DETECTING AND CHARACTERIZING STELLAR COMPANIONS TO

EXOPLANET HOST STARS

A thesis presented to the faculty of AS San Francisco State University In partial fulfilment of The Requirements for PH VS

- W 5 g Master of Science In Physics: Astronomy

by

Justin Wittrock

San Francisco, California

December 2016 Copyright by Justin Wittrock 2016 CERTIFICATION OF APPROVAL

I certify that I have read DETECTING AND CHARACTERIZING

STELLAR COMPANIONS TO EXOPLANET HOST STARS by Justin

Wittrock and that in my opinion this work meets the criteria for approv­ ing a thesis submitted in partial fulfillment of the requirements for the degree: Master of Science in Physics: Astronomy at San Francisco State

University.

Dr. Stephen Kane, PhD Astrophysics Associate Professor of Physics and Astronomy

Dr. Adrienne Cool, PhD Astronomy Professor of Physics and Astronomy

D^/Joseph Barranco, PhD Astropf Associate Professor of Physics and Astronomy DETECTING AND CHARACTERIZING STELLAR COMPANIONS TO

EXOPLANET HOST STARS

Justin Wittrock San Francisco State University 2016

A factor that can affect the detection of exoplanets is the binarity of the host stars.

Such a factor cannot be easily dismissed since the multiplicity of the stellar systems within our own Milky Way are quite common and that such systems can place further constraints on orbital dynamics and evolution. We used the Differential

Speckle Survey Instrument (DSSI) at the Gemini-North Observatory to obtain AO images at 692 nm and 880 nm bands. From our survey, we detect stellar companions to the known exoplanet host stars HD 2638 and HD 164509. The stellar companion to HD 2638 has been previously detected, but the companion to HD 164509 is newly discovered. The results from observations and the stellar isochrone models are consistent with the detected companions being late-type M dwarfs. The non- detection of stellar companions to the remaining systems provides constraints on the possible presence of additional planets in those systems.

I certify that the Abstract is a correct representation of the content of this thesis.

Date ACKNOWLEDGMENTS

I’d like to thank the people who have supported and encouraged me in my reaching the academic goals. I give my thanks to my parents for their loving support, especially when I'm so far away from home. I also want to thank the SFSU faculty, students, and the entire Physics

& Astronomy Department. Ever since my arrival nearly 2 1/2 years ago, my knowledge and experience have exploded, and I have become progressively confident of my skill sets and am more prepared for the increasingly challenging path in the future. I give my thanks to my thesis defense committees Stephen Kane, Adrienne Cool, and Joe Barranco for their time and support. Thank you Stephen for your tireless support, guidance, and effort while my stay at SFSU; you have made it possible for me to get where I am at now. It has been a real pleasure learning from you, and I look forward to continue working with you in the future!

v TABLE OF CONTENTS

1 Introduction...... 1

2 Observations and Target Selections...... 4

2.1 Stellar Companion S u rv e y ...... 4

2.2 Background on HD 164509 and HD 2638 ...... 15

3 Data Reduction...... 18

4 Results...... 47

4.1 Discoveries of Stellar Companions...... 47

4.1.1 HD 2638 ...... 48

4.1.2 HD 164509 ...... 49

4.1.3 Stellar Isochrone F ittin g ...... 50

4.1.4 Proper Motion and Astrometry ...... 52

4.2 Constraints on Presence of Stellar Companions...... 54

5 Implications of the Orbital D ynam ics...... 63

6 Conclusion...... 67

References...... 69

vi LIST OF TABLES

Table Page

2.1 Stellar Properties of Kepler and ROBO-AO RV Exoplanet Host Stars

with Null-Detection I ...... 6

2.1 Stellar Properties of Kepler and ROBO-AO RV Exoplanet Host Stars

with Null-Detection I ...... 7

2.1 Stellar Properties of Kepler and ROBO-AO RV Exoplanet Host Stars

with Null-Detection I ...... 8

2.1 Stellar Properties of Kepler and ROBO-AO RV Exoplanet Host Stars

with Null-Detection I ...... 9

2.1 Stellar Properties of Kepler and ROBO-AO RV Exoplanet Host Stars

with Null-Detection I ...... 10

2.2 Stellar Properties of Kepler and ROBO-AO RV Exoplanet Host Stars

with Null-Detection I I ...... 10

2.2 Stellar Properties of Kepler and ROBO-AO RV Exoplanet Host Stars

with Null-Detection I I ...... 11

2.2 Stellar Properties of Kepler and ROBO-AO RV Exoplanet Host Stars

with Null-Detection I I ...... 12

2.2 Stellar Properties of Kepler and ROBO-AO RV Exoplanet Host Stars

with Null-Detection I I ...... 13

2.2 Stellar Properties of Kepler and ROBO-AO RV Exoplanet Host Stars

with Null-Detection I I ...... 14

2.3 Stellar k, Planetary Properties...... 16

vii 4.1 DSSI Astrometry & Photometry Results...... 48

4.2 Stellar Companion Isochrone Fitting R esults...... 51

4.3 Limiting M agnitudes...... 56

4.3 Limiting M agnitudes...... 57

4.3 Limiting M agnitudes...... 58

4.3 Limiting M agnitudes...... 59

4.3 Limiting M agnitudes...... 60

4.3 Limiting M agnitudes...... 61

4.3 Limiting M agnitudes...... 62

viii LIST OF FIGURES

Figure Page

3.1 Top left and top right are Gemini DSSI speckle images of HD 2638

at 692 nm and 880 nm, respectively. The field-of-view is 2.8" x 2.8".

As indicated in both images, North is up and East is to the left. The

source in the center is HD 2638, and a bright source to the bottom

and slightly to the left of the main star is the stellar companion. Bot-

ton left and bottom right are sensitivity plots of HD 2638 at 692 nm

and 880 nm, respectively. Each plot shows the limiting magnitude

(difference between local maxima and minima) as a function of ap­

parent separation from HD 2638 in arcsec. The dashed line is a cubic

spline interpolation of the 5a detection limit. Both plots were gen­

erated from top left and right corresponding images. Both images

and sensitivity plots indicate the presence of stellar companion with

magnitude differences of 4 and 3, respectively, and separation of

0.5". The Gemini diffraction limits are 0.021” and 0.027” at 692 nm

and 880 nm, respectively...... 21

ix 3.2 Top left and top right are Gemini DSSI speckle images of HD 164509

at 692 nm and 880 nm. The field-of-view is 2.8" x 2.8” . As indicated

in both images, North is up and East is to the left. The source in the - ft IL ■ center is HD 164509, ana a Bright source to the bottom and right of

the main star is the stellar companion. The arrow in the left image in­

dicates the location of the companion. Bottom left and bottom right

are sensitivity plots of HD 164509 at 692 nm and 880 nm, respec­

tively. Each plot shows the limiting magnitude (difference between

local maxima and minima) as a function of apparent separation from

HD 164509 in arcsec. The dashed line is a cubic spline interpolation

of the 5a detection limit. Both plots are generated from top left and

right corresponding images. Both images and sensitivity plots indi­

cate the presence of stellar companion with magnitude difference of

4 and separation of 0.5" at 880 nm. The Gemini diffraction limits

are 0.021” and 0.027” at 692 nm and 880 nm, respectively...... 22

3.3 Limiting magnitude plots...... 23

3.4 Limiting magnitude plots (cont.) ...... 24

3.5 Limiting magnitude plots (cont.) ...... 25

3.6 Limiting magnitude plots (cont.) ...... 26

3.7 Limiting magnitude plots (cont.) ...... 27

3.8 Limiting magnitude plots (cont.) ...... 28

x 3.9 Limiting magnitude plots (cont.) ...... 29

3.10 Limiting magnitude plots (cont.) ...... 30

3.11 Limiting magnitude plots (cont.) ...... 31

3.12 Limiting magnitude plots (cont.) ...... 32

3.13 Limiting magnitude plots (cont.) ...... 33

3.14 Limiting magnitude plots (cont.) ...... 34

3.15 Limiting magnitude plots (cont.) ...... 35

3.16 Limiting magnitude plots (cont.) ...... 36

3.17 Limiting magnitude plots (cont.) ...... 37

3.18 Limiting magnitude plots (cont.) ...... 38

3.19 Limiting magnitude plots (cont.) ...... 39

3.20 Limiting magnitude plots (cont.) ...... 40

3.21 Limiting magnitude plots (cont.) ...... 41

3.22 Limiting magnitude plots (cont.) ...... 42

3.23 Limiting magnitude plots (cont.) ...... 43

3.24 Limiting magnitude plots (cont.) ...... 44

3.25 Limiting magnitude plots (cont.) ...... 45

3.26 Limiting magnitude plots (cont.) ...... 46

, ;i;. f f f f ! , i i O ■ \ h

xi 4.1 Stellar isochrone models of HD 2638 (left) and HD 164509 (right).

The black dot near the top is the primary star, the dark blue dot

near the bottom is the average model of the companion, and the red

dot is the observed companion. Note that in both cases, the model

fits well with the observation...... 51

4.2 The proper motion of the HD 2638 primary (solid circles) and sec­

ondary (open squares) over time. The measurements presented in

this work are shown in red. The dashed lines link the primary and

secondary for the first and last observations in the sequence, and for

our observation...... 53

5.1 Plots of critical semi-major axis ac vs orbital eccentricity e (solid line)

for HD 2638 (left) and HD 164509 (right). The dashed lines indicate

the 1(7 uncertainties in the relationship and the horizontal dotted lines

represent the semi-major axes of the known planets...... 64 1

Chapter 1

Introduction

Exoplanet, or extra solar planet, is defined as a planet that orbits a star other than our Sun. The discoveries of a few exoplanets during the 1990’s has led to an establishment of a new and exciting astronomical branch known as the exoplanetary science. As of this writing, at least 3,500 exoplanets have been confirmed. Various techniques have been used to detect planets, such as radial velocity (RV) signatures, transits, direct imaging, microlensing, among others. Characterizing the exoplanets has become an increasingly common trend; however, the detection of planets still remains a strong focus in the exoplanetary field. A significant factor that can affect the detection of exoplanets is the binarity of the host stars. In fact, it is believed that nearly half of all sun-like stars are part of a multiple-star system (Raghavan et al., 2010). This high-rate of multiplicity has also been found in exoplanet host stars through follow-up of Kepler candidates (Everett et al., 2015; Kraus et al., 2016) and

Robo-AO observations of RV exoplanet host stars (Riddle et al., 2015). 2

The mere presence of a binary companion can substantially affect astrometric and RV measurements of the host star, and cause severe blended contamination for transit experiments (Cartier et al., 2015; Ciardi et al., 2015; Gilliland et al.,

2015). For example, Ciardi et al. (2015) studied the effect of undetected stellar companions on the Kepler planets’ radii and found that if the host star is assumed to be single, then the exoplanet’s radius become 1.5 times smaller than it actually is. It is therefore imperative to verify the multiplicity of exoplanet host stars to ensure correct interpretation of exoplanet signals. Moreover, the binarity of the stars can place further constraints on planetary formation. Holman & Wiegert

(1999) explored the orbital stability of the planets in the presence of a binary star system. Additionally, correlations between planets’ mass and their period (Zucker h

Mazeh, 2002) and eccentricities (Eggenberger et al., 2004) were examined. Several binary systems have been studied, such as a Centauri (Benest, 1988), Sirius (Benest,

1989), r] Coronae Borealis (Benest, 1996), and 30 Arietis B (Kane et al., 2015;

Roberts et al., 2015), which provide us rich information on orbital dynamics in a

N-body system.

