The Pennsylvania State University

The Graduate School

Department of Astronomy and Astrophysics

RADIO OBSERVATIONS OF THE - BOUNDARY

A Dissertation in

Astronomy and Astrophysics

by

Matthew Philip Route

 2013 Matthew Philip Route

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

August 2013

The dissertation of Matthew Philip Route was reviewed and approved* by the following:

Alexander Wolszczan Evan Pugh Professor of Astronomy and Astrophysics Dissertation Advisor Chair of Committee

Lyle Long Distinguished Professor of Aerospace Engineering, and Mathematics Director of the Computational Science Graduate Minor Program

Kevin Luhman Associate Professor of Astronomy and Astrophysics

John Mathews Professor of Electrical Engineering

Steinn Sigurdsson Professor of Astronomy and Astrophysics Chair of the Graduate Program for the Department of Astronomy and Astrophysics Special Signatory

Richard Wade Associate Professor of Astronomy and Astrophysics

Donald Schneider Distinguished Professor of Astronomy and Astrophysics Head of the Department of Astronomy and Astrophysics

*Signatures are on file in the Graduate School

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ABSTRACT

Although and brown dwarfs have been hypothesized to exist for many , it was only in the last two decades that their existence has been directly verified. Since then, a large number of both types of substellar objects have been discovered; they have been studied, characterized, and classified. Yet knowledge of their magnetic properties remains difficult to obtain. Only radio emission provides a plausible means to study the magnetism of these cool objects. At the initiation of this research project, not a single exoplanet had been detected in the radio, and only a handful of radio emitting brown dwarfs were known. This project was launched to attempt to detect emission from brown dwarfs cooler than spectral type L3.5, the coolest brown dwarf detected prior to this project, and also to attempt to discover radio emission from nearby exoplanets. These objects are known to emit radio waves via the gyrosynchrotron and electron cyclotron maser instability mechanisms. By analyzing flaring radio emission from these objects, we would therefore gain insight into their magnetic field properties and the characteristics of the surrounding plasma environment. This dissertation presents the results from surveys of 33 brown dwarfs, 18 exoplanetary systems, and one additional M dwarf for flaring radio emission, conducted with the 305-m Arecibo radio telescope at a center frequency of 4.75 GHz using the broadband, fast-sampled Mock spectrometer. During the course of these surveys, we failed to detect flaring radio emission from any exoplanets, including the young exoplanetary system HR 8799, which theoretical work indicated may have strong magnetic fields capable of generating radio emission at gigahertz frequencies due to their relatively hot temperatures and high . Such a detection would provide an exciting alternative to the previous unsuccessful low radio frequency searches for the emission from exoplanets orbiting middle-aged, solar type . Among the brown dwarfs we examined, many were not observed to emit bursts of radio emission, with a successful detection rate of 6%. However, we have detected flaring radio emission from four ultracool dwarfs, two of which are new: the L1 dwarf J1439284+192915 and the T6.5 dwarf J10475385+2124234. Among the two known sources that we have detected, J07464256+2000321, an L dwarf binary system, and TVLM 513-46546, a periodically emitting M9 dwarf, we have conducted a lengthy observing campaign of the latter. These observations allow for an unprecedented examination of the burst morphology of the source in time and frequency domains over several years. Our investigation of this source has also resulted in the tantalizing possibility that the temporal properties of the radio bursts go through cycles over the course of months. The discovery of J1047+21 dramatically extends the temperature range over which brown dwarfs appear to be at least sporadic radio-emitters, from ~1,900 K (L3.5) down to ~900 K (T6.5). Follow up observations of this object indicate that while it has detectable quiescent emission, its flaring behavior appears to lack any periodic component. The detection of radio emission from J1439+19, while tentative, is potentially significant due to its relatively slow rotation, which may have implications for dynamo generation theory.

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TABLE OF CONTENTS

List of Figures ...... vi

List of Tables ...... ix

Acknowledgements ...... x

Chapter 1 Classification of Substellar Objects ...... 1

1.1. Definitions ...... 1 1.2. Theory of Substellar Objects ...... 3 1.2.1. Stellar Interior Physics ...... 3 1.2.2. Interior Physics of Substellar Objects ...... 4 1.2.3. Structural Properties of Substellar Objects ...... 6 1.3. Exoplanets ...... 8 1.3.1. A Brief History of Exoplanet Discoveries ...... 8 1.3.2. Exoplanet Characterization ...... 9 1.3.3. Exoplanet Magnetic Fields ...... 13 1.4. Brown Dwarfs ...... 22 1.4.1. A Brief History of Brown Dwarf Discoveries ...... 22 1.4.2. Brown Dwarf Characterization ...... 23 1.4.3. Characterization of Activity and Magnetic Properties of Brown Dwarfs ...... 27 1.5. Dissertation Outline...... 33

Chapter 2 Radio Emission Mechanisms ...... 35

2.1. Overview ...... 35 2.1.1. Solar System Planetary Radio Emission ...... 35 2.1.2. Solar Radio Emission ...... 37 2.1.3. Stellar Radio Emission ...... 39 2.1.4. Ultracool Dwarf Radio Emission ...... 39 2.2. Gyrosynchrotron Emission ...... 45 2.3. The Electron Cyclotron Maser Instability ...... 46 2.3.1. History ...... 46 2.3.2. Physics of the Electron Cyclotron Maser ...... 46

Chapter 3 Instrumentation and Computation ...... 55

3.1. Observing Instrumentation ...... 55 3.1.1. Arecibo Radio Telescope ...... 55 3.1.2. C-band Receiver ...... 56 3.1.3. Wideband Arecibo Pulsar Processor ...... 58 3.1.4. Mock Spectrometer ...... 58 3.2. Signal Processing and Computation ...... 59 3.2.1. Calculation of Stokes Parameters ...... 59 3.2.2. Description of Data Products ...... 60

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3.2.3. Data Processing Pipelines ...... 60 3.2.4. Computational Results ...... 63

Chapter 4 The Arecibo Survey for Radio Emission from Exoplanets ...... 65

4.1. Motivation ...... 65 4.2. Target Selection and Observations ...... 66 4.3. Results ...... 69 4.4. Discussion ...... 75

Chapter 5 The Arecibo Surveys for Radio Emission from Brown Dwarfs ...... 78

5.1. Overview ...... 78 5.2. Target Selection and Observations ...... 79 5.3. Results ...... 85 5.4. Discussion ...... 93 5.5. Inferences About the Ultracool Dwarf Population ...... 95 5.5.1. Statistical Analysis on Rotational Velocities ...... 95 5.5.2. Monte Carlo Simulator ...... 98 5.6. Arecibo A2776 Survey ...... 104

Chapter 6 Ultracool Dwarf Discoveries and Investigations ...... 107

6.1. TVLM 513-46546 ...... 107 6.1.1. Observations of TVLM 513 ...... 107 6.1.2. Flares and Flare Properties ...... 109 6.1.3. Physical Properties of the Source and Plasma Environment ...... 118 6.1.4. TVLM 513 Flare Timing Analysis ...... 120 6.2. 2MASS J10475385+2124234 ...... 121 6.2.1. Background Information on the Source ...... 121 6.2.2. The Detection of Radio Flares from J1047+21 ...... 121 6.2.3. Discussion on the Source of the Radio Emission ...... 125 6.2.4. Quiescent Radio Emission from J1047+21 ...... 127 6.3. 2MASS J1439284+192915 ...... 129 6.3.1. Background Information on J1439+19 ...... 129 6.3.2. The Detection of Flares from J1439+19 ...... 129

Chapter 7 Conclusions ...... 132

7.1 Summary ...... 132 7.2 Future Work ...... 134

Bibliography ...... 135

Appendix A Physical Quantities and Units ...... 143

Appendix B Monte Carlo Distributions ...... 144

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LIST OF FIGURES

Figure 1.01. Central temperature of substellar objects...... 5

Figure 1.02. The -radius relationship of substellar objects ...... 7

Figure 1.03. The evolution of with age for substellar objects ...... 8

Figure 1.04. Observations and models of the transmission spectrum of the transiting exoplanet HD 189733b...... 10

Figure 1.05. Interiors of the Solar System gas giants ...... 12

Figure 1.06. The density of transiting exoplanets ...... 13

Figure 1.07. Integrated Ca K flux as a function of period for two exoplanets ...... 15

Figure 1.08. A scaling law relating magnetic field strength to available energy flux ...... 17

Figure 1.09. Empirically derived flux densities and peak emission frequencies for exoplanets...... 19

Figure 1.10. Maximum emission frequencies and flux densities for exoplanets ...... 20

Figure 1.11. The magnetic field evolution of substellar objects ...... 21

Figure 1.12. The first indisputable brown dwarf, as seen by HST Wide Field Camera 2 (WFC2) ...... 23

Figure 1.13. Detailed, high signal to noise spectra of various brown dwarfs ...... 25

Figure 1.14. spectra of brown dwarfs ...... 26

Figure 1.15. Comparison of infrared spectral peaks for late spectral types ...... 27

Figure 1.16. Trends in the ratio of radio to bolometric in cool dwarfs ...... 30

Figure 1.17. Trends in ratio of radio luminosity to bolometric luminosity, given object rotation ...... 31

Figure 1.18. Trends in activity as a function of projected rotational velocity ..... 32

Figure 2.01. Comparison of radio emissions from the radio-emitting Solar System .. 37

Figure 2.02. Examples of solar type II and IV flares as observed by Geostationary Satellite (GOES) ...... 38

Figure 2.03. Radio flux density time series from the source LP944-20 ...... 40

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Figure 2.04. 2MASS J0036+18: the first brown dwarf found to emit radio waves periodically...... 41

Figure 2.05. High resolution time series of flux densities for TVLM 513 ...... 44

Figure 2.06. The bunching of electrons in the effective cyclotron phase space due to rf electric forces ...... 47

Figure 2.07. The bunching of electrons in the effective cyclotron phase space due to × forces ...... 48

Figure풗⊥ 2.08푩. Diagram⊥ of the loss cone electron distribution function ...... 50

Figure 2.09. The ring and shell electron distributions ...... 51

Figure 2.10. Generation of magnetic field-aligned electric currents ...... 52

Figure 2.11. Generation of the horseshoe distribution ...... 53

Figure 3.01. The Arecibo C-band receiver beam pattern ...... 57

Figure 3.02. The AGATE (Arecibo Graphical and Analysis Tool Ensemble) GUI in action ...... 62

Figure 4.01. Is it ECMI emission from HD 285968? ...... 70

Figure 4.02. Potential ECMI radio emission from ...... 71

Figure 4.03. Graphical representation of the upper limits from the Arecibo exoplanet survey ...... 75

Figure 5.01. The detection of a radio burst from J0746+20 ...... 86

Figure 5.02. Graphical representation of radio luminosities for ultracool dwarf targets in the Arecibo radio surveys ...... 93

Figure 5.03. Histogram of rotational velocities ...... 96

Figure 5.04. Probability plot of both radio-active and radio-inactive populations ...... 97

Figure 5.05. Histogram of rotational velocities of ultracool dwarfs ...... 99

Figure 5.06. Histogram of TVLM flare flux densities, as will be described in Chapter 6 ...... 101

Figure 5.07. Histogram of observing sessions ...... 102

Figure 5.08. Histogram of instrumental sensitivities ...... 103

Figure 6.01. A broadband burst of left circularly polarized emission ...... 110

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Figure 6.02. Recent observation of the “Large Left” feature ...... 111

Figure 6.03. The “Double Right” morphology ...... 112

Figure 6.04. The “Double Right” morphology strikes again ...... 113

Figure 6.05. The “Narrow Bright Right” feature ...... 114

Figure 6.06. The “Narrow Bright Right” feature reappears ...... 115

Figure 6.07. Histogram of TVLM 513 flare flux densities ...... 118

Figure 6.08. Phase fitted periodic radio emission from TVLM 513 ...... 120

Figure 6.09. The discovery of radio flares from J1047+21 ...... 123

Figure 6.10. Two more radio flares for J1047+21 ...... 124

Figure 6.11. The evolution of the Jovian radio power spectrum before, during, and after the Shoemaker Levy 9 impact events ...... 126

Figure 6.12. The detection of quiescent radio emission from J1047+21 ...... 128

Figure 6.13. A single burst from J1439+19 ...... 130

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LIST OF TABLES

Table 1.01. Summary of properties of exoplanetary radio emission power mechanisms ...... 19

Table 1.02. Summary of stellar spectral types and properties...... 24

Table 2.01. Summary of electron cyclotron emission and absorption processes...... 49

Table 3.01. Computational results from the MOCK processing pipeline ...... 63

Table 3.02. Computational results from the ARECIBO processing pipeline...... 63

Table 4.01. The exoplanet survey targets...... 67

Table 4.02. Exoplanet radio observations for Arecibo observing program A2471 ...... 68

Table 4.03. Radio detection values for the exoplanet portion of the A2471 survey...... 72

Table 4.04. Exoplanet radio detection upper limits in physical units ...... 74

Table 5.01. Properties of A2471 and A2623 ultracool dwarfs...... 80

Table 5.02. The brown dwarf observing log for program A2471 ...... 82

Table 5.03. The ultracool dwarf observing log for program A2623...... 83

Table 5.04. Frequency dependent detection limits of the brown dwarfs in the A2471 survey ...... 88

Table 5.05. Frequency dependent detection limits of the ultracool dwarfs in the A2623 survey...... 89

Table 5.06. Physical results of the A2471 and A2623 radio surveys ...... 91

Table 5.07. Ultracool dwarf targets for the A2776 survey...... 105

Table 6.01. Proof of concept observations of TVLM 513 ...... 108

Table 6.02. Observing log of additional TVLM 513 data sets, taken as part of Arecibo observing program A2803...... 108

Table 6.03. Summary of TVLM 513 emission features for 2008-2013 ...... 116

Table 6.04. Summary of the four detected flares from J1047+21...... 125

Table A.01. Physical quantities and units...... 143

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ACKNOWLEDGEMENTS

I would like to take this opportunity to thank first and foremost my family. My parents, Gary and Cheryl, my brother Brian, and yes, even pets have all played a role in making this research possible. Their love and devotion have been the bedrock of the evolution of my life. They have been there to support and encourage me from the beginning, and it is only fitting that they should be mentioned prominently here at this final step toward acquiring a PhD in astrophysics. I wonder if my career plans would have been the same without their showing me Halley’s Comet when I was very young, and without making many trips to the non-fiction section of the children’s library as well. Whether teaching me to read and picking me up from school, helping me with math homework and bridge building, taking me to educational enrichment activities, or offering good counsel and sound advice, they have always been there for me and this PhD and accompanying minor will be as much theirs as mine. Nor will I forget those excellent teachers who have helped me along the way. At the top of the list is Mrs. Lou Martin, who encouraged my studies in math and “space” and helped much more than any other teacher to ensure that I would be here today. Next would have to be two outstanding science teachers in middle school, Mrs. Pennington and Mr. Vickery. From the former I learned that studies in the physical sciences requires hard meticulous work, but that learning physics and chemistry allowed for great understanding of the natural world, with the potential to solve many problems in everyday life. From the latter, we two had a lot of fun discussing physics and astronomy; I thank him for taking the time to patiently answer all sorts of my questions about them, and for firing my curiosity in the sciences. I would also like to warmly thank Mr. Chuck Kay, for being an outstanding high school chemistry teacher and transforming chemistry from a lot of hard work to a lot of good fun with his constant humor. No doubt he would say that my writing this has made my dissertation “verbose”, but I am grateful to him for making my first steps into college chemistry, quantum mechanics, and precise experimentation fun and inspiring. I would also like to thank Jeff Valenti for inspiring me to study exoplanets, providing good career advice, and being a good friend. It is with a bittersweet sentiment that I acknowledge that some of them will not have the opportunity to read this, but their efforts need to be recognized and honored all the same. I would also like to extend my gratitude to my advisor, Dr. Alex Wolszczan, for providing me with the opportunity to conduct truly groundbreaking science. I thank him for allowing me to learn much from our interactions and his example. I have enjoyed many a conversation that we have had together where we probe the depths of the data and what it is telling us about the physics of ultracool dwarfs. I also wish to thank Dr. Richard Wade, for working with me on quite a variety of data sets these past few years, and providing critical support that has allowed me to continue work on this project, as well as a number of others. I also offer my heartfelt thanks to Hongyan Xiang, for being my close, caring companion these past few years, from the days of preparation for my candidacy exam to the present. This dissertation has been tremendously improved by the input from my committee members, and I am certain that as they examine the pages that follow, they will find their suggestions and the answers to a number of items that have made us curious as this project has developed. I also acknowledge aid from Phil Perillat (NAIC) in developing the MOCK processing pipeline and making it fully operational. The department staff have helped me greatly over the years by answering the many questions I have had about graduate school processes and procedures (and even more so around dissertation defense time) and for helping to make the atmosphere of the department both friendly and supportive.

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This research project has been made possible by a number of organizations and grants that I would like to mention here. First, I would like to thank the Pennsylvania State University Department of Astronomy and Astrophysics as well as the Center for Exoplanets and Habitable Worlds. Without the research experience and continued financial support of these institutions, this dissertation would not be possible. Second, I would like to extend my gratitude to the Eberly College of Science for the Nellie H. and Oscar L. Roberts Graduate Fellowship, which aided in my transition when I first entered into the PhD program at PSU. Third, I would like to mention my appreciation for the NASA Pennsylvania Space Grant Consortium for their generous support of my research in the past two years. Fourth, I would also like to thank the Zaccheus Daniel Trust for providing financial support to allow me to conduct radio observations in person at Arecibo Observatory and also for providing partial funding of the presentation of these results at the American Astronomical Society meeting in Long Beach, CA, USA in January 2013. For the remainder of the support for my attendance at that meeting I extend my gratitude to the Dr. Gerald A. Soffen Memorial Fund.

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Everything harmonizes with me which is harmonious to thee, O Universe. -Marcus Aurelius Antoninus, Meditations, IV.23 Roman Emperor, Stoic Philosopher

1

Chapter 1

Classification of Substellar Objects

1.1. Definitions

Since this dissertation will discuss extrasolar planets (exoplanets, hereafter), brown dwarfs, and ultracool dwarfs, the topic must be explored as to how we will distinguish between them, as well as make the distinction between them and other objects. At the outset, we define ultracool dwarfs as consisting of both stars of spectral type M7 and later, and brown dwarfs as including spectral classes L, T, and Y, but excluding exoplanets. As will be discussed in the section on rotation and activity, there are good physical reasons for bundling cool, low mass hydrogen burning stars together with all brown dwarfs. Now, however, we must attempt to make a distinction between exoplanets and brown dwarfs, if one is possible. The discussion will be framed in terms of four criteria, including characteristics of the objects, the circumstances of their surrounding environment, their cosmogony, and what culture says about them (Basri & Brown 2006). First, we can examine the topic in light of the physical, measurable properties of the objects. We may begin by noting that both of these classes of objects are substellar, and so are not massive enough to have ever fused hydrogen in their cores. This sets the upper mass boundary for the objects that we will be interested in as ~0.07 solar masses ( ), also known as the hydrogen-burning minimum mass (HBMM, Chabrier & Baraffe 2000). However, the trouble ⨀ begins when we are asked to make the distinction among substellar objects, differentiating푀 among brown dwarfs, planets, and smaller objects. That is, there is no given mass limit at which an object becomes a , nor at which a planet may be considered a brown dwarf. Yet when we consider the objects within the Solar System, no one would argue that a rectangular asteroid or a potato-shaped comet is a planet. These examples illuminate the idea that a planet ought to be at least round, which has the physical implication that a body’s shape should be governed by the force of gravity, and not by the material strength of the body. Yet other mass limits may be important, including:

• The mass at which convection occurs in the interior (Rayleigh number). • The mass at which gravitational energy per atom exceeds ~1 eV, which causes the modification of the interior of an object by chemical processes. • The mass at which the central pressure of an object is large enough to cause materials to have significantly greater density (bulk modulus). • The mass at which free electron degeneracy pressure becomes comparable to normal pressure (2 masses, MJ). • The mass at which nuclear fusion processes, beginning with deuterium, occur in the core (~13 MJ).

2 In addition to physical changes due to mass differences, we may also consider the generation of luminosity. Terrestrial planets slowly radiate away the heat remaining from their formation, as well as heat created by the radioactive decay of elements in their interiors. Meanwhile, gas giants slowly contract over time, thereby releasing gravitational potential energy. For the vast majority of the lives of brown dwarfs, they too generate luminosity through their slow contraction and radiation of heat. However, for objects of 13 MJ in mass, these objects fuse deuterium, lithium, and other isotopes, but not hydrogen, for at least 50 million years of their lives. While these fusion processes do not dominate the luminosity≳ of the objects until a mass threshold of ~15 MJ is reached, the fact that they occur at all and alter the composition of brown dwarfs may denote a distinguishable difference between them and planets, even if they do not change the interior structure or long term evolution of the objects (Chabrier et al. 2007). Second, we may analyze the surrounding environment that the substellar object finds itself in. An object that is massive enough may absorb or clear residual planetesimals near its during its formation. This is certainly the case of many of the commonly referred to planets in the Solar System, although they may have accompanying bodies that orbit them, such as satellites, or objects in orbital resonances, such as the Trojan asteroids for Jupiter. However, within the Solar System there are round, massive objects such as Ceres, Pluto, and Sedna that are still surrounded by planetesimals, from the asteroid or Kuiper belts, respectively. It is interesting to note that in both belts, an object of approximately one mass would be required to clear these belts of the debris to create planetesimal-free zones similar in size to those found elsewhere in the Solar System (Stern & Levinson 2002). Some troubling aspects, though, with this analysis of the surrounding environment are that a mass limit cannot be calculated without knowing the structure of the remainder of the system and that the mass limit is dependent upon distance from the central . On the upper mass end, it should be noted that disks around stars have some difficulty in forming objects larger than ~10 MJ, yet small enough to not fuse hydrogen, yielding the “brown dwarf desert” (de Pater & Lissauer 2010). Third, we examine the origins of the bodies themselves. If they form in a disk around a central star through the accretion of planetesimals, this fits the classical view of how the cores of the planets in the Solar System formed. However, Boss (1997) suggested that gas giants could be formed directly from the rapid collapse of a region of a cold, massive disk. Would this distinction matter? A number of subsequent models show small disks forming around accreting cores, and this must certainly be true of how the gas giants formed. Yet the largest problem with attempting to distinguish between objects in this manner is that the formation mechanism may not leave any observable difference between the objects. Finally, we must consider the case of the planets found orbiting the pulsar PSR 1257+12 (Wolszczan & Frail 1992). Since these objects would have orbited interior to the central star during its supergiant phase, they must not have been formed in the same disk as the central star, and may have formed during the formation of the neutron star, which as an additional point, does not fuse hydrogen in its core. Fourth, we may look to rather unscientific cultural distinctions to guide us in our understanding. Many civilizations noted that the planets moved in a distinct fashion compared to the background stars, and during the Scientific Revolution, it became understood exactly how and why this happens. Although which objects in the Solar System have been defined as planets has changed over time (consider the cases of Ceres and Pluto), the popular notion of a planet is a large round body that a central star. While this may be a good starting place, the discovery of myriad exoplanets in a variety of situations has shown the inadequacy of this definition. With these considerations in mind, these objects will be defined as follows. The brown dwarf definition, which follows below, is derived by compiling the definitions and observations of others (Basri 2000; Chabrier et al. 2000; de Pater & Lissauer 2010) and compromising among them:

3

(1) Any free floating object that appears to have formed as a result of independent gravitational collapse in the interstellar medium, yet less massive than 0.07 (HBMM) is a brown dwarf. ⨀ (2) Any object that has solar and is greater in mass than 13 MJ, but less푀 than HBMM, that forms within a disk and orbits one or more stars or stellar remnants is a brown dwarf. This definition changes to 11.0 MJ if the object has thrice the metallicity of the , and 16.3 MJ if the metallicity is zero (Spiegel et al. 2011).

Part (2) of the above definition has the virtue of combining two threads mentioned above: a deuterium burning interior (11.0 - 16.3 MJ) and the observations regarding the difficulty in the production of objects (~10-60 MJ) in disks. For the definition of planets, we yield to the International Astronomical Union (IAU) definition (IAU 2006) provided in Resolution 5A, but exchanging “Sun” for “star or stellar remnant,” and which may be used in their plural form:

(1) A "planet" is a celestial body that (a) is in orbit around (a) star(s) or stellar remnant(s), (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighborhood around its orbit.

(2) A "dwarf planet" is a celestial body that (a) is in orbit around (a) star(s) or stellar remnant(s), (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, (c) has not cleared the neighborhood around its orbit, and (d) is not a satellite.

(3) All other objects, except satellites, orbiting (a) star(s) or stellar remnant(s) shall be referred to collectively as "Small Solar System Bodies.”

1.2. Theory of Substellar Objects

1.2.1. Stellar Interior Physics

The foundation of our understanding of the physics of the interiors of brown dwarfs and planets is based on the same equations used to describe . This simplified description applies to a non-rotating, non-magnetic sphere. Here, a Lagrangian coordinate based on mass is used (Kippenhahn & Weigert 1994):

= (1.01) 휕푟 1 2 휕푚 4휋푟 휌 = (1.02) 2 휕푃 퐺푚 1 휕 푟 4 2 2 휕푚 − 4휋푟 휌 − 4휋푟 휕푡

4

= (1.03) 휕푙 휕푇 1 휕푙푛휌 휕푃 푛 휈 푃 휕푚 휀 − 휀 − 푐 휕푡 − 휌 �휕푙푛푇�푃 휕푡 = (1.04) 휕푇 퐺푚푇 4 휕푚 − 4휋푟 푃 ∇ = , = 1, … (1.05) 휕푋푖 푚푖

휕푚 휌 푗 푗푖 푘 푖푘 In these equations, r is radius, m is� mass,∑ 푟 p− is∑ density,푟 � 푖 G is the gravitational constant, and cP is the specific heat at constant pressure. εn and ευ denote the energy generation by nuclear reactions and the energy that has gone into neutrino production, respectively. denotes the temperature gradient that results in energy transport, and can either take the form = to indicate energy transport by radiation, or = to mean energy transported∇ by 푟푎푑 convection. The first equation is simply a rearrangement of the result of differentiating∇ ∇ the equation for the density of a sphere. The ∇second∇푎푑푖푎푏푎푡푖푐 equation is for hydrostatic equilibrium, with an acceleration term available for an object that may undergo radial pulsations. The third equation is a statement of the conservation of energy within a star, describing the production of luminosity via nuclear reactions. The fourth equation describes the transport of energy from the interior. Finally, the fifth equation describes how relative mass abundances, Xi, change via nuclear reactions. All of these equations apply for planets and brown dwarfs, although equation (5) is rather insignificant. In planets, it would encompass the conversion of elements via nuclear decay, while in brown dwarfs it would involve the fusion of deuterium (D) and lithium (Li) to other products. Additionally, the effects of power generation (1.03) by nuclear reactions is reduced in importance for these objects compared with stars. For giant planets and brown dwarfs, the dominant source of luminosity is gravitational contraction.

1.2.2. Interior Physics of Substellar Objects

The interiors of substellar objects are constrained by the equations of stellar structure mentioned previously. The interiors, therefore, range in central density from 103 g cm-3 (at the hydrogen burning limit, 0.07 ) to 10 g cm-3 (Saturn, 5.0 x 10-4 ) with 푐 corresponding central temperatures of 107 K to 104 K, respectively.휌 Under≃ these ⨀ 푐 ⨀ conditions, the majority of the interiors푀 of휌 these≃ objects are fully ionized H+푀/He2+ plasma. Under these conditions, the degeneracy parameter푇푐 ≃ can be calculated푇푐 ≃ by:

/ = 3.314 × 10 (1.06) 푘푇 휇푒 2 3 −6 휓 푘푇퐹 ≈ 푇 � 휌 � which yields values of ≤ 0.1 in these objects, where T is the central temperature, TF is the Fermi temperature, k is Boltzmann’s constant, µe is the mean electron molecular weight, and ρ is the density (Chabrier & Baraffe 2000). During formation, it is the fact that these cores become electron degenerate that halts their further collapse. Energy generation in sub- stars is overwhelmingly the result of nuclear fusion via the Proton-Proton I chain. However, since all of the objects we examine here are below the

5 HBMM, this reaction sequence does not work in its entirety. The nuclear fuels that are used in substellar objects are summarized below.

Figure 1.01. Central temperature of substellar objects of various masses as a function of age of the body. At the left hand side, TH, TLi, and TD represent the hydrogen burning, lithium burning, and deuterium burning temperature, respectively. The figure also shows that the minimum mass for H burning is 0.07 ,for Li burning is 0.06 , and for D burning is 0.013 . Source: Chabrier and Baraffe (2000). ⨀ ⨀ ⨀ 푀 푀 푀 From this diagram it becomes readily apparent that exoplanets should retain deuterium throughout, since their defined mass is too low (< 13 MJ, which is equivalent to 0.013 ), while brown dwarfs will destroy it via nucleosynthesis. The diagram also shows that some objects will ⨀ burn Li in their cores, and so remove it completely from the object, but if the age of an푀 object is ≥108 years and still retains Li, it is clearly a brown dwarf. Likewise, objects older than 107 years that still retain deuterium are considered planets. The presence of deuterium is a testable, and observable means of distinguishing exoplanets from brown dwarfs in accordance with the given definitions, as deuterium readily forms HDO which can be observed in the infrared (Toth 1997). The reason why Li or D burning in the cores of brown dwarfs will deplete these elements throughout the object is that objects below ~0.4 are subject to energy transport via convection, which effectively mixes the entire object (Stevenson 1991). The convective flux can ⨀ be calculated by 푀

/ ( ) / ( ) / (1.07) 푙 2 1 2 1 2 3 2 퐹푐표푛푣 ∝ 휌푣푐표푛푣퐶푃훿푇 ∝ 푄 �퐻푃� 푃휌 퐶푃푇 ∇ − ∇푒

6 with

= (1.08) 휕푙푛휌

푄 − �휕푙푛푇�푃 where vconv is the convective velocity, CP is the specific heat at constant pressure, δT is the temperature difference between the convective flow and the surrounding environment, Q is the volume expansion coefficient, l is the mixing length, HP is the pressure scale height, P is the environment pressure, is the temperature gradient, and e is the convective eddy temperature gradient. These low mass∇ objects may also transport energy∇ via conduction in their interiors, which becomes more efficient as the objects cool and is made possible when their cores become degenerate enough. In this case, the conductive flux is described by

= (1.09)

and 퐹푐표푛푑 퐾푐표푛푑∇푇

= (1.10) 3 4푎푐 푇 푐표푛푑 퐾 3 휌휅푐표푛푑 -15 where κcond is the conductive opacity and a is the radiation density constant, a = 7.57 x 10 erg cm-3 K-4. This is an especially important mechanism for cooling for older brown dwarfs in the 0.02-0.07 mass range. How rotation influences the interior structure will be discussed in the section on activity. 푀⨀

1.2.3. Structural Properties of Substellar Objects

The relationship between mass and radius of these substellar objects, and how the relation depends on metallicity, is shown in Figure 1.02.

7

Figure 1.02. The mass-radius relationships of substellar objects. The upper dot-dashed line represents this relationship for objects that are 6 x 107 yr old, while the solid line represents the relationship for objects 5 x 109 yr old. In these two instances, the objects have solar metallicity. The dashed line is the mass-radius relationship for objects of age 5 x 109 years, and 1% solar metallicity. The radii of known objects are given, including Jupiter (J). Source: Chabrier and Baraffe (2000).

For masses M > 0.2 , the interior pressure is supplied by classical ideal gas pressure. The minimum in the diagram at M = 0.06-0.07 occurs as the equation of state begins to be ⨀ dominated by pressure from 푀the degenerate electron gas. Toward lower masses, partial ⨀ degeneracy pressure and classical ionic Coulomb푀 pressure support the interior against contraction. For a given mass, an object with lower metallicity has less opacity and so is smaller. Next, the evolution of the effective temperature of substellar objects is shown in Figure 1.03.

8

Figure 1.03. The evolution of effective temperature with age for substellar objects. The solid lines represent temperature evolution for objects of solar metallicity with masses given in units of , and without dust opacity. Dotted lines represent the same conditions, only with dust opacity added. The dashed line represents the temperature decline for an object of 0.3 and 1% solar ⨀ metalli푀 city. Source: Chabrier and Baraffe (2000). ⨀ 푀 From this diagram it is clear that objects that do not undergo fusion continuously cool, but never balance the forces of gravitational contraction. This property of never reaching thermal equilibrium is another distinguishing feature between stars and brown dwarfs. Again, we see that the consequence of a lower metallicity is lower opacity, which means more energy is radiated to space. The result is that to maintain thermal equilibrium and initiate nuclear fusion processes, a higher internal temperature is required.

1.3. Exoplanets

1.3.1. A Brief History of Exoplanet Discoveries

After a number of years of searching, the first exoplanets were discovered by a rather non-obvious method. In 1992, A. Wolszczan and D. A. Frail (1992) reported the discovery of at least two planets of masses 2.8 and 3.4 located at distances of 0.47 AU and 0.36 AU, respectively, from the millisecond pulsar PSR 1257+12. 푀⨁ 푀⨁

9 It would not be until a few years later that a planet was detected around a solar-type star, with the discovery of the system (Mayor & Queloz 1995). However, this system too changed perceptions about the circumstances in which planets would be found, as the planet was found to have a mass of 0.47 MJ, at a distance from its parent star of 0.05 AU- much closer than expected for a gas giant. Yet this detection and its oddities would reveal as much about Nature as about the technique by which the planet was discovered. The detection was accomplished via the method, which was the most successful means of detecting exoplanets prior to the launch of the Kepler spacecraft. Seven means of detecting exoplanets have been successfully employed to date. These include: pulsar timing, radial velocity, , transit photometry, transit timing variations, microlensing, and direct imaging (de Pater & Lissauer 2010). While this dissertation will discuss the potential to detect exoplanets by another method, namely via their radio emission, a review of the currently used detection methods and their efficacy is beyond the scope of this paper. Nevertheless, it should be noted that the majority of these methods only reveal the masses and orbital properties of unseen exoplanets, with the exception of the transit method and direct imaging. As transits provide information about the radii of exoplanets, when this information is coupled with the radial velocity method, it allows for a determination of the bulk densities of these objects. Additionally, transmission spectroscopy allows us to probe the chemical composition of the upper atmospheres of transiting exoplanets. With direct imaging, the light from exoplanets can be directly detected, as in the HR 8799 system that contains four young, hot giant planets (Marois et al. 2008, 2010). This has the benefit of permitting direct near-infrared spectroscopy of such exoplanets, which allows for the discovery of molecular species that inhabit their atmospheres and an inspection of their cloud cover (Oppenheimer et al. 2013). Such information allows for a comparison of their spectra to both brown dwarfs and planets within the Solar System.

