The Influence of Low-Mass Companions Around AGB Stars

Home , Brown dwarf

From Binaries to Asymmetric Outﬂows: The Inﬂuence of Low-mass Companions Around AGB Stars

Jason T. Nordhaus

Submitted in Partial Fulﬁllment of the Requirements for the Degree Doctor of Philosophy

Supervised by Professor Eric G. Blackman Department of Physics and Astronomy The College Arts and Sciences

University of Rochester Rochester, New York

2008 ii

To my mom and dad iii

Curriculum Vitae

The author was born November 24, 1980 in Concord, Massachusetts. He graduated from the University of Rochester with a Bachelor of Science degree in Physics and Astronomy and a Bachelor of Arts degree in Mathematics in 2003. Upon completion of his undergraduate education, he entered the doctoral program in the Department of Physics and Astronomy at the University of Rochester. In May 2004 the author received a Master of Arts degree in Physics from the University of Rochester. The author received a Department of Energy Frank J. Horton Fellowship (2004-2008) in addition to a Department of Education GAANN fellowship (2003-2006).

Selected Publications

• Nordhaus, J., Minchev, I., Sargent, B., Forrest, W., Blackman, E. G., De Marco, O., Kastner, J., Balick, B., Frank, A. 2008 MNRAS, submitted

• Edgar, R. G., Nordhaus, J., Blackman, E., Frank, A. 2008 ApJL, in press

• Nordhaus, J., Blackman, E. G., Frank, A. 2007 MNRAS, 376, 599

• Minchev, I., Nordhaus, J., Quillen, A. 2007 ApJL, 664, 31

• Watson, D. M., Leisenring, J. M., Furlan, E., Bohac, C. J., Sargent, B., Forrest, W. J., Calvet, N., Hartmann, L., Nordhaus, J. T., Green, J. D., Kim, K. H., Sloan, G. C., Chen, C. H., Keller, L. D., d’Alessio, P., Najita, J., Uchida, K. I., Houck, J. R. 2007, ApJS, submitted

• Nordhaus, J., Blackman, E. G. 2006, MNRAS370, 2004

• Blackman, E. G., Nordhaus, J., Thomas, J. H. 2006 New Astronomy, 11, 452 iv

• Nordhaus, J., Blackman, E. G. 2008 to appear in AIP Proceedings of the IXth Torino Workshop on AGB Nucleosyntheis

• Nordhaus, J., Blackman, E. G. 2007, in Asymmetric Planetary Nebulae IV, eds. R. L. M. Corradi, A. Manchado, N. Soker (in ASP Conference Series: San Francisco), in press

• Blackman, E. G., Nordhaus, J. 2007, in Asymmetric Planetary Nebulae IV, eds. R. L. M. Corradi, A. Manchado, N. Soker (in ASP Conference Series: San Francisco), in press v

Acknowledgments

This work would not have been possible without the support and encouragement of my thesis advisor, Dr. Eric Blackman. His guidance, patience and scientific insight were instrumental throughout my graduate career. I also wish to thank my fellow graduate compatriots, Dave Clader and Ivan Minchev for invaluable friendship, stim- ulating scientific & non-scientific discussions and for an endless supply of much needed distractions. I wish to acknowledge institutions which provided financial support and assis- tance. In particular, the Department of Physics and Astronomy at the University of Rochester. Financial support for this work was provided by the Laboratory for Laser Energetics through a U.S. Department of Energy Horton Fellowship and a U.S. Department of Education GAANN Fellowship. I would also like to thank my parents, Kurt and Sherri, and sisters, Miranda and Tiffany, for their love and support. Finally, I wish to thank my wife Lea for her unconditional love and encouragement. vi

Abstract

The study of intermediate mass, evolved stars is undergoing renewed interest due to recent observational and theoretical results suggesting that binarity is fundamental for shaping post-Asymptotic Giant Branch and Planetary Nebula outflows. Despite extensive research, the physical mechanism responsible for transitioning from a spherical Asymptotic Giant Branch (AGB) star to an asymmetric post-AGB object is poorly understood. In an effort to understand how binaries may produce asymmetries, this thesis presents several theoretical studies which explore the effect of low-mass companions on evolved star outflows. This thesis consists of four separate projects: (1.) Close companions may become engulfed by the evolved star and in-spiral during a common envelope phase. Common envelope evolution can lead to three different consequences: (i.) equatorial ejection of material (ii.) spin-up of the envelope resulting in an explosive dynamo-driven jet and (iii.) tidal shredding of the companion into an accretion disk which ejects a poloidal wind. (2.) In addition, we study a dynamical, large-scale α − Ω interface dynamo operating in an AGB star in both an isolated setting and a setting in which a low-mass companion is embedded inside the envelope. The back reaction of the fields on the shear is included and differential rotation and rotation deplete via turbulent dissipation and Poynting flux. For the isolated star, the shear must be resupplied in order to sufficiently sustain the dynamo. Furthermore, we investigate the energy requirements that convection must satisfy to accomplish this by analogy to the Sun. For the common envelope case, a robust dynamo results, unbinding the envelope under a range of conditions. (3.) Wide binaries can interact with the wind of the evolved primary. The gravitational influence of the secondary focuses material in the equatorial plane. The vii companion induces spiral shocks which may anneal amorphous grains into crystalline dust. This work presents a physical mechanism to produce crystalline dust in AGB star binaries. (4.) We present a spectral modeling technique which constrains the geometry of evolved star nebulae. We apply our technique to HD 179821 which exhibits a double peaked spectral energy distribution (SED) with a sharp rise from ∼ 8 − 20 µm. Such features have been associated with dust shells or inwardly truncated circumstellar disks. In order to compare SEDs from both systems, we employ a spherically symmetric radiative transfer code and compare it to a radiative, inwardly truncated disc code. As a case study, we model the broad-band SED of HD 179821 using both codes. Shortward of 40 µm, we find that both models produce equivalent fits to the data. However, longward of 40 µm, the radial density distribution and corresponding broad range of disc temperatures produce excess emission above our spherically symmetric solutions and the observations. For HD 179821, our best fit consists of a Teff = 7000

K central source characterized by τV ∼ 1.95 and surrounded by a radiatively driven, spherically symmetric dust shell. The extinction of the central source reddens the broad-band colours so that they resemble a Teff = 5750 K photosphere. We believe that HD 179821 contains a hotter central star than previously thought. Our results provide an initial step towards a technique to distinguish geometric diﬀerences from spectral modeling. viii

Contents

CurriculumVitae...... iii Acknowledgments...... v Abstract...... vi

Introduction 1 1.1Post-MainSequenceEvolution...... 1 1.1.1 AsymptoticGiantBranchEvolution...... 1 1.1.2 Post-AGBPhase...... 2 1.2 Support for the Binary Hypothesis ...... 4 1.2.1 ObservationalIndications...... 4 1.2.2 MagneticShaping...... 5 1.3ThesisStructure...... 5 References...... 7

Low-mass Binary Induced Outﬂows from Asymptotic Giant Branch Stars 9 2.1Abstract...... 9 2.2Introduction...... 10 2.3CommonEnvelopeEvolution...... 11 2.3.1 EnvelopeBindingEnergy...... 12 2.3.2 Orbital Energy and Angular Momentum Evolution ...... 14 2.4CommonEnvelopeEvolutionScenarios...... 17 2.4.1 SecondaryInducedEnvelopeExpulsion...... 17 2.4.2 Secondary Induced Envelope α − ΩDynamo...... 20 2.4.3 DiscDrivenOutﬂow...... 24 CONTENTS ix

2.5DiscussionofObservationalImplications...... 25 2.5.1 ObservationalConsequences...... 26 2.5.2 ApplicationstospeciﬁcPPNeandPNesystems...... 27 2.6Conclusions...... 29 References...... 31

Isolated versus Common Envelope Dynamos in Planetary Nebula Pro- genitors 35 3.1Abstract...... 35 3.2Introduction...... 36 3.3 Dynamos, Common Envelopes and Isolated AGB Evolution ...... 37 3.4DynamicalEquations...... 39 3.4.1 EvolutionofΩand∆Ω...... 41 3.4.2 Evolution of α ...... 43 3.5NumericalResults...... 44 3.5.1 IsolatedDynamoWithoutReseeding∆Ω...... 45 3.5.2 IsolatedDynamoWithReseeding∆Ω...... 47 3.5.3 CommonEnvelopeDynamo...... 49 3.6MorphologyofMagneticOutﬂows...... 54 3.7Conclusions...... 56 References...... 58

Towards a Spectral Technique for Determining Material Geometry Around Evolved Stars: Application to HD 179821 61 4.1Abstract...... 61 4.2Introduction...... 62 4.3 HD 179821: post-AGB or red supergiant? ...... 64 4.4PhotosphericModelsandExtinction...... 66 4.5InnerWall,Edge-onDiskModels...... 68 4.6 Spherical Shell Models ...... 72 4.7Summary...... 77 CONTENTS x

The Formation of Crystalline Dust in AGB Winds from Binary Induced Spiral Shocks 83 5.1Abstract...... 83 5.2Introduction...... 83 5.3NumericalStudy...... 85 5.4Results...... 85 5.5Discussion...... 87 5.5.1 GrainAnnealing...... 87 5.5.2 ShockTemperatureScaling...... 90 5.5.3 DustFormation...... 91 5.6Conclusion...... 91 xi

List of Tables

4.1PhotometricData...... 68 4.2 Color Corrected IRAS ﬂuxes, Submillimeter Data for HD 179821 . . . 69 4.3ModelSummary...... 76 xii

List of Figures

1.1 Left (IRC +10216; V bank): Typically spherical AGB mass loss is revealed by spherical reﬂection nebulosities. Center (CRL 2688; [OI]): every time a reﬂection or neutral nebula is seen around a post-AGB star, a bipolar symmetry is present. Right (He 2-47; Hα): when post-AGB stars heat up, the young ionized PNe always have bipolar or multi-polar morphologies. [Credits: Mauron & Huggins (2000); Sahai et al. (1998); Sahai & Trauger (1998)] ...... 3

2.1 Left: Density and mass proﬁles for our model AGB star. The dotted line is the core-envelope boundary. Right: Mach number and sound speed as a function of radius. The Mach number is computed from the Keplerian motion of the planet inside the envelope. The motion is supersonic everywhere and thus justiﬁes our choice of accretion radius (Bondi 1952)...... 13 2.2 Infall time as a function of position inside the envelope of the AGB star (left) and interpulse AGB star (right). The solid line represents a

companion of mass 0.02 M and the dotted line is a secondary of mass

0.2 M...... 16 LIST OF FIGURES xiii

2.3 Three possible outcomes of our CE evolution. (a.) The companion becomes embedded in the stellar envelope, orbital separation is reduced, eventually resulting in unbinding the envelope equatorially. (b.) The companion spirals in, the envelope is spun up causing it to differentially rotate. The presence of a deep convective zone, coupled with the differential rotation, generates a dynamo in the envelope. (c.) The companion is shredded into an accretion disc around the core. The disc then drives an outflow which, in principle, can unbind the envelope. . 18 2.4 For various efficiencies α (see Eq. 1), the solid line shows the radius at which the change in orbital energy equals the binding energy of the envelope for the beginning of the AGB star (left) and interpulse AGB star (right). The dotted vertical line marks the core-envelope boundary. The long-dashed line represents the radius at which the companion is tidally shredded by the core. The short-dashed line is where the companion first fills its Roche lobe, initiating mass transfer to the envelope. 19 2.5 The solid line depicts the energy required to unbind the envelope for the AGB star (left) and interpulse AGB star (right), if the secondary is not tidally shredded as it traverses the envelope. The dashed lines represent the amount of energy deposited into the envelope from the change in orbital energy of the secondary for efficiency parameter α

(Eq. 1). For α =1.0, a m2 =0.02 M brown dwarf delivers enough energy to blow oﬀ the AGB envelope at r ∼ 1010 cm. For α =0.3, the brown dwarf must traverse all the way to the core-envelope boundary before supplying enough energy to unbind the system. For smaller α,

a m2 =0.02 M companion cannot unbind the AGB envelope before spiraling down to a radius where an interface dynamo might participate

in unbinding the envelope. For the interpulse AGB star, a 0.02 M brown dwarf can supply enough orbital energy to unbind the envelope for α =1.0andα =0.3...... 21 LIST OF FIGURES xiv

2.6 Two rotation proﬁles for our 3.0 M AGB star. The solid curve represents the spin up of an initial stationary envelope by an infalling 0.02

M brown dwarf. The dotted curve is the rotation proﬁle generated in Blackman et al. 2001 in which a main sequence star exhibiting solid body rotation conserves angular momentum of spherical mass shells during its evolution onto the AGB. The solid vertical line marks the core boundary and the short-dashed line represents the base of the convective zone. The long-dashed line is the base of the diﬀerential rotation zone used in Blackman et al. 2001...... 23

3.1 A meridional slice of the dynamo geometry. The left figure shows the global geometry of the AGB star. The right figure is a close-up view of the dashed region on the left. The α-effect is driven by convection

and occurs in layer of thickness L1 above the differential rotation zone. The poloidal component of the field is pumped downwards into the differential zone, where it is wrapped torodially due to the Ω-effect. . . 39 3.2 The differential rotation energy is allowed to drain through field amplification and turbulent dissipation. In this figure, k =5× 10−11 cm−1, z t cp =0.01, Q =5.0. We define, [PF,dis] ≡ 0 E[PF,dis] (t ) dt and label

M (PF)andT (dis) on the top right plot to distinguish between the thermal and magnetic contributions to the binding energy. For the left −4 −5 figure, cφ =10 while the right has cφ =10 . Peak field strengths are a factor of ∼ 5 − 10 less then those obtained in (Blackman et al. 2001). Differential rotation energy is drained in < 20 yrs. Lowering

cφ results in the differential rotation energy draining at a slower rate, allowing the field to sustain for longer periods of time (∼ 40 − 50 yrs). However,peakfieldstrengthsremainthesame...... 46 3.3 Results for reseeding differential rotation through convection. In the left figure, f = 1 corresponding to maximum convective resupply. Rotation is drained through Poynting flux but cannot sustain a dynamically important dynamo. In the figure on the right, f = 0 (no resupply of ∆Ω). The rotation rate is fixed, corresponding to a buildup of Poynting flux intheinterfacelayer...... 48 LIST OF FIGURES xv

3.4 Convective resupply results in a steady-state differential rotation profile. For the left column, the envelope of the poloidal, toroidal and Poynting flux is plotted. The Poynting flux is sustained at ∼ 5 × 1034 erg/s. The sustained Poynting flux supplies enough energy to unbind the envelope 5 of our 3 M model at the end of the AGB phase (∼ 10 yrs). In this −5 −3 figure, cφ =10 and f =10 implying that only ∼ 0.1% of the cascade energy must be converted into differential rotation energy to supply the requisite Poynting flux. This model predicts a magnetically dominatedexplosion...... 50 3.5 Rotation profiles generated from the transfer of angular momentum from companion to envelope in our AGB star. In both figures, the solid curves represent the resulting profiles for companions of masses

0.05 (top), 0.02 and 0.01 (bottom) M. For the left ﬁgure, the dashed curve represents the Keplerian velocity while the dashed-dotted curve

is the sound speed. The 0.05 M companion initially spins up the envelope such that the inner region is rotating faster then the Keplerian velocity. Mass redistribution ensues and transfers matter outward until the rotation profile drops below Keplerian. The right figure presents the angular velocity corresponding to the left figure. The dash-dot vertical line is the approximate radius at which the companion is tidally shredded. The large-dash vertical line is the boundary of the shear layer in Blackman et al. 2001 while the small dash line is the base of the

convection zone. These proﬁles assume that αCE =0.3...... 52 LIST OF FIGURES xvi

3.6 Interface dynamo resulting from the in-spiral of a 0.02 M brown dwarf in the interior of our model AGB star. The differential rotation zone extends from the base of the convection zone to the radius at which the secondary is tidally shredded (Nordhaus & Blackman 2006). In this −4 −4 −3 model, PM =10 and Q =5,Ω0 =2.3×10 rad/s, ∆Ω0 =2.5×10 rad/s and δ/L = 1. In the left column, the envelope of the Poynting flux (top), toroidal field (middle) and poloidal field (bottom) are drawn with a solid line. The insets represent the time evolution from 0 to 0.2 yrs. The vertical scale of the insets are the same as the corresponding largerfigure...... 53

3.7 Interface dynamo resulting from the in-spiral of a 0.05 M brown dwarf. −6 −4 In this model PM =10 , Q =5,δ/L =1,Ω0 =5× 10 rad/s and −3 ∆Ω0 =2.5 × 10 rad/s. The insets represent the time evolution from 0 to 0.2 years. The vertical scale of the insets are the same as the correspondinglargerﬁgure...... 55

4.1 Top: ISO SWS spectra of HD 179821 and post-AGB object HD 161796. In both objects, there is a steep rise between the 10 and 20 µmfeatures possibly indicating a transition region to the optically thick outer wall

or shell. HD 179821 was de-reddened using AV = 2 while HD 161796

was corrected using AV =1.2. Bottom: ISO spectrum of the post-RSG IRC +10420...... 67 4.2 Our best fit wall models. The top figure corresponds to µ =0.25 while the bottom corresponds to µ =0.45...... 71 4.3 Another fit to the wall model for glassy olivine (top) and glassy bronzite (bottom). The inclination in both figures is µ =0.25...... 73 4.4 Our spherical shell model (dark line). The dust temperature at the inner and outer radii are 128 K and 41 K. Even though the central radiation source is a T = 7000 K photosphere, the detached shell reddens the central source so that it resembles a T = 5750 K photosphere (thin line). The silicate features are fit using a mixture of glassy, amorphous silicates with a small component of FeO...... 75 LIST OF FIGURES xvii

5.1 Volumetric density renderings of the wind emitted by a 1 M primary,

with a 0.25 M secondary in a 6 AU orbit. The view along the z axis is shown on the left, that along the x axis on the right. The binary orbits in the z =0plane...... 86

5.2 Temperature structure of the wind emitted by a 1 M primary, with a

0.25 M secondaryina6AUorbit...... 88 1

Chapter 1

Introduction

The study of intermediate mass, evolved stars is an important topic of active research due to recent observational and theoretical results suggesting that binarity is fundamental for shaping post-Asymptotic Giant Branch and Planetary Nebula outflows. In this thesis, we present several theoretical studies which explore the effect of low-mass companions on an evolved star. In particular, close companions may be engulfed during post-main sequence evolution and eject material toroidally or via collimated bipolar outflows. Wider binaries can gravitationally focus evolved star winds and drive spiral shocks in equatorial outflows. In addition to the physics of binary interactions, we also present a spectral modeling technique that can be applied to unresolved, evolved stars to constrain the geometry of the circumstellar nebulae.

