amplitude of 0.02 mag. Analysis of the photometric time series divided into shorter sections shows that this oscillation persists over the entire 3 year span ∼ of the data and, despite its low amplitude, it has a FAP < 0.001%. On the other hand, it is not present in our RV data for this star and it would be hard to envision how could it be related to the observed 647 day RV periodicity. Moreover, the 4.3 day period corresponding to the frequency of maximum power of p-mode oscillations predicted from Kjeldsen & Bedding (1995) is obviously much shorter than observed.

Evidently, additional high-cadence photometric observations of HD 96127 are needed to clarify the nature of this 25 day periodicity.

The mean values of the BVS and the BC for this star are 243.3 52.5 and 85.2 44.5 ± ± 1 ms− and the correlations between the RV and the BVS and BC variations are not significant, with r = 0.21 for the BVS and r = 0.17 for the BC, respectively. 54

2.6.3 Jitter - Metallicity Correlation

The low signal-to-noise planet detections around the K2 giants, HD 240237 and

HD 96127 demonstrate that the intrinsic RV noise in giants restricts the utility of the

Doppler velocity method, especially in the case of long periods and large orbital radii, for which its sensitivity degrades for dynamical reasons. This effect has been studied by

Hekker et al. (2006), who have shown that the rms RV noise, σRV , of K giants has a

1 median value of 20 m s− and it tends to increase toward later spectral types. Similarly, ∼ a negative correlation has been found between σRV and the stellar surface gravity (Hatzes

& Cochran 1998; Hekker et al. 2008).

A short timescale, low amplitude RV noise commonly observed in giants appears to be the manifestation of undersampled solar-like oscillations (Hekker et al. 2006, 2008;

Quirrenbach et al. 2011). In particular, the recent photometric studies of K giants by the

CoRoT and Kepler missions (Baudin et al. 2011; Ciardi et al. 2011; Gilliland et al. 2011;

Hekker et al. 2011) have shown a prominent presence of such oscillations in these stars.

More specifically, Kjeldsen & Bedding (1995) have proposed that the velocity amplitude associated with the p-mode oscillations scales as v L/M (Eqn. 2.1), or equivalently osc ∼ 4 as Teff /g,whereTeff , and g are the effective temperature and the surface gravity of the star. As shown, for example, by Hekker et al. (2006, 2008) and D¨ollinger et al. (2011), observations are in a general agreement with these scalings.

In order to compare the observed trend in the RV data for K giants to the Kjeldsen

& Bedding (1995) prediction more quantitatively, we have used the empirical dependen- cies of B V color and log(g) on Teff for giants (Alonso et al. 1999; Hekker & Mel´endez − 55

2007) to generate a semi-analytical function that relates σ to the observed B V for RV − different stellar metallicities ([Fe/H]). The observed 30 values of σRV have been taken from the published discoveries of substellar companions to K giants in Table 2.4, as post-

fit residuals after the removal of the Keplerian signal from the RV data. This sample selection has been motivated by the work of Hekker et al. (2008), which shows that am- plitudes of RV periodicities in K giants are generally independent of stellar parameters, whereas the RV noise left over after their removal tends to correlate with the B V color − and anti-correlate with log(g). Consequently, our approach practically ensures that the remaining short-term noise exceeding the instrumental RV precision is intrinsic to the star, given the observed absence of planets with orbital radii smaller than 0.6 AU around

K giants (Johnson et al. 2007; Sato et al. 2008a; Niedzielski et al. 2009a). Moreover, as the RV precision and sampling patterns characterizing the ongoing GK giant surveys are quite similar, any selection effects that could influence the RV jitter measurements can be safely ignored.

In Figure 2.6, the measured values of σ as a function of B V are compared RV − with the Kjeldsen & Bedding relationship expressed in terms of these two observables as described above. The apparent increase of RV noise with the decreasing stellar metal- licity becomes more evident if plotted out directly. The calculated Pearson correlation coefficient for this relationship is -0.71. The origin of this trend is most likely related to the fact that higher metallicity (opacity) of the star lowers its temperature, which decreases the amplitude of p-mode oscillations, while lower metallicity has the opposite effect. 56

One interesting consequence of the observed σRV -[Fe/H] dependence in K giants is that it must affect the analyses of a correlation between the planet frequency and metallicity of these stars (Pasquini et al. 2007; Hekker & Mel´endez 2007; Ghezzi et al.

2010). No clear agreement has been reached so far, as to whether the observed correlation is weaker than in the case of dwarf stars (Fischer & Valenti 2005), or not. The effect unraveled here creates an apparent preference for higher metallicity stars to be more frequent hosts to detectable planets, so that the published studies must be biased by this trend.

2.7 Long Period Systems

Typical periods for planets around giants are on the order of one year or longer, requiring multiple years of observations to characterize their orbits. The longest such period announced to date, detected by D¨ollinger et al. (2009), is just over three years. In

Gettel et al. (2012a), we report the detection of a planet in a nearly 6 year orbit around

HD 219415. In this case, we are close to encountering the wide-orbit limit of planet detection, which results from the sensitivity of the Doppler velocity method reaching the noise level determined by the intrinsic RV jitter of giant stars.

2.7.1 HD 219415

RVs of HD 291415 (BD+55 2926) were measured at 57 epochs over a period of

2650 days from July 2004 to October 2011 (Table 2.7). The S/N for these measurements ranged from 150 to 290. The exposure time ranged between 268 and 600 s. The estimated

1 median RV uncertainty for this star was 6.4 m s− . 57

The radial velocity variations of HD 219415 over a 7 year period are shown in

Figure 2.7, together with the best-fit model of a Keplerian orbit 2.2. At 5.7 years, this orbit has the longest period of any planet detected by our survey. For the assumed stellar mass of 1.0 M#, the planetary companion has a minimum mass of m2 sin i = 1.0 MJ , in a 3.2 AU, eccentric orbit. The FAP for this signal is <0.01%.

1 The Kjeldsen-Bedding amplitude estimate for this star is 1 m s− . Because the

1 post-fit residual of 9 m s− rms RV jitter is comparable to the formal measurement error, there was no need to increase it to account for the intrinsic RV variations.

Although the photometric data from two sources exist for HD 219415, neither offers a sufficient phase coverage of this very long orbit. We have used 218 WASP measurements (Pollacco et al. 2006) were made between 54388 and 54312, giving a mean magnitude of V =9.17 0.05. The additional 59 measurements from NSVS averaged at ± V =8.93 0.03. Neither of these data sets exhibits periodic brightness variations. ± 1 The mean value of the BVS for this star is 4.7 26.8ms− and the correlation − ± between the RV and the BVS is not significant, with a Pearson coefficient of r = -0.01.

The photometry derived RV and BVS amplitudes due to a the presence of a spot are 21-34

1 1 ms− and 23-36 m s− , respectively and are comparable to the observed RV variability.

However, if the radial velocity variations of HD 219415 were caused by a starspot, the period of the signal would be approximately equal to the stellar rotation period. While our period estimate of 140 1200 days is highly uncertain, it is inconsistent with the ∼ ± observed RV variations of the star. 58

2.7.2 Noise Floor

The range of orbital radii of planets discoverable around giants is restricted by stellar evolution and the √a minimum mass scaling of the Doppler velocity method.

Indeed, no planet around a K giant with an orbital radius smaller than 0.6 AU has been detected so far (Niedzielski et al. 2009a; D¨ollinger et al. 2009), in general agreement with the theoretical estimates based on the influence of tidal effects and stellar mass-loss on orbital evolution (Villaver & Livio 2009; Nordhaus et al. 2010; Kunitomo et al. 2011).

At the other end of the range of orbital sizes, the HD 219415 planet reported in this paper illustrates the detectability limits of wide orbit, long-period planets imposed by the enhanced intrinsic RV jitter in giants. This effect has been studied by Hekker et al.

(2006), who have demonstrated that the rms RV noise, σRV , of K giants has a median

1 value of 20 m s− and it tends to increase toward later spectral types. ∼ Both these limits are outlined in Figure 2.9. Evidently, planets down to Saturn- mass should be easily detectable around early giants over the 0.1-0.5 AU range of orbital radii, but their existence is apparently impaired by the dynamical effects of stellar evo- lution. For wide orbits, a 1 MJ planet around a 2 M# star would have a RV signal of

1 <20 m s− for a 1 AU, and could be buried in the intrinsic RV noise of a late-type ≥ giant. This detection threshold will become more important as the time baseline of the ongoing giant surveys continues to expand, and it will eventually place a practical upper limit on long-period planet detection around evolved stars. 59

2.8 Systems with Ramps

The selection criteria of our survey have been designed to reject targets that show

1 a RV ramp of >1kms− in preliminary measurements over the period of 2-3 months.

1 However, stars with a ramp of <1kms− over that time continue to be observed, if they

1 exhibit >20 m s− RV scatter around this trend. This has the net effect of rejecting close binaries, but allowing the detection of planets in widebinarysystems.Indeed, several of the planetary systems detected by PTPS, including BD+48 738 and BD+20

1 274, show long-term radial velocity trends with linear drift velocities of order 1 m s−

1 day− , suggesting that these stars have binary companions.

2.8.1 BD+48 738

RVs of BD+48 738 (AG +49 313) were measured at 54 epochs over a period of

2500 days from January 2004 to November 2010 (Table 2.8). The exposure times ranged between 420 and 1200 seconds depending on observing conditions. The S/N ratio ranged

1 between 90 to 342. The estimated median RV uncertainty for this star was 7 m s− .

The RV measurements of BD+48 738 over a 6 year period are shown in Figure

2.10. They are characterized by a long-term upward trend, with superimposed periodic variations. The best-fit Keplerian orbit model for the periodic component, with a circular orbit approximation for the observed trend, is given in Table 2.2. For the assumed stellar mass of 0.7 M#, the planetary companion has a minimum mass of m2 sin(i) = 0.91 MJ , in a 393 day, moderately eccentric orbit with a semi-major axis of 0.95 AU. The FAP for 60 this signal is <0.01%. Within errors, this solution is not sensitive to a particular choice of eccentricity to model the outer orbit.

A simultaneous characterization of the two orbits is difficult, as the outer com- panion’s period is much longer than the time baseline of our measurements. However, the curvature of the observed trend is statistically significant, with a FAP value of 0.01%.

This makes it feasible to constrain a range of possible two-orbit models by fitting for parameters of the inner planet over a grid of fixed solutions for the long-period orbit.

2 We have chosen to search for a χ minimum over a wide range of values in the a m − sin(i) e space following the method of Wright et al. (2007). The results are shown in − Figure 2.11 with contours marking the 1σ,2σ and 3σ confidence levels computed under the assumption that the post-fit residual noise has a Gaussian probability distribution.

To place limits on a range of the wide orbit models allowed by the available

RV data, we considered solutions within the 2σ contour and further restricted them to those with e<0.8, above which the occurrence of low mass stellar companions to F7-K primaries falls off(Halbwachs et al. 2005). For the same reason, models involving planet- mass companions were limited to those with e<0.6 (Butler et al. 2006). We tested the stability of these orbits, by carrying out many N-body simulations using the MERCURY

4 code (Chambers 1999). Orbits from the grid in Figure 2.11 were integrated for 10 years over a range of a, m sin(i) and e values within the 2σ contour.

As Figure 2.11 clearly shows, the curvature of the long-period orbit is not yet sufficient to produce tight constraints on the outer companion to BD+48 738. Although only a narrow range of massive planets out to a 10 AU is still allowed, it is much more ∼ likely that the companion’s minimum mass is in a brown dwarf or a low-mass star range 61 and that its orbit is at least moderately eccentric. Continuing observations of the star will help placing tighter constraints on the orbiting bodiesinthisinterestingsystem.

The only photometric database available for this star originates from the WASP measurements (Pollacco et al. 2006). The WASP data are contemporaneous with our

RV measurements and give a mean value of V =9.41 0.03, with no detectable periodic ± variations.

We have also derived bisectors and line curvatures for all the RV measurement

1 epochs, and obtained the mean values of BVS = 149.6 30.2 m s− and BC = 49.4 27.4 ± ± 1 ms− . Time variations of these parameters are not correlated with the observed RV variability and yield the corresponding correlation coefficients of r = 0.11 for the BVS and r = -0.08 for the BC time sequences, respectively.

2.8.2 BD+20 274

RVs of BD+20 274 (AG +20 153) are listed in Table 2.9. They were measured at

43 epochs over a period of 2550 days from October 2004 to October 2011. The S/N values ranged from 170 to 312. The exposure time was selected according to actual weather conditions and ranged between 527 and 824 s. The estimated median RV uncertainty

1 for this star was 6 m s− .

Radial velocity variations of BD+20 274 over a 7 year period are shown in Figure

2.13. They are characterized by a long-term upward trend, with superimposed periodic variations. The best-fit Keplerian orbit model for the periodic component, with the trend modeled as a circular orbit, is given in Table 2.2. For the assumed stellar mass of

0.8 M#, the planetary companion has a minimum mass of m2 sin(i) = 4.2 MJ , in a 578 62 day, mildly eccentric orbit with a semi-major axis of 1.3 AU. The FAP for this signal is

< 0.01%.