1.3.2. Exoplanet Characterization

From the preceding section, we have seen that the detection of an exoplanet allows for the calculation of its various orbital parameters as well as an estimate of the mass of the planet itself. Many of the planets have only lower mass determinations due to the unknown of the system. We have also seen that the power of the transit method lies in its ability to characterize exoplanets further, by providing radius information, which allows for a determination of the bulk composition of the object. In what other ways may we characterize an exoplanet, than simply by its mass and radius? Soon after the discovery of 51 Pegasi, a number of other approximately Jovian-mass exoplanets were detected close to their parent stars. It was hypothesized that because of the temperatures of these planets, that they would have atmospheric components, such as dust, that would make them directly detectable rather easily (Seager & Sasselov 1998). While this hypothesis proved false, it nevertheless pointed to the fact that the modeling of “hot Jupiter” atmospheres, including their structure and composition, could be begun on the basis of the orbital properties of the bodies and the application of the principles of radiative transfer. The next step in exoplanet characterization began with the detection of the first transiting exoplanet, HD 209458b (Charbonneau et al. 2000; Henry et al. 2000). This led to the hypothesis that transmission spectroscopy could be used to identify the atmospheric constituents of such exoplanets via their atomic and molecular absorption features (Seager & Sasselov 2000).

10 Transmission spectroscopy occurs when the host star’s light passes through the upper atmosphere of the planet, and the light acquires some of the spectral lines of the atmosphere. Only a couple years later, this prediction would be borne out with the detection of atomic sodium in HD 209458b’s spectrum with the Hubble Space Telescope (Charbonneau et al. 2002).

Figure 1.04. Observations and models of the transmission spectrum of the transiting exoplanet HD 189733b. Triangles represent observations conducted with the Hubble Space Telescope (HST). The colored lines represent two models, of which the model containing both methane and water better fits the observations. Source: Swain et al. (2008).

A further development related to exoplanet transits (or primary eclipses) was the detection of the first secondary eclipses with the of the objects TreS-1b (Charbonneau et al. 2005) and HD 209458b (Deming et al. 2005). Secondary eclipses are caused when a planet travels behind its host star. Prior to a secondary eclipse, both a planet and its host star contribute to the spectrum of the system. When the planet disappears behind the star, its flux is then removed from the system. By subtracting this component (the star-only component) from the combined flux, the spectrum of the planet can be determined. If optical wavelengths are used to perform these measurements, then the planetary albedo is determined. If infrared wavelengths are used instead, information is revealed about the composition and temperature profile of the atmosphere. Together, this information allows for a determination of the temperature-pressure structure of the atmosphere, as well as inferences about global atmospheric circulation (Seager & Deming 2010). Observations of planetary atmospheres naturally lead us to information about the interiors of “hot .” As exemplified by the case of Spitzer observations of the eccentric (e = 0.93) planet HD 80606b, time-dependent observations made in the infrared during periastron allow for the detection of changes in the flux observed from the substellar hemisphere (Laughlin et al.

11 2009). These alterations are the result of planetary rotation, and since the planet experiences pseudosynchronous rotation, these flux measurements provide clues about energy dissipation in the planet’s interior (Seager & Deming 2010). Further understanding of the interiors of exoplanets has been relegated to the realm of uncertain theoretical modeling, due to the difficulty of measurements to understand the interiors of these planets. The evolution of the physical properties of exoplanets has been discussed in Sections 1.2.2 and 1.2.3. Regarding giant exoplanets, there is significant uncertainty in the construction of models of the interiors of exoplanets due to a lack of knowledge of the equations of state (EOS) of the constituent components as well as a lack of understanding of the structure of the nearest gas giants, Jupiter and Saturn (Fortney & Nettelmann 2010). Equations of state provide information about the density-pressure-temperature relationship of various elements. There are no fewer than seven EOS that may be used to describe experimental hydrogen data, and no fewer than four for helium. Additional EOS are required to describe metals. Thus, due to the diversity of models that are poorly constrained at higher pressures, there are a variety of consequent potential structures. These models may be validated with the gas giants Jupiter and Saturn, as well as ice giants Uranus and Neptune. These planets have been visited by a variety of spacecraft that have provided information on a number of parameters, including bulk mass, radius, 1-bar (0.1 MPa) temperature, angular velocity, gravitational moments of inertia such as J2 and J4, and upper atmospheric composition (Fortney & Nettelmann 2010). Even so, due to the great uncertainties in the models, fundamental questions such as the size and nature of Jupiter’s core, the amount of metallicity in the outer and inner envelopes of Jupiter and Saturn, and the amount of oxygen in the Jovian interior (Wong et al. 2004) remain unanswered. Moreover, the predictions of these models are completely wrong in various instances, including: underestimating Saturn’s luminosity by 50% (Pollack et al. 1977, Fortney and Hubbard 2003), the underluminous nature of Uranus compared to Neptune (Hubbard et al. 1995), and the derivation of incorrect gravity fields for a fully differentiated Uranus and Neptune (Fortney & Nettelmann 2010).

12

Figure 1.05. Interiors of the Solar System gas giants. Y denotes the He mass fraction. For reference, the atmosphere of the Earth has a pressure of about 0.1 MPa (or 1 bar) at the surface. Source: Guillot 1999.

Given these difficulties, it is unsurprising that the interiors of exoplanets are ill- constrained. Observationally, the only constraints on interiors are given by planet radius, mass, age, temperature, and interior energy dissipation. From these constraints alone difficulties immediately arise since many gigayear-aged Jupiter-mass planets have radii in excess of 1.2 RJ, which cannot be plausibly explained by incident solar radiation, tidal dissipation (Ibgui & Burrows 2009 and references therein), evaporation (Baraffe et al. 2004), preferential evaporation of He instead of H (Hansen & Barman 2007), or energy deposition in exoplanetary atmospheres due to thermal tides (Arras & Socrates 2010). The extent of this problem can be seen in Figure 1.06.

13

Figure 1.06. The density of transiting exoplanets. The solid lines represent the radii of exoplanets of various masses at distances of 0.02 and 0.045 AU from their host stars for pure H/He composition, and absolutely no metals based on models. This is unrealistic and exoplanets above this line must be puffed up by an unknown mechanism. The dot-dashed line represents the radii of planets with a 25 Earth-mass metallic core. Below this, another solid line represents the radii for planets made of pure water. Source: Fortney and Nettlemann (2010).

A number of theories to explain the puffiness of exoplanet atmospheres remain, however, the theory of inflation by Ohmic dissipation (Batygin & Stevenson 2010), which will be discussed in the following section, appears promising in that it can adequately explain both giant exoplanets that appear over-inflated as well those with apparently normal radii. The consideration of this theory also leads to the recognition that some exoplanetary properties, such as magnetism, have not been measured at all. Among smaller exoplanets, Valencia et al. (2006) explored scaling laws to describe the interior structures of terrestrial planets with Mercury- Super-Earth masses. This included studying how planetary radius, mantle thickness, and core radius could be computed for various masses and compositions. This was followed by an investigation of the lithospheres of such planets, and an examination of how mass and water content contributes to plate tectonics on such worlds (Valencia et al. 2007). Although theories exist to describe the interiors of smaller exoplanets, it will evidently be quite some time before the observations exist to explore the veracity of these predictions.

1.3.3. Exoplanet Magnetic Fields

As alluded to previously, astronomers may have already observed the indirect influence of magnetic fields on gas giant exoplanet interiors, as a large number of exoplanets appear to have larger radii than predicted for their ages and temperatures. Recent theoretical work (Batygin & Stevenson 2010) shows that the atmospheres of all gas giant exoplanets may be influenced by

14 Ohmic dissipation in the convective envelopes of these objects. The idea is that in the deep interior (P > 300 bars) an inner envelope exists that consists of ionized hydrogen. At lower pressures and at a greater distance from the core, the outer envelope should consist of partially ionized alkali metals such as Na and K. Zonal jets in the outer atmosphere moving in a dipolar field would induce current to flow from the poles to the equator, forming a loop where the induced current penetrates the interior. The of the heat released from this induced current would be on the order of 10-6 - 10-2 of the solar irradiation, depending on the strength of the wind speed and the planetary magnetic field. Applying this idea and varying the interior metallicity, the researchers found that they could account for the radius of HD 209458b, Tres-4b, and HD 189733b, assuming magnetic field strengths approximately similar to those found in Christensen et al. (2009). Knowledge of gas giant exoplanet metallicity, coupled with a theoretical maximum limit to inflation that can be produced by this method provides testable hypotheses of this theory in the future. Exoplanet magnetic fields have also been searched for in other ways. Cuntz et al. (2000) hypothesized that extrasolar giant planets would interact with their parents stars, leading to a higher level of chromospheric, transition region, and coronal activity, including increased flaring, in a fashion analogous to that found for RS CVn stars (e.g. Ayres & Linsky 1980). They posited that the mechanisms for doing this would include both tidal interactions and magnetic field interactions. The tidal interactions would include the generation of acoustic and magnetic waves as well as a subsurface α-effect, while magnetic interactions would most likely result in coronal reconnection events betwixt the planetary magnetosphere and stellar active regions, accompanied by heightened X-ray production. This line of research was followed up by Shkolnik et al. (2003) who carried out observations of Ca II H and K lines (393.3 and 396.8 nm, respectively) of five “hot Jupiter” systems. The researchers found evidence that Ca K intensity increased in a periodic fashion for HD 179949, and that the periodicity of the increased flux was synchronous with its exoplanet’s . Furthermore, they reasoned that while magnetic effects would cause only one active region on the star at the sub-planet point, tidal effects would cause two tidal bulges, resulting in increased activity near the sub-planet and anti-planet parts of the star. As they found only one Ca K enhancement per period, they determined that the increase in chromospheric activity that they witnessed was the result of magnetic effects. Follow-up observations indicated that both HD 179949 and υ Andromedae appeared to have cyclical chromospheric variation that could be attributed to their orbiting “hot Jupiters” (Shkolnik et al. 2005, 2008), as shown in Figure 1.07.

15

Figure 1.07. Integrated Ca K flux as a function of period for two exoplanets. Circles denote data taken in August 2001, squares data from July 2002, triangles from August 2002, and diamonds from September 2003. The integrated fluxes are line residuals from a normalized mean spectrum of each source. Notice, however, that neither source fits all of the data; HD 179949 activity matches 75% of the data, while υ And fits only 50% of the data. Source: Shkolnik et al. (2005).

However, a word of caution is required here, as the peak Ca emission does not correspond to either the sub-planetary or anti-planetary points as suggested by theory for either “hot Jupiter.” Rather, peak Ca K emission leads the planet by 60° in the case of HD 179949, and also leads the planet by 169° in the case of υ And. Similar work by Santos et al. (2003) also was suggestive of enhanced photometric variability that could be the result of the orbiting planet around HD 192263, although in this case the activity also did not conform to theory, lagging the sub-planetary point by 90°. Another promising result that may be explained by the star-planet interaction comes from X-ray observations of exoplanet hosting stars. Using archival Röntgensatellit (ROSAT) data, Scharf (2010) searched for a correlation between orbiting planetary mass and X-ray luminosity. He found that host star X-ray luminosity scales in a regular way with planets less than 0.15 AU from their host stars. Furthermore, theoretical work allows the planetary magnetic field strength to be determined from stellar X-ray luminosity. Depending on the scaling law used, these results indicate that a 10 MJ exoplanet has a magnetic field strength 8 - 64 times stronger than a 1 MJ exoplanet. The most promising means, however, of studying exoplanet magnetic fields may be via radio emission. Several planets in the Solar System emit detectable radio waves by a variety of radio mechanisms, as will be discussed in more detail in Section 2.1.1. However, searches for exoplanets with current technology have not yielded very promising results. A blind search of ~1,800 nearby F, G, and K dwarfs at 74 MHz using Very Large Array Low-frequency Survey (VLSS) data resulted in no detections of magnetospheric radio emission from exoplanets (Lazio et al. 2010). The authors reported that based on theoretical considerations and applicable scaling laws, they suspect their 3σ sensitivity (10-33 mJy) was not good enough by a factor of ~100 to detect exoplanets with radio luminosities comparable to that of Jupiter. Thus, it appears that a potentially novel means of detecting exoplanets, by their periodic radio emission as they orbit their parents stars, has not worked out to date. Nevertheless, a number of targeted surveys have been enacted to attempt to determine the frequency and luminosity of exoplanetary radio emission. Even a single detection would offer

16 guidance as to how to continue the search. A number of searches have been completed, using a variety of instruments, including (Lecavelier des Etangs 2011 and references therein): Ukrainian T-shaped Radio Telescope (UTR) at 10-30 MHz (1σ ~1.6 mJy sensitivity), Very Large Array (VLA) at 74 MHz (1σ ~50 mJy), 325 MHz (1σ ~0.58 mJy), 1425 MHz (1σ ~16 µJy), and Giant Metrewave Radio Telescope (GMRT) at 150 MHz (1σ ~10 mJy), 244 MHz (1σ ~ 0.7 mJy), 610 MHz (1σ ~50 µJy). Yet these have all failed to detect radio emission from exoplanets. Lecavelier des Etangs et al. (2011) sought radio emission from HD 189733b and HD 209458b and reasoned that by comparing radio emission from the star-planet system at different phases of the planetary orbit, they would be able to distinguish exoplanet emission. Their search, which has been the most sensitive to date, was conducted at 150 MHz using GMRT. While they did not detect radio emission for HD 209458b (3σ ~ 3.6 mJy) or HD 189733 (3σ ~ 2.1 mJy), they reported a marginal 2.7σ detection (1.9±0.7 mJy) of a source 13” away from the exoplanetary system. One explanation is that the emission could actually be from the star or exoplanet as it is within the half-power beam width (17”). However, this detection should be met with skepticism for two other reasons. With an apparent separation from HD 189733 of 13”, this would be equivalent to 250 AU, and the density of stellar wind that could give rise to radio emission would be extremely weak. Also, there is no signature of a radio eclipse present in the light curve for the data. Similar GMRT observations at the same frequency of “hot Neptune” HAT-P-11 showed that on one occasion it produced radio activity consistent with an eclipse of a planetary magnetosphere with a flux of 3.87 +/-1.29 mJy (Lecavelier des Etangs et al. 2013). They calculate that the planetary magnetic field is ~50 G in strength powered by coronal mass ejections. Also like the previous attempt, this detection comes with caveats. First, the detected emission was from a point 14” away from the system, where the half-power beam width is 16”. Secondly, a repeated observation taken over a later failed to detect any such emission. Thirdly, although the authors determine that the electron cyclotron maser instability (ECMI) is the most likely mechanism for their alleged detection of radio emission from an exoplanet, it is interesting to note that while polarization information was collected, it was not used to test this hypothesis. Several research groups have tried to examine the nature of radio emission from exoplanets. The starting point is estimation of the strengths of exoplanet magnetic fields by extrapolation from planets in the Solar System. Christensen and Aubert (2006) devised a scaling relation for Solar System planetary geodynamo strengths, based on the available thermodynamic energy flux. This relation was generalized to strongly density-stratified, rapidly rotating spheres to attempt to explain both planetary and stellar magnetic field generation (Christensen et al. 2009). This relation is described by:

= / ( ) / (1.11) 2 〈퐵 〉 1 3 2 3 2휇0 표ℎ푚 0 and 푐푓 〈휌〉 퐹푞

( ) ( ) / ( ) / / = 4 (1.12) ( ) 1 푅 푞푐 푟 퐿 푟 2 3 휌 푟 1 3 2 3 2 푉 푟1 푞0 퐻푇 푟 〈휌〉 with 퐹 ∫ � � � � 휋푟 푑푟

= (1.13) 푐푝 퐻푇 훼푔

17

where is the mean squared magnetic field averaged over the volume V of the spherical shell, µ0 is permeability,2 c is a constant of proportionality, fohm ≤ 1 is the ratio of ohmic dissipation to total dissipation,〈퐵 〉 is the normalized density, F is a dimensionless efficiency factor defined by the second equation, and q0 is a reference convective energy flux. In the second equation, qc is convective energy〈휌 flux,〉 L is the length scale of the convective shell, and HT is the density scale height defined in the third equation. In the third equation, cp is the heat capacity, alpha is the thermal expansivity, and g is the gravitational acceleration. All variables are in the standard SI meter-kilogram-second system. These equations are used to devise a scaling relation that can then be compared to the known magnetic field properties of planets in the Solar System and various types of stars as depicted in Figure 1.08.

Figure 1.08. A scaling law relating magnetic field strength to available energy flux. Magnetic energy density (J m-3) is compared to bolometric flux (J m-3). The inset zooms in on the cluster of points around the “Stars” label. Blue denotes values for stars, red for old M dwarfs, pink for M dwarfs with observed magnetic fields. Yellow denotes 0.1 -1.1 stars with longer rotational periods (P > 10 days) and green those with shorter periods. The gray ellipse shows the ⨀ magnetic field properties of a 7 MJ exoplanet, while the brown ellipse is 푀for a brown dwarf of effective temperature ~ 1,500 K. Note that stars coded by yellow and green symbols have radiative cores, so it would be surprising if the scaling law applied to them. Source: Christensen et al. (2009).

18 It is interesting to note from this scaling law that exoplanets should have magnetic field strengths of 5-12 times Jupiter’s for 5-10 MJ exoplanets, and that a 1 Gyr old, 1,500 K brown dwarf of mass 0.05 should have a magnetic field strength of ~100 G. However, a few words of caution must be noted when considering this scaling model. First, while the scaling law ⨀ appears to fit planets푀 and M dwarfs, the relation does not work for the majority of planets in the Solar System with magnetic fields, including Mercury, Saturn, Uranus, and Neptune. Second, the diagram underestimates the spread in M dwarf magnetic field strengths; while in the diagram they cover roughly one order of magnitude, Reiners & Basri (2010) showed that M dwarf magnetic field strengths varied over nearly three orders of magnitude. Third, more massive stars are not explained by the relation and most likely do not conform to the theory due to their radiative cores. The next step in understanding potential exoplanet radio emission is to understand the mechanisms that power it, as discussed by Lazio et al. (2004). Lazio et al. used an empirical radiometric Bode’s law, derived from the magnetized Solar System planets, to calculate properties of the expected radio emission from exoplanets, including maximum emission frequency and median radio power due to a stellar wind. They suggested the rather promising result that massive exoplanets could be easily detectable at relatively high frequencies (e.g. HD 168433c at 2.67 GHz) using the two equations below, for the radiated power and cutoff frequency, respectively.

. . . ~4 × 10 (1.14) 1 33 휔 0 79 푀 푑 −1 6 11 푟푎푑 10 ℎ푟 푀퐽 5 퐴푈 푃 푊 � � � �/ � � ~23.5 (1.15) 5 3 휔 푀 3 휈푐 푀퐻푧 �휔퐽� �푀퐽� 푅퐽 where ω is the rotation period, M is the mass, and d is the length of the semi-major axis. All quantities are normalized to the corresponding Jupiter quantities. Farrell et al. (1999) describe how Equation 1.14 has somewhat strange exponents due to the statistical spread in the magnetic moments of various magnetized Solar System planets. Equation 1.15 is a consequence of Blackett’s law (1947) relating a planet’s magnetic moment to its mass and rotation rate.

19

Figure 1.09. Empirically derived flux densities and peak emission frequencies for exoplanets. Bars denote the range of emission frequencies up to the cutoff of the source. Jupiter’s cutoff frequency is established by the vertical dashed line. Source: Lazio et al. 2004.

Grieβmeier et al. (2007) asserts, however, that a number of assumptions made in this analysis were quite generous, including large magnetic moments that had been disproven (Blackett 1947, 1952) and unrealistically large core radii. Grieβmeier et al. (2007) suggested that there are four mechanisms to power radio emission: kinetic energy, magnetic energy, unipolar interaction, and coronal mass ejection (CME) driven emission. In the kinetic energy scenario, the input power for radio emission is derived from the solar wind protons impacting the magnetosphere, while in the magnetic energy scenario, the power is derived from the Poynting flux. The unipolar interaction model is a special case of the magnetic energy scenario, only with a weakly magnetized or un-magnetized exoplanet. Finally, in the CME case, violent stellar eruptions power the radio emission in a special case of the kinetic energy mechanism.

Power Mechanism Emission Location Equation Notes Kinetic energy Magnetopause Magnetic energy Magnetopause 3 2 푃 ∝ 푛푣푒푓푓푅푆 Unipolar interaction Stellar wind between star 2 2 푒푓푓 ⊥ 푆 0.4 and planet 푃 ∝ 푣 퐵2 푅2 푒푓푓 ⊥ 푖표푛 푓푝푙푎푠푚푎 Coronal mass ejection Magnetopause 푃 ∝ 푣 퐵 푅 푐 ≾ Table 1.01. Summary of properties of exoplanetary radio emission power3 mechanisms.2 푓 푒푓푓 푆 푃 ∝ 푛푣 푅 In Table 1.01, P is power, n is the stellar wind density, veff is the stellar wind velocity in the reference frame of the exoplanet, B is the component of the stellar wind magnetic field perpendicular to its flow Rs is the magnetosphere standoff distance, and Rion is the ionosphere radius. fplasma and fc are the plasma and cutoff frequencies, respectively. The cutoff frequency

20 denotes the maximum frequency of radio emission, which is the same as the cyclotron frequency at the strongest magnetic field. Using scaling laws for the magnetic moments of the planets, there were a number of conclusions drawn from this work. This included that maximum emission frequency for known exoplanets at that time should be between 0 and 200 MHz, of which emission < 5 - 10 MHz would be undetectable at the terrestrial surface due to the terrestrial ionospheric cutoff. As the exoplanets at higher frequencies have negligible fluxes, they recommend searching for exoplanet radio emission in the 10 - 70 MHz range. In general, the magnetic energy model provided greater flux, and the unipolar model showed that no exoplanet would be detectable due to the frequency cutoff condition give in the table. The researchers concluded that based on their analysis, only 2 - 8% of exoplanets should have detectable radio emission.

Figure 1.10. Maximum emission frequencies and flux densities for exoplanets. This figure uses calculations from the magnetic energy model, which is the “best-case” scenario for radio emission. The shaded region represents frequencies not accessible at the terrestrial surface due to the ionosphere. Solid lines and filled circles denote previous failed detection attempts (circles are VLA, the square is GMRT). Triangles denote predicted values. The various lines denote the sensitivity of various radio telescopes: UTR-2 (solid lines), Low Frequency Array (LOFAR, dash-dotted lines), Long Wavelength Array (LWA, left dotted line), Square Kilometer Array (SKA, right dotted line). Source: Grieβmeier 2007.

The magnetic field evolution of brown dwarfs and exoplanets built on the works of Grieβmeier et al. (2007) and Christensen et al. (2009) and was studied by Reiners and Christensen (2010). Their model considers the case of energy deposition into an exoplanetary/ brown dwarf magnetosphere via the kinetic energy of a nearby stellar wind. The equations to describe this are:

/ (1.16) 2 3 1 푀푠푡푎푟̇ 푀푑푖푝 2 2 where 푃 ∝ 푑 � 푎 �

21

. . = × / / / × 1 (1.17) / 3 2 4 0 17 1 6 1 3 11 6 푀푑푖푝 √2 푀 퐿 푅 � − 푀 푀퐽� The dipole moment of the exoplanet/brown dwarf, Mdip, has units of kG. In the first equation, Mstar is the stellar wind mass loss and M, L, and R describe the mass, luminosity, and radius of the exoplanet or brown dwarf, respectively. d is the distance the system is from Earth, and a is the semi-major axis of the exoplanet from its host star. As stellar wind mass is difficult to measure directly, the value is scaled on the basis of X-ray emission from the star. These formulas are then used to determine how the magnetic field strengths of various substellar mass objects evolve with time as shown. The magnetic field values are derived as calculated from (Christensen et al. 2009).

Figure 1.11. The magnetic field evolution of substellar objects. The gray region denotes the evolution path taken by a solar type star. Source: Reiners and Christensen (2010).

The conclusion from these works is that a number of exoplanets should have magnetic fields made detectable by the electron cyclotron maser instability mechanism. A number of exoplanets should emit at frequencies of 0 - 161 MHz, with fluxes of 0.1-700 mJy, with tau Bootis b having the strongest magnetic field and greatest detectable flux density. However, not a single exoplanet magnetic field has been convincingly detected to date. Nevertheless, based on their evolution curves, the authors helpfully point out “very young and massive planets may harbor magnetic fields up to one kilo-Gauss, which may be detectable in a few systems in the near future” (Reiners & Christensen 2010). Finally, there is one serious objection to the search for radio emission from “hot Jupiters” as has been conducted so far. As Melrose (1999) pointed out, these “hot Jupiters” will be in a very dense stellar wind due to their close proximity to their parent stars. It could very well be that reconnection events power ECMI, but that the radio emission is strongly self-absorbed in the

22 plasma environment. This then would have two potential consequences. The first, and more unlikely consequence, is that only the fundamental frequency is absorbed in this fashion, but higher harmonic frequencies escape the plasma environment and will be weakly detectable. The second, and more likely consequence of this scenario, however, is that the exoplanets would not be detectable in the radio at all.

1.4. Brown Dwarfs

1.4.1. A Brief History of Brown Dwarf Discoveries

The search for brown dwarfs has consisted of the usage of three different methods (Basri 2000). The first method includes the search for older brown dwarfs in the field that are observed to have lower temperatures and later spectral types than those for stars. The second method entails a dynamical search for brown dwarfs. For this method, the movements of stars are observed to hunt for radial reflex motions due to unseen companions. This technique has been of immense value in finding exoplanets, as described previously, but also reveals the presence of brown dwarfs that are more massive than exoplanets, yet less massive than stars. The third method involves searching clusters for young brown dwarfs, yet relies upon an accurate determination of the age of the cluster, so as to precisely estimate the temperature and luminosity of the prospective brown dwarfs. The search for objects of substellar mass began after the publication of Kumar’s (1963) work on hydrogen-burning in low mass stars, that indicated that fusion would not work below a certain mass (HBMM of about 0.1 ). These objects were labeled “brown dwarfs” by Tarter (1975). ⨀ The first potential brown dwarf푀 candidate was GD 165B, a companion to a that was uncovered during a survey of such objects (Becklin & Zuckerman 1988). It was found to be a very red, faint object that had a strange spectrum unlike any M dwarf, with molecular absorption characteristics different from those of Jupiter (Kirkpatrick et al. 1993). The determination of its cool effective temperature of ~1,600 - 2,400 K led to its classification as a member of spectral class L. Kirkpatrick et al. (1999a) suggested that it was actually a brown dwarf. (This object is classified as an L4 brown dwarf today.) The second potential candidate was detected during a radial velocity survey of nearby stars. Latham et al. (1989) reported the discovery of “a probable brown dwarf”, HD 114762b, causing a 0.6 km s-1 reflex velocity in its host star, which led to the computation of the minimum mass of the companion of 11 MJ. However, the object could not be classified as an exoplanet, brown dwarf, or low-mass hydrogen burning star due to the effects of the unknown orbital inclination of unseen companion, which remains undetermined to this (Kane et al. 2011). Later, researchers focused on attempting to detect brown dwarfs in young clusters, as these would reveal brown dwarfs when they were hottest and most luminous as well as provide age information to more accurately ascertain their masses. Two such detections were reported, of PPl 15 and 1, both in the cluster (Stauffer et al. 1994; Rebolo et al. 1995). At the time of their detection, however, the age of the Pleiades was recently revised upwards making their status as brown dwarfs uncertain (Basri 2000). It was only after the detection of lithium in

23

both objects that their masses were shown to be 55-70 MJ, making them true brown dwarfs (Basri et al. 1996; Rebolo et al. 1996). After the discovery of a handful of potential brown dwarf candidates residing in young clusters, the first brown dwarf that was unquestioningly recognized as such was Gl 229B. The object was found during a coronographic survey that searched for brown dwarf companions around low-mass stars within 15 pc (Nakajima et al. 1995). The researchers examined stars that were at least 109 years old, so that any low luminosity companions would be clearly distinguishable as brown dwarfs, having cooled and radiated away energy from gravitational contraction. On the basis of its low luminosity and the absorption of methane in the near infrared (Oppenheimer et al. 1995), the object was shown to have a temperature of < 1,200 K. The coupling of this information with brown dwarf cooling models then revealed that the mass range for this object is ~20-50 MJ (Burrows & Liebert 1993).

Figure 1.12. The first indisputable brown dwarf, as seen by HST Wide Field Camera 2 (WFC2). The brown dwarf is the small round blob to the right. Source: Nakajima et al. (1995).

1.4.2. Brown Dwarf Characterization

The starting point for our discussion of brown dwarf characterization is the way in which brown dwarfs have been classified into spectral types. This classification scheme was devised by Morgan, Keenan, and Kellman (MK, 1943) and contains two key pieces of information for each star: its temperature and its luminosity class. The temperature scale is given in Table 1.02.

24

Spectral Class Color Temperature (K) Prominent Spectral Lines O Blue-violet 30,000-50,000 Ionized atoms, He+ B Blue-white 11,000-30,000 Neutral He, some H A White 7,500-11,000 Strong H, some ionized metals F Yellow-white 5,900-7,500 H and ionized metals, Ca+, Fe+ G Yellow 5,200-5,900 Neutral and ionized metals, Ca+ K Orange 3,900-5,200 Neutral metals M Red-orange 2,500-3,900 Strong TiO, Neutral Ca Table 1.02. Summary of stellar spectral types and properties. Source: Comins (2013).

There are five possible luminosity classes to accompany these spectral types. They include: I (supergiants), II (bright giants), III (normal giants), IV (), and V ( stars). However, following the discovery of brown dwarfs with various spectral features as mentioned earlier that did not fit into any of these groups, it became apparent that a scheme needed to be devised to aid our discussion of them, and to group objects together by similar physical properties. The spectral classification scheme for low mass stars and brown dwarfs has three components: a temperature (and cloudiness) component, a gravity component, and a metallicity component. Classification of substellar objects began with an analysis of their spectral lines at optical and infrared wavelengths, which naturally led to their categorization roughly by temperature. M dwarfs from the MK scheme are known for strong bands of TiO and VO. Kirkpatrick et al. (1999b) proposed that the new features found in cooler, redder objects than M dwarfs be given spectral class names L, T, and Y. Optically, early L-dwarfs would exhibit the TiO and VO bands like M dwarfs, but also contained neutral alkali atomic lines (Na I, K I, Rb I, and Cs I) with some hydride bands (CrH, FeH, and CaOH) as well. Mid-L dwarfs would have stronger Na I and K I lines, stronger hydride bands (including CaH and MgH now), but the TiO and VO bands would be gone. Moving smoothly into late-L and early-T classes, H2O would increase, Na I and K I would continue to increase in strength, and the hydrides would disappear. By late-T, the Na I and K I lines near 700 nm would have blended together.

25

Figure 1.13. Detailed, high signal to noise spectra of various brown dwarfs. Moving from upper left to lower right goes from warmer (earlier) to cooler (later) types. Alkali and alkaline earth lines are given in green, hydride features in red, and molecular bands in orange. The blue Celtic- cross symbol denotes contaminants from Earth-based telluric absorption features. Source: Kirkpatrick (2005).

Similarly, the classes have distinct features in the near infrared (1.0 - 2.3 µm). Again, the starting point for infrared classification is that early L dwarfs have spectroscopic features similar to those found in late M dwarfs, including neutral atomic lines (Na, Fe, K, Al, Ca), with weak bands of FeH and CO, and strong bands of H2O. As we move from early L to late L and early T, the spectrum appear less as a gradually declining slope and more like three peaks that become increasingly sharp. At early T, methane absorption near 1.2 µm becomes prominent. Finally, toward late T, the bump near 2 µm becomes flattened by collisionally-induced H2 absorption. At longer infrared wavelengths, more methane absorption features become apparent and a CO band near 4.7 µm grows in strength as well. Near 10 µm the signature of ammonia also begins to appear for late T dwarfs.

26

Figure 1.14. Infrared spectra of brown dwarfs. The spectra are again ordered by temperature as in Figure 1.13. Source: Kirkpatrick (2005).

Finally, this leads us to spectral class Y, a classification that was suggested by Kirkpatrick et al. (1999b), but would take over a decade to turn into reality. Observations of source WISEP J182831.08+265037.8, detected by the Wide-field Infrared Survey Explorer (WISE) spacecraft, led to the report of it being representative of a new class of substellar object. Its infrared spectrum is dominated by H2O and CH4 features just like the T dwarfs, but the peaks at 1.25 µm and 1.58 µm are nearly equivalent in flux, whereas in T dwarfs the peak at longer wavelength is much smaller than the one at shorter wavelength. Other sources detected in the survey has similar features, with an apparent steepening of these two peaks as shown in Figure 1.15. The authors suggest that the hollowing out of the 1.58 µm peak toward shorter wavelengths is the result of additional absorption from NH3 (Cushing et al. 2011).

27

Figure 1.15. Comparison of infrared spectral peaks for late spectral types. The T6-T9 spectra were derived from the SpeX instrument onboard the NASA Infrared Telescope Facility, while the Y0 spectrum was obtained from HST Wide Field Camera 3. Note the sharpening of both peaks as the object becomes cooler. Source: Cushing et al. (2011).