1.1 Post-Main Sequence Evolution

1.1.1 Asymptotic Giant Branch Evolution

After exhausting core hydrogen and helium burning, intermediate-mass stars (< 8 M) enter the AGB phase. The structure of an AGB star consists of an electron degenerate C-O core surrounded by a He shell underneath a H-rich envelope. The star is luminous 3 4 3 (∼ 10 −10 L) but cool (Teff < 3×10 K) and has expanded to ∼ 200 times its main- sequence radius. Initially, a quiet period in which nuclear burning is limited to the He shell deﬁnes the early-AGB phase. Hydrogen burning above the He-shell eventually dominates and marks the transition to the thermal pulsing AGB phase. As the H- CHAPTER 1. INTRODUCTION 2 shell burns, the mass of the underlying He-shell increases. Eventually, the He-shell reignites in a thermo-nuclear runaway and is commonly referred to as a thermal pulse (TP; Schwarzschild Harm 1965). The sudden increase in energy release extinguishes H-burning during which the convective zone can penetrate into the interior regions and dredge up C-rich material. As a result of the dredge-ups incurred by thermal pulses, the surface of the star is enriched with nuclear burning products. In particular, the initially oxygen-rich (C/O < 1) AGB star can become carbon-rich (C/O > 1) if it undergoes 3rd dredge-up (Iben 1975). If AGB evolution were strictly determined by nuclear burning processes, then the chemistry of the remnant nebula would depend only on the nuclear processing of the progenitor star. Unfortunately, mass-loss timescales exceed nuclear burning timescales by up to four orders of magnitude in the AGB phase. Thus, AGB termination results from strong mass-loss experienced during this phase. The mass-loss process is poorly understood and likely dependent on dust formation from the thermal pulse process (see Sedlmayr & Dominik 1995 for a review). If however, the AGB star is part of a binary, the picture is less clear and the evolution complicated. Average mass-loss rates −5 in isolated stars during the AGB phase are typically M˙ ∼10 M/yr, depleting the stellar envelope in ∼ 104 − 105 yrs. Typical AGB wind velocities are slow (∼ 10 − 15 km/s) and spherical. The depletion of the envelope eventually results in a detached nebula and signiﬁes the end of the AGB star and the beginning of the post-AGB phase.

1.1.2 Post-AGB Phase

The post-AGB phase is short (∼ 103 − 104 yrs) and poorly understood. The eﬀective temperature is increasing while the luminosity remains fairly constant. Once the central white dwarf reaches a temperature of ∼ 104 K, the circumstellar nebula (if present) ionizes and shines as PN. For a review on post-AGB stars see (van Winckel 2003). Originally, the ejected nebulae were thought to be spherical and originate from quasi-steady mass loss by an isolated star during the AGB phase. As the core heated, the surrounding ionized nebula would reveal spherical symmetry. This view has changed since high resolution optical telescopes (particularly the Hubble Space Tele- scope) revealed highly asymmetric structures consisting of disks, bipolar outﬂows and CHAPTER 1. INTRODUCTION 3 bullet-like ejecta (for a review see Balick and Frank 2002). The origin of the asymmetry and the physical mechanisms responsible for shaping have remained elusive for nearly three decades. Until recently, the textbook explanation of PNe shaping involved an interacting spherically symmetric “fast” wind preceded by an equatorial “slow” wind (Kwok et al. 1978). As the fast wind encounters the slow wind, it becomes collimated in the polar direction. Unfortunately, this scenario is only able to explain a subset of the older PNe and categorically fails to explain the younger, post-AGB progenitors and young PNe (Sahai 2002).

Figure 1.1 Left (IRC +10216; V bank): Typically spherical AGB mass loss is revealed by spherical reﬂection nebulosities. Center (CRL 2688; [OI]): every time a reﬂection or neutral nebula is seen around a post-AGB star, a bipolar symmetry is present. Right (He 2-47; Hα): when post-AGB stars heat up, the young ionized PNe always have bipolar or multi-polar morphologies. [Credits: Mauron & Huggins (2000); Sahai et al. (1998); Sahai & Trauger (1998)]

The post-AGB phase is likely fundamental as it marks the onset of extreme asymmetry (see Fig. 1.1; Sahai & Trauger 1998). However, post-AGB stars are short lived with < 400 objects presently known (Szczerba et al. 2007).Therefore, this phase of post-main sequence evolution is not well studied. A number of physical processes may be involved in shaping post-AGB outflows. These include: magnetic launch & collimation, binary interactions, and accretion disk formation & evolution. Constraining formation theories observationally is difficult as CHAPTER 1. INTRODUCTION 4 the bipolar engines are often shielded by the remnant reflection nebula. Nevertheless, a growing body of observational and theoretical work suggests that binary interactions may be the unifying ingredient to deciphering asymmetry in this elusive phase of stellar evolution.

1.2 Support for the Binary Hypothesis

Here we present some of the evidence suggesting binarity is a common theme in intermediate mass, evolved star evolution.

1.2.1 Observational Indications

Recently, a comprehensive and extensive survey of CO emission revealed that nearly all post-AGB objects with known CO emission (∼ 80%) feature large momentum excess over what can be supplied by radiation pressure - often 103 − 104 times larger (Bujarrabal et al. 2001). Clearly, an additional momentum source must be present and a natural candidate is a binary companion. Binaries are attractive as two-thirds of all stars are thought to reside in multiple systems (Duquennoy & Mayor 1991). In addition, momentum can be exchanged from the companion star to the primary star through tidal, wind or common envelope interactions. Radial velocity (RV) surveys have been carried out to determine the fraction of central stars of PN. Preliminary results indicate that RV variability is common and that the true binary fraction may be of order unity (De Marco et al. 2004; Sorensen and Pollacco 2004; Afˇsar & Bond 2005). However, wind and pulsation also contribute to RV variability in evolved stars, making this fraction uncertain (De Marco et al. 2007). Adding additional credence to the binary hypothesis are population synthesis studies that predict more PNe than observed (Moe & De Marco 2006). If it is assumed that PNe only form from binary interactions (particularly common envelope interactions), then population synthesis predictions are comparable with observations (De Marco 2006; Moe & De Marco 2006). These studies suggest the formation rate of PNe is 1/3 the formation rate of white dwarfs and support the claim that observed PNe are the descendants of interacting binary systems (Soker 2006; Soker & Subag 2005). While CHAPTER 1. INTRODUCTION 5 this percentage is lower then the percentage of binary stars, it may suggest only close to intermediate companions are responsible for asymmetric shaping.

1.2.2 Magnetic Shaping

It was previously suggested that an isolated star with a strong toroidal magnetic field could create the equatorial density enhancements needed for bipolar collimation in post-AGB/PNe (Garc´ıa-Segura et al. 1999, 2005). While these simulations were successful in recreating a wide array of shapes, the origin and evolution of the magnetic field was neglected. In particular, as large-scale magnetic fields amplify, differential rotation energy is drained from the engine. This back-reaction can shut down the dynamo, after which the fields decay. Nordhaus et al. (2007) demonstrated that an isolated star cannot sustain the necessary field strengths to power bipolarity unless convectivion actively re-supplies differential rotation. However, if convection fails, not all is lost as a binary companion can supply the additional energy and angular momentum needed to amplify and sustain sufficient magnetic fields. This is particularly important as magnetic fields appear to be responsible for jet collimation in post-AGB objects (Vlemmings et al. 2006) and are present in the central stars of PNe (Jordan et al. 2005).

1.3 Thesis Structure

The research presented in this thesis aims to better understand the eﬀect of a binary in an evolved star system.

Chapter 2 presents a study of the in-spiral of a low-mass companion (< 0.3 M: planet, brown dwarf, low-mass main sequence star) embedded in an AGB envelope during a common envelope (CE) phase. Common envelopes form when the expanding primary overflows its Roche lobe and both the companion and primary core become immersed (Iben & Livio (1993); Paczynski (1976)). During in-spiral, the secondary transfers additional energy and angular momentum to the CE and can eject it. For low mass companions, a CE phase can lead to three different mass ejection consequences: (i) direct ejection of envelope material resulting in a predominately equatorial outflow, (ii.) spin-up of the envelope resulting in the possibility of powering CHAPTER 1. INTRODUCTION 6 an explosive dynamo-driven jet and (iii.) tidal shredding of the companion into a disk which facilitates a disk-driven jet. These scenarios can launch material both equatorially and poloidally and may naturally lead to the disk-jet lag of a few hundred years observed by Huggins (2007). The common envelope interaction for low-mass companions is particularly relevant as the first white dwarf + brown dwarf post-CE binary was recently discovered (Maxted et al. 2006). As a continuation of this work, a dynamo operating in a CE is presented in detail in Chapter 3. The interplay of strong shear and a deep convective zone can generate dynamically important, large-scale magnetic fields via an α − Ω dynamo. As the magnetic field strengthens, differential rotation energy is drained to support this growth. When the rigorous back-reaction of the field amplification on the shear is included, the dynamo becomes a transient phenomena lasting ∼ 100 yrs. In particular, for an isolated star, the magnetic field is not strong enough to provide the extreme shaping seen in many post-AGB/PNe unless convection can re-supply differential rotation during the AGB phase. However, in the common envelope case, a robust dynamo results and is able to supply the necessary energy and momentum to eject the envelope for a wide range of binary systems. This work suggests that the inclusion of MHD processes is essential for understanding the CE phase and missing from current 3-D, hydrodynamic simulations of common envelopes. Since binary companions are expected to influence outflow shapes, it is important to observationally determine the geometry of post-AGB stars. In Chapter 4, a spectral modeling strategy and technique are presented that can be applied to evolved stars to constrain the geometry (disks or spherical shells) of their ejected nebulae whether or not the sources are resolved in images. We apply this technique to HD 179821 and show explicitly where significant spectral degeneracies exist between the two geometries. The models can be distinguished spectrally only with data above 40 µm. In general, the importance of considering both disk-like and spherical geometries for evolved stellar nebulae is exacerbated by the fact that disks are very natural when significant angular momentum and/or companions are present (de Ruyter et al. 2006). When the sources are not spatially resolved, this technique constrains the geometry. Chapter 5 presents 3-D, hydrodynamic simulations of the interaction of an AGB wind with a low-mass companion in a wide orbit. The gravitational influence of the CHAPTER 1. INTRODUCTION 7 secondary focuses material in the equatorial plane. The companion induces spiral shocks which may anneal amorphous grains into crystalline dust. This work presents a physical mechanism to produce crystalline dust in AGB binary systems. This study is relevant for post-AGB systems in which high degrees of crystallinity appear to be observationally associated with binarity (Molster et al. 2002).

References

Afˇsar, M., & Bond, H. E. 2005, Memorie della Societa Astronomica Italiana, 76, 608

Balick, B., & Frank, A. 2002, ARA&A, 40, 439

Bujarrabal, V., Castro-Carrizo, A., Alcolea, J., & S´anchez Contreras, C. 2001, A&A, 377, 868

De Marco, O., Bond, H. E., Harmer, D., & Fleming, A. J. 2004, ApJ, 602, L93

de Marco, O. 2006, Planetary Nebulae in our Galaxy and Beyond, 234, 111

De Marco, O., Wortel, S., Bond, H. E., & Harmer, D. 2007, ArXiv e-prints, 709, arXiv:0709.1508

de Ruyter, S., van Winckel, H., Maas, T., Lloyd Evans, T., Waters, L. B. F. M., & Dejonghe, H. 2006, A&A, 448, 641

Duquennoy, A., & Mayor, M. 1991, A&A, 248, 485

Garc´ıa-Segura, G., Langer, N., R´o˙zyczka, M., & Franco, J. 1999, ApJ, 517, 767

Garc´ıa-Segura, G., L´opez, J. A., & Franco, J. 2005, ApJ, 618, 919

Huggins, P. J. 2007, ApJ, 663, 342

Iben, I., Jr. 1975, ApJ, 196, 525

Iben, I. J., & Livio, M. 1993, PASP, 105, 1373

Jordan, S., Werner, K., & O’Toole, S. J. 2005, A&A, 432, 273

Kwok, S., Purton, C. R., & Fitzgerald, P. M. 1978, ApJ, 219, L125 CHAPTER 1. INTRODUCTION 8

Mauron, N., & Huggins, P. J. 2000, A&A, 359, 707

Maxted, P. F. L., Napiwotzki, R., Dobbie, P. D., & Burleigh, M. R. 2006, Nature, 442, 543

Moe, M., & De Marco, O. 2006, ApJ, 650, 916

Molster, F. J., Waters, L. B. F. M., Tielens, A. G. G. M., & Barlow, M. J. 2002, A&A, 382, 184

Nordhaus, J., Blackman, E. G., & Frank, A. 2007, MNRAS, 376, 599

Paczynski, B. 1976, Structure and Evolution of Close Binary Systems, 73, 75

Sahai, R., & Trauger, J. T. 1998, AJ, 116, 1357

Sahai, R., Hines, D. C., Kastner, J. H., Weintraub, D. A., Trauger, J. T., Rieke, M. J., Thompson, R. I., & Schneider, G. 1998, ApJ, 492, L16

Sahai, R. 2002, Revista Mexicana de Astronomia y Astroﬁsica Conference Series, 13, 133

Schwarzschild, M., Harm, R. 1965, ApJ, 142, 855

Sedlmayr, E., & Dominik, C. 1995, Space Science Reviews, 73, 211

Soker, N., & Subag, E. 2005, AJ, 130, 2717

Soker, N. 2006, ApJ, 645, L57

Sorensen, P., & Pollacco, D. 2004, Asymmetrical Planetary Nebulae III: Winds, Struc- ture and the Thunderbird, 313, 515

Szczerba, R., Si´odmiak, N., Stasi´nska, G., & Borkowski, J. 2007, A&A, 469, 799 van Winckel, H. 2003, ARA&A, 41, 391

Vlemmings, W. H. T., Diamond, P. J., & Imai, H. 2006, Nature, 440, 58 9

Chapter 2

Low-mass Binary Induced Outﬂows from Asymptotic Giant Branch Stars

2.1 Abstract1

A significant fraction of planetary nebulae (PNe) and proto-planetary nebulae (PPNe) exhibit aspherical, axisymmetric structures, many of which are highly collimated. The origin of these structures is not entirely understood, however recent evidence suggests that many observed PNe harbor binary systems, which may play a role in their shaping. In an effort to understand how binaries may produce such asymmetries, we study the effect of low-mass (< 0.3 M) companions (planets, brown dwarfs and low- mass main sequence stars) embedded into the envelope of a 3.0 M star during three epochs of its evolution (Red Giant Branch, Asymptotic Giant Branch (AGB), interpulse AGB). We find that common envelope evolution can lead to three qualitatively different consequences: (i) direct ejection of envelope material resulting in a predominately equatorial outflow, (ii) spin-up of the envelope resulting in the possibility of powering an explosive dynamo driven jet and (iii) tidal shredding of the companion into a disc which facilitates a disc driven jet. We study how these features depend on the secondary’s mass and discuss observational consequences.

1Originally published as Nordhaus & Blackman 2006 MNRAS 370, 2004 CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 10

2.2 Introduction

Deviation from spherical symmetry in planetary nebulae (PNe) and protoplanetary nebular (PPNe) can be pronounced (Soker 1997, Balick & Frank 2002, Bujarrabal et al. 2004). Understanding the origin of the asymmetries is an ongoing aim of current research. A variety of scenarios have been proposed to explain the transition from progenitor to planetary nebula. As low- and intermediate-mass main sequence stars evolve onto the Asymptotic Giant Branch (AGB), enhanced stellar wind mass loss leads to depletion of the hydrogen envelope around the central core. Recent surveys (Sahai 2000, Sahai 2002) of AGB and post-AGB stars have revealed spherical symmetry leading to the conclusion that any shaping process must occur in a relatively short time just before the birth of the PNe in the PPNe, or AGB phase (Bujarrabal et al. 2001). Bipolar outflows in either the AGB or post-AGB phase could produce such structures. However, the mechanism by which the bipolar winds are produced remains to be fully understood. Binary interactions, large-scale magnetic fields and high rotation rates of isolated AGB stars may all play some role in explaining the observed structures: Frank et al. 1994 appealed to a superwind induced by a thermal helium flash as a possible production mechanism for bipolar planetary nebulae. Soker 2002 argued that such a model does not account for the observational link between aspherical mass loss and asymptotic wind. Such an observational correlation could be explained by a binary system in which the companion is a low-mass star or brown dwarf (Soker 2004). AGB and post-AGB remnant central stars are known to possess magnetic fields (Bains et al. 2004 and Jordan et al. 2005). In addition, direct evidence of a magnetically collimated jet in an evolved AGB star has been detected (Vlemmings et al. 2006), further suggesting some dynamical role for magnetic fields. Magnetic outflows from single stars have been proposed as mechanisms for shaping PPNe and PNe (Pascoli 1993; Blackman et al. 2001a). However, single star models may be unable to sustain the necessary Poynting flux required to maintain an outflow through the lifetime of the AGB phase unless differential rotation is reseeded by convection or supplied by a binary (Blackman 2004, Soker 2006). A model in which a disc driven magnetic dynamo driven outflow is sustained by accretion from a shredded secondary was pursued in (Blackman et al. 2001b). CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 11

In this respect, it is noteworthy that recent studies support the claim that most, if not all, observed planetary nebulae are the result of a binary interaction (De Marco et al. 2004, Sorensen and Pollacco 2004, De Marco & Moe 2005, Mauron & Huggins 2006). While this conclusion is based on observations and population synthesis studies, Soker 2006b points out that the corresponding formation rate of PNe from such studies is 1/3 the formation rate of white dwarfs. This supports the claim that binary stars may produce the more prominently observed planetary nebulae (Soker & Subag 2005). The question of just how a binary shapes a PNe or PPNe remains a topic of active research. In this paper, we explore the effects of an embedded low-mass companion inside the envelope of a 3 M star during three epochs of its evolution off the main sequence (Red Giant Branch (RGB), AGB and interpulse AGB). A common envelope (CE) facilitates mass ejection in several ways: The in-spiral of the secondary toward the core deposits orbital energy and angular momentum in the envelope. This directly ejects and/or spins up the envelope. In the latter case, any enhanced differential rotation could aid in magnetic field generation, which in turn could drive mass loss. In section 2, we describe the stellar models used and derive the basic equations for in-spiral and for the transfer of energy and angular momenutum from the secondary to the envelope. Results for different evolutionary epochs are discussed in section 3. We present observational implications and applications to specific systems in section 4 and conclude in section 5.

2.3 Common Envelope Evolution

Under certain conditions, Roche lobe overflow in close binary systems results in both companions immersed in a CE (Paczynski 1976, Iben & Livio 1993). Once inside, velocity differences between companion and envelope generate a drag force that acts to reduce the orbital separation of the companion and core. Orbital energy is deposited into the envelope during the in-spiral process. Some of this energy is radiated away while the rest is available to reduce the gravitational binding energy of the envelope. The efficiency with which orbital energy unbinds envelope matter is of central importance to CE evolution. This is commonly incorporated into a parameter, α,which CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 12 represents the fraction of orbital energy available for mass ejection as follows:

Ebind = α∆Eorb, (2.1) where ∆Eorb is the change in orbital energy of the binary and Ebind is the energy required to unbind envelope material. In principle, knowledge of the binding energy and α determines how much material is ejected, and in the case of complete envelope ejection, final binary separation distances. Such studies have been performed for a variety of different systems under a range of conditions of which the following are a small sample (Yungelson et al. 1995, Dewi & Tauris 2000, Taam & Sandquist 2000, Politano 2004). We investigate the effect of embedding planets, brown dwarfs and low-mass main sequence stars into an envelope of a 3 M star during various epochs of its evolution off of the main sequence. That the secondary mass represents a small perturbation to the initial envelope configuration allows us to neglect detailed radiative and hydrodynamical effects. We present as simplified a picture as possible in order to elucidate basic phenomonological consequences of the interaction.