This thesis presents new results on stellar companions to the exoplanet host stars

HD 2638 and HD 164509. The stellar companion to HD 2638 has been previously detected and characterized (Riddle et al., 2015; Roberts et al., 2015). However, this is an independent detection, and this paper shall present an independent analysis of that system. In the meanwhile, the companion to HD 164509 has not been 3

previously reported. The remaining systems, which have null detection of stellar companions, are analyzed for any constraints they may place on the hypothetical presence of exoplanets and brown dwarfs. In Chapter 2 we briefly discusses the method of detection, the range' of targets that were selected for analysis, and the properties of null-detection systems, HD 2638, and HD 164509, along with their known exoplanets. Chapter 3 discusses the details of the data reduction. Chapter

4 presents the results from the data analysis and stellar isochrone fitting. Chapter

5 explains the potential implication of those findings for the planetary systems, including limits to the eccentricities of the binary companion that allow orbital stability as well as the range of distances where we may expect lower mass objects to exist. Chapter 6 provides discussion of further work and concluding remarks. 4

Chapter 2

Observations and Target Selections

2.1 Stellar Companion Survey

A large survey project was established to detect exoplanet host stars’ low-mass stel­ lar companions. The observations that this thesis covers are a small portion of that survey. At least 70 stars were observed in July 2014 using the Differential Speckle

Survey Instrument, or DSSI (Horch et al., 2009); that instrument was stationed at the Gemini-North Observatory at the time of observations. Those stars were selected from the Kepler and ROBO-AO observation databases of RV exoplanet host stars. Tables 2.1 and 2.2 list those targets and their corresponding properties, including the number of exoplanets they’re hosting, taken from multiple literature and exoplanet databases (see reference section). The DSSI used two different filters,

692 nm and 880 nm, to acquire the AO images of those targets. The 692 nm filter has FWHM of 40 nm, and the 880 nm filter has FWHM of 50 nm. All images 5

became subjected to data reduction; more details on data reduction are provided in the next chapter. Afterward, the images were directly examined using the ds9 program for any bright source appearing next to the target. The two particular targets, HD 164509 and HD 2638, are described in the next section. Table 2.1. Stellar Properties of Kepler and ROBO-AO RV Exoplanet Host Stars with Null-Detection I

Star Spectral Type Apparent Mag my Proper Motion a, S (mas/yr) Parallax (mas) Distance (pc) Planet

B D +14 4559 K2 V 9.7768 235.80,1.78 20.68 ± 1.24 48.36 ± 2.90 1 B D +48 738 K0 III 9.14 3 .7 ,-6 .5 2.85 ±0 350.88 ± 0.00 1 GJ 581 M3 V 10.5759 -1227.67,-97.78 160.91 ±2.62 6.21 ±0.10 3 GJ 649 M2 V 9.7165 -114.07,-506.26 96.67 ± 1.39 10.34 ±0.15 2 GJ 849 M3 V 10.3672 1130.27,-19.27 109.94 ± 2.07 9.10 ± 0 .1 7 1 HD 1461 G3 V 6.6029 416.87,-143.83 43.02 ±0.51 23.25 ±0.28 2 HD 1502 K0 IV 8.5196 74.64,-18.15 6.28 ±0.75 159.24 ± 19.02 1 HD 3651 K0 V 6.03 -461.32,-370.02 90.42 ± 0.32 11.06 ±0.04 2 HD 4313 G5 IV 7.9939 -5.14,6.69 7.3 ± 0.76 136.99 ± 14.26 1 HD 5319 K3 IV 8.2069 -4.93, -49.66 8.74 ± 0.86 114.42 ± 11.26 2 HD 5891 G5 III 8.2541 2.64,-41.89 3.98 ± 1.21 251.26 ±76.39 1 HD 6718 G5 V 8.5834 192.24,19.77 18.23 ±0.76 54.85 ±2.29 1 HD 7449 F8 V 7.6205 -160.79,-138.95 25.69 ± 0.48 38.93 ± 0.73 2 HD 8574 F8 V 7.2497 250.87,-158.06 22.44 ± 0.53 44.56 ± 1.05 1 HD 9446 G5 V 8.5125 192.01,-53.99 19.1 ± 1.06 52.36 ±2.91 2 HD 10697 G5 IV 6.4169 -44.75,-105.35 30.7 ± 0 .4 3 32.57 ±0.46 1 Table 2.1 (cont’d)

Star Spectral Type Apparent Mag Proper Motion a. S (mas/yr) Parallax (mas) Distance (pc) Planets

HD 12661 G6 V 7.567 -107.12,-174.69 28.61 ±0.61 34.95 ± 0.75 HD 13189 K2 II 7.6968 2.62,5.32 1.78 ±0.73 561.80 ±230.40 HD 13931 GO V 7.7426 99.03,-183.19 22.61 ±0.66 44.23 ±1.29 HD 16175 GO V 7.4156 -38.90, -40.37 17.28 ±0.67 57.87 ±2.24 HD 16400 G5 III 5.8154 40.18,-42.91 10.81 ± 0 .4 5 92.51 ±3.85 IID 16760 G5 V 8.8411 7 9 .2 0 ,-1 0 7 .4 9 22 ± 2.35 45.45 ± 4.86 HD 17092 K0 III 7.73 3 7 .9 ,-1 3 .6 9.2 ± 5 .5 108.70 ± 64.98 HD 136118 F9 V 7.0513 -122.69,23.72 21.47 ±0.54 46.58 ± 1.17 HD 136418 G5 IV 8.0279 -19.66,-181.92 10.18 ±0.58 98.23 ± 5.60 HD 137510 GO IV 6.3856 -54.91,-5.39 24.24 ±0.51 41.25 ±0.87 HD 139357 K4 III 6.1335 -18.32,1.64 8.47 ± 0 .3 118.06 ±4.18 HD 142245 K0 IV 7.6302 -55.58,-20.82 9.13 ± 0 .6 2 109.53 ± 7.44 HD 143107 K3 III 4.2992 -77.07,-60.61 14.73 ± 0.21 67.89 ± 0.97 HD 143761 G O V 5.5246 -196.63,-773.02 58.02 ± 0.28 17.24 ± 0.08 HD 145457 KO III 6.7416 -18.34,36.89 7.98 ± 0.45 125.31 ±7.07 HD 145675 KO V 6.7595 131.83,-297.54 56.91 ± 0.34 17.57 ±0.10

- 4 Table 2.1 (cont’d)

Star Spectral Type Apparent Mag Proper Motion a. S (mas/yr) Parallax (mas) Distance (pc) Planet

HD 149143 GO IV 8.0354 -9.26,-87.31 16.12 ±0.83 62.03 ±3.19 1 HD 152581 K0 IV 8.5372 11.49,-15.79 5.39 ± 0 .9 6 185.53 ±33.04 1 HD 154345 G8 V 6.907 123.27,853.63 53.8 ±0.32 18.59 ±0.11 1 HD 155358 GO V 7.3946 -222.45,-215.97 22.67 ±0.48 44.11 ±0.93 2 HD 156279 K0 V 8.2107 -1.21,161.21 27.32 ± 0.44 36.60 ± 0.59 1 HD 156668 K3 V 8.5711 -71.16,217.36 40.86 ± 0.86 24.47 ± 0.52 1 HD 158038 K2 II 7.6439 48.35, -59.04 9.65 ± 0.74 103.63 ± 7.95 1 HD 163607 G5 IV 8.1487 -75.74,120.05 14.53 ±0.46 68.82 ±2.18 2 HD 164922 G9 V 7.151 389.41,-602.03 45.21 ±0.54 22.12 ±0.26 2 HD 167042 K1 IV 6.1356 107.94,247.35 19.91 ±0.26 50.23 ± 0.66 1 HD 170693 K2 III 4.9835 105.83, -27.24 10.36 ± 0 .2 96.53 ± 1.86 1 HD 171028 GO IV 8.31 -43.8,-13.4 9.1 ± 7 .8 109.89 ±94.19 1 HD 173416 G8 III 6.2114 21.11,58.23 7.17 ± 0 .2 8 139.47 ±5.45 1 1 1 cn 0 CM HD 177830 KO IV 7.3455 00 16.94 ±0.63 59.03 ±2.20 2 HD 180314 KO III 6.7743 47.19,19.71 7.61 ± 0 .3 9 131.41 ±6.73 1 HD 187123 G2 V 7.9689 143.18,-123.91 20.72 ± 0.53 48.26 ± 1.23 2 Table 2.1 (cont’d)

Star Spectral Type Apparent Mag Proper Motion a, S (mas/yr) Parallax (mas) Distance (pc) Planets

HD 190228 G5 IV 7.452 105.2,-69.82 16.23 ±0.64 61.61 ±2.43 1 HD 192263 K2.5 V 7.931 -61.13,261.37 51.77 ±0.78 19.32 ± 0.29 1 HD 197037 F7 V 6.9226 -62.47, -220.96 30.93 ± 0.38 32.33 ± 0.40 1 HD 199665 G6 III 5.6682 -48.75, -34.43 13.28 ±0.31 75.30 ± 1.76 1 HD 200964 K0 IV 6.6386 94.99,50.47 13.85 ±0.52 72.20 ± 2.71 2 HD 206610 K0 IV 8.5066 2.35,2.34 5.16 ±0.95 193.80 ± 35.68 1 HD 208527 M l III 6.4842 2.00,15.30 2.48 ± 0.38 403.23 ± 61.78 1 HD 210277 G8 V 6.6823 85.07, -449.74 46.38 ± 0.48 21.56 ±0.22 1 HD 210702 K1 IV 6.0932 -3.15,-18.02 18.2 ± 0 .3 9 54.95 ±1.18 1 HD 217014 G2 V 5.5865 207.25,60.34 64.07 ±0.38 15.61 ±0.09 1 HD 217107 G8 IV 6.3124 -6.35,-15.80 50.36 ±0.38 19.86 ±0.15 2 HD 217786 F9 V 7.9103 -88.78,-170.13 18.23 ±0.72 54.85 ±2.17 1 HD 218566 K3 V 8.7269 632.56, -97.02 35.02 ± 1.14 28.56 ± 0.93 1 HD 219828 GO IV 8.1795 -4 .1 5 ,4 .1 4 13.83 ± 0.74 72.31 ±3.87 2 HD 220074 M2 III 6.4885 7.68, -5.43 3.08 ± 0.43 324.68 ± 45.33 1 HD 220773 F9 V 7.2306 26.90, -222.87 19.65 ± 0.65 50.89 ± 1.68 1 Table 2.1 (cont’d)

Star Spectral Type Apparent Mag my Proper Motion a, S (mas/yr) Parallax (mas) Distance (pc) Planets

HD 221345 K0 III 5.3841 286.72, -84.22 12.63 ±0.27 79.18 ±1.69 1 HD 222155 G2 V 7.2445 195.33,-117.13 20.38 ±0.62 49.07 ±1.49 1 HD 231701 F8 V 9.0929 63.85,16.46 8.44 ± 1.05 118.48 ±14.74 1 HD 240210 K3 III 8.33 18.0,7.9 7 ± 2 .6 142.86 ± 53.06 1 HD 240237 K2 III 8.2959 -0.74,-5.13 0.19 ±0.72 5263.16 ± 19944.60 1

Table 2.2. Stellar Properties of Kepler and ROBO-AO RV Exoplanet Host Stars with Null-Detection II

Name M* (M 0 ) R* (Re) U (Le ) Te (K) log g (cm/s2) Age (Gyr) [Fe/H]