Characterization of the orbit of the more distant companion is difficult, as its period is much longer than the time baseline of our measurements. As there is little cur- vature to the observed trend, the most straightforward approach is to use the measured

1 1 linear RV drift rate, V˙ 0.81 m s− day− , to approximate the companion mass (in M ) ∼ J as a function of orbital radius (Bowler et al. 2010):

2 V˙ a m2 1.95 (2.2) ≈ (1ms−1 day−1)!1AU "

This shows that, for a 3 AU the outer companion becomes a brown dwarf and ≥ at a 7 AU the outer companion has a mass of 80 M , becoming another star. These ≥ J limits can be further restricted with the 0.4 M# minimum companion mass derived ∼ from the above provisional fit of a partial circular orbit to the RV data for BD+20 274.

1 The post-fit residuals for this model exhibit a large, 35 m s− rms noise. Assuming that this RV jitter is due to solar-like oscillations, the Kjeldsen-Bedding relation predicts

1 an amplitude of 27 m s− for this star. To account for these variations, we have ∼ 1 quadratically added 30 m s− to the RV measurement uncertainties before performing the least-squares fit of the orbit.

The photometry available for this star consists of 243 ASAS measurements (Poj- manski 2002), made between MJD 52625 and 55166. These data give a mean magnitude of the star of V =9.34 0.02. There are also 44 epochs of usable photometric obser- ± vations of this star available from the Northern Sky Variability Survey (NSVS; Wo´zniak 63 et al. 2004) with the mean V =9.11 0.02. Neither of these time series exhibits periodic ± brightness variations.

1 The mean value of the BVS for this star is 28.3 30.7ms− . No correlations ± between the RV variations and those of the BVS were found, with a correlation coefficient of r = -0.14. The calculated RV and BVS amplitudes due to the presence of a spot are

1 1 30 m s− and 6 m s− , respectively, which is much less than the observed variability.

2.8.3 Binary Companions

The dynamical constraints from these partial orbits are not highly restrictive, making it difficult to characterize the companions. However, further information about the secondaries can be obtained by examining the stellar spectra. The spectra of BD+20

274 do not show signs of lines from a second star, even in the stellar template which has

S/N = 355. If we assume that the companion must have S/N 10 to be detectable, ∼ this suggests that the luminosity ratio between the two objects is of order 1300, or ∼ about 8 magnitudes. As the absolute magnitude of a typical giant star is Mbol =0.08, the maximum mass of a MS companion is 0.5 M#. By examining the cross-correlation function used in the line bisector measurements in the manner of Queloz (1995), this estimate can be further restricted. Using the many lines in the CCF template increases the signal, giving a detectable line intensity ratio for the two stars of 3200. This ∼ corresponds to a secondary that is 9 magnitudes fainter, or about 0.3 M# for a main ∼ sequence star. Both these limits are consistent with those discussed above.

The more interesting of the stars with incomplete orbits is the case of the K0 giant, BD+48 738. In addition to a 0.91 M planet moving in a 1AU, 400 day ≥ J ∼ ∼ 64 orbit around the star, it exhibits a long-term RV trend with detectable curvature, which indicates the presence of another, more distant companion. The emerging curvature of this trend is not yet sufficient to determine whether the object has a substellar mass, or is a low-mass star.

In this context, it is interesting to note that there has been a growing number of detections of substellar companions to giants that have minimum masses in excess of

10 MJ , making them candidates for either brown dwarfs or supermassive planets (Lovis

& Mayor 2007; Liu et al. 2008; Sato et al. 2008a; D¨ollinger et al. 2009). In two cases, double brown dwarf - mass companions have been discovered suggesting the possibility that they originated in the circumstellar disk, similar to giant exoplanets (Niedzielski et al. 2009b; Quirrenbach et al. 2011). If the outer companion to BD+48 738 proves to be substellar, we may have another interesting case of an inner Jupiter-mass planet and a more distant, brown dwarf - mass body orbiting the same star.

In principle, such a system could form from a sufficiently massive protoplanetary disk by means of the standard core accretion mechanism (Ida & Lin 2004), with the outer companion having more time than the inner one to accumulate a brown dwarf like mass. A more exotic scenario could be envisioned, in which the inner planet forms in the standard manner, while the outer companion arises from a gravitational instability in the circumstellar disk at the time of the star formation (e.g. Kraus et al. 2011). In any case, it is quite clear that this detection, together with the other ones mentioned above, further emphasizes the possibility that a clear distinction between giant planets and brown dwarfs may be difficult to make (see, for example, Oppenheimer & Hinkley

2009). 65

2.9 Unresolved Systems

While the detection of planets around giant stars is necessary for a complete picture of planet formation, it is inherently more challenging than detecting planets around dwarfs. The increased stellar jitter makes it more difficult to characterize orbits of a given mass and semi-major axis, and this is especially true if a system has multiple planets. As such, there are several PTPS targets that are clearly RV-variable, but a conclusive orbital solution is not yet available.

Many of these cases will be resolved with further monitoring.However,insystems with multi-year periods, observing additional whole orbits can require a prohibitively large time baseline. In these cases, a practical solution is to present the available data and the best families of solutions.

2.9.1 HD 102103

RVs of HD 102103 (BD+15 2374, HIP 57320) were measured at 111 epochs over a period of 2680 days from February 2004 to June 2011 (Table 2.10). The exposure times ranged between 58 and 240 s depending on observing conditions. The S/N values were

1 consistently about 250. The estimated median RV uncertainty for this star was 5 m s− .

This is one of the most heavily sampled stars in our survey and it has proven to be one of the most challenging. There are multiple, close periodicities in the radial velocity signal, at 490, 290, 250 and 670 days. These produce several families of ∼ ∼ ∼ ∼ potential orbital solutions, none of which adequately reproduce the observed variations. 66

Combining two or more of these periodicities produces orbital solutions that are dynam- ically unstable. This system has been analyzed repeatedly over the course of the survey though acquiring further RV measurements has not led to much improvement in the fit.

The two families of solutions that best represent the data are shown in Figures

2.15 and 2.16, with parameters in Table 2.3. The 490 and 670 d orbits are both ∼ ∼ 2 highly eccentric and have similar χ values. Both orbits produce an adequate model of portions of the RV data, though neither is a good fit to the entire series of observations.

1 The post-fit residuals of both models have an rms error of 15 m s− , compara-

1 ble to the 19 m s− Kjeldsen-Bedding estimate for the RV jitter amplitude of this star.

1 To account for these variations, we have quadratically added 15 m s− to the RV mea- surement uncertainties prior to modeling the orbits. The FAPs for both solutions are

<0.01%.

As with BD+48 738, the orbit of the distant companion is much longer than the time baseline of our measurements. However, the curvature of the observed trend is statistically significant, with a FAP value of 0.04%. Again, we constrain a range of possible two-orbit models with a grid search, shown in Figure 2.19. The curvature of the long-period orbit is not yet sufficient to produce tight constraints on the outer companion to HD 102103. Though some solutions allow for a brown dwarf - mass object, it is more likely that the companion is a low-mass star.

Again, we can constrain the mass of the long-period orbit by examining the stellar spectra. Like with BD+20 274, the stellar template of HD 102103 star does not show lines from a companion. Given a S/N of 420, the luminosity ratio of the two objects is of order 8 magnitudes and the maximum mass of a MS companion is 0.5 M#.Usingthe 67 lines in the CCF template, this estimate can be further restricted to a luminosity ratio of 9 magnitudes, or about 0.3 M# for a main sequence star.

1 The mean value of the BVS for this star is 42.3 24.7 m s− . No correlation ± between the RV variations and those of the BVS were found, with a correlation coefficient of r = 0.02. The calculated RV and BVS amplitudes due to a the presence of a spot

1 1 are 40 m s− and 5 m s− , respectively, and comparable to the observed RV variability.

While our estimate for the rotation period of the star is highly uncertain, 360 1300 ∼ ± days, it is consistent with the observed RV variations of the star.

Because this star is relatively bright, the only photometry reliable database avail- able for this star is from 76 Hipparcos measurements (Perryman & ESA 1997), made between MJD 47878 and 48961. The mean magnitude of the star calculated from these data is V =6.68 0.01, with no detectable periodic variations. HD 102103 also appears ± in the ASAS database (Pojmanski 1997). The original saturation limit of this survey is

V 8, though more recent observations are broken into multiple exposures, changing ∼ the saturation limit to V 6.5. We obtained a light curve of non-saturated exposures ∼ from the authors and found no significant periodicities. The photometry series from both databases are shown in Figures 2.17 and 2.18.

With the available data, there are no indications that the periodic radial velocity variations may be due to stellar activity and the presence of a substellar companion remains the most compelling explanation. There are two families of orbital solutions that provide equally good fits to the data and we cannot provide definitive planet parameters at this time. To better understand the nature of these radial velocity variations, it would be advantageous to continue taking RV measurements through another periastron 68 passage. As this would require over a year of additional observations, a more immediate solution may be to make the data public as is. Input from other members of the scientific community may provide more complex analyses of the radial velocity measurements and perhaps a more conclusive orbital solution.

2.10 Highlights of the PTPS Survey

The Penn State-Toru´nPlanet Search has been responsible for a number of signif- icant developments in the study of planets around giant stars. Our published detections, together with new, confirmed systems that will soon be published, comprise 30% of the ∼ planet population around giants. The vast majority of known systems contain a single planet, while two of our detections show clear signs of multiplicity. In addition, several of our stars have wide binary components, and these are nearly the only examples of multi-stellar systems known among planet-hosting giants.

With such a large sample of targets, it will become possible for PTPS to carry out a statistical study of stellar properties, including masses, radii, metallicity and rotational velocities. It would also be beneficial to better understand how these characteristics relate to RV jitter levels, and thus the limits on planet detectability. To this end I carried out a preliminary study of intrinsic variability caused by p-mode oscillation and

find that the amplitude of these oscillations is inversely related to metallicity. This is an especially interesting result as it is not yet clear whether the metallicity-planet frequency correlation seen in dwarfs is also found in giants. The relationship found here creates a preference for higher metallicity stars to be more frequent hosts to detectable planets, so that the published studies must be biased by this trend. 69

Among our published detections are two stars that highlight the limits on orbital radii at which planets around giants are detectable with radial velocities. At 0.61 AU, HD

102272 b has one of the smallest semi-major axes of any planet yet found around a giant star, second only to HD 32518 at 0.59 AU (D¨ollinger et al. 2009). This is consistent with theoretical models of orbital evolution due to tidal effects and stellar mass-loss, which predict that closer planets may be ejected or consumed as the host ascends the giant branch. At the other extreme, the detection of distant planets is limited by the decreasing signal. For a fixed Doppler precision, the minimum detectable mass increases as √a. While this is true for all types of stars, it is especially relevant in giants due to their higher intrinsic RV variability. With an orbit of 3 AU, HD 219415 is approaching ∼ the limits of detectability.

Table 2.1. Stellar Parameters

Parameter HD240237 BD+48738 HD96127 BD+20274 HD102103 HD219415

V 8.19 9.14 7.43 9.36 6.51 8.94 B V 1.68 0.03 1.25 0.05 1.50 0.01 1.36 0.07 1.17 0.01 1.00 0.03 Sp− Type K2± III K0± III K2± III K5± III K0± III K0± III Teff [K] 4361 10 4414 15 4152 23 4296 10 4489 25 4820 20 π[mas] –± –± 1.85 ±0.89 –± 4.80 ±0.87 –± log(g)1.660.05 2.24 0.06 2.06 ± 0.09 1.99 0.05 2.45 ± 0.11 3.51 0.06 [Fe/H] -0.26 ± 0.07 -0.20 ± 0.07 -0.24 ± 0.10 -0.46 ± 0.07 -0.06 ± 0.13 -0.04 ± 0.09 ± ± ± ± ± ± log(L!/L!)2.49 0.20 1.69 0.33 2.86 0.47 1.96 0.18 2.13 0.21 0.62 0.15 ± ± ± ± ± ± M!/M! 1.69 0.42 0.74 0.39 0.91 0.25 0.8 0.2 1.7 0.3 1.0 0.1 ± ± ± ± ± ± R!/R! 32 11113517 17.3 0.9 19.2 1.2 2.9 0.4 ± ± ± ± ± ± Vrot[km/s] 1 1 0.5 2.0 1.5 2.7 1.5 1.1 1.5 ≤ ≤ ≤ ± ± ± 70

Table 2.2. Orbital Parameters

Parameter HD 240237b BD+48 738b HD 96127b BD+20 274b HD 219415b

P [days] 745.7 13.8 392.6 5.5 647.3 16.8 578.2 5.4 2093.3 32.7 ± ± ± ± ± T0 [MJD] 54292.0 28.3 54457.2 28.5 53969.4 31.0 53920.5 33.2 53460.9 57.7 K [m/s] 91.5 ±12.8 31.9 ±2.6 104.8 ±10.6 121.4 ±6.4 18.2 ±2.2 e 0.4±0.1 0.2 ±0.1 0.3 ±0.1 0.21 ±0.06 0.40 ±0.09 ω [deg] 108.1± 21.8 358.9± 31.1 162.0± 18.2 108.5± 38.1 207.0± 12.3 ± ± ± ± ± m2sin(i)[MJ ]5.30.914.04.21.0 a [AU] 1.9 1.0 1.4 1.3 3.2 2 χ 1.1 1.1 1.3 1.7 2.0 Post-fitrms[m/s] 36.0 16.0 50.0 35.8 8.8

