A Dissertation entitled A Variability Study of Y Dwarfs: A Spitzer Space Telescope Program by Jesica Lynn Trucks Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Physics with concentration in Astrophysics Dr. Michael Cushing, Committee Chair Dr. S. Thomas Megeath, Committee Member Dr. Rupali Chandar, Committee Member Dr. Richard Irving, Committee Member Dr. Stanimir Metchev, Committee Member Dr. Cyndee Gruden, Interim Dean College of Graduate Studies The University of Toledo August 2019 Copyright 2019, Jesica Lynn Trucks This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author. An Abstract of A Variability Study of Y Dwarfs: A Spitzer Space Telescope Program by Jesica Lynn Trucks Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Physics with concentration in Astrophysics The University of Toledo August 2019 I present the results of a search for variability in 14 Y dwarfs consisting 2 epochs of observations, each taken with Spitzer for 12 hours at [3.6] immediately followed by 12 hours at [4.5], separated by 122{464 days and found that Y dwarfs are variable. We used not only periodograms to characterize the variability but we also utilized Bayesian analysis. We found that using different methods to detect variability gives different answers making survey comparisons difficult. We determined the variability fraction of Y dwarfs to be between 37% and 74%. While the mid-infrared light curves of Y dwarfs are generally stable on time scales of months, we have encountered a few that vary dramatically on those time scales. When we combined the variability frac- tions of L and T dwarfs with our variability fractions of Y dwarfs the results support the standard paradigm which suggests that clouds are responsible for the observed variability because of the cloudy!cloud free!cloudy nature of the LTY spectral se- quence. We have determined the rotation periods of 5 Y dwarfs ranging from 2.44 hours to 8.42 hours, with two additional tentative periods. We also considered the oblateness of Y dwarfs as rotation period is one factor in its calculation. One of our targets WISE 0359−54 has a very small period so we showed that depending on its' mass it could have an oblateness comparable to that of Jupiter or Saturn. We also determined that with its short, consistent period across all four light curves, it would make a perfect candidate for future variability studies with JWST. Interestingly we iii found that our survey failed to detect any small amplitude variability (< 0.5%) even though it is sensitive down to 0.2%, but is not due to observational bias. We con- firmed that the maximum amplitude increases as a function of spectral type. We find that the average [4.5]/[3.6] amplitude ratio is less than unity which suggests that hot spots may be the physical mechanism of the observed variability. As [3.6] and [4.5] probe similar atmospheric layers unsurprisingly we find no phase changes in the light curves for WISE 0359−54. iv To my dad Ronald L Trucks, who has always taught me to reach for the stars. Acknowledgments I would like to say thanks to my advisor Michael Cushing who worked with me on this project. I would also like to say thanks to Kevin Hardegree-Ullman for his work on this project. I would like to say thanks to my parents and family who have supported me throughout the long journey to get to this point. This work is based on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. Support for this work was provided by NASA. vi Contents Abstract iii Acknowledgments vi Contents vii List of Tables ix List of Figures xi 1 Introduction and Background Material 1 1.1 Introduction . 1 1.2 What is a brown dwarf? . 2 1.3 Theory of substellar objects: Interiors . 3 1.4 Theory of substellar objects: Atmospheres . 8 1.5 L, T, and Y dwarfs . 13 1.5.1 L dwarfs . 13 1.5.2 T dwarfs . 14 1.5.3 Y dwarfs . 15 1.6 Previous variability studies . 16 1.7 Conclusion . 18 2 The Search for Variability 22 2.1 Motivation . 22 vii 2.2 Observations and Data Reduction . 23 3 Data Analysis 30 3.1 Variability Analysis . 30 3.1.1 A Visual Inspection . 30 3.1.2 Variability Fractions . 31 3.1.2.1 Bayesian Analysis . 32 3.1.2.2 Periodogram Analysis . 37 3.1.3 Variability Fraction Confidence Intervals . 41 3.2 Discussion . 44 3.2.1 Variability Fractions . 44 3.2.2 Rotation Periods . 46 3.2.3 Semi-Amplitudes . 49 3.2.4 Phases . 52 4 Conclusions and Future Prospects 54 4.1 Conclusions . 54 4.2 Future Prospects . 