BD±14 4559 0.82 ±0.02 0.78 ± 0.02 0.32 ± 0 .0 1 4948 ± 25 4.57 ±0.03 6.9 ±4.2 0.17 ± 0 .0 6 B D +48 738 0.74 ± 0.39 11 ± 1 49 ± 37.2 4519 ± 30 2.51 ± 0 .0 3 ± -0.24 ±0.02 GJ 581 0.306 ±0.011 0.299 ± 0.007 0.01146 ±0.00061 3457 ± 22 4.96 ± 0.25 9.44 ± 0.58 -0.15 ±0.08 GJ 649 0.527 ±0.013 0.495 ±0.012 0.04308 ± 0.00276 3741 ± 39 4.76 ±0.12 9.42 ± 0.57 0.03 ± 0.08 GJ 849 0.482 ± 0.048 0.47 ±0.018 0.03079 ± 0.00315 3530 ± 60 4.8 ± 0 .1 4 9.4 ± 0 .5 8 0.37 ± 0.08 HD 1461 1.07 ± 0 .0 1 1.08 ± 0 .0 1 1.2 ± 0 .0 1 5807 ± 20 4.39 ± 0 .0 1 4 ± 0 .7 0.16 ± 0 .0 3 HD 1502 1.46 ± 0 .0 4 4.5 ± 0 .1 11.5 ± 0 .2 5006 ± 25 3.29 ± 0.02 3 ± 0 .3 -0.01 ±0.06 HD 3651 0.88 ± 0.02 0.86 ± 0 .0 1 0.51 ± 0 .0 1 5271 ± 26 4.51 ± 0 .0 2 6.9 ± 2 .8 0.19 ± 0 .0 2 HD 4313 1.49 ± 0 .0 4 5.2 ± 0 .1 14 ± 0 .2 4920 ± 21 3.18 ±0.02 3 ±0.3 0.11 ±0.07 HD 5319 1.2 ± 0 .1 4 ± 0 .1 8.2 ± 0 .1 4888 ± 39 3.3 ± 0.04 6.1 ± 1 .4 0.15 ± 0 .0 3 HD 5891 1.1 ± 0 .1 9.1 ± 0 .2 39.1 ± 0 .4 4796 ± 41 2.57 ± 0 .0 5 5.7 ± 1.5 -0 .3 7 ± 0 .0 4 HD 6718 0.97 ± 0 .0 2 1.02 ±0.03 1.06 ±0.02 5805 ± 46 4.4 ± 0.03 6.2 ± 2 -0.11 ±0.05 HD 7449 1.05 ± 0 .0 2 1.02 ± 0 .0 2 1.26 ± 0 .0 2 6060 ± 42 4.44 ± 0.02 2.2 ± 1.3 -0.11 ±0.01 HD 8574 1.17 ± 0 .0 2 1.38 ±0.04 2.35 ± 0.04 6092 ± 56 4.22 ±0.03 4.4 ±0.6 0.06 ± 0.07 HD 9446 1.04 ± 0 .0 3 1.03 ± 0 .0 3 1.06 ± 0 .0 3 5790 ± 45 4.43 ± 0.03 3.7 ±2 0.09 ±0.05 HD 10697 1.12 ± 0 .0 1 1.7 ± 0.1 2.8 ± 0 .0 4 5674 ± 93 4 ± 0 .0 3 7.5 ± 0.4 0.15 ± 0 .0 4 o Table 2.2 (cont’d)

Name M* (M 0 ) R* (* © ) L* (LG) Te (K) log g {cm/s2) Age (Gyr) [Fe/H]

HD 12661 1.09 ± 0 .0 1 1.08 ± 0 .0 1 1.13 ±0.01 5714 ±22 4.4 ± 0 .0 1 3.3 ± 0 .6 0.36 ± 0 .0 5 HD 13189 1.08 ± 0 .1 7 ± ± 4228 ± 242 2.09 ± 0 .6 1 ± -0 .5 ± 0 .1 4 HD 13931 1.07 ±0.02 1.17 ±0.03 1.48 ± 0.03 5902 ± 52 4.33 ± 0 .0 3 5.3 ± 1.3 0.07 ± 0 .0 1 HD 16175 1.3 ± 0 .0 5 1.69 ±0.03 3.35 ±0.02 6009 ± 44 4.09 ± 0 .0 2 4.1 ± 0 .8 0.37 ± 0 .0 3 H D -16400 1.4 ± 0 .1 11.2 ± 0 .2 59.8 ± 0.4 4799 ± 24 2.49 ± 0.03 3.2 ±0.5 0 ± 0.04 HD 16760 0.93 ±0.01 0.835 ± 0.005 0.58 ±0.002 5518 ± 11 4.56 ± 0 .0 1 1.3 ± 0 .9 0 ± 0.02 HD 17092 1.246 ± 0 .1 7 9 10.439 ± 1.31 43.64 ± 11.23 4596 ± 65 2.45 ± 0 .1 7 5.58 ± 2.669 0.05 ± 0.04 HD 136118 1.15 ±0.03 1.54 ±0.03 3.03 ±0.01 6135 ± 37 4.12 ±0.03 5.3 ±0.6 -0.01 ±0.053 HD 136418 1.2 ± 0 .1 3.5 ±0.1 6.9 ±0.1 4997 ± 40 3.43 ±0.04 5 ± 1 -0.09 ±0.03 HD 137510 1.41 ± 0 .0 1 1.91 ± 0 .0 3 4.33 ±0.01 6032 ± 44 4.02 ± 0.02 3.1 ± 0 .2 0.29 ± 0 .1 2 HD 139357 1.1 ± 0 .1 14.4 ± 0 .4 73.5 ± 1.3 4454 ± 39 2.2 ± 0 .1 7.2 ± 1.8 0.19 ± 0 .0 5 HD 142245 1.52 ± 0 .0 5 5.2 ± 0 .1 13.1 ± 0 .2 4831 ± 28 3.19 ± 0 .0 3 3.1 ± 0 .3 0.23 ± 0.03 HD 143107 1.44 ± 0 .1 8 21 ± 0 151 ± 0 4436 ± 56 1.94 ± 0 .1 5 1.74 ± 0 .3 7 -0.22 ±0.03 HD 143761 0.889 ± 0.03 1.3617 ±0.0262 1.706 ±0.042 5627 ± 54 4.121 ±0.018 9.1 ± 1 -0.31 ±0.05 HD 145457 1.5 ± 0.1 9.4 ± 0 .2 41 ± 1 4772 ± 45 2.66 ± 0 .0 5 2.8 ± 0 .6 -0.13 ±0.03 HD 145675 0.97 ± 0 .0 1 0.93 ±0.01 0.61 ±0.01 5313 ± 18 4.48 ± 0.02 4.6 ± 1.5 0.5 ± 0 .0 6 Table 2.2 (cont’d)

Name M* (M0) (#©) L* (Le) Te (K) log g (cm/s2) Age (Gyr) [Fe/H]

HD 149143 1.21 ± 0 .0 3 1.5 ± 0 .1 2.2 ± 0.1 5792 ± 58 4.17 ± 0 .0 3 4.8 ± 0 .8 0.45 ± 0.07 HD 152581 1 ±0.1 5.4 ± 0 .1 16.1 ± 0 .2 4991 ± 45 3 ± 0 .1 7.2 ± 2 -0 .3 ± 0 .0 2 HD 154345 0.9 ± 0 .0 1 0.85 ± 0 .0 1 0.62 ± 0.002 5557 ± 15 4.53 ± 0 .0 1 4.1 ± 1.2 -0.09 ± 0.02 HD 155358 1.1 ±0.1 1.36 ± 0 .0 3 2.11 ± 0 .0 2 5966 ± 53 4.2 ± 0 .0 4 1.9 ± 4 .5 -0.62 ±0.02 HD 156279 0.93 ± 0 .0 2 0.94 ± 0 .0 2 0.7 ± 0 .0 1 5449 ± 31 4.45 ± 0.03 7.4 ± 2 .2 0.14 ± 0 .0 1 HD 156668 0.75 ± 0 .0 1 0.73 ± 0.01 0.27 ± 0 .0 1 4857 ± 18 4.58 ± 0 .0 1 10.2 ± 2.8 -0.04 ±0.05 HD 158038 1.5 ± 0 .1 4.9 ± 0 .1 11.9 ± 0 .1 4839 ± 29 3.23 ± 0.03 3.2 ± 0 .4 0.16 ± 0 .0 5 HD 163607 1.1 ± 0 .0 2 1.8 ± 0.1 2.6 ± 0.1 5508 ± 15 3.98 ± 0 .0 1 8.3 ± 0 .5 0.22 ± 0 .0 2 HD 164922 0.874 ±0.012 0.999 ±0.017 0.703 ±0.017 5293 ± 32 4.387 ±0.014 7.9 ± 2 .7 0.16 ± 0 .0 5 HD 167042 1.46 ± 0 .0 5 4.4 ± 0 .1 10.7 ± 0 .1 4989 ± 32 3.31 ± 0 .0 3 3.1 ± 0 .3 -0.01 ±0.06 HD 170693 1.1 ± 0.1 20.6 ± 0.6 145 ± 3 4414 ± 40 1.8 ± 0.1 6.5 ± 1.7 -0.41 ±0.03 HD 171028 0.98 ± 0.04 2 ± 0.2 3.9 ± 0 .5 5771 ± 46 3.84 ± 0.03 8.2 ± 1.1 -0.47 ±0.02 HD 173416 1.8 ± 0 .2 13 ± 0 .3 80 ± 2 4790 ± 37 2.5 ± 0 .1 1.8 ± 0 .7 -0.15 ±0.03 HD 177830 1.1 ±0.1 3.4 ± 0 .1 5.3 ± 0 .1 4735 ± 31 3.39 ± 0.04 10.2 ± 1.7 0.09 ± 0.04 HD 180314 2.3 ± 0 .1 8.7 ± 0 .3 40 ± 1 4946 ± 55 2.92 ± 0.05 0.9 ± 0 .2 0.11 ± 0 .0 4 HD 187123 1.06 ± 0 .0 2 1.17 ± 0 .0 3 1.44 ± 0 .0 2 5853 ± 53 4.32 ± 0.03 5.6 ± 1.3 0.13 ± 0 .0 3 Table 2.2 (cont’d)

Name M* (M0) R+ (RQ) L* (Le ) Te (K) log g (cm/s2) Age (Gyr) [Fe/H]

HD 190228 1.18 ± 0 .0 4 2.4 ± 0 .1 4.4 ± 0 .2 5352 ± 30 3.73 ± 0.02 5 ± 0 .5 -0.24 ±0.06 HD 192263 0.78 ± 0.02 0.73 ± 0.01 0.3 ± 0 .0 1 4980 ± 20 4.59 ± 0.02 5.9 ± 3 .9 -0.01 ±0.05 HD 197037 1.063 ±0.022 1.105 ±0.023 1.568 ±0.074 6150 ± 34 4.37 ± 0.04 3.408 ± 0.924 -0.16 ±0.03 HD 199665 2.1 ± 0 .1 7.8 ± 0 .3 35 ± 1 5037 ± 57 2.98 ± 0.04 1 ± 0.1 0.1 ± 0 .0 2 HD 200964 1.4 ± 0 .1 4.7 ± 0 .1 12.8 ± 0.2 5059 ± 34 3.23 ± 0.03 3.1 ± 0 .4 -0.16 ±0.03 HD 206610 1.51 ± 0 .0 5 6 ± 0.2 18 ± 1 4836 ± 30 3.05 ± 0.03 3 ± 0 .3 0.09 ± 0.05 HD 208527 1.6 ± 0 .4 51.1 ± 8 .3 621.3 ± 205.8 4035 ± 65 1.4 ± 0 .2 2 ± 1.3 -0.09 ±0.16 HD 210277 0.96 ± 0.02 1.05 ± 0 .0 3 0.92 ± 0.03 5530 ± 40 4.37 ± 0.03 8.8 ± 1.9 0.26 ± 0 .0 2 HD 210702 1.47 ± 0 .0 4 4.9 ± 0 .1 12.9 ± 0 .1 4946 ± 25 3.22 ± 0 .0 2 3.1 ± 0 .3 -0.05 ±0.04 HD 217014 1.09 ± 0 .0 2 1 13 ± 0 .0 3 1.34 ± 0 .0 3 5857 ± 39 4.37 ± 0.02 3.8 ± 1.1 0.2 ± 0 .0 2 HD 217107 1.08 ± 0 .0 1 1.11 ± 0.02 1.14 ± 0 .0 1 5676 ± 31 4.38 ± 0.02 4.2 ± 1 0.37 ± 0 .0 2 HD 217786 1.03 ± 0 .0 2 1.27 ± 0 .0 4 1.93 ± 0 .0 4 6031 ± 55 4.23 ± 0.03 6.8 ± 0 .9 -0.14 ±0.01 HD 218566 0.8 ± 0 .0 1 0.77 ± 0 .0 2 0.3 ± 0 .0 1 4880 ± 16 4.57 ± 0 .0 2 8 ± 3 .1 0.17 ± 0 .0 4 HD 219828 1.2 ± 0 .0 4 1,58 ± 0 .0 4 2.74 ± 0 .0 3 5921 ± 53 4.11 ± 0 .0 3 5.2 ± 0 .8 0.16 ± 0 .0 4 HD 220074 1.2 ± 0 .3 49.7 ± 9 .5 531.6 ±211.7 3935 ± 110 1.1 ± 0.2 4.5 ± 2 .8 -0.25 ±0.25 HD 220773 1.154 ±0.003 1.73 ± 0 .0 2 3.16 ± 0 .0 1 5852 ± 26 4.02 ± 0 .0 1 6.3 ± 0 .1 0.11 ± 0 .0 3 Table 2.2 (cont’d)

Name M* (M 0 ) R* (Re) L* (Le) Te (K) log g (cm/s2) Age (Gyr) [Fe/H]

HD 221345 1.2 ± 0 .2 11 ± 0 .3 56 ± 1 4775 ± 49 2.4 ± 0 .1 5.6 ± 3 -0.29 ±0.03 HD 222155 1.05 ± 0 .0 1 1.7 ± 0 .1 2.9 ± 0 .1 5814 ± 4 3 4 ± 0 .0 1 8.1 ± 0 .4 -0.09 ±0.02 HD 231701 1.23 ± 0 .0 1 1.48 ± 0 .0 5 2.94 ± 0 .0 5 6211 ± 7 1 4.18 ± 0 .0 3 3.7 ± 0 .5 0.04 ± 0.02 HD 240210 1.241 ± 0 .2 3 8 19.293 ± 4.399 115.9 ±53.5 4316 ± 78 1.91 ± 0 .2 1 5.085 ± 3.089 -0.14 ±0.03 HD 240237 0.614 ±0.076 0.587 ± 0.274 0.1183 ±0.1109 4422 ± 101 1.69 ± 0 .2 4 4.42 ± 4.007 -0.24 ± 0.06 15

2.2 Background on HD 164509 and HD 2638

HD 164509 and HD 2638 were observed during the night of 2014 July 22 and 23, respectively. The detailed stellar and planetary parameters of the HD 2638 and

HD 164509 systems are shown in Table 2.3.