Table 2.3. Possible Orbital Solutions for HD 102103

Parameter Solution1 Solution2

P [days] 678.2 3.2 493.0 2.5 ± ± T0 [MJD] 53656.3 9.3 53697.4 7.6 K [m/s] 42.1 ±5.7 23.5 ±3.0 e 0.63 ±0.05 0.53 ±0.06 ω [deg] 353.5± 4.5 330.0± 9.2 ± ± m2sin(i)[MJ ]2.01.1 a [AU] 1.8 1.5 2 χ 1.0 1.0 Post-fitrms[m/s] 15.3 15.1 71

Table 2.4. Planet-Hosting Giants with Published RMS Values

−1 Name B-V log(g)[Fe/H]M!/M! R!/R! rms [m s ]Reference BD+20 2457 1.25 3.17 -1.0 2.8 49 60 Niedzielski et al. (2009b) BD+48 738 1.25 2.24 -0.2 0.74 11 16 Gettel et al. (2012b) HD 11977 0.93 2.90 -0.21 1.91 10 29 Setiawan et al. (2005) HD 13189 1.47 1.07 -0.58 4 50 42 Hatzes et al. (2005) HD 17092 1.25 3.0 0.18 2.3 11 16 Niedzielski et al. (2007) HD 32518 1.11 2.10 -0.15 1.13 10 18 D¨ollinger et al. (2009) HD 81688 0.99 2.22 -0.36 2.1 13 24 Sato et al. (2008a) HD 96127 1.50 2.06 -0.24 0.91 20 50 Gettel et al. (2012b) HD 102272 1.02 3.07 -0.26 1.9 10 15 Niedzielski et al. (2009a) HD 104985 1.03 2.62 -0.35 2.3 11 27 Sato et al. (2003) HD 119445 0.88 2.40 0.04 3.9 20 13.7 Omiya et al. (2009) HD 139357 1.20 2.9 -0.13 1.35 12 14 D¨ollinger et al. (2009) HD 145457 1.04 2.77 -0.14 1.9 10 10 Sato et al. (2010) HD 173416 1.04 2.48 -0.22 2 13 18.5 Liu et al. (2009) HD 180314 1.00 2.98 0.20 2.6 9 13 Sato et al. (2010) HD 240210 1.65 1.55 -0.18 1.25 11 25 Niedzielski et al. (2009b) HD 240237 1.68 1.68 -0.26 1.69 20 34 Gettel et al. (2012b) NGC 2423 No 3 1.21 - 0.14 2.4 - 18 Lovis & Mayor (2007) NGC 4349 No 127 1.46 - -0.12 3.9 - 13 Lovis & Mayor (2007) γ Leo A 1.13 1.59 -0.49 1.23 40 43 Han et al. (2010) * Tau 1.01 2.64 0.17 2.7 14 10 Satoetal.(2007) ι Dra 1.18 2.24 0.03 1.05 13 10 Frink et al. (2002) ξ Aql 1.02 2.66 -0.21 2.2 12 22 Sato et al. (2008a) 4UMa 1.20 1.8 -0.25 1.23 - 30 D¨ollingeretal.(2007) 11 Com 0.99 2.5 -0.35 2.7 19 25.5 Liu et al. (2008) 11 UMi 1.40 1.60 0.04 1.8 24 28 D¨ollinger et al. (2009) 14 And 1.03 2.63 -0.24 2.2 11 20 Sato et al. (2008b) 18 Del 0.93 2.82 -0.05 2.3 9 15 Sato et al. (2008a) 42 Dra 1.19 1.71 -0.46 0.98 22 14 D¨ollinger et al. (2009) 81 Cet 1.02 2.35 -0.06 2.4 11 9 Sato et al. (2008b) 72

Table 2.5: Relative Radial Velocity Measurements of HD 240237

1 1 Epoch [MJD] RV [m s− ] σRV [m s − ] 53188.39793 83.7 7.3 53545.43082 59.3 7.8 53654.28150 -5.7 8.9 53663.09284 -65.0 8.1 53664.25192 -66.6 5.1 53893.44619 122.4 6.6 53897.43174 161.8 8.3 53900.44113 123.0 6.1 53903.41408 113.6 8.9 53906.45211 129.3 7.0 54021.25319 61.8 4.5 54041.06348 102.9 6.2 54057.02965 175.2 6.0 54057.16257 173.4 8.1 54075.12739 132.2 5.3 54092.10329 147.2 6.7 54110.05038 194.7 8.1 54277.40802 55.1 7.5 54282.39529 49.3 5.3 54331.26734 -34.7 6.6 54360.18436 -29.2 6.1 54438.14524 54.9 6.4 54440.13141 18.4 4.7 54474.05096 25.0 7.2 54628.44381 37.0 5.5 54632.43929 51.8 4.7 54633.42385 43.6 7.2 54639.38022 119.8 8.2 54725.35386 147.5 10.3 54743.31509 94.9 5.1 54758.09993 145.2 7.8 54777.22166 129.9 6.8 54792.16502 175.7 7.2 54812.12646 106.2 6.7 54844.04772 190.2 8.4 55049.45087 56.2 7.6 55073.23259 -23.0 11.5 55097.18015 19.1 7.2 55118.24693 7.6 16.6 55118.29165 8.1 7.1 73

Table 2.6: Relative Radial Velocity Measurements of HD 96127

1 1 Epoch [MJD] RV [m s− ] σRV [m s − ] 53026.53749 -777.2 9.0 53026.54185 -775.3 8.5 53367.37012 -1114.1 4.5 53686.48016 -907.8 4.5 53721.40397 -804.9 5.9 53729.38407 -900.5 5.1 53736.34525 -916.9 7.8 53743.33658 -811.9 7.1 53752.29643 -879.8 6.4 53764.28676 -876.5 4.1 53794.19661 -875.5 6.9 53833.10419 -817.3 3.7 53844.28240 -832.5 5.4 53844.28410 -831.7 4.3 53844.28580 -826.9 6.1 53865.23660 -918.7 5.3 53865.23833 -920.6 5.4 53865.24019 -927.9 3.3 53865.24261 -919.8 2.6 53865.24509 -924.6 4.9 53877.19750 -905.2 7.7 53901.12750 -991.1 9.0 53901.12920 -992.5 6.9 53901.13090 -1003.2 7.8 54035.51530 -966.9 10.2 54035.51907 -985.7 7.3 54045.50512 -949.8 6.4 54080.41056 -1042.7 4.6 54121.29308 -937.0 5.4 54121.29877 -936.7 5.0 54156.19835 -870.1 8.3 54156.43557 -889.9 6.5 54190.11983 -838.9 4.6 54194.11568 -908.2 5.9 54194.11953 -897.9 5.9 54212.26824 -827.2 6.2 54212.27186 -843.2 6.1 54224.23445 -894.3 7.0 54242.19050 -943.1 5.1 54264.13327 -798.4 9.5 54437.44407 -867.4 5.0 54480.32430 -869.3 16.8 54483.30162 -1021.7 5.2 54506.47125 -860.1 6.0 54527.19861 -997.1 9.3 54548.14498 -992.4 6.1 Continued on Next Page. . . 74

Table 2.6 – Continued

1 1 Epoch [MJD] RV [m s− ] σRV [m s − ] 54553.12181 -930.6 6.5 54560.09780 -967.2 6.4 54597.23256 -1018.5 7.1 54870.48390 -934.4 7.6

Table 2.7: Relative Radial Velocity Measurements of HD 219415

1 1 Epoch [MJD] RV [m s− ] σRV [m s − ] 53187.40006 -11.7 7.6 53525.43966 -1.5 8.8 53545.42248 -23.1 7.6 53626.17152 -16.5 7.7 53627.17216 -5.7 6.2 53629.17049 -1.1 6.6 53629.35712 -21.3 6.7 53633.15274 -14.5 7.3 53635.15738 -20.4 5.7 53641.13173 -6.3 6.3 53642.13987 -2.4 6.9 53655.10601 6.7 6.5 53663.25945 11.8 7.0 53892.44493 1.0 7.4 53892.44889 5.7 6.7 53892.45286 21.5 5.8 53895.43792 12.3 7.2 53895.44190 18.2 6.7 53895.44587 14.0 6.4 53899.40469 10.5 7.1 53899.40864 13.5 7.2 53899.41261 10.3 8.4 53901.42493 8.6 12.8 53901.42890 22.7 10.5 53901.43287 5.1 12.1 53904.43579 -0.3 5.4 53904.43976 -7.4 5.9 53904.44373 5.1 5.5 53911.40384 10.9 5.6 53911.40817 8.1 5.1 53911.41250 2.3 5.0 54076.13801 2.6 6.0 54096.08539 23.3 7.3 54347.41372 -3.7 6.8 54375.32882 4.5 5.1 Continued on Next Page. . . 75

Table 2.7 – Continued

1 1 Epoch [MJD] RV [m s− ] σRV [m s − ] 54400.07298 3.8 5.8 54426.18997 20.2 6.0 54454.10736 17.8 7.7 54698.44253 7.5 6.3 54727.35885 16.3 7.3 54755.10432 -6.4 6.9 55049.45800 -0.8 5.8 55084.39427 -11.1 5.9 55110.30134 -17.7 7.4 55199.05491 -0.3 7.8 55444.20009 -18.0 6.0 55468.13783 -37.3 6.0 55730.42347 13.8 5.7 55749.36916 -8.1 6.1 55758.34505 -6.1 6.2 55768.29091 -12.5 5.6 55779.46525 1.0 6.5 55796.43008 -5.2 4.6 55813.22070 -4.1 5.7 55821.17612 2.0 6.3 55830.32469 0.5 6.2 55840.30572 -7.1 6.0

Table 2.8: Relative Radial Velocity Measurements of BD+48 738

1 1 Epoch [MJD] RV [m s− ] σRV [m s − ] 53033.65040 -721.3 11.6 53337.60326 -633.0 8.0 53604.86380 -615.7 7.4 53680.90190 -544.3 6.6 53681.65521 -552.3 7.8 53970.86815 -553.0 5.9 54006.77500 -519.2 6.3 54022.73748 -526.3 6.7 54034.69078 -470.7 5.6 54048.65158 -471.8 6.8 54071.79441 -483.0 3.8 54086.56153 -495.7 5.0 54101.71295 -493.5 4.5 54121.67129 -481.9 8.9 54121.68284 -489.5 6.6 54134.63773 -497.1 9.2 54149.60381 -515.6 8.8 Continued on Next Page. . . 76

Table 2.8 – Continued

1 1 Epoch [MJD] RV [m s− ] σRV [m s − ] 54159.58385 -513.4 5.9 54162.57425 -503.5 6.6 54341.85828 -491.4 7.6 54365.78790 -480.4 6.3 54381.96192 -453.8 5.7 54399.68128 -458.0 6.6 54423.63082 -427.9 5.6 54440.79597 -433.9 5.4 54475.71081 -449.5 4.8 54507.61437 -451.5 5.9 54687.89250 -417.5 7.9 54713.82938 -432.2 7.4 54729.77925 -409.6 8.3 54744.74995 -383.3 11.7 54759.92066 -403.3 6.5 54774.68442 -402.6 8.0 54786.85953 -411.2 7.6 54794.61064 -361.8 6.8 54812.59536 -377.5 7.1 54821.55344 -378.8 7.0 54857.66375 -375.1 9.3 54883.60178 -336.9 6.0 55048.92340 -397.6 4.9 55073.84747 -407.6 6.0 55102.77619 -417.5 3.4 55172.57767 -357.1 8.3 55198.71716 -352.9 4.9 55222.66132 -343.9 7.1 55246.58682 -300.8 7.5 55246.61535 -308.4 8.5 55249.61437 -328.3 6.2 55444.83373 -387.4 4.5 55468.74896 -368.4 7.1 55493.71079 -406.5 5.5 55493.71948 -404.3 6.3 55498.68716 -347.8 5.1 55513.63941 -366.4 6.4

Table 2.9: Relative Radial Velocity Measurements of BD+20 274

1 1 Epoch [MJD] RV [m s− ] σRV [m s − ] 53299.17090 -1446.2 8.7 53629.46776 -1122.8 6.2 Continued on Next Page. . . 77

Table 2.9 – Continued

1 1 Epoch [MJD] RV [m s− ] σRV [m s − ] 53954.38543 -946.8 5.3 54014.22433 -971.8 4.7 54057.10443 -847.7 5.1 54067.27214 -793.8 6.2 54073.24994 -782.8 5.6 54338.32091 -325.7 6.5 54359.47756 -354.9 6.6 54377.41906 -348.7 5.7 54407.14137 -376.1 6.1 54442.05559 -319.7 5.4 54504.07923 -350.3 6.3 54670.41663 -321.2 6.7 54723.28207 -288.9 6.2 54743.23171 -171.8 6.9 54758.18574 -182.2 7.0 54773.34312 -82.4 8.3 54830.18984 -14.2 7.0 54861.11542 37.2 7.3 55048.39243 115.1 6.8 55073.31980 -0.9 7.8 55074.30710 58.4 5.7 55102.23907 36.0 5.4 55410.38790 464.9 4.7 55412.38876 400.3 4.9 55413.39281 437.3 5.1 55416.37806 400.5 5.1 55467.22365 476.2 8.5 55468.23303 473.3 5.8 55475.42403 489.0 4.5 55482.20431 532.5 6.8 55491.17869 467.0 6.4 55520.28880 540.6 6.8 55526.27547 495.8 7.0 55530.27249 592.9 7.0 55538.04299 508.4 7.6 55552.22245 549.1 6.3 55566.17674 572.6 5.9 55571.16468 561.7 7.2 55760.43565 483.4 5.7 55789.35501 469.6 5.2 55847.39550 646.4 5.0 78