2.3.1 Envelope Binding Energy

Our stellar model consists of a 3 M main sequence star whose evolution is followed through the AGB phase with X =0.74 (mass fraction of hydrogen), Y =0.24 (mass fraction of helium), Z =0.02 and no mass loss (S. Kawaler - personal communication, Fig. 2.1). A range of evolutionary models allows consideration of various positions and times at which the expanding envelope engulfs the orbiting brown dwarf. We focus on three main epochs in the evolution: (i) near the tip of the ﬁrst Red Giant Branch, (ii) the beginning of the Asymptotic Giant Branch and (iii) the quiet period between thermal pulses on the AGB branch. In each case, we calculate the energy required to unbind the envelope mass above a given radius, r (measured from the center of the primary’s core) as follows: MT GM(r) Ebind(r)=− dm(r), (2.2) M r where MT is the total mass of the star and M is the mass interior to the companions orbital radius. Here it is assumed that the core and envelope do not exchange energy CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 13

Figure 2.1 Left: Density and mass profiles for our model AGB star. The dotted line is the core-envelope boundary. Right: Mach number and sound speed as a function of radius. The Mach number is computed from the Keplerian motion of the planet inside the envelope. The motion is supersonic everywhere and thus justifies our choice of accretion radius (Bondi 1952). during the CE phase and that ejection of material has no bearing on core structure. The values we determine for the binding energy in all three epochs are comparable to results from an estimation method first proposed by Webbink (1984) and further refined by Dewi & Tauris (2000) and Tauris & Dewi (2001). Explicitly calculating the binding energy for each evolutionary epoch fixes our efficiency parameter α between 0and1. 9 For the RGB star, our model core radius rc ∼ 3.5 × 10 cm with the envelope 11 extending out to a radius r ∼ 7 × 10 cm. At the chosen time in the RGB phase, thecorecontains0.41M and the energy required to unbind the entire envelope (∼ 1048 ergs) is the largest of our three epochs. Once the star has ascended onto the 9 AGB, the core contracts to a radius of 2.9 × 10 cm and the envelope expands to r 12 =5.7× 10 cm. The core has increased its mass to 0.55 M and the energy required to unbind the entire envelope decreases to 1.3 × 1047 ergs. For the interpulse AGB 9 phase, the core has contracted to a rc ∼ 1.6× 10 cm while the envelope has expanded 13 to r∗ ∼ 1.3 × 10 cm. The envelope binding energy has been further reduced to 5.7 × CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 14

46 10 ergs with the core containing 0.58 M. We ﬁnd that the interpulse AGB phase is most favorable for binary induced envelope ejection since the range of masses and radii required to deposit favorable orbital energy into the envelope is greatest in this phase. We discuss these results in detail in section 3.

2.3.2 Orbital Energy and Angular Momentum Evolution

The immersion of the secondary in the envelope of the giant results in a reduction of the separation distance between core and companion. To calculate the in-spiral and angular momentum transfer, we need to equate the rate of energy lost by drag to the change in gravitational potential energy. The motion of a body under the inﬂuence of a central potential while incurring a drag force has been well studied and a general set of equations can be found in Pollard 1979. Here we limit ourselves to the case where orbital eccentricity is negligible, such that the planet exhibits approximate Keplerian motion at each radii. Under these conditions, the energy per unit time released by the secondary mass takes the following form:

2 − 3 Ldrag = ξπRaρ(v venv) , (2.3) where v =(vr,vφ, 0) is the companion velocity, ρ theenvelopedensity,venv the envelope velocity, Ra the accretion radius measured from the center of the companion, and ξ is a dimensionless factor dependent upon the Mach number of the companions motion with respect to the envelope. For supersonic motion, ξ is greater than or equal to 2 (Shima et al. 1985). The orbital motion of the planet is supersonic everywhere inside the orbit (see Fig. 2.1) and for simplicity, we assume a value of ξ =4.The value of ξ acts only to slightly increase or decrease the in-spiral time of the secondary, while leaving the underlying physics unchanged. The accretion radius is then given by

∼ 2Gm2 Ra 2 , (2.4) (v − venv) and represents the region around the secondary inside of which matter is gravitationally attracted to the secondary as it passes through the envelope. If the companion moves close enough to the core, tidal eﬀects can shred it. We estimate the shredding radius (measured from the center of the primay’s core) from balancing the diﬀerential gravitational force across the size of the companion R2 (measured from the center CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 15

d GM Gm2 of the companion) with its self gravity, that is, 2 R2 2 , which yields dr r R2 3 2M 2 rs m2 R . To determine the companion size, R2, we separate our objects into three distinct groups: planets (m2 ≤ 0.0026 M; Zapolski & Salpeter 1969), brown dwarfs (0.0026

0.92 m2 R2 = R. (2.6) M

As the separation between core and companion decreases, the secondary begins to ﬁll its Roche lobe. An approximation for the Roche lobe radius is given by (Eggleton 1983) 0.49q2/3r R = , (2.7) RL 0.6q2/3 + Ln(1 + q1/3) where q is the ratio of secondary mass to core mass and r is the binary separation distance. Once RRL = R2, mass transfer ensues. The time rate of change of gravitational potential energy of the binary is given by:

dU Gm2v dM M = r − . (2.8) dt r dr r

As the secondary traverses the envelope, the drag luminosity must be supplied by the change in gravitational potential energy. Therefore, we equate (3) and (8) using (4) and obtain an equation for the infall velocity. This yields

4ξπGm2rρ vr = , (2.9) dM − M 2 2 dr r vr +¯vφ wherev ¯φ = vφ − venv vφ for slowly rotating stars. In addition, vr vφ everywhere inside the envelope. Eq. (9) agrees with the limit of a general set of equations found in Alexander et al. 1976 under these circumstances. The time scale for infall from a CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 16

Figure 2.2 Infall time as a function of position inside the envelope of the AGB star (left) and interpulse AGB star (right). The solid line represents a companion of mass

0.02 M and the dotted line is a secondary of mass 0.2 M.

∼|r | position inside the envelope can then be estimated as τ vr (see Fig. 2.2). The in-spiral time is slightly shorter for the AGB star than for the interpulse AGB star. In the outer reaches of the envelope, τ is comparable to the lifetime on the AGB (∼ 105 yrs), but sharply drops to ∼ 1 yr just inside the outer radius. As a consequence of the in-spiral process, the secondary loses orbital energy and angular momentum. The reduction in orbital energy is given by:

GMT m2 GMm2 ∆Eorb(r)= − , (2.10) 2ro 2r where ro ∼ r is the stellar radius. In practice, we expect ro to be slightly less then r since material in the outer reaches of the envelope exerts little drag force, thereby significantly extending the infall time (see Fig. 2.2). In addition to transfer of orbital energy, as the secondary moves closer to the core, conservation of angular momentum results in a spin up of the initially stationary envelope. We assume that the lost orbital angular momentum is transferred to spherical shells of the envelope. In reality, most of the angular momentum may be confined close to the orbital plane resulting in latitudinal differential rotation in addition to that expected in the radial direction. A CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 17 more equatorially concentrated deposition of angular momentum could therefore lead to even more differential rotation than considered herein, and a more robust dynamo. The simple equations in this section allow us to crudely investigate different outcomes of CE evolution. Equations (1), (2), (5), (6) and (10) determine the depth at which various mass secondaries can penetrate into the star before depositing enough energy to unbind envelope material and Eq. (9) gives the radial component of velocity during in-spiral. In the next section, we discuss different CE end states that result from analyzing these equations.

2.4 Common Envelope Evolution Scenarios

We outline three qualitatively different scenarios that can occur once the secondary is immersed in the envelope of a given stellar evolution phase: (i) the secondary provides enough orbital energy to directly unbind the envelope (or a portion of it) by itself, (ii) the secondary induces differential rotation in the envelope which can power a dynamo therein, unbinding the envelope or (iii) the secondary is shredded into a disc around the core, which can lead to a disc driven outflow. These scenarios are presented schematically in Fig. 2.3. Below we discuss each in depth and comment on their observational implications in Sec. 4.

2.4.1 Secondary Induced Envelope Expulsion

As the secondary enters the primary’s envelope, the mutual drag transfers angular momentum to the latter and the secondary spirals in. For an RGB star, envelope accretion onto brown dwarf secondaries was previously studied (Livio & Soker 1984,

Soker et al. 1984). The stellar model consisted of a 0.88 M giant with a core mass of

0.72 M during hydrogen and helium shell burning phase. The evolution of the giant was subsequently followed during in-spiral. The authors found that the secondary evaporated if its mass was below an initial critical value (mcrit 0.005 M). When the secondary exceeded this mass, it instead grew to 0.14 M, independent of its initial supercritical mass. The evolution was followed until the envelope was ejected, leaving a close binary system. For each evolutionary phase and ﬁxed value of α, we calculate the radius at which CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 18

Figure 2.3 Three possible outcomes of our CE evolution. (a.) The companion becomes embedded in the stellar envelope, orbital separation is reduced, eventually resulting in unbinding the envelope equatorially. (b.) The companion spirals in, the envelope is spun up causing it to differentially rotate. The presence of a deep convective zone, coupled with the differential rotation, generates a dynamo in the envelope. (c.) The companion is shredded into an accretion disc around the core. The disc then drives an outflow which, in principle, can unbind the envelope. CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 19

Figure 2.4 For various efficiencies α (see Eq. 1), the solid line shows the radius at which the change in orbital energy equals the binding energy of the envelope for the beginning of the AGB star (left) and interpulse AGB star (right). The dotted vertical line marks the core-envelope boundary. The long-dashed line represents the radius at which the companion is tidally shredded by the core. The short-dashed line is where the companion first fills its Roche lobe, initiating mass transfer to the envelope. the orbital energy released equals that of the binding energy of the envelope for a range of secondary masses (see Fig. 2.4). When the star has just reached the RGB phase, we find that no objects under 0.5

M can unbind the envelope before they are tidally shredded. Even if the companion is not shredded, extracting enough orbital energy to expel the envelope requires pen- etrating to the inner most regions where physical contact with the core results. Thus, we do not expect low-mass secondaries inside our model RGB star to produce helium white dwarfs. As the star enters its AGB phase, the envelope expands and the core contracts, thereby lowering the binding energy. In this case, we find a range of masses and efficiencies for which the CE interaction can expel the envelope directly (without magnetic fields). A 0.15 M companion provides enough orbital energy (for α =0.4) to unbind the envelope when it reaches a radius of 3 × 1010 cm. For the interpulse AGB CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 20 star, the binding energy is further reduced from the initial AGB, extending the range of masses and drag efficiencies that can unbind the system. Even if only 20 percent of the orbital energy is available for envelope ejection (α =0.2), a 0.2 M secondary can expel the envelope at 5 × 1010 cm. The binding energy as a function of position is shown in Fig. 2.5. In addition, the orbital energy that a 0.02 M companion supplies as it traverses the envelope is also shown.

2.4.2 Secondary Induced Envelope α − Ω Dynamo

Outflow production mechanisms that extract rotational energy may be required to explain the observed high power bipolar features of PN and PPNe, since radiation driving is insufficient (Bujarrabal 2001). Magnetic field generation inside the AGB envelope may provide a way of extracting this energy and collimating an outflow. Magnetically mediated outflows in an isolated AGB star have been studied from different perspectives (e.g. Pascoli 1993, Blackman et al. 2001, Soker & Zoabi 2002) and outflows from binary + disc systems (Reyes-Ruiz & Lopez 1999, Regos & Tout 1995, Soker & Livio 1994, Blackman et al. 2001b) have also been considered. Here we focus on outflows from binary induced dynamos in the stellar envelope, and discuss accretion driven outflows in the next section. The AGB phase of stellar evolution provides the conditions needed to power an α − Ω dynamo analagous to those studied in the sun, white dwarfs, and supernova progenitors (Parker 1993, Thomas et al. 1995, Blackman, Nordhaus & Thomas 2006). The combination of a deep convective envelope and differential rotation could generate large-scale magnetic fields. Blackman et al. 2001 investigated an interface dynamo in the context of our 3.0 M AGB model. They assumed that the star was initially rotating on the main sequence with a rotation rate of 200 km/s. Assuming that evolution off the main sequence conserves angular momentum on spherical shells results in a differentially rotating AGB star (see Fig. 2.6). Large-scale saturated fields of B ∼ 5 × 104 G can then be calculated at the base of the convection zone. But to drive a magnetic outflow, the dynamo must operate over the entire lifetime of the AGB phase (∼ 105 yrs) until enough matter has been radiatively bled from the envelope for the magnetic ”spring” like a jack-in-the-box. Unfortunately, field amplification drains energy from differential rotation and acts to transfer angular momentum from the core CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 21

Figure 2.5 The solid line depicts the energy required to unbind the envelope for the AGB star (left) and interpulse AGB star (right), if the secondary is not tidally shredded as it traverses the envelope. The dashed lines represent the amount of energy deposited into the envelope from the change in orbital energy of the secondary for efficiency parameter α (Eq. 1). For α =1.0, a m2 =0.02 M brown dwarf delivers enough energy to blow off the AGB envelope at r ∼ 1010 cm. For α =0.3, the brown dwarf must traverse all the way to the core-envelope boundary before supplying enough energy to unbind the system. For smaller α,am2 =0.02 M companion cannot unbind the AGB envelope before spiraling down to a radius where an interface dynamo might participate in unbinding the envelope. For the interpulse AGB star, a 0.02 M brown dwarf can supply enough orbital energy to unbind the envelope for α =1.0and α =0.3. CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 22 to the envelope, slowing down the core within 100 yrs. Anisotropic convection does provide a possible mechanism for reseeding the differential rotation (c.f. Rudiger 1989) and maintaining a steady AGB rotation profile (Blackman 2004), but more work is needed to assess the viability of the single star mechanism. Alternatively, a binary companion may, via a CE phase, supply enough differential rotation to the envelope that the resulting amplified Poynting flux is large enough to unbind the envelope within a few years (Blackman 2004). We study this concept more carefully here. During the CE, the transfer of angular momentum and orbital energy to the envelope induces in-spiral of the companion. Fig. 3 shows the envelope rotation profile produced when a 0.02 M brown dwarf travels from the outer part of the envelope to the core boundary at the beginning of the AGB phase. The differential rotation profile from the single star approach of Blackman et al. 2001 is presented for comparison. The magnitude of rotation generated from a binary interaction during the CE phase is a factor of 10 greater in the interface region and can therefore supply a significantly larger amount of differential rotation energy for a dynamo. In principle, if the secondary could penetrate all the way to the core-envelope boundary (Fig. 2.5), an additional region of energy could be tapped. However, the penetration depth of the secondary is limited by tidal shredding, while the energy available for field amplification is constrained by how far the poloidal field can diffuse into the differential rotation zone (see Blackman, Nordhaus & Thomas 2006 for details). It should be noted that an interface dynamo will rapidly drain the available differential rotation energy (Blackman, Nordhaus, Thomas 2006) so unless the differential rotation is reseeded by convection, the outflow produced by such a dynamo would be explosive and last < 100 years. This is suggestive of ansae further comment on this in section 4.2. For lower mass companions, the transfer of angular momentum may not produce strong enough differential rotation to drive a robust dynamo. The effect of a modest AGB dynamo (Soker 2001b) might be to produce more sunspots near the stellar equator. Dust formation is increased near these cool spots, enhancing the radiative mass loss rate there. If such a modest dynamo could last long enough, the formation of elliptical PNe might be aided by this mechanism. Further study of an α − Ω interface dynamo produced from a secondary induced CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 23

Figure 2.6 Two rotation profiles for our 3.0 M AGB star. The solid curve represents the spin up of an initial stationary envelope by an infalling 0.02 M brown dwarf. The dotted curve is the rotation profile generated in Blackman et al. 2001 in which a main sequence star exhibiting solid body rotation conserves angular momentum of spherical mass shells during its evolution onto the AGB. The solid vertical line marks the core boundary and the short-dashed line represents the base of the convective zone. The long-dashed line is the base of the differential rotation zone used in Blackman et al. 2001. CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 24 rotation profile is warranted (and in progress). Preliminary results from our investigation of an interface dynamo operating in the AGB star model are encouraging. For a differential rotation profile generated by the in-spiral of a 0.02 M companion (Fig. 2.6), we obtain cycle periods of ∼ 0.1 yr with the transient dynamo lasting 0.5 − 1yr.

2.4.3 Disc Driven Outﬂow

In the event that the secondary cannot supply enough orbital energy to directly unbind the envelope or spin it up enough to power a dynamo, the secondary will be shredded from tidal forces as it nears the core. The companion’s physical radius, R2, expands to fill its Roche lobe, at which point, mass transfer to the envelope ensues. Eventually, near the core, tidal shredding occurs. After several dynamical periods, the remnant secondary mass forms an accretion disc which may be capable of producing collimated outflows (Blackman et al. 2001). This scenario differs from Morris 1987 in which the secondary strips material from the AGB primary and acquires a disc. Soker & Livio 1994 investigated disc formation scenarios and found that a disc could form around the primary core when a ∼ 1M main sequence secondary is embedded in an AGB envelope. At the end of the CE phase, after the primary has shed its envelope, the secondary expands, loses matter and forms a disc around the primary. This is qualitatively similar to disc formation in cataclysmic variables, in which matter is stripped off a low-mass companion and forms a disc around a compact primary. Such a disc may be able to power collimated outflows during the proto-PNe phase. This situation can occur if the companion directly ejected much of the envelope and avoided tidal shredding. In the present work, we focus only on low-mass companions, and on discs formed inside the CE from tidally destruction of this companion. Reyes-Ruiz & Lopez 1999 investigated initial binary configurations which lead to disc formation inside an AGB envelope from Roche lobe overflow of companions with masses between 0.001 − 1.0 M. Matter flowing through the inner Lagrangian point falls inward unless it has enough angular momentum to remain in Keplerian orbit. For secondary masses above 0.05 M, matter stripped off the secondary falls all the way to the core surface and therefore does not form an accretion disc. For massive planets and smaller brown dwarfs, an accretion disc can form. CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 25

Reyes-Ruiz & Lopez 1999 also study, the evolution of the resulting disc. They find that a geometrically thin accretion disc forms after an initial mass redistribution stage of ∼ 1yr. For a 0.03 M brown dwarf secondary with ≥ 10% of its mass forming a disc, − 5 −7 t 4 −1 the accretion rate is found to be ∼ 3× 10 104 M yr . For a 3 Jupiter mass secondary, the resulting disc is thinner and cooler with the accretion rate dropping −8 − 5 −1 × t 4 to 4 10 104 M yr . These estimates for mass flow are comparable to those of young stellar objects where an accretion disc outflow connection has been established for similar values (Hartigan et al. 1995). In Fig. 2, we show the distance from the core at which various mass secondaries fill their Roche lobes or shred for our AGB and interpulse AGB model stars. If the orbital energy deposited in the envelope is insufficient to unbid it, then the secondary continues migrating toward the core. Tidal effects become increasingly important and we expect objects that penetrate deep enough to be tidally shredded into a disc (see Fig. 2.4). Brown dwarfs and massive planets shred to form a disc while low-mass stellar companions, because of their large radii (∼ 2 × 1010 cm), may contact the core directly before forming a disc. If the shredding of the companion results in an accretion disc (see Fig. 2.3), a disk outflow similar to those observed in other astrophysical objects such as young stellar objects, X-ray binaries and active galactic nuclei is possible. Disc driven outflows can sustain their observable lifetime longer than the interface dynamos. Thus extended bipolarities extending from the PPNe phase into the PNe phase are suggested of disc mediated outflows rather than merely the explosive outflow of an interface type dynamo discussed above.