Physically, this class is related to the temperatures of the objects. L dwarfs span the temperature range ~2,500 K - ~1,300 K, while T dwarfs span ~1,500 K - ~ 500 K. It is interesting to note that the optical features as described previously correlate strongly with temperature, except for early T dwarfs, and correlate less strongly for infrared features. This is believed to be due to the effects of clouds (Kirkpatrick 2005). For Y dwarfs, models indicate that the temperature of the sources detected by Cushing et al. (2011) are 350 K -500K, making them much cooler than T dwarfs, and intermediate in temperature between T dwarfs and Jupiter. Since all substellar objects in the Jupiter mass- HBMM regime at a given temperature have similar radii but simply differ in mass, the difference in mass is distinguishable by its effects on gravity sensitive spectral lines. That different mass objects should cool to the same temperature is a result of their age; thus, determination of the gravity and temperature of a cool dwarf is a means to determine its age given models of cooling, as in Figure 1.03. The gravity component has four possible subclasses: α, β, γ, and δ, which correspond to dwarf ages of 1 Gyr, ~ 100 Myr, ~10 Myr, and ~1 Myr. The spectral lines used for these measurements include those found in H2O, K I at 1.25 µm, Na I at 2.21 µm, and FeH at 1.20 µm (Kirkpatrick 2005,≳ Luhman 2012). The final component to the classification method is metallicity. Metallicity has three categories: d, sd, and esd, which represent solar metallicity, moderately low metallicity, and very low metallicity, respectively (Gizis 1997). Put together, a very metal poor, high gravity, 5 Gyr old brown dwarf with methane and ammonia lines, for example, would be labeled esdL8α.

1.4.3. Characterization of Activity and Magnetic Properties of Brown Dwarfs

In Section 1.2.2, we explored the equations governing the interior structure, but that exploration was based on the simplified case of objects that do not rotate. In Section 1.3.3., we

28 introduced magnetism and how it is generated in central dynamos. What about the rotation of brown dwarfs and how does that rotation influence interior structure and dynamo generation? The generation of a magnetic field in stars is the result of the αΩ dynamo (Parker 1955). Starting with the concept by Elsasser (1950) that fluid motions may regenerate various magnetic- field configurations, Parker proposed that a rotating sphere of a conducting fluid would generate a magnetic dipole. In addition, a star with differential rotation (such as the Sun, where the rotation period at the equator is much less than near the poles) would generate a toroidal field, which, having loops oriented meridionally, would cause feedback that strengthens the dipole field. Observationally, Kraft (1967) made observations of chromospheric activity and rotation, and found that the two were linked. Noyes et al. (1984) determined that the chromospheric activity that they witnessed was correlated with the inverse of a parameter called the Rossby number:

= (1.18) 푃

푅푂 휏푐 where P is the observed rotation period and τc is the convective overturn time at the bottom of the . However, for the twisting of field lines to occur from differential rotation, the field must be generated at the transition layer between convective and radiation zones. As M dwarf and cooler objects lack a radiative zone, another mechanism may be required to explain magnetic field generation in these objects. Dobler et al. (2006) found that no new explanation was required to explain magnetic field generation in M dwarfs; previous modeling efforts that suggested the αΩ dynamo would not operate had lacked three spatial dimensions and thus returned erroneous results. Durney et al. (1993) suggested that small-scale turbulence from rapid rotation and convection would generate magnetic fields, but these would be localized in nature, rather like the Sun’s surface magnetic field. Chabrier and Küker (2006) proposed the α2 mechanism, which suggested fully-convective bodies would only generate a large scale toroidal field.

1.4.3.1. Hα and X-ray activity

Once it was learned that rotation and activity were correlated, researchers sought to tie other measures of stellar activity together. For the Sun, activity takes place in the chromosphere, transition region, and the corona, all of which are heated by magnetism. This magnetic energy is released via X-rays, Hα emission, and radio emission. In a study of stars of spectral types F-M, Güdel and Bez (1993) found that X-ray and radio activity were correlated. They suggested that stellar magnetism was causing the nonthermal acceleration and heating of a population of electrons, which generated X-ray and radio waves together in stellar coronae. The Güdel-Benz relation is given as:

log log + 15.5 (1.19)

푋 푅 where LX and LR are the X-ray and radio퐿 ≲luminosities퐿 of the star, respectively. This relation was believed to hold for all stars. However, at cooler temperatures, the neutral fraction of atomic species becomes larger, which was predicted to inhibit coupling between magnetic field lines and the atmosphere, thereby potentially reducing nonthermal emission (Meyer & Meyer-Hofmeister 1999; Mohanty et al. 2002).

29 Several surveys have illuminated the topic of rotation and activity further. Reiners and Basri (2010) conducted high-resolution spectroscopy on 63 ultracool dwarfs of spectral types M7- M9.5. Regarding rotation, they found that older dwarfs rotated slower, a result that shows that rotational braking, whereby particles trapped in the magnetic field cause drag, retards the rotation of these objects just as it does for stars. They also found that later M dwarfs rotate more rapidly than early types. With respect to Hα activity, they found that all M7-M8.5 dwarfs show Hα emission, while 83% of types M9-M9.5 did not. By examining the magnetically-sensitive FeH absorption lines in their sample, they were able to infer the strength of the magnetic fields of these ultracool dwarfs. They found almost no variation in the strength of magnetic fields across their sample although a full 62% of ultracool dwarfs have magnetic field strengths ≥ 1kG. These results can be understood in aggregate. For objects with RO > 0.1, magnetic activity increased as the rate increased. However, for smaller values of RO (more rapid rotation) activity and magnetic field generation saturated and simply maintained a roughly constant level. This means that all objects rotating faster than 3 km s-1 have saturated their activity. Very slow M7 and M8 rotators had very low magnetic field strengths. Yet once the threshold value given above had been reached, there was no correlation between rotation and the generation of magnetic flux. Generally, Hα emission and magnetic field strength appear to be related such that greater magnetic fields produce more Hα emission. But Hα activity appeared to decline with later spectral type, presumably due to cooler temperatures resulting in more neutral atmospheres, and there appears to be no strong correlation between rotation and Hα production.

1.4.3.2. Radio Activity

As objects rotate even faster, it becomes impossible to measure their magnetic activity with Zeeman splitting due to its obfuscation by rotational broadening (Morin et al. 2010, Reiners and Basri 2010). Yet radio, Hα, and X-ray emission are still viable means of looking for activity in even rapid rotators. Efforts combining these facts and extending work such as that by Basri and Reiners (2010) down to spectral type L8 were summarized in McLean et al. (2012).

30

Figure 1.16. Trends in the ratio of radio to bolometric luminosity in cool dwarfs. From spectral type M2 to L3.5, there appears to be a trend of increasing radio emission for later spectral types. Note that circles denote quiescent sources while squares represent radio flares, and arrows depict upper limits. Data in red are from the source given, while gray data are from the literature prior to the publication of the source. Source: McLean et al. (2012).

From Figure 1.16, it can be seen that there appears to be an increase in the ratio of radio luminosity to bolometric luminosity at lower temperatures. This can most likely be understood as radio emission remaining relatively constant while the temperatures of the objects drop. Meanwhile, in Figure 1.17, rotation and radio activity appear to be uncorrelated for objects later than spectral type M7, although for v sin i > 20 km s-1, there may be indications of increasing radio emission.

31

Figure 1.17. Trends in ratio of radio luminosity to bolometric luminosity, given object rotation. While a trend can be seen and fitted for early M dwarfs (black fitted line), no such trend exists for later types. Note that circles denote quiescent sources while squares represent radio flares, and arrows depict upper limits. The level of activity appears to saturate for v sin i ~ 3 km s-1, at -7.7 LR/Lbol ≈ 10 . Source: McLean et al. (2012).

How radio, Hα, and X-ray emission vary with rotational velocity is summarized together in Figure 1.18. Note the general decline in Hα and X-ray activity among ultracool dwarfs as projected rotational velocity increase.

32

Figure 1.18. Trends in activity luminosities as a function of projected rotational velocity. Again, circles denote quiescent sources while squares represent activity flares, and arrows depict upper limits. All activity indicators saturate at v sin i ~ 3 km s-1 for spectral types M0-M6.5. Source: McLean et al. (2012).

This decline in these two activity indicators most likely is the result of one of three factors: increasingly neutral atmospheres, centrifugal stripping, or a reduction in the efficiency of energy transport into a corona, if the corona exists. Meanwhile, at the top of the figure, it appears that there is a trend toward increasing radio activity as rotational velocity increases. Thus for ultracool dwarfs, Figure 1.18 indicates that Hα and X-ray emission cease to be an accurate probe of interior dynamo activity and magnetic field strength, while radio is the sole viable means of understanding ultracool dwarf magnetism.

33 1.4.3.3. Radio Activity Energetics and Plasma Considerations

It was mentioned in Section 1.3.3 that theory suggests that the power for the emission is provided by various stellar wind-magnetosphere interactions. In this section, we review potential sources of energy and plasma for the radio activity observed in ultracool dwarfs. One potential energy source is acoustic heating. Ulmschneider et al. (1996) hypothesized that acoustic waves resulting from turbulent magnetic dynamo activity could result in coronal particle acceleration. However, the energy coming from this mechanism would be rather low and it would have difficulty in explaining persistent radio emission, which has been detected for ultracool dwarfs. Another energy source is magnetic reconnection. During magnetic reconnection (Bastian et al. 1998, Sturrock 1999), twisted magnetic field lines break and reconnect, releasing energy, and accelerating electrons away from the event. The electrons would have a power-law energy distribution, which would give rise to synchrotron emission (Schopper et al. 1999). Persistent, low-level radio emission would then be maintained by a large number of smaller flares (Neupert 1968). Mohanty et al. (2002) suggested that reconnection would drive magnetic stresses in the upper atmosphere that would drive activity in ultracool dwarfs. A potential source of energy and plasma could be accretion from a companion. In this scenario, a system analogous to the Jupiter-Io system would exist and emit radio waves (Goldreich & Lyndon-Bell 1969). Even if the ultracool dwarf has no companion, there still is the possibility of accretion from the interstellar medium (ISM). This was first considered to explain radio flaring in ultracool dwarfs (UCDs) by Burgasser & Putman (2005), but they found that the ISM plasma density was too low to maintain a corona. Schrijver (2009) calculated that a UCD with a 1.5 kG magnetic field travelling at a typical velocity through the ISM of ~ 40 km s-1 would receive energy transferred to its magnetosphere from the kinetic energy of the ISM impacting upon it. This energy transfer would be equivalent to 1017-1018 erg s-1, which is much lower than the emitted X-ray and Hα luminosities from these objects by a factor of ~105-108. Nichols et al. (2012) criticized this treatment as being too simplistic since it neglected the effects of rotation from the object that creates the magnetosphere. In their analysis, ISM plasma is accreted through traversing the interstellar medium, but the energy to power radio emission comes not only from the kinetic energy of the ISM plasma being accreted. They suggest that a magnetosphere- ionosphere coupling current system is established which provides additional power for radio emission from rotational shear between the angular velocity of the core of the ultracool dwarf and angular velocity of the plasma above the ionosphere.

1.5. Dissertation Outline

We have now examined a good deal of introductory material about the current state of knowledge concerning exoplanets and ultracool dwarfs. In the following chapters of this dissertation, we will continue the threads of discussion begun here, and illuminate our efforts to try to increase the body of knowledge that is known about them. The dissertation outline is:

• Chapter 2 will discuss radio emission mechanisms, as illuminated by a number of case studies. These case studies will reveal information about the radio activity of planets,

34 stars, and ultracool dwarfs, but our main concern will be to use them to guide our analysis of the emission.

• Chapter 3 will examine the instrumentation used to conduct surveys and detailed observations in this study, which were accomplished with the Arecibo Radio Telescope. Here we will also discuss this project’s efforts to calibrate and analyze the data, with an eye toward doing so in the best traditions of software engineering.

• Chapter 4 will describe efforts to conduct a sensitive radio survey of nearby exoplanets, and explain what can be learned from these results.

• Chapter 5 will describe the brown dwarf surveys that were conducted at the Arecibo Observatory. It will include a description of the sources, the detection of calibration sources, and conduct statistical analyses of the bulk results. This will also describe our attempts to infer properties about the radio activity of the entire population of brown dwarfs using a Monte Carlo simulator. This chapter will close by mentioning work that is in progress on a new brown dwarf survey.

• Chapter 6 will discuss the key new source detections that have resulted from this survey. It will also examine the promising work that is currently in progress on the best-studied ultracool dwarf, TVLM-513.

• Chapter 7 will conclude this dissertation; it will review key findings and examine the prospects for future work.

35

Chapter 2

Radio Emission Mechanisms

2.1. Overview

In Chapter 1, we conducted a broad overview of substellar objects. We briefly discussed the history of their detections, how exoplanets and brown dwarfs are characterized, and we discussed the properties of the magnetic activity for both populations of objects. In the present chapter, we will focus on the particular aspects of their radio emission. First, we will mention several case studies that allow us to gain insight into the mechanisms of radio emission, and this will be followed by theoretical descriptions of how the emission mechanisms operate.

2.1.1. Solar System Planetary Radio Emission

In the Solar System, we are fortunate to have three key cases with which to study radio emission from magnetized planets: the Earth, Jupiter, and Saturn. Since the Earth is the best studied among the three, let us start there. Benediktov (1965) reported detecting natural radio emissions from the Earth. In 1974, Gurnett (1974) determined that the energy for the radio emissions was supplied by solar substorms, and that the magnetosphere was turning this energy into radio waves with an efficiency of 1-10%. Hilgers et al. (1991) found that the emission came from 0.5- 3 Earth radii above the magnetic poles in shell-like distributions. It was also shown that reconnection events energized the charged particles and accelerated them toward the night side of the planet. In situ measurements by a fleet of spacecraft were required to illuminate the physical properties of the Earth’s radio emission, called the auroral kilometric radiation, or AKR. Its peak emission was at a few hundred kilohertz, but the bandwidth stretched from 20 kHz to several GHz (Gurnett 1974). The typical power released was ~107 W, while during intense storms, the radio emission could cause as much as 109 W of emitted radiation. The brightness temperatures generated by these events were 1010 K - 1024 K, indicating that the emission mechanism had to be coherent and could not be gyrosynchrotron emission (Jackson 1962). Polarization measurements (Gurnett and Green 1978) indicated that the strongest emission was right circularly polarized emission, but weaker left circularly polarized emission was also present. Among the spacecraft sent to the auroral cavities to learn about the AKR, the Fast Auroral Snapshot Explorer (FAST) mission (Carlson et al. 1998, Ergun et al. 1998a,b,c) had the best instrumentation and returned the most interesting results. It showed that the terrestrial cyclotron frequency in the region it traversed was ~360 kHz. The radio-emitting region had a size of ~150 km, and was greater in longitudinal extent than latitudinal extent. Electrons were found to have energy ranges of 0-10 keV. The AKR itself is made up of a number of small streaks, showing narrowband (~0.1 kHz) emission.

36 Although from a single mission, these measurements provided very detailed constraints about the radio emission received from the Earth, as well as a thorough description of the plasma environment that gives rise to the radio emission. The hypothesized radiation mechanism for this radio emission is the electron cyclotron maser instability (ECMI). Jupiter, with its strong magnetic field, also has significant radio emission. Radio emission from Jupiter is emitted at frequencies of 10 kHz - ≥20 GHz (de Pater & Lissauer 2010). Five types of radio emission have been observed: Jovian decimetric radiation, Io-controlled decametric radiation, non-Io decametric radiation, hectometric radiation, and kilometric radiation. The decimetric radiation is the result of synchrotron radiation and ranges in frequency from 74 MHz - ≥20 GHz and is concentrated in the magnetic plane and at high magnetic latitudes. It appears to be correlated to the solar wind and perturbed by the presence of inner satellite Amalthea. The decametric radiation occurs at a frequency of 4 - 40 MHz and can be divided into emission modified by Io and the remainder. The Io- controlled decametric radiation is the result of the generation of a plasma torus by volcanic activity on Io, and the propagation of Alfvén waves excited by Io. S-shaped bursts, which are emitted at 10 MHz, reach peak brightness temperatures of 1018 K are tied to this activity. Both non-Io decametric and hectometric radiation are related to auroral field lines, with the latter at greater distances from the planet. The kilometric radiation also occurs at high magnetic latitudes, but due to its temporal lag compared to Jupiter’s rotation, the source of the electrons that causes it is presumably at the outer edge of the Io plasma torus. The proposed radiation mechanism for all of these types of radio emission, except the decimetric radiation, is the electron cyclotron maser caused by ring-shell or horseshoe electron distributions (Gurnett et al. 2002, Treumann 2006). Farther away from the Sun, Cassini shed light on the Kronian magnetic field and ECMI during its tour of Saturn. The Kronian equivalent of the AKR is the Saturn kilometric radiation (SKR) and is observed at frequencies of 3 – 1,200 kHz. This radiation is emitted in the Right X- mode (RX mode) and is observed perpendicular to magnetic field lines that exhibit auroral activity (Kurth et al. 2009). As in the terrestrial case, the ECMI appears to result from an acceleration of hot electrons, with temperatures of 6-9 keV, toward the planet from a region near 5 Saturn radii above the planet, and frequencies slightly below and approaching the local cyclotron, or cutoff, frequency (Lamy et al. 2010, Mutel et al. 2010).

37

Figure 2.01. Comparison of radio emissions for the radio-emitting Solar System planets. With the exception of AKR, the remaining abbreviated emissions are all Jovian: decametric (DAM), decimetric (DIM), hecotmetric (HOM), broadband kilometric (bKOM), narrowband kilometric (nKOM), quasi-periodic (QP), and S-shaped decametric (S). They are all suspected to stem from electron cyclotron maser emission. Radio emission from Saturn, Uranus, and Neptune are also shown. Source: Zarka (1998).

2.1.2. Solar Radio Emission

A number of types of radio emission come from the Sun. There are several types of thermal, incoherent types of radio emission. They include: blackbody radiation, thermal bremsstrahlung from the chromosphere, gyroresonance emission above active regions, and coronal bremsstrahlung near coronal loops (Gary and Hurford 1994). When the Sun is active and releases flares, several radiation processes may dominate the flare activity. These include gyrosynchrotron radiation, plasma radiation, and the electron cyclotron maser. These processes give rise to the five classical types of solar flares (White 2007), along with a number of other types. The classical solar flare types are: • Type I- “noise storm” flares, which contain both continuum and flare components. They occur in the 100-400 MHz frequency range and occur in drifting chains where the components have instantaneous bandwidth of 10-20 MHz. They may last for hours. • Type II- they begin during a flare at approximately the same time that soft X-rays are released. They slowly drift to lower frequencies with time. They are thought to be the

38 result of plasma emission at both the fundamental and harmonic frequency, and are thought to be caused by coronal shocks. • Type III- drift rapidly in time and frequency, and tend to occur at 20 - 50 MHz. Plasma radiation is thought to be the source of them. • Type IV- they are broadband with fine structure. They tend to be associated with active regions on the Sun, and 88% of the time are also associated with Type II flares. Their features are generally attributed to maser activity (Aschwanden 1990a,b; Bastian 1998; Fleishman 2006), which may or may not be true. • Type V- tend to be associated with Type III bursts, except are lower in frequency and longer in duration- they can last up to a minute.

Figure 2.02. Examples of solar type II and IV flares as observed by Geostationary Satellite (GOES). Soft X-ray emission peaked at the time the type II burst began. Source: White (2007).

While gyrosynchrotron emission is not thought to be responsible for any of the major flare types, it is emitted during flares and peaks at higher frequencies than these classical flare types, at 5 - 10 GHz (Bastian et al. 1998). Another flare type, solar microwave spikes, has high 12 brightness temperatures TB~10 K and has nearly 100% circular polarization. They range in frequency from 100 MHz – 5 GHz and have typical durations of < 0.1 s (Treumann 2006).

39 2.1.3. Stellar Radio Emission

In 1994, Lang (1994) probed the radio emission from stars of spectral types G, K, and M using the Very Long Baseline Interferometer (VLBI). Lang argued that the flaring emission that he noted in dwarf M stars pointed to coherent radiation processes. The supporting evidence for this assertion was that the flares exhibited rapid rise times (≥ 20 ms) indicating small source regions, 100% circular polarization, and high brightness temperatures of >1015 K. He suggested that either coherent plasma radiation or ECMI could explain the coherent emission processes. Observations of the binary UV Ceti with the Very Long Baseline Interferometer (VLBI) by Benz et al. (1998) suggested a complex picture of radio emission. They noted that the total circular polarization from the system was only 10%, which indicated that the radiation was gyrosynchrotron emission, and they detected that the primary star has large coronal loops stretching out to 2-4 stellar radii. However, on top of this background gyrosynchrotron emission, they observed the presence of radio flares from the primary star, which were 100% right circularly polarized. Bingham et al. (2001) used Benz et al.’s work to suggest that due to the polarization fraction alone gyrosynchrotron radiation could be ruled out as an emission source and suggested that the emission mechanism was the electron cyclotron maser. Stepanov et al. (2001) observed the dwarf M star AD Leonis (M3.5) with the radio telescope at Effelsberg at 4.85 GHz. Here too, completely right circularly polarized radio 10 emission was detected with a high brightness temperature (TB~ 5 x 10 K), leading the team to conclude that the emission was also the result of a coherent emissions process. However, while they considered the electron cyclotron maser, they drew the conclusion that gyroresonance absorption would prevent the mechanism from operating. They therefore advocated plasma emission as the radiation mechanism instead. Finally, Osten and Bastian (2006) revisited AD Leonis with the Arecibo Radio Telescope and WAPP spectrometer (to be described in Chapter 3), and returned to the source in 2008 (Osten and Bastian 2008). This team also detected 100% right circularly polarized emission from the source, and calculated a brightness temperature of TB 4 x 1014 K. In their first publication on the star, they concluded that the source of the emission was coherent plasma emission, while in the second paper they drew the opposing conclusion based≳ on the detection of rapid, drifting striations which better fit the electron cyclotron model.

2.1.4. Ultracool Dwarf Radio Emission

Our saga of the detection of radio emission from ultracool dwarfs begins in 1999 December. The Chandra X-Ray Observatory had detected an X-ray flare from M9 ultracool dwarf LP 944-20 (Rutledge et al. 2000). The star is relatively close to us, at a distance of 5 pc, and was found to have an X-ray luminosity during flaring of 1.2 x 1026 ergs s-1. Berger et al. used the Very Large Array (VLA) to observe the object and detected a radio source (Berger et al. 2001). The source was found to emit three radio flares during their observations, at both 4.9 and 8.5 GHz.

40

Figure 2.03. Radio flux density time series from the source LP944-20. For all three flare events, the flaring activity occurs on a background of quiescent radio emission from the source. Squares denote measurements at 8.5 GHz, while circles represent measurements at 4.9 GHz. The third panel contains a model (dashed line) of synchrotron emission for that flare. Note the frequency of maximum emission occurs at 8.5 GHz, in the second panel. Source: Berger et al. (2001).

The observed radio emission was surprising since it violated the Güdel-Benz relationship by 2 x 104. They calculated a brightness temperature of the radio emission of 2 x 108 K in quiescence and 4 x 109 K during flaring activity. Brightness temperature is calculated:

2 × 10 (2.01) , −2 푅 9 2 −2 푇푏 ≈ 퐹휈 푚퐽푦푑푝푐휈퐺퐻푧 �푅퐽� where Fυ,mJy is the flux density of peak emission measured in mJy, d is the distance to the source in pc, and R is the size of the source region, normalized to Jupiter radii. The researchers hypothesized that the emission mechanism was a form of synchrotron radiation, as the brightness temperature was too low and the circular polarization fraction was only ~30%, ruling out any coherent process. As the peak frequency emission occurred at 8.5 GHz, coupled with inferences about other parameters, they calculated a magnetic field strength of 5 G. That the object should have such a weak magnetic field when other M dwarfs can have magnetic field strengths of kG, was supported by low Hα emission, its old age, and its rapid rotation which was thought to quench dynamo action. Finally, the authors hypothesized that the combination of X-ray and radio emission pointed to magnetic reconnection in a corona-type environment as being the cause of the emission.

41 A number of radio surveys of ultracool dwarfs followed to attempt to reveal similar sources. Berger (2002) observed 12 sources at a center frequency of 8.46 GHz and found that three were observed to flare and emit quiescent emission, including TVLM 513-46546 (M9), 2MASS J0036159+182110 (L3.5), and BRI 0021-0214 (M9.5). Among these, TVLM 513 and J0036+18 were shown to flare at the 0.5 - 1.0 mJy level and had > 60% circular polarization. For these three sources, by assuming that the size scale of the emitting region is 0.1 - 4 RJ, brightness temperatures of 108 - 1011 K could be calculated. The combination of potentially high brightness temperatures and large circular polarization fractions for the two sources suggested that a coherent emission process could be at work. Magnetic field strength estimates ranged from 5 - 50 G for BRI 0021 to 20 - 350 G for TVLM 513 and J0036+18, depending upon assumptions concerning the energetics of the accelerated electrons. If the source of the radio emission was a coherent process such as ECMI or plasma emission, the magnetic field strengths involved could be B 1,500 kG. Berger et al. (2005) found that 2MASS J0036+18 exhibits periodic radio emission with a 3 hr. period, as shown in Figure 2.04. ≳

Figure 2.04. 2MASS J0036+18: the first brown dwarf found to emit radio waves periodically. The top panel shows the emission at a center frequency of 8.46 GHz, while the bottom panel depicts emission at 4.86 GHz. Emission in Stokes I (intensity) is in black, while Stokes V emission (circular flux density) is in gray. The time resolution is 10 minutes. A periodic signature is evident at 4.86 GHz. This source is also the coolest detected brown dwarf before the work presented in this dissertation. Source: Berger et al. (2005).

42

Burgasser & Putman (2005) identified two quiescent radio sources and one flaring radio source, DENIS 1048-3956 during a survey of seven nearby M and L dwarfs. The radio flares 13 from DENIS 1048 had ~100% circular polarization and TB 10 K, indicating that the radiation was caused by a coherent emission process and that the dwarf had a magnetic field B ~ 1kG. Berger (2006) examined 21 M, L, and T dwarfs and found that≳ three of them had persistent radio emission, with low amounts (< 30%) of circular polarization. One source, 2MASSW J0746425+200032 consists of an L0+L1.5 pair and has periodic radio emission (Berger et al. 2009) that was first reported in a survey of 8 ultracool dwarfs (UCDs; Antonova et al. 2008). A large survey of 104 UCDs by McLean et al. (2012) also detected a source that varies periodically in quiescence (McLean et al. 2011). But a survey of 32 UCDs by Antonova et al. (2013) found none. However, the best-studied ultracool dwarf to date has been TVLM 513. Before its radio detection, TVLM 513 was detected by Tinney et al. (1993) from the 2MASS catalog (designation 2MASS J15010818+2250020) and determined to be an M9 dwarf located relatively nearby at a distance of 10.5 pc. Leggett et al. (2001) determined that Lbol ~ -3.65 and Teff ~ 2,200 K. Lithium was found to be absent in its spectrum so the object is not a brown dwarf and M > 0.06 . Its radius is approximately 0.1±0.01 based on models (Chabrier et al. 2000). Following the ⨀ detection of its radio activity in 2002 (Berger 2002), a number of activity indicators were푀 ⨀ examined. It was found to have variable푅 Hα emission (Mohanty & Basri 2003, Reid et al. 2002) and rapid rotation, with v sin i ~ 60 km s-1. A search for physical companions (Close et al. 2003) found none within 1.05 - 52.5 AU of the star. Following its detection in 2002, Osten et al. (2006) revisited TVLM 513, interleaving measurements of it at 1.4 GHz, 4.8 GHz, and 8.4 GHz. Her group marginally detected it at 1.4 GHz, but definitively detected the source at the other frequencies. The calculation of the polarization fraction showed that the source was only ~15% polarized, but had a high brightness 9 temperature TB > 10 K. As they searched at multiple wavelengths, they were able to determine a spectral index ( = ) of α ≈ -0.4. They noted periodic variation in the source, with tentative periodicity of either 2.1훼 or 2.8 hours. However, they did not notice any flares in their data set. Hallinan푆휈 et al.휈 (2006) conducted follow-up observations with the VLA at both 4.88 and 8.44 GHz. This team found that at low time resolution the degree of circular polarization was ~13% as Osten’s team had found, but that at higher time resolution, the degree of circular polarization was greater. Lomb-Scargle periodogram analysis (Lomb 1976, Scargle 1982) indicated that the radio emission had a periodicity of ~ 2 hr. Given the known rotational velocity of the star, it appears that the radio emission is synchronized with its rotation. With the period- folded light curves constructed, it became apparent that TVLM 513 has left and right circularly polarized flares that occur one immediately after the other, and could have an apparent cancellation effect at low time resolution (see Figure 2.05). Yet even when not flaring, there is quiescent radio emission of ~200 µJy. But what does this emission tell us about the emission mechanism? Based on the flux that Hallinan et al. received from the source of 0.4 mJy, they inferred a brightness temperature of 9 -2 3.7x10 (L/RJ) . This means that for an emitting region nearly the size of a brown dwarf disk, the brightness temperature is great enough that it excludes gyrosynchrotron emission as a mechanism. Dulk and Marsh (1982) showed that the effective temperature of gyrosynchrotron radiation was limited to ~1x109 K. Additionally, the rapid change in polarization may be indicative of a highly directed nature to the emission, as would be found for a coherent emission mechanism. Another possibility is that the directed emission is the result of relativistic beaming during synchrotron emission perpendicular to the magnetic field. But this possibility has two

43 problems. First, the source of the electrons would need to be ultra-relativistic, and it is not clear how such a population would arise in the environment of an ultracool dwarf. Second, synchrotron radiation has a maximum degree of polarization of ~10%, which is clearly violated in the case of flaring behavior as recorded at high temporal resolution. These clues led Hallinan et al. (2006) to consider coherent emission processes, of which two may be applicable: coherent plasma radiation and electron cyclotron maser emission. Plasma radiation is defined by

/ 9 (2.02) 1 2 푝푒 푒 where υpe is the frequency of maximum emi휈 ssion≈ 푛and n푘퐻푧e is the number density of electrons. In astrophysical situations, plasma radiation is typically a low frequency phenomenon, usually applicable for υp 1 GHz (Güdel 2002). Plasma radiation at higher frequencies is usually inhibited by Bremsstrahlung. This led Hallinan et al. to contemplate electron cyclotron maser emission, which could≲ adequately explain all properties of the radiation. Once the emission mechanism is determined, the condition for ECMI to operate in the absence of plasma emission:

1 2 (2.03) 휈푝푒 2 휈푐푒 may be used to determine the local plasma density: ≪

< 1.24 × 10 (2.04) 10 2 푒 퐺퐻푧 -3 where υce is the frequency of maximum emission푛 in GHz, and휈 ne is in particles per cm (Treumann 2006). Cyclotronic emission immediately allows for a determination of the magnetic field strength, via

= 2.8 (2.05) 푒퐵

푐푒 2휋푚푒 which was found to be 1.7 - 3 kG in the case휈 of TVLM≈ 513. 퐵In 푀퐻푧equation 2.05, e is the charge of an electron, B is the strength of the magnetic field, me is the mass of an electron, and υce is the gyration frequency. This emission frequency is also known as the cutoff frequency, and represents the maximum frequency at which ECMI may operate at the fundamental frequency. A derivation of the magnetic field strength from this equation, therefore, represents an upper limit to the maximum strength of the field. Hallinan et al. (2007) revisited TVLM 513 with the VLA array and analyzed their observations at even higher time resolution than previously. High-resolution time series showed that the degree of circular polarization reached 100%. This temporal detail also allowed for a more refined determination of the period (1.958 hr) and demonstrated that the periodicity was stable over a year. The period was subsequently refined to 1.96733±0.00002 hr by periodogram analysis after further data collection (Doyle et al. 2010). Berger et al. (2008) conducted multi-wavelength observations of TVLM 513 simultaneously, in radio, infrared, optical, ultraviolet, and X-ray wavelengths. They pointed to a scenario in which the low-level quiescent radio emission is the result of gyrosynchrotron emission, generated by a magnetic field B 102 G. The flaring emission, they conceded, appeared to be better represented as being the result of ECMI. However, they suggested that the flaring emission observed is not generated ≲by a stable region in a dipolar magnetic field. Rather,

44 the researchers argued that as some authors have not observed flaring behavior, this means that there are multiple transient magnetic hot spots with larger magnetic fields, or that the emission comes from a multipolar field. They noted sinusoidally varying Hα which appeared to coincide with the rotational period of TVLM 513. They observed no ultraviolet emission (such as could 24 -1 be observed from auroral activity) and computed an X-ray luminosity of Lx ≈ 8.5 x 10 erg s based on Chandra X-Ray Observatory measurements.

Figure 2.05. High resolution time series of flux densities for TVLM 513. Both top and bottom panels were recorded for a center frequency of 8.44 GHz. Both left and right circularly polarized bursts are present, except near 8.7 hr, where the LCP burst was likely missed due to off-source calibration. Source: Hallinan et al. (2007).

Hallinan et al. (2008) applied the high resolution timing methods they demonstrated on TVLM 513 to the sources LSR J1835+3259 (an M8.5 dwarf) and 2MASS J00361617+1821104, which had previously been shown to emit periodically. They found that both sources emitted periodic, 100% circularly polarized flares on top of constant, background, unpolarized radio emission. Due to the high brightness temperatures involved and the large degree of circular polarization, the researchers ruled out gyrosynchrotron radiation as the emission mechanism for the flares. These observations supported the notion that these bright radio flares are caused by ECMI operating in the presence of kG magnetic fields. Furthermore, the authors asserted that the unpolarized emission coming from J0036+18 was not the result of gyrosynchrotron emission, but was a result of ECMI emission becoming depolarized as it traversed the magnetosphere of the ultracool dwarf. They reasoned that this was the case due to the flux density and duty cycle of more weakly polarized interpulses matching those of the 100% circularly polarized flares. As their timing is between the main pulses, the witnessed weaker polarization could be the result of

45 an observing effect, as the radio emission propagates through the walls of a plasma cavity and become depolarized. From the history of observations of cool dwarfs, it is clear that two emission mechanisms dominate the discussion: gyrosynchrotron emission and electron cyclotron maser. These will be discussed in Sections 2.2 and 2.3.