HD 2638 is a G5V star that is about 50 pc away toward the constellation of

Cetus (ESA, 1997; van Leeuwen, 2007). It is believed to be part of a wide binary system with the nearby star HD 2567. Shaya k. Oiling (2011) performed a Bayesian analysis of both stars’ astrometry; the result yielded 99% chance of both stars being true companions. However, Roberts et al. (2015) argued that, barring any errors in the measurement of the stars’ parallax, they are separated by 6.8 pc, making them not gravitationally bound. HD 2638 is known to host one planet, HD 2638b, with a mass of approximately 0.48 M j (Moutou et al., 2005). Riddle et al. (2015) discovered that HD 2638 has a stellar companion while examining the system with

ROBO-AO. Roberts et al. (2015) analyzed the orbital dynamics of the primary star and the stellar companion and determined that the masses of the components are

0.87 Mq and 0.46 M©, respectively. Moreover, they inferred that the spectral types are G8V and M1V and that they are separated by about 28.5 AU, giving them an orbital period of around 130 years (Roberts et al., 2015). Ginski et al. (2016) performed additional astrometric and photometric analysis on the system and found that the mass of the companion star is 0.425^o;o95 Ms-

HD 164509 is a G5V star that is about 52 pc away toward the constellation Table 2.3. Stellar & Planetary Properties

Properties HD 2638a>6 HD 164509c

Stellar Spectral Typed G5V G5V M* (M0)e 0.87 ± 0 .0 3 1.10 ± 0 .0 1 R* (^o)e 0.81 ± 0 .0 2 1.11 ± 0 .0 2 L* {LqY 0.42 ± 0 .0 1 1.31 ± 0 .0 2 Te (K )e 5173 ± 26 5860 ± 31 log g (c m /s2)e 4.55 ± 0.03 4.38 ± 0.02 Age (Gyr)e 5.1 ± 4 .1 3.2 ± 0 .8 [Fe/H] 0.16 ± 0 .0 5 0.21 ± 0 .0 3 Apparent Magnitude niv^ 9.58 8.24 Proper Motion (a, 5) (m as/yr)f -105.63,-223.46 -7.40,-20.98 Parallax (mas)f 20.03 ± 1.49 19.07 ±0.97 Distance (pc)f 49.93 ±3.71 52.44 ±2.67

Planetary Mp sin i (M j) 0.48 0.48 ± 0.09 P (Days) 3.43752 ± 0.00823876 282.4 ± 3.8 a (AU) 0.044 0.875 ± 0.008

aWang & Ford (2011)

bMoutou et al. (2005)

cGiguere et al. (2012)

dESA (1997)

eBonfanti et al. (2016)

fvan Leeuwen (2007) 17

of Ophiuchus (ESA, 1997; van Leeuwen, 2007). It is known to host one planet,

HD 164509b, with a mass of approximately 0.48 M j (Giguere et al., 2012). Giguere et al. (2012), upon examining the RV data, found that it displays “a residual linear trend of 5.1±0.7 m s_1 year-1, indicating the presence of an additional longer period companion in the system” . Sirothia et al. (2014) studied this system and reported a 150 MHz radio signature of 18 ± 6 mJy. The authors speculated that it could be caused by a massive moon “orbiting a rapidly-rotating giant planet” ; however, they emphasized that more analysis is needed before such a conclusion can be reached. 18

Chapter 3

Data Reduction

Final reconstructed images were produced from the speckle data sequences using

methods that have been described in previous papers (e.g. Horch et al., 2012, 2015),

but the main points will be briefly described here. The raw speckle data are stored as

FITS data cubes consisting of 1000 single short-exposure frames, where each frame is

a 256 x 256-pixel image (with pixel size of about 0.01” across) centered on the target.

Frames are bias-subtracted, and then an autocorrelation is formed. These are then

summed to generate a final autocorrelation for the entire observation. We Fourier

transform this to obtain the spatial frequency power spectrum of the observation.

The same operations are then performed on an unresolved star (effectively a point

source) that lies close on the sky to the science target. By dividing the power spectrum of the science target by that of the point source, we deconvolve the effects of the speckle statistics, and arrive at a diffraction-limited estimate of the true power spectrum of the object. 19

Returning to the raw data frames, we next form the image bispectrum of each

frame, which is the Fourier transform of the triple correlation, as described in

Lohmann et al. (1983). This data product is known to contain information that

can be used to calculate the phase of the object’s Fourier transform, which we do

using the relaxation algorithm of Meng et al. (1990). By taking the square root

of the deconvolved power spectrum and combining it with this phase estimate, we

generate a diffraction-limited estimate of the (complex) Fourier transform of the

object. Finally we multiply this with a Gaussian low-pass filter of width similar

to the diffraction limit of the telescope, and inverse-transform to arrive at the final

reconstructed image.

Using the reconstructed images, we can study the statistics of local maxima that

occur as a function of separation from the central star in order to derive a detection

limit curve versus separation. We follow the method described in Horch et al.

(2011). By computing the average and standard deviation of the maxima inside

annuli that have different mean separations from the primary star, we estimate the

5-sigma detection limit as the mean value plus five times the standard deviation,

converted to a magnitude difference. For Gemini data, this is done centering annuli

at distances of 0.1, 0.2, 0.3, ..., 1.2 arcsec. We then use a cubic spline interpolation to

develop a smooth detection limit curve at all separations in between the two extreme limits. Curves like this are shown in Figures 3.1 and 3.2. The sensitivity plots for the remaining targets are listed in the next several pages. An important note that 20

must be made is that the 880 nm plots for HD 12661, HD 136118, HD 142245, and

HD 145457 indicated the detection of an “object” at ~ 7 ” . Those particular hits are actually artifacts caused by the instrument and are dismissed as false positives. 21

12 ...... ’ ■ 1'" ' ’ 1 1 • " 1 1 I 1 ' ' 1 .■ ’ —' T T..'..■,— ’ □ □ 10 _ □ : °D ns^ h - aD JO a 8 a n - □ n W1 rfr ftff HiYfRri i nmftl iiftffln fillffi liii if : z p 6 ...... -

47a 0 Limiting Am = 4.96 Limiting An* = 4.63 2 Limiting Am = 4.45 □ Local Maxima " Limiting Am = 3.83 P Local Maxima " 'if Local Minima . Local Minima . o L 0 .—i--1--1--1--1--1-- 1--1--.--1--i--1--.-- 1--.--L_i—i__ ___ I__ i—i—i— 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Separation [arcsec] Separation [arcsec]

Figure 3.1 Top left and top right are Gemini DSSI speckle images of HD 2638 at 692: nm and 880 nm, respectively. The field-of-view is 2.8" x 2.8". As indicated in both images, North is up and East is to the left. The source in the center is HD 2638, and a bright source to the bottom and slightly to the left of the main star is the stellar companion. Botton left and bottom right are sensitivity! plots of HD 2638 at 692 nm and 880 nm, respectively. Each plot shows the limiting magnitude (dif­ ference between local maxima and minima) as a function of apparent separation from HD 2638 in arcsec. The dashed line is a cubic spline interpolation of the 5a detection limit. Both plots were generated from top left and right corresponding images. Both images and sensitivity plots indicate the presence of stellar companion with magnitude differences of 4 and 3, respectively, and separation of 0.5". The Gemini diffraction limits are 0.021” and 0.027” at 692 nm and 880 nm, respectively. 22

;' . u ; J i > IffISi -•

Figure 3.2 Top left and top right are Gemini DSSI speckle images of HD 164509 at 692 mn and 880 rim. The field-of-view is 2.8" x 2.8” . As indicated in both images, North is up and East is t% the left. The source in the ceiiter is HD 164509, and a bright source to the bottom and right of the main star is the stellar companion. The arrow in the left image indicates the location of the companion. Bottom left and bottom right are sensitivity plots of HD 164509 at 692 nm and 880 nm, respec­ tively. Each plot shows the limiting magnitude (difference between local maxima and minima) as a function of apparent separation from HD 164509 in arcsec. The dashed line is a cubic spline interpolation of the 5a detection limit. Both plots are generated from top left and right corresponding images. Both images and sensitivity plots indicate the presence of stellar companion with magnitude difference of 4 and separation of 0.5" at 880 nm. The Gemini diffraction limits are 0.021” and 0.027” at 692 nm and 880 nm, respectively. iue . Lmtn antd plots magnitude Limiting 3.3 Figure

Magnitude Difference Magnitude Difference Magnitude Difference a BD+4 59 t 9 n () 1 45 a 80 nm 880 at 4559 +14 D B (b) nm 692 at 4559 +14 D B (a) c BD+8 3 a 62 m d BD+8 3 a 880 at 738 +48 D B (d) nm 692 at 738 +48 D B (c) e G 51 t 9 nm 692 at 581 GJ (e) f G 51 t 8 nm 880 at 581 GJ (f) 23 iue . Lmtn antd pos (cont.) plots magnitude Limiting 3.4 Figure

Magnitude Difference Magnitude Difference Magnitude Difference . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 % r L_, Jgf g J : -- L.—1 J . . miig m = .4 Local Maxima a; 4.44 = Am iting im L Lim iting Am = 3.21 3.21 = Am iting Lim i tng A 34 ° Local* ° 3.40 = Am g itin lim D . -- e H 10 a 62 nm 692 at 1502 HD (e) c H 16 a 62 nm 692 at 1461 HD (c) 1 __ -- miig m = 5.20 = Am iting im L L im iting Am = 4.15 4.15 = Am iting im L a G 69 t 9 nm 692 at 649 GJ (a) 4.23 = Am iting im L . . __ -- . . __ -- par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S I . I I . . -- i 1—r--T- r-T—T-T 1. . □ -- °D ° □ . __ -- I I I . I . I I I . . -- □ 1 ... . □□ . ------■ T 1 ° --- .. oa ; Local '"I- " ''""I- r 1 ■» 1 -■-» oa Minima Local --- Local Minima . oa i Local . --- 1 --- -- 1 o □' no i --- -- . > __ -- . • __ -- . 02 . 06 . 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 1.0 0.8 0.6 0.4 0.2 0.0 miig m = 4.29 = Am iting im L miig m = .4 I ' 1 » I« ° 3.54 = Am iting im L miig m = 3.39 = Am iting im L . 04 . 08 1.0 0.8 0.6 0.4 0.2 d H 16 a 80 nm 880 at 1461 HD (d) f H 10 a 80 nm 880 at 1502 HD (f) L im iting Am = 4.97 4.97 = Am iting im L b G 69 t 8 nm 880 at 649 GJ (b) L im iting Am = 4.27 4.27 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S Lcl aia ' Maxima Local a a Local Maxima ' ' Maxima Local a oa Mnm . Minima Local oa Mnm . Minima Local oa Minima Local 24 iue . Lmtn antd lt (cont.) plots magnitude Limiting 3.5 Figure