2.5 Discussion of Observational Implications

As a consequence of our model, outﬂow composition, collimation and direction vary based on the mass of the secondary embedded in the envelope. In section 4.1, we discuss observational implications of our three ejection scenarios (Fig. 2.3) and the possibility that they could operate in conjunction. In section 4.2, we comment on speciﬁc PPNe and PNe in the context of our CE framework. CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 26

2.5.1 Observational Consequences

The three basic ejection scenarios are shown in Fig. 2.3. When the envelope is ejected purely via orbital energy deposition from the secondary, the corresponding PPNe outflows will reside primarily in the equatorial plane (see Fig. 2.3a). There is numerical evidence from simulations that a binary induced equatorial outflow is confined to an opening angle of ∼ 20 - 30 degrees (Terman & Taam 1996). Sandquist et al. 1998 follow the three-dimensional hydrodynamical evolution of an AGB star with companions of 0.4 − 0.6 M. The binary interaction funnels material and expels it along the equator. If the rotation axis of the central star can be determined, then the identification of an equatorial outflow suggests a CE origin. Many PNe exhibit equatorial tori (Su et al. 2003, Bujarrabal et al. 1998, Castro- Carrizo et al. 2002), some of which are falling back towards the core. This could be explained by a CE interaction that did not supply enough energy to unbind the envelope. Note that very small companions fall into the core without much envelope ejection. For very large mass companions, the radius at which the envelope is expelled increases, also resulting in a small amount of matter in the equatorial outflow. There is therefore an intermediate value of the companion mass which maximizes the amount of equatorial ejecta. As compared to a high-mass, high density torus, a low-mass, low density torus may provide inadequate shielding from the central, illuminated white dwarf. As a consequence, molecule formation in the equatorial torus is reduced. A companion that expels the entire envelope would create more shielding of the outer parts of the torus, leading to more molecule survival. In the event that the secondary cannot directly unbind material, the companion may induce differential rotation which ejects the envelope via a magnetic dynamo driven outflow (Fig. 2.3b). Such an outflow would be predominantly poloidal, likely collimated and aligned with the central rotation axis. The launching and shaping of the outflow could occur close to the central core and the role of a magnetic field at larger distances may be less important. In addition, a torioidal magnetic pressure “sandwich” across the equator acould squeeze some material out equatorially (Matt et al. 2004). The overall outflow expected from a magnetic outflow is thus predominantly poloidal with a smaller equatorial component. CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 27

If the secondary is shredded into an accretion disc around the core, a disc driven outflow is possible (Fig. 2.3c). In this case, the outflow may exhibit chemical signatures of the destroyed secondary. The atmospheres of brown dwarfs are oxygen-rich, in contrast to certain carbon-rich AGB stars. Water and carbon monoxide are present in a range of brown dwarf classes (Geballe et al. 2002, Burgasser et al. 2002). If the companion is a brown dwarf, a disc driven outflow can expel oxygen-rich material along the poles. This may lead to the formation of crystalline silicates along the rotational axis. If the secondary is a low-mass main sequence star, it may be difficult to detect any difference in outflow material if the primary is of similar composition. As the CE phase evolves, a combination of the three above scenarios might occur. For instance, differential rotation supplied during the CE phase may trigger a dynamo in the stellar envelope. The companion continues its in-spiral and eventually forms a disc which later drives an outflow. In this case, two winds are launched from the system, both along the polar axis. The dynamo driven outflow is expected to occur in a burst, whereas the disc driven outflow might last 104 yrs (Blackman et al. 2001). Alternatively, a companion may supply enough energy to directly unbind envelope material but subsequently shred into a disc. The bulk of the mass is ejected along the equator while the disc material is ejected along the rotation axis. In short, each of the three possibilities in Fig. 2.3 represent specific scenarios which may occur in conjunction or individually. More work is needed to elucidate the detailed possibilities.

2.5.2 Applications to speciﬁc PPNe and PNe systems

Hsia, Ip & Li 2006 took time series photometric observations of the young planetary nebulae, Hubble 12 (HB 12; PN G111.8-02.8). The authors found evidence for an eclipsing binary at the center in which the companion is a low-mass object (m2 < 0.443

M). In addition, there is evidence of reflection off of the secondary in the I and R bands. The extended hourglass-like envelope of Hubble 12 suggests jet collimation. In the context of our CE scenarios, such a collimated structure would result from either a dynamo driven outflow in the stellar envelope or a disc driven outflow around the progenitor core. A low enough mass binary companion is required to produce a significant polar outflow. For α =0.6 and a binary separation r ∼ 8 × 1010 cm, as CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 28 suggested by Hsia, Ip & Li 2006, the maximum mass that can result in a polar outflow without expelling much of the envelope equatorially is approximately m2 ≤ 0.2M.

For α =0.3, the limit is m2 ≤ 0.4 M. If the AGB progenitor were more evolved when the CE phase commenced, then the upper limit on the corresponding masses would be lower. For instance, if the companion were immersed in our interpulse AGB star,

α =0.6 would require m2 ≤ 0.08 M while α =0.3 yields m2 ≤ 0.17 M. Therefore, it seems likely that the mass of the companion in Hubble 12 is at least a factor of 2 or 3 less then the upper limit proposed by Hsia, Ip & Li 2006. HD 44179, nicknamed the Red Rectangle, is a proto-PNe in which the secondary in the central binary is a low-mass post-AGB star (Men’shchikov et al. 2002). The system consists of a disk with bipolar outflows emanating from the central region. CO maps suggest that the circumstellar disk is in approximate Keplerian rotation (Bujarrabal et al. 2003). In addition, the expanion velocity in the outer region is quite low (∼ 0.4kms−1) suggesting that the disk is bound to the central binary. It may be that equatorial matter ejected during a CE phase did not fully escape. The disk material then fell backwards until the resulting angular momentum was sufficient to remain in a stable orbit. Recent Spitzer IRS data from the Red Rectangle show evidence of oxygen-rich material in the carbon-rich bipolar outflows (Markwick-Kemper et al. 2005) in addition to the oxygen-rich material in the circumbinary disc (Waters et al. 1998). A possible evolutionary explanation for the disc composition, is that the progenitor incurred rapid equatorial mass loss while the star was still oxygen-rich. The carbon-rich interior layers were exposed and used to shape the bipolar outflows. The oxygen-rich material in the carbon-rich outflows may be the result of a jet from a disk composed of a shredded brown dwarf or planet. NGC 7009 is a PNe, exhibiting complex morphology that includes two distinct ansae far from the central source. Fernández et al. 2004 analyzed the kinematics of the ansae and determined expansion velocities and proper motion. For a distance of 0.86 kpc to NGC 7009, the diameter of the ansae ∼ 3.8×1016 cm with a radial velocity of ∼ 1.3 × 107 cm/s measured away from the nebulae. This gives an upper limit for 2 the burst time of the ansae (τa 100 yrs). Thus an interface dynamo operating ∼ 10 years may be responsible for the production of ansae in some planetary nebulae. CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 29

2.6 Conclusions

We have studied the implications of embedding a range of low-mass (m2 < 0.3M) companions into the envelope of a 3.0 M star during three epochs of its evolution: For RGB stars, we find that envelope ejection is unlikely. However, for AGB and interpulse AGB stars, we find scenarios that can lead to partial or complete envelope ejection. For an AGB star and conventional efficiency parameters (0.3 <α<0.6), we find that massive brown dwarfs can directly eject the envelope equatorially. Lower mass companions that do not directly eject the envelope may spiral in far enough to induce a differential rotation mediated dynamo that ejects material poloidally. In addition, the companion may be shredded into a disc, possibly facilitating a disc driven outflow. For the interpulse AGB star, the envelope has significantly expanded, further lowering the energy required to unbind the system. In this phase, it is easiest for the envelope to be ejected. For systems in which the envelope is directly ejected, the expected outflow is equatorial with a torus-like appearance. The amount of envelope material contained in the outflow is determined by the mass of the secondary and the penetration depth of the companion. Shallow penetration depths may be indicative of higher mass companions and result in lower tori masses and less molecule formation rates in the expanding outflow. Systems which form discs or incur dynamos are expected to generate polar outflows. If the companion is a brown dwarf that gets shredded inside the envelope of a carbon-rich AGB star, contamination of the polar outflow may result in the formation of crystalline silicates or other oxygen-rich substances. When the dynamo occurs in the envelope, via the induced envelope differential rotation, and there is no reseeding of this differential rotation, the outflow can only last < 100yr. This would imply a poloidal poweful but swift jet burst (e.g. ansae) in the PPNe phase. A disc dynamo may be required for a disc mediated magnetic outflow but this would be powered by accretion, which falls off more gradually in time. The power from a disc mediated outflow would therefore produce an observable outflow over a longer time scale, and into the PNe phase (Blackman et al. 2001b). To build on the current results, more detailed calculations are needed to include the three dimensional nature of the binary interaction, the angular distribution of the induced outflow mass and composition, the operation of a dynamo, the inclusion of a CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 30 wider range of companion masses, and the possibility of an initally rotating envelope.

Acknowledgements

We thank A. Frank, W. Forrest, J. Kastner, and I. Minchev for useful discussions and comments. We would also like to thank S. Kawaler for use of his evolutionary models. JTN acknowledges ﬁnancial support of a Horton Fellowship from the Laboratory for Laser Energetics through the Department of Energy and HST grant AR-10972. EGB acknowledges support from NSF grants AST-0406799, AST-0406823, and NASA grant ATP04-0000-0016 (NNG05GH61G). CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 31

References

Alexander, M. E., Chau, W. Y., & Henriksen, R. N. 1976, ApJ, 204, 879

Bains, I., Gledhill, T. M., Richards, A. M. S., & Yates, J. A. 2004, in Asymmetrical Planetary Nebulae III eds. M. Meixner, J. H. Kastner, B. Balick & N. Soker, ASP Conf. Series, 313, 562

Balick, B., & Frank, A. 2002, ARA&A, 40, 439

Blackman, E. G., Frank, A., Markiel, J. A., Thomas, J. H. & Van Horn, H. M. 2001 Nature, 409, 485

Blackman, E. G., Frank, A., & Welch, C. 2001, ApJ, 546, 288

Blackman, E. G., Nordhaus, J. T. & Thomas, J. H. 2006 New Astronomy, 11, 452

Blackman, E. G. 2004, in ASP Conf. Ser. 313: Asymmetrical Planetary Nebulae III: Winds, Structure and the Thunderbird, 313, 401

Bondi, H. 1952, MNRAS, 112, 195

Bujarrabal, V., Alcolea, J., & Neri, R. 1998, ApJ, 504, 915

Bujarrabal, V., Castro-Carrizo, A., Alcolea, J., & S´anchez Contreras, C. 2001, A&A, 377, 868

Bujarrabal, V., Neri, R., Alcolea, J., & Kahane, C. 2003, A&A, 409, 573

Burgasser, A. J., et al. 2002, ApJ, 564, 421

Burrows, A., Hubbard, W. B., Saumon, D., &Lunine, J. I. 1993, ApJ, 406, 158

Castro-Carrizo, A., Bujarrabal, V., S´anchez Contreras, C., Alcolea, J., & Neri, R. 2002, A&A, 386, 633

De Marco, O., Bond, H. E., Harmer, D., & Fleming, A. J. 2004, ApJ, 602, L93

De Marco, O. & Moe, M. 2005, in Planetary Nebulae as Astronomical Tools Eds: R. Szczerba, G. Stasinska and S. K. Gorny (AIP Conference Proceedings) (astro- ph/0511356) CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 32

Dewi, J. D. M., & Tauris, T. M. 2000, A&A, 360, 1043

Durney, B.R., & Robinson, R.D. 1981, ApJ, 253, 290

Eggleton, P. P. 1983, ApJ, 268, 368

Fern´andez, R., Monteiro, H., & Schwarz, H. E. 2004, ApJ, 603, 595

Frank, A., van der Veen, W. E. C. J., & Balick, B. 1994, A&A, 282, 554

Geballe, T. R., et al. 2002, ApJ, 564, 466

Hartigan, P., Edwards, S., & Ghandour, L. 1995, ApJ, 452, 736

Hsia, C. H., Ip, W. H. & Li, J. Z. in press, AJ 2006, astro-ph/0603224

Iben, I. J., & Livio, M. 1993, PASP, 105, 1373

Jordan, S., Werner, K., & O’Toole, S. J. 2005, A&A, 432, 273

Livio, M., & Soker, N. 1984, MNRAS, 208, 763

Livio, M., & Soker, N. 2002, ApJ, 571, L161

Markwick-Kemper, F., Green, J. D., & Peeters, E. 2005, ApJ, 628, L119

Matt, S., Frank, A., & Blackman, E. G. 2004, ASP Conf. Ser. 313: Asymmetrical Planetary Nebulae III: Winds, Structure and the Thunderbird, 313, 449

Mauron, N., Huggins, P. J. in press AA 2006, astro-ph/0602623

Men’shchikov, A. B., Schertl, D., Tuthill, P. G., Weigelt, G., & Yungelson, L. R. 2002, A&A, 393, 867

Morris, M. 1987, PASP, 99, 1115

Paczynski, B. 1976, IAU Symp. 73: Structure and Evolution of Close Binary Systems, 73, 75

Parker, E. N. 1993, ApJ, 408, 707

Pascoli, G. 1993, Journal of Astrophysics and Astronomy, 14, 65 CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 33

Politano, M. 2004, ApJ, 604, 817

Pollard, H. 1979, Celestial Mechanics (Mathematical Association of America)

Regos, E., & Tout, C. A. 1995, MNRAS, 273, 146

Reyes-Ruiz, M., & Lopez, J. A. 1999 ApJ, 524, 952

R¨udiger, G. 1989, Diﬀerential rotation and stellar convection (Berlin: Verlag)

Sahai, R. 2000, ASP Conf. Ser. 199: Asymmetrical Planetary Nebulae II: From Origins to Microstructures, 199, 209

Sahai, R. 2002, Revista Mexicana de Astronomia y Astroﬁsica Conference Series, 13, 133

Sandquist, E. L., Taam, R. E., Chen, X., Bodenheimer, P., & Burkert, A. 1998, ApJ, 500, 909

Shima, E., Matsuda, T., Takeda, H., & Sawada, K. 1985, MNRAS, 217, 367

Soker, N. 1997, ApJS, 112, 487

Soker, N. 2001 MNRAS, 324, 699

Soker, N. 2001, MNRAS, 324, 699

Soker, N. 2002, A&A, 386, 885

Soker, N. 2004, in Asymmetrical Planetary Nebulae III eds. M. Meixner, J. H. Kastner, B. Balick & N. Soker, ASP Conf. Series, 313, 562

Soker, N. 2006, PASP, 118, 260

Soker, N. submitted to ApJ Letters 2006 astro-ph/0603113

Soker, N., Livio, M., & Harpaz, A. 1984, MNRAS, 210, 189

Soker, N., & Livio, M. 1994, ApJ, 421, 219

Soker, N., & Subag, E. 2005, AJ, 130, 2717 CHAPTER 2. LOW-MASS BINARY INDUCED OUTFLOWS 34

Soker, N., & Zoabi, E. 2002, MNRAS, 329, 204

Sorensen, P., & Pollacco, D. 2004, ASP Conf. Ser. 313: Asymmetrical Planetary Nebulae III: Winds, Structure and the Thunderbird, 313, 515

Su, K. Y. L., Hrivnak, B. J., Kwok, S., & Sahai, R. 2003, AJ, 126, 848

Taam, R. E., & Sandquist, E. L. 2000, ARA&A, 38, 113

Tauris, T. M., & Dewi, J. D. M. 2001, A&A, 369, 170

Terman, J. L., & Taam, R. E. 1996, ApJ, 458, 692

Thomas, J. H., Markiel, J. A., & van Horn, H. M. 1995, ApJ, 453, 403

Tout, C. A., & Pringle, J. E. 1992, MNRAS, 256, 269

Vlemmings, W. H. T., Diamond, P. J., & Imai, H. 2006, Nature, 440, 58

Waters, L. B. F. M., et al. 1998, Nature, 391, 868

Webbink, R. F. 1984, ApJ, 277, 355

Yungelson, L., Livio, M., Tutukov, A., & Kenyon, S. J. 1995, ApJ, 447, 656

Zapolski, H. S., & Salpeter, E. E. 1969, ApJ, 158, 809 35

Chapter 3

Isolated versus Common Envelope Dynamos in Planetary Nebula Progenitors

3.1 Abstract1

The origin, evolution and role of magnetic fields in the production and shaping of proto- planetary and planetary nebulae (PPNe, PNe) is a subject of active research. Most PNe and PPNe are axisymmetric with many exhibiting highly collimated outflows, however, it is important to understand whether such structures can be generated by isolated stars or require the presence of a binary companion. Toward this end we study a dynamical, large-scale α − Ω interface dynamo operating in a 3.0 M Asymptotic Giant Branch star (AGB) in both an isolated setting and one in which a low-mass companion is embedded inside the envelope. The back reaction of the fields on the shear is included and differential rotation and rotation deplete via turbulent dissipation and Poynting flux. For the isolated star, the shear must be resupplied in order to sufficiently sustain the dynamo. Furthermore, we investigate the energy requirements that convection must satisfy to accomplish this by analogy to the sun. For the common envelope case, a robust dynamo results, unbinding the envelope under a range of conditions. Two qualitatively different types of explosion may arise: (i) magnetically

1Originally published as Nordhaus, Blackman & Frank 2007 MNRAS 376, 599 CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 36 induced, possibly resulting in collimated bipolar outﬂows and (ii) thermally induced from turbulent dissipation, possibly resulting in quasi-spherical outﬂows. A range of models is presented for a variety of companion masses.