Table 2.10: Relative Radial Velocity Measurements of HD 102103

1 1 Epoch [MJD] RV [m s− ] σRV [m s − ] 53042.49427 -418.5 6.7 53183.11965 -381.2 4.8 53366.42793 -273.6 10.8 53367.40995 -271.2 7.0 53389.34521 -289.6 7.0 53476.11432 -242.1 4.3 53476.29217 -228.8 4.0 53480.10452 -247.4 4.1 53481.29347 -213.1 4.2 53486.28836 -223.0 3.8 53487.27481 -256.7 3.5 53492.24259 -237.9 4.4 53498.25269 -266.2 3.8 53507.22394 -234.8 4.3 53508.22336 -261.9 4.2 53522.19795 -242.5 4.7 53525.18405 -246.2 4.7 53539.13056 -246.7 5.6 53542.11805 -238.3 5.2 53543.13033 -246.4 5.3 53544.12645 -231.8 4.9 53693.50495 -98.2 3.7 53694.50344 -116.1 3.3 53695.51211 -118.7 3.8 53696.51091 -107.9 3.4 53697.49660 -98.3 3.4 53700.49304 -97.0 3.7 53703.49155 -97.7 4.9 53705.47093 -107.7 4.1 53710.47729 -112.0 4.4 53723.44173 -109.0 4.6 53730.41458 -103.8 4.6 53736.39175 -90.9 5.8 53742.38536 -97.4 4.1 53758.35039 -92.6 4.7 53764.32168 -100.8 4.1 53773.29710 -86.0 4.8 53778.48461 -62.8 4.9 53792.24279 -82.3 4.6 53797.22627 -103.9 4.2 53801.22920 -109.5 5.1 53811.18571 -103.6 4.2 53820.35750 -89.7 4.5 53832.14802 -94.1 5.3 53838.12730 -83.8 4.2 53888.18488 -63.1 5.3 Continued on Next Page. . . 79

Table 2.10 – Continued

1 1 Epoch [MJD] RV [m s− ] σRV [m s − ] 53891.15497 -71.5 4.7 53894.16230 -77.1 4.8 53901.13467 -61.9 5.3 54053.52394 -12.3 3.7 54055.51434 7.2 4.4 54057.51392 -4.5 3.6 54060.52872 -2.3 4.1 54060.53064 2.5 4.2 54062.50576 8.6 4.4 54064.49499 -1.0 5.3 54064.49770 4.8 4.8 54066.48792 4.4 4.1 54068.49137 -10.9 5.4 54068.49795 -18.9 5.0 54080.45786 21.9 4.6 54095.43359 1.8 5.5 54095.43589 4.9 5.2 54108.39122 12.0 5.7 54108.39457 18.4 4.9 54127.33124 47.7 5.4 54140.30357 25.3 6.4 54140.47677 60.2 4.8 54155.24837 50.8 5.2 54155.25060 55.6 4.3 54177.39441 68.6 4.3 54180.18225 67.7 4.6 54193.33262 78.9 4.1 54212.27885 70.0 4.0 54224.25230 90.4 4.3 54225.25238 83.0 5.1 54226.25425 97.0 5.0 54242.21388 107.9 4.4 54258.17001 85.2 5.2 54432.49910 141.2 4.3 54437.49361 148.5 5.2 54452.44064 123.5 5.8 54474.38548 173.4 5.0 54506.47924 182.7 5.1 54521.24649 156.5 5.2 54544.19109 178.1 5.9 54562.13175 171.4 5.5 54589.24548 193.5 5.2 54807.46725 255.3 5.2 54840.38484 273.1 6.2 54865.33233 283.1 7.6 54865.33557 287.2 5.1 54890.22285 298.0 6.5 Continued on Next Page. . . 80

Table 2.10 – Continued

1 1 Epoch [MJD] RV [m s− ] σRV [m s − ] 54908.18163 294.4 4.9 54929.14501 311.7 6.7 55344.20258 391.0 5.9 55350.16265 355.4 5.4 55356.17847 378.7 6.0 55362.15062 378.0 5.6 55520.52029 418.0 5.3 55549.43324 402.3 6.7 55577.37057 431.8 6.0 55581.35036 421.7 4.8 55607.27479 450.4 5.2 55637.19227 453.6 5.1 55652.33771 470.3 5.2 55674.10713 504.8 5.4 55680.09852 523.8 5.2 55687.25389 503.0 9.5 55702.21345 520.5 5.4 55727.13853 516.4 5.3 81

3

2.5

2

1.5

1

0.5 log L/Lsun 0

-0.5

-1

-1.5 3.85 3.8 3.75 3.7 3.65 3.6 3.55 log Teff [K] Fig. 2.1 The PTPS target stars, with 225 giants (grey dots), 350 red clump giants ∼ ∼ (blue dots), 225 subgiants (dark blue dots) and 100 dwarfs (black dots). ∼ ∼ 82

Fig. 2.2 Top: Radial velocity measurements of HD 240237 (circles) and the best-fit single planet Keplerian model (solid line). Bottom: The post-fit residuals for the single planet model. 83

Fig. 2.3 HD 240237 data folded at the best-fit orbital period. From top to bottom: (a) 1 Radial velocity measurements with the best-fit model (b) Bisector Velocity Span (m s− ) 1 (c) Bisector Curvature (m s− ) (d) Hipparcos photometry. 84

Fig. 2.4 Top: Radial velocity measurements of HD 96127 (circles) and the best-fit single planet Keplerian model (solid line). Bottom: The post-fit residuals for the single planet model. 85

Fig. 2.5 HD 96127 data folded at the best-fit orbital period. From top to bottom: (a) 1 Radial velocity measurements with the best-fit model (b) Bisector Velocity Span (m s− ) 1 (c) Bisector Curvature (m s− ) (d) Hipparcos photometry. 86

Fig. 2.6 Top: Post-fit rms RV error for Keplerian orbit models as a function of the B V color for giant stars with published substellar companions (open circles), the stars − discussed in Gettel et al. (2012b) (filled circles), and stars with new, unpublished planet candidates from this survey (triangles). Theoretical predictions of the p-mode oscillation amplitude as a function of B V , derived from a modified Kjeldsen-Bedding relationship, − are shown as a set of curves for five fixed values of [Fe/H]. The shaded region indicates the range of RV precision of the different giant star planet surveys. Bottom: The same data plotted as a function of the observed [Fe/H]. Also shown are the theoretical curves for two fixed values of B V . − 87

Fig. 2.7 Top: Radial velocity measurements of HD 219415 (circles) and the best-fit single planet Keplerian model (solid line). Bottom: The post-fit residuals for the single planet model. 88

Fig. 2.8 HD 219415 data folded at the best-fit orbital period. From top to bottom: (a) 1 Radial velocity measurements with the best-fit model (b) Bisector Velocity Span (m s− ) (c) WASP photometry. 89

Fig. 2.9 Discovery space for RV planets around dwarfs (small dots) and giant stars (large 1 dots). A detection sensitivity for typical jitter amplitudes in early giants ( 20 m s− )is ∼ indicated by dashed line, with HD 219415 b shown below this limit (star). The shaded region marks the range of minimum orbital radii predicted by theory. The dash-dotted line at 10 R# marks the typical radius of an early giant. 90

Fig. 2.10 Top: Radial velocity measurements of BD+48 738 (circles) and the best-fit model consisting of a circular approximation for the long-period orbit, and a 390 day planetary orbit (solid line). Bottom: The post-fit residuals for the above model. 91

) 100 Jup m sin i (M

10

10 100 a (AU)

2 Fig. 2.11 Contours of χ and e in a - m sin i space of best-fit orbits to the RV data 2 for the outer companion of BD+48 738, with χ in gray scale. The solid contours mark 2 the levels at which χ increases by 1, 4 and 9 from the minimum, which corresponds to the 1σ,2σ and 3σ confidence intervals. The dashed contours approximately mark the levels of the eccentricity of 0.2, 0.4, 0.6 and 0.8, from the inner to the outer contour, 4 respectively. Orbits interior to the grey contour are found to be stable for at least 10 years. 92

Fig. 2.12 BD+48 738 data folded at the best-fit orbital period. From top to bottom: (a) Radial velocity measurements with the best-fit inner planet model and the outer orbit 1 1 removed (b) Bisector Velocity Span (m s− ) (c) Bisector Curvature (m s− )(d)WASP photometry. 93

Fig. 2.13 Top: Radial velocity measurements of BD+20 274 (circles) and the best-fit model consisting of the circular orbit of a long-period companion, and a 582 day planetary orbit (solid line). Middle: The RV measurements and best-fit model after the subtraction of the long-term circular orbit. Bottom: The post-fit residuals for the two orbit model. 94

Fig. 2.14 BD+20 274 data folded at the best-fit orbital period. From top to bottom: (a) Radial velocity measurements after the removal of the outer orbit, along with the 1 best-fit inner planet model (b) Bisector Velocity Span (m s− ) (c) ASAS photometry. 95

Fig. 2.15 Top: Radial velocity measurements of HD 102103 (circles), the best-fit model consisting of the circular orbit of a long-period companion, and a 680 day planetary orbit (solid line). Middle: The RV measurements and best-fit model after the subtraction of the long-term circular orbit. Bottom: The post-fit residuals for the two orbit model. 96

Fig. 2.16 Top: Radial velocity measurements of HD 102103 (circles), the best-fit model consisting of the circular orbit of a long-period companion, and a 490 day planetary orbit (solid line). Middle: The RV measurements and best-fit model after the subtraction of the long-term circular orbit. Bottom: The post-fit residuals for the two orbit model. 97

Fig. 2.17 HD 102103 data folded at the 678 d orbital solution. From top to bottom: (a) Radial velocity measurements after the removal of the outer orbit, along with the 1 best-fit inner planet model (b) Bisector Velocity Span (m s− ) (c) Hipparcos photometry (d) ASAS photometry. 98

Fig. 2.18 HD 102103 data folded at the 493 d orbital solution. From top to bottom: (a) Radial velocity measurements after the removal of the outer orbit, along with the 1 best-fit inner planet model (b) Bisector Velocity Span (m s− ) (c) Hipparcos photometry (d) ASAS photometry. 99

1000 ) Jup

100 m sin i (M

10 100 a (AU)

2 Fig. 2.19 Contours of χ and e in a - m sin(i) space of best-fit partial orbits to the RV data 2 for the outer companion of HD 102103, with χ in gray scale. The solid contours mark 2 the levels at which χ increases by 1, 4, and 9 from the minimum, which correspond to the 1σ,2σ, and 3σ confidence intervals. The dashed contours approximately mark the levels of the eccentricity of 0.4, 0.6, and 0.8, from the inner to the outer contour, respectively. The dotted lines mark the estimated upper limits to the mass of the companion. 100

Chapter 3

Observations of Radial Velocity Stable M Dwarfs

There has been great interest in recent years in detecting planets around low mass stars, taking advantage of the increased stellar reflex motion to detect the smallest possible planets with the available RV precision. These stars produce a majority of their light redward of 6000 A,˚ and so are not optimized for iodine cell surveys. The ∼ region between 6000-9000 A˚ has no comparable laboratory absorption medium, but ∼ instead contains several bands of telluric water vapor and oxygen lines. These features

1 are stable to <10 m s− and readily observable with current technology, providing a means to calibrate wavelengths across the R-band and making the flux in this region available for radial velocity surveys.

To that end, it is valuable to determine the radial velocity precision attainable by using R-band telluric lines as a wavelength standard. To test their utility, I performed a mock survey with the Hobby-Eberly Telescope (HET) on stars previously observed to be radial velocity stable, giving us a recoverable null signal. Observations were made in a fashion similar to the planet searches ongoing at HET (Niedzielski et al. 2009a; Cochran et al. 2004), using the High-Resolution Spectrograph (HRS) in queue-scheduled mode.

Most observations were made through the iodine gas cell, allowing for a comparison between our calibration technique and the more conventionalmethod. 101

3.1 Targets

The target list was selected from a group of RV stable early M dwarfs. These stars were observed with the HET by Endl et al. (2003) as part of a planet survey and each was

1 found to have an rms variability of <10 m s− . Though nine stars were observed, three of these were later discarded as they were observed less than five times. The remaining targets are shown in Table 3.1.

Endl’s target list was based on Gliese’s Catalog of Nearby Stars (Gliese & Jahreiss

1991) and compared with the ROSAT All-Sky Survey to rule out X-ray emission (H¨unsch et al. 1999). The latter criteria should limit starspot activity and decrease RV variability.

The RV scatter reported in the original paper was found to be dominated by photon noise.

Six telluric standards were also observed, one for each M dwarf. Each of these

1 is a rapidly rotating A star with V sin(i) > 120 km s− , ensuring that the few stellar lines are heavily broadened. Thus, the observed spectrum only contains features from the Earth’s atmosphere. The telluric standards were chosen from a list of HET standard stars and selected for their proximity to our targets.

3.2 Data Collection

The spectrograph was used in the R = 60,000 resolution mode with the gas cell

(I2) inserted in front of the spectrograph slit, and it was fed with a 2” fiber. The

316g6948 cross-disperser configuration was used, allowing access both to most of the I2 cell spectrum and the water vapor band at 820 nm, which is not available with the ∼ 316g5936 configuration typically used for radical velocity measurements with the iodine 102 cell. The spectra consist of 33 echelle orders recorded on the blue CCD (505-699 nm) and 19 orders on the red one (695-892 nm).