2.2. Gyrosynchrotron Emission

Gyrosynchrotron emission has a number of fundamental properties that can be used to distinguish it from other radiation mechanisms. It is the result of a population of mildly relativistic electrons orbiting magnetic field lines and emitting radiation as they are accelerated. This radiation has the properties of being incoherent, and exhibiting a small degree of circular polarization, generally < 10%. The brightness temperature associated with this mechanism is usually ~107-109 K in environments such as those found around ultracool dwarfs. For ultracool dwarfs, we can inspect how to calculate various parameters of the emission mechanism. Since gyrosynchrotron radiation is the result of radiation from a population of relativistic electrons, a power-law distribution of these electrons is typical, and can be written in terms of the Lorentz factor (γ):

( ) (2.06) −푝 where the Lorentz factor is defined as: 푁 훾 ∝ 훾

/ = 1 (2.07) 2 −1 2 푣 2 with v the speed of the electrons, and c the speed 훾of light.� − A푐 typical� value for p is ~3 in this case (Osten et al. 2006). Based on this distribution, a number of equations related to the emission mechanism can be written:

. . × = 0.3 × 10 . . (2.08) 2 3 −0 21−0 37 sin 휃 1 93 cos 휃−1 16푐표푠 휃 3 10 푟푐 � 퐵 � = 1.8 × 10 sin ( ) . . (2.09) 4 0 23 0 77 푚 . 푒 . 휈 , = 2.5 × 10√ 휃 푛 푅 (sin퐵 ) 퐻푧 (2.10) −41 2 48 3 −1 52 휈 푚 푒 where rc is a covering factor,퐹 υm is the frequency퐵 of maximum푅 푛 radio휃 flux,휇퐽푦 Fυ,m is the maximum flux density, θ is the pitch angle between the magnetic field and the line of sight, B is the magnetic field strength, R is the characteristic length of the radiation emitting region, and ne is the radiating electron density (Dulk & Marsh 1982). Typically, rc takes on values of < 25%, θ is 10 13 -3 given values of 20-80°, and for UCDs, ne~ 10 -10 cm (van den Besselaar et al. 2003). The result is that magnetic field strengths as calculated by gyrosynchrotron radiation are always smaller than those calculated by electron cyclotron masing activity.

46 2.3. The Electron Cyclotron Maser Instability

2.3.1. History

The theory behind the electron cyclotron maser instability was discovered by three physicists independently: Twiss (1958), Gaponov (1959), and Schneider (1959). They all realized that within a plasma, high-frequency electromagnetic waves should be amplified by a resonant interaction between the charged electrons within the plasma at the Doppler shifted electron cyclotron frequency (Treumann 2006). Hirshfield and Bekefi (1963) made the step of applying theory to the real world, suggesting that planetary magnetospheres would serve as excellent laboratories to test our understanding of the phenomenon. In particular, they suggested that the Jovian decametric radiation could be caused by this emission mechanism. Wu and Lee (1979) attempted to explain detected AKR radiation using an ECMI loss-cone distribution, where hot electrons lose energy to colder ionospheric plasma via collisions. Fine resolution observations of the AKR (Gurnett and Anderson 1981) revealed that the loss-cone hypothesis was untenable due to the intense fine structure of the radiation. Winglee and Dulk (1986) surpassed this problem by devising the “ring” and “shell” distributions which would result from field- aligned electric currents.

2.3.2. Physics of the Electron Cyclotron Maser

While referred to as a “maser,” this phenomenon is not the result of quantum effects and inverted particle populations. However, the electrons participating in masing are bunched together in momentum space, such that the slight detuning (instability) of the ambient electric field stimulates the electrons to emit (or absorb) radiation in a way that leads to linear amplification of the emission as will be discovered in this section. The model for how the electron cyclotron maser operates is as follows (Chu 2004). We imagine a group of electrons orbiting in the z = 0 plane about a magnetic field locate at B0ez. The electron velocities have two components: an axial component (along ez) and a transverse component (in the x-y plane). These electrons are perturbed by a right circularly polarized electromagnetic wave, with E and B of constant magnitude, propagating along ez. This wave has fields described by

= cos( ) + sin( ) (2.11)

⊥ 0 푧 풙 푧 풚 퐸 = 퐸 � 휔푡sin−( 푘 푧 풆 ) +휔푡cos−( 푘 푧 풆 � ) (2.12) 푘푧푐 ⊥ 0 푧 풙 푧 풚 We can define an effective퐵 cyclotron휔 퐸 phase�− angle휔푡 − by푘 푧 풆 휔푡 − 푘 푧 풆 �

= + (2.13) 푑 Ω푒

Ω푒푓푓 푑푡 휙푒푓푓 ≅ 푘푧푣푧 훾

47 The effective phase angle allows us to compare the gyrating frequency and axial motion of the electrons with the rotating frequency and axial propagation of the incident wave. The effective phase angle allows us to completely represent when the electron motion and wave propagation are synchronized. Resonance and synchronism occur when

= (2.14)

푒푓푓 The electrons are perturbed from휔 their Ωzero-order orbits in the z = 0 plane by two main mechanisms: azimuthal bunching and axial bunching. Examining Figure 2.06, we wish to examine the behavior of the electrons separated by the y axis. For –π/2 < ΔΦeff < π/2, > 0, and considering the effect of the electric field on the electrons, < 0, so that the electrons ⊥ ⊥ lose energy. This has the relativistic effect of reducing the Lorentz factor, and thus the푣 relativistic∙ 퐸 masses of the electrons are decreased, resulting in a phase advance푭 a∙s푣 given⊥ by equation 2.13. Similarly, electrons on the opposite (left-hand side) of the circle experience a phase lag for the opposite reason. The net effect is that the electrons are bunched together.

Figure 2.06. The bunching of electrons in the effective cyclotron phase space due to rf electric forces. Electrons with –π/2 < ΔΦeff< π/2 lose energy, while those on the opposite side of the phase circle gain energy. The bunching forces the electrons to move toward the point marked “center of bunch.” Source: Chu (2004).

For azimuthal bunching that occurs with , emission of radiation occurs, while results in the absorption of energy. 푒푓푓 Now we turn our attention to Figure 2.07.Ω Considering≤ 휔 the Lorentz force, we know that 푒푓푓 onΩ the≥ right휔 -hand side of the circle, > 0, thus × = and F=-evBez, resulting in a downward drift. For the left-hand side of the circle, similar reasoning allows us to determine that an upward drift occurs. 풗⊥ 풗⊥ 푩⊥ 푣퐵풆풛

48

Figure 2.07. The bunching of electrons in the effective cyclotron phase space due to × forces. Electrons with –π/2 < ΔΦeff< π/2 experience deceleration in the axial direction, while those on the opposite side of the circle experience accelaration. The net effect is for the 풗electrons⊥ 푩⊥ to bunch at the location marked. Source: Chu (2004).

The result is axial bunching such that for , absorption of radiation occurs, while , results in the emission of energy. The conditions that give rise of azimuthal and axial 푒푓푓 bunching then, give rise to competition between theΩ two≤ processes.휔 푒푓푓 Ω ≥ The휔 linear equations of motion become

( ) = × ( + ) (2.15) 푑 푒 푑푡 훾푚푒풗 −푒푬⊥ − 푐 풗 퐵0풆풛 푩⊥ = cos ( ) (2.16) 푑 푒퐸0푣⊥ 2 푑푡 훾 − 푚푒푐 휔푡 − 푘푧푧 − 휙 = 1 cos ( ) 2 (2.17) 푑 −푒퐸0 푣⊥ 푘푧푣푧 2 푑푡 푣⊥ 훾푚푒 � − 푐 − 휔 � 휔푡 − 푘푧푧 − 휙 = 1 sin ( ) (2.18) 푑 Ω푒 푒퐸0 푘푧푣푧

푑푡 휙 훾 − 훾푚푒푣⊥ � − 휔 � 휔푡 − 푘푧푧 − 휙 = cos ( ) (2.19) 푑 −푒퐸0푣⊥ 푘푧 푣푧 2 푑푡 푧 훾푚푒 휔 푐 푧 The energy transfer푣 mechanisms� are −summarized� 휔푡 by− Table푘 푧 −2.01.휙 It should be noted that in order to conserve axial angular momentum, a variation in γ resulting from a variation in also alters vz. A distinction is made between the bunching mechanisms: some are inertial bunching and others are force bunching. Inertial bunching mechanisms affect the system 풗⊥ indirectly, either through γ or vz. Even after the force is terminated, the perturbation will continue to grow. Force bunching mechanisms directly result from the driving force; once the force is removed, the perturbation stops as well.

49

Driving Relevant Modulated Phase Physical Effect on Force Equation Quantity Bunching Nature Energy Transfer tangential 2.16 γ Azimuthal Relativistic; Stimulated to inertial cyclotron 푬⊥ bunching emission ⊥ 풗× 2.19 vz Axial Nonrelativistic; Stimulated inertial cyclotron 풗⊥ 푩⊥ bunching emission normal to 2.18 Centripetal Azimuthal Nonrelativistic; Cyclotron acceleration force bunching resonance 푬⊥ absorption ⊥ 풗 tangential 2.17 Axial Nonrelativistic Cyclotron to resonance 푬⊥ 풗⊥ absorption Table풗⊥ 2.01. Summary of electron cyclotron emission and absorption processes. Source: Chu (2004).

In plasmas, the bunching mechanisms can be triggered by plasma instabilities. Solutions to the dispersion relations are = + . The instabilities (ωi) only occur in regions where the condition for resonance and synchronism occur. The dispersion relations휔 for휔 the푟 electron푖휔푖 cyclotron maser mechanism give rise to various modes of electromagnetic waves both along and perpendicular to the magnetic field. The vast majority of the maser emission detected in the AKR is in the free space, right-circularly polarized RX mode. Some left-circularly polarized OL mode (also emitted perpendicular to the magnetic field) and right circularly polarized RZ mode (emitted parallel to the magnetic field) emission are also present, but at much smaller magnitudes. Thus, we will restrict our discussion to these alone (Treumann 2006). The above treatment applies to a cold, monoenergetic particle distribution only, and so serves as a useful model for the initial linear state of a plasma. In reality, this model needs to be extended via loss-cone and shell distribution models, which will be discussed briefly in the following paragraphs. Instead of electrons having a single energy, in any physical environment they will have an energy distribution, which in the case of the lose-cone maser, takes on the following form (Treumann 2006):

( , ) = ( ) exp (2.20) ( )2 2푗 −푝 2 푓0 푝⊥ 푝∥ 퐴 푝⊥ � ∆푝 � where represents the component of electron momentum parallel to the magnetic field, A is a normalization constant, and j > 0, defines the loss cone index. Such a distribution is depicted in Figure 푝2.08,∥ and is characterized by the absence of electrons at small pitch angles (Dory et al. 1965), resulting in a cone structure in velocity space indicating where electrons are removed. This distribution of electrons is warm and at least weakly relativistic. It only operates when < , and specifically when the ratio of plasma frequency to cyclotron frequency is between 0.2 and 0.8. The larger j is, the wider the loss cone, and the more efficient the operation 푝푒 푐푒 휔of the maser.휔 Yet, the maximum width of the loss cone can be no more than 40° between sides of the loss cone, and the center of the cone must be perpendicular to the magnetic field. Also, for

50 the maser to operate, the electron temperature must exceed a certain value or absorption dominates rather than emission.

Figure 2.08. Diagram of the loss cone electron distribution function. The loss cone is the triangular region at the left of the distribution, where almost no electrons exist. The darker ellipse near the loss cone represents the resonance ellipse for loss cone masing. Source: Treumann (2006).

In the case of the Earth, a loss cone effect is caused by the atmosphere, which absorbs electrons at shallow pitch angles. These electrons then are removed from the distribution. However, detailed numerical simulations by Pritchett (1986) showed that the loss-cone emission mechanism was rather inefficient, and hence, could not describe the in situ measurements made of the AKR. Simply too few electrons have a positive perpendicular velocity space gradient and participate in the process before they are lost, thus, a different distribution needs to be considered. The next such distribution is the ring-shell distribution. The energy distribution of a cold ring-shell distribution is given by (Treumann 2006):

( , ) = ( ) ( ) (2.21) 1

푓0 푝⊥ 푝∥ 2휋푝⊥ 훿 푝⊥ − 푝푅 훿 푝∥ In this equation, pR denotes the ring momentum, which is ~0.4c. and are the parallel (along magnetic field) and perpendicular electron momenta, respectively. This can be extended to three dimensions to provide the complete shell energy distribution function푝∥ given푝⊥ by:

( , ) = ( + ) (2.22) 1 2 2 2 푓0 푝⊥ 푝∥ 2휋푝푆 훿 푝⊥ 푝∥ − 푝푆 where pS denotes the shell momentum and is of similar magnitude to pR.

51

Figure 2.09. The ring and shell electron distributions. The ring distribution is at left (a) and the shell distribution at right (b). The ring distribution may smear out and become a shell distribution, hence it being referred to sometimes as a “ring-shell” distribution. Source: Treumann (2006).

The instability condition, for which the masing process begins, is

1 > 2 (2.23) 1 휔푝푒 2 푅 4 휔푐푒 for the ring distribution and 훾 −

1 > 2 (2.24) 3 휔푝푒 2 푠 8 휔푐푒 for the shell distribution, where 훾 −

= 1 + 2 (2.25) 푝푖 2 2 훾푖 � 푚푒푐 and i can be either r or s distributions. Both distributions undergo exponential growth during amplification, but the intensity and growth rate is faster for the ring-shell distribution due to its smaller symmetry, and hence, lower stability. The growth factor saturates at 6% perpendicular emission for the ring distribution and 3% for the complete shell distribution. The growth appears to be triggered once large enough values for the perpendicular electron momenta in the distributions are achieved. For these distributions, the result is that the emission is confined to the RX emission mode with fundamental emission beneath the electron cyclotron fundamental emission frequency. For large emission angles from the perpendicular, the behavior again mirrors that of the loss-cone distribution, in that no significant emission escapes at angles less than 70° from the direction along the magnetic field lines (yielding a cone width of ~40°).

52 In the context of Solar System magnetized planets, and presumably, exoplanets, and possibly, ultracool dwarfs, it should be noted how the ring/shell distributions are altered by their surrounding environments. For these magnetized objects, there is a global magnetic field, which is dipolar in structure, although it may have multipolar structure, and local fields of smaller magnitude. In the polar (auroral) regions, an electric potential gradient exists between the upper atmosphere and the magnetosphere. This electric potential difference creates an electric field, which points away from the magnetized object. This electric field creates auroral cavities (at least, for the best studied case, the Earth) by accelerating electrons downward and ions upwards. This arrangement is displayed in figure 2.10.

Figure 2.10. Generation of magnetic field-aligned electric currents. Magnetic field lines are along the narrow reddish-orange lines pointing downward, which also denote upward flowing electrons. The magnetic field-aligned electric fields caused by = , are shown in blue and point upward away from the magnetized object (planet, exoplanet, ultracool dwarf, star). Electrons flow downward toward the ionosphere in these regions,푬 creating−∇Φ auroral cavities. The converging perpendicular E┴ arrows give rise to the Pedersen currents (horizontal red arrows) that close the current loop. Green dotted lines denote negative potential regions, while solid green lines denote positive potential regions. The increased ionospheric electron density due to this phenomenon is shown in dotted red lines in the lower part of the figure. Source: Treumann (2006).

53 At the time that the plasma encounters the electric field and becomes rarefied, the plasma frequency drops and the electron cyclotron maser may function. Electrons that bombard the atmosphere ionize atmospheric gases and gives rise to the aurora. This description of the environment of a magnetized planet with its global dipolar field and field-aligned electric current was considered by Chiu and Schulz (1978). In this environment, near the poles magnetic field lines bundle together and create a magnetic mirror. They found that in these polar regions, the ring/shell distributions were deformed into a “horseshoe” distribution. Low temperature electrons were excluded from the distribution while more energetic electrons were accelerated by the magnetic mirror and deflected to higher pitch angles in accordance with the adiabatic invariant.

Figure 2.11. Generation of the horseshoe distribution. At left, the converging parallel electric field lines accelerate electrons, yet also deflect their momenta to greater perpendicular momenta values. This phenomenon results in the horseshoe electron distribution, represented in velocity space at right. The red circle denotes the horseshoe resonance line, while the green arcs display the loss cone resonance lines. Source: Treumann (2006).

Within the auroral cavities, the picture can be very complex. Spacecraft measurements have indicated that the cavities are highly inhomogenous and have a number of smaller scale mechanisms which give rise to maser activity. One of these is that if two clouds of ions with opposing drift motions encounter one another, their electric fields will either converge or diverge. When this occurs, a plasma cavity is generated as an upward pointing ionic beam accelerates away from the merger, and a similar electron beam is accelerated downward. Another inhomogeneity is the presence of “electron phase space holes.” They are created when currents excite kinetic plasma instabilities that trap electrons in wave-electric potentials that have their own electron distribution functions. As these holes travel through space, they absorb and emit

54 radiation at slightly different frequencies. This gives rise to very fine structure in dynamic spectra of ECM emission, with frequency scales of ~1 Hz, and time scales of ~0.5 s. Some have questioned the efficacy of electron cyclotron maser emission in the context of a denser surrounding environment, most notably Melrose (1999). Two dimensional simulations of ECM emission in a plasma cavity suggest that at the boundaries, the RX mode may be transformed into the RZ mode, and then upon reaching less dense media, retransformed into the RX mode. The re-transformed emission is indeed attenuated, with some of the energy being diverted to the R mode, which moves parallel to the magnetic field lines. This conclusion is slightly different from previous work which had shown that at boundaries, the RX mode would transform into the LO mode (Pritchett et al. 2002). We have thus concluded our examination of the properties of the radio emission that comes from the various emission mechanisms. The two main contenders to explain the radio emission from planets and ultracool dwarfs have been explained in detail and we will examine the results of this dissertation in light of these two mechanisms alone. Clearly it can be seen from this description that polarization fractions and brightness temperatures provide powerful means to distinguish between the two types of radio emission observed in the that come from substellar objects.

55

Chapter 3

Instrumentation and Computation

In this chapter, we will examine the instrumentation and signal processing that were required to make this dissertation even possible. It should be emphasized that the success of this project was due in no small part to the great sensitivity of the Arecibo radio telescope, and the new Mock spectrometer, with its capability to process over 1 GHz of signal bandwidth at a time. Following an overview of this instrumentation, we will examine the software that processes the vast amount of data created from the radio surveys described in Chapters 4 and 5, and transforms them into exquisite data products of scientific value.

3.1. Observing Instrumentation

3.1.1. Arecibo Radio Telescope

The Arecibo radio telescope is the main feature of Arecibo Observatory, part of the National Astronomy and Ionosphere Center, located in Arecibo, Puerto Rico, USA. The telescope has been used for radar imaging of planetary surfaces and Near Earth Objects (NEOs), the timing of pulsars, the tracing of hydrogen within the , the measurement of magnetic fields, the study of radio-emitting molecules in space, and very recently, the observation of electron cyclotron maser emission from ultracool dwarfs. The Arecibo radio telescope is a 305-m fixed dish telescope and is the largest radio telescope in the world. It has the capability to observe between 47 MHz (λ = 6 m) and 10 GHz (λ = 3 cm). Suspended 137 m above the 305-m primary reflector, which has a geometry of a spherical cap, is a triangular platform. This platform contains a circular track upon which an azimuth arm rotates. Attached to this azimuth arm is a Gregorian dome that contains secondary and tertiary reflectors to focus incoming radio waves (Salter 2009). Due to its large collection area, the telescope is the most sensitive in the world. Its sensitivity, ΔS, is calculated by

= (3.01) 푛 2푘푇 ∆푆 퐴√퐵휏 Where k is Boltzmann’s constant, Tn is the system noise temperature, A is the effective area of the radio telescope, B is the observing bandwidth, and τ is the observation length in time (Burke & Graham-Smith 2010).

56 3.1.2. C-band Receiver

The C-band receiver operates in the frequency range of 3.95-6.05 GHz1. However, at any given time, there is only enough bandwidth to retrieve a maximum of 1.1 GHz from the receiver. The sensitivity of the system varies as a function of frequency. For our surveys, the frequency bandpass that we used was 4.239 GHz to 5.262 GHz, which has an accompanying sensitivity of ~ 8 K/Jy. The system temperature is approximately 25 - 30 K at this frequency range. The native polarization of the receiver is dual linear. The Half-Power Beam-Width (HPBW) is 1.15’ in azimuth x 1.18’ in zenith angle and a pointing accuracy of ~5.” The beam pattern, which varies as a function of observing frequency, may be examined in Figure 3.01.

1 http://www.naic.edu/~astro/RXstatus/Cband/Cband.shtml#basic

57

Figure 3.01. The Arecibo C-band receiver beam pattern. The four rows represent the beam pattern as depicted at 4500, 4860, 5000, and 5400 MHz, from top to bottom. The left panels show the percent instrumental efficiency and the right panels depict 2D cross-sections of the beam in units of arcseconds. Notice the inefficiency of the side lobes relative to the main beam (Salter, personal communication).

58 3.1.3. Wideband Arecibo Pulsar Processor

The Wideband Arecibo Pulsar Processor (WAPP) spectrometer was the first spectrometer we used for any of the data collection in this entire dissertation. The WAPP features an 8 bit A/D converter and has 1.5 bit (3 level) and 3.125 bit (9 level) quantization2. The WAPP spectrometer allows for the recording of data spanning 800 MHz, divided into 8 subcorrelators, consisting of 100 MHz each. Since the subcorrelators are arranged to provide frequency coverage between 4300 MHz and 5300 MHz, there is incomplete frequency coverage for this bandwidth. Thus, subcorrelators 1-8 cover the following frequencies: 4300 - 4400 MHz, 4425 - 4525 MHz, 4550 - 4650 MHz, 4675 - 4775 MHz, 4825 - 4925 MHz, 4950 - 5050 MHz, 5075 - 5175 MHz, and 5200 - 5300 MHz. Each subcorrelator has 2048 channels, offering 48.8 KHz frequency resolution. All four Stokes parameters, I, Q, U, and V are recorded simultaneously. The data were recorded in 10-minute scans that are binned to 1.0 s data resolution.

3.1.4. Mock Spectrometer

The MOCK spectrometer replaced the WAPP spectrometer in 2009. It is an FFT spectrometer featuring 2 x 7 processors with 12-bit A/D sampling. It has 14 field-programmable gate arrays (FPGA) distributed such that each of seven spectrometer boxes has two: one for high band, one for low band3. During single-pixel mode observing as is done during this project, only the high band FPGAs are used. The cross correlation of two boards per box (frequency band) allows for a determination of the four Stokes parameters of the signal coming from the source. Each of the seven boxes measures 172.032 MHz of bandwidth and their distribution across the C-band receiver frequency range is such as to provide complete coverage between 4200 – 5300 MHz. The boxes overlap in frequency coverage, but the seven boxes have the following bandpasses: 4239 - 4411 MHz (box 0), 4380 - 4552 MHz (box 1), 4522 - 4694 MHz (box 2), 4664 - 4836 MHz (box 3), 4806 - 4978 MHz (box 4), 4948 - 5120 MHz (box 5), and 5090 - 5262 MHz (box 6). Each box contains 8192 channels, offering 20.9 KHz frequency resolution. This division of the 173 MHz bandpass into 8192 channels is accomplished with a low pass digital filter with a polyphase filter bank that improves separation among channels. The native time resolution of each Mock spectrometer box is 190.47 µs for 8192 channels. For our purposes, all MOCK data were recorded in 10-minute scans, sampled every 0.1 s, as this represented a good compromise between fast sampling and instrumental sensitivity.

2 http://www.naic.edu/~wapp/ 3 http://www.naic.edu/~phil/hardware/pdev/singlePixelSpecs.html

59 3.2. Signal Processing and Computation

3.2.1. Calculation of Stokes Parameters

For radio telescopes, polarization information is determined by measuring one of two pairs of orthogonal polarization states, either perpendicular linear polarization states, or right and left-circularly polarized states. Once these are received from the antenna as two distinct outputs, they are passed through phase-stabilized amplifiers before being processed to derive the Stokes parameters (Burke & Graham-Smith 2010). The conversion to Stokes parameters is straightforward. For two perpendicular linear polarizations, the parameters are formally calculated by:

2 2 I = 2 2 Q = (3.02) U = <2ExEy cos Δφ> V = <2ExEy sin Δφ> while for two orthogonal circular polarizations it is calculated by:

I+V = Q+iU = (3.03) Q-iU = I-V =

In reality, the computation of the Stokes parameters from the two orthogonal linear polarizations in the C-band receiver is done somewhat differently (Mock 2009). The hardware computes four scalar values:

S0 = 2 Ex x Ex* S1 = 2 Ey x Ey* (3.04) S2 = 2 Re(Ey x Ex*) S3 = 2 Im(Ey x Ex*)

which are then manipulated into the desired Stokes parameters:

I = (1/2) (S0+S1) Q = (1/2) (S0-S1) (3.05) U = S2 V = S3

60 3.2.2. Description of Data Products

WAPP spectrometer data products were provided to us calibrated. Each data set contained 600 s of data from each of 8 subcorrelators. These data sets are 157 MB in size and consist of floating point numbers stored in a binary file. Mock spectrometer data sets are typically 751 MB in size per box, for one ten-minute scan of a source and stored in FITS files. During observing, seven boxes of data are collected simultaneously. In between data sets, there is a 10-second calibration-on scan followed by a 10- second calibration-off scan, which together generate another 26 MB of data. This results in a data accumulation rate of nearly 32 GB/ hour. The data are un-calibrated and while most of the data consists of floating point numbers, the timing information is provided in double precision numbers. We have acquired nearly 4.4 TB of raw data during the A2471 and A2623 radio surveys (Chapters 4 and 5) as well as during observing campaigns of objects of interest (Chapter 6).

3.2.3. Data Processing Pipelines

3.2.3.1. Overview

The data processing capabilities that I will describe here have been developed in the Interactive Data Language (IDL). This was chosen for a number of reasons, including: it is in use at Arecibo Observatory and selecting to use this same language could be useful in terms of program interoperability, it is a standard programming language of the astrophysical and planetary science communities, and its vectorization facilitates mathematical operations on matrices. Two data processing pipelines were devised for this project. The first data processing pipeline (ARECIBO) was developed to remove trends and clean up reduced data from the WAPP spectrometer. This data were stored in binary data files that contained a 3D matrix of flux density values (in Jy) where the dimensions of the data cube were channels x Stokes parameters x time samples. This pipeline also included the production of graphical results, such as time series plots and dynamic spectra (time-frequency spectrograms). To facilitate the discovery of burst features, a GUI was added, called Arecibo Graphical Analysis Tool and Ensemble (AGATE). When the Mock spectrometer became available, the ARECIBO pipeline was subtly adjusted to allow for processing of either WAPP data sets or Mock spectrometer data sets. With the initiation of the 2010 A2471 survey (Chapters 4 and 5), we began using the Mock spectrometer, thus, a new pipeline was constructed. The MOCK pipeline takes un- calibrated raw data from the Mock spectrometer and calibrates it. This raw data is a collection of floats stored in a data cube with dimensions 8192 channels x 2 polarizations x 5994 time samples. The end product is a header file and binary data file containing 8192 channels x 4 polarizations x 5994 time samples that can be directly placed into the previous data pipeline; thus, its output data is in the same format as the WAPP data files. Arecibo Observatory’s software engineer, Phil Perillat, guided the development of this pipeline. Additionally, algorithms were added to the ARECIBO pipeline to allow for the automated removal of radio frequency interference (RFI) and

61 the generation of multiple diagnostic files including those related to azimuth and zenith angle and statistics on the sensitivity of the various boxes. Further graphical results were also added. In total, nearly 6,700 lines of code have been written to accomplish all of this. Roughly 40% of those lines are required by the MOCK calibration pipeline, 40% are used by the ARECIBO pipeline to permit de-trending, RFI removal, and graphics production, and the final 20% is used by the AGATE GUI.

3.2.3.2. The MOCK Pipeline

The MOCK pipeline is primarily used to take raw data directly from the Mock spectrometer, calibrate it, and compute the four Stokes parameters from it. The first task is to read the science, calibration-on, and calibration off data files from the hard disk. The raw data provide information about the temperatures of the two linear polarizations and the correlation of these temperatures. Then, the calibration files are used to determine the channel-by-channel response of the spectrometer, normalize these, and remove the artifacts that result from edge effects. After this bandpass correction has been accomplished, the data are scaled and the four Stokes parameters computed. The next step then is to compute a linear fit to the phase information and correct it. Next, based on altitude and azimuth information from the files, receiver gain values are calculated. These are then used to convert the data values from temperature values to flux density values. These flux density values are then written to disk and a header file containing everything needed for subsequent ARECIBO processing trimmed and produced.

3.2.3.3. The ARECIBO Pipeline

The ARECIBO pipeline is a collection of routines that extract useful science from properly calibrated data files from both WAPP and Mock spectrometers. First, it reads in the calibrated data file and accompanying header file. As the header file contains information about frequency array structure, this is created as well. Next, data is integrated in time and frequency domains, if desired. Usually Mock data is too noisy to operate on at its native resolution, so it is then integrated such that 4 frequency channels and 9 temporal samples are combined into one data value, for each Stokes parameter. This combination of data values has an averaging effect on flux density across the samples. The pipeline continues then by “de-trending” the data, which removes instrumental artifacts in the time and frequency domains. This is very important because even though the data are calibrated to a local oscillator, the radio data contains large fluxes from the system temperature which need to be removed. A polynomial of the following form is subtracted in both time and frequency domains:

= (3.06) ′ 푛 푗 푖 푖 푗=0 푗 푖 where yi’ is the “de-trended” data value, y푦i is the푦 original− ∑ data푎 푥 value, n is the order of the j polynomial, aj is the coefficient to the de-trending solution for the particular exponent j, and xi is time sample number or the frequency channel number that corresponds to yi. Typical values for

62 which the de-trending appears to yield the best results are n = 2 and n = 4, with n = 4 working best due to the pseudo-sinusoidal Stokes I intensity variations that are characteristic of the system. The computation of the best-fit polynomial to the data is determined in a least-squares fashion. The de-trending procedure also contains the means to smooth the data in time and frequency. At this point, the pipeline iteratively removes RFI. It passes through the data three times, removing two types of RFI. The first type removed is where a channel is always bad and has permanent RFI. The second type that is removed occurs when there are transient burst of RFI, from satellite signals, cell phones, airplanes, etc. In both cases, the RFI is detected in a statistical sense and replaced with mean noise values. In the midst of this iterative process, the de-trending algorithm is repeated and sinusoidal variations (common in Stokes I at Arecibo) may be fitted and removed. With this processing completed, now data products are generated. These include:

• Data on how the altitude and azimuth vary with time, used to make sure the telescope was on source and also used to diagnose whether Stokes I bursts may be related to ground reflectivity. • Summary statistics, used to calculate the standard deviation (noise) from the data set. • Time series information for Stokes V and Stokes I. • Dynamic spectra (time-frequency spectrogram) images. • Images that merge the time series data with the dynamic spectra, as will be seen in Chapters 4, 5, and 6.

As a final tool, the Arecibo Graphical Analysis Tool Ensemble (AGATE) graphical user interface was developed, as shown in Figure 3.02. In the initial stages of processing, this tool was very useful to interactively operate on data to attempt to find which parameters were consistently the best for data processing. Nowadays, with the optimal parameters determined for signal processing, it is obsolete.

Figure 3.02. The AGATE (Arecibo Graphical and Analysis Tool Ensemble) GUI in action. Here, the 2008-12-29, Scan 13 of TVLM 513 is depicted. In the dynamic image, a band of left- circularly polarized emission is faintly apparent as a horizontal darker region. In the line graph, it is more visible.

63 3.2.4. Computational Results

The computational results for the MOCK and ARECIBO pipelines can be found in Tables 3.01 and 3.02.

Number of Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Mean Standard Elements (s) (s) (s) (s) (s) (s) Deviation (s) 1.96 x 108 45.478 54.965 55.39 55.268 55.017 53.22 4.33 9.82 x 107 26.083 26.12 28.339 26.346 26.069 26.59 0.98 4.91 x 107 15.856 15.823 15.831 15.856 15.842 15.84 0.01 Table 3.01. Computational results from the MOCK processing pipeline.

Number of Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Mean Standard Elements (s) (s) (s) (s) (s) (s) Deviation (s) 1.96 x 108 810.562 824.211 717.297 811.3 807.47 794.17 43.45 1.96 x 107 92.005 73.947 68.424 68.21 82.879 77.09 10.24 1.96 x 106 9.768 9.692 9.195 9.26 9.244 9.43 0.27 Table 3.02. Computational results from the ARECIBO processing pipeline.