3.2 Introduction

Most planetary and proto-planetary nebulae (PNe, PPNe) are highly aspherical and exhibit a diversified morphology of axisymmetric structures and/or collimated jets. However, the production of such richly varied systems and shaping mechanisms, remains an open topic (Balick and Frank 2002). A central question is whether a binary is required to produce such asymmetries or if an isolated Asymptotic Giant Branch star (AGB) is sufficient. Recently, detection of magnetic fields in AGB stars (Etoka & Diamond 2004, Bains et al. 2004) and the central stars of PNe (Jordan et al. 2005) has sustained interest in magnetic launching and collimation mechanisms. Observational evidence of a magnetically collimated jet in an evolved AGB star (Vlemmings et al. 2006) further suggests that the magnetic field may play a dynamical role. Single star magnetic outflow models have been proposed as mechanisms for producing and shaping PPNe and PNe (Pascoli 1997, Blackman et al. 2001). Whether such models can power and shape the PPNe is uncertain (Soker 2006). In particular, envelope dynamos are expected to be short (< 100 yrs) and drain differential rotation energy rapidly (Blackman 2004), making it unlikely that isolated stars can produce observed asymmetries. If convection can resupply differential rotation energy, then an envelope dynamo in an isolated AGB star may be viable. Anisotropic convection in the sun resupplies differential rotation through the λ-effect (Rüdiger 1989, Rüdiger & Hollerbach 2004), however it is not clear if such a mechanism operates in AGB stars. Rather than single star models, the observed asymmetries may instead be the result of energy and angular momentum supplied by binary interactions. This is supported by recent surveys suggesting that most, if not all PNe involve binary systems (De Marco et al. 2004, Sorensen and Pollacco 2004, Moe & De Marco 2006, Mauron and Huggins 2006). Although there are many different types of binary interactions and outcomes, here we focus on common envelope (CE) evolution in the context of PNe progenitors

(Iben & Livio 1993). A common envelope model in which low-mass (< 0.3 M) CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 37 companions were embedded into the envelope of a 3.0 M AGB star was investigated in Nordhaus & Blackman 2006. The CE evolution is advantageous as it can supply angular momentum in an extremely short period (< 1 yr) and produce a range of PPNe outﬂows. Such a model would predict white dwarf + brown dwarf close binaries that survive the CE phase. Recently, a WD+ BD binary in a close orbit has been detected (Maxted et al. 2006, Burleigh et al. 2006). A separation distance of 0.65

R indicates that the system incurred a common envelope phase in which the brown dwarf was responsible for ejecting the progenitor envelope. This further motivates more detailed study of CE induced PNe. In this paper, we reinvestigate the magnetic model presented in Blackman et al. 2001 in more detail, in an effort to determine the viability of a single star dynamo. We compare the results to a model in which the rotation profile is supplied by a CE phase as in Nordhaus & Blackman 2006. In section 2, we review previous work, compare single star evolution to that resulting from a CE interaction and focus on the depth that the poloidal field can diffuse into the shear zone. We present our interface dynamo in section 3, including the detailed back reaction of the fields on the shear, the generation of heat through turbulent dissipation and the spin down of the star due to Poynting flux. In Section 4, we present the results of our model for three cases: (i) an isolated dynamo in which convection does not resupply differential rotation, (ii) an isolated dynamo in which a fraction of the convective energy resupplies differential rotation energy and (iii) a dynamo resulting from the in-spiral of a low-mass (≤ 0.05

M) companion inside the stellar envelope. We conclude in section 5.

3.3 Dynamos, Common Envelopes and Isolated AGB Evo- lution

A central issue in magnetic PNe progenitor models is whether an isolated AGB star can sustain the necessary field strengths and corresponding Poynting flux to unbind the stellar envelope and produce collimated outflows. Several authors have appealed to various mechanisms with which to produce magnetically mediated outflows in isolated settings (Tout & Pringle 1992, Pascoli 1993, Pascoli 1997, Blackman et al. 2001, Soker & Zoabi 2002, Matt et al. 2004). Soker & Zoabi 2002 appeal to an α2 − Ωdynamo CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 38 operating in the AGB envelope as a means of enhancing dust formation near magnetic cool spots on the stellar surface. The corresponding fields are not strong enough to dynamically alter the geometry, however enhanced mass-loss near the spots could form an elliptical PN. Such a model does not produce strongly bipolar PNe. Other authors have investigated α − Ω dynamo models which tap into the differential rotation energy reservoir between core and convective zone. Pascoli 1997 solved for a steady-state, radial dynamo model from inside the AGB core to produce fields throughout the envelope. Toroidal field strengths of 106 G are obtained at the surface of the core with poloidal field strengths about an order of magnitude lower. No back-reaction of the fields on the rotation profile was included. Blackman et al. 2001 investigated a simplistic interface dynamo model (Parker

1993, Thomas et al. 1995) operating at the base of the convective zone in our 3 M AGB star (see Fig. 4.1). Angular momentum is conserved on spherical shells as the star evolves off the main sequence and the resulting rotation profile is used to calculate field strengths. To drive PPNe, the corresponding dynamo must operate through the entire lifetime of the AGB phase (∼ 105 yrs) until radiation pressure has bled most of the envelope material away. Only then can the Poynting flux unbind the remaining material. But, there are challenges for this model. The differential rotation zone is chosen to be ∼ 1/2 of the total distance from core to convective zone and ∼ 1/2the length of the convective region. This results in only a small fraction of the free shear energy available for field amplification. The majority of the shear energy is located deeper, near the core-envelope boundary. The actual thickness of the differential rotation layer tapped by the dynamo is uncertain. If more of the shear energy were extracted, the envelope could be blown off too early. On the other hand, any dynamo operating beneath the envelope would drain differential rotation on time scales short compared to the AGB lifetime. Only if the differential rotation is re-seeded might this problem be overcome. Even in the sun, the complex interaction between anisotropic convection and the resupply of differential rotation is not fully understood. Recently, the role of downward pumping and penetration depth in the solar tachocline has been investigated (Browning et al. 2006, Dikpati et al. 2006). If isolated star models fail to generate sufficient Poynting flux, common envelope evolution provides an alternative mechanism with which to supply significant differen- CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 39

Convective Zone

r = rc + L1 Core α - layer ^ z Convection Zone

^ Shear Zone r = rc x y^ Ω - layer

r = rc - L

Figure 3.1 A meridional slice of the dynamo geometry. The left figure shows the global geometry of the AGB star. The right figure is a close-up view of the dashed region on the left. The α-effect is driven by convection and occurs in layer of thickness L1 above the differential rotation zone. The poloidal component of the field is pumped downwards into the differential zone, where it is wrapped torodially due to the Ω-effect. tial rotation energy over very short periods (∼ 1− 10 yrs). The in-spiral of a low-mass secondary (< 0.3 M) through the envelope of a 3.0 M star in the AGB phase was investigated in Nordhaus & Blackman 2006. Three qualitative scenarios were found dependent on the mass of the companion: (i) direction ejection of envelope material resulting in an equatorial outflow, (ii) spin-up of the envelope resulting in an explosive dynamo driven jet along the rotational axis and (iii) tidal shredding into a disc which facilitates a jet. In this paper, we investigate (ii) further, in addition to presenting results for an isolated star dynamo.

3.4 Dynamical Equations

In order to determine the temporal behavior of the large-scale magnetic field, we employ the mean-field induction equation which results from averaging the standard induction equation in the presence of helical velocity fluctuations. The result is (Parker 1979) CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 40

2 ∂tB = ∇×E+ ∇× U × B + λ∇ B (3.1) = ∇×(αB)+∇× U × B + ∇× β∇×B + λ∇2B where U is the mean velocity field, B the mean magnetic field, λ the micro-physical magnetic diffusivity, β the turbulent diffusion such that λ β, α the pseudo-scalar helicity coefficient, and E =< u × b >= αB + β∇×B the turbulent electromotive force (Moffatt 1978). Although we envision the dynamo engine operating in a spherical or quasi-spherical AGB star, for present purposes we work in local Cartesian coordinates. Such interface dynamo models have been employed in a variety of systems ranging from late type stars (Robinson & Durney 1982) to white dwarfs (Markiel et al. 1994) to supernova progenitors (Blackman, Nordhaus & Thomas 2006). The coordinate system and global geometry is presented in Fig. 4.1. The convection zone extends from the stellar surface to the interface at r = rc. In this layer, convective twisting motions convert buoyant toroidal field into poloidal field through the α-effect. Below the convection layer, the differential rotation zone shears poloidal field back into toroidal field through the Ω- effect. Defining the vector potential as A =(Ax, A, Az) and decomposing the mean

ﬁeld into toroidal and poloidal components, B =(0, B,∂xA), generates two coupled equations for the time evolution of both components of the magnetic ﬁeld. In order to capture aspects of the 2-D geometry within the framework of our simple

Cartesian 0.5-D model, we break the turbulent diﬀusion into two distinct values: βp, corresponding to the poloidal ﬁeld which grows primarily in the convective region and

βφ, corresponding to the toroidal field which is amplified in the differential rotation zone. We also employ βφ as the turbulent diffusion coefficient for the toroidal velocity. Since the convective region is highly turbulent and the differential rotation zone is more weakly turbulent, we have that βφ βp. The ratio of these can be defined as ≡ βφ the turbulent magnetic Prandtl number as Prp βp . Then, assuming axisymmetry (i.e. ∂yS = 0) for all mean quantities S and defining the velocity field as U =(0, U,u), we obtain

− 2 − − − 2 2 ∂tB = α∂xA ∂zα∂xA + ∂xA∂zU u∂zB uB/L + βφ ∂x + ∂z B (3.2) CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 41

2 2 ∂tA = αB + βp ∂x + ∂z A. (3.3) where B∂zu ∼ uB/L represents a buoyant loss of magnetic flux and u>0 (to be made explicit later). We further assume that the Fourier transforms of the fields are proportional to delta functions implying that the mean-field has one large scale.

We correspondingly deﬁne B,A =[B(t),A(t)] ei(kxx+kzz) where A(t)andB(t)are 2 2 2 complex valued functions of time. Then, setting k = kx + kz and using ∂zU

−rc∆Ω/L yields the following

∆Ω ∂ B = αk 2A − ik r A − iuk B − uB/L − β k2B (3.4) t x x c L z φ 2 ∂tA = αB − βpk A, (3.5) where the rotation profile across the differential rotation layer varies from Ω at the interface to Ω + ∆Ω at rc − L. Thus, ∆Ω is a measure of the shear in the differential rotation zone. If ∆Ω = 0, then the system exhibits solid body rotation. In addition, we parameterize the turbulent diffusion coefficients as [βφ,βp]=[cφ,cp]vL1,wherecφ and cp are distinct dimensionless constants and v is a typical convective velocity in the α-layer. For the loss of toroidal flux due to magnetic buoyancy, we use the following ex- pression for the rise velocity of a magnetic flux tube (Parker 1955, Thomas et al. 1995):

2 3Q a 2 |B|2 3Q V u = = A (3.6) 8 L 4πρv 32 v where a (assumed to be L/2) is the radius of the flux tube, V A is the Alfvén velocity associated with the large scale field and Q is a dimensionless constant of order unity.

3.4.1 Evolution of Ω and ∆Ω

As differential rotation energy is tapped by field amplification, the corresponding Poynting flux drains rotational energy at the interface. In addition, turbulent diffusion converts differential rotation energy into heat which may also be used to unbind the AGB envelope. Therefore, to investigate the interaction between field amplification, differential rotation and rotation, we derive equations for the evolution of ∆Ω and Ω. The mean-field Navier-Stokes equation is given by CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 42

1 ∂ U = −U ·∇U + B ·∇ B + β ∇2U (3.7) t 4πρ φ where ρ is the ﬂuid density, βφ the turbulent viscosity and we have assumed that b B and u U in the weakly turbulent shear layer. Then, taking they ˆ-component (see Fig. 4.1) yields the following

1 ∂ U ∂ A∂ B + β ∂2 + ∂2 U. (3.8) t 4πρ x z φ x z

Using the fact that, ∂zU −rc∆Ω/L, we can link ∆Ω with U as follows −∂t (rc∆Ω) = ∂t U (rc) − U (rc − L) ∂t L∂xU . (3.9)

Subtracting the time-dependent velocity equation at rc − L from rc and using the relation ∂tU|rc − ∂tU|rc−L ∼ L∂z∂tU|rc yields the following

L − 2 − ∂zρ − βφ ∂t∆Ω = kxkz Re(A)Re(iB)+Re(iA)Re(B) kxkzRe(iA)Re(iB) 2 ∆Ω, 4πrcρ ρ L (3.10) wherewehaveassumedρ = ρ and thus ∂zρ ∼ (ρ2 − ρ1) /L is the change in density across the shear layer. In addition to the dynamic shear, we allow for the rotational energy of the field- anchored matter to drain via Poynting flux. No appreciable toroidal field amplification occurs above the interface, so we calculate the Poynting flux at the base of the convection zone. The total integrated Poynting flux at rc is given by

c L = E × B · dSc mag 4π − 3 Re(B)Re(∂xA)Ωrc . (3.11)

When the toroidal and poloidal fields are out of phase, there is a maximum magnetic luminosity that is not the respective product of the maximum individual field strengths (Blackman, Nordhaus & Thomas 2006). This is a generic feature of our interface dynamo solutions and will be presented in Section 4. To arrive at a dynamical equation for Ω, we must calculate the available rotational energy in the shear layer. We estimate the rotational energy in the differential rotation CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 43

∼ 2 2 zone as Erot M∆Ωrc Ω /2. Various mass secondaries can supply a range of diﬀerential rotation in addition to rotational energy. For a 0.05 M brown dwarf, the total shear energy from the convective boundary to the tidal shredding radius is ∼ 5 × 1047 ergs in the AGB envelope. This is approximately 4 times the binding energy of the entire AGB envelope. As the star evolves into its thermal pulsing phase, the convective zone deepens and both the thickness and mass of the shear layer shrink. It may also be possible to power an interface dynamo during a later phase in the stars evolution. In this paper, we focus on the beginning of the AGB phase. Equating the time derivative of the rotational energy with the magnetic luminosity gives

Re(B)Re(∂zA)Lrc ∂tΩ . (3.12) M∆Ωδ In arriving at Eq. (3.12), we have multiplied the available rotational energy by a factor of δ/L. The penetration length, δ, represents the depth at which the poloidal field can diffuse into the shear layer. If δ/L = 1, the total shear energy in the differential rotation layer is available for extraction. We estimate the penetration depth as the distance that the poloidal field can diffuse into the shear layer during a cycle period. 1 2L 2 0 In the kinematic limit, the cycle period is given as τ =2π α0∆Ω0krc where α and ∆Ω0 are the initial values (Blackman, Nordhaus & Thomas 2006). The cycle period does increase in the dynamical regime, however it does not change appreciably from its initial value. Therefore, τ serves as a lower limit for the cycle period. Correspondingly, we define the penetration depth as

1 δ (βφτ) 2 . (3.13)

3.4.2 Evolution of α

In addition to a dynamical equation for shear, α quenching can be understood through magnetic helicity conservation (Kleeorin & Ruzmaikin 1982, Blackman & Field 2002, Brandenburg & Subramanian 2005). In the absence of boundary terms, magnetic helicity is well conserved and the build up of A · B corresponds to a build up of large- scale ﬁeld. The small-scale helicity then grows to equal and opposite magnitude of the large-scale helicity. To maintain simplicity, here we appeal to a parametrized form CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 44 of α which approximates the non-linear quenching (Blackman, Nordhaus & Thomas 2006). We adopt the following proﬁle 2 − B /8π α = α0 (Ω/Ω0) Exp γ 2 (3.14) ρ1v /2

2 L1Ω0 0 ≡ where α cα rc , cα a dimensionless constant, Ωo the initial rotation rate at the interface and ρ1 the density in the middle of the convective region.

3.5 Numerical Results

To investigate various interface dynamo configurations, Eqs. (4), (5), (10) and (12) are solved numerically, the solutions of which represent the time evolution of Bφ, Bp, ∆Ω and Ω. In each case, we employ a 1 G seed field for the real components of both the toroidal and poloidal field. The fields grow until they are quenched through a drain of the available differential rotation energy. In all cases, the saturated dynamo is Ω-quenching dominated and not α-quenching limited in contrast to Blackman et al. 2001. We focus on three types of shell dynamos: (i) that of an isolated AGB star, (ii) that of an isolated AGB star in which convection resupplies differential rotation, (iii) that of an AGB star which has been spun up by a companion in-spiraling through the stellar envelope. We use independent radial rotation profiles for the above cases to calculate the initial value of ∆Ω. For the isolated AGB star, we assume that as the star evolves off the main sequence, angular momentum is conserved on spherical shells yielding a rotation profile ∝ r−2. We consider this case in detail in Section 4.1. Because convective energy may resupply differential rotation energy analogous to what occurs in the sun, we consider a range of resupply rates in Section 4.2. In Section 4.3, we consider a rotation profile generated from the in-spiral of a low-mass secondary through the stellar envelope. The in-spiral time is short compared to the AGB lifetime and rapidly creates a strong shear region beneath the convective zone. In addition, the in-spiral time is less than or equal to a cycle period, τ, so the angular momentum and energy are supplied to the dynamo on time scales short compared to its growth time. CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 45

3.5.1 Isolated Dynamo Without Reseeding ∆Ω

It has been suggested (Blackman et al. 2001), that isolated AGB stars may be able, through dynamo action, to unbind their envelopes and produce collimated outflows. As the star expands onto and through the AGB branch, the core contracts while the envelope expands, creating a shearing profile throughout the interior. A differential rotation zone, coupled with the above convective region provides conditions for large- scale field amplification. However, field growth requires draining differential rotation energy. In the sun, the rotation profile is re-established through a transfer of convective energy by way of the λ-effect (Rüdiger & Hollerbach 2004). This results in a steady- state rotation profile and a magnetic cycle with quasi-steady peak field. However, if convection does not resupply differential rotation energy, any resultant dynamo would be a transient phenomenon. Blackman et al. 2001 investigated an isolated shell dynamo operating in the AGB phase of our model star. The depth of the differential rotation zone was taken to be ∼ 1/2 the distance from the base of the convective zone to the stellar core. In addition, ∆Ω and Ω were assumed to be constant and independent of the magnetic field. Thus, the dynamo lasted indefinitely and sustained a toroidal field of ∼ 5 × 104 G at the interface. The arbitrarily long lifetime was essential because in order for the large-scale field to drive a self-collimated outflow, the dynamo must last until the end of the AGB phase after the star has radiatively bled most of its envelope material. To alleviate the assumption of steady ∆Ω and Ω and to study the backreaction of field growth on the shear, we apply our dynamical dynamo model using parameters in Blackman et al. 2001. We fix the thickness of the differential rotation zone (L =4.6 × 1010 cm), the −6 −1 rotational speed at the interface (Ω0 =5× 10 rad s ), and the shear profile across the Ω-layer. We then lower the value of βφ. This lengthens the dynamo lifetime and determines the relative fraction of energy deposited into magnetic or heat sinks. Fig.

3.2 shows the isolated interface dynamo for two different values of βφ. In both cases, the depth of the differential rotation zone is fixed and the shear energy in that zone is available for field amplification. The toroidal and poloidal fields are out of phase and thus generate an oscillatory Poynting flux. Maximum toroidal field strengths of ∼ 5 × 103 G are obtained, while the poloidal field is significantly lower, with values CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 46

2 of Bp ∼ 2 × 10 G at the interface. In both cases, the time integrated Poynting flux and turbulent dissipation generate ∼ 10−5 times the binding energy of the envelope. Therefore, the current parameters can not produce a dynamically influential magnetic outflow or significant heating from turbulent dissipation in the shear zone. If an isolated interface dynamo were to be viable, a deeper shear zone would be required.