The observing strategy for each target was to take 5-10 observations over the course of one observing trimester, to test for lack of short-term variability. These obser- vations were made between December 2009 and March 2010. Most observations consist of a 6-11 minute exposure of the target star taken through the iodine cell. The exposure time was chosen to produce S/N = 200 at 720 nm, in one of the water vapor bands. A calibration image was made for each epoch, typically at the end of the night, to track small changes in the instrumental point-spread function (PSF), with the gas cell illumi- nated by the flatfield lamp. An additional image was taken for the first observation of each target, of the target star without the iodine cell, directly before or after the normal star+iodine exposure. These stellar-only observations are used as template observations in the iodine technique.

Making the equivalent template observations for the telluric technique (i.e. stellar observations without telluric lines) is impossible with a ground-based telescope. Instead,

I took a second series of observations in December 2010 and February 2011 with higher

S/N and removed the telluric features from the spectra afterward. A S/N = 400 template observation was taken for each target, without the iodine cell. These were broken into 2 or 3 exposures as needed to prevent the CCDs from saturating. Directly before or after the template observation, a telluric standard star was observed, with S/N ranging from

600-1000. Because all of the telluric features in the spectra of our M dwarfs are blended with stellar features, these telluric standards can provide a more accurate measure of atmospheric line strengths. However, as the atmospheric conditions can change very 103 rapidly, it is necessary to observe the target star and the telluric standard back-to-back.

As with the stellar template exposures, these observations were broken into multiple exposures.

3.3 Data Reduction

I reduced the M dwarf data using the recent REDUCE IDL package by Piskunov

& Valenti (2002). REDUCE has advantages over the traditional IRAF scripts, as its optimal extraction algorithm results in less noise and automatically corrects bad pixels.

It is also highly adaptable and conducive to scripting. I developed a pipeline to select and reduce images of a given HET configuration for each epoch. This pipeline was later refined by Wang (2012) and has become the standard reduction pipeline for the Penn

State Doppler programs.

The HRS red CCD contains a few bad columns that are nearly parallel to the echelle orders and cross several orders over the length of the chip. These can be avoided by using a binary pixel mask. The blue CCD contains very few intrinsic defects, however it suffers from a bright artifact across one corner presumably caused by light reflected inside the spectrograph. This effect is quite pronounced in the 316g5936 configuration, crossing several orders and interfering with REDUCE’s automated order location routine.

The position and shape of the artifact changes slightly between epochs, requiring a mask large enough to cover the full range of affected pixels. In the 316g6948 configuration, this bright streak is present but much less prominent, affecting a small region near the edge of the CCD. As there is little signal in this region, these pixels are usually discarded and it is not necessary to use a mask. 104

The reduction method follows standard echelle reduction techniques, beginning with generation of a mean bias frame to subtract read noise and a master flat frame to scale the pixel to pixel gain variations to the average gain oftheCCD.TheREDUCE package introduced two algorithms, one for locating orders and another for spectral decomposition. The former automatically identifies clusters of pixels that may be related and merges neighboring clusters of pixels into an order, then generates a polynomial fit to each order location. We use a third order polynomial fit and with the use of masks as described above, find this to be robust against order mis-identification. However this algorithm is computationally expensive and we find it sufficient to identify orders by generating a map from the order locations of one epoch and allowing for small translations of the orders between epochs (Wang 2012).

Spectral order decomposition breaks down an order S into a spectrum f and its spatial profile g, a monochromatic image of the illuminated slit, ideally aligned along the detector columns:

S(x, y)=f(x) g(y y0(x)) (3.1) × −

In practice, the image is then convolved with the PSF of the spectrograph and discretely sampled by pixels of significant size. As echelle orders are slightly curved, they cross between detector rows over the length of the CCD, causing variations in the maximum detected flux. In addition, HRS orders are noticeably diagonal to the detector rows.

To reproduce these flux variations, it is necessary to oversample the spatial profile by a factor M. The default value used by REDUCE is M = 12, though we found it necessary to double the oversampling to limit ringing in the fit of the spatial profile. The 105 decomposition algorithm also smooths the spatial profile, limiting the effect of cosmic rays and bad pixels. The spatial profiles and spectra are stored for ‘swaths’ of a few hundred pixels each and used throughout the remaining reduction process.

The scattered light background is estimated by making a linear fit to the bottom of the spatial profile of each order, at each column, and filtering these fits along the order. The scattered light at each pixel is calculated by linear interpolation and then subtracted.

The master flat frame is normalized to prevent the low-signal regions of the orders from amplifying noise in the science images. This can be particularly important with a fiber-fed spectrograph, as the low-signal regions of the flat frame may correspond to the low-signal regions of the science images. This effect is mitigated for HRS as the calibration fiber is significantly wider than the science fiber. The spatial profiles and spectra created during the order composition are used to construct a template for normalizing the flatfield. The spectra from all swaths are used to create an order shape function. The spatial profiles from the nearest swaths are linearly interpolated to each column of an order and scaled to the shape function, then divided to normalize the column.

After bias subtraction, flatfield normalization and scattered light subtraction, the science images are optimally extracted. This technique creates a two-dimensional image of the spatial illumination profile at each wavelength. In REDUCE, this is done using the decomposition algorithm described above. This treatment is only truly appropriate if the PSF can be represented as a separable function in row and column offset from the

PSF centroid. This condition is not met for a fiber-fed spectrograph, but it is generally 106 adequate for smoothly varying spectra (Bolton & Schlegel 2010). The spectra then can be continuum normalized using the order shape functions determined during the normalization of the flatfield, though in practice we simply store these values and leave the extracted spectra in counts.

3.4 Wavelength Calibration with ThAr

Both the RV pipelines and the telluric modeling code require a ‘first guess’ of the wavelength solution to function. Within the iodine region, this guess is a stored wave- length solution created during a previous run of the pipeline. For all other wavelength regions, the guess is created using the Thorium-Argon (ThAr) calibration spectra taken for each epoch.

The ThAr spectrum has features over the entire spectral range of HRS, from 390 nm to 1.1 µm. However, it is a less than adequate calibration source for precision work, as the images are taken through a different fiber than the stellar spectra. This difference in the optical path can cause changes in the wavelength zero point and dispersion as the conditions in the spectrograph change. As a result, the wavelength solution obtained

1 using ThAr can be expected to vary by up to 100 m s− night-to-night (Norris et al. ∼ 2011). This level of precision is generally a sufficient starting point.

The ThAr exposures are 20 s each and typically taken at the end of the night, though they were occasionally taken in conjunction with the science images. The orders are extracted without optimization to save computing time. While REDUCE provides 107 an interactive wavelength calibration package, I opted to use the IRAF routine ECIDEN-

TIFY due to familiarity. The wavelength solution was fit using sixth-order Chebyshev polynomials and automatically adjusted to match the ThAr exposure for each epoch.

I applied the ThAr wavelength solution to the M dwarf spectra as input to the tel- luric modeling code. As shown in Figure 3.2, this calibration was frequently insufficient.

TERRASPEC (Bender 2012) generates atmospheric spectra using their fundamental line frequencies and it does not have the ability to alter the input wavelength scale. As such, if the input wavelength scale is incorrect, the observed telluric lines will not be properly modeled and removed, producing distinctive artifacts in the corrected spectrum.

This effect is most pronounced when the the ThAr exposures were taken at the beginning or end of the night. Due to the other concurrent observing programs at

HET, the configuration of the cross-disperser was usually changed between the science observations and the ThAr observations. We find that the cross-disperser setting is only repeatable to within 1-2 pixels. To ameliorate this effect, the ThAr exposures were taken immediately before or after the science observations during the second series of observations. The resulting ThAr wavelength scale is then sufficient for modeling telluric features, as shown in Figure 3.3. 108

Table 3.1. Radial Velocity Stable Targets

Star Spectral Type V (mag) Published RV Scatter (m/s)

GJ 184 M0 V 9.93 7.3 GJ 272 M2 V 10.53 4.0 GJ 277.1 M0 V 10.49 8.7 GJ 281 M0 V 9.61 6.6 GJ 328 M1 V 9.99 6.2 GJ 353 M2 V 10.19 9.4

Fig. 3.1 Example spectra of GJ 272 (top) and the corresponding telluric standard (bot- tom). 109

Fig. 3.2 Top: TERRASPEC fitting a model telluric spectrum (red) to an M dwarf observation (blue). Bottom: The observation with the telluric features subtracted. The obvious offset between the theoretical and observed telluric features is partly due to the ThAr wavelength scale changing when the cross-disperser is moved between observations. 110

Fig. 3.3 Same as in Fig. 3.2. Here the ThAr observation was taken immediately before the stellar observation and the wavelength scale is consistent, allowing the telluric features to be better modeled and removed. 111

Chapter 4

Forward Modeling of Radial Velocity Measurements

Using the M dwarf mock survey data described in Chapter 3, I studied the radial velocity precision attainable with R-band water vapor and molecular oxygen lines. The spectral range of the observations also allows for RV measurements to be made using the traditional iodine cell. In this chapter I describe the absorption cell method of measuring radial velocities and adapt it for use with telluric absorption lines. I present results obtained with one band and discuss the expected results of the remaining bands.

4.1 Iodine Technique

The method of measuring radial velocities with an iodine absorption cell was pioneered by the California Planet Search (Marcy & Butler 1992; Butler et al. 1996).

This technique greatly improved on previous calibration work, reaching a nearly photon-

1 limited precision of 3 m s− and has since been widely adopted for planet searches. In this work, I used a version of the Doppler code that has evolved from these works and been modified for use with HET.

4.1.1 Requirements for Precise Doppler Measurements

Prior to the development of the iodine cell, Doppler measurements were conven- tionally made using an emission lamp for reference. This method often introduces large 112 systematic radial velocity errors due to the different optical paths of the science and cali- bration images. The starlight and lamp light interact with the optical components of the spectrograph in slightly different locations, causing small but significant differences in the location of each wavelength. In addition, the emission lamp spectra are generally taken at a separate time from the science spectra. This allows for small thermal variations and adjustments in the spectrograph flexure between exposures, causing non-negligible changes in the spectrograph dispersion and point-spread function (PSF), and resulting

1 in radial velocity shifts of over 200 m s− (Duquennoy & Mayor 1991). These errors can be greatly reduced by using an absorption cell as a calibrator, as this requires the science and calibration images to have the same optical path and the reference spectrum to be measured simultaneously with the stellar spectrum.

Even with these precautions, it is necessary to account for changes in the PSF with time and wavelength. In principle, the PSF of a spectrograph should have the shape of a sinc function, caused by the top-hat function of the slit. In practice, zonal aberrations in the optics cause structure on top of this shape. As the collimated beam of light shifts over time, this structure may change, manifesting as spurious Doppler shifts.

Use of a collimator mask and an optical fiber feed make the spectrograph illumination more consistent, but do not fully eliminate this effect (Hunter & Ramsey 1992). The optical path through the spectrograph also depends on wavelength, causing the PSF shape to be dependent on the echelle order and position along the order. In the case of an adjustable grating such as on HRS, the PSF is primarily determined by the CCD column rather than by wavelength. To measure radial velocities precisely, it is necessary to measure the PSF in many locations, across the full wavelength range utilized. 113

Molecular iodine was selected as an absorption medium as it is stable and has many narrow features over a broad range of wavelengths, from 5000 to 6200 A,˚ with at least 2 features per A.˚ It is also a convenient medium for use in a laboratory setting, as it is nonlethal and has a strong line absorption coefficient, producing line depths of greater than 10% with a path length of only a few centimeters. However, its density of spectral lines produces numerous, unavoidable blends with the features of the target star.

As such, it is not possible to measure individual line positions and the radial velocity measurements must instead be made by modeling the combined spectrum, as described in the next section.

4.1.2 Modeling the Observations

The observations of a radial velocity time series consist of the spectrum of a star taken through the iodine cell, with numerous calibration features superimposed. These observations can be modeled as

I (λ)=k[TI (λ)I (λ +∆λ)] PSF (4.1) obs 2 s ∗

where TI2 is the transmission function of the iodine cell, Is is the intrinsic stellar spec- trum, ∆λ is the stellar Doppler shift, k is a normalization factor and “*” represents convolution (Butler et al. 1996). The PSF is allowed to vary over time, along with the wavelength zeropoint and dispersion of the spectrograph. In practice, the observed spec- trum is broken into 80 pixel, 2 A˚ blocks and each block is modeled separately. Figure ∼ 4.1 illustrates this process. 114

This model requires TI2 and Is as input. The iodine transmission function is expected to be stable over time and so must only be obtained once. It was measured using a Fourier transform spectrometer (FTS), resulting in a spectrum that is fully resolved and oversampled. The PSF of the instrument can be neglected at such high

resolution, thus the observed spectrum is gives a realistic representation of TI2 .TheFTS spectrum gives an absolute vacuum wavelength scale and provides a reference against which to measure the PSF of HRS.

Obtaining the intrinsic stellar spectrum, Is, is a more complicated problem. Each target star is observed at least once without the I2 cell in place, either directly before or after a typical star+iodine exposure. Ideally this template observation is made with high signal to noise ( 500), though for all but one target (GJ 281) the templates were ∼ observed with S/N 200. These observations consist of I *PSF and not the intrinsic ∼ s spectrum itself. Is is obtained by deconvolving the PSF from the template observation, using a modified Jansson technique.