Magnitude Difference Magnitude Difference . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 i tng A 4.09 = Am g itin lim miig m = 4.67 = Am iting im L i ti m 4.53 = Am g in it lim . 04 . 08 1.0 0.8 0.6 0.4 0.2 e H 51 a 62 nm 692 at 5319 HD (e) c H 41 a 62 nm 692 at 4313 HD (c) a H 35 a 62 m() D 61 t 8 nm 880 at 3651 HD (b) nm 692 at 3651 HD (a) L im iting Am = 5.30 5.30 = Am iting im L L im iting Am = 5.39 5.39 = Am iting im L Lim iting Am = 5.25 5.25 = Am iting Lim par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S a Local Maxima ' ' Maxima Local a Lcl aia ' Maxima Local a □ Local Maxima Maxima Local □ oa Minima Local oa Mnm . Minima Local oa Minima Local I as o' 2 . 02 . 06 . 1.0 0.8 0.6 0.4 0.2 0.0 miig m = 4.28 = Am iting im L miig m = 4.31 = Am iting im L . 04 . 08 1.0 0.8 0.6 0.4 0.2 . 04 . 08 1.0 0.8 0.6 0.4 0.2 f H 51 a 80 nm 880 at 5319 HD (f) ran 880 at 4313 HD (d) miig m 5.21 = Am iting im L L im iting Am = 5.15 5.15 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S a Local Maxima ' ' Maxima Local a Local Local oa Minima Local iue . Lmtn antd pos (cont.) plots magnitude Limiting 3.6 Figure

Magnitude Difference Magnitude Difference Magnitude Difference . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 miig m = 4.32 = Am iting im L e H 74 a 62 nm 692 at 7449 HD (e) c H 61 a 62 nm 692 at 6718 HD (c) a H 59 a 62 nm 692 at 5891 HD (a) Lim itin g Am = 4.80 4.80 = Am g itin Lim par in [ cs c] se rc [a tion ra a ep S Lcl aia “ Maxima Local a oa Minima Local . 02 . 06 . 1.0 0.8 0.6 0.4 0.2 0.0 miig m - 4.20 - Am iting im L d H 61 a 80 nm 880 at 6718 HD (d) f H 74 a 80 nm 880 at 7449 HD (f) b H 59 a 80 nm 880 at 5891 HD (b) L im iting Am = 4.95 4.95 = Am iting im L par in [ cs c] se rc [a tion ra a ep S Local Local 1.2 26 iue . Lmtn antd pos (cont.) plots magnitude Limiting 3.7 Figure

Magnitude Difference Magnitude Difference Magnitude Difference . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 miig m = 4.75 = Am iting im L i ti m = 4.53 = Am g in it lim . 04 . 08 1.0 0.8 0.6 0.4 0.2 . 04 . 08 1.0 0.8 0.6 0.4 0.2 e H 167 t 9 nm 692 at 10697 HD (e) c H 94 a 62 nm 692 at 9446 HD (c) a H 87 a 62 nm 692 at 8574 HD (a) L im iting Am = 5.24 5.24 = Am iting im L L im iting Am = 5.18 5.18 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S oa Minima Local oa Mxm “ Maxima Local Local Local miig m = 4.10 = Am iting im L miig m 4.49 = Am iting im L L im iting Am = 4.45 4.45 = Am iting im L . 04 . 08 1.0 0.8 0.6 0.4 0.2 . 04 . 08 1.0 0.8 0.6 0.4 0.2 . 04 . 08 1.0 0.8 0.6 0.4 0.2 f H 167 t 8 nm 880 at 10697 HD (f) d H 94 a 80 run 880 at 9446 HD (d) ■ L im iting Am — 4.80 4.80 — Am iting ■ im L b H 87 a 80 nm 880 at 8574 HD (b) L im iting Am = 5.08 5.08 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S ° L00®1 Local Local oa Minima Local " Maxima Local oa Minima Local 27 iue . Lmtn antd pos (cont.) plots magnitude Limiting 3.8 Figure a Magnitude Difference Magnitude Difference S’ o' 2 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ...ill nu . ° • ° ° ’ - l a ' a ° / ° a D □ ° ° D miig m Am iting im L L im iting Am = 4.03 4.03 = Am iting im L miig m = 4.51 = Am iting im L a e H 191 t 9 nm 692 at 13931 HD (e) a H 161 t 9 n b H 161 t 8 nm 880 at 12661 HD (b) nm 692 at 12661 HD (a) c H 119 t 9 n d H 119 t 8 nm 880 at 13189 HD (d) nm 692 at 13189 HD (c) miig m Am iting im L miig m 5.33 — Am iting im L miig m 5.22 = Am iting im L JU-A—1--1 par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S 0 __ = 1 ■ 1 1 1 3.55 = 5.05 ------U_.. . i . . 1 ■ - I ' 'D I 'ID' '□ I. - ■ ■ I Lcl aia ' Maxima Local □ ° □ Local Maxima Maxima Local □ Local Maxima □0 oa Minima Local oa Minima Local oa Minima Local d d --- 2 8 cfl S> . 02 . 06 . 1.0 0.8 0.6 0.4 0.2 0.0 0 L im iting Am = 3.84 3.84 = Am iting im L miig m = .3 Local D 3.73 = Am iting im L miig m = 4.16 = Am iting im L . 04 . 08 1.0 0.8 0.6 0.4 0.2 . 04 . 08 1.0 0.8 0.6 0.4 0.2 f H 191 t 8 nm 880 at 13931 HD (f) L im iting Am = 5.15 5.15 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S ° L00®1 Uaxlma oa Minima Local oa i Local Local Local * iue . Lmtn antd pos (cont.) plots magnitude Limiting 3.9 Figure

Magnitude Difference Magnitude Difference Magnitude Difference . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 miig m = 2.28 = Am iting im L . 04 . 08 1.0 0.8 0.6 0.4 0.2 e H 170 t 9 n () D 66 a 80 nm 880 at 16760 HD (f) nm 692 at 16760 HD (e) c H 140 t 9 run 692 at 16400 HD (c) a H 115 t 9 n () D 67 a 80 nm 880 at 16175 HD (b) nm 692 at 16175 HD (a) L im iting Am = 4.22 4.22 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ c ec] rca [a tion ra a ep S Lcl aia ' Maxima Local □ oa Mnm . Minima Local i . 02 . 06 . 1.0 0.8 0.6 0.4 0.2 0.0 0% 1 D.o.cyj' a \ ' ' r i —I —i —I —i —I i I . I . i i I— i— i— i— I— i— i— i— I— i— — L im iting Am = 2.99 2.99 = Am iting im L d H 140 t 8 nm 880 at 16400 HD (d) . 04 . 08 1.0 0.8 0.6 0.4 0.2 miig m = 3.66 = Am iting im L D°-aa par in [ cs c] se rc [a tion ra a ep S par in [ c c] e rca [a tion ra a ep S

I l t , c o L ° ___ . oa knxa . kinlxna Local ___ . ___ I Maxima; ___ i ___ >_ 1.2 29 iue .0 iiig antd pos (cont.) plots magnitude Limiting 3.10 Figure

Magnitude Difference Magnitude Difference Magnitude Difference . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0 miig m = 4.03 = Am iting im L miig m = .9 o 4.49 = Am iting im L e H 161 a 62 nm 692 at 136418 HD (e) c H 161 a 62 nm 692 at 136118 HD (c) a H 102 t 692 at 17092 HD (a) L im iting Am = 4.£ 4.£ = Am iting im L miig m = 5.37 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S □ Local Maxima Maxima Local □ oa Minima Local oa Maxima Local oa Minima Local I I g as 10 12 0 2 4 6 8 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 k ' , fa i 1—.—i—.—.—.—i—.—.—.—i—■ . - i - - [■ ? e r i miig m = 3.59 = Am iting im L miig m 40 n LocaiMaxima' n 4.07 = Am iting im L miig m 4.27 = Am iting im L d H 161 a 80 nm 880 at 136118 HD (d) f H 161 a 80 nm 880 at 136418 HD (f) . 04 . 08 . 1.2 1.0 0.8 0.6 0.4 0.2 . 04 . 08 1.0 0.8 0.6 0.4 0.2 b H 102 t 8 nm 880 at 17092 HD (b) I: L im iting Am = 4.52 4.52 = Am iting im L miig m = 5.07 = Am iting im L miig m = 5.07 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S □ . . . . , . i . . . i Lcl aia ' Maxima Local a Local Local oa Mnm . Minima Local oa Mnm . Minima Local - 30 iue .1 iiig antd ljs (cont. plcjts magnitude Limiting 3.11 Figure

Magnitude Difference Magnitude Difference Magnitude Difference . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 0. 0. 0. 06 . 1.2 1.0 0.6 .6 0 .4 0 .2 0 0.0 t . i . . . Qt 2 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 - i tng A 4.30 = Am g itin lim lim itin g Am - 4.27 4.27 - Am g itin lim (e) HD 142245 at 692 692 at 142245 HD (e) c H 195 a 62 run 692 at 139357 HD (c) i i i i . _i a H 171 a 62 nm 692 at 137510 HD (a) L im iting Am = 5.01 5.01 = Am iting im L miig m = 4.92 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S _ Lcl aia ' Maxima Local □ Lcl aia “ Maxima Local □ oa Mnm . Minima Local oa Minima Local 11111 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 0. . 1.0 0.8 .6 0 0.4 0.2 0.0 L im iting Am = 3.04 3.04 = Am iting im L d H 195 a 80 nm 880 at 139357 HD (d) f H 12:5 t 8 nm 1422:45 880 at HD (f) b H 171 a 80 nm 880 at 137510 HD (b) . 04 . 08 1.0 0.8 0.6 0.4 0.2 par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S a oa Mxm ; Maxima Local oa Mnm . Minima Local 31 iue .2 iiig antd pos (cont.) plots magnitude Limiting 3.12 Figure

Magnitude Difference Magnitude Difference Mag] 2 ' 121 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 e H 136 (uy 9 a 62 m f H 136 (uy 9 a 80 nm 880 at 19) (July 143761 HD (f) am 692 at 19) (July 143761 HD (e) c H 130 (uy 5 a 62 m d H 130 (uy 5 at 8 nm a.t 880 25) (July 143107 HD (d) nm 692 at 25) (July 143107 HD (c) . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 a H 130 (uy 9 a 62 m b H 130 (uy 9 a 80 nm 880 at 19) (July 143107 HD (b) nm 692 at 19) (July 143107 HD (a) miig m = 4.33 = Am iting im L L im iting Am = 5.32 5.32 = Am iting im L ..... par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S □ Local Maxima Maxima Local □ oa Minima Local . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 1.0 0.8 0.6 0.4 0.2 0.0 miig m = 1 n .17 4 = Am iting im L miig m 4.05 = Am iting im L L im iting Am = 5.25 5.25 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S □ Local Local □ oa Maxima Local oa Minima Local Local iue .3 iiig antd pos (cont.) plots magnitude Limiting 3.13 Figure

Magnitude Difference Magnitude Difference io: 12: ot 2 . 02 . 06 . 10 . 00 . 04 . 08 . 1.2 1.0 0.8 0.6 0.4 0.2 0.0 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 o' 2 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 c H 136 (uy 5 a 62 nm 692 at 25) (July 143761 HD (c) a H 136 (uy 4 a 62 nm 692 at 24) (July 143761 HD (a) -

miig m - 4.42 - Am iting im L miig m = 4.09 = Am iting im L (e) HD 145457 at 692 692 at 145457 HD (e) miig m = 4.95 = Am iting im L miig m = 4.81 = Am iting im L par in [ csec Se ato ar ec] se rc [a tion ra a ep S c] e s rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S Lcl aia ' Maxima Local a p Local Maxima Maxima Local p oa Minima Local oa Minima Local 11111 f H 155 a 80 nm 880 at 145457 HD (f) . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 d H 136 (uy 5 a 80 nm 880 at 25) (July 143761 HD (d) . 02 . 06 . 10 1.2 1.0 nm 880 at 0.8 24) (July 143761 HD 0.6 (b) 0.4 0.2 0.0 i L im iting Am = 4.33 ° ° 4.33 = Am iting im i L mi g m 3.72 = Am ng iU im L L im iting Am = 4.6 4.6 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S □ Local Local □ 1x10,11 ; Maxima oa Minima Local Local iue .4 iiigmgiue lt (cont.) plots magnitude Limiting 3.14 Figure