55 A Bayesian Parameter Tables 75 viii List of Tables 1.1 Field brown dwarf observablesa........................ 3 1.2 Variability Fraction of L and T dwarfs. 18 2.1 Y Dwarf Targets . 25 3.1 ∆ BIC Values . 35 3.2 Periods and Semi-Amplitudes for Variable-Source Models . 36 3.3 Y Dwarf Variability Summary . 40 3.4 Survey Completeness . 42 3.5 Rotation Periods of Y Dwarfs . 46 A.1 WISEJ0146+4234 . 76 A.2 WISEJ0350−56 ............................... 77 A.3 WISEJ0359−54 ............................... 78 A.4 WISEJ0410+15 . 79 A.5 WISEJ0535−75 ............................... 80 A.6 WISEJ0713−29 ............................... 81 A.7 WISEJ0734−71 ............................... 82 A.8 WISEJ1405+55 . 83 A.9 WISEJ1541−22 ............................... 84 A.10 WISEJ1639−68 ............................... 85 A.11 WISEJ1738+27 . 86 A.12 WISEJ1828+26 . 87 ix A.13 WISEJ2056+14 . 88 A.14 WISEJ2220−36 ............................... 89 x List of Figures 1-1 Evolution of luminosity (in L ) of isolated solar-metallicity red dwarf stars and substellar-mass objects versus age (in years). Adapted from Burrows et al. (2001). 4 1-2 Evolution of the central temperature (Tc) in Kelvin of isolated solar- metallicity red dwarf stars and substellar-mass objects versus age (in years). Adapted from Burrows et al. (2001). 5 1-3 Evolution of the radius (R) in gigacentimeters of isolated solar-metallicity red dwarf stars and substellar-mass objects versus age (in years). Adapted from Burrows et al. (2001). 7 1-4 Equilibrium composition of a gas at solar metallicity as a function of tem- perature for two different pressures (chemical models Bailey and Kedziora- Chudczer (2012); Figure from Bailey (2014)). 8 1-5 Plot of the abundance of elements as a function of atomic number. The bubbles contain molecules/atoms/condensates that play an important role in substellar atmospheres. Adapted from Burrows et al. (2001) . 9 1-6 Temperature Pressure profiles of various temperature objects. Equi-abundance curves for the dominate forms of C and N. Condensate curves illustrating where in the atmosphere specific molecules will form. 10 1-7 Illustration of different cloud layers at different temperatures (Lodders 2004). 11 xi 1-8 Low temperature model spectra over plotted with their blackbody curve (Spectra references; Marley et al., 2002; Saumon and Marley, 2008; Morley et al., 2014; Hauschildt et al., 2003). 12 1-9 Left: Red optical spectral sequence of the optical L dwarf sequence. Right: Near-infrared spectral sequence of the near-infrared L dwarf sequence. Figure from Cushing (2014). 19 1-10 Left: Red optical spectral sequence of the optical T dwarf sequence. Right: Near-infrared spectral sequence of the near-infrared T dwarf sequence. Figure from Cushing (2014). 20 1-11 Left: J and H band spectra of Y0, Y1, and Y2 spectral standards. Figure from Cushing (2014). 21 2-1 [3.6] (blue) and [4.5] (red) light curves for the Y0 dwarf WISE 0359−54, taken on January 4, 2013 (top) and April 13, 2014 (bottom). The light curves observed on January 4, 2013 (top) shows periodic variability at both wavelengths with a semi-amplitude of 4.2% and 2.8% with periods of 2.41 hours and 2.45 hours respectively. The light curves observed on April 13, 2014 (bottom) shows periodic variability at both wavelengths with a semi-amplitude of 2.5% and 2.2% with a common period of 2.44 hours. 27 2-2 Normalized IRAC [3.6] (blue) and [4.5] (red) photometry for the fourteen Y dwarfs in our sample. The epoch 1 data is found in the left panel and the epoch 2 data is found in the right panel. For display purposes only, outliers have been removed as described in x3.1.2.1. Note that the scale of the ordinate is different for [3.6] and [4.5] light curves. 28 xii 2-2 Normalized IRAC [3.6] (blue) and [4.5] (red) photometry for the fourteen Y dwarfs in our sample. The epoch 1 data is found in the left panel and the epoch 2 data is found in the right panel. For display purposes only, outliers have been removed as described in x3.1.2.1. Note that the scale of the ordinate is different for [3.6] and [4.5] light curves. 29 3-1 Epoch 1 periodograms for the 14 Y dwarfs in our sample. The grey dashed lines give the 5% (95% confidence) False Alarm Levels which give the power levels above which we would expect to see power less than 5% of the time under the null hypothesis of pure gaussian noise (no variable signal). Any object with power in its periodogram above this level is considered variable.