The runtime for the MOCK calibration pipeline is entirely acceptable for the amount of processing that occurs. It appears to scale approximately linearly with the number of elements evaluated. About 90% of the runtime is used by the procedure that performs the data calibration into units of flux density and computes the four Stokes parameters. The runtime for the ARECIBO pipeline is acceptable for small data sets, but becomes very large for large data sets. Nearly 80-90% of the runtime is absorbed by two procedures. The procedure that integrates the data in time and frequency at the user’s request uses nearly 40% of the runtime for small-medium sized data sets and 30% for large data sets. The routine that performs baseline subtraction and smoothing operations in the time and frequency domains, accounts for 40% of the runtime for small-medium data sets and 55-60% of the runtime for large data sets. In my measurements of runtime, one of the glaring deficiencies of using IDL was its lack of use of multiple cores. IDL advertises “thread pool” functions, which use multiple CPUs to speed up certain calculations. However, analysis of CPU usage suggests that thread pool functions are used less than 10% of the time for most of the software, with the exception of the integration function, which is completely dependent on thread pool function total. It is interesting to note how few IDL functions use the thread pool; in this project despite attempting to multithread wherever possible, only dindgen, findgen, min, max, total, and where are used. The most computationally expensive part of the pipelines, de-trending and baseline subtraction, which feature for loops that involve polynomial fitting and baseline subtraction, are not helped in any way through the availability of multiple cores via the thread pool (i.e. the loops are not unrolled despite being “embarrassingly parallelizable”). Should these pipelines be used much more extensively in the future than today, it may be worthwhile to migrate certain portions of the software to C or C++ to improve computational performance, and to combine these translated components with OpenMP or MPI to achieve a greater degree of parallelization. Additionally, given the constraint that IDL will not use virtual memory, future software development projects may consider using Matlab and C++

64 instead, should sampling rates and data set size outstrip the increase in available research computing memory. However, these modifications were not made during this research project for a number of reasons. First, the data processing runtime is completely acceptable and is not the rate-limiting step for analysis; the acquisition and retrieval of data from Arecibo Observatory is. Second, the issue of maintaining program operability with Arecibo Observatory is a valid concern as the expansion of this observing program or the exchange of software or personnel between Arecibo Observatory and Pennsylvania State University would necessitate a common programming language. Third, neither C nor Matlab are widely used in the astronomical community.

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Chapter 4

The Arecibo Survey for Radio Emission from Exoplanets

4.1. Motivation

In Section 1.3.3, we noted that there have been a number of attempts to detect radio emission from exoplanets. The impetus for doing so is that while radio emission from an exoplanet has never been detected before, it could reveal interesting physics about the exoplanet itself. From the radio emission, we could potentially learn about the magnetic field strength of the objects and study their plasma environments. A single detection of radio emission from an exoplanet would serve as a useful guide for searching for others, by showing us at what frequency and what flux density emission may be typical. The detection of a single exoplanetary magnetic field would also help to guide theoretical work on the nature of exoplanetary interiors, in terms of dynamo generation and structure. We have seen that theories are already in place that examine how to generate exoplanetary magnetic fields and at what strength they could possibly be found (Lazio et al. 2004; Christensen et al. 2009; Reiners & Christensen 2010), as well as that describe how radio emission may be powered (Grieβmeier et al. 2007). However, at the time of the initiation of our survey, there were no detections of radio emission from exoplanets despite a number of attempted surveys (Lazio et al. 2010 and references therein), and now at the writing of this dissertation, only hints of marginal detections (Lecavelier des Etangs et al. 2011; Lecavelier des Etangs et al. 2013). Given these theoretical models of the functioning of magnetic dynamos and the predicted magnetic field strengths, it seemed plausible that the HR 8799 planetary system could be detectable at high radio frequencies. The HR 8799 system is thought to be a < 100 million year old system featuring four detected high-mass planets, with masses of 5MJ to 40 MJ each, depending on the age of the system. Given their high temperatures (~800 K – 1,100 K), their bolometric luminosities are relatively large and they may have more internal energy than typical to power a magnetic field. Due to the uncertainties in Figure 1.09, and that the objects have brown dwarf-like luminosities (Oppenheimer et al. 2013), it seemed possible that the planets may emit at an observing frequency that we are sensitive to, even though a previous search of the system for radio emission using the Jansky Very Large Array (Osten 2011) did not detect anything. This system would be our prime target and we would search for radio emission from other exoplanets based on the following reasoning. Perhaps the theoretical magnetic field evolution models warrant a degree of skepticism since they lacked much observational guidance and could not adequately predict the magnetic field strengths of several of the known magnetized planets. The magnetic field strength of Jupiter was known to be 14 G at the poles (Bagenal & van Allen 1999), with the magnetic fields of Mercury, Earth, Saturn, Uranus, and Neptune known as well, although considerably weaker in magnitude (de Pater & Lissauer 2010). While dynamo models predicted the strengths of the terrestrial and Jovian magnetic fields quite well, they failed miserably for Saturn, and were simply not applicable to Mercury and the ice giants Uranus and Neptune. These objects provided the lower bounds on magnetic field strength. The upper bounds on magnetic fields strengths were

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provided by brown dwarfs, the coolest of which, L3.5 dwarf 2MASS J0036159+182110, still maintained a ~1.7 kG field (Hallinan et al. 2008) and was mentioned in Chapter 2. Based on observational evidence alone, the magnetic field strengths of exoplanets, then, should exist somewhere in between. Alternatively, an exoplanet’s magnetosphere could induce magnetic activity in its parent star that would result in detectable radio emission (Cuntz et al. 2000). This effect would be similar to the known cases of magnetic interaction, including RS CVn stars and ML-dwarf binaries (Dempsey et al. 1993; Silvestri et al. 2006; Berger et al. 2009). If this magnetic interaction gave rise to local active regions at the stellar surface, they could presumably result in strong local magnetic fields analogous to those that accompany sunspots. The darkest regions of sunspots, pores and umbrae, have measured magnetic field strengths of 1.5 – 3.5 kG (Penn & Livingston 2010). If induced active region magnetic fields were similar to solar ones, then nonthermal particle acceleration in the vicinity of these active regions would be detectable by our instruments. Given these reasons, we searched for emission from exoplanets using the criteria that will be described in the next section. We desired to look for signs of exoplanetary magnetism by two methods: the observation of electron cyclotron maser instability (ECMI) emission or significantly (> 10%) circularly polarized gyrosynchrotron emission from the exoplanets themselves, and the same types of radio emission from the parent star that was induced by the presence of the exoplanet’s nearby magnetosphere. By conducting our search with the Arecibo Radio Telescope, we would use the most sensitive radio telescope in the world, which, with the Mock spectrometer, featured the most advanced backend available, providing much greater bandwidth over which to simultaneously search for radio emission. Through leveraging these technological advancements, we hoped to discover the first radio emission from an exoplanet.

4.2. Target Selection and Observations

To conduct the survey, a list of targets was constructed using a number of selection criteria, which are given in order of decreasing importance. First, targets were selected that could be easily observable from the radio telescope at Arecibo Observatory, as we wish to leverage its impressive sensitivity. However, as the giant 305-m dish is fixed, this restricted our choice of targets to of 0 to +38°. Second, targets were chosen that are < 50 pc from Earth, to try to observe sources with great enough flux for detection. Third, sources with greater masses were selected so that they would have greater internal energy, both from gravitational contraction and from the nuclear decay of radioactive isotopes (Christensen et al. 2009). Fourth, planets that were close to their parent stars were chosen, and so they had smaller semi-major axes. Such planets would encounter a greater stellar wind flux and should have more energy transferred to their magnetospheres to power stronger radio emission (Reiners and Christensen 2010). Due to the small number of planets given the first two selection criteria, the constraints for additional targets were loosened somewhat so that a large enough sample could be developed. Two of these exoplanet systems are especially noteworthy. The first is the HR 8799 system, which consists of young, hot planets and was a motivating factor for our survey. The second system, which contains HD 114762b, is also worthy of mention since historically, its mass M sin i ~ 11 MJ (Latham et al. 1989) is rather high for an exoplanet and due to orbital inclination effects, the source may actually be a brown dwarf. If this is the case, a radio survey may reveal an unusually strong magnetic field that would suggest this.

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A table describing the properties of the selected observing candidates is shown in Table 4.01.

Name R.A. Dec. Mass Host Semimajor Distance Bolometric (hh mm ss) (deg mm ss) (MJ) Star Axis (pc) Luminosity Type (AU) Log ( ) HD 10697b 01 44 55 20 04 59 6.12 G5 2.13 32.56 -7.5 푳⨀ epsTau 04 28 37 19 10 50 7.6 K0 1.93 45 -7.5 HD285968 04 42 56 18 57 29 0.0265 M2.5 0.066 9.4 -12.0 V HD38529 05 46 34 01 10 05 12.7 G4 3.68 42.43 -6.8 HD46375 06 33 12 05 27 46 0.249 K1 IV 0.041 33.4 -11.0 HD50554 06 54 42 24 14 44 4.9 F8 2.38 31.03 -7.7 55Cnc d,e 08 52 37 28 20 02 3.835, G8 V 5.77, 0.038 13.02 -8.0 0.034 GJ436 11 42 11 26 42 23 0.072 M2.5 0.02872 10.2 -12.0 HD102195 11 45 42 02 49 17 0.45 K0V 0.049 28.98 -9.5 HD106252 12 13 29 10 02 29 6.81 G0 2.61 37.44 -7.4 HD 114762 13 12 19 17 31 01 11 F9V 0.363 40.6 -7.0 70Vir 13 28 26 13 47 12 7.44 G4V 0.48 22 -7.3 HD 178911b 19 09 03 34 35 59 6.292 G5 0.32 46.73 -7.5 HD189733 20 00 43 22 42 39 1.13 K1- 0.03099 19.3 -9.0 K2 HD195019 20 28 17 18 46 12 3.7 G3 0.1388 20 -8.0 HD 209458b 22 03 10 18 53 04 0.685 G0 V 0.04707 47 -9.5 51 Peg 22 57 27 20 46 07 0.468 G2 IV 0.052 14.7 -9.5 HR 8799 23 07 29 21 08 03 5- 40, kA5 68,38,24,15 39.4 -5.1 b,c,d,e each hF0 mA5 V; λ Boo Table 4.01. The exoplanet survey targets. The object HD 114762 may be an exoplanet or a brown dwarf given its high mass, and is truly on the boundary between these objects. The HR 8799 is a young system featuring multiple hot planets, with host star information provided by Gray & Kaye (1999) and planetary data from Marois et al. (2008, 2010). Planetary luminosities for the other sources represent their intrinsic luminosities and are inferred from Baraffe et al. (2003).

These exoplanets were observed as part of Arecibo Observatory observing program A2471, conducted from January 2010 to September 2011. Half of the targets surveyed were brown dwarf targets, which will be discussed in Chapters 5 and 6. The observing log for these observations is given in Table 4.02. Every source was observed for at least one hour in total.

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Source Date Scans Time on Center Bandpass Beam Size Source Frequency (MHz) (arcmin) (ks) (MHz) epsilon Tauri 20100108 7 4.2 4750 4239-5262 1.15 x 1.18 20101217 4 2.4 4750 4239-5262 1.15 x 1.18 20101220 4 2.4 4750 4239-5262 1.15 x 1.18 51 Pegasi 20110718 7 4.2 4750 4239-5262 1.15 x 1.18 20110907 5 3 4750 4239-5262 1.15 x 1.18 55 Cancri 20110102 8 4.8 4750 4239-5262 1.15 x 1.18 GJ 436 20100106 6 3.6 4750 4239-5262 1.15 x 1.18 HD 10697 20101220 4 2.4 4750 4239-5262 1.15 x 1.18 HD 38529 20100108 6 3.6 4750 4239-5262 1.15 x 1.18 HD 46375 20100109 5 3 4750 4239-5262 1.15 x 1.18 20100110 1 0.6 4750 4239-5262 1.15 x 1.18 HD 50554 20100108 2 1.2 4750 4239-5262 1.15 x 1.18 20100109 1 0.6 4750 4239-5262 1.15 x 1.18 20101218 8 4.8 4750 4239-5262 1.15 x 1.18 20101219 4 2.4 4750 4239-5262 1.15 x 1.18 HD 102195 20100107 6 3.6 4750 4239-5262 1.15 x 1.18 HD 106252 20100107 6 3.6 4750 4239-5262 1.15 x 1.18 HD 114762 20100107 1 0.6 4750 4239-5262 1.15 x 1.18 20110102 7 4.2 4750 4239-5262 1.15 x 1.18 HD 178911 20110719 7 4.2 4750 4239-5262 1.15 x 1.18 HD 189733 20110906 12 7.2 4750 4239-5262 1.15 x 1.18 HD 195019 20110719 10 6 4750 4239-5262 1.15 x 1.18 HD 209458 20110719 6 3.6 4750 4239-5262 1.15 x 1.18 20110906 7 4.2 4750 4239-5262 1.15 x 1.18 HD 285968 20100109 6 3.6 4750 4239-5262 1.15 x 1.18 20101218 5 3 4750 4239-5262 1.15 x 1.18 HR 8799 20101217 12 7.2 4750 4239-5262 1.15 x 1.18 20101218 9 5.4 4750 4239-5262 1.15 x 1.18 20100106 7 4.2 4750 4239-5262 1.15 x 1.18 Table 4.02. Exoplanet radio observations for Arecibo observing program A2471. For this survey, we attempted to observe all sources for approximately one hour. The date format is YYYYMMDD.

The data were collected with the C-band receiver onboard the Arecibo radio telescope and recorded with the Mock spectrometer, in 10 minute scans, with 0.1 s temporal resolution and 21 kHz frequency resolution. In between scans, a calibration on scan of a local oscillator, followed by a calibration off scan were recorded. The data were then processed via the MOCK calibration pipeline and the Arecibo data analysis and products pipeline as discussed in Section 3.2.

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4.3. Results

Not a single exoplanet was detected with this survey; however, given our detection sensitivity, we may place upper limits on how much radio emission they may emit at the monitored center frequency of 4.75 GHz. The only interesting radio emission that was detected for the exoplanet portion of the survey is structure as shown in Figures 4.01 and 4.02. However, similar emission patterns were observed for epsilon Tauri, HD 38539, HD 46375, HD 50554, and HD 285968. HD 285968b is a 0.0265 MJ exoplanet and it is hard to imagine that it should generate a kG strength magnetic field just as the 12.7 MJ HD 38539b would. Given their similar morphology, appearance in a number of scans for these targets, and similarity to known radio frequency interference (RFI) patterns seen in other scans, we concluded that these lines are examples of RFI. Our discussion will now attempt to explain why this survey ended in failure. Generally speaking, the greatest amount of RFI can be found in box 6 (center frequency 5176 MHz). Even after processing, significant amounts of RFI remained in this box typically rendering it unusable for the purposes of further analysis. Box 0 (center frequency 4325 MHz) also generally has a large amount of RFI, unfortunately, this RFI can be mixed in with signals of scientific interest. Detections of source signals in this box and the box with the next lowest center frequency (4466 MHz) are of key importance since they allow us to probe lower magnetic field strengths of substellar objects, where we are more likely to detect bursts of radio emission given the magnetic field strengths presumed to be involved. The detection limits shown in Table 4.03 are calculated using statistics compiled from all the observation scans of each object in the given survey. These detection limits are found for each particular 172 MHz box by integrating the flux density from all of the channels in each box. They show the variation in detection limits for the individual sources at the given center frequencies of the MOCK box, which serves as a useful indicator of the amount of RFI that can be found near each center frequency. A typical 1σ detection limit value is 0.3 - 0.4 mJy during the course of this survey. In principle, the signal from the lower six boxes (omitting the box with the largest center frequency due to its persistent RFI) could be added together to improve the signal to noise ratio by a further ~√6 (reducing the typical 1σ limit to 0.12-0.16 mJy). However, in practice we did not do this due to the spotty and varying nature of remaining RFI signals unique to each box, which led to a higher detection limit when this method was applied.

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Figure 4.01. Is it ECMI emission from HD 285968? The left panels show dynamic spectra and the right panels depict their corresponding time series. In the dynamic spectra, black denotes left circular polarization, white denotes right circular polarization, and gray neither. Note the twin dark lines near t = 200 s, then again near t = 550 s. Although tempting to think this left circularly polarized emission may come from the planetary companion, this emission is illustrative instead of typical RFI in box 0.

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Figure 4.02. Potential ECMI radio emission from epsilon Tauri. A pair of left circularly polarized lines appears near t = 200 s in the time-frequency spectrograms. As the features are similar to those found in Figure 4.01 and a number of other scans from exoplanets, they are clearly RFI.

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Object 4325 4325 4466 4466 4608 4608 4750 4750 4892 4892 5034 5034 5176 5176 MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz Mean σm Mean σm Mean σm Mean σm Mean σm Mean σm Mean σm 51 Peg 0.841 0.623 0.689 0.357 0.543 0.29 1.808 1.412 0.9 0.549 0.615 0.366 2.206 0.424 55 Cnc 0.663 0.311 0.328 0.013 0.501 0.117 0.952 0.649 0.356 0.016 0.382 0.01 3.74 1.088 70 Vir 0.699 0.600 0.349 0.007 0.36 0.014 0.36 0.018 0.364 0.016 0.407 0.017 0.871 0.097 Eps Tau 0.607 0.295 0.367 0.033 0.39 0.044 0.497 0.288 0.42 0.102 0.469 0.188 1.961 1.567 GJ 436 0.565 0.149 0.349 0.018 0.345 0.011 0.359 0.01 0.368 0.013 0.402 0.011 0.755 0.133 HD 10697 0.433 0.126 0.435 0.155 0.361 0.01 0.356 0.014 0.368 0.014 0.394 0.028 3.302 1.023 HD 38529 0.703 0.39 0.475 0.026 0.469 0.032 0.493 0.031 0.489 0.019 0.524 0.026 1.395 0.232 HD 46375 0.518 0.245 0.378 0.023 0.487 0.1 1.19 0.237 0.391 0.013 0.417 0.016 0.827 0.137 HD 50554 0.364 0.109 0.346 0.025 0.459 0.104 0.561 0.15 0.362 0.02 0.38 0.015 3.013 1.493 HD 102195 0.523 0.093 0.434 0.025 0.446 0.031 0.453 0.014 0.482 0.037 0.516 0.022 1.163 0.451 HD 106252 0.528 0.239 0.398 0.053 0.407 0.048 0.43 0.063 0.428 0.063 0.458 0.048 1.013 0.559 HD 114762 0.647 0.437 0.38 0.068 0.52 0.053 0.803 0.319 0.417 0.11 0.441 0.108 3.116 1.403 HD 178911 0.455 0.038 0.429 0.036 0.44 0.048 0.442 0.046 0.449 0.045 0.469 0.027 3.688 0.627 HD 189733 0.596 0.282 0.386 0.043 0.426 0.061 0.395 0.042 0.412 0.099 0.694 0.299 2.351 0.474 HD 195019 0.523 0.168 0.401 0.07 0.42 0.049 0.407 0.078 0.416 0.106 0.426 0.072 2.478 0.813 HD 209458 0.428 0.094 0.385 0.038 0.408 0.045 0.378 0.029 0.396 0.063 0.511 0.137 2.3 0.394 HD 285968 0.466 0.101 0.355 0.036 0.469 0.131 0.949 0.388 0.371 0.034 0.396 0.047 1.714 0.936 HR 8799 0.747 0.624 0.348 0.018 0.367 0.047 0.376 0.037 0.362 0.021 0.385 0.018 3.388 1.392

Table 4.03. Radio detection values for the exoplanet portion of the A2471 survey. Two columns are available for each of the seven boxes: a “mean” value column and a standard deviation column (σm). Since no source was detected in the radio, each mean value is the mean of the 1σ uncertainties of the time series of the box scans. The reported σm value, then, describes the uncertainty in means. All units are in mJy.

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With the detection limits in hand, we can now compute physically meaningful detection limits for the sources. The flux density values obtained from box 1 (center frequency 4466 MHz) were used to perform these calculations. This box is relatively free of RFI across all objects and all observing times, making it useful to compare upper limits across all objects within this survey. The box generally also has many of the lowest mean signal variances, making it representative of the lowest signal levels we could indeed detect.

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Object Mass Distance 4466 MHz Time 4466 MHz 3σ Bolometric Radio Radio Lrad/Lbol (MJ) (pc) Series Mean Upper Limit Luminosity Luminosity Luminosity (Log ( )) (mJy) (mJy) (Log ( )) (Log ( )) (log LRJ) ⨀ 51 Peg 0.468 14.7 0.689 2.067 -9.5 -9.206 6.972 0.294 푳 ⨀ ⨀ 55 Cnc 3.835 13.02 0.328 0.984 -8.5 푳 -9.634 푳 6.689 -1.134 70 Vir 7.44 22 0.349 1.047 -7.5 -9.151 6.671 -1.651 Eps Tau 7.6 45 0.367 1.101 -7.5 -8.508 6.630 -1.008 GJ 436 0.072 10.2 0.349 1.047 -12 -9.819 6.732 2.181 HD 10697 6.12 32.56 0.435 1.305 -7.5 -8.715 6.724 -1.215 HD 38529 12.7 42.43 0.475 1.425 -6 -8.447 6.736 -2.447 HD 46375 0.249 33.4 0.378 1.134 -11 -8.754 6.667 2.246 HD 50554 4.9 31.03 0.346 1.038 -7.5 -8.856 6.639 -1.356 HD 102195 0.45 28.98 0.434 1.302 -9.5 -8.817 6.734 0.683 HD 106252 6.81 37.44 0.398 1.194 -7.5 -8.632 6.678 -1.132 HD 114762 11.02 39.46 0.38 1.14 -6 -8.607 6.655 -2.607 HD 178911 6.292 46.73 0.429 1.287 -7.5 -8.407 6.687 -0.907 HD 189733 1.13 19.3 0.386 1.158 -9 -9.221 6.722 -0.221 HD 195019 3.7 20 0.401 1.203 -8.5 -9.174 6.734 -0.674 HD 209458 0.685 47 0.385 1.155 -9.5 -8.449 6.645 1.051 HD 285968 0.027 9.4 0.355 1.065 -12 -9.882 6.745 2.118 HR 8799 5-40 39.4 0.348 1.044 -5.1 -8.646 6.621 -3.546

Table 4.04. Exoplanet radio detection upper limits in physical units. Using the 1σ mean flux density value for the 4466 MHz box from Table 4.03, the formal (3σ) upper limit to the radio detection can be calculated. From this flux density value, physically meaningful quantities can be derived. The two “Radio Luminosity” columns give the upper limit flux densities in terms of the luminosity of the Sun, and in terms of the radio luminosity of Jupiter. Finally, we can examine the ratio of the radio to bolometric luminosities.

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4.4. Discussion

We can plot the results of Table 4.04 in Figure 4.03, which provides the context for these calculated upper limits to the radio luminosities of the sources.

Figure 4.03. Graphical representation of the upper limits from the Arecibo exoplanet survey. For comparison, Jupiter is at lower right and at lower left, the radio to bolometric luminosity ratios of various quiescent and flaring ultracool dwarfs are shown. The dashed line divides the brown dwarf and exoplanet regimes; this division is not physically meaningful, but rather the plot is structured to provide context for the upper limits for the observed exoplanets. There is no simple mass distinction between spectral types, or between brown dwarfs and exoplanets, as discussed in Chapter 1. From this plot, it is readily apparent that our sensitivity to radio emission is a factor of 103-105 too low, compared to the activity of ultracool dwarfs. Exoplanet upper limits from this survey are depicted as downward-pointed triangles, while the quiescent (filled circles), and flaring (asterisks) luminosity ratios are for ultracool dwarfs from the literature (McLean et al. 2012).

From Figure 4.03, we note that our radio survey spanned nearly five magnitudes of radio- bolometric luminosity ratios! Our observations of the exoplanets highlight several problems with this method. First, as we searched for radio emission from these objects at C-band frequencies,

76 they would need to have been generated by kilo-Gauss magnetic fields to be detected, and they were not. From our observations, the failure to detect both the young system HR 8799 and the potential brown dwarf HD 114762, which offered the best chances for radio detection, demonstrate the difficulty of this task in the most optimistic of cases. Both systems contain substellar objects that have masses of ~5-40 MJ, and so should have significant internal energy for the generation of magnetic fields. The failure to detect these objects suggests that their magnetic fields are actually quite weak (or have quite small radio luminosities). This is supported by theoretical work from Christensen et al. (2009) and Reiners and Christensen (2010). However, Lazio et al. (2004) suggested that under optimal conditions, radio emission can be expected at frequencies of only a factor of two lower than we searched. In light of this work and knowledge of the operation of the electron cyclotron maser, should radiation occur at the lowest harmonic instead of the fundamental frequency, as may happen for denser plasma, searching for radio emission at 4.75 GHz is not completely unreasonable. Second, we note that while Jupiter has a radio-bolometric luminosity ratio of ~10-8, our observations are not sensitive enough by nearly 107 to detect it, so that the line of upper limits in Figure 4.03 moves to the upper right when it needs to move toward the lower right should we wish to succeed in detecting exoplanetary radio emission. While lowering the frequency of observation by a factor of ~100 is easily possible, we can still see that an additional increase of sensitivity of nearly 105 is required in instrumentation before we can hope to detect radio emission from even nearby exoplanets. Such a discrepancy between current instrumentation and what is needed to complete the goals suggest that emission from exoplanets will not be accessible without significant advances in detection methods and radio technology. Another potential problem could be the proximity of the exoplanets to their parent stars, which could be problematic in two ways. First, if the criticism of Melrose (1999) is in fact true, that exoplanets closer to their parent stars face denser stellar winds that prevent ECMI from occurring, or perhaps, escaping from the auroral cavities of the planets, then no search for radio emission from “hot Jupiters” will succeed. While theory suggests that ECMI has no problem escaping from inhomogeneous plasma layers, this has yet to be observed in practice. Thus, although all of the arguments concerning the injection of kinetic energy into the magnetosphere could be true, the processes would not lead to radio emission. A second difficulty, though, with exoplanets being located close to their stars is the possibility of slower rotation leading to decreased dynamo activity and a magnetic field reduced in strength. The mechanism for this could be simple tidal locking, but could also be a reduction in rotation due to the raising of atmospheric tides as some have suggested is the cause of the slow Venusian rotation (Correia & Laskar 2001; Correia 2003a, b). Geometry may also play a factor in these results. Most of the exoplanets in this survey have masses determined by the radial velocity method, which works when there is a significant portion of the stellar reflex motion along our line of sight. This suggests that for these detected planets, if the magnetic field is more or less aligned with the planet’s spin axis, which is roughly perpendicular to the orbital motion of the exoplanet, then radiation emitted perpendicular to the magnetic axis should be visible from Earth. In the context of ECMI emission (Section 2.3), this is an excellent situation as the most prominent mode of emission, the RX mode, is emitted perpendicular to the magnetic field. However, HR 8799 presents an altogether different geometry: it was detected by direct imaging and the system is almost face-on from our point of view. This means that the exoplanet poles are most likely pointed toward us, and in the context of ECMI emission, efficient RX-mode radiation is not emitted in the direction of Earth. While it is possible that a Uranus-type planet may exist in the system, such that its magnetic and spin axes are roughly aligned or anti-aligned to its orbital motion, it is highly unlikely that all four planets would exhibit this behavior. The weaker R-mode points along the magnetic axis and is therefore

77 accessible to our observations, but it is much less efficient and should yield weaker radio emission. Finally, our observations indicate that a related effect was not observed, namely, the production of ECMI emission from the parent stars of these exoplanets as produced by the exoplanet magnetospheres interacting with stellar magnetic fields, or the exoplanet’s gravity raising tides on the star and causing greater activity that way. Such emission could potentially be observed at 4.75 GHz due to strong stellar fields, but was not.

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Chapter 5

The Arecibo Surveys for Radio Emission from Brown Dwarfs

Note: a large quantity of the material presented in this chapter will be significantly similar to the paper Route, M. & Wolszczan, A. 2013, ApJ, in press.

5.1. Overview

In Chapter 4, we learned that the detection of radio emission from exoplanets would greatly advance our understanding of their magnetism and interior structure. We also learned that only half of the first targeted radio survey consisted of exoplanet targets, the other half consisted of brown dwarfs. The properties of those sources will be described in Section 5.2. This chapter will also discuss two more surveys that have been initiated following the first, one of which is currently in progress (Section 5.6). Here, we will discuss all of these observations, and their accumulated results. Sources that were detected and have additional science value will be discussed in detail in Chapter 6 and only briefly mentioned here. This chapter will also attempt to make inferences about the radio emission activity of the entire population of ultracool dwarfs based on the results of our surveys (Section 5.5). But first, we wish to discuss why a search of radio emitting brown dwarfs might be interesting. It was noted that at the time of the initiation of this radio survey that the coolest known brown dwarf was an L3.5 dwarf named 2MASS J00361617+1821104, which also happened to emit radio waves periodically. It had an inferred temperature of 1,900 K (Vrba et al. 2004) and was known to be a moderate rotator (v sin i ~ 15 km s-1; Schweitzer et al. 2001). This dwarf maintained a ~ 1.7 kG magnetic field (Hallinan et al. 2008) and its periodic radio emission could indicate that the radio emission was synchronized to its rotation period, if an adequate inclination angle was chosen (Berger et al. 2005). However, its radio activity seemed unlikely given its low temperature and presumably neutral atmosphere. Could even cooler brown dwarfs harbor strong kG magnetic fields that had yet to be detected? Beyond this L3.5 dwarf, there is a range of spectral classes to search for radio emission, including later class L, all of class T, and class Y (which was unknown at the start of our survey). It seemed then that a large temperature range remained to be examined to search for radio emission from these objects. While Berger (2006) had observed a relatively large number of T dwarfs, he and other researchers had failed to discover radio emission from any of them. Additionally, the detection of radio emission from brown dwarfs of later spectral classes would be helpful for our understanding of magnetic field generation in brown dwarfs and in exoplanets. The number of known radio emitting brown dwarfs was small, so additional radio emitters would be helpful to understand how typical their magnetic properties are. Also, detection of radio emission from later brown dwarfs would serve to better constrain the parameter space that should be searched for exoplanetary radio emission, by providing a better estimate to the upper bound of exoplanet magnetic field strength.

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Perhaps, with the aid of the most sensitive radio telescope available and its recently upgraded spectrometer capabilities, a survey of radio emission from cool brown dwarfs would succeed where others had failed…

5.2. Target Selection and Observations

As discussed in Section 4.2, a list of brown dwarf targets was assembled to accompany the exoplanet targets for the first survey, A2471. Fourteen brown dwarfs were selected. The criteria for their selection were similar to those for exoplanets. First, we chose targets that were in the range of the telescope, 0 to +38°. Second, the brown dwarf targets had to be < 50 pc away from the Earth to maximize their received flux. Third, brown dwarfs were chosen to be of later spectral types whenever possible, particularly later than L3.5, since there were no detected radio emitting brown dwarfs beyond that. In the second survey, A2623, no exoplanet targets were selected. For this second survey, 29 brown dwarfs were targeted and one ultracool dwarf, TVLM 513. This was due to our lack of positive results for the exoplanets and the encouraging results we did obtain for certain brown dwarf candidates. For the A2471 survey, we attempted to observe all objects for approximately 1 hour; while for the A2623 survey, we changed our strategy to attempt to observe every target for at least two hours, so that it would be closer to the minimum rotational period of an active ultracool dwarf. The A2623 survey had one unfortunate overarching technical issue, however, which was that one linear polarization amplifier was shown to be unstable relative to the first survey (Salter, personal communication). During this second survey, it became apparent that J10475385+2124234 was a flaring radio source. We therefore requested, and obtained, additional time to observe the object during project A2610. However, as these observations were going on at the same time as the main survey, in this dissertation they will be dealt with as an extension of the A2623 survey. This additional time to be used to attempt to observe another radio burst from the object was provided from December 2010 to February 2011. The target list for all A2471 and A2623 ultracool dwarfs is shown in Table 5.01, along with a number of physical properties of these objects.

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Right Ascension Declination Spectral Teff Distance Lbol v sin i Radio Flux Name (hh mm ss) (dd mm ss) Type (K) (pc) (Log ( )) (km s-1) (uJy) References J00325937+1410371 00 32 59 +14 10 37 L8 1566 33.18 -4.55# 1 푳⨀ J0036159+182110 00 36 16 +18 21 10 L3.5 1923 8.76 -4.51 134/720 2 J0039191+211516 00 39 19 +21 15 17 T7.5 840* 11.11 -5.41# 3 J01514155+1244300 01 51 41 +12 44 30 T1 1288 21.4 -4.54# 1 J02074284+0000564 02 07 42 +00 00 56 T4.5 1230 28.69 -4.74# 1,4 J0326137+295015 03 26 14 +29 50 15 L3.5 1981 32.26 -4.62# 5 J03284265+2302051 03 28 42 +23 02 05 L8 1534 30.18 -4.55# 6 J03454316+2540233 03 45 43 +25 40 23 L0 2426 26.95 -3.56 7 J07003664+3157266 07 00 37 +31 57 27 L3.5 1870* 12.2 -3.88# 29.9 <78 8,9 J07271824+1710012 07 27 18 +17 10 01 T8 770* 9.08 -5.58# 10 J07464256+2000321 07 46 43 +20 00 32 L0.5 2338A 12.21 -3.93 224/15000 11 J08251958+2115521 08 25 20 +21 15 52 L7.5 1383 10.66 -5.21 <45 6 J0850359+105716 08 50 36 +10 57 16 L6 1486A 31.39 -4.34# 5,12 J085911+101017 08 59 11 +10 10 17 T7 920* 26-36 -5.26# 13 J09121469+1459396 09 12 14 +14 59 39 L8 1390* 20.48 -4.55# 14,15 J09373487+2931409 09 37 34 +29 31 40 T7 920* 6.14 -5.26# 10,16 J10475385+2124234 10 47 53 +21 24 23 T6.5 869 10.56 -5.35 <45 4,17 J11122567+3548131 11 12 26 +35 48 13 L4.5 1740* 21.72 -4.16# 28.7 6,9,15 J11463449+223053 11 46 35 +22 30 53 L3 2060A 27.17 -3.96# 23.9 5,18,19 J115739+092201 11 57 39 +09 22 01 T2.5 1390* 24-34 -4.55# 13 J123828+095351 12 38 28.5 +09 53 51 T8.5 <770* 20 <-5.58# 20,21 J131508+082627 13 15 08 +08 26 27 T7.5 840* 19-28 -5.41# 13 J1328550+211449 13 28 55 +21 14 49 L5 1819 32.26 -4.22# 5 J133553+113005 13 35 53 +11 30 05 T9 <770* 10-10.6 -5.58# 21

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J14243909+0917104 14 24 39 +09 17 10 L4 1800* 31.55 -4.04 32.5 <96 22,23,24 J1439284+192915 14 39 28 +19 29 15 L1 2264 14.37 -3.67# 11.1 5,9,18 J144601+0024519 14 46 01 +00 24 52 L6 1570* 22 -4.34# 2,4 J15232263+3014562 15 23 22 +30 14 56 L8 1330 18.62 -5.27 <45 6,15 J16241436+0029158 16 24 14 +00 29 15 T6 1002 11 -5.16 36.6 <36 25,26,27 J16322911+1904407 16 32 29 +19 04 40 L8 1346 15.24 -5.31 21.8 <54 5,18,24,28 J1711457+223204 17 11 46 +22 32 04 L6.5 1545 30.2 -4.39# 4,6 J1841086+311727 18 41 09 +31 17 27 L4 V 2032 40 -4.09# 4,6 J21011544+1756586 21 01 15 +17 56 58 L7.5 1327 33.18 -4.5# 4,6 TVLM-513 15 01 08 +22 50 02 M9 2200 10.5 -3.59 190/980 ##

Table 5.01. Properties of A2471 and A2623 ultracool dwarfs. Asterisks denote temperatures inferred from Vrba et al. (2004). Bolometric luminosities inferred from Vrba et al. (2004) are denoted (#), while the TVLM 513 references can be seen in Chapter 2 (##). Sources that have a numerical value for their radio flux are in the form quiescent/flaring when two values are given. References are: (1) Geballe et al. (2002); (2) Reid et al. (2000); (3) Mugrauer et al. (2006); (4) Vrba et al. (2004); (5) Kirkpatrick et al. (1999); (6) Kirkpatrick et al. (2000); (7) Kirkpatrick et al. (1997); (8) Thorstensen & Kirkpatrick (2003); (9) Blake et al. (2011); (10) Burgasser et al. (2002); (11) Antonova et al. (2008); (12) Dupuy & Liu (2012); (13) Pinfield et al. (2008); (14) Wilson et al. (2001); (15) Perryman et al. (1997); (16) Schilbach et al. (2009); (17) Burgasser et al. (1999); (18) Dahn et al. (2002); (19) Bailer-Jones & Mundt (2001); (20) Kirkpatrick et al. (2012); (21) Burningham et al. (2008); (22) Faherty et al. (2009); (23) Becklin & Zuckerman (1988); (24) Mohanty & Basri (2003); (25) Strauss et al. (1999); (26) Tinney et al. (2003); (27) Zapatero Osorio et al. (2006); (28) Basri et al. (2000). Source: Route & Wolszczan (2013).