Magnitude Difference Magnitude Difference Magnitude Difference 0 0. 4 0. 8 1. .2 1 .0 1 .8 0 .6 0 .4 0 .2 0 .0 0 e H 128 a 62 nm 692 at 152581 HD (e) c H 194 a 62 m d H 194 a 80 nm 880 at 149143 HD (d) nm 692 at 149143 HD (c) a H 157 a 62 m b H 157 a 80 nm 880 at 145675 HD (b) nm 692 at 145675 HD (a) par in [ cs c] se rc [a tion ra a ep S 0 0. 4 0. 8 1. 1.2 .0 1 .8 0 .0 0 .4 0 .2 0 .0 0 f H 128 a 80 nm 880 at 152^81 HD (f) par in [ cs c] se rc [a tion ra a ep S ,I I, , : ,I 34 iue .5 iiigmgiue lt (cont.) plots magnitude Limiting 3.15 Figure

Magnitude Difference Magnitude Difference Magnitude Difference 0 0. 4 0. 8 1. 1.2 .0 1 .8 0 .6 0 .4 0 .2 0 .0 0 o: 2 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 _ j D□□ ___ a / * L im iting Am = 4.75 4.75 = Am iting im L * i i I i i mi ng Am = 2. 3 .9 2 = m A g in it im L i ti m — 3.37 — Am g in it lim i ti m - 3.70 - Am g in it lim (e) HD 156279 at 692 692 at 156279 HD (e) c H 155 a 62 nm 692 at 155358 HD (c) a H 144 a 62 nm 692 at 154345 HD (a) L im iting Am Am iting im L lim it in g Am = 4.96 4.96 = Am g in it lim _ i i I i i par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S __ i i I i i 53 .5 4 = __ i . I i i a _ L00*1 i ■ ■ . ■ I i , oa Mnm . Minima Local oa Mnm _ Minima Local ' Maxima Local oa Minima Local Maxima Local 11111 Maxima Maxima ; . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 i tng A = 3.60 = Am g itin lim d H 155 a 80 nm 880 at 155358 HD (d) f H 167 a 80 nm 880 at 156279 HD (f) b H 144 a 80 nm 880 at 154345 HD (b) lim it in g Am = 4.72 4.72 = Am g in it lim par in [ cs c] se rc [a tion ra a ep S par in [ csec] e s rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S Local Local 35 iue .6 iiig antd pos (cont.) plots magnitude Limiting 3.16 Figure

Magnitude Difference Magnitude Difference Magnitude Difference 10 I2r . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 t , Ot 2 . 02 . 06 . 1.0 0.8 0.6 0.4 0.2 0.0 - - * L im iting Am = 4.51 4.51 = Am iting im L * i tn A 3.30 = Am iting Lim miig m = 4.48 = Am iting im L i tng A 3.90 = Am g itin lim e H 130 a 62 nm 692 at 163607 HD (e) c H 183 a 62 nm 692 at 158038 HD (c) a H 166 a 62 nm 692 at 156668 HD (a) . 04 . 08 1.0 0.8 0.6 0.4 0.2 L im iting Am = 5.24 5.24 = Am iting im L miig m = 5.18 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S D nB^ P ^ nnB D D □ ...... _ □ " jp ® a a Local Maxima ' ' Maxima Local a Local Maxima Maxima Local oa Minima Local Local Local oa Minima Local . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 i. i I « .i. i -i « .i. I ii. L.I..I g n i t i m i L miig m = 4.22 = Am iting im L miig m 35 D °a Ma k°oal D 3.53 — Am iting im L d H 183 a 880 at 158038 HD (d) f H 130 a 80 nm 880 at 163607 HD (f) b H 166 a 80 nm 880 at 156668 HD (b) . 04 . 08 1.0 0.8 0.6 0.4 0.2 . 04 . 08 1.0 0.8 0.6 0.4 0.2 I I I I . I 1 I . miig m = 4.95 = Am iting im L L im iting Am * 5.07 5.07 * Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S m = .0 □ 4.40 = Am j i i .. i i .1. i, > i i I i i ------. „■ --- . 1 oa Minima Local °a Maxima L°cal oa Mnm . Minima Local " Maxima Local - oa Mil Local --- I L. I 1 36 iue .7 iiigmgiue lt (cont.) pldts magnitude Limiting 3.17 Figure

Magnitude Difference Magnitude Difference Magnitude Difference 0.0

e H 109 a 62 nm 692 at 170693 HD (e) c H 174 a 62 m d H 174 a 80 nm 880 at 167042 HD (d) nm 692 at 167042 HD (c) 0.2 a H 142 a 62 m b H 142 a 80 nm 880 at 164922 HD (b) nm 692 at 164922 HD (a)

par in [ cs c] se rc [a tion ra a ep S 0.4

0.6

0.8

1.0

1.2 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 L im iting Am = 2.74 ° ° 2.74 = Am iting im L f H 109 a 80 nm 880 at 170693 HD (f) par in [ cs c] se rc [a tion ra a ep S oa Maxim* Local oa Minima Local 37 38

(a) HD 171028 at 692 nm (b) HD 171028 at 880 nm

12 r I ■ b ■ I ...... □

Limiting Am = 3.33 ° Local Maxinia L i m i t i n g Am = 3.75 ° 10041 Maxima ; 0 ...... i „ , ...... 1 . . . I ...... Local Minima Local Minima 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.2 0.4 0.6 0.8 1.0 Separation [arcsec] Separation [arcsec]

(c) HD 173416 at 692 nm (d) HD 173416 at 880 nm

12

XI3

0 0.0 0.2 0 .4 0 .6 0.8 110 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Separation [arcsec] Separation [arcsec]

(e) HD 177830 at 692 run (f) HD 177830 at 880 nm

Figure 3.18 Limiting magnitude plots (cont.) iue .9 iiigmgiuepos (cont.) plots magnitude Limiting 3.19 Figure

Magnitude Difference Magnitude Difference Magnitude Difference . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 e H 102 a 62 m f H 102 a 80 nm 880 at 190228 HD (f) nm 692 at 190228 HD (e) c H 172 a 62 nm 692 at 187123 HD (c) a H 101 a 62 m b H 101 a 80 nm 880 at 180314 HD (b) nm 692 at 180314 HD (a) par in [ cs c] se rc [a tion ra a ep S . 02 . 06 . 10 1.2 1.0 0.S 0.6 0.4 0.2 0.0 i r miig m = 3.93 = Am iting im L d H 172 a 80 nm 880 at 187123 HD (d) ...... miig m = 4.34 = Am iting im L par in [ cs c] se rc [a tion ra a ep S ' \ i u o Local Maxima Maxima Local o oa Mnm . Minima Local ' 39 iue .0 iiig antd pos (cont.) plots magnitude Limiting 3.20 Figure

Magnitude Difference Magnitude Difference Magnitude Difference 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0

i » . . » I i i aa/ g n i t i m i L miig m = 1.85 = Am iting im L (e) HD 199665 at 692 692 at 199665 HD (e) c H 173 a 62 nm 692 at 197037 HD (c) 0.2 a H 126 a 62 nm 692 at 192263 HD (a) miig m 3.55 - Am iting im L ’ / miig m = 4.30 = Am iting im L

par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S 0.4 Am = 3.82 3.82 = Am I

> ■ i i . i . i I . i i 1 i . ■ >1 . 0.6

0.8

118 Mxm ; 1x1081 Maxima p a Local Maxima ' ' Maxima Local a oa Minima Local oa Mnm . Minima Local 1.0 11111

1.2 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 1.0 0.8 0.6 0.4 0.2 0.0 . I . I . ■ . . I i . I I II. miig m =3. 9 .8 3 = Am iting im L miig m = .4 L0081 o 3.34 = Am iting im L d H 173 a 80 nm 880 at 197037 HD (d) f H 196 a 80 nm 880 at 199665 HD (f) b H 126 a 80 nm 880 at 192263 HD (b) era , -q , ' era miig m = 4.48 = Am iting im L ^ ^ t a a a par in [ csec] e s rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S _ L - . J . . . L .. J __ I __ a 1 _

I__ oa Minima Local Maxima Local oa Minima Local _ . . . . 1 aia ; Maxima 40 iue .1 iiig antd lt (cont.) plots magnitude Limiting 3.21 Figure

Magnitude Difference Magnitude Difference Magnitude Difference c H 261 a 62 m d H 261 a 80 nm 880 at 206610 HD (d) nm 692 at 206610 HD (c) a H 206 a 62 m b H 206 a 80 nm 880 at 200964 HD (b) nm 692 at 200964 HD (a) 41 iue .2 iiigmgiuepos (cont.) plots magnitude Limiting 3.22 Figure

Magnitude Difference Magnitude Difference j — miig m = 4.23 = Am iting im L L im iting Am = = Am iting im L miig m = 4.14 = Am iting im L e H 270 a 62 run 692 at 217107 HD (e) —I i I i I i I i 1 i i I i i i I i i i I i i— i Ii— c H 200 a 62 nm 692 at 210702 HD (c) . 04 . 08 1.0 0.8 0.6 0.4 0.2 a H 207 a 62 nm 692 at 210277 HD (a) 2 0. 6 0. 0 1. .0 1 .8 0 .6 0 .4 0 .2 0 . 04 . 08 1.0 0.8 0.6 0.4 0.2 L im iting Am = 4.88 4.88 = Am iting im L L im iting Am = 4.27 4.27 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S 12 D 2 .1 4 oa Minima Local oa Mxm ' Maxima Local oa Mnm _ Minima Local Maxima Local oa Minima Local Local Maxima Maxima Local __ . __

i __ ^ t 1 1 u a> s- a V 0 - 10 2 . 12 ; o - 2 - 4 - 6 - 8 0.0 miig m = .5 ^>ca^ ° 4.35 = Am iting im L miig m = 4.48 = Am iting im L miig m 4.42 = Am iting im L d H 200 a 80 run 880 at 210702 HD (d) f H 270 a 80 nm 880 at 217107 HD (f) b H 207 a 80 nm 880 at 210277 HD (b) . 04 . 08 1.0 0.8 0.6 0.4 0.2 . 04 . 08 1.0 0.8 0.6 0.4 0.2 L im iting Am = 4.74 4.74 = Am iting im L L im iting Am = 5.05 5.05 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S □ Local Maxima Maxima Local □ oa Minima Local oa Minima Local oa Mxm * Maxima Local oa Minima Local Maxima iue .3 iiigmgiuepos (cont.) plots magnitude Limiting 3.23 Figure

Magnitude Difference Magnitude Difference Magnitude Difference . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 or,. , . > 2h . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 i ti m = 4.51 = Am g in it lim miig m = 4.07 = Am iting im L e H 286 a 62 nm 692 at 218566 HD (e) c H 278 a 62 nm 692 at 217786 HD (c) a H 271 a 62 nm 692 at 217014 HD (a) miig m = 5.20 = Am iting im L L im iting Am = 4.60 4.60 = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S . .... oa Minima Local Local Maxima Maxima Local oa Mnm . Minima Local ' Maxima Local . 02 . 06 . 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 1.0 0.8 0.6 0.4 0.2 0.0 miig m = 4.44 = Am iting im L f H 28>6 t 8 nm 218f>66 880 HD at (f) d H 278 a 80 nm 880 at 217786 HD (d) b H 271 a 80 nm 880 at 217014 HD (b) . 04 . 08 1.0 0.8 0.6 0.4 0.2 i L im iting Am = 5.16 5.16 = Am iting im i L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S Lcl aia ' Maxima Local □ oa Mnm . Minima Local iue .4 iiigmgiue lt (cont.) plots magnitude Limiting 3.24 Figure