To properly extract Is, the model PSF used to deconvolve each block must accu- rately represent the PSF at the time the template observation was made, in the corre- sponding region of the CCD. These PSFs are ideally measured by observing a rapidly

rotating B star through the iodine cell, producing a TI2 *PSF absorption spectrum. In practice, these measurements are made using the iodine cell illuminated by the flatfield lamp. These observations are then modeled using the FTS iodine spectrum convolved with a best-fit to the PSF. The original PSF model described in Valenti et al. (1995) was constructed from a sum of a central Gaussian with variable width and pairs of satellite

Gaussians of variable height at fixed positions determined bytheslitwidth.ThePSF 115 model used in this work consists of the first ten Gauss-Hermite polynomials. Both of these models can reproduce smooth but asymmetric PSFs, though the Hermite poly- nomials were chosen as they require fewer assumptions about the PSF structure, i.e.

predetermining the locations of satellite Gaussians. The synthetic TI2 *PSF spectrum is then fit to the iodine flat observation using a standard Levenberg-Marquardt non-linear least-squares optimization. There are 2 free parameters for the wavelength scale and 11 more for the PSF model, one for each polynomial plus the width of the Gaussian term.

The best-fit PSF is removed from each block and the deconvolved stellar template is stored for future use.

Once Is has been recovered, each radial velocity measurement can be fully mod- eled. This is a similar process to fitting the PSF, with the wavelength scale and PSF model allowed to vary and with the stellar Doppler shift, z, as an additional free param- eter. For both of these processes, the synthetic spectrum is oversampled by a factor of four times the observed pixel size to utilize the high-frequency information in the iodine spectrum. The FTS iodine spectrum is resampled at this spacing using a spline interpo- lation. The deconvolved stellar template is splined onto the Doppler-shifted wavelength scale, also oversampled by a factor of four. The shifted stellar template is multiplied by the iodine spectrum and convolved with the PSF, then this model spectrum is rebinned to match the observed pixel sizes using a spline integration.

In practice, the modeling process is carried out in three passes. On the first pass, all 14 parameters are allowed to vary. On the second, the best-fit dispersion for each block is fixed and on the third, the PSF parameters are forced to vary smoothly between blocks. After the final pass, the individual blocks are weighted by the number of counts 116

2 and filtered to remove those with high χ values or anomalous velocities. The remaining velocities are then averaged to produce a single measurement for each epoch. Finally, each of these velocities is referenced to the Solar System barycenter using a routine by

1 McCarthy (1995) based on the JPL ephemerides that is capable of 0.01 m s− precision.

4.1.3 Results with Iodine Calibration

As described in Chapter 3, the M dwarf spectra were observed through the iodine cell, allowing for a comparison between radial velocities measured with telluric and iodine calibration. The 316g6948 cross-disperser setting was used, in contrast to the 316g5963 setting used for most HRS iodine work. This modification allows for access to redder telluric features, at the cost of losing one order of the iodine spectrum. After rejecting blocks near the edge of the blaze function, 449 blocks with iodine features are available for radial velocity measurements.

The RV time series for each target are shown in Figures 4.2 - 4.7, with velocity values given relative to the deconvolved stellar template. Two precision values are re- ported for each target, σALL, the standard deviation of the velocity scatter over time and σINT , the median internal velocity uncertainty. σBIN, the standard deviation of the velocities binned by epoch, is also calculated, though it is only differs from σALL

1 for GJ 277.1. The internal precision ranges from 5.6-9.5 m s− . The scatter values are

1 larger, ranging from 7.9-16.2 m s− . These scatter values are also mostly larger than

1 those reported by Endl et al. (2003), 4.0-9.4 m s− , except in the case of GJ 277.1 where my scatter is slightly smaller than the published value. 117

Endl et al. (2003) identify four major sources of radial velocity scatter: (1) intrinsic variability of the targets, (2) instrumental stability, (3) photon noise and (4) algorithmic noise. Each of the targets is a low-activity, early M dwarf, so the intrinsic stellar ‘jitter’

1 is expected to be <5ms− (Gomes da Silva et al. 2012) and should not be a primary source of error. Likewise, HRS has been used in many other RV surveys and found to

1 have a long-term overall precision of 3ms− (Cochran et al. 2003). ∼ Photon noise is a more significant factor. Only blocks in the central portion of the CCD are used for RV measurements to ensure adequate signal. The observations were designed to produce S/N 200 at 7200 A˚ and while the actual signal varied with ∼ observing conditions, most observations have a reported S/N > 150. However, due to the shape of the Blaze function the signal is decreased in the iodine region, with typical values of S/N 100. This suggests that the internal precision could be improved by a ∼ factor of two in a survey optimized for iodine calibration.

There are multiple possible sources of ‘algorithmic noise’, as the Doppler code has not yet been fully optimized for use with HET or with M dwarfs. An inaccurate PSF model would cause increased velocity errors, though Wang (2012) find that the current

Gauss-Hermite model gives similar results to the previously used sum of Gaussians. The deconvolution algorithm is a more likely culprit. In the last few years, the CPS team has replaced the Jansson algorithm I used in this work with a customized routine, increasing their RV precision (Howard et al. 2009). In addition, M dwarf spectra are difficult to deconvolve, as a well-measured continuum is necessary and the continuum in M dwarfs is obscured by their prolific metal lines. 118

The barycentric correction is one further source of error, as the topocentric veloc-

1 ity of the observatory changes by 2ms− per minute, over the course of a 10 minute ∼ ∼ observation. Ideally the flux-weighted mid-point of the observation would be used to calculate the barycentric correction, however HET is not equipped with a photometer to make such measurements. Instead, the temporal mid-point of the observation is used,

1 introducing error of up to a few m s− .

4.2 Modification of the Iodine Technique for Telluric Features

In this work I have followed the procedure established in Section 4.1.2 to measure radial velocities using telluric features in place of iodine, with two major modifications.

First, the atmosphere changes over time, requiring an atmospheric transmission function

T⊕ customized for each epoch. Second, unlike the iodine cell, the Earth’s atmosphere cannot be removed from the optical path of the starlight. This makes obtaining IS more difficult.

I generate T⊕ from synthetic telluric spectra using TERRASPEC, an IDL GUI program that uses the atmospheric modeling code LBLRTM, as described in the following section. I use TERRASPEC to measure the column density of water vapor and molecular oxygen for each RV observation and telluric standard, and store these values for use inside the Doppler code. At the point in the Doppler code where the FTSiodinespectrum would normally be read, the column densities are input to TERRASPEC, which builds the corresponding T⊕ model. These synthetic spectra have R = 500,000 and provide an absolute vacuum wavelength calibration. 119

Blake et al. (2007) constructed the intrinsic stellar spectra by using synthetic L dwarf spectra with Teff and V sin(i) values optimized to the target star. I chose not to use synthetic Is as M dwarf models in general do not adequately reproduce the observed spectra (e.g. Maness et al. 2007). These discrepancies are likely due to incomplete and incorrect line lists for molecular features such as TiO. Instead, a high S/N observation is made of each target star and deconvolved, as with iodine. These deconvolved stellar templates are then cleaned of telluric features using TERRASPEC. This process is de- scribed more fully in Sections 4.3-4.4. The observation modeling procedure, analogous to that of iodine calibration, is shown in Figure 4.8.

4.3 Modeling Telluric Spectra

The synthetic telluric spectra are constructed with LBLRTM (Clough et al. 2005), using the optimization program TERRASPEC (Bender 2012). LBLRTM is a flexi- ble line-by-line radiative transfer code designed to produce accurate model atmospheric transmission spectra. It takes the HITRAN line database as input, including the pressure shift coefficient, the halfwidth temperature dependence and water vapor self-broadening

(Rothman et al. 2009). All calculations are performed in frequency space. LBLRTM uses Voigt line profiles for all atmospheric layers and had been validated against ob- served atmospheric radiance spectra. It is accurate to 0.5%, with errors primarily due ∼ to limits on the knowledge of line parameters.

TERRASPEC is used to fit model telluric spectra to the telluric features in a normalized observed spectrum. It can take a user-defined atmospheric model or one of several preset models. In this work, I used the 50-layer 1976 US Standard Atmosphere 120 and set the observatory location to correspond to HET, with a latitude of 30.68◦ N, altitude of 2025 m and a zenith angle of 35◦. I include lines from the seven most prevalent molecules - H2O, CO2,O3,N2O, CO, CH4 and O2 - to construct these spectra, though only H2O and O2 have major features in the R-band.

Calculations are performed for individual orders of either the M dwarf spectra or telluric standards. These observed spectra are first continuum normalized using the or- der shapes calculated by REDUCE and transformed into wavenumbers. TERRASPEC performs a least-squares fit using the routine MPFITFUN to optimize several model pa- rameters. These include the column density of water or oxygen as appropriate, multiple parameters for a PSF model and an offset parameter for the stellar continuum. The PSF model consists of a central Gaussian with up to four satellites, where the width of the central Gaussian and the heights of the satellite Gaussians are adjustable. In practice,

I use a single pair of satellites. If the observed spectrum contains stellar features, these are omitted from the fit by manually selecting regions of stellar contamination. Due to the proliferance of M dwarf features, only strong and isolated stellar lines were masked.

This process is illustrated in Figure 4.9.

TERRASPEC outputs a high resolution best-fit telluric model, this same model rebinned to the resolution of the observed spectrum and the observed spectrum cleaned of telluric features by dividing out the rebinned model. It also produces a best-fit model of the PSF. The best-fit parameters are not automatically stored, though I created a log of these parameters for the most utilized spectra.

TERRASPEC can also be used much more simply, generating a synthetic spec- trum from a given set of atmospheric conditions. I used this function within the Doppler 121 code, bypassing the GUI entirely. The stored column density was read from the pa- rameter log and used to generate T⊕ for each epoch, without the PSF broadening or continuum offset included. As each observation consists of multiple orders with H2O and O2 features, there are multiple column density measurements for each image. The

2 column density should be constant with wavelength, so the order with the smallest χ value is chosen as the best measurement. In practice, the water column values are consistent to within 0.1 cm between orders. ∼

4.4 Generating Stellar Templates

Obtaining Is is one of the most complex parts of this method. Here I will describe both the procedure as I intended it to be carried out and the modifications made for the initial tests, which utilize the additional data available in the iodine region (Section 4.5).

Each M dwarf target has one high S/N observation made directly before or after the observation of a telluric standard. The telluric standards are analogous to the iodine

flat observations, containing T⊕*PSF. The telluric standards are input to TERRASPEC to obtain the best-fit column density values, which are then stored. T⊕ is recreated inside the PSF modeling code, using a GUI-less call to TERRASPEC, and the best-fit

PSF and wavelength scale are measured by optimizing T⊕*PSF to the observed telluric standard.

This PSF is then used to deconvolve the stellar template, producing Is with su- perimposed telluric features. The template is cleaned of telluric lines with TERRASPEC to recover the intrinsic stellar spectrum. In practice, the deconvolution is carried out in

2 A˚ chunks while the telluric removal is done order by order for efficiency. This requires 122 the stellar template to be pieced together prior to removing the telluric lines and then interpolated on to the wavelength scale of the original blocks.

The iodine features overlap with a water vapor band in order 16 of the blue chip between 5870-5905 A.˚ This allows for the deconvolved stellar template created ∼ using the iodine RV pipeline to be re-used for the telluric calibration. This template was constructed using the iodine flatfield images to calculate the PSF, as described in

Section 4.1.2, with the additional step of removing the water vapor features. To save computing time, I did not re-optimize the telluric model to the deconvolved template, and instead reconstructed the telluric model from the stored best-fit parameters of the original observation.

4.5 Testing at 5900 A˚

Recycling the stellar template from the iodine pipeline greatly simplifies the mod- eling process. I have focused my efforts on testing this variation of forward-modeled tel- luric calibration and understanding its limits, rather than obtaining more general results with the full set of R-band telluric features.

These tests require stellar observations made without the gas cell, in contrast to the original experiment. Each M dwarf target has at least two observations without iodine, one taken in the initial series of observations and a higher S/N observation taken about a year later. However, the relative weakness of the water vapor features in the 5900 A˚ region caused most of these observations to have little radial velocity ∼ information content. The precipitable water vapor content of the atmosphere during these epochs clustered around three values: 0.3, 0.5 and 0.9 cm. For the weaker two 123 values, it is difficult to distinguish telluric lines over the more pronounced stellar features.

No single target has two epochs with 0.9 cm of water vapor, but the stellar template observation of GJ 277.1 was broken into two separate observations to prevent the CCD from saturating. This provides a recoverable null signal, as there should be no change between the observations.

I used only blocks with telluric features stronger than 2% in the radial velocity calculation, producing a much truncated version of the deconvolved stellar template of

GJ 277.1 with 18 blocks spanning 5871-5905 A.˚ With this small sample it is feasible ∼ to examine the results of each block individually and three of these were removed from the template due to consistently poor visual fits near the Na doublet. The iodine radial velocity code contains a filtering algorithm to reject bad blocks after the forward mod- eling process is completed. It removes blocks with low photon count, high χ values or velocity measurements that significantly deviate from the median value, but is designed for observations with large numbers of blocks. I adapted these criteria for a small sample size, rejecting blocks with χ values 2σ above the mean, with low photon count or veloci- ties greater than 2σ away from the mean. This resulted in two blocks being removed for poor fits and one more removed due to large velocity scatter.