T M

T εε εε

Figure 3.2 The differential rotation energy is allowed to drain through field amplification and turbulent dissipation. In this figure, k =5× 10−11 cm−1, c =0.01, z p t Q =5.0. We define, [PF,dis] ≡ 0 E[PF,dis] (t ) dt and label M (PF)andT (dis)on the top right plot to distinguish between the thermal and magnetic contributions to −4 −5 the binding energy. For the left figure, cφ =10 while the right has cφ =10 .Peak field strengths are a factor of ∼ 5 − 10 less then those obtained in (Blackman et al.

2001). Differential rotation energy is drained in < 20 yrs. Lowering cφ results in the differential rotation energy draining at a slower rate, allowing the field to sustain for longer periods of time (∼ 40−50 yrs). However, peak field strengths remain the same.

Ahighercφ allows the poloidal component of the field to diffuse deeper into the toroidal zone, thus extracting more differential rotation energy. Hence, the depth of the shear layer is determined by the value of cφ.IfwefixL as the distance from the base of the convective zone to the core, then the corresponding fields diffuse all the −6 way to the stellar core for Prp ≥ 10 . This unbinds the envelope at the beginning of CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 47 the AGB phase. In addition, we can constrain how far the fields would have to diffuse in order to unbind the AGB envelope. If the poloidal field diffuses to ∼ 5 × 109 cm 31 −3 −1 within the stellar interior, then M∆Ω =1.7 × 10 gand∆Ω=1.5 × 10 rad s . 47 This corresponds to E∆Ω ∼ 1.5 × 10 ergs which is comparable to the binding energy of the envelope. However, in these cases, the dynamo would blow off the envelope prematurely and such a circumstance would contradict observations of AGB lifetimes 105 yrs. If an isolated shell dynamo is to be consistent with observations, the dynamo must be sustained during the end of the AGB phase.

3.5.2 Isolated Dynamo With Reseeding ∆Ω

Convection might reinforce differential rotation analogous to what occurs in the sun. Thermal energy and a negative entropy gradient drive convective turbulence. In the Kolmogorov framework, energy cascades from the large-scale to the dissipative scale at a rate given by ∂ v3 ∼ l = D (3.15) ∂t l where l is a length scale, vl the corresponding velocity and D is independent of scale (Shu 1992). For our PNe progenitor, we use the large-scale convective velocity, v = 5 vl =10, cm/s corresponding to the approximate thickness of the convective zone, l = L1. We envision adding a resupply term to Eq. (10), in which a fraction, f,of the turbulent energy cascade rate resupplies shear. To determine this term, we equate (15) with the time rate of change of kinetic energy in the shear zone and arrive at 3 ∂∆Ωc Mc v = f 2 , (3.16) ∂t M∆Ω L1L ∆Ω where ∆Ωc is the shear that would be resupplied by the turbulent cascade. By adding the right side of Eq. (16) to Eq. (10), we can investigate the full range of convective resupply scenarios from f = 0 (no convective resupply) to f = 1 (maximum convective −5 resupply). In addition, we fix the following values: ∆Ω0 =1.5 × 10 rad/s, Ω0 = −6 10 −2 5 × 10 rad/s, L =4.6 × 10 cm, cp =10 and Q =5.0. We consider two sub-scenarios for the convective resupply dynamo: Ω dynamically evolving and Ω constant. In the first case, Poynting flux is allowed to spin down the envelope at the interface. This requires magnetic buoyancy, which appears in Eq. (4) as terms proportional to uB/L. The left graph in Fig. 3.3 presents the result for CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 48 dynamical Ω. Rotation is drained by Poynting flux and we take the most extreme best case of 100 % (f = 1) of the turbulent energy cascade rate resupplying differential rotation energy. This does establish a constant ∆Ω. However, the bulk of the Poynting flux is drained in a short burst (≤ 10 yrs). It is unfeasible to generate the requisite energy required to produce a magnetically dominated explosion in this case.

T M εε εε

Figure 3.3 Results for reseeding differential rotation through convection. In the left figure, f = 1 corresponding to maximum convective resupply. Rotation is drained through Poynting flux but cannot sustain a dynamically important dynamo. In the figure on the right, f = 0 (no resupply of ∆Ω). The rotation rate is fixed, corresponding to a buildup of Poynting flux in the interface layer.

For the second case (Ω constant), we consider the possibility that the field is stored in the interface layer until the corresponding aggregate Poynting flux is able to blow up the envelope through a magnetic ”spring” effect. If the field is trapped, Poynting flux does not emerge from the layer and thus does not spin down the envelope. Even though the dynamo equations for the two cases are mathematically identical, in the case of steady rotation terms proportional to uB/L can be interpreted as diffusion rather than buoyant loss. The right plot in Fig. 3.3 shows a constant Ω with f =0(no convective resupply). Constant rotation results in a decay of the differential rotation energy. However, since Ω is constant, the α-effect is non-zero and thus is continually pumping poloidal field into the shear layer. The achieved poloidal field strength is CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 49 negligible and energetically insignificant. It cannot blow off the envelope. Finally we consider the case in which ∆Ω is resupplied and Ω is constant. Fig. 3.4 demonstrates that convective resupply coupled with a constant Ω results in a sustained Poynting flux. The Poynting flux of ∼ 5×1034 erg/s sustained over a period of 105 yrs is enough to overcome the binding energy of the envelope and produce a −5 magnetically driven envelope expulsion. For cφ =10 ,0.1% of the energy cascade rate has been used to resupply the differential rotation and marks the approximate −5 minimum threshold fraction required to blow off the envelope. If cφ ≥ 5 × 10 ,then the rate of heat produced from turbulent dissipation is greater than the Poynting flux, resulting in thermally induced envelope expulsion. Although it is not known whether a mechanism for resupplying differential rotation operates in AGB stars (e.g. Rüdiger & Hollerbach 2004), we have demonstrated that such an effect may facilitate a dynamo driven envelope expulsion, provided both Ω and ∆Ω are sustained.

3.5.3 Common Envelope Dynamo

In a close binary system, Roche lobe overflow can result in both companions immersed inside a common envelope (Paczynski 1976, Iben & Livio 1993). A drag force due to the velocity difference between companion and envelope, induces in-spiral of the secondary. As a result, orbital energy and angular momentum are transfered from companion to common envelope. For low-mass secondaries, the in-spiral time can be extremely fast (≤ 1 yr) supplying the requisite angular momentum on time scales much shorter then the AGB lifetime (Nordhaus & Blackman 2006). As the companion traverses the envelope, the transfer of orbital energy alone may be enough to unbind it. However, if the companion cannot supply the necessary orbital energy, in-spiral continues until the secondary is tidally shredded into a disk. In addition, angular momentum transfer spins up the envelope resulting in a differentially rotating stellar interior. Assuming that the AGB star is initially stationary, we can calculate the corresponding rotation profile generated by in-spiral of a companion. The change in orbital energy, in virial equilibrium, of the secondary is given as

GMT m2 GMm2 ∆Eorb(r)= − , (3.17) 2r 2r CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 50

T εε

Figure 3.4 Convective resupply results in a steady-state differential rotation profile. For the left column, the envelope of the poloidal, toroidal and Poynting flux is plotted. The Poynting flux is sustained at ∼ 5×1034 erg/s. The sustained Poynting flux supplies enough energy to unbind the envelope of our 3 M model at the end of the AGB phase 5 −5 −3 (∼ 10 yrs). In this figure, cφ =10 and f =10 implying that only ∼ 0.1% of the cascade energy must be converted into differential rotation energy to supply the requisite Poynting flux. This model predicts a magnetically dominated explosion.

where MT is the total mass of the star, m2 the secondary mass, M the enclosed mass at position r, and r is the stellar radius. A fraction, αCE∆Eorb of the orbital energy CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 51

released by the companion is available for mass ejection. If αCE∆Eorb ≥ Ebind,where

Ebind is the envelope binding energy, then the secondary has expelled the envelope. In order to calculate the rotation proﬁle of the AGB star, we use the gravitational potential energy released by the secondary to spin-up spherical shells as follows:

2 αCE∆Eorb = IsΩs (ri) , (3.18) where Is is the moment of inertia of a thin shell, Ωs the angular velocity of the shell and ri the outer radius of the shell. Solving for the rotation proﬁle of a shell yields

1 2 3 αCE∆Eorb Ωs (r0)= 2 (3.19) 2 Msri where Ms is the shell mass. We study the limit in which the orbital eccentricity is negligible, resulting in the companion exhibiting Keplerian motion at all radii (Pollard 1979). Fig. 3.5 shows envelope rotation proﬁles for companions with masses ranging from 0.01 to 0.05 M.

Also shown is the Keplerian velocity, vK, and the sound speed, cs inside the envelope. Higher mass companions supply enough orbital energy to spin-up the envelope above its Keplerian value at a given radius. The rotational energy will then redistribute via outward mass transfer until Keplerian rotation is re-established. This effect can be seen in the envelope rotation profile generated by a 0.05 M secondary. It also occurs for larger mass companions, however we do not investigate those as we would expect similar results. The dashed-dotted vertical line shows the approximate radius at which the companion is tidally shredded and spin-up of the envelope ceases. Below this depth the companion would form a disk and the mechanism of angular momentum transfer would be different. In reality the rotation profile should be solved for self- consistently, but this becomes particularly important as soon as the rotational energy exceeds that associated with the sound speed. We have not incorporated this non- linear effect explicitly, and hence our approach of redistributing the excess rotational energy in the inner regions in Fig. 3.5 is crude. As can be seen from Fig. 3.5, a range of companion masses can produce varying amounts of rotation and differential rotation. To investigate how this shear energy is deposited, we apply the rotation profiles in Fig. 3.5 along with the parameters of the stellar model to our interface dynamo. For a 0.02 M brown dwarf secondary, CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 52

Figure 3.5 Rotation profiles generated from the transfer of angular momentum from companion to envelope in our AGB star. In both figures, the solid curves represent the resulting profiles for companions of masses 0.05 (top), 0.02 and 0.01 (bottom)

M. For the left figure, the dashed curve represents the Keplerian velocity while the dashed-dotted curve is the sound speed. The 0.05 M companion initially spins up the envelope such that the inner region is rotating faster then the Keplerian velocity. Mass redistribution ensues and transfers matter outward until the rotation profile drops below Keplerian. The right figure presents the angular velocity corresponding to the left figure. The dash-dot vertical line is the approximate radius at which the companion is tidally shredded. The large-dash vertical line is the boundary of the shear layer in Blackman et al. 2001 while the small dash line is the base of the convection zone. These profiles assume that αCE =0.3.

5 −4 toroidal field strengths of ∼ 1×10 G are obtained (see Fig. 3.6). For Prp =10 ,the decay of the shear energy and toroidal field are long (∼ 25 yrs) and occur over several thousand cycle periods. Therefore, in Fig. 3.6, the solid line represents the envelope of the dynamo while the smaller insets show a ”zoomed-in” region to demonstrate the oscillatory nature of the fields. For these parameters, the heat generated from turbulent dissipation is greater then the time-integrated Poynting flux, thus we identify this as a thermally induced model. CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 53

M εε

Figure 3.6 Interface dynamo resulting from the in-spiral of a 0.02 M brown dwarf in the interior of our model AGB star. The differential rotation zone extends from the base of the convection zone to the radius at which the secondary is tidally shredded −4 −4 (Nordhaus & Blackman 2006). In this model, PM =10 and Q =5,Ω0 =2.3 × 10 −3 rad/s, ∆Ω0 =2.5 × 10 rad/s and δ/L = 1. In the left column, the envelope of the Poynting flux (top), toroidal field (middle) and poloidal field (bottom) are drawn with a solid line. The insets represent the time evolution from 0 to 0.2 yrs. The vertical scale of the insets are the same as the corresponding larger figure. CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 54

In Fig. 3.7, we present a model in which the time-integrated Poynting ﬂux is large enough to unbind the stellar envelope. In this case, the companion is a 0.05

M brown dwarf and spins-up the envelope until it is shredded into a disk. For this −6 model, Prp =10 with the corresponding Poynting flux decaying in ∼ 100 yrs. Peak toroidal and poloidal field strengths are comparable to results from Fig. 3.6, however the lower Prp results in less differential rotation energy being converted into heat. Therefore, we identify this as a magnetically dominated model. Both magnetically dominated and thermally driven models can be produced for a range of companion masses and diffusion coefficients. The resultant outflows for the two cases are expected to be qualitatively different. For interface-dynamo-driven winds, the launching and shaping of the outflow could occur close to the core. Such an outflow is expected to be collimated, predominately poloidal and aligned with the central rotation axis and may be responsible for shaping features in Abell 63 (Mitchell et al. 2006). On the other hand, if heat is the primary driver mediating the transition from progenitor to PPNe, the resulting outflow is probably quasi-spherical. Bipolar, magnetically collimated PNe could be the result of our low Prp, common envelope magnetically dominated models.

3.6 Morphology of Magnetic Outﬂows

While this paper has focused on the generation of magnetic fields within the star, here we comment on previous work on the interaction between rotation and magnetic fields in shaping PNe and PPNe outflows on larger scales. For both isolated stars and binary systems, the strength of the magnetic field carried by the fast wind can influence the geometry of the nebula. Chevalier & Luo 1994 present simplified shaping results for weakly magnetized winds in an isolated star. While the corresponding outflows are not particularly elongated, it is possible to produce more highly collimated jets if the magnetized wind is shocked close to the stellar surface. These results have been corroborated by numerical simulations (Rozyczka & Franco 1996). In contrast to magnetized winds, radiatively driven outflows in a rotating star display an equatorial density enhancement (Bjorkman & Cassinelli 1993). As rotation increases, gas compression is enhanced and may lead to the formation of a circumstellar CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 55

T εε

Figure 3.7 Interface dynamo resulting from the in-spiral of a 0.05 M brown dwarf. −6 −4 −3 In this model PM =10 , Q =5,δ/L =1,Ω0 =5×10 rad/s and ∆Ω0 =2.5×10 rad/s. The insets represent the time evolution from 0 to 0.2 years. The vertical scale of the insets are the same as the corresponding larger figure. torus. A fast wind colliding with the torus may then collimate a poloidal outflow even in a weakly magnetized flow (Garc´ıa-Segura et al. 1999). Such a situation may be relevant both in the single star and common envelope scenarios. During in-spiral, the secondary can significantly spin-up the common envelope. Fast rotation rates may CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 56 lead to envelope deformation thus enhancing equatorial densities (Soker 1992). Fast differential rotation is a common ingredient required for the generation of strong magnetic fields. Garc´ıa-Segura et al. 2005 investigated the relationship that rotation and magnetic fields have on expected PNe shapes. As rotation and field strength increase, the resulting outflows become elongated along the rotation axis (Garc´ıa-Segura et al. 1999). Such a result might be the large scale manifestation of a dynamo operating within the common envelope.

3.7 Conclusions

Extraction of rotational energy is likely fundamental to the formation of multipolar PPNe and PNe. Magnetic dynamos can play an intermediary role in facilitating the extraction of rotational energy. Here, we have studied a large-scale, dynamical interface dynamo operating in the envelope of a 3.0 M AGB star. The back reaction of field amplification on the shear is included as are the drain of rotation and differential rotation via both turbulent dissipation (thermally induced) and Poynting flux (magnetically induced). Two different dynamos are studied: (i) that of an isolated star and (ii) that of a common envelope system in which the secondary is a low-mass companion (< 0.05 M). For the isolated case, we find that only when two conditions are met can the single star dynamo drive PPNe. First, ∆Ω must be re-seeded. This may occur by analogy to the λ-effect in the sun (Rüdiger & Hollerbach 2004). Secondly, Ω must be constant. This implies that the field is stored in the shear layer until the end of the AGB phase. When these two stringent conditions are met, a small fraction of the energy cascade rate can provide the necessary shear energy to sustain the interface dynamo (in some cases as little as 0.1%). Not only is the dynamo maintained, but the time-integrated Poynting flux is large enough to overcome the envelope binding energy. Whether or not isolated star dynamos can produce a PPNe, a binary interaction can do so more robustly for a wide range of cases. Common envelope evolution is advantageous in several ways. Energy and angular momentum are supplied very quickly (< 1 yr) and often in less than or equal to a dynamo cycle period, allowing the dynamo to operate once the secondary has completed its in-spiral. For our common envelope dynamo model, a range of companion masses can easily supply enough differential CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 57 rotation energy to power either a dynamo driven jet or a thermally driven outflow. A magnetically dominated explosion likely produces a collimated, poloidal outflow while that of a thermally induced explosion is expected to be more spherical. We have highlighted some of the basic key issues of isolated and common envelope dynamos, however, more detailed research is needed in both areas. The viability of anisotropic convection reseeding differential rotation must be determined. If convection cannot reseed shear, then we are faced with the proposition that binary interactions are required to produce axisymmetric PNe. In the CE case, the complex interaction between companion and envelope, multi-dimensional aspects of the dynamo, realistic rotation profiles of isolated stars and the inclusion of a wider array of secondary masses are just a few of the many problems which warrant future work. Constraints on the turbulent diffusion coefficient as a function of radius also need to be determined. The physics involved in transitioning from a dynamo to a fully active jet must be understood.

Acknowledgements

We thank Noam Soker for identifying a needed correction which lead to an improved manuscript. We would also like to thank Ivan Minchev for useful discussions and comments and Steve Kawaler for use of his evolutionary models. JTN acknowledges ﬁnancial support of a Horton Fellowship from the Laboratory for Laser Energetics through the U. S. Department of Energy and HST grant AR-10972. EGB acknowledges support from NSF grants AST-0406799, AST-0406823, and NASA grant ATP04-0000- 0016 (NNG05GH61G). AF acknowledges support from JPL Spitzer grant 1278931, NSF grant AST-0507519 and DOE grant DE-F03-02NA00057. CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 58

References

Bains, I., Richards, A. M. S., Gledhill, T. M., & Yates, J. A. 2004, MNRAS, 354, 529

Balick, B., & Frank, A. 2002, ARA&A, 40, 439

Bjorkman, J. E., & Cassinelli, J. P. 1993, ApJ, 409, 429

Blackman, E. G., Frank, A., Markiel, J. A., Thomas, J. H. & Van Horn, H. M. 2001 Nature, 409, 485

Blackman, E. G., & Field, G. B. 2002, Physical Review Letters, 89, 265007

Blackman, E. G. 2004, in ASP Conf. Ser. 313: Asymmetrical Planetary Nebulae III: Winds, Structure and the Thunderbird, 313, 401 Edited by Margaret Meixner, Joel H. Kastner, Bruce Balick and Noam Soker.