Magnitude Difference Magnitude Difference Magnitude Difference . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ■ . . ... ■, 1 ■>, . . . 1 . . . 1 ■ I i tng A 42 D Local* D 4.25 = Am g itin lim miig m - 3.21 - Am iting im L e H 207 a 62 nm 692 at 220773 HD (e) c H 207 a 62 nm 692 at 220074 HD (c) a H 292 a 62 nm 692 at 219828 HD (a) miig m = 4.94 = Am iting im L L im iting Am = 3.f 3.f = Am iting im L par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S .. 1...1 .... . 1 . .1. . ,1,1. oa If Local oa Minima Local Local Maxima Maxima Local I 53 a}

4 0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 8 1.0 .8 0 0.6 0.4 0.2 0.0 L im iting Am = 4 .22 .22 4 = Am iting im L miig m = 4.31 = Am iting im L d H 207 a 80 nm 880 at 220074 HD (d) f H 207 att nm 220773 880 HD (f) b H 292 a 80 nm 880 at 219828 HD (b) —1—'—'— miig m = 4.87 = Am iting im L L im iting Am = 4.67 4.67 = Am iting im L n D n ° par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S 1 f cP- ■fl —I— □ n .a1* ^"ran- [ . c . ° d a a S3-

, a 1 0 0 0 1 a oa Minima Local oa Mnm . Minima Local ' Maxima Local Maxima ; 44 iue .5 iiig antd pos (cont.) plots magnitude Limiting 3.25 Figure

Magnitude Difference Magnitude Difference Magnitude Difference . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0

L im iting Am = 3.91 3.91 = Am iting im L e H 210 a 02 m f H 210 a 80 nm 880 at 231701 HD (f) nm 092 at 231701 HD (e) c H 225 a 62 nm 692 at 222155 HD (c) a H 214 a 62 nm 692 at 221345 HD (a) 0.2

par in [ cs c] se rc [a tion ra a ep S par in [ cs c] se rc [a tion ra a ep S 0.4

0.6

0.8 °

Local oa Minima Local 1.0

1.2 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 . 02 . 06 . 10 1.2 1.0 0.8 0.6 0.4 0.2 0.0 L im iting Am = 3.93 3.93 = Am iting im L d H 22 5 t 8 nm 880 at 55 222} HD (d) b H 214 a 80 nm 880 at 221345 HD (b) par in [ cs c] se rc [a tion ra a ep S aton [ cs c] se rc [a n tio ra a p e S °

oa Minima Local Maxima Local 45 iue .6 iiigmgiuepos (cont!) plots magnitude Limiting 3.26 Figure

Magnitude Difference Magnitude Difference 0 0. 4 0. 8 1. .2 1 .0 1 .8 0 .6 0 .4 0 .2 0 .0 0 c H 203 a 62 m d H 203 a 80 nm 880 at 240237 HD (d) nm 692 at 240237 HD (c) a H 201 a 62 m b H 201 a 80 nm 880 at 240210 HD (b) nm 692 at 240210 HD (a) par in [ cs c] se rc [a tion ra a ep S 0 0. 4 0. 8 1. 1.2 .0 1 .8 0 .6 0 .4 0 .2 0 .0 0 par in [ cs c] se rc [a tion ra a ep S 47

Chapter 4

Results

As described in the previous chapters, the DSSI images of approximately 70 targets

were directly examined for any bright source. Of those stars that were examined,

only two stars, HD 2638 and HD 164509, yielded a positive hit (see Figures 3.1 and

3.2).

4.1 Discoveries of Stellar Companions

Based on the specifications of DSSI while stationed at Gemini (Horch et al., 2015), the separation measurement uncertainties are generally 2 mas, given the intrinsic

faintness of the stellar companions to both HD 2638 and HD 164509. Moreover, the position angle has an uncertainty of ~ 0.2°, and the uncertainties for the magnitude difference between primary and secondary stars are derived from Horch et al. (2004).

The details of the measurements and their uncertainties are provided in Table 4.1.

The sensitivity plots provided in Figures 3.1 and 3.2 show the magnitude differ- 48

Table 4.1. DSSI Astrometry Sz Photometry Results

Measurements HD 2638 HD 164509 692 nm 880 nm 692 nm 880 nm

Position Angle E of N (°) 167.7 ± 0 .2 167.7 ± 0 .2 202.5 ± 0 .2 202.6 ± 0 .2 Apparent Separation (") 0.511 ±0.002 0.513 ±0.002 0.697 ±0.002 0.697 ±0.002 Projected Separation (AU) 25.5 ± 1.9 25.6 ± 1.9 36.5 ± 1.9 36.5 ± 1.9 Am* 3.83 ±0.2 2.80 ±0.2 5.53 ±0.4 4.41 ±0.4

*Note: Ain is the apparent magnitude difference between the primary and secondary stars. Am values are extracted from the sensitivity plots.

ence between local maxima and minima in the corresponding image as a function

of the separation from the primary host star. The construction of these sensitivity

plots is described in more detail by Howell et al. (2011). As shown in the sensitivity

plots, the limiting resolution of DSSI with Gemini is ~ 0.05". The Gemini diffrac­

tion limits are 0.021” and 0.027” at 692 nm and 880 nm, respectively. Each of the

two stars is discussed here and their corresponding results are described separately

below.

4.1.1 HD 2638

Prior to submitting this work, we learned that Riddle et al. (2015) has detected

HD 2638’s stellar companion. We present our results as an independent detection of this companion. Both DSSI images from Figure 3.1 show a bright source to the bottom and slightly to the left of HD 2638. Based on the magnitude differences 49

from Table 4.1, the stellar companion appears to be brighter at 880 nm than it

is at 692 nm, implying that the stellar companion is a late-type star, possibly a

M-type star. According to Roberts et al. (2015), the companion’s spectral type is

M1V, which seems to be in agreement with our assessment. Our calculations of the

projected separation between HD 2638 and its companion star yield 25.5 ± 1.9 AU

at 692 nm and 25.6 ± 1 .9 AU at 880 nm, which is close to Roberts et al. (2015)’s

28.5 AU physical separation. Note that the apparent close companion to the north

of the primary in each image is within the limiting resolution of the instrument and

is thus an artifact of the speckle image processing.

4.1.2 HD 164509

Figure 3.2 contains two images that display a source southwest of HD 164509. The

magnitude differences of this system imply that the stellar companion is considerably

fainter than the host star by a factor of almost 100 at 880 nm and more than 100

at 692 nm. In fact, it is so faint at 692 nm that it is difficult to detect in the image.

Despite the fact that HD 164509 is more luminous than HD 2638, the considerable faintness of HD 164509’s companion as compared to HD 2638’s implies that this stellar companion is a very cool, late-type star. Based on the data from Table 4.1, the physical separation between HD 164509 and its companion is 36.5 ± 1.9 AU. To compare, the planet Neptune is about 30 AU from our Sun, and the result falls short of the dwarf planet Pluto’s average distance of 39.5 AU. Since HD 164509 is slightly 50

more massive than our Sun and with the given distance between the host star and its companion, this leads to credence that the faint object may be gravitationally bound to HD 164509. One interesting thing to point out is that this dim star may be “an additional longer period companion” that Giguere et al. (2012) speculated when they came across the RV data’s residual linear trend. As of this writing, there has been no confirmation of HD 164509 hosting a stellar companion.

4.1.3 Stellar Isochrone Fitting

One can employ a stellar isochrone fit to reveal the detected stellar companions5 properties. The methodology used for this analysis is described byEverett et al.

(2015) and Teske et al. (2015). Briefly, the method maps out the probability distri­ bution of the primary star using Dartmouth stellar isochrones (Dotter et al., 2008).

The inputs for this analysis are the stellar properties shown in Table 2.3. The combi­ nation of the resulting probability distributions for the primary with the multi-band observations described in Section 2 produce a probability distribution for the prop­ erties of the secondary. Such a result assumes that it is a bound companion that falls on the same isochrone as the primary.

The results of our isochrone fits for the stellar companions are shown in Table 4.2.

The derived stellar properties are consistent with both of the companion stars being late-type main sequence stars (M dwarfs). Note that both our mass determination

(Table 4.2) and projected separation (Table 4.1) for the HD 2638 stellar companion 51

Table 4.2. Stellar Companion Isochrone Fitting Results

Parameters HD 2638B HD 164509B

M* (M q) 0.48 ±0.03 0.42 ± 0.03 R* (Re) 0.46 ± 0.02 0.40 ± 0.02 U (L0 ) 0.030 ± 0.005 0.020 ±0.003 T e(K ) 3571 ± 48 3446 ± 43 log g (cm /s2) 4.80 ±0.02 4.85 ± 0.02

HD 2638 HD 164509

692-880 692-880

Figure 4.1 Stellar isochrone models of HD 2638 (left) and HD 164509 (right). The black dot near the top is the primary star, the dark blue dot near the bottom is the average model of the companion, and the red dot is the observed companion. Note that in both cases, the model fits well with the observation. 52

match well with the results obtained by Roberts et al. (2015). The results from

our isochrone fitting are shown in Figure 4.1 for HD 2638 (left) and HD 164509

(right). The color-magnitude diagrams include the set of isochrones that are within

±la of the primary star metallicity. The black data point represents the primary star and the red data point shows the location of the secondary based upon the measurements described in Section 2. The dark blue data point is the average location of the secondary based upon the probability distributions of the isochrone fitting. The location of the secondary from measurements and from isochrone fits are consistent with one another, indicating that the assumption of the secondary being bound to the primary is indeed a valid assumption.

4.1.4 Proper Motion and Astrometry

One can take a further step in confirming that the detected companions are bound to the targets. That step is analyzing the common proper motion of the stars in the sky.

HD 2638’s stellar companion has been known just long enough for it to have data on proper motion. In fact, “Fourth Interferometric Catalog of Binary Stars”

(see description in Hartkopf et al. (2001)) has sufficient data for that system. The available time frame ranges from 2012.67 to 2015.74. Figure 4.2 shows the locations of the primary star and secondary star with respect to the primary star’s starting position during the first epoch 2012.67. The filled circles indicate the primary star’s 53

0.5

0.0 E -Primary, 2012.67 ,

-1 .5 -1 .0 -0 .5 0.0 0.5 1.0 RA (arcsec)

Figure 4.2 The proper motion of the HD 2638 primary (solid circles) and secondary (open squares) over time. The measurements presented in this work are shown in red. The dashed lines link the primary and secondary for the first and last observations in the sequence, and for our observation. 54

positions, and the open squares indicate the secondary star’s positions. The two measurements presented in this work, which on this scale are indistinguishable, are shown in red. Dotted lines link the primary and secondary for the first and last observations in the sequence, and for our 692-nm observations. The proper motions

(see Table 2.3) are drawn from van Leeuwen (2007). This figure demonstrates that

the pair of stars are clearly moving together.

HD 164509 has been recently discovered, so there only exists a single measure­ ment provided here. In other words, we do not have sufficient data to do the proper motion or astrometric analysis. Fortunately, there should be few issues in performing further observations of this star over the next few years; one can see from Table 2.3 that HD 164509’s proper motion is much smaller than that for HD 2638. Even though the given proper motion is quite small, it is still well above the minimum constraint for the speckle observations.

4.2 Constraints on Presence of Stellar Companions

Even though the remaining systems have not yielded a hit, such results nevertheless provide an important contribution to the stellar companion survey. Given that the field-of-view of the images is 2.8" x 2.8", no detection of stellar companions around the chosen targets tells us that we should not expect any stellar object within 1.4” of the target. Of course, a stellar companion can exist beyond the DSSI’s field-of-view.