With the remaining 12 blocks, the two observations have an internal precision of 159.3 m/s and 167.8 m/s, respectively, and median velocities consistent to within these errors. The velocities for each block are shown in Figure 4.10. The high velocity uncertainty is partly due to the small number of available blocks. It is possible to extrapolate to a larger wavelength range by assuming equal error contributions by each block. The precision then scales as 1/√N,whereN is the number of blocks. In this 124 configuration, there are 449 blocks available for iodine measurements. Assuming a similar

1 number of blocks with usable telluric features, the velocity precision scales to 27 m s− .

As a comparison, I ran the same 15 block deconvolved stellar template through the iodine pipeline and analyzed the results of one observation taken through the iodine cell.

The selected image was made at about the same time of year as the template observation, so the barycentric shift of the telluric features should be similar. The velocities for each

1 block are shown in Figure 4.11. The resulting internal precision was 127 m s− ,with two blocks removed by the filtering algorithm for large scatter. This scales to a precision

1 of 22 m s− for the entire iodine region, notably worse than the actual measurements made with the full set of iodine blocks. However, this region is expected to have reduced precision due to the telluric features. While these features have been removed from the template, the telluric cleaning procedure may leave artifacts. Additionally, this region is near the edge of the usable portion of this order and has lower than average signal. Both of these sources of error also apply to the measurements made with telluric calibration, so it is encouraging that both methods produce similar results.

4.6 Extrapolation to Other Bands

To gain a more realistic picture of the number of usable telluric features through- out the red region, I have calculated the Q values of model telluric spectra. Q is a measure of the flux-independent radial velocity information content of a spectrum de-

fined by Bouchy et al. (2001) as

ΣW (i) Q = (4.2) #ΣA0(i) # 125 where A0 is the intensity of the spectrum in photoelectrons and i is pixel number. W is an optimal weighting function proportional to the inverse square of the Doppler shift of each pixel and thus proportional to the square of the line slope.

2 2 λ (i)(∂A0(i)/∂λ(i)) W (i)= 2 (4.3) A0(i)+σD

As a result, Q is maximized in regions with many sharp spectral features. Figures 4.12 and 4.13 show the Q values in 2 A˚ blocks of the intrinsic telluric spectrum, with 1.0 cm and 0.5 cm precipitable water vapor, respectively. These spectra have an initial

1 resolution of R = 500,000 but were then convolved with a 1 km s− rotation kernel to mimic the high frequency information loss due to the rotational broadening of a typical target star spectra. While all of the blocks between 5000 A˚ and 9000 A˚ have a non-zero

Q value, the usable regions are limited to the stronger bands oftelluriclines,witha stronger water column producing higher Q values. Figure 4.14 shows the equivalent Q values for the FTS spectrum of the HET iodine cell, also rotationally broadened and with similarly high resolution. These Q values are more consistent in magnitude, though across a more limited wavelength range.

The information content of the target star is also a factor in the utility of a given spectral region. I have repeated these tests for a model Solar spectrum (Castelli &

Kurucz 2004) and a model M dwarf spectrum with Teff = 3800K, log(g) = 5.0 and [M/H]

= 0.0 (Allard et al. 2011), as shown in Figures 4.15 and 4.16. The calculated Q values for the Solar spectrum are similar to those reported by Bouchy et al. (2001). While 126 individual Solar blocks have a much stronger information content than the M dwarf, the median values in 100 A˚ bins differ by less than a factor of two.

Bouchy et al. (2001) compute a photon-limited velocity error, ∂V , from the in- formation content, as c ∂V = (4.4) Q√N where N is the total number of photoelectrons in the spectral region. I computed the total Q value for each combination of target star and calibration medium as

1 1 1 = + (4.5) Qtot Q∗ Qcal and use this to calculate a velocity precision for each block. Two different values of photoelectron counts were used, first for the idealized case of 40,000 counts per resolution element, or S/N=200 regardless of wavelength. In the second case, I took the number of counts from several observations with reported S/N=200 to incorporate the effect of the HRS blaze function. Here I used a 316g5963 setting observation of a G4 dwarf to approximate a Solar-type star and 316g6948 setting observations for the M dwarfs.

The combined velocity precision of all 2 A˚ blocks is given in Table 4.1. Un- surprisingly, the velocity precision values obtained with uniform S/N are consistently better than those obtained with the realistic S/N distributions and include more blocks than are typically usable with HRS. The photon-limited precision measured for the Solar spectrum with iodine is consistent with the results of Butler et al. (1996) for the level of signal (Figures 4.17 and 4.21). The M dwarf spectrum measured with iodine has lower precision, as shown in Figures 4.18 and 4.22, both as a result of the lower Q value and 127 the decreased S/N in the iodine region with the 316g6948 cross-disperser setting. Indeed, the velocity precision obtained with the observed S/N distribution suggests that photon noise is a significant portion of the RV scatter observed for each M dwarf target.

Using telluric calibration, blocks with Q<2000 contribute little to the overall precision. This leaves 300-400 blocks, depending on the nightly water column, that ∼ would likely be included in an implementation of this calibration method over the entire red region. The photon-limited velocity precision attainable with these blocks is 7-11 m ∼ 1 s− , again dependent on the water column and S/N distribution. The velocity precision per block is shown in Figures 4.19, 4.20, 4.23 and 4.24.

However, this precision estimate assumes stable fiducials and does not account for

1 the variability of the telluric features. Scaling the 168 m s− velocity precision obtained with 12 blocks to all usable telluric blocks yields a relatively modest precision of 31 m

1 1 s− with 1.0 cm water vapor and 35 m s− with 0.5 cm. As with the iodine calibration, there are several factors that will allow for better precision in the future, including higher

S/N and improvements to the PSF and deconvolution algorithms.

1 With a precision of 10 m s− , a telluric-calibrated radial velocity survey would ∼ be able to detect Neptune-mass planets around M dwarfs throughout the habitable zone.

1 With 30 m s− , Neptune-mass planets are still detectable in the inner portion of the ∼ habitable zone. This level of precision is also suitable for surveys around stars with inherent RV noise, such as late K giants and flaring stars. 128

Fig. 4.1 The iodine cell technique, as illustrated with a representative block. Upper Left: The observation (Xs) and best-fit model (solid line) are shown with residuals (dots) plotted above. Upper Right: The best-fit model is constructed from the deconvolved stellar template (solid line) and the FTS iodine spectrum (dotted line). Lower Left: The best-fit PSF for this block. 129

Fig. 4.2 Radial velocity measurements of GJ 184, relative to the stellar template observa- tion. σALL gives the velocity scatter of these measurements and σINT gives the median internal measurement error. 130

Fig. 4.3 Radial velocity measurements of GJ 272, relative to the stellar template observa- tion. σALL gives the velocity scatter of these measurements and σINT gives the median internal measurement error. 131

Fig. 4.4 Radial velocity measurements of GJ 277.1, relative to the stellar template ob- servation. σALL gives the velocity scatter of these measurements and σINT gives the median internal measurement error. 132

Fig. 4.5 Radial velocity measurements of GJ 281, relative to the stellar template observa- tion. σALL gives the velocity scatter of these measurements and σINT gives the median internal measurement error. 133

Fig. 4.6 Radial velocity measurements of GJ 328, relative to the stellar template observa- tion. σALL gives the velocity scatter of these measurements and σINT gives the median internal measurement error. 134

Fig. 4.7 Radial velocity measurements of GJ 353, relative to the stellar template observa- tion. σALL gives the velocity scatter of these measurements and σINT gives the median internal measurement error. 135

Fig. 4.8 The telluric calibration technique, as illustrated with a sample block. Upper Left: The observation (Xs) and best-fit model (solid line) are shown with residuals (dots) plotted above. Upper Right: The best-fit model is constructed from the deconvolved stellar template (solid line) and the model telluric spectrum (dotted line). Lower Left: The best-fit PSF for this block. 136

Fig. 4.9 Example of modeling telluric features with TERRASPEC. The observed spec- trum is shown in light blue and the telluric model is shown in red. The dark blue regions are stellar features that have been omitted from fitting. 137

Fig. 4.10 Histogram of velocities measured in the 5900 A˚ region using telluric calibration, with the first observation shown as a solid red line and the second observation shown as a dotted black line.

Fig. 4.11 Histogram of velocities measured in the 5900 A˚ region using iodine calibration. 138

Fig. 4.12 Q value of a model telluric spectrum with 1.0 cm precipitable water vapor, 1 convolved with a 1 km s− rotation kernel, as a function of wavelength in 2 Ablocks.˚ 139

Fig. 4.13 Q value of a model telluric spectrum with 0.5 cm precipitable water vapor, 1 convolved with a 1 km s− rotation kernel, as a function of wavelength in 2 Ablocks.˚ 140

1 Fig. 4.14 Q value of the FTS iodine spectrum convolved with a 1 km s− rotation kernel, as a function of wavelength in 2 Ablocks.˚ 141

Fig. 4.15 Q value of a model solar spectrum (Castelli & Kurucz 2004), as a function of wavelength in 2 Ablocks.˚ 142

Fig. 4.16 Q value of a model M dwarf spectrum with Teff = 3800K, log(g) = 5.0 and 1 [M/H] = 0.0 (Allard et al. 2011), convolved with a 1 km s− rotation kernel, as a function of wavelength in 2 Ablocks.˚ 143

Table 4.1. Photon Limited Velocity Precision

1 1 Precision (m s− ) # of Blocks Precision (m s− ) # of Blocks Uniform S/N Uniform S/N Observed S/N Observed S/N

Solar with I2 1.7 529 2.5 512 M0 V with I2 4.1 534 9.7 514 M0 V with Tellurics: 1.0 cm PWV 7.3 1560 9.7 1474 1.0 cm PWV, Q>2000 7.7 401 10.4 356 0.5 cm PWV 8.2 1560 11.1 1474 0.5 cm PWV, Q>2000 8.6 315 11.1 273 144

Fig. 4.17 Histogram of velocity precision per block calculated from Q value, for a model solar spectrum (Castelli & Kurucz 2004) and and FTS iodine spectrum, with constant S/N = 200 per resolution element.

Fig. 4.18 Histogram of velocity precision per block calculated from Q value, for a model M0 dwarf spectrum (Allard et al. 2011) and FTS iodine spectrum, with constant S/N = 200 per resolution element. 145

Fig. 4.19 Histogram of velocity precision per block calculated from Q value, for a model M0 dwarf spectrum and model telluric spectrum, with constant S/N = 200 per resolution element and 1.0 cm precipitable water vapor.

Fig. 4.20 Histogram of velocity precision per block calculated from Q value, for a model M0 dwarf spectrum and model telluric spectrum, with constant S/N = 200 per resolution element and 0.5 cm precipitable water vapor. 146

Fig. 4.21 Histogram of velocity precision per block calculated from Q value, for a model solar spectrum and and FTS iodine spectrum, with photon statistics derived from an HRS observation of a G4 dwarf.

Fig. 4.22 Histogram of velocity precision per block calculated from Q value, for a model M0 dwarf spectrum and and FTS iodine spectrum, with photon statistics derived from an HRS observation of GJ 277.1 through the iodine cell. 147

Fig. 4.23 Histogram of velocity precision per block calculated from Q value, for a model M0 dwarf spectrum and model telluric spectrum, with 1.0 cm precipitable water vapor and photon statistics derived from an HRS observation of GJ 277.1 without the iodine cell.

Fig. 4.24 Histogram of velocity precision per block calculated from Q value, for a model M0 dwarf spectrum and model telluric spectrum, with 0.5 cm precipitable water vapor and photon statistics derived from an HRS observation of GJ 277.1 without the iodine cell. 148

Chapter 5

Summary & Future Prospects

5.1 Summary

This thesis contains two projects that each focus on a facet of radial velocity planet detection. In the first portion, I present results from a search for planets around evolved stars, including the discovery of five planetary systems. These systems illustrate many of the features of planets orbiting giants that distinguish them from those around

Solar-type stars. In the second portion, I describe the expansion of the absorption cell calibration method to use telluric features in the R-band, accessing a redder spectral region than can be reached with an iodine cell and utilizing the increased flux of redder stars, including M dwarfs and giants, in that region.

5.1.1 Planets around Giant Stars

There are a small but growing number of planet detections around evolved stars and this population shows statistical differences from the population of planets around dwarfs. In Chapter 2, I describe the observations and analysis of six targets from the

Penn State-Toru´nPlanet Search for substellar companions to evolved stars, the largest of such surveys to date. These systems highlight the distinctive features of a radial velocity survey for planets around giants. 149

The observations are made using HET, with the standard iodine cell calibration

1 technique, and obtain a typical radial velocity precision of 6-10 m s− . The orbits are ∼ modeled as best-fit six-parameter Keplerian orbits, and the line bisector measurements and any available photometry are examined for potential stellar contamination.

Taken as a whole, these systems are typical of those found around giant stars, each consisting of planets with masses of one to several Jupiters and periods of one to several years. All known planets orbiting giants have a semi-major axis greater than 0.6 AU, ∼ possibly due to planetary engulfment or orbital evolution as the host star expands. The masses of planets around giants also appear to be larger that those around dwarfs, an effect that may scale with the mass of the host star, as a result of the increased disk mass of larger stars. Our results reinforce these trends.