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The A2471 survey targets were observed from January 2010 to July 2011. All sources were observed for 1-2 hours, with the exception of J1047+21, which will be discussed in detail in Section 6.2. The observing log for this survey can be found in Table 5.02.

Source Date Scans Time on Center Frequency Bandpass Beam Size Source (ks) (MHz) (MHz) (arcmin) J00325937+1410371 20101217 6 3.6 4750 4239-5262 1.15 x 1.18 J0039191+211516 20101218 8 4.8 4750 4239-5262 1.15 x 1.18 J01514155+1244300 20101217 7 4.2 4750 4239-5262 1.15 x 1.18 20101218 2 1.2 4750 4239-5262 1.15 x 1.18 J03284265+2302051 20100109 4 2.4 4750 4239-5262 1.15 x 1.18 20101217 9 5.4 4750 4239-5262 1.15 x 1.18 20101220 4 2.4 4750 4239-5262 1.15 x 1.18 J07271824+1710012 20101219 1 0.6 4750 4239-5262 1.15 x 1.18 20110102 9 5.4 4750 4239-5262 1.15 x 1.18 20110103 11 6.6 4750 4239-5262 1.15 x 1.18 J09373487+2931409 20110103 6 3.6 4750 4239-5262 1.15 x 1.18 J10475385+2124234 20100106 6 3.6 4750 4239-5262 1.15 x 1.18 20101130 11 6.6 4750 4239-5262 1.15 x 1.18 20101201 11 6.6 4750 4239-5262 1.15 x 1.18 20101202 10 6 4750 4239-5262 1.15 x 1.18 20101203 11 6.6 4750 4239-5262 1.15 x 1.18 20101204 12 7.2 4750 4239-5262 1.15 x 1.18 20101205 12 7.2 4750 4239-5262 1.15 x 1.18 20101206 8 4.8 4750 4239-5262 1.15 x 1.18 20101207 12 7.2 4750 4239-5262 1.15 x 1.18 20101218 12 7.2 4750 4239-5262 1.15 x 1.18 20110102 12 7.2 4750 4239-5262 1.15 x 1.18 20110103 11 6.6 4750 4239-5262 1.15 x 1.18 20110111 7 4.2 4750 4239-5262 1.15 x 1.18 20110120 12 7.2 4750 4239-5262 1.15 x 1.18 20110207 7 4.2 4750 4239-5262 1.15 x 1.18 20110208 4 2.4 4750 4239-5262 1.15 x 1.18 J123828+095351 20110103 6 3.6 4750 4239-5262 1.15 x 1.18 J144601+0024519 20110316 6 3.6 4750 4239-5262 1.15 x 1.18 J15232263+3014562 20110315 6 3.6 4750 4239-5262 1.15 x 1.18 J16322911+1904407 20110315 6 3.6 4750 4239-5262 1.15 x 1.18 20110316 6 3.6 4750 4239-5262 1.15 x 1.18 J1711457+223204 20110315 5 3 4750 4239-5262 1.15 x 1.18 20110316 4 2.4 4750 4239-5262 1.15 x 1.18 J1841086+311727 20110718 5 3 4750 4239-5262 1.15 x 1.18

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J21011544+1756586 20091230 1 0.6 4750 4239-5262 1.15 x 1.18 20110718 12 7.2 4750 4239-5262 1.15 x 1.18 Table 5.02. The brown dwarf observing log for program A2471. Notice that the source J1047+21 was observed for far longer than the typical hour, as it had become apparent that the source was a flaring radio source. All other sources were observed for a total of 1-2 hours. The date format is YYYYMMDD. Note: this table benefited from “The M, L, T, and Y dwarf compendium,” DwarfArchives.org, 6 Dec. 2002.

The A2623 survey consisted solely of ultracool dwarf targets which were observed from October 2011 until April 2012. All sources were observed for at least 2 hours, with the observing log for these observations recorded in Table 5.03.

Source Date Scans Time on Center Frequency Bandpass Beam Size Source (ks) (MHz) (MHz) (arcmin) J0036159+182110 20111105 11 6.6 4750 4239-5262 1.15 x 1.18 J0039191+211516 20111027 11 6.6 4750 4239-5262 1.15 x 1.18 J01514155+1244300 20111010 7 4.2 4750 4239-5262 1.15 x 1.18 20111028 6 3.6 4750 4239-5262 1.15 x 1.18 J02074284+0000564 20111105 2 1.2 4750 4239-5262 1.15 x 1.18 20111119 5 3 4750 4239-5262 1.15 x 1.18 J0326137+295015 20111020 5 3 4750 4239-5262 1.15 x 1.18 20111022 4 2.4 4750 4239-5262 1.15 x 1.18 20111119 4 2.4 4750 4239-5262 1.15 x 1.18 J03284265+2302051 20111021 6 3.6 4750 4239-5262 1.15 x 1.18 20111028 1 0.6 4750 4239-5262 1.15 x 1.18 J03454316+2540233 20111010 10 6 4750 4239-5262 1.15 x 1.18 20111020 2 1.2 4750 4239-5262 1.15 x 1.18 20111021 1 0.6 4750 4239-5262 1.15 x 1.18 20111022 2 1.2 4750 4239-5262 1.15 x 1.18 J07003664+3157266 20111119 11 6.6 4750 4239-5262 1.15 x 1.18 20120208 5 3 4750 4239-5262 1.15 x 1.18 20120209 4 2.4 4750 4239-5262 1.15 x 1.18 J07271824+1710012 20111119 2 1.2 4750 4239-5262 1.15 x 1.18 J07464256+2000321 20120207 12 7.2 4750 4239-5262 1.15 x 1.18 20120208 2 1.2 4750 4239-5262 1.15 x 1.18 20120210 8 4.8 4750 4239-5262 1.15 x 1.18 20120306 8 4.8 4750 4239-5262 1.15 x 1.18 20120307 10 6 4750 4239-5262 1.15 x 1.18 20120405 3 1.8 4750 4239-5262 1.15 x 1.18 20120406 5 3 4750 4239-5262 1.15 x 1.18 20120407 4 2.4 4750 4239-5262 1.15 x 1.18 20120429 9 5.4 4750 4239-5262 1.15 x 1.18

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J08251958+2115521 20120208 7 4.2 4750 4239-5262 1.15 x 1.18 20120209 3 1.8 4750 4239-5262 1.15 x 1.18 20120209 3 1.8 4750 4239-5262 1.15 x 1.18 J0850359+105716 20120209 12 7.2 4750 4239-5262 1.15 x 1.18 J085911+101017 20120210 12 7.2 4750 4239-5262 1.15 x 1.18 J09121469+1459396 20120210 4 2.4 4750 4239-5262 1.15 x 1.18 20120211 2 1.2 4750 4239-5262 1.15 x 1.18 J09373487+2931409 20120208 9 5.4 4750 4239-5262 1.15 x 1.18 J10475385+2124234 20120209 14 8.4 4750 4239-5262 1.15 x 1.18 20120211 1 0.6 4750 4239-5262 1.15 x 1.18 J11122567+3548131 20120211 7 4.2 4750 4239-5262 1.15 x 1.18 J11463449+223053 20120208 12 7.2 4750 4239-5262 1.15 x 1.18 J115739+092201 20120210 12 7.2 4750 4239-5262 1.15 x 1.18 J131508+082627 20120209 12 7.2 4750 4239-5262 1.15 x 1.18 J1328550+211449 20120211 12 7.2 4750 4239-5262 1.15 x 1.18 J133553+113005 20120210 7 4.2 4750 4239-5262 1.15 x 1.18 J14243909+0917104 20120208 12 7.2 4750 4239-5262 1.15 x 1.18 J1439284+192915 20120209 7 4.2 4750 4239-5262 1.15 x 1.18 J15232263+3014562 20120211 3 1.8 4750 4239-5262 1.15 x 1.18 J16241436+0029158 20120309 4 2.4 4750 4239-5262 1.15 x 1.18 J16322911+1904407 20120309 4 2.4 4750 4239-5262 1.15 x 1.18 20120329 9 5.4 4750 4239-5262 1.15 x 1.18 20120331 9 5.4 4750 4239-5262 1.15 x 1.18 J1711457+223204 20120310 4 2.4 4750 4239-5262 1.15 x 1.18 20120311 3 1.8 4750 4239-5262 1.15 x 1.18 20120330 9 5.4 4750 4239-5262 1.15 x 1.18 J21011544+1756586 20111110 6 3.6 4750 4239-5262 1.15 x 1.18 TVLM-513 20120310 1 0.6 4750 4239-5262 1.15 x 1.18 20120311 1 0.6 4750 4239-5262 1.15 x 1.18 20120329 6 3.6 4750 4239-5262 1.15 x 1.18 20120330 6 3.6 4750 4239-5262 1.15 x 1.18 20120331 7 4.2 4750 4239-5262 1.15 x 1.18 Table 5.03. The ultracool dwarf observing log for program A2623. The date format is YYYYMMDD. Note: this table also benefited from “The M, L, T, and Y dwarf compendium,” DwarfArchives.org, 6 Dec. 2002.

As in Chapter 4, the data were recorded with the Mock spectrometer, in 600 s scans, with 0.1 s temporal resolution and 21 kHz frequency resolution. In between science scans, calibration scans were taken with an electronic oscillator. The data were then processed via the MOCK calibration pipeline and the Arecibo data analysis and products pipeline as discussed in Section 3.2.

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In this second survey, two calibration sources were added as well, to compare the results from our survey with those for known sources, and to inspect the long term stability of these sources. The two added calibration sources were J0036159+182110 and J07464256+2000321 (J0746+20 hereafter). J0036159+182110 (J0036+18) was discussed in detail in Section 2.1.4, as the first ultracool dwarf shown to emit periodically. J0746+20 is a binary source that was also shown to have strong periodic radio emission (Berger et al. 2009).

5.3. Results

The first survey, A2471, was a resounding success. Only a single source was observed to flare out of the fourteen observed, but its detection was of great importance. The flaring source, J10475385+2124234, was a very cool, T6.5 brown dwarf. It will be discussed in more detail in Section 6.2. The second survey, A2623, was also successful. We were able to detect the calibration source, J0746+20, but not the source J0036+18. This is because while J0746+20 flares on a timescale of minutes, J0036+18 slowly varies over the course of a few hours. One of the limitations of the Arecibo Radio Telescope is that while it is very sensitive to rapid bursts, it is rather insensitive to long-term fluctuations since it does not record the absolute value of the flux densities received. A detection of a burst from J0746+20 is shown in Figure 5.01. Also during the course of this survey, we conducted some follow-up observations of TVLM 513. The results of these observations, as well as a complete description of all of our observations of this source, will can be found in Section 6.1. We were also fortunate to have detected a new source during the second survey. It is the L1 brown dwarf J1439284+192915. It will be discussed in detail in Section 6.3. Overall, our rate of detection of flaring radio emission from brown dwarfs is 6%. This figure includes brown dwarfs from types L0 – T9. It is interesting to note that this success rate is equivalent to that found by Antonova et al. (2013), who reported a ~6% detection rate for all ultracool dwarfs observed at that time. The sample studied by that research team included spectral types M7 and later, with few sources in the T spectral class. These results suggest that all ultracool dwarfs (M7 – Y) may have a radio detection probability of ~6%.

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Figure 5.01. The detection of a radio burst from J0746+20. The left column displays dynamic spectra of the source for each of the seven Mock boxes, while the right column shows time series plots that correspond to them. Note the large amount of interference in the sixth and seventh boxes. The radio flare from the source can be easily seen in the three lowest frequency boxes.

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The problems associated with radio frequency interference were discussed in Chapter 4. But it is helpful to reiterate that during the course of these surveys, a typical 1σ uncertainty value is 0.3-0.4 mJy. While these surveys detected a total of four sources, that means a large number of targets remain that were not detected. We can, however, compute upper limits for their flaring radio emission. In Table 5.04 the box-by-box detection limits are reported for the A2471 survey, while in Table 5.05, the detection limits for the A2623 survey are recorded. Finally, in Table 5.06 these results are compiled into physically meaningful quantities. Some sources are observed in both A2471 and A2623 surveys; their statistics are merged into Table 5.06 in normal statistical fashion. It is worth noting that in Table 5.06 we also examine the statistics of the detection limits. The upper limit may be calculated from either the standard deviation of the time series in the cleanest box (which was used in Chapter 4) or by adding together all channels in the best six boxes into a time series and computing a standard deviation from that. We should not use all seven boxes since the one at highest frequency is always noisy and complete RFI removal from it results in almost no signal. Constructing this cumulative time series from all six boxes should yield a ~√6 improvement in the signal-to-noise ratio, as pointed out in Chapter 4. It is worth noting, however, that this is clearly not the case; for the majority of ultracool dwarfs, the standard deviation from the 4466 MHz box is lower than the cumulative one. How can this be? It might seem that if the boxes are all processed simultaneously, a curve is fit to them all, and correlated signals between boxes introduced. However, this is not how the Arecibo data products pipeline works, as described in Chapter 3. The boxes are processed independently, with frequency and temporal baselines fit and subtracted from them individually. The answer seems to be that RFI must be correlated among boxes, and when the boxes are added, the signals add instead of averaging out. Thus, even when the boxes appear clean, correlated noise occurs on the ~0.4 mJy level.

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Object 4325 4325 4466 4466 4608 4608 4750 4750 4892 4892 5034 5034 5176 5176 MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz

Mean σm Mean σm Mean σm Mean σm Mean σm Mean σm Mean σm

J00325937+1410371 0.507 0.193 0.367 0.034 0.355 0.019 0.356 0.015 0.373 0.012 0.378 0.011 3.461 1.025 J0039191+211516 0.535 0.189 0.362 0.051 0.358 0.034 0.376 0.036 0.365 0.018 0.391 0.023 3.003 0.481 J01514155+1244300 0.446 0.296 0.425 0.166 0.54 0.145 0.561 0.186 0.363 0.013 0.383 0.018 3.5 0.692 J03284265+2302051 0.474 0.217 0.348 0.016 0.432 0.077 0.839 0.418 0.373 0.032 0.394 0.02 2.723 1.419 J07271824+1710012 0.391 0.067 0.344 0.024 0.476 0.107 0.72 0.241 0.359 0.024 0.385 0.039 3.279 0.868 J09373487+2931409 0.703 0.488 0.622 0.487 0.448 0.216 0.44 0.227 0.452 0.23 0.477 0.243 4.195 1.802 J144601+0024519 1.344 1.039 0.366 0.018 0.377 0.019 0.43 0.073 0.444 0.063 0.458 0.027 11.278 6.198 J16322911+1904407 0.396 0.061 0.357 0.036 0.451 0.095 0.618 0.274 0.423 0.08 0.44 0.045 5.73 2.917 J1238285+095351 0.352 0.016 0.342 0.014 0.442 0.109 0.381 0.029 0.357 0.012 0.383 0.012 4.452 1.682 J15232263+3014562 0.394 0.065 0.352 0.038 0.414 0.043 1.059 0.297 0.387 0.043 0.414 0.034 6.052 1.431 J1711457+223204 0.36 0.012 0.343 0.012 0.439 0.118 0.601 0.205 0.373 0.028 0.405 0.022 4.401 0.648 J1841086+311727 0.706 0.366 1.232 0.875 0.621 0.456 1.878 1.213 1.437 0.487 0.85 0.438 5.406 4.118 J21011544+1756586 1.278 1.077 0.942 0.382 0.753 0.447 3.631 1.154 1.783 0.906 0.983 0.971 2.634 0.821

Table 5.04. Frequency dependent detection limits of the brown dwarfs in the A2471 survey. Two columns are available for each of the seven boxes: a “mean” value column and a standard deviation column (σm). Each mean value is the mean of the 1σ uncertainties of the time series of the box scans. The reported σm value, then, describes the uncertainty in means. All units are in mJy.

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Object 4325 4325 4466 4466 4608 4608 4750 4750 4892 4892 5034 5034 5176 5176 MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz

Mean σm Mean σm Mean σm Mean σm Mean σm Mean σm Mean σm

J0036159+182110 0.434 0.053 0.393 0.066 0.396 0.039 0.395 0.066 0.431 0.132 0.734 0.156 2.749 0.533 J0039191+211516 0.446 0.085 0.393 0.034 0.417 0.037 0.407 0.056 0.394 0.034 0.797 0.272 3.24 1.348 J01514155+1244300 0.578 0.314 0.418 0.076 0.452 0.056 0.436 0.085 0.446 0.076 0.807 0.381 4.781 1.973 J02074284+0000564 0.557 0.078 1.045 0.506 1.199 1.038 1.002 0.443 0.559 0.025 1.48 0.298 4.222 2.852 J0326137+295015 0.574 0.163 0.431 0.054 0.442 0.058 0.438 0.055 0.494 0.126 0.702 0.127 3.557 0.547 J03284265+2302051 0.443 0.082 0.43 0.075 0.45 0.11 0.441 0.111 0.396 0.041 0.741 0.24 2.563 0.905 J03454316+2540233 0.435 0.075 0.402 0.051 0.419 0.06 0.43 0.082 0.431 0.057 0.666 0.194 3.109 0.856 J07003664+3157266 1.372 1.314 0.485 0.093 0.487 0.089 0.561 0.09 0.689 0.119 3.828 2.602 7.933 3.912 J07271824+1710012 0.546 0.07 0.527 0.044 0.523 0.036 0.499 0.06 0.683 0.192 0.802 0.472 3.069 1.203 J07464256+2000321 0.578 0.226 0.464 0.109 0.446 0.067 0.46 0.105 0.546 0.145 3.539 1.418 5.581 1.762 J08251958+2115521 0.527 0.329 0.414 0.073 0.413 0.038 0.499 0.142 0.561 0.134 3.357 1.399 6.268 2.832 J0850359+105716 0.467 0.106 0.434 0.068 0.492 0.116 0.594 0.178 0.517 0.125 3.934 1.903 7.082 2.436 J085911+101017 0.427 0.078 0.43 0.062 0.485 0.104 0.519 0.154 0.612 0.172 3.388 0.744 7.265 1.679 J09121469+1459396 0.456 0.059 0.491 0.055 0.512 0.056 0.59 0.132 0.725 0.175 3.753 1.988 8.201 2.254 J09373487+2931409 0.433 0.086 0.394 0.048 0.394 0.049 0.397 0.068 0.601 0.167 3.07 0.41 5.917 0.819 J10475385+2124234 0.467 0.121 0.406 0.049 0.419 0.057 0.487 0.141 0.565 0.119 2.977 1.493 4.286 1.359 J11122567+3548131 0.719 0.277 0.491 0.059 0.501 0.059 0.513 0.037 1.091 0.171 5.866 1.292 10.298 2.284 J11463449+223053 0.867 0.732 0.382 0.026 0.425 0.079 0.39 0.033 0.531 0.111 1.984 0.349 3.47 0.773 J115739+092201 1.506 1.465 0.558 0.149 0.609 0.184 0.737 0.236 0.604 0.141 2.403 0.545 3.677 1.141 J131508+082627 0.422 0.055 0.488 0.103 0.517 0.136 0.52 0.103 0.534 0.102 2.829 0.917 4.236 1.22 J1328550+211449 0.817 0.803 0.386 0.031 0.396 0.042 0.421 0.087 0.545 0.097 2.66 0.784 3.819 0.672 J133553+113005 0.403 0.055 0.414 0.041 0.444 0.08 0.597 0.134 0.449 0.016 2.27 0.519 3.366 0.376 J14243909+0917104 0.418 0.097 0.539 0.164 0.528 0.104 0.49 0.083 0.862 0.466 3.697 1.197 5.869 1.943 J1439284+192915 0.429 0.076 0.419 0.043 0.396 0.031 0.556 0.147 0.503 0.055 3.401 1.166 4.508 0.844

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J15232263+3014562 0.478 0.057 0.358 0.001 0.386 0.008 0.399 0.018 0.606 0.053 2.193 0.165 3.506 0.027 J16241436+0029158 0.538 0.037 1.158 0.367 1.922 1.212 1.324 0.599 0.59 0.034 3.419 1.488 5.24 0.81 J16322911+1904407 0.504 0.132 0.435 0.069 0.425 0.069 0.426 0.057 0.517 0.094 2.776 1.048 3.718 1.581 J1711457+223204 0.406 0.038 0.384 0.035 0.404 0.037 0.398 0.056 0.472 0.054 1.963 0.428 3.005 1.01 J21011544+1756586 0.836 0.182 0.522 0.055 0.538 0.109 0.537 0.116 0.486 0.074 0.731 0.205 3.634 1.262 TVLM-513 0.559 0.173 0.449 0.113 0.473 0.092 0.479 0.11 0.581 0.14 2.793 0.744 2.74 1.142

Table 5.05. Frequency dependent detection limits of the ultracool dwarfs in the A2623 survey. Two columns are available for each of the seven boxes: a “mean” value column and a standard deviation column (σm). As in Table 5.04, each mean value is the mean of the 1σ uncertainties of the time series of the box scans. The reported σm value, then, describes the uncertainty in means. All units are in mJy.

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4466 MHz 3σ Cumulative 3σ Bolometric Radio Radio Lrad/Lbol Object Spectral Distance Upper Limit Upper Limit Luminosity Luminosity Luminosity (Log ( )) Type (pc) (mJy) (mJy) (Log ( )) (Log ( )) (Log LRJ)

⨀ J00325937+1410371 L8 33.18 1.101 1.925 푳-4.55⨀ -8.773푳⨀ 6.656 푳-4.223 J0036159+182110 L3.5 8.76 1.179 0.954 -4.51 -9.900 6.791 -5.390 J0039191+211516 T7.5 11.11 1.14 0.878 -5.41 -9.708 6.759 -4.298 J01514155+1244300 T1 21.4 1.262 0.917 -4.54 -9.094 6.747 -4.554 J02074284+0000564 T4.5 28.69 3.135 1.476 -4.74 -8.445 7.078 -3.705 J0326137+295015 L3.5 32.26 1.293 1.011 -4.62 -8.727 6.722 -4.107 J03284265+2302051 L8 30.18 1.044 0.877 -4.55 -8.878 6.644 -4.328 J03454316+2540233 L0 26.95 1.206 0.808 -3.56 -8.914 6.710 -5.354 J07003664+3157266 L3.5 12.2 1.455 2.955 -3.88 -9.521 6.849 -5.641 J07271824+1710012 T8 9.08 1.101 0.79 -5.58 -9.898 6.761 -4.318 J08251958+2115521 L7.5 10.66 1.242 2.551 -5.21 -9.707 6.797 -4.497 J0850359+105716 L6 31.39 1.302 2.405 -4.34 -8.748 6.566 -4.408 J085911+101017 T7 26.36 1.29 1.936 -5.26 -8.904 6.738 -3.644 J09121469+1459396 L8 20.48 1.473 2.059 -4.55 -9.065 6.811 -4.515 J09373487+2931409 T7 6.14 1.227 1.599 -5.26 -10.191 6.834 -4.931 J11122567+3548131 L4.5 21.72 1.473 3.354 -4.16 -9.014 6.806 -4.854 J11463449+223053 L3 27.17 1.146 1.807 -3.96 -8.929 6.689 -4.969 J115739+092201 T2.5 29 1.674 2.82 -4.55 -8.708 6.832 -4.158 J1238285+095351 T8.5 20 1.026 0.648 -5.58 -9.243 6.671 -3.663 J131508+082627 T7.5 23.4 1.464 1.835 -5.41 -8.952 6.798 -3.542 J1328550+211449 L5 32.26 1.158 2.238 -4.22 -8.775 6.679 -4.555 J133553+113005 T9 10.3 1.242 1.307 -5.58 -9.737 6.799 -4.157 J14243909+0917104 L4 31.55 1.617 2.121 -4.04 -8.650 6.811 -4.610 J144601+0024519 L6 22 1.098 3.071 -4.34 -9.131 6.690 -4.791

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J15232263+3014562 L8 18.62 1.211 1.135 -5.27 -9.233 6.742 -3.963 J16241436+0029158 T6 11 3.474 2.508 -5.16 -9.233 7.200 -4.073 J16322911+1904407 L8 15.24 1.217 1.388 -5.31 -9.405 6.760 -4.095 J1711457+223204 L6.5 30.2 1.109 1.1 -4.39 -8.851 6.667 -4.461 J1841086+311727 L4 42.43 3.696 1.623 -4.09 -8.033 7.106 -3.943 J21011544+1756586 L7.5 47 3.172 2.677 -4.5 -8.011 7.037 -3.511

Table 5.06. Physical results of the A2471 and A2623 radio surveys. Using the 1σ mean flux density value for the 4466 MHz box from Tables 5.04 and 5.05, the formal (3σ) upper limit to the radio detection can be calculated. From this flux density value, physically meaningful quantities can be derived. For comparison, the 3σ upper limit calculated from summing the flux over all good boxes is presented in a column as well. Detected sources J0746+20, J1047+21, J1439+19, and TVLM 513 are detected sources and so are not present in this listing of upper limits. The two “Radio Luminosity” columns give the upper limit flux densities in terms of the luminosity of the Sun, and in terms of the radio luminosity of Jupiter. Finally, we can examine the ratio of the radio to bolometric luminosities. Source: Route & Wolszczan (2013).

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5.4. Discussion

We can compare the upper limits to the radio luminosities as calculated in the previous section to those from the literature, as in Figure 5.02. From the figure, it is clear that our radio surveys have done much to fill in the gap between radio emission from planets in the Solar System, and radio emission from brown dwarfs.

Figure 5.02. Graphical representation of radio luminosities for ultracool dwarf targets in the Arecibo radio surveys. Quiescent radio emission (filled circles) and flaring radio emission (asterisks) are from the literature. Upper limits from our surveys are represented by downward pointing triangles. The two new discoveries made during our surveys are denoted by filled stars; J1047+21 is at T6.5, and J1439+19 is at L1. The filled circle at L5 (Burgasser et al. 2013) was published after the key discovery in Route & Wolszczan (2012). Motivated by our detection of J1047+21, Williams et al. (2013) examined it and detected quiescent emission, which is the filled circle at T6.5. Jupiter is off somewhere to the lower right.

Several points need to be made concerning how these surveys compare to other similar ones. The cumulative detection probability for both surveys is 6% for newly observed sources.

94 This figure is in agreement with the detection probability value derived by Antonova et al. (2013). That this value should be the same, even though a large number of our sources were of spectral type T, is suggestive that the same flaring statistics that apply to ultracool dwarfs of range M7-L3.5, where most surveys have been conducted, also apply to the T spectral class. On the other hand, there is a large methodological difference between this survey and a number of other surveys (i.e. Krishnamurthi et al. (1999), Berger (2006), Phan-Bao et al. (2007), McLean et al. (2012)). In these surveys, a source was analyzed for bursts of radio emission only after the source was detected in quiescence. While this procedure allows for very deep radio imagery with small noise values when data is collected over the course of hours, it has the potential to wash out radio flares not far above the 3σ noise level. The resultant flare signal to noise ratio falls off as

~ (5.01) 푡

푆 �푇 where t is the temporal length of the burst, while T is the observation length. We recommend, therefore, that future research efforts also conduct time series analyses of their radio data, in a search for rapid, low intensity bursts. There are a few statements that can be made about all of the detected ultracool dwarfs as a group. First, their distances are all less than 15 pc from Earth. Part of this is due to the fact that we selected sources that were less than 50 pc from Earth, but more important is the fact that at as sensitive as Arecibo is, it is not sensitive enough to objects with such small radio luminosities at greater distances. Second, all detected objects have calculated magnetic field strengths of 1.8 kG; this is derived from using the maximum frequency of radio emission that we detected as an estimate for the cutoff frequency of the radio emission. As we are only examining objects ≳with a C-band receiver, there is a range of magnetic field strengths to which we are sensitive. The other targets that we observed may very well have detectable radio emission at lower frequencies corresponding to weaker magnetic fields. Third, all detected objects have large polarization fractions, indicating high degrees of circular polarization. Fourth, these objects all have large brightness temperatures, in all cases larger than 6 x 109 K in the most conservative scenario, when we assume that the emitting region has size of order 1 RJ. Should we instead calculate brightness temperatures on the basis of light travel time arguments by measuring the time scale of smallest fluctuations, we find many brightness temperatures that are comfortably greater than 1010 K. The high brightness temperatures coupled with the information regarding high degrees of circular polarization, point unambiguously to the electron cyclotron maser instability as being the root cause of the detected radio emission. Given Figure 5.02, we may inspect the population of detected radio emitting ultracool dwarfs for trends. We noted in Figure 1.16 that the trend of an increasing radio luminosity to bolometric luminosity ratio was best explained by radio emission remaining constant while the bolometric luminosity decreased. It appears that this trend continues to at least L5. However, from Figure 5.02 it appears that this trend disappears by T6.5. At some point, this relation reaches a peak radio-bolometric luminosity ratio and then either levels out, or perhaps slowly declines. This can be seen by the fact that the quiescent emission from J1047+21 is lower than that of 2MASS J13153094−2649513AB (the L5 dwarf; J1315-26 hereafter), although we should entertain this conclusion cautiously given the few number of points involved. At any rate, a level amount of activity, stretching from the detected J1315-26 to J1047+21 would be indicative of rising level of radio activity, since temperature decreases. On the other hand, if we consider Jupiter as well and connect it with J1047+21, then after radio emission peaking at some spectral type ≥ L5, radio emission falls precipitously with bolometric luminosity.

95 What statements can be made regarding the undetected sources from the surveys? It could be that they simply do not emit radio waves to which we are sensitive, due to intrinsic weakness in the emission, or the sources being too far away. The sources may emit radio waves at lower frequencies due to weaker magnetic fields. The undetected objects may also emit radio waves, but we simply were not observing them during the time in their rotational period that they were emitting. Radio emission is highly beamed, so it could be that our line of sight does not intersect the emission cone of the radiation. To attempt to better understand these effects, we examine the statistics of the ultracool dwarf population as described by our surveys and the surveys in the literature. Later, we will describe a Monte Carlo simulator constructed based on these statistics and summarize what it reveals about the radio emission activity of ultracool dwarfs.

5.5. Inferences About the Ultracool Dwarf Population

Individual ultracool dwarfs have been shown to have low-level quiescent or flaring radio emission. Do they have common properties that we can use to assess our theoretical understanding of the nature of radio emission from ultracool dwarfs?

5.5.1. Statistical Analysis on Rotational Velocities

A promising line of inquiry is that regarding the relationship between rotation and radio emission. In Section 1.4.3, we saw that these were related in that rotation up to a certain velocity increased internal dynamo activity. Figure 1.18 suggested that radio activity may actually increase for ultracool dwarfs as a function of rotational velocity. We can assess this statistically. From the literature, we can put together rotational velocity information about ultracool dwarfs (Zapatero Osorio et al. 2006; McLean et al. 2012) and combine this with the knowledge of which sources exhibit quiescent and flaring radio emission. This information was summarized in McLean et al. (2012) and is also derived from the surveys of ultracool dwarfs presented here. A statistical test may be performed to determine if the rotational velocities of the radio- active ultracool dwarfs are different from those of the radio-quiet dwarfs. A histogram of the two populations appears in Figure 5.03. We can perform a two-sample t-test on the means of the two populations’ rotational velocities to test the hypotheses, letting µA denote the mean rotational velocity of the population of radio-active sources, and µI denoting the mean rotational velocity of the population of radio-inactive sources. The null hypothesis is that the mean rotational velocities for the two populations are the same, indicating that rotational plays no role in radio emission. The alternative hypothesis, then, is that it does play a role.

Ho: µA = µI (5.02) Ha: µA ≠ µI (5.03)

96

Histogram of Rotational Velocities

Variable 25 Radio-active RVs Radio-inactive RVs

20 y c

n 15 e u q e r F 10

5

0 10 20 30 40 50 60 70 Rotational Velocity (km/s)

Figure 5.03. Histogram of rotational velocities. Both radio-active and radio quiet ultracool dwarf histograms are displayed here.