Table 4.3 tabulates the inner and outer exclusion radii, limiting magnitudes at 55

0.1 and 0.2 AU, and the distance modulus for each target. The exclusion radii are the range of physical distances from the host star that are observable within the Gemini

DSSI’s field-of-view. They are calculated using the distance provided in Tables 2.1 and 2.2. The minimum radius is constrained by the fact that the instrument can only resolves individual targets at a minimum separation of 0.05” . As mentioned before, the maximum separation is 1.4” , which provides a constraint on the outer exclusion radius. Thus, the exclusion radii “exclude” the region where stellar companions may exist. The distance modulus is calculated using the distances. Table 4.3. Limiting Magnitudes

Name Exclusion Radius (AU) 5cr Am Limit (692 nm) 5cr Am Limit (880 nm) m — M Inner Outer 0.1” 0.2” 0.1” 0.2”

BD+14 4559 4.84 67.70 3.92097 4.32193 3.92697 4.62457 3.42 BD+48 738 35.09 491.23 3.09 5.01 3.72 4.74 7.73 GJ 581 0.62 8.70 4.36 5.14 4.29 5.23 -1.03 GJ 649 1.03 14.48 3.40 4.23 3.39 4.27 0.07 GJ 849 0.91 12.73 4.01 4.55 3.95 4.55 -0.21 HD 1461 2.32 32.54 3.21 4.15 3.54 4.89 1.83 HD 1502 15.92 222.93 4.44 5.20 4.29 4.97 6.01 HD 2638 4.99 69.90 4.45 4.96 3.83 4.63 3.49 HD 3651 1.11 15.48 4.53 5.25 4.31 5.15 0.22 HD 4313 13.70 191.78 4.67 5.39 4.28 5.21 5.68 HD 5319 11.44 160.18 4.09 5.30 4.15 5.23 5.29

Ol Table 4.3 (cont’d)

Name Exclusion Radius (AU) 5a Am Limit (692 nm) 5cr Am Limit (880 nm) m — A Inner Outer 0.1” 0.2” 0.1” 0.2”

HD 5891 25.13 351.76 4.41 5.37 4.43 5.31 7.00 HD 6718 5.49 76.80 4.32 4.80 4.20 4.95 3.70 HD 7449 3.89 54.50 4.28 4.91 4.21 4.80 2.95 HD 8574 4.46 62.39 4.53 5.18 4.45 5.06 3.24 HD 9446 5.24 73.30 4.75 5.24 4.49 5.08 3.59 HD 10697 3.26 45.60 4.50 5.20 4.10 4.80 2.56 HD 12661 3.50 48.93 4.51 5.22 4.16 5.15 2.72 HD 13189 56.18 786.52 4.03 5.33 3.73 4.87 8.75 HD 13931 4.42 61.92 3.55 5.05 3.84 4.97 3.23 HD 16175 5.79 81.02 3.44 5.03 4.08 5.30 3.81 HD 16400 9.25 129.51 2.28 4.22 2.99 3.66 4.83 Table 4.3 (cont’d)

Name Exclusion Radius (AU) 5a Am Limit (692 nm) 5a Am Limit (880 nm) m — M Inner Outer 0.1” 0.2” 0.1” 0.2”

HD 16760 4.55 63.64 3.93 4.99 3.81 4.77 3.29 HD 17092 10.87 152.17 3.11 4.64 4.27 5.07 5.18 HD 136118 4.66 65.21 4.49 5.37 4.07 5.07 3.34 HD 136418 9.82 137.52 4.03 4.99 3.59 4.52 4.96 HD 137510 4.13 57.76 4.27 4.92 3.84 4.83 3.08 HD 139357 11.81 165.29 2.83 4.73 3.74 4.65 5.36 HD 142245 10.95 153.34 4.30 5.01 4.73 5.30 5.20 HD 143107 6.79 95.04 4.33 5.32 4.05 5.25 4.16 HD 143107 6.79 95.04 4.44 5.19 4.26 5.20 4.16 HD 143761 1.72 24.13 2.65 3.66 4.17 4.96 1.18 HD 143761 1.72 24.13 4.09 4.81 3.72 4.68 1.18 Table 4.3 (cont’d)

Name Exclusion Radius (AU) 5a Am Limit (692 nm) 5

HD 143761 1.72 24.13 4.42 4.95 4.33 5.19 1.18 HD 145457 12.53 175.44 4.44 4.96 4.62 5.15 5.49 HD 145675 1.76 24.60 4.30 5.13 4.18 5.34 1.22 HD 149143 6.20 86.85 4.39 4.96 4.12 5.09 3.96 HD 152581 18.55 259.74 4.52 5.09 4.53 5.05 6.34 HD 154345 1.86 26.02 3.70 4.96 3.60 4.72 1.35 HD 155358 4.41 61.76 3.37 4.75 3.34 4.55 3.22 HD 156279 3.66 51.24 2.93 4.53 4.22 4.86 2.82 HD 156668 2.45 34.26 3.90 5.18 3.53 4.71 1.94 HD 158038 10.36 145.08 4.48 5.24 4.22 5.07 5.08 HD 163607 6.88 96.35 3.30 4.51 4.40 4.95 4.19 Table 4.3 (cont’d)

Name Exclusion Radius (AU) 5a Am Limit (692 5a Am Limit (880 nm) m — M Inner Outer 0.1” 0.2” 0 . 1” 0 .2”

HD 164509 5.24 73.41 3.90 4.15 4.00 4.52 3.60 HD 164922 2.21 30.97 3.69 4.88 3.64 4.76 1.72 HD 167042 5.02 70.32 3.22 3.84 4.29 5.15 3.50 HD 170693 9.65 135.14 2.58 4.05 2.74 3.84 4.92 HD 171028 10.99 153.85 3.84 4.09 4.00 4.45 5.20 HD 173416 13.95 195.26 3.33 3.51 3.75 4.01 5.72 HD 177830 5.90 82.64 3.13 3.23 4.05 4.29 3.86 HD 180314 13.14 183.97 3.23 3.48 4.13 4.46 5.59 HD 187123 4.83 67.57 3.89 3.98 3.93 4.34 3.42 HD 190228 6.16 86.26 3.82 4.03 4.07 4.56 3.95 HD 192263 1.93 27.04 1.85 3.55 3.34 4.21 1.43

Oi O Table 4.3 (cont’d)

Name Exclusion Radius (AU) 5a Am Limit (692 nm) 5

HD 197037 3.23 45.26 4.07 4.25 4.05 4.63 2.55 HD 199665 7.53 105.42 3.82 4.30 3.89 4.48 4.38 HD 200964 7.22 101.08 1.97 3.18 3.70 4.60 4.29 HD 206610 19.38 271.32 4.15 4.60 4.52 5.00 6.44 HD 208527 40.32 564.52 4.02 4.17 3.84 4.10 8.03 HD 210277 2.16 30.19 4.14 4.27 4.42 5.05 1.67 HD 210702 5.49 76.92 4.12 4.54 4.48 4.74 3.70 HD 217014 1.56 21.85 4.07 4.60 3.49 4.24 0.97 HD 217107 1.99 27.80 4.23 4.88 4.35 5.27 1.49 HD 217786 5.49 76.80 4.51 5.20 4.44 5.16 3.70 HD 218566 2.86 39.98 4.41 5.19 4.20 5.18 2.28 Table 4.3 (cont’d)

Name Exclusion Radius (AU) 5a Am Limit (692 nm) 5cr Am Limit (880 nm) m — M Inner Outer 0.1” 0.2” 0.1” 0.2”

HD 219828 7.23 101.23 4.41 5.19 4.31 5.12 4.30 HD 220074 32.47 454.55 3.21 3.89 4.31 4.67 7.56 HD 220773 5.09 71.25 4.25 4.94 4.22 4.87 3.53 HD 221345 7.92 110.85 4.43 5.00 3.93 4.87 4.49 HD 222155 4.91 68.69 3.91 4.15 4.24 4.61 3.45 HD 231701 11.85 165.88 4.10 4.18 4.10 4.31 5.37 HD 240210 14.29 200.00 3.72 4.13 3.72 4.25 5.77 HD 240237 526.32 7368.42 3.30 4.65 4.52 5.18 13.61 63

Chapter 5

Implications of the Orbital Dynamics

The presence of stellar companions can pose a significant challenge for orbital sta­

bility and formation scenarios for planets in such systems (Ngo et al., 2015; Wang et

al., 2015). Issues regarding planet formation include protoplanetary disc truncation,

grain condensation, and planetesimal accumulation (see Thebault h Haghighipour

(2014) and references therein). To test that our observations are consistent with the

presence of the planets, we use the orbital dynamics results of Holman & Wiegert

(1999) for test particles in binary systems. Specifically, we calculate the critical semi-major axis, ac, beyond which planetary orbits would be unstable in the sys­ tems. The resulting plots of ac as a function of binary eccentricity e are shown in Figure 5.1. The values of ac were calculated using Equation 1 from Holman &

Wiegert (1999): 64

Figure 5.1 Plots of critical semi-major axis ac vs orbital eccentricity e (solid line) for HD 2638 (left) and HD 164509 (right). The dashed lines indicate the la uncertainties in the relationship and the horizontal dotted lines represent the semi-major axes of the known planets.

ac =[(0.464 ± 0.006) + (-0.380 ± 0.010)/z + (-0.631 ± 0.034)e (5.1) + (0.586 ± 0.061)/xe + (0.150 ± 0.041)e2 + (-0.198 ± 0.074)fie2]ab

where ab is the binary semi-major axis. The mass ratio, ji, is calculated as

/x — m2 /(mi + m2 ) where mi and m2 are the masses of the primary and secondary

respectively. Using the values from Tables 4.1 and 4.2, we have /jl = 0.357±0.009 and ab = 25.5 AU for HD 2638, and n - 0.274 ±0.006 and ab - 36.5 AU for HD 164509.

Note that this assumes the projected separations are the true semi-major axes of the binary companions. If this criterion were to be relaxed, then the maximum eccentricity will vary. Including both the uncertainties in Equation 5.1 and /i, we 65

include lines for the la uncertainties as dashed lines in Figure 5.1. The semi-major axes of the known planets (see Table 2.3) are represented in each case by a horizontal dotted line. These figures show the stability of the planetary orbits remain secure for most values of the binary eccentricity. The maximum binary eccentricities (where the planetary semi-major axis lines intersect the eccentricity lines) are e = 0.94±0.26 and e = 0.87 ± 0.21 for HD 2638 and HD 164509 respectively.

Given that the planets were discovered with the RV technique, it is worth pausing to consider the effect of the stellar binary companions on the planetary interpretation of the RV data. Using the stellar parameters of the primary and secondary from

Tables 2.3 and 4.2 respectively, along with the projected separations from Table 4.1, we calculate the expected orbital periods and RV semi-amplitudes for each system.

For HD 2638, the minimum orbital period is ~ 1 10 years with a maximum RV semi­ amplitude of ~2.4 km/s. For HD 164509, the minimum orbital period is ~180 years with a maximum RV semi-amplitude of ~1.7 km/s. As noted in Section 2, the Kepler solution to the HD 164509 RVs includes a linear trend, though the time baseline since discovery is insufficient to characterize the nature of the trend. Assuming the minimum separations above, the companions cannot be confused with the planetary signals and thus have no effect on the planetary interpretation of the RV data. It also should be noted that the RV semi-amplitude of HD 164509b is 14.2 ± 2.7 m/s

(Giguere et al., 2012).

The remaining systems with null-detection are by no mean useless. In fact, 66

they contribute to the set of limits on what type of object we may expect within the exclusion radii if a detection takes place. Thus, future RV detection can be

attributed to planets or brown dwarfs instead of a star. 67

Chapter 6

Conclusion

Determining the stellar architecture of planetary systems is an on-going process, improving as the capability to detect faint stellar companions increases. Stellar binarity can have a profound effect on exoplanetary systems, both in terms of for­ mation processes and long-term orbital stability. Thus determining the binarity of known exoplanet host stars is a critical step in the characterization of those systems.

Here we have presented detections of stellar companions to two known exoplanet host stars: HD 2638 and HD 164509. Though the stellar companion to HD 2638 was previously detected by Roberts et al. (2015) at wavelengths between 1 and 2.5

/mi, the new data from DSSI will provide additional information of the astrome­ try of the companion and the stellar properties, given that the passbands used are particular to the DSSI camera. We have shown that the detected companions have properties consistent with them both being M dwarfs, and the isochrone analysis shows that they are both likely to be gravitationally bound to the host stars. For- 68

tunately, the presence of the stellar companions do not pose serious orbital stability

problems for the known exoplanets, making the overall architecture of the systems self-consistent. These planetary systems represent additional interesting examples

of planet formation and evolution in the presence of multiple stars.

Lastly, we presented the remaining systems in which 110 stellar companion is

detected. Given that the field-of-view is 2.8" x 2.8", we can rule out most stellar

objects within 1.4” of the host stars. This leaves us with the region where the

distances are beyond the DSSI’s field-of-view of 1.4". The exclusion radii listed in

Table 4.3 offer physical range of distances where any future detection of objects via

RV method may be limited to planets or brown dwarfs. 69

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