Two of the stars demonstrate the high intrinsic RV noise often seen in giant stars,

1 ranging from 20 to 50 m s− , with amplitudes correlated with B V color and anti- ∼ − correlated with log(g). The RV variations of HD 240237 are indicative of a planet with

M2 sin(i) = 5.3 MJ in a 746 day, eccentric orbit, with a large post-fit rms noise of

1 35 m s− . The RV variations of HD 96127 also show a large post-fit rms noise of 50

−1 ms , around a best-fit planet model with a minimum mass of 4.0 MJ in a 647 day,

1.42 AU, moderately eccentric orbit. Undersampled p-mode oscillations appear to be a major contributor to this noise, with oscillation amplitudes scaling as v L/M, osc ∼ as per Kjeldsen & Bedding (1995). This relationship can be translated into a semi- analytical dependence of σ on observables B V color and metallicity. Comparing RV − this predicted relationship to the post-fit residuals of the published planets around giant stars, I find that increased jitter amplitude is anti-correlated with metallicity, making 150 metal-rich giants easier targets for a planet search. This effect is particularly interesting as giant stars may lack the correlation between host star metallicity and planet frequency seen in dwarfs, contrary to the results expected from a detection bias toward metal-rich giants.

The increased RV jitter seen in giant stars makes it more difficult to detect planets, particularly those with large orbital radii and long periods. HD 219415 approaches the limits of detectability, with a Jupiter mass planet in a 5.7 year, 3.2 AU eccentric orbit.

This planet has the longest period of any yet detected around a giant star, by nearly a factor of two. The host star has a Kjeldsen-Bedding jitter amplitude estimate of 1 ∼ 1 ms− , making its excess RV noise negligible. However, a more typical value of 20 m ∼ −1 s stellar jitter is greater than the amplitude of a 1 MJ planet orbiting much beyond 1

AU, burying the planet signal. While the signal of such a planet can be recovered with sufficient observations, this noise threshold ultimately limits the detection of long-period planets.

In addition to the planetary signal, two stars show long-term radial velocity trends

1 1 of order 1ms− day− that are suggestive of binary companions. BD+20 274 has a ∼ planetary companion with a minimum mass of m2 sin(i) = 4.2 MJ , in a 578 day, mildly eccentric orbit with a semi-major axis of 1.3 AU and a trend with very little curvature.

The linear RV drift rate of this trend can be used to approximate companion mass, indicating a brown dwarf mass for an orbit of a 3 AU and a stellar mass for a 7 ≥ ≥ AU. The stellar spectrum lacks any observable features from the secondary, indicating that the maximum mass of the long-period companion is 0.3 M#. The RV variations ∼ 151 of BD+48 738 are best modeled as a planet with a minimum mass of 0.91 MJ in a 393- day, moderately eccentric orbit superimposed on a large circular orbit. It is difficult to characterize the long orbit as its period is much greater than the span of the observations, though the curvature is statistically significant. A grid search of a m sin(i) e space − − combined with N-body simulations suggests that the most likely orbital solutions are for a brown dwarf companion or low mass star orbiting within 40 AU.

If the long-period companion is substellar, it would join a small but growing number of close brown dwarfs orbiting giants. Some of these systems have multiple brown dwarfs, suggesting they formed from the same disk. The formation mechanism of these objects is unknown, though it may simply be a result of the core accretion model acting on the massive disks of the giants’ main sequence progenitors.

The final system, HD 102103, remains something of a mystery. Despite exten- sive observations, there is no clear orbital solution. Instead, there are two families of solutions, with 680 and 490 day periods, that both adequately fit portions of the RV ∼ ∼ data though not the entire series. As neither the available photometry or the bisector variations are correlated with the radial velocity variations, the RV signal may indeed be caused by orbital motion. Though observationally expensive, an additional cycle of

RV measurements may be able to provide a better orbital solution.

These five planet detections constitute a significant fraction of the known planets around giant stars and were made as part of a major survey, the ultimate goal of which is to provide a consistent sample of planetary systems around evolved stars. Over 300 stars of the initial 1000 show signs of hosting substellar companions and the priority ∼ for the next few years is to obtain enough observations to reliably characterize these 152 potential detections. Based on previous surveys, we expect that at least 50 of the PTPS targets are planet hosts. This large sample will allow us to conduct a statistical study of stellar masses, radii and metallicity, as well as the limits on planet detectability due to stellar noise.

5.1.2 Measuring Radial Velocities with Telluric Lines

Most planet searches to date have been conducted in optical light, though efforts are now underway to conduct precision surveys in the near infrared, as this region con- tains the greatest component of the flux of the lowest mass stars. The spectral region in between, approximately the R-band, is also of interest for this reason, as it provides access to the increased red flux of K and M dwarf stars, and is easily observable with existing instruments.

There are several bands of both water vapor and molecular oxygen lines in the region between 6000-9000 A˚ and studies of these bands consistently find that they ∼ 1 are stable to <10 m s− . Unlike an emission lamp spectrum, the telluric spectrum is observed at the same time and with the same optical path as the stellar spectrum, greatly reducing spurious Doppler shifts due to thermal variations and spectrograph flexure.

To study the utility of these telluric features as a radial velocity calibrator, I carried out a mock survey of nearby early M dwarfs known to be stable to within <10

1 ms− , providing a recoverable null signal. Each star was observed between five and ten times over a span of a few months, with observations made through the iodine cell to provide a comparison between the two calibration methods. One further observation was made of each target with high S/N, taken in sequence with a telluric standard, to 153 measure the spectrograph PSF and to better characterize the atmospheric conditions at the time of observation.

Radial velocities are measured in a similar manner to the iodine technique, with observations forward modeled as a combination of an intrinsic stellar spectrum plus a radial velocity shift, an intrinsic calibrator spectrum andabest-fitPSF.Theintrinsic calibrator spectrum is created from a model telluric spectrum with line strengths opti- mized to each observation. The intrinsic stellar template is generated by deconvolving the best-fit PSF and removing the telluric features.

I tested this method on one spectral order near 5900 A˚ which contains both ∼ iodine and water vapor features. This allows the deconvolved stellar template generated from the iodine calibration technique to be recycled, greatly simplifying the process.

Both the telluric and iodine calibration results for this small region can be scaled to entire available spectral region, with precision improving as √N,whereN is the number of 2 A˚ blocks. I estimate the number of blocks available in R-band telluric region by calculating Q, the radial velocity information content of synthetic spectra and retaining blocks with Q>2000. The number of usable blocks is 300-400, depending on the ∼ 1 precipitable water vapor content, and resulting in a precision of 30-35 m s− . ∼ In comparison, the results of this region using iodine calibration scale to 20 m ∼ 1 s− for the full iodine region. This is a modest precision for this technique and there are several potential areas for improvement. The S/N ratio in this spectral region is up to a factor of two lower than is desirable in a typical iodine survey and photon noise is

1 a significant source of the 5-10 m s− radial velocity uncertainty in the results of the full iodine region. After accounting for this effect, the RV scatter is still larger than 154 expected for low-activity M dwarfs, suggesting that the Doppler code can be better optimized for HRS. The template deconvolution algorithm in particular will be replaced in future iterations of the pipeline.

Both of these effects also limit the precision of the telluric calibration and with

1 these improvements, a <10 m s− precision should be attainable in the R-band. This precision is sufficient to detect Neptune-mass planets in the habitable zone of low-mass stars, which would become priority targets for higher precision follow-up. This calibra- tion technique is optimal for redder stars with a moderate amount of intrinsic noise, including flaring stars, giants, and faint K and M stars where increased flux is a neces- sity. As it requires no equipment beyond computer models, telluric calibration can add precision RV capabilities to any high-resolution optical spectrograph.

In the future, I will implement the telluric calibration over the full red region, incorporating the necessary changes to the pipeline and observing strategy suggested by the current results. I will determine the utility of each molecular band and ultimately provide a precision radial velocity calibration method that better uses the flux of red stars. 155 Bibliography

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Appendix

Permissions

The following pages contain notice of permission from the copyright holders for reuse of the following works:

Substellar-Mass Companions to the K-Giants HD 240237, BD +48 738 and HD 96127 Gettel, S., Wolszczan, A., Niedzielski, A., Nowak, G., Adam´ow, M., Zieli´nski, P. & Ma- ciejewski, G. 2012, Astrophysical Journal, 745, 28

Planets around the K-Giants BD+20 274 and HD 219415 Gettel, S., Wolszczan, A., Niedzielski, A., Nowak, G., Adam´ow, M., Zieli´nski, P. & Ma- ciejewski, G. 2012, Astrophysical Journal, 756, 53

Figure 3, Extra-solar planets: Detection methods and results Santos, N. C. New Astronomy Reviews, 2008, 52, 54

Figure 6, No planet for HD 166435 Queloz, D., Henry, G. W., Sivan, J. P., Baliunas, S. L., Beuzit, J. L., Donahue, R. A., Mayor, M., Naef, D., Perrier, C., & Udry, S. 2001, A&A, 379, 279

Figure 4, Metallicities of Planet-Hosting Stars: a Sample of Giants and Subgiants Ghezzi, L., Cunha, K., Schuler, S. C., & Smith, V. V. 2010, Astrophysical Journal, 725, 721

Figure 2, Evolved stars suggest an external origin of the enhanced metal- licity in planet-hosting stars Pasquini, L., D¨ollinger, M. P., Weiss, A., Girardi, L., Chavero, C., Hatzes, A. P., da Silva, L., & Setiawan, J. 2007, A&A, 473, 979

Figure 3, Korean-Japanese Planet Search Program: Substellar Companions around Intermediate-Mass Giants Omiya, M., Han, I., Izumiura, H., Lee, B.-C., Sato, B., Kim, K.-M., Yoon, T. S., Kambe,E., Yoshida, M., Masuda, S., Toyota, E., Urakawa, S., & Takada-Hidai, M. 2011, in American Institute of Physics Conference Series, Vol. 1331, American Institute of Physics Conference Series, ed. S. Schuh, H. Drechsel, & U. Heber, 122129 168 169 170 171

To whom it may concern

I am preparing my dissertation entitled A Search for Planets around Red Stars (the Work) to be published by ProQuest through UMI Dissertation Publishing. I would ap- preciate permission to reproduce the following item in both print and electronic form, any derivative products and in publisher authorized distribution by third party distribu- tors, aggregators and other licensees such as abstracting and indexing services. I should be grateful for nonexclusive perpetual world rights in all languages and media. Unless you indicate otherwise, I will use the complete reference given below as the credit line. In case you do not control these rights, I would appreciate it if you could let me know to whom I should apply for permissions.

Figure 4, ‘Metallicities of Planet-Hosting Stars: a Sample of Giants and Subgiants’, Ghezzi, L., Cunha, K., Schuler, S. C., & Smith, V. V., Astrophysical Journal, 725, 721, 2010

For your convenience a copy of this letter may serve as a release form: the duplicate copy may be retained for your files. Thank you for your prompt attention to this request. Permission has been obtained from the author, as attached below.

Yours sincerely, Sara Gettel 172 Vita Sara Gettel

Pennsylvania State University Phone: (989) 992-5963 Department of Astronomy and Astrophysics E-mail: [email protected] 421 Davey Lab Citizenship: US University Park, PA 16802 Last Updated 10 Sept. 2012

Education Pennsylvania State University Anticipated Dec. 2012 Ph.D. Astronomy & Astrophysics Dissertation: ASearchforPlanetsAroundRedStars Thesis Advisor: Professor Alex Wolszczan

Pennsylvania State University May 2012 M.S. Astronomy & Astrophysics

University of Michigan 2002 – 2006 B.S. Honors Physics

Research Pennsylvania State University 2008 – 2012 Experience Dissertation Research Advisor: Professor Alex Wolszczan -Developedradialvelocitymethodusingtelluriclines -Detectedsub-stellarcompanionstoGKgiantstars -Developedhigh-resolutionEchellereductionpipeline -Optimizedplanetdetectabilityasafunctionofstellarmetallicity

Pennsylvania State University 2007 – 2008 Second Year Research Project Advisor: Professor Larry Ramsey -CharacterizedperformanceoftestbedNIRspectrograph -ModeledtelluriclinesinMdwarfspectra

University of Michigan 2004 – 2006 Thesis Research Advisor: Professor Timothy McKay -SearchedforWUMastarsinROTSE-Iarchivaldata

Teaching Teaching Assistant, Pennsylvania State University 2006 – 2008 Experience -Led1-2labsectionspersemesterforAstro11Introductory Astronomy Lab -Operatedsmalltelescopesforstudentobservingprojects

Honors Sigma Pi Sigma, inducted 2006

Selected Planets around the K-Giants BD+20 274 and HD 219415 Publications Gettel, S.,Wolszczan,A.,Niedzielski,A.,Nowak,G.,Adam´ow,M.,Zieli´nski,P. & Maciejewski, G., Astrophysical Journal,756(2012)53

Substellar-Mass Companions to the K-Giants HD 240237, BD +48 738 and HD 96127 Gettel, S.,Wolszczan,A.,Niedzielski,A.,Nowak,G.,Adam´ow,M.,Zieli´nski,P. & Maciejewski, G., Astrophysical Journal,745(2012)28

ANewCatalogof1022BrightContactBinaryStars Gettel, S. J.,Geske,M.T.&McKay,T.A.,Astronomical Journal,131(2006)621-632