Before we can use the two-sample t-test, both populations must be large and/or normally distributed. We can construct probability plots to analyze this as in Figure 5.04.

97

Probability Plot of Radio-active RVs, Radio-inactive RVs Normal - 95% CI

99.9 Variable Radio-active RVs 99 Radio-inactive RVs

95 Mean StDev N AD P 90 31.08 17.98 13 0.254 0.672 20.73 16.89 115 4.502 <0.005 80

t 70 n 60 e

c 50 r 40 e

P 30 20 10 5

1

0.1 -50 -25 0 25 50 75 100 125 Data

Figure 5.04. Probability plot of both radio-active and radio-inactive populations. The population of radio emitting ultracool dwarf rotational velocities appears to be normally distributed. The inactive dwarf rotational velocities are not, but due to the large size of the population, the t-test is still valid.

From this plot, the condition that the rotational velocities from the radio-active sources are normally distributed appears to hold true: all data points are within the confidence intervals. However, for the population of rotational velocities from the radio-inactive sources, there is significant departure from normality, as a number of points are beyond the confidence bounds. Yet the sample size is 115, which is much greater than 30, the typical threshold population size considered for the application of the Central Limit Theorem. Thus, the two-sample t-test is valid for this problem. Next, we must decide whether to use pooled standard deviations to enhance the statistics of this analysis. Given that one population only has 13 sources, it would be advantageous to use pooled standard deviations if they are similar in magnitude. The ratio of the standard deviations of the two populations is 1.06, well within the recommended range for the usage of this method of 1/√2 < SA/SI < √2, where SA is the standard deviation of the active population and SI is the standard deviation of the inactive population. We perform the t-test under the hypothesis conditions described earlier, with the output from Minitab shown below.

Two-sample T for Radio-active RVs vs Radio-inactive RVs

N Mean StDev SE Mean Radio-active RVs 13 31.1 18.0 5.0 Radio-inactive R 115 20.7 16.9 1.6

Difference = mu (Radio-active RVs) - mu (Radio-inactive RVs)

98

Estimate for difference: 10.3500 95% CI for difference: (0.5059, 20.1940) T-Test of difference= 0 (vs not =):T-Value = 2.08 P-Value = 0.039 DF =126 Both use Pooled StDev = 17.0000

The result is that the p-value = 0.039 < 0.05. Thus, with 95% confidence, we can reject the null hypothesis that the mean rotational velocities of the two populations are similar. We can go a step further and refine the analysis. Since theory indicates that radio-active sources generally have more rapid rotation, we can rewrite the hypothesis test. Specifically, we wish the alternative hypothesis to be stronger; we wish to know if the radio emitting sources actually rotate faster than the inactive sources, we do not simply want to know if they are different. If we set up the hypothesis test as:

Ho: µA = µI (5.04) Ha: µA > µI (5.05)

to reflect this, then the result is:

Two-sample T for Radio-active RVs vs Radio-inactive RVs

N Mean StDev SE Mean Radio-active RVs 13 31.1 18.0 5.0 Radio-inactive R 115 20.7 16.9 1.6

Difference = mu (Radio-active RVs) - mu (Radio-inactive RVs) Estimate for difference: 10.3500 95% lower bound for difference: 2.1073 T-Test of difference = 0 (vs >): T-Value = 2.08 P-Value = 0.020 DF = 126 Both use Pooled StDev = 17.0000

Again, the p-value is 0.02 < 0.05, indicating that we can reject the null hypothesis with 95% confidence. This analysis lends support to the notion that the mean rotational velocity of the population of radio-active ultracool dwarfs is greater than the mean rotational velocity of the population of radio-inactive ultracool dwarfs.

5.5.2. Monte Carlo Simulator

Based on the results from the two surveys presented here and the results from previous surveys, we can construct a Monte Carlo simulator to study the population of all ultracool dwarfs and make inferences about that population based on the detection statistics. In this section, the construction of such a simulator will be explained and its key findings described.

5.5.2.1. Simulator Construction

The Monte Carlo simulator as implemented here consists of six distributions: a rotational period distribution, a flare-type probability distribution, a flare flux density distribution, a

99 distribution of observations lengths, a distribution of observation sensitivity thresholds, and a final detection distribution. The following paragraphs will describe these distributions in detail. The projected rotational period distribution uses the summarized rotational velocity data presented in McLean et al. (2012), which contained rotational velocities for M7-L8 ultracool dwarfs, and from Zapatero Osorio et al. (2006), which extended the rotational velocity knowledge to type T8. These projected rotational velocities (v sin i) were then converted to rotational periods by assuming the objects had radii of 1 RJ, which should be within ±10% of the true radius of such objects. Next, a normalized histogram was created and an empirically derived curve fit to the results. Two good fits were determined which hinged on the viability of the accurate reporting of objects with rotational periods of 40 hours or more. A number of these objects actually have rotational periods with a lower limit of 40 hours, which creates a small peak in frequency on the histogram.

Figure 5.05. Histogram of rotational periods of ultracool dwarfs. The sources for this data are Zapatero Osorio et al. (2006) and McLean et al. (2012).

This peak was assumed to not really exist, and since the rotational periods could have any value > 40 hours, they were excluded from fitting, so that the best fit to the data was a double- peaked Gaussian of the form

. . ( ) = 0.3875 . + 0.124 . 푥−3 726 2 푥−10 14 2 (5.06) −� 1 566 � −� 7 978 � If, however, there is a real푓 cluster푥 of rotationa푒 l periods of 40-45 푒hrs., then the best fit solution would be a 6th order polynomial. It should be emphasized that this fit most likely has no physical

100 meaning that it represents, it is simply an empirical fit that will allow us to model the distribution and randomly select rotational velocities with frequencies that mirror those observed in nature. This f(x) is the probability distribution function for this physical property of ultracool dwarfs modeled by the simulator, and can be used as described in Appendix B. The other empirical fits to physical properties that follow can be used similarly in the Monte Carlo simulator. Using the information given in McLean et al. (2012) added to the results of our survey, we can estimate the flaring behavior of a sample of ultracool dwarfs of spectral type ≥ M7. However, when compiling the statistics, it is worth noting that many surveys do not construct time series data, and so while they may have bursting ultracool dwarfs in their data, they have failed to detect them, as discussed previously. We will only include, therefore, those survey results where bursting sources could have been detected. This includes the surveys Berger et al. (2002), Burgasser & Putman (2005), Berger (2006), Antonova et al. (2008), McLean (2011), Antonova et al. (2013), and this work. In total, then, 96 sources were surveyed and 8 sources were detected. Of these eight flaring objects, four of them (TVLM-513, LSR J1835+3, J0746+20, J0036+18) are sources of periodic flares, while the remaining four (DENIS 1048, BRI B0021-0, J1047+21, J1439+19) appear to flare only sporadically during their survey detection. Our preliminary results suggest that J1047+21 (Route & Wolszczan 2012) and J1439+19 do not flare periodically. We also note that while LP944-20 is a known flaring source, it was discovered to emit radio waves after it was known to already emit X-rays (Berger et al. 2001). It is therefore omitted from many of these considerations. A preliminary word of caution also needs to be added here. Since the McLean et al. (2012) paper publishes results for spectral types M-L3.5, this treatment assumes that the flaring behavior probabilities extend down to T8 and beyond. This may or may not be the case; however, at this time there are no theoretical papers that suggest a change in the internal dynamo mechanism between spectral types L3.5 and T8 that may result in different magnetic activity and hence differing flaring behavior. The difference in atmospheric composition, which may alter flaring behavior, has been discussed previously in the introduction. For the purposes of this dissertation, we have bundled together spectral types later than M7 and studied them together, thus, to be consistent we will assume that the flaring behavior probability is not a function of spectral type. Another advisory note is that any of these sporadically flaring sources may turn out to be periodically flaring if observed enough with sufficient temporal resolution. It may also be that the sources are periodic, but that the time between flaring events is much longer than the rotational periods of the objects. For these cases, given the way in which the Monte Carlo flare detection algorithm works, objects that flare less than once per rotational period are classified as intermittently flaring sources. Next, we wish to construct a flare flux density distribution. Physically, this combines two effects into one distribution: the spatial density of ultracool dwarfs (primarily their distance), and the strength of their flares. Observationally, the effects are not distinguishable so we simply construct a distribution for the flare flux density per object. In order to generate a flare flux density distribution, we use the results from our extensive monitoring campaign of TVLM 513, which will be discussed in Section 6.1. A normalized histogram (Figure 5.06) was computed for these detected flares, which were then fit with a power law of the form

( ) = 0.3958 0.2601( 1.25) . (5.07) 0 2326 as shown in Figure 5.06. 푓 푥 − 푋 −

101

Figure 5.06. Histogram of TVLM flare flux densities, as will be described in Chapter 6. A power law fit has been applied.

Now we focus our discussion on the properties from the observational side of the situation. First, we want to construct a distribution of how long we can continuously observe a single source. This distribution will very much depend on the capabilities of the observing radio telescope and on the scheduling parameters of the observing site. To illuminate the results of this survey, the continuous observation lengths that were conducted at Arecibo Observatory have been compiled. A normalized histogram has been constructed and this data, without fitting has been used as the probability distribution function for the simulator (see Figure 5.07). It should be noted that the observation lengths occur in integral multiples of 10-minute intervals (the length of a single scan) and this characteristic has been carried through into the simulated observations.

102

Figure 5.07. Histogram of observing sessions. This histogram depicts the typical length of time that one may observe a source continuously at Arecibo Observatory, given instrumental effects and scheduling constraints.

Next, we examine the sensitivity threshold, which will also depend on the telescope and instruments used to conduct the observations. These results have been compiled for all ultracool dwarf observations during the course of the surveys, regardless of weather and observing conditions. These data were combined to yield Tables 5.05 and 5.06. A normalized histogram was constructed for these results as presented in Figure 5.08. Both single and double Gaussian profiles were attempted as fits to the sensitivity behavior. However, the double Gaussian is superior in that it accounts for the excess frequency of observations clustered around a sensitivity of 1.34 mJy. The result of this best-fit curve is

. . ( ) = 0.2494 . + 0.124 . 푥−1 075 2 푥−1 339 2 (5.08) −� 0 1182 � −� 0 2893 � 푓 푥 푒 푒

103

Figure 5.08. Histogram of instrumental sensitivities. This compiles the sensitivities by object as observed with the Arecibo Radio Telescope.

With all of the distributions computed, how should we proceed to determine if a source is detected or not? When a source has a detectable flare, if its rotational period is less than the observation period, the flare will certainly be detected. However, if this is not the case, and the rotational period is longer than the observation length, we require a means to determine if the flare is detected. The probability of detection is scaled by the ratio of the observation length to the rotational period, and then a uniform distribution (the “detection distribution”) is used to determine if the flare is detected or not. The simulator is then run with the generation of these parameters, and a final algorithm is used to determine whether sources were detected. To summarize, sources are detected under the following conditions:

• A source is aperiodic and its flare flux density exceeds the sensitivity for the observation. No rotation information is of interest because the source is randomly flaring. • A source is periodic, its flare flux density exceeds the sensitivity for the observation, and the observation length is greater than its rotational period. • A source is periodic, its flare flux density exceeds the sensitivity for the observation, the observation length is less than the rotational period, but a draw from the detection distribution results in a detection.

If none of these conditions is satisfied, the object is not detected by the survey as a flaring source. The simulator was then run to generate a large number of ultracool dwarfs (N 104 sources) and their accompanying survey observing conditions. Each source is then either detected as flaring or not by the algorithm described above. The bulk number of detected≳ sources were found to agree roughly with the number detected by the survey as presented in Section 5.3, and Antonova et al. (2013), thus ensuring that the results from the Monte Carlo simulator were validated.

104 5.5.2.2. Simulation Results

A few inferences about the population of ultracool dwarfs can be made from our simulator, although the uncertainties on these parameters are large as will be described. First, the simulator indicates that the population of radio-flaring ultracool dwarfs is actually ~2.5 times bigger than observed based on the observing statistics. That is, to arrive at a similar bulk number of detected sources, the simulator results reveal which sources were flaring intermittently and sporadically, yet were not detected and why this happened. Among this much greater set of flaring objects, the simulator predicts that ~25% of the UCDs are periodically flaring sources, with the remaining 75% being intermittently flaring sources which flare on timescales much larger than their rotational periods. Finally, the simulator indicates that the reasons for the failure to detect this much larger flaring population is that ~50% are missed merely due to the observing constraints of Arecibo Observatory; namely, that the maximum potential observing time is ~2 hours. Nearly 80% of sources are not observed due to the instrumentation not being sensitive enough to detect their bursting behavior, while approximately 30% are missed due to both factors: not enough sensitivity and the observing sessions not being long enough. The above results must be considered in the light of the limitations of the simulator. Two distributions in particular are not well known: the “flare-type distribution” and the “flare flux density distribution.” The “flare type” distribution is based on only eight known flaring ultracool dwarfs, making the normalized uncertainty for this distribution approximately 12%. For the 88 ultracool dwarfs not observed to flare in the flare-type distribution, these may actually be sources that flare but merely were not observed to do so. This contributes to the uncertainty in the actual size of the flaring population. The fit to the flare flux density distribution requires special skepticism due to the fact that the fit to the distribution itself comes from a single M9 source. It is unknown if the flare flux density distribution will be the same for cooler objects. While the flare flux density distribution was modeled by a weak power law, research into the flux distribution of solar flares indicated that they have either an exponential or steep power law distribution, which does not agree well with these results (Isliker & Benz 2001). The applicability, though, of this fact to ECMI-induced flaring is also unknown, as the steep power law model was devised for a type of solar radiation unrelated to Type IV radio bursts which are the ones thought to be caused by ECMI. It could also be that the power law fitting the flare flux densities will become steeper with improved instrumental sensitivity that enhances the ability to detect weaker flares. Additionally, in the simulator sporadically flaring sources are modeled as sources that flare randomly on timescales much larger than their rotational periods. It could very well be that these sources actually have “recharge” times that result from mass loading of the magnetic field lines, or the accumulation of energy to drive the emission mechanism. Both of these instances are even more poorly understood than the distributions used to construct the simulator, which is why the sporadically flaring sources are modeled as they are.

5.6. Arecibo A2776 Survey

Given that the two radio surveys have discovered new and interesting brown dwarfs for further study, we have begun a third survey at Arecibo Observatory, A2776. This survey will search for radio emission from a third set of ultracool dwarfs, of spectral types M8-T9. Forty

105 recently discovered ultracool dwarfs were selected with refined constraints, learned from our experiences doing the previous two ultracool dwarf surveys. Again, the first constraint is that the sources be located in the 0 to +38° declination range so that Arecibo’s fixed dish may view them. Second, as most detected radio-active brown dwarfs have been relatively close, and all of our detected sources are < 20 pc from Earth, we have made this a criteria of our search, improving upon the previous constraint of searching for radio emission from objects < 50 pc away. Third, we again preferred later spectral types to ferret out the coolest radio flaring brown dwarfs. Fourth, we restricted our sources to a range of coordinates for which radio observatories receive fewer requests so as to maximize our chances of viewing the sources. This right ascension range is 21-2 hours and 7-14 hours. The construction of this survey builds on our previous experience in a number of ways. One is searching a closer volume of space. A second improvement is that this survey will be dual band, using the C-band receiver (as in the A2471 and A2623 surveys) and the S-band “high” receiver. The C-band receiver has a center frequency of 4.8 GHz, while the S-band “high” receiver has a center frequency of 3.5 GHz. This would allow us to probe weaker magnetic fields than previously, down to 1.25 kG. It could potentially allow for the determination of spectral indices for sources, if they can be detected at both frequencies. A third improvement is that all sources will be observed for two or more hours per band, which has the virtue of observing each source through, potentially, a large fraction of its rotational period. We saw in the previous section on population inference how most brown dwarfs have rotation periods of 2-4 hours, and these may be more active. A fourth improvement is that instrumentation at Arecibo Observatory has been repaired such that a single object can be observed for almost 2.5 hours, compared to 2 hours previously. This also ties in with the previous sentiment about better understanding how potentially periodic rotation and radio activity may be linked. The proposed targets are given in Table 5.07. Observations for this proposal using the C- band receiver alone were begun March 2013. At the time of this writing, 25 of the 40 sources have been observed for their required 2 hours in this band, although the data calibration and detailed analysis are still pending.

Spectral Right Ascension Declination Distance Designation Type (hh mm ss) (dd mm ss) (pc) Binary SDSS J000013.54+255418.6 T4.5 00 00 13.5 25 54 18 14.12 LP 349-25 A M8 00 27 55.9 22 19 33 14.37 x 2MASSW J0036159+182110 A L3.5 00 36 16.2 18 21 10 8.76 x 54 Psc B T7.5 00 39 18.9 21 15 17 11.11 x 2MASSW J0045214+163445 L2 00 45 21.4 16 34 45 14 2MASS J01092170+2949255 M9.5 01 09 21.7 29 49 26 18 2MASS J07003664+3157266 A L3.5 07 00 36.6 31 57 27 11.36 x 2MASS J07271824+1710012 T8 07 27 18.2 17 10 01 9.08 SDSS J074149.15+235127.5 T5 07 41 49.2 23 51 28 18 SDSS J074201.41+205520.5 T5 07 42 01.3 20 55 20 15.04 WISEPA J075003.84+272544.8 T8.5 07 50 03.8 27 25 45 14.1 SDSS J075547.87+221215.6 T6 07 55 48.0 22 12 17 18 2MASS J08105865+1420390 M9 08 10 58.7 14 20 39 17.8 SDSS J082519.45+211550.3 L7.5 08 25 19.7 21 15 52 10.7

106

WISE J083811.45+151115.1 T6.5 08 38 11.6 15 11 16 20 SDSS J090023.68+253934.3 L6 09 00 23.7 25 39 35 18.6 SDSS J092308.70+234013.7 L1 09 23 08.6 23 40 15 13.7 2MASS J09373487+2931409 T7 09 37 34.9 29 31 41 6.12 SDSS J104307.51+222523.5 L8 10 43 07.6 22 25 24 16 SDSS J104335.08+121314.1 L7 10 43 35.1 12 13 15 14.6 SDSS J110401.29+195922.3 L4 11 04 01.3 19 59 22 18 WISE J111838.70+312537.9 T8.5 11 18 38.7 31 25 38 8.29 x WISEPC J112254.73+255021.5 T6 11 22 54.7 25 50 22 16.9 WISEPC J121756.91+162640.2 T9 12 17 56.9 16 26 40 6.7 SDSS J121951.45+312849.4 L8 12 19 51.6 31 28 50 19 Ross 458 C T8 13 00 41.7 12 21 15 11.43 x 2MASS J13004255+1912354 L1 13 00 42.6 19 12 35 13.9 ULAS J130217.21+130851.2 T8.5 13 02 17.2 13 08 51 14 2MASS J13142039+1320011 M7 13 14 20.4 13 20 01 16.4 PSO J201.0320+19.1072 T3.5 13 24 07.7 19 06 26 20 ULAS J133553.45+113005.2 T9 13 35 53.5 11 30 05 10.34 HN Peg B T2.5 21 44 28.5 14 46 08 18.39 x WISEPC J215751.38+265931.4 T7 21 57 51.4 26 59 31 19.1 WISEPC J223937.55+161716.2 T3 22 39 37.6 16 17 16 18.3 2MASS J22443167+2043433 L6.5 22 44 31.7 20 43 43 19 2MASS J22541892+3123498 T4 22 54 18.9 31 23 50 14 ULAS J232123.79+135454.9 T7.5 23 21 23.8 13 54 59 14 2MASS J23391025+1352284 T5 23 39 10.3 13 52 28 18 WISEPC J234446.25+103415.8 T9 23 44 46.3 10 34 16 15.6 2MASSW J2349489+122438 L4 23 49 49 12 24 39 19.6 Table 5.07. Ultracool dwarf targets for the A2776 survey. The sources are ordered by right ascension. The spectral types and distances are given, and objects that are actually binary systems are marked with an “X.” This table benefited from “List of Brown Dwarfs,'' http://www.johnstonsarchive.net/astro/browndwarflist.html, 2012.

107

Chapter 6

Ultracool Dwarf Discoveries and Investigations

Note: a large quantity of the material presented in this chapter will be significantly similar to the papers Route, M. & Wolszczan, A. 2012, ApJ, 747, L22 and Route, M. & Wolszczan, A. 2013, ApJ, in press.

Of all the objects observed in our surveys, we detected flaring radio emission from a total of four sources. Two of these sources, J07464256+2000321 (J0746+20, hereafter) and TVLM 513-46546 (TVLM 513) were previously known to be radio-flaring objects. The examination of J0746+20 was done for calibration purposes and analysis tool validation. The observation of TVLM 513 was undertaken for two main reasons: as a known flaring source, it could be used to develop and test the instrumentation and software analysis methods discussed in Chapter 3, and to examine the long-term magnetic field stability of a well observed source. Furthermore, by observing these sources we were able to construct time-frequency spectrograms of their bursting behavior and derive frequency drift rates. J0746+20 was discussed in Section 5.3. In this chapter, we will focus on the monitoring campaign of TVLM 513 and the two new sources that were identified in these surveys: 2MASS J10475385+2124234 (hereafter J1047+21) and 2MASS J1439284+192915 (hereafter J1439+19).

6.1. TVLM 513-46546

TVLM 513 has had an important role to play in the history of the study of ultracool dwarf radio emission. Its key properties were discussed in Section 2.1.4. In this section, the totality of our observations of TVLM 513 will be described. These observations have spanned nearly five years, starting in December 2008 and continuing through to April 2013. This allows us to examine the evolution of the radio emission and magnetic field from this object over a longer time scale and in more detail than has been done previously.

6.1.1. Observations of TVLM 513

Our first observations of TVLM 513 were conducted with the WAPP spectrometer. These observations were mostly used to establish that the Arecibo instrumentation could easily detect radio flares from the source. In essence, the observations were a “proof of concept” for the surveys that searched for radio emission from exoplanets and brown dwarfs as described in Chapters 4 and 5. The acquisition of these data sets was also of key importance in the development of analysis software. The observing log for this test period is shown in Table 6.01.

108 While only a few hours of data were collected, several types of radio flares were recorded, indicating that a survey of ultracool dwarfs and exoplanets could work.

Source Date Scans Time on Center Frequency Bandpass Beam Size Source (MHz) (MHz) (arcmin) (ks) TVLM513 20081228 2 1.2 4800 4300-5300 1.15 x 1.18 20081229 4 2.4 4800 4300-5300 1.15 x 1.18 20081230 9 5.4 4800 4300-5300 1.15 x 1.18 20090104 4 2.4 4800 4300-5300 1.15 x 1.18 Table 6.01. Proof of concept observations of TVLM 513. These observations span only a few days in December 2008 to January 2009. Multiple flare events were detected, showing that the project would work. The date format is YYYYMMDD.

After the completion of the A2623 survey, we obtained additional time to attempt to spot radio flares from TVLM 513 as part of project A2803. These observations took place from October 2012 to March 2013. The observing log for this campaign is shown in Table 6.02.

Time on Center Frequency Bandpass Beam Size Date Scans Source (ks) (MHz) (MHz) (arcmin) 20121027 12 7.2 4750 4239-5262 1.15 x 1.18 20121028 6 3.6 4750 4239-5262 1.15 x 1.18 20121229 6 3.6 4750 4239-5262 1.15 x 1.18 20130113 6 3.6 4750 4239-5262 1.15 x 1.18 20130202 11 6.6 4750 4239-5262 1.15 x 1.18 20130212 8 4.8 4750 4239-5262 1.15 x 1.18 20130214 7 4.2 4750 4239-5262 1.15 x 1.18 20130217 11 6.6 4750 4239-5262 1.15 x 1.18 20130222 12 7.2 4750 4239-5262 1.15 x 1.18 20130225 11 6.6 4750 4239-5262 1.15 x 1.18 20130228 11 6.6 4750 4239-5262 1.15 x 1.18 20130306 11 6.6 4750 4239-5262 1.15 x 1.18 20130307 7 4.2 4750 4239-5262 1.15 x 1.18 20130308 14 8.4 4750 4239-5262 1.15 x 1.18 20130317 12 7.2 4750 4239-5262 1.15 x 1.18 20130328 12 7.2 4750 4239-5262 1.15 x 1.18 Table 6.02. Observing log of additional TVLM 513 data sets, taken as part of Arecibo observing program A2803. The date format is YYYYMMDD.

109 6.1.2. Flares and Flare Properties

In our observations, we have observed a number of flaring events, with a number of different morphologies. Samples of the diversity of flaring that occurs from TVLM 513 can be seen in accompanying Figures 6.01-6.06. They are grouped together in pairs by morphology. For each set, the older data is introduced and described, and then its most recent analogue is presented. If WAPP data is available, it is used as the older data set to better exemplify the recurrence of similar features over time. It should be emphasized that the usage of dynamic spectra that occurs in the following pages represents a novel means to examine substellar objects. While dynamic spectra (time- frequency spectrograms) are ubiquitous in electrical engineering, have been used to study terrestrial and Jovian planetary radio emission, and are commonly used to investigate solar flare phenomenon, they have never been applied to exoplanets or ultracool dwarfs. This represents a major technological advance in the field allowing more physics of the source and its environment to be extracted from the data.

110

Figure 6.01. A broadband burst of left circularly polarized emission. This contains the “Large Left” feature, where a strong and wide left-circularly polarized signal stretches across the entire bandpass. This was taken with the WAPP spectrometer, and is dated 2008-12-29.

111

Figure 6.02. Recent observation of the “Large Left” feature. This dynamic spectrum is from the Mock spectrometer, and is dated 2013-03-17. Thus, this feature has been stable over the course of 4.5 years.

112

Figure 6.03. The “Double Right” morphology. In the fourth subcorrelator from the top, it can easily be seen that there is a double-peaked feature as the right-circularly polarized flare evolves from higher to lower frequencies with time. A smaller left circular polarized feature is visible at lower right. This data set was taken on 2008-12-30 with the WAPP spectrometer.

113

Figure 6.04. The “Double Right” morphology strikes again. Whereas Figure 6.03 shows the double peak structure being most prominent at 4870 MHz, here it is most easily seen at 4600 MHz instead. Thus, the morphology is the same, but the frequency has shifted some over the course of 4.5 years. This set is from 2013-02-22.

114

Figure 6.05. The “Narrow Bright Right” feature. This feature does not appear in any older WAPP spectrograms. The feature is a narrow, strong burst of right circularly polarized emission. Peak flux density is reached at ~4900 MHz with a flux density of ≥ 4 mJy. A pair of left- circularly polarized emission bursts appears to be present at the left of the spectrograms. This data set was taken on 2013-02-25.

115

Figure 6.06. The “Narrow Bright Right” feature reappears. Nearly the same item as Figure 6.05, but the peak flux density is reached at ~4400 MHz, also with a peak flux density of ≥ 4 mJy. This data set was taken on 2013-03-06, so the feature is only stable on a timescale of weeks.

116 The accumulated flaring properties, which include data from December 2008 to April 2013 are presented here in Table 6.03, with an accompanying histogram of the flare distribution in Figure 6.07. Flux Brightness Time of Duration Density Polarization Drift Rate B Temperature Peak (MJD) (s) (mJy) (%) (MHz/s) (G) (K) 54829.497616 70 -4.986 -36 -16 1786 4.4 x 1010 54829.503403 100 -3.732 -100 -13 1786 3.3 x 1010 54830.507951 25 -2.097 -58 -20 1786 1.9 x 1010 54830.509699 23 3.175 100 22 1786 2.8 x 1010 54830.516979 60 2.994 100 -11 1786 2.6 x 1010 56015.314082 11 -3.07 -81 140 1786 2.7 x 1010 56015.316854 11 -1.371 -69 - 1786 1.2 x 1010 56016.303931 25 1.183 85 55 1786 1.0 x 1010 56016.304776 70 -1.36 -72 -40 1786 1.2 x 1010 56227.693470 23 3.468 100 - 1786 3.1 x 1010 56227.700584 31 2.425 34 -10 1786 2.1 x 1010 56290.545011 9 2.433 100 - 1786 2.1 x 1010 56290.560490 7 2.043 100 - 1786 1.8 x 1010 56305.493899 133 0.371 9 10 1786 3.3 x 1010 56305.496552 52 1.595 100 -30 1786 1.4 x 1010 56305.505938 38 2.455 83 -23 1786 2.2 x 1010 56335.417783 43 1.934 100 -20 1786 1.7 x 1010 56335.449815 62 1.524 43 40 1786 1.3 x 1010 56335.460637 49 -2.727 98 - 1786 2.4 x 1010 56337.417304 19 -1.165 100 -5 1786 1.0 x 1010 56337.427649 50 4.69 100 - 1786 4.1 x 1010 56337.431876 14 -1.742 66 - 1786 1.5 x 1010 56340.431263 34 3.453 100 - 1786 3.0 x 1010 56340.434554 28 -1.957 100 -26 1786 1.7 x 1010 56340.441262 44 -2.434 100 - 1786 2.1 x 1010 56340.447741 59 2.371 100 40 1786 2.1 x 1010 56340.448533 40 2.704 92 40 1786 2.4 x 1010 56345.415138 23 -1.343 100 - 1786 1.2 x 1010 56345.422096 29 2.607 100 50 1786 2.3 x 1010 56345.428032 30 2.366 100 -14 1786 2.1 x 1010 56348.351927 49 1.443 100 - 1786 1.3 x 1010 56348.356044 32 -1.984 100 - 1786 1.8 x 1010 56348.361084 50 -2.143 100 -45 1786 1.9 x 1010

117

56348.365492 34 4.4 100 - 1786 3.9 x 1010 56351.370647 39 1.294 100 - 1786 1.1 x 1010 56351.375740 90 3.923 100 30 1786 3.5 x 1010 56351.380042 63 -2.241 100 - 1786 2.0 x 1010 56351.384398 61 5.252 84 - 1786 4.6 x 1010 56351.385597 26 3.17 64 -12 1786 2.8 x 1010 56357.332877 46 -1.495 21 9 1786 1.3 x 1010 56357.337292 98 -1.353 33 11 1786 1.2 x 1010 56357.340492 129 -1.52 52 8 1786 1.3 x 1010 56357.345730 83 3.845 60 -70 1786 3.4 x 1010 56358.326691 58 2.793 81 - 1786 2.5 x 1010 56358.328584 30 1.858 100 - 1786 1.6 x 1010 56359.377022 139 -1.88 19 -25 1786 1.7 x 1010 56359.387450 109 3.377 100 55 1786 3.0 x 1010 56368.356096 101 -3.335 100 -6 1786 2.9 x 1010 56379.293834 35 1.688 40 - 1786 1.5 x 1010 56379.295168 52 -4.472 100 -37 1786 3.9 x 1010 56379.306565 78 -3.465 100 - 1786 3.1 x 1010 56379.307097 28 2.014 100 - 1786 1.8 x 1010 56379.313575 68 -2.057 100 -25 1786 1.8 x 1010 Table 6.03. Summary of TVLM 513 emission features for 2008-2013. Left polarizations are denoted by a negative Stokes V flux density. A dash in place of a drift rate means that there was no measurable drift in the emission. The magnetic field estimate is a lower limit, as the cutoff frequency for the emission was not reached in clean portions of the Mock spectrometer bandpass. Brightness temperatures are computed assuming the source emission region is approximately 1 Jovian radius in size.

118

Figure 6.07. Histogram of TVLM 513 flare flux densities. These Stokes V flux densities are presented in Table 6.03.

6.1.3. Physical Properties of the Source and Plasma Environment

From the known properties of TVLM 513, such as its distance and the accompanying radio observations described in Section 6.1.2, a number of properties of the source and its physical environment can be determined. These include: • The magnetic field strength and geometry, which can be determined via the cutoff frequency, which can be computed from the local cyclotron frequency. The properties of the field can be inferred from the short-term and long-term temporal behavior of the observed emission. • The radio emission mechanism, as made distinguishable based on the criteria given in Chapter 2. • The size of the radio-emitting region, for which an upper limit can be determined by measuring the time scale of the shortest temporal variations, and invoking a light travel time argument. Another possible method is to infer the source size from measurements of the magnetic field strength, and frequency drift rate of radio bursts, assuming the field geometry and velocity of the emitting plasma along the field lines, as given in Equation 6.02 on the following page. • The rotational period of the object can be inferred by the measurement of periodic bursts of emission. This method is applied to determine the rotational periods of the interiors of the giant planets in the Solar System (de Pater & Lissauer 2010).

119

• Observations of radio emission over the course of years can reveal the long-term stability of the magnetic field of UCDs. • The binarity of a system can be established based on subtle changes in the arrival times of bursts of radio emission from a periodically emitting object. • Plasma motion along the line of sight is indicated by the frequency drift observed in time- frequency spectrograms. • The electron density of the plasma causing the radio emission can be computed from the local cyclotron frequency, assuming that it has to be higher than the local plasma frequency in order to escape the plasma.

There are some notable features observed in the TVLM flares, which can be thought of as the result of a cone of plasma emitting via the ECMI mechanism that crosses into and then out of our line of sight, as mentioned in Section 2.3.2. They exhibit both left and right circular polarizations. Polarization fractions for the flare events are high, generally ≥ 60%. From the time series data, we can examine the temporal behavior of the bursts. The smallest temporal features recorded with the WAPP spectrometer were at the limit of the temporal resolution of the instrument (0.99965 s). The same is also true of bursts recorded with the Mock spectrometer (0.1 s). Recalling our discussion of the AKR, to distinguish clearly fine striation in the broadband radio emission, frequency resolutions of ~1 Hz and ~0.5 s are required. While we have sufficient temporal resolution to search for such striation, we do not have adequate frequency resolution to do so. The dynamic spectra can then be leveraged to examine how bursts evolve in both time and frequency. Frequency drift rates range from -70 MHz s-1 to +140 MHz s-1, and appear to be uncorrelated with other burst features. We investigated whether this phenomenon of frequency drift could be the result of plasma causing dispersion of the radio emission, as described by Equation 6.01 (Lorimer & Kramer 2005).