Blackman, E. G., Nordhaus, J. T. & Thomas, J. H. 2006 New Astronomy, 11, 452

Brandenburg, A., & Subramanian, K. 2005, Phys. Rep., 417, 1

Browning, M. K., Miesch, M. S., Brun, A. S., & Toomre, J. 2006, ApJ, 648, L157

Burleigh, M. R., Hogan, E., Dobbie, P. D., Napiwotzki, R., & Maxted, P. F. L. 2006, ArXiv Astrophysics e-prints, arXiv:astro-ph/0609366

Chevalier, R. A., & Luo, D. 1994, ApJ, 421, 225

De Marco, O., Bond, H. E., Harmer, D., & Fleming, A. J. 2004, ApJ, 602, L93

Dikpati, M., Gilman, P. A., & MacGregor, K. B. 2006, ApJ, 638, 564

Etoka, S., & Diamond, P. 2004, MNRAS, 348, 34

Garc´ıa-Segura, G., Langer, N., R´o˙zyczka, M., & Franco, J. 1999, ApJ, 517, 767

Garc´ıa-Segura, G., L´opez, J. A., & Franco, J. 2005, ApJ, 618, 919

Iben, I. J., & Livio, M. 1993, PASP, 105, 1373

Jordan, S., Werner, K., & O’Toole, S. J. 2005, A&A, 432, 273 CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 59

Kleeorin, N., & Ruzmaikin, A. A. 1982, Magnetohydrodynamics 18, 116

Markiel, J. A., Thomas, J. H., & van Horn, H. M. 1994, ApJ, 430, 834

Matt, S., Frank, A., & Blackman, E. G. 2004, ASP Conf. Ser. 313: Asymmetrical Planetary Nebulae III: Winds, Structure and the Thunderbird, 313, 449 Edited by Margaret Meixner, Joel H. Kastner, Bruce Balick and Noam Soker.

Mauron, N., & Huggins, P. J. 2006, A&A, 452, 257

Maxted, P. F. L., Napiwotzki, R., Dobbie, P. D., & Burleigh, M. R. 2006, Nature, 442, 543

Mitchell, D. L., Pollacco, D., O’Brien, T. J., Bryce, M., Lopez, J. A., Meaburn, J., & Vaytet, N. M. H. 2006, ArXiv Astrophysics e-prints, arXiv:astro-ph/0611268

Moe, M., & De Marco, O. 2006, ArXiv Astrophysics e-prints, arXiv:astro-ph/0606354

Moﬀatt, H. K. 1978, Cambridge, England, Cambridge University Press, 1978. 353 p.,

Nordhaus, J., & Blackman, E. G. 2006, MNRAS, 370, 2004

Paczynski, B. 1976, IAU Symp. 73: Structure and Evolution of Close Binary Systems, 73, 75

Parker, E. N. 1955, ApJ, 121, 491

Parker, E. N. 1979, Oxford, Clarendon Press; New York, Oxford University Press, 1979, 858 p.,

Parker, E. N. 1993, ApJ, 408, 707

Pascoli, G. 1993, Journal of Astrophysics and Astronomy, 14, 65

Pascoli, G. 1997, ApJ, 489, 946

Pollard, H. 1979, Celestial Mechanics (Mathematical Association of America)

Robinson, R. D., & Durney, B. R. 1982, A&A, 108, 322

Rozyczka, M., & Franco, J. 1996, ApJ, 469, L127 CHAPTER 3. ISOLATED VS. COMMON ENVELOPE DYNAMOS 60

Rudiger, G. 1989, New York : Gordon and Breach Science Publishers, c1989.

Rüdiger, G., & Hollerbach, R. 2004, The Magnetic Universe: Geophysical and Astro- physical Dynamo Theory, by Günther Rüdiger, Rainer Hollerbach, pp. 343. ISBN 3-527-40409-0. Wiley-VCH , August 2004.

Shu, F. H. 1992, Physics of Astrophysics, Vol. II, by Frank H. Shu. Published by University Science Books, ISBN 0-935702-65-2, 476pp, 1992.

Soker, N. 1992, ApJ, 389, 628

Soker, N., & Zoabi, E. 2002, MNRAS, 329, 204

Soker, N. 2006, PASP, 118, 260

Sorensen, P., & Pollacco, D. 2004, ASP Conf. Ser. 313: Asymmetrical Planetary Nebulae III: Winds, Structure and the Thunderbird, 313, 515 Edited by Margaret Meixner, Joel H. Kastner, Bruce Balick and Noam Soker.

Thomas, J. H., Markiel, J. A., & van Horn, H. M. 1995, ApJ, 453, 403

Tout, C. A., & Pringle, J. E. 1992, MNRAS, 256, 269

Vlemmings, W. H. T., Diamond, P. J., & Imai, H. 2006, Nature, 440, 58 61

Chapter 4

Towards a Spectral Technique for Determining Material Geometry Around Evolved Stars: Application to HD 179821

4.1 Abstract1

HD 179821 is an evolved star of unknown progenitor mass range (either post-Asymptotic Giant Branch or post-Red Supergiant) exhibiting a double peaked spectral energy distribution (SED) with a sharp rise from ∼ 8 − 20 µm. Such features have been associated with ejected dust shells or inwardly truncated circumstellar discs. In order to compare SEDs from both systems, we employ a spherically symmetric radiative transfer code and compare it to a radiative, inwardly truncated disc code. As a case study, we model the broad-band SED of HD 179821 using both codes. Shortward of 40 µm, we find that both models produce equivalent fits to the data. However, longward of 40 µm, the radial density distribution and corresponding broad range of disc temperatures produce excess emission above our spherically symmetric solutions and the observations. For HD 179821, our best fit consists of a Teff = 7000 K central

1Originally published as Nordhaus, Minchev, Sargent, Blackman, Forrest, De Marco, Kastner, Balick & Frank MNRAS 2008 - in review CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 62

source characterized by τV ∼ 1.95 and surrounded by a radiatively driven, spherically symmetric dust shell. The extinction of the central source reddens the broad-band colours so that they resemble a Teff = 5750 K photosphere. We believe that HD 179821 contains a hotter central star than previously thought. Our results provide an initial step towards a technique to distinguish geometric diﬀerences from spectral modeling.

4.2 Introduction

HD 179821 (IRAS 19114+0002; V1427 Aql; SAO 124414; AFGL 2423) is an evolved star surrounded by gas and dust ejected during a phase of mass-loss. The luminosity of this object is undetermined as the Hipparcos parallax measurement ([0.18 ± 1.12 mas]; Perryman et al. 1997) allows for any distance greater than 1 kpc. HD 179821 is either a close post-Asymptotic Giant Branch (post-AGB) star (D =1kpc,Mi ∼ 3− 4

M) or a distant, massive (D =5− 6kpc,Mi ∼ 20 − 30 M) post-Red Supergiant (post-RSG). The post-AGB phase of stellar evolution is a short (∼ 103 yrs) period in which initially intermediate-mass main sequence stars (< 8 M) transition from the Asymptotic Giant Branch to the planetary nebula (PN) phase. In contrast, the progenitors of Red Supergiants are massive main-sequence stars (> 8 M) evolving toward the Wolf-Rayet stage and may end their lives as supernovae. For a short review on the post-RSG status of HD 179821, see Oudmaijer et al. (2008). In both phases, mass is ejected into the circumstellar environment. Distinguishing between these classes of objects can be difficult. In this paper, we model the broad-band SED of HD 179821 using two distinct radiative transfer codes. The first code, “DUSTY”, computes radiative transfer through a spherically symmetric shell with canonical density profile ρ(r) ∝ r−2 (Ivezićetal. 1999). The second code computes radiative transfer through an axisymmetric, flared disc with canonical density profile ρ(r) ∝ r−3/2 (D’Alessio et al. 2001, 2005). While we believe the mid-IR and radio imaging of HD 179821 indicates a roughly spherical nebula, the point of this paper is to determine whether spectral modeling, through the use of distinct radiative transfer codes, can constrain geometric features of evolved star nebulae. Thus, HD 179821 serves as a test case for this investigation. We model HD 179821 for both nebular geometries and investigate the degeneracies CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 63 between the SED model fits. In addition, we present and compare the ISO spectrum of HD 179821 to the post-AGB object HD 161796 and post-RSG object IRC +10420. All three objects display a strong mid-IR excess and exhibit steep increases in their SED’s beyond 8 microns. In Section 2, we discuss the enigmatic nature of HD 179821 in both the post-RSG and post-AGB scenarios. In Section 3, we describe our synthetic photospheres and extinction corrections. In Section 4, we present our SED model fits from the radiative transfer disc code. In Section 5, we present our model fits from DUSTY and identify wavelength regions in which degeneracies occur between the two codes.

For intermediate mass stars below 8 M, the late stages of stellar evolution are characterized by transitions from quasi-spherical mass-losing AGB stars to complex aspherical post-AGB objects. Many post-AGB objects feature toroidal density enhancements, bipolar jets and an array of other non-spherically symmetric features, the origin of which is unknown (Balick and Frank 2002). In addition, most post-AGB objects display a large momentum excess above what would be supplied by radiation pressure (Bujarrabal et al. 2001). While the origin of the additional source of momentum is unclear, a binary companion is an attractive candidate as energy and angular momentum can transfer from the secondary to the primary (Nordhaus & Blackman 2006). This hypothesis is supported by recent observational (De Marco et al. 2004, 2007) and theoretical (Moe & De Marco 2006; Soker 2006) efforts suggesting that a significant fraction of PNe may be descendants of interacting binaries. Binary companions can influence mass loss in many ways. A common envelope phase, even for low-mass companions, can lead to equatorial outflows, poloidal outflows and the formation of discs (Reyes-Ruiz & López 1999, Nordhaus & Blackman 2006, Nordhaus et al. 2007, Nordhaus & Blackman 2007). For wider binaries, low-mass companions can induce spiral waves and convert amorphous dust to crystalline dust via annealing (Edgar et al. 2007). For massive stars, the end stages of stellar evolution are poorly understood. The post-red supergiant (post-RSG) phase is among the most luminous and uncertain epochs of post-main sequence stellar evolution. Like their intermediate mass conter- parts, post-RSG’s are thought to be ejecting a substantial portion of their mass (Decin et al. 2006). However, a massive circumstellar envelope has only been detected (scat- CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 64 tered light, IR emission, molecular line emission) around the post-RSG IRC +10420, thus making a comparison with HD 179821 difficult (Kastner & Weintraub 1995). Mass-loss may be consistent with a radiation driven spherically symmetric outflow (Castro-Carrizo et al. 2007). However, if HD 179821 does indeed display a momentum excess in its ejected nebula (Bujarrabal et al. 2001), then it is not unreasonable for a binary companion to have influenced the outflow and produced asymmetries. Inter- estingly, the WFPC2 images of Ueta et al. 2000 show collimated bipolar structures emerging from the dust shell. These may be remnant jets propagating through the envelope. There is also evidence for slight clumpy regions in both OH maser and mid- IR emission (Gledhill et al. 2001; Kastner & Weintraub 1995). A density asymmetry may also be present as the 13CO line profiles are asymmetric (Bujarrabal et al. 1992). The spectral energy distribution of HD 179821 exhibits a double-peaked shape, indicative of a stellar photospheric component and ejected dusty component. The spectral energy distribution (SED) is consistent with photospheric emission to ∼ 8 µm at which point there is a steep increase until the second peak at ∼ 25 µm. The overall SED of HD 179821 is thus remarkably similar to that of the transitional young stellar object CoKu Tau/4 (see Fig. 2 of D’Alessio et al. 2005), which has been well modeled as a dusty disc with an inner hole. The sharp, interior wall of the disc is illuminated by the central source and produces the excess infrared emission. HD 179821 also exhibits an evacuated interior region between the central object and hence, the system might be modeled similarly to CoKu Tau/4. However, the dust envelope of HD 179821 could also be a detached spherical shell and past modeling efforts have treated it as such (Surendiranath et al. 2002; Buemi et al. 2007; Castro-Carrizo et al. 2007).

4.3 HD 179821: post-AGB or red supergiant?

HD 179821 (galactic coordinates (l = 35.62◦, b =-4.96◦) is usually classiﬁed as a G5 star (Hrivnak et al. 1989; see §2.1). It exhibits large mm-wave CO line widths (∼ 70 km/s) centered on the local standard of rest velocity VLSR ∼ 100 km/s (Zuckerman & Dyck 1986; Bujarrabal et al. 1992). OH masers have been detected (Likkel 1989; Gledhill et al. 2001) and the presence of a ∼ 10 µm silicate feature conﬁrm that this object is oxygen-rich (O/C 2.6; Reddy & Hrivnak 1999). CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 65

On the whole, the chemical composition of HD 179821 differs from that of an average F supergiant and is consistent with a post-AGB star (Reddy & Hrivnak 1999). In particular, an overabundance of s-process elements suggest extra-mixing during the AGB phase and is further supported by a low isotopic 12C/13C ≤ 5 ratio consistent with deep mixing in a post-AGB object (Charbonnel 1995; Josselin & Lèbre 2001). Underabundances of carbon and the s-process element zirconium suggest that HD 179821 left the AGB before the third dredge up, consistent with its O-rich properties. The presence of an active photochemistry and the production of HCO+ are detected in the outflows of many post-AGB objects including HD 179821 (Josselin & Lèbre 2001). Currently HCO+ has only been detected in one red supergiant star (VY CMa; Ziurys et al. 2007). In general, the chemical composition is similar to that of high latitude, hot post- AGB stars and in particular bears a strong resemblance to HD 161796 (Thévenin et al. 2000; Reddy & Hrivnak 1999). The ISO SWS spectrum of HD 179821 and broad-band SED also appear very similar to that of the post-AGB star HD161796 (= IRAS 17436+5003 = V814 Her = SAO 30548) (see Fig. 4.1). Also shown in Fig. 4.1 is the ISO SWS spectrum of the post-RSG IRC +10420 (=V1302 Aql = IRAS 19244+1115). All three spectra show a substantial infrared excess, however there are differences between HD 161796 and IRC +10420. The similarities in the ISO spectra for HD 179821 and HD 161796 suggest that both systems have undergone similar mass-loss histories. Based on the kinematic distance of ∼ 6 kpc, HD 179821 is a post-RSG. However, this result should be viewed with caution as the methods used to derive the kinematic distance are not valid for the galactic coordinates of HD 179821 (Josselin & Lèbre 2001). If in fact HD 179821 is 6 kpc away, then its latitude indicates a position of 500 pc above the galactic plane. This location is approximately 5-6 times the scale height for supergiants (Scheffler & Elsaesser 1987). The strength of the OI triplet line and the distance determined from the interstellar Na I D1 and D2 components imply that the object is very luminous (Reddy & Hrivnak 1999). Na and Na I emission at 2.21 µm is similar to that detected in known supergiants (Hrivnak et al. 1994) and abundances of some molecules are 40 times lower than the averages in post-AGB objects (Quintana-Lacaci et al. 2007). CO CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 66 outflow observations also support the post-RSG hypothesis (Bujarrabal et al. 2001). In particular, they found a quasi-spherical, unique component to the wind with a large outflow velocity of Vexp =33− 35 km/s. This is higher than most post-AGB spherical wind outflow velocities (∼ 10 − 15 km/s) (Kastner & Weintraub 1995). In short, whether this object is a post-AGB star evolving toward a PNe phase or a post-RSG star whose fate is to explode as a SNe remains unresolved.

4.4 Photospheric Models and Extinction

Because of uncertainty in line-of-sight visual and IR extinction (interstellar + circumstellar), the reduction in magnitude of the HD 179821 spectrum at a given wavelength is unknown. The inferred extinction must at least be enough to make the maxima of the double peaks equal on the de-reddened SED. Adopted values of Av have ranged from 1.8 to 4 (van der Veen et al. 1994; Hrivnak et al. 1989; Surendiranath et al. 2002; Hawkins et al. 1995).

The choice of Av can greatly influence the inferred geometry of the system. The flux ratio of the peak of the infrared excess to that of the peak of the photosphere, α, determines the fraction of the central radiation intercepted by circumstellar material. If α ∼ 1, then the circumstellar material is intercepting most of the radiation from the central object, corresponding to a spherical shell geometry. If, however, α<1, the geometry can be torus- or disc-like with radiation from the central source escaping through bipolar cavities. Increasing Av raises the corrected photospheric emission relative to the longer infrared wavelengths, which are only marginally affected by extinction. The photometric data is presented in Tables 1 and 2. Since the extinction is unknown, the temperature of the central source may be uncertain. Low-resolution spectra have classified HD 179821 as a luminous G-supergiant (G Ia Bidelman 1981; G4 0-Ia Keenan 1983; G5 Ia Buscombe 1984; G5 Ia Hrivnak et al. 1989) while the spectral type inferred from high-resolution spectra indicates

Teff = 6800 K (Zacs et al. 1996), Teff = 6750 K (Reddy & Hrivnak 1999) corresponding to an F star. In addition, Arkhipova et al. 2001 conclude from their 1999 spectra that HD 179821 was an F star in the 1990’s. Therefore, we employ synthetic photospheres of Teff = 5750 K (G spectral type) and Teff = 7000 K (F spectral type) corresponding to Av values of 2 and 3 respectively (Kurucz 1993). For both radiative CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 67

Figure 4.1 Top: ISO SWS spectra of HD 179821 and post-AGB object HD 161796. In both objects, there is a steep rise between the 10 and 20 µm features possibly indicating a transition region to the optically thick outer wall or shell. HD 179821 was de-reddened using AV = 2 while HD 161796 was corrected using AV =1.2. Bottom: ISO spectrum of the post-RSG IRC +10420. CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 68

Table 4.1. Photometric Data

Object UBVJ HKs

HD 179821 10.81 9.49 7.89 5.371 4.998 4.728

Note. — Magnitude summary for HD 179821. UBV measurements are on the Johnson system and are reproduced from Hrivnak et al. 1989. JHKs measurements are from the 2MASS point source catalogue (Skrutskie et al. 2006).

transfer models, we assume the central source is a Teff = 7000 K star. However if the surrounding nebula is optically thick, the broad-band colours are reddened and the central source obscured. We model the full spectral energy distribution of HD 179821 in order to fit photometric (optical, 2MASS, sub-millimeter, millimeter) and spectroscopic (ISO) data. In particular, we compare SED model fits from both codes to investigate degeneracies between circumstellar dust geometries. In Section 4, we present an inwardly truncated, flared disc model. The inner wall absorbs radiation from the central source and marks the transition to the optically thick outer disc. The circumstellar material in this case corresponds to a torus-like geometry. In Section 5, we present a spherically symmetric shell model using the radiative transfer code DUSTY.

4.5 Inner Wall, Edge-on Disk Models

The central star of HD 179821 is assumed to be located at 5 kpc with the following properties: Teff = 7000 K, R = 287 R, M =8M. For these parameters, we are implicitly assuming that the system is a post red supergiant. However, since our model scales with distance, our modeling results could also apply to a post-AGB system at 1kpc.

We consider an optically-thick disc with an inner wall at radius r = Rw and height CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 69

Table 4.2. Color Corrected IRAS ﬂuxes, Submillimeter Data for HD 179821

F12µm F25µm F60µm F100µm F450µm F800µm F1100µm

32± 3 700 ± 50 430 ± 30 160 ± 30 1.22 ± 0.12 0.227 ± 0.017 0.058 ± 0.009

Note. — All presented ﬂuxes have units of Janskys. Data is reproduced from van der Veen et al. 1994. ISO spectra is processed according to Sloan et al. 2003 where multiplicative corrections are used for all wavelengths.

Hw. The wall marks the transition between the evacuated interior region and the optically-thick, outer disc. The wall is illuminated at normal incidence by the central object and is assumed to be uniform in the vertical direction. The radial structure is solved according to D’Alessio et al. 2005. At wavelengths > 35 µm, emission is dominated by the outer disc. Here, we focus on fitting the ISO spectrum in the case of an edge-on disc and discuss fitting the sub-millimeter and millimeter wavelengths in Section 5. We assume spherical dust grains in the wall atmosphere of size distribution n(a) ∼ −3.5 a between minimum and maximum radii amin and amax (Mathis et al. 1977). Opacities are calculated using Mie theory (Wiscombe 1979). We consider several silicate compositions (Henning et al. 1999, Jäger et al. 2003). For each composition, we vary two parameters not constrained a priori: height of the wall and disc inclination angle. In addition, we vary amin and amax to obtain the best spectral fit, leaving the power-law index fixed. The shape of the spectrum between ∼ 8−30 µm allows us to rule out several silicate compositions. The 10 µm silicate feature is smooth and does does not show evidence of the substructures associated with crystalline components. This most likely indicates that the silicates are glassy and amorphous. Therefore, we can immediately disregard crystalline silicates of mean cosmic composition (Mg0.5Fe0.43Ca0.03Al0.04SiO3; Jaeger et al. 1994) as they contribute substructures not observed in the smooth silicate features. Additionally, the glassy silicates from Jaeger et al. 1994, do not fit the spectrum CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 70 longward of 30 µm and hence, we rule them out. Hot shell circumstellar silicates (Os- senkopf et al. 1992) do not provide a reasonable fit to the ISO spectrum. If instead we use cool shell circumstellar silicates (Ossenkopf et al. 1992), we can fit the 10 µm feature but can not match the emission longward of 20 µm. We obtain reasonable fits to the ISO spectrum of HD 179821 using glassy pyroxene (optical constants from Henning & Mutschke 1997 and Dorschner et al. 1995), glassy

olivine (Mg1Fe1SiO4; Dorschner et al. 1995) and glassy bronzite (Dorschner et al. 1988). Fig. 4.2 presents our ﬁts for glassy pyroxene for two diﬀerent inclinations:

µ ≡ cos(i)=0.25 (left) and µ =0.45 (right). For both figures, the temperature, T0, at the innermost radius of the wall is 128 K (see D’Alessio et al. 2005). In addition, the minimum and maximum grain radii which best fit the ISO spectrum are given by amin =0.005 µmandamax =1.0 µm. We have tried many different values of amax over our range of parameters and grains of ∼ 1 µm and larger are required for our 3 best fits. For the left model in Fig. 4.2, the position of the wall is Rw =3.7 × 10 AU 3 with a height of Hw =1.73 × 10 AU. We find good agreement up to 20 µmatwhich point our model undershoots the observed SED. If µ is increased (i.e. tilted more toward face-on), as in the right figure, it is possible to increase the emission slightly at 20 µm however the flux at 18 µm starts to deviate from the ISO spectrum. The position of the wall in this model is the same, but a 3 slightly shorter wall is required; Hw =1.69 × 10 AU. Fig. 4.3, compares disc models obtained for two different silicate compositions: glassy olivine (top) and glassy bronzite (bottom). For the top figure, the best fit 3 requires a slightly hotter wall, T (ri) = 131 K, located at Rw =6.3 × 10 AU. The 3 wall height is given as Hw =3.4 × 10 AU. For olivine, we require amin =0.005 µm and amax =5.0 µm for our best fit, however, while we find good overall agreement between 2 and 45 µm, our model produces excess emission between 15 and 18 µm. 3 3 For bronzite, we find that T0 = 128 K with Rw =6.7 × 10 AU and Hw =3.7 × 10

AU. For this model, the grain sizes are amin =0.005 µmandamax =2.0 µm. 3 Using all three silicate compositions, we ﬁnd that Rw =5.2 ± 1.5 × 10 AU and 3 Hw =2.7 ± 1.0 × 10 AU with the wall dust temperature ranging from 128 to 131 K. With a limited library of dust opacity data, we cannot determine the exact composition of the wall, other than to suggest that it could be a mixture of our suggested materials CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 71

Figure 4.2 Our best fit wall models. The top figure corresponds to µ =0.25 while the bottom corresponds to µ =0.45. CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 72 or perhaps could be fit by other amorphous silicates. For instance, Justtanont et al. 1992 fit the 10 and 20 µm features from their UKIRT CGS3 spectra using a colder (∼ 90 − 95 K) mixture of olivine and magnetite. To summarize, we found satisfactory fits to the ISO spectrum with the disc code but could not fit photometry longward of 40 µm. We aim to compare modeling results from spherical and disc codes in regimes which might produce overlap. Thus, we study the shell model in the next section.

4.6 Spherical Shell Models

We use the spherically symmetric, radiative transfer code DUSTY (Ivezić et al. 1999). Given an incident radiation field and specified dusty region, the code self-consistenly calculates the emergent flux including dust scattering, absorption and emission in a spherical, non-rotating environment. In addition, for radiatively driven winds, DUSTY computes wind structure by jointly solving the hydrodynamic equations. The dust density profile within the shell is given as ρ(r) ∝ r−2, consistent with a constant mass loss rate. DUSTY was previously used to model HD 179821. Surendiranath et al. 2002 pro- 3 duced a best fit shell model with an inner radius of ri =8.7×10 AU and temperature

T (ri) = 130 K. However, it is difficult to tell how good a fit it is as they omit the ISO spectra in their model. Buemi et al. 2007 also modeled HD 179821 using DUSTY and obtained a slightly cooler shell (T (ri) = 110K) located at a farther distance 3 (ri =12.0 × 10 AU). However, neither investigation used the ISO spectrum to constrain their models. We reproduced both previous DUSTY models. However, when overlaid on the SED with the added constraint of the ISO spectrum, neither model proved satisfactory. As the ISO spectrum provides the most stringent constraints on model parameters, our fit improves previous work.

For our spherical model, the temperature at the inner shell boundary (T (ri) = 128 K) was varied until the model infrared excess matched the ISO spectrum. We ﬁx −3.5 the grain distribution as n(a) ∝ a and vary the maximum, amax, and minimum, amin, grain sizes. The equilibrium temperature of a dust grain depends on size and composition. Small grains superheat while large grains exhibit blackbody emission. At each radius within the nebula, DUSTY assumes that the dust grains are at the same CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 73

Figure 4.3 Another ﬁt to the wall model for glassy olivine (top) and glassy bronzite (bottom). The inclination in both ﬁgures is µ =0.25. CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 74 temperature. This approximation is a generic feature of both codes used in this paper and warrants acknowledgment. Additionally, both codes assume isotropic scattering. Future work should incorporate anisotropic scattering in both geometries. ≡ ro In addition, we vary the ratio of the outer to inner shell radius, Y ri .The central radiation source is assumed to be the same 7000 K model photosphere used previously in §4. The optical depth through the shell at 0.55 µm is also varied. We opt for a radiatively driven wind and vary the composition of the grains.

Our best ﬁt to the data yields an optical depth through the shell of τV =1.95±0.03.

In addition, we ﬁnd a good ﬁt using minimum and maximum grain sizes amin =0.005

µmandamax =0.25 µm. We find the ratio of the outer to inner shell radius produces ≡ ro ± similar results for Y ri =15 2. The best fit is obtained using a dust composition such that 95% of the grains are a mixture of amorphous silicates with the other 5% composed of iron oxide (17:1:1:1 ratio of interstellar silicates to glassy olivine to glassy pyroxene to wustite Draine & Lee 1984; Dorschner et al. 1995; Henning et al. 1995). We have extensively varied the grain composition using our limited library and found this composition to yield the best result. Wustite (FeO; Henning et al. 1995) is included as it provides a slight source of long wavelength emission between 40 and 50 µm which could not be fit by extending the outer shell radius or increasing the maximum grain size. However, even by including wustite, our model still has a slight deficit of emission in the 40 − 50 µm region. Wustite is featureless and the boost in emission is minor, thus we can not say with any certainty whether it is present in HD 179821. Our spherical shell result is presented in Fig. 4.4. The model spectrum (solid dark line) is plotted on the Av = 2 dereddened, T = 5750 K spectrum. Even though the central radiation source is a F-star (T = 7000 K), an optical depth through the shell of τV =1.95 obscures the photosphere so that it resembles a G-star (T = 5750 K). In particular the overall fit appears quite good in fitting data longward of 40 µm. Both our disc and shell models produce similar results for the ISO spectrum. Sub-millimeter and millimeter photometry highlights the main difference between a shell spectrum (small range of temperatures) and a disc spectrum (broad range of temperatures). 3 The best shell fit yields an inner radius of ri =9.8 × 10 AU which is in excellent agreement with mid-IR images and polarimetry observations (Gledhill et al. 2001). CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 75

Figure 4.4 Our spherical shell model (dark line). The dust temperature at the inner and outer radii are 128 K and 41 K. Even though the central radiation source is a T = 7000 K photosphere, the detached shell reddens the central source so that it resembles a T = 5750 K photosphere (thin line). The silicate features are ﬁt using a mixture of glassy, amorphous silicates with a small component of FeO. CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 76

Table 4.3. Model Summary

ro Model Composition eff 0 min max w V ≡ T T a a µH τ Y ri

Disc KKµm µmAU Fig. 4.2 Pyroxene 7000 128 0.05 1.0 0.25 1.73×103 -- Fig. 4.2 Pyroxene 7000 128 0.05 1.0 0.45 1.69×103 -- Fig. 4.3 Olivine 7000 131 0.005 5.0 0.25 3.40×103 -- Fig. 4.3 Bronzite 7000 128 0.005 2.0 0.25 3.70×103 -- Shell Fig. 4.4 Mixture 7000 128 0.005 0.25 - - 1.95 15

Note. — Summary of our disc and spherical shell models.

The placement of the inner shell radius is also in agreement with Surendiranath et al. 2002, however we obtain an outer shell radius, r0, that is a factor of 6 smaller. This result may be more in line with polarization images in the near-IR which show a circularly symmetric reflection nebula with a diameter of 15, a factor of ∼ 0.75 times our outer radius (Kastner & Weintraub 1993). Buemi et al. 2007 assumed to a n(a) ∝ a−6 dust distribution power law when fitting HD 179821 with DUSTY. While they arrived at a slightly cooler, closer shell, we found a satisfactory fit without appealing to steeper distributions by using a hotter central star. It is useful to mention that we reproduced both previous model fits (Surendiranath et al. 2002; Buemi et al. 2007). When the ISO spectrum was included, neither of those two previous models matched observations. In general, with a Teff = 5750 K central source, we could not reproduce the infrared excess. To match the shape and peak of the infrared excess required a hotter, obscured central source (Teff = 7000 K).

Additionally from our fit, the dust temperature in the outer shell is T (ro)=41 K. DUSTY also provides an estimate of the mass outflow rate although this value should be treated with caution as it has an inherent uncertainty of ∼ 30%. Varying the gravitational correction by 50% produces no discernible effect on the spectrum CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 77 and is responsible for the uncertainty in the mass outflow rate (see Ivezić et al. 1999 −4 −1 for more detail). Our derived outflow rate is M˙ =2× 10 M yr again in good agreement with Surendiranath et al. 2002 and a factor of ∼ 5 less then Buemi et al. 2007. We summarize results below.

4.7 Summary

We have modeled the broad-band spectral energy distribution of HD 179821 using two distinct radiative transfer codes: one corresponding to a spherical shell geometry with ρ (r) ∝ r−2,andonetoadiscgeometrywithρ (r) ∝ r−3/2. Under these assumptions, both codes provided equally good fits for similar dust compositions and size distributions shortward of 40 µm. However, longward of 40 µm, only the spherical shell model reproduces the observations. The radial dust density profile and corresponding range of temperatures present in the disc provide excess emission above the spherical shell solution and cannot fit the data. A wavelength of ∼ 40 µm marks the boundary for discerning the model fits. It should be noted that the density profiles need not uniquely indicate a particular geometry. If the densities deviate from the anticipated theoretical values of ρ (r) ∝ r−2 (shell), ρ (r) ∝ r−3/2 (disc), then the infrared excess is likely coupled to the density distribution rather than the geometry. The effect of changing the density profile in both codes should be investigated before comparative spectral modeling is established as a reliable method for distinguishing geometric differences. Based on our detailed spectral modeling, we conclude that the nebula around HD

179821 is a radiatively driven shell. The dust is mainly composed of small (amax =0.25 µm) amorphous, glassy silicates. Interior to the shell is an evacuated region in addition to the central radiation source. The central star is most likely a T = 7000 K star obscured such that it appears as a T = 5750 K star (optical depth of τV ∼ 1.95 through the spherical shell). This may aid in explaining previous conflicting spectral classifications. The dimensions of our shell agree well with previous observations and provide a good fit to the ISO spectrum. We compared the ISO spectrum to that of HD 161796, a confirmed post-AGB object (e.g. Fig. 4.1). In particular, the ISO spectra and broad-band SED look remarkably similar. Because our results scale with distance, our spectral modeling CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 78 does not provide insight into whether HD 179821 is a post-AGB or post-RSG. However, the similarity of the ISO spectra suggests that HD 161796 and HD 179821 experienced a very similar mass-loss history.

Acknowledgements

JTN acknowledges ﬁnancial support of a Horton Fellowship from the Laboratory for Laser Energetics through the U. S. Department of Energy and HST grant AR-10972. In addition, we thank P. D’Alessio and N. Calvet for use of their disk codes. IM acknowledges support from NSF grant ASST-0406823 and NASA grant NNG04GM12G. EGB acknowledges support from NSF grants AST-0406799, AST-0406823, and NASA grant ATP04-0000-0016 (NNG05GH61G). AF acknowledges support from JPL Spitzer grant 1278931, NSF grant AST-0507519 and DOE grant DE-F03-02NA00057. CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 79

References

Arkhipova, V. P., Ikonnikova, N. P., Noskova, R. I., Sokol, G. V., & Shugarov, S. Y. 2001, Astronomy Letters, 27, 156

Balick, B., & Frank, A. 2002, ARA&A, 40, 439

Bidelman, W. P. 1981, AJ, 86, 553

Buemi, C. S., Umana, G., Trigilio, C., & Leto, P. 2007, A&A, 462, 637

Bujarrabal, V., Alcolea, J., & Planesas, P. 1992, A&A, 257, 701

Bujarrabal, V., Castro-Carrizo, A., Alcolea, J., & S´anchez Contreras, C. 2001, A&A, 377, 868

Buscombe, W. 1984, MK Spectral Classiﬁcations. Sixth General Catalogue, Evanston: Northwestern University, 1984

Calvet, N., et al. 2005, ApJ, 630, L185

Castro-Carrizo, A., Quintana-Lacaci, G., Bujarrabal, V., Neri, R., & Alcolea, J. 2007, A&A, 465, 457

Charbonnel, C. 1995, ApJ, 453, L41

D’Alessio, P., Calvet, N., & Hartmann, L. 2001, ApJ, 553, 321

D’Alessio, P., et al. 2005, ApJ, 621, 461

Decin, L., Hony, S., de Koter, A., Justtanont, K., Tielens, A. G. G. M., & Waters, L. B. F. M. 2006, A&A, 456, 549

De Marco, O., Bond, H. E., Harmer, D., & Fleming, A. J. 2004, ApJ, 602, L93

De Marco, O., Wortel, S., Bond, H. E., & Harmer, D. 2007, ArXiv e-prints, 709, arXiv:0709.1508

Dorschner, J., Friedemann, C., Guertler, J., & Henning, T. 1988, A&A, 198, 223

Dorschner, J., Begemann, B., Henning, T., Jaeger, C., & Mutschke, H. 1995, A&A, 300, 503 CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 80

Draine, B. T., & Lee, H. M. 1984, ApJ, 285, 89

Edgar, R. G., Nordhaus, J., Blackman, E., & Frank, A. 2007, ArXiv e-prints, 709, arXiv:0709.2292

Gledhill, T. M., Yates, J. A., & Richards, A. M. S. 2001, MNRAS, 328, 301

Hawkins,G.W.,Skinner,C.J.,Meixner,M.M.,Jernigan,J.G.,Arens,J.F.,Keto, E., & Graham, J. R. 1995, ApJ, 452, 314

Henning, T., Begemann, B., Mutschke, H., & Dorschner, J. 1995, A&AS, 112, 143

Henning, T., & Mutschke, H. 1997, A&A, 327, 743

Henning, T., Il’In, V. B., Krivova, N. A., Michel, B., & Voshchinnikov, N. V. 1999, A&AS, 136, 405

Hrivnak, B. J., Kwok, S., & Volk, K. M. 1989, ApJ, 346, 265

Hrivnak, B. J., Kwok, S., & Geballe, T. R. 1994, ApJ, 420, 783

Jaeger, C., Mutschke, H., Begemann, B., Dorschner, J., & Henning, T. 1994, A&A, 292, 641

Ivezi´c, Z., Nenokva, M., & Elitzur, M. 1999, User Manual for DUSTY, University of Kentucky Internal Report

J¨ager, C., Il’in, V. B., Henning, T., Mutschke, H., Fabian, D., Semenov, D., & Voshchinnikov, N. 2003, Journal of Quantitative Spectroscopy and Radiative Trans- fer, 79, 765

Josselin, E., & L`ebre, A. 2001, A&A, 367, 826

Jura, M., & Werner, M. W. 1999, ApJ, 525, L113

Justtanont, K., Barlow, M. J., Skinner, C. J., & Tielens, A. G. G. M. 1992, ApJ, 392, L75

Kastner, J. H., & Weintraub, D. 1993, Luminous High-Latitude Stars, 45, 151

Kastner, J. H., & Weintraub, D. A. 1995, ApJ, 452, 833 CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 81

Keenan, P. C. 1983, Bulletin d’Information du Centre de Donnees Stellaires, 24, 19

Kraemer, K. E., Sloan, G. C., Price, S. D., & Walker, H. J. 2002, ApJS, 140, 389

Kurucz, R. L. 1993, ATLAS9, CD-ROM 13 (Cambridge, MA: Smithsonian Astrophys- ical Observatory)

Likkel, L. 1989, ApJ, 344, 350

Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425

Moe, M., & De Marco, O. 2006, ApJ, 650, 916

Nenkova, M., Ivezi´c, Z.,ˇ & Elitzur, M. 2000, Thermal Emission Spectroscopy and Analysis of Dust, Disks, and Regoliths, 196, 77

Nordhaus, J., & Blackman, E. G. 2006, MNRAS, 370, 2004

Nordhaus, J., Blackman, E. G., & Frank, A. 2007, MNRAS, 376, 599

Nordhaus, J., & Blackman, E. G. 2007, ArXiv e-prints, 707, arXiv:0707.3792

Oudmaijer, R., Davies, B., de Wit, W.-J., & Patel, M. 2008, ArXiv e-prints, 801, arXiv:0801.2315

Ossenkopf, V., Henning, T., & Mathis, J. S. 1992, A&A, 261, 567

Perryman, M. A. C., et al. 1997, A&A, 323, L49

Quintana-Lacaci, G., Bujarrabal, V., Castro-Carrizo, A., & Alcolea, J. 2007, A&A, 471, 551

Reddy, B. E., & Hrivnak, B. J. 1999, AJ, 117, 1834

Reyes-Ruiz, M., & L´opez, J. A. 1999, ApJ, 524, 952

Scheﬄer, H., & Elsaesser, H. 1987, Physics of the Galaxy and Interstellar Medium, Berlin and New York, Springer-Verlag, 1987, 503 p.

Skrutskie, M. F., et al. 2006, AJ, 131, 1163

Sloan, G. C., Kraemer, K. E., Price