= 4.15 × 10 (6.01) 6 1 1 푑 2 2 휈1 휈2 0 푒 In this equation, Δt is the∆ temporal푡 broadening� of− the �signal∫ 푛 in푑푙 ms, the bandpass over which the frequency drift is observed is given by ν2- ν1, and ne is the dispersion measure which has units of cm-3 pc observed over path length dl. However, such dispersion would have resulted in a frequency drift over a very short time of < 54 ms, which is shorter than the shortest detected features in the dynamic spectra that have a time scale of 0.1 s. Thus, another mechanism to explain the frequency drift is required, such as the motion of the emitting plasma itself. That the frequency drifts can be both positive and negative indicates that plasma may either move toward or away from us in the star’s magnetic field along our line of sight. This drift rate may be used to determine the velocity of plasma in a magnetic field, since motion toward (away) from a magnetized object would yield a larger (smaller) magnetic field strength as the local cyclotron frequency changes. If the drift is the result of plasma motion along a magnetic field line, then the following equation can be used to calculate the velocity of the plasma (Osten & Bastian 2008):

/ 47 / (6.02) 1 3 −4 3 0 where v is the velocity, a is the length of 푣the≈ source푎퐵 region휈̇휈 size, B0 is the magnetic field strength, is the frequency drift rate, and υ is the center frequency of the drifting radio emission. The calculated plasma velocities derived from this formula for these data are comparable to those 휈̇

120 found in the solar wind and during coronal mass ejections (CMEs), of 300-1000 km s-1 for a source region 1 RJ across (Treumann 2006, de Pater & Lissauer 2010). If the source emitting region is smaller in size, such as closer in extent to those found in the AKR (~ 150 km), the plasma velocities are correspondingly smaller (~400 m s-1).

6.1.4. TVLM 513 Flare Timing Analysis

The analysis of the data taken during A2803 is an ongoing process. Our intention is to tabulate the times at which a number of burst features occur, including peak flux density, onset of the formation of a Stokes V envelope prior to the peak emission, and the time at which the envelope decays back to normal noise levels, thereby extending Table 6.03. Previous work (Hallinan et al. 2007, Doyle et al. 2010) has already demonstrated what the approximate periodicity of the object is. For the data that is in our possession, however, we may examine the long-term stability of the detectable radio flares and so analyze whether the previously found periodicity to the emission is constant. The results are shown in Figure 6.08.

TVLM 513 Phase Fitted Residuals 1000

500

0 2012.7 2012.8 2012.9 2013 2013.1 2013.2 2013.3

-500 Postfit Residuals (s) Residuals Postfit -1000

-1500 (Year)

Figure 6.08. Phase fitted periodic radio emission from TVLM 513. It can clearly be seen that clusters of bursts occur at progressively earlier times than expected from the phase fitted solution. Error bars denoted the uncertainty of the peak position, which have been conservatively estimated as the half width of the pulse envelope.

In this graph, a phase fit is constructed for the first six bursts of radio emission. When this fit is held constant, it is clear that the bursts come earlier in phase over time. The progression

121 is not exact in that each burst does not occur sooner than the previous one. Rather, clusters of bursts of emission can be seen to group at earlier and earlier times. This phenomenon is new and has yet to be mentioned in the literature. As such, its origin is unknown, although we may speculate as to its cause. One solution is that this change in burst periodicity is the result of interior dynamo activity, which alters the global dipolar magnetic field on timescales of months. Another solution is that the radio emission may come from an active region and local magnetic field, similar to a sunspot area. The decreasing time between radio bursts may then be tied to motion of the active region across the surface, such that the region drifts from the poles toward mid-latitudes. As stars undergo differential rotation, where rotation at the equator is faster than near the poles, this would have the effect of speeding up the rates at which flaring emission is observed. Since starspots have local magnetic fields, this latitude drift would not result in a change in emission frequency, which we have not observed. Previous studies (Hallinan et al. 2007; Doyle et al. 2010) have shown that the radio emission from TVLM 513 is stable over the course of years and maintains periodic emission. We believe that this stability is the result of two factors. First, no observing campaign of the source has been as extensive as this one, nor been conducted with as much temporal resolution. Most likely, the source was not studied with enough detail over a long enough time for accumulated phase shifts in the radio emission to become apparent. Second, the pairing of our results with previous ones indicates that the radio emission progressively shortens, but then resets. This would result in a cyclical behavior to the radio emission with a periodicity of months to years, upon which the radio emission related to the rotational period is superimposed.

6.2. 2MASS J10475385+2124234

6.2.1. Background Information on the Source

J1047+21 was found in the Two Micron All Sky Survey (2MASS) during a separate search for brown dwarfs (Burgasser 1999). Subsequent 2MASS photometry and near-infrared spectroscopy allowed for the absorption due to the presence of water and methane to be determined and the categorization of the object as a T6.5V dwarf (Burgasser et al. 2002), with an effective temperature of approximately 794-962 K at a distance of only 10.3 pc (Vrba et al. 2004). Its rotational period is unknown. The object does not appear to be a member of a binary system, out to a separation of ~ 4 AU and a ≥ 0.4 mass ratio (Burgasser et al. 2003a). Although the object is a weak Hα emitter (Burgasser 2003b), observations at the VLA showed that the brown dwarf was radio-inactive, with a 45 µJy upper limit of its radio flux (Berger 2006).

6.2.2. The Detection of Radio Flares from J1047+21

Our observations of this object were described in Section 5.2. Significantly, our search for bursting radio emission from this source revealed that it has sporadic bursts with peak flux density of up to 2.7 mJy and 89% circular polarization (Route and Wolszczan 2012). The high

122 brightness temperature of this object is indicative of emission via the electron cyclotron maser instability (ECMI). The result is real and is not the result of source confusion. While radio in the neighborhood of J1047+21 exist, it is highly unlikely that they contribute to the observed flaring behavior. The C-band receiver at Arecibo Observatory has an ellipsoidal beam pattern, with a half-power beam width (HPBW) at 4500 MHz of approximately 1.15’ in azimuth and 1.18’ in zenith angle. The HPBW shrinks at higher frequencies (Salter, personal communication). The nearest radio sources to J1047+21 are two radio galaxies, FIRST J104806.0+212559 and FIRST J104807.3+212600, located at distances of 3.43’ and 3.72’ respectively, from our source (Becker 2003). Since both galaxies are beyond the first radio side lobe that is less than 2’ from the center of the beam, the flux from both sources contribute negligibly to these results. In Figures 6.09 and 6.10, we present the flares in pairs. They are presented in chronological order of their detection, while the summary of their properties can be found in Table 6.04.

123

Figure 6.09. The discovery of radio flares from J1047+21. The event at left is from 2010-01-06 and the event at right is from 2012-12-05. The darkened horizontal line near 4400 MHz and the dark vertical block near 400s represent strong radio frequency interference that was excised from the image. At right, note that the individual spikes of emission have different frequency drift rates and directions. Morphologically, these two bursts are similar. In these dynamic spectra, black represents right circular polarization. Source: Route & Wolszczan (2012).

124

Figure 6.10. Two more radio flares for J1047+21. The event at left is from 2011-02-07 and the event at right is from 2013-05-06. Both features have weaker degrees of circular polarization than the first two events, especially the bursts at left. It may be noteworthy that both flares also have similar flare morphology, yet their structures differ from the previous two. The grayscale in this image is reversed from other dynamic spectra in this dissertation to enhance image clarity. Source: Route & Wolszczan (2012).

125

Frequency of Flux Maximum Time of Peak Duration Density Flux Density Polarization Drift Rate TB (MJD) (s) (mJy) (MHz) (%) (MHz/s) B (G) (K,1 RJ) 55202.355252 47 2.7 4466 89 0 1695 3.0x1010 55535.407212 123 1.3 4750 72 -110 1695 1.3x1010 55599.229936 55 0.8 4466 19 -55 1695 6.7x109 56418.987053 30 1.88 4466 33 0 1695 2.1x1010 Table 6.04. Summary of the four detected flares from J1047+21. Right polarizations are denoted by a positive Stokes V flux density. The 1σ uncertainty in all flux densities is ±0.2 mJy. The magnetic field strength values are lower limits, as the cutoff frequency was not observed within the Mock bandpass. Brightness temperatures are computed assuming the source emission region has a characteristic length of approximately 1 Jovian radius.

The bursts of radio emission emanating from this source appear to be aperiodic. However, by assuming that the first three bursts are the result of a periodic phenomenon, we constrained the periodicity of the burst activity to 2.08±0.05 hrs in multiples up to 2.775 days. Later observations in 2013 further constrained this period to longer than a continuous observation, or 2.5 hrs in length, in multiples up to 2.775 days. These results suggest that for short periods, the bursting may be derived from a global structure stable over long time periods, i.e. bursting related to ECMI from the global magnetic field. Alternatively, for periods at the upper portion of this range, these may be indicative of periodicity that results from the interaction of the brown dwarf’s magnetosphere with an orbiting companion that is injecting plasma into the system. In the Solar System, terrestrial ECMI events called the AKR are the result of plasma supplied by the solar wind, and powered by reconnection events in the terrestrial magnetotail caused by solar substorms (Treumann 2006). Also, bursts of radio emission from a binary pair of brown dwarfs have previously been detected in the 2MASSW J0746425+200032 system, which is composed of an L0 and L1.5 pair, but both components of this pair are warmer and more massive than J1047+21 (Berger et al. 2009). For an isolated source such as J1047+21 without a host star’s stellar wind that is as cool as 800-900 K, the production of plasma to fuel the ECMI outbursts is therefore problematic. Due to the large amount of time that has passed between the third and fourth burst, we are not able to phase connect this burst with the others at this time.

6.2.3. Discussion on the Source of the Radio Emission

If this brown dwarf is an intermittent emitter, what is the source of its emission then? In Section 1.4.3, several possibilities for the source of the radiation were listed. Magnetic reconnection is a possibility that onto which our observations cannot shed any light. Burgasser et al.’s (2003) observations suggest that the source of plasma and energy for activity does not come from matter being injected into the system as in the Jupiter-Io system. What about other sources of accretion? We cannot assess here the possibility of accretion from the interstellar medium, but the possibility of accretion of a cometary or asteroid body can be examined. Fortunately, we have a template to work from to analyze this possibility, namely, the impact of Comet Shoemaker Levy 9 (SL9) with Jupiter in July 2004. Jupiter has been known to emit various types of nonthermal radiation since the 1970s. One source of this radiation is a population of relativistic (1-300 MeV) electrons trapped in the

126 inner Jovian magnetosphere. This results in the emission of synchrotron radiation, which has a peak emission frequency of ~800 MHz and a flux density of 3.5- 5 Jy. The emission varies sinusoidally by ±15% as Jupiter rotates (de Pater et al. 1995). Before, during, and after the impact events, a global network of eleven radio telescopes observed the microwave radiation from Jupiter. The observing campaign began in June 1994 and ended in October 1994, while the impact events occurred from July 16-22, 1994. The resultant spectrum from these observations is shown in Figure 6.11.

Figure 6.11. The evolution of the Jovian radio power spectrum before, during, and after the Shoemaker Levy 9 impact events. The top set of data points and lines correspond to immediately after the impact (July), followed by data and lines for months after the impacts beneath them, finally followed by pre-impact data. The straight lines represent least-squares fits for the split domain of less than and greater than 0.9 GHz during and after the impact events, and less than/equal than 1.3 GHz before the impacts (de Pater et al. 1995).

From these observations, we can observe a number of characteristics of the radio emission. First, the radio emission does change in a discernible way from before to after the impacts, and this change in the power spectrum lasts for several months. Second, the increase in radio flux from synchrotron radiation immediately after the impact increases by nearly 2 Jy in magnitude at frequencies greater than 800 MHz, and still remains elevated by approximately 1 Jy at these frequencies three months later. Thirdly, the increase in radio flux is not uniform across the entire bandpass observed; rather, it is negligibly greater immediately after the impact, and decreases three months later. The spectrum has also hardened, with increased emission from more energetic electrons. The hardening further increases in October as opposed to July. Finally, de Pater et al. note that during the same time that the spectrum is seen to harden, the linear polarization of the emission increases by about 2% at wavelengths of 11-20 cm. The maximum brightness temperature of radio emission from the impacts was given as 450K (de Pater et al. 1995).

127 While the exact mechanism that results in all of this is unknown, the best guess is that it is the result of three effects. First, the electrons are energized by the impact events via a collisionless magnetohydrodynamic shock (MHD). This accelerates low energy electrons, thus increasing the overall energy of the electron population and hardening the spectrum. Second, this MHD shock also has the effect of scattering the pitch angles of the accelerated electrons, causing more to diffuse radially and so increasing electron energies, and again, decreasing the population of low-energy electrons (which are located at greater distances from Jupiter and “see” lower magnetic field strengths). The final effect is that the comet fragment impacts inject dust into the system, which degrade electron energies overall, but more so low-energy electrons. This effect would take longer to occur and is the hypothesized mechanism for the observed hardening of the radio spectrum between the impacts in July 1994 and the observations in October 2004 (de Pater et al. 1994, 1995; Dessler & Hill 1994; Ip 1994). We can use the information summarized above to determine the brightness temperature of such an event at J1047+21. We know that the brightness temperature of the radio emission is 450 K. However, the synchrotron emission is dependent on the magnetic field strength of the object since

= (6.02) 4 2 2 2 2 2푞 퐵 훾 훽 푠푖푛 훼 2 3 (Rybicki & Lightman 2004). In this푃 equation3푚 P푐 is the emitted power, q is the electric charge, B is the magnetic field strength, γ is the Lorentz factor, β is v/c, α is the pitch angle of the electrons involved in the emission, and m is their mass. The Jovian equatorial magnetic field strength is approximately 4 G, while J047+21 has polar magnetic field strength of ~1,600 G. By setting this power output equal to the blackbody luminosity and assuming that the emitting region of the impact is the same on both objects, we can derive that an SL9 impact would have a brightness temperature of ~9,000 K on J1047+21. The computed value is much lower than the brightness temperatures that we derive from observations, which are ~1010-1011 K. Furthermore, an SL9 impact event gives rise to a burst of synchrotron radiation, which should be ~10% linearly polarized, perhaps spiking at ~12% linear polarization after the impact event. However, J1047+21 has been shown to have ~89% circularly polarized radio emission. Finally, the ultracool dwarf J1047+21 appears to lack a disk and solar system- like debris, making the impact of a comet or similar sized body with the ultracool dwarf highly unlikely. We can therefore conclusively rule out an SL9 style event as the cause of the bursting activity observed at J1047+21.

6.2.4. Quiescent Radio Emission from J1047+21

Guided by our discovery, recently Williams et al. (2013) searched for quiescent emission from J1047+21 using the Very Large Array (VLA). They detected a radio source in the location where J1047+21 should be with a flux of 16.5±5.1 µJy at 5.8 GHz. Additionally, they found no Stokes V emission, but as the measurement was rather imprecise, they could only place loose constraints on the degree of circular polarization as being ≤ 80%. This detection is shown in Figure 6.12.

128

Figure 6.12. The detection of quiescent radio emission from J1047+21. The blue crosshairs denote the location of J1047+21 and a faint source can be detected there. In the inset, the 1σ VLA confidence region is shown by the red ellipse, while the blue ellipse shows the 1σ confidence for the position of J1047+21 from Vrba et al. (2004). Source: Williams et al. (2013).

The detection of radio flaring emission from J1047+21 is of key significance to understanding ultracool dwarf radio emission. This source is nearly 1,000 K cooler than the previous coolest brown dwarf for which radio emission was detected, the L3.5 dwarf 2MASS J0036159+182110 (Berger 2002). This detection shows that despite the colder temperatures and more neutral atmospheres of T dwarfs, they may generate kG strength magnetic fields in their interiors. Such a result dramatically expands the number of objects that may harbor such fields, and that may have detectable magnetism. This detection also suggests that even colder objects, such as spectral class Y and exoplanets, may emit detectable radio waves via the ECMI mechanism, which may allow us to study their magnetic fields and surrounding plasma environments.

129 6.3. 2MASS J1439284+192915

6.3.1. Background Information on J1439+19

J1439+19 was also initially detected in the 2MASS archive, and was selected for follow up study based on the degree of redness of its J-Ks color (Kirkpatrick et al. 1999). Due to the nearly equivalent strength of its TiO, CrH, and FeH absorption features as measured by the Low Resolution Imaging Spectrograph at the W. M. Keck Observatory in Hawaii, the object was classified by Kirkpatrick et al. (1999) as an L1 brown dwarf. Its distance was determined to be 14.37 pc based on its trigonometric , and it has an effective temperature of 2,273 K (Dahn et al. 2002). Kinematic arguments suggest that its age is approximately 3.2 Gyr (Seifahrt et al. 2010). J1439+19 appears to be single, as no companion has been detected out to ~4.3 AU and > 0.2 mass ratio (Reid et al. 2008). Little is known about J1439+19 regarding its activity. Its rotational period has been measured to be nearly 11 hours (Blake et al. 2010). Previous radio observations of the source conducted with the Very Large Array (VLA) suggested that this ultracool dwarf was radio-quiet, with a 78 µJy upper limit of its radio flux at 8.46 GHz (McLean et al. 2012).

6.3.2. The Detection of Flares from J1439+19

This survey has revealed that this object may in fact be a radio-flaring source. We have observed only a single radio burst from this dwarf, and thus its activity is tentative pending future confirmation. The burst has a flux density of 1.06 ± 0.30 mJy, which peaks at a frequency of 4325 MHz, as shown in Figure 6.13. The emission if 91% right circularly polarized. It is also noteworthy that this ultracool dwarf has a relatively slow projected rotational velocity; if the flare event is real, this would make J1439+19 the slowest rotating radio flaring ultracool dwarf known, with v sin i = 11.1 km s-1. However, the object would not be the slowest radio emitting ultracool dwarf as two other sources, J0952210-192431 (McLean et al. 2012) and J14563983-280947 (Burgasser & Putman 2005) have rotational velocities of 6 km s-1 (Reid et al. 2002) and 8 km s-1 (Reiners & Basri 2010), respectively. The magnetic field properties of this ultracool dwarf, therefore, have the potential to place constraints on the dynamo properties of ultracool dwarfs.

130

Figure 6.13. A single burst from J1439+19. Although this burst is weak, it is strongly right circularly polarized and has a high brightness temperature, indicating that it is the result of the ECMI emission mechanism. This tentative detection awaits confirmation. The grayscale in this image is reversed from other dynamic spectra in this dissertation to enhance image clarity. Source: Route & Wolszczan (2013).

131 We can estimate the brightness temperature of the source using equation 2.01, and find a value of 1.4 x 1011 K, assuming that the emission region has a radius approximately equivalent to the brown dwarf’s radius. Under the assumption that the electron cyclotron maser is the cause of the emission, the derived magnetic field strength would be >1.5 kG. From the spectrogram, we can also measure its drift rate as 69 MHz s-1. For J1439+19, this yields a corresponding plasma velocity of ~370 km s-1, which is comparable to the velocities of plasma released during coronal mass ejections on the Sun.

This chapter has presented key results of the radio surveys that we have conducted. Our ongoing observing campaign of TVLM 513 has produced interesting results and we seek to build on our vast data set to better understand the temporal evolution of its magnetic field structure and radio emission. The discovery of J1047+21 has done much to advance the field and show that the principles that govern radio emission in ultracool dwarfs of spectral types earlier than L4 may apply to a wide range of cool objects, potentially extending to spectral type Y and exoplanets. This discovery may bridge the ultracool dwarf and planet radio emitting regimes. Finally, J1439+19 awaits follow up observations to show if it is truly a new radio emitting brown dwarf, and if so, whether this emission is periodic and related to its rotation.

132

Chapter 7

Conclusions

7.1 Summary

In this dissertation, we have covered an array of topics concerning the radio emission activity of two classes of objects: exoplanets and brown dwarfs. In Chapter 1, we formulated definitions to attempt to classify substellar objects on the basis of their physical properties. This classification scheme was not arbitrary, but merged theoretical understanding with observational constraints to help separate ultracool dwarfs, brown dwarfs, and exoplanets into physically meaningful classes. We went on to review the current state of exoplanet discovery and characterization, noting that a lot of work still needs to be done to understand the magnetic properties of exoplanets and that our understanding of their interiors is lacking. With any luck the Juno mission to Jupiter will help to enlighten us as to its internal structure and so better constrain, or perhaps eliminate, models of gas giant interiors. We also examined the classification scheme for brown dwarfs, and noted that objects cooler than spectral type M7 had special properties, which showed they should be bundled together and labeled ultracool dwarfs. These objects have characteristic patterns of Hα, X-ray, and radio activity that separate them from warmer M dwarfs and other stars. In Chapter 2, we examined the radiation mechanisms for these cool, substellar objects. This discussion was motivated by a review of our understanding of planetary radio emission in the Solar System, as well as stellar radio emission elsewhere. For the Solar System planets, we are fortunate to have two key radio emitters: the Earth and Jupiter. Jovian radio emission can serve as a useful analogue for the emission we expect to find from exoplanets, and should have some transferable properties to our study of ultracool dwarf radio emission. But the Earth, as much historically as now, provides the means through which we truly come to understand the laws that Nature follows, and examine them up close so that we may apply them everywhere in the Universe. By sending spacecraft into the terrestrial auroral cavities, we correctly came to understand the conditions and reasons why the electron cyclotron maser instability (ECMI) gives rise to the auroral kilometric radiation. While the Sun is the closest and best-studied star, it is interesting to note that we receive so much information from it via radio, that we have difficulty untangling the emission processes that go on there. But the detection of radio emission from a handful of ultracool dwarfs, in particular, LP944-20, 2MASS J0036159+182110, and TVLM 513 has done much to illuminate our understanding of their radio emission, their magnetic fields, and their plasma environments. From their careful study, we have learned that gyrosynchrotron emission and ECMI dominate their radio emission. This provides us with the means to understand better the magnetism and radio emission from even cooler objects. Chapter 3 saw the discussion of the instrumentation at the Arecibo Observatory and how research conducted there would leverage two very important factors in radio astronomy: sensitivity and bandwidth. Arecibo Observatory is the largest radio telescope in the world, and due to its large collecting area, it offers superior sensitivity. This is supported by innovative electronics that continue to harness technological developments for increased scientific gain. In

133 particular, the development of the Mock spectrometer with its 1.1 GHz bandpass allows for an unprecedented monitoring of a wide range of frequencies simultaneously, which probe a corresponding wide range of magnetic field strengths in the radio emission paradigm. These instruments were supported by elegantly designed software that was written in the best traditions of software engineering. The analysis tools that were developed allow for a significant advance in the way radio emission from ultracool dwarfs could be examined, allowing for analysis of signals in frequency, time, and intensity simultaneously via dynamic spectra, whereas previous efforts had only examined simple time series of observations. Next, in Chapter 4, we learned that all risky ventures do not end in success and scientific breakthroughs. The Arecibo search for radio emission from exoplanets did not work out. Many researchers have sought radio emission from exoplanets in the hopes of detecting them in a novel wavelength regime, but also because of the magnetic properties of an object that are accessible to radio observational means alone. A single detection of radio emission from an exoplanet and the subsequent determination of the properties of its magnetic field would be a huge step forward in the study of exoplanets. Such a detection would guide future efforts as to the emission frequency and flux densities that could be expected for other sources. It would address substantial concerns about the capability of exoplanets to generate radio emission, especially when they are very close to their parent stars. Unfortunately, this effort, as so many others before us, has ended in failure. Nevertheless, our search for radio emission from exoplanets was part of a diversified portfolio of substellar targets. Chapter 5 described the results of two separate surveys of ultracool dwarfs for radio emission. While we did not detect radio waves from many sources, the detections we have made have proven useful in advancing the scientific endeavor. The detection of the very cool, ~900 K T6.5 dwarf J10475385+2124234 caused a stir in the community, as it tremendously expanded the temperature range over which ultracool dwarfs were found to emit GHz radio waves that were indicative of kG magnetic fields. This was followed by the detection of the L1 dwarf J1439284+192915, which, while less surprising, was still a valuable contribution to the population of radio emitting ultracool dwarfs. Only nine ultracool dwarfs are known to emit radio flares, and two of those were discovered by the research efforts reported in this dissertation. Given both our successes and failures, we could examine the statistics of the radio emitting and radio inactive populations, and find that their rotational velocities clearly were different. Using various frequency distributions for the physical properties of ultracool dwarfs, we were able to make inferences about the true size of the radio emitting population, and reveal the reasons for why such a large population has not yet been detected. During the course of researching the distributions for the Monte Carlo simulator, it became apparent that less than half of the previous radio surveys had examined the time series of the data, potentially failing to detect weaker bursts from sources. This is a shortcoming that future research efforts need to address. In Chapter 6, we launched into a detailed study of the radio emitting sources J10475385+2124234 (J1047+21), J1439284+192915 (J1439+19), and the well-known source TVLM 513. The presentation of dynamic spectra for these sources represents a major technological advance in the field, allowing for much more information to be revealed about the sources under investigation. The discovery of several flares from J1047+21 not only provides verification that the target is a flaring radio source, but also places constraints as to how flaring and rotational period may relate in this object. Utilizing our cutting-edge data collection instrumentation and analysis tools to their fullest extent, we have also examined the properties of its plasma environment. Furthermore, the detection of a kG strength magnetic field at a T6.5 dwarf such as this one suggests that there may be a number of cool objects, possibly extending toward exoplanets, that harbor strong magnetic fields. For J1439+19, follow up work will be required to show if it is truly a radio-emitting source, and if so, under what conditions. Its detection may place constraints on the operation of dynamo generation due to its relatively slow

134 rotation. Finally, we have collected a number of observations of the source TVLM 513, and coupled with the information from the literature, we are in the process of assessing the long-term stability of its magnetic field and emission. Our detailed observations conducted over a period of several years allows for an unprecedented study of radio burst morphology as well as an examination of the stability of these burst features over a long period of time. Preliminary results suggest that while the long term flaring behavior of TVLM 513 is periodic, on shorter timescales the burst activity has an underlying mysterious cycle to it.

7.2 Future Work

In some sense, the future is now. The forthcoming work in this subfield of astrophysics should proceed along two avenues of inquiry, and at the time of this writing, we are following both to see where they lead us. Since only a handful of radio emitting ultracool dwarfs are known, more must be found. The detection of more sources will give us more opportunities to test our understanding of the interior physics that give rise to their magnetic fields, as well as improve our understanding of the conditions that cause ECMI emission. Specifically, the discovery of radio waves from cooler and lower mass brown dwarfs will help guide our searches for, and understanding of, exoplanetary magnetism. This can be accomplished by searching for radio emission over a wider range of frequencies, and extending our searches to lower frequencies in particular. The discovery of more radio emitting ultracool dwarfs will also allow us to better understand the ultracool dwarf population in aggregate, so we may make increasingly useful and interesting inferences about them. Thus, more surveys of brown dwarfs are needed, at a number of frequencies, with as much sensitivity as possible, and at least one second temporal sampling. Such an effort is already underway with our A2776 survey at Arecibo Observatory. Once the sources are found, they need to be studied in detail. This includes analysis in both time and frequency domains, at high resolution. Key properties of the emitting sources can be divined from the analysis of time-frequency spectrograms. High temporal resolution data will allow for examinations of the fine structure of radio bursts, which may allow for information about source region sizes, the properties of ECMI growth curves, or ECMI emission geometry to be established. All three would advance our thinking. Very high-resolution frequency analysis of very close sources with high signal to noise may allow for the detection of narrowband striations that would conclusively prove that the radio emission that we suspect is the result of ECMI actually is so. The examination of detected sources over long periods of time (years, perhaps) may allow the stability of their radio emitting magnetic structures to be assessed. Still unknown at this time is whether the radio emission comes from permanent magnetic structures (such as the global dipolar field of the Earth) or smaller, transient, local magnetic structures (such as magnetic loops or hot spots). In the more distant future, when radio telescopes and instrumentation have improved by two or more orders of magnitude, the search for radio emission from exoplanets should be conducted in earnest. This should take the form of searching a wide range of frequencies over a wide range of times for a number of planetary configurations.

135

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143

Appendix A

Physical Quantities and Units

Constant Symbol Value (SI units) AU 1.49599 x 1011 m Boltzmann Constant k 1.38066 x 10-23 J K-1 Earth mass 5.9742 x 1024 kg Electron charge e 1.60218 x 10-19 C ⨁ -31 Electron mass m푀e 9.10938 x 10 kg Electron volt eV 1.60218 x 10-19 J Erg erg 1.0 x 10-7 J s-1 Gravitational Constant G 6.6773 x 10-11 M3 kg-1 s-2 Jansky Jy 1.0 x 10-26 J s-1 m-2 Hz-1 27 Jupiter mass MJ 1.8986 x 10 kg 7 Jupiter radius (mean) RJ 6.9911 x 10 m pc 3.08568 x 1016 m Radiation density a 7.57 x 10-15 erg cm-3 K-4 Speed of light c 2.99792 x 108 m s-1 3.827 x 1026 J s-1 Solar mass 1.9891 x 1030 kg 퐿⨀ 푀⨀

144 Appendix B

Monte Carlo Distributions

Let f(x) represent the probability density function for a distribution. In the context of this dissertation, such distributions have been used repeatedly in Section 5.5. In that section, we saw that a distribution was generally coarsely determined by a normalized histogram created from empirical data that was then fit with a best-fit curve, f (x). Let g(x) then represent the cumulative distribution function as defined below (Bevington & Robinson 2003).

( ) = ( ) (B.01) 푎 In many cases in the Monte Carlo simulator,푔 푎 we randomly∫−∞ 푓 푥 generate푑푥 g(a) using a standard random number generator, which produces values [0,1] from a uniform distribution. Once g(a) is generated, then the right hand sign of Equation B.01 is solved for a. The value of a then represents the value of the random variable drawn from the distribution modeled by f(x). Since the Monte Carlo simulator described in Section 5.5 used Python, the numerical solver in module SymPy performs these calculations. Random number generation is performed with Python module NumPy.

145 VITA Matthew P. Route Department of Astronomy and Astrophysics Phone: (814) 865-8485 Pennsylvania State University E-mail: [email protected] 421 Davey Lab University Park, PA 16802 Webpage: http://www.astro.psu.edu/people/mpr201

EDUCATION Pennsylvania State University Ph.D. Astronomy and Astrophysics (Computational Science minor) August 2013 Thesis: Radio Observations of the Brown Dwarf-Exoplanet Boundary Advisor: Alexander Wolszczan Johns Hopkins University M.A. Physics and Astronomy May 2007 University of Colorado, Boulder B.A. Physics; Astronomy (Mathematics minor) cum laude May 2005 Thesis: Monte Carlo Simulations of Meteoroid Bombardment of Saturn’s B Ring Advisor: Joshua E. Colwell

RESEARCH EXPERIENCE AT PENNSYLVANIA STATE UNIVERSITY • Radio observations of brown dwarfs and extrasolar planets. Monte Carlo simulations of observations and flaring events. Advisor: Alex Wolszczan. • Analysis of optical/ UV photometry of hot subdwarfs from the PG catalog, with Richard Wade and Brad Barlow. • Analysis of Arctic snowflake radar scattering and automated recognition of snow crystals and droplets to determine water content, using Matlab with Hans Verlinde, Kultegin Aydin, and Giovanni Botta. • Analysis of companions of planetary nebulae nuclei, with Robin Ciardullo and Richard Wade. • Analysis of the UV and X-ray spectra of AM CVn stars, with Michael Eracleous, Derek Fox, and Richard Wade. • Development of exoplanet detection via spectral analysis of telluric lines, with Alex Wolszczan and Sara Gettel.

TEACHING EXPERIENCE AT PENNSYLVANIA STATE UNIVERSITY Teaching Assistant 2008-2010 ASTR 11 Elementary Astronomy Laboratory; ASTR 140 Life in the Universe; ASTR 320 Observational Astronomy Laboratory

AWARDS AT PENNSYLVANIA STATE UNIVERSITY National Research Council Recommended Proposal 2013 Dr. Gerald A. Soffen Memorial Travel Grant 2012 NASA Pennsylvania Space Grant Consortium Fellowship 2011-2013 NASA JPL Planetary Science Summer School Travel Grant 2011 Zaccheus Daniel Fellowship 2009, 2012 Nellie H. and Oscar L. Roberts Graduate Fellowship 2008

PEER-REVIEWED PUBLICATIONS AT PENNSYLVANIA STATE UNIVERSITY • Van Der Horn, J., Route, M., Verlinde, H., Richardson, S., Yu, G., Jensen, A., Botta, G. “Automated Detection, Measurement, and Classification of Ice Crystal Aggregates,” In preparation, July 2013. • Wade, R. A., Route, M., Barlow, B. N., Stark, M. A., Green, R. F. “Candidate Hot Stars Among the Objects Rejected from the Palomar-Green Catalog: An Updated Assessment Using GALEX Photometry,” In preparation, July 2013. • Wade, R., Gronwall, C., Ciardullo, R. B., Route, M., Bond, H. “Improved Distances to Planetary Nebulae from Resolved Companion Stars.” In preparation, July 2013. • Route, M., Wolszczan, A., “The 5 GHz Arecibo Search for Radio Flares from Ultracool Dwarfs,” The Astrophysical Journal, in press, 2013 [arXiv: 1306.1152]. • Diniega, S., Sayanai, K., Balcerski, J., Carande, B., Diaz-Silva, R., Fraeman, A., Guzewich, S., Hudson, J., Nahm, A., Potter-McIntyre, S., Route, M., Urban, K., Vasisht, S., Benneke, B., Gil, S., Livi, R., Williams, B., Budney, C., Leslie, L. “Mission to the Trojan Asteroids: Lessons Learned During a JPL Planetary Science Summer School Mission Design Exercise.” Planetary and Space Science, Volume 76, February 2013. • Route, M. & Wolszczan, A. “The Arecibo Detection of the Coolest Radio-Flaring Brown Dwarf.” The Astrophysical Journal, 747, L22, 10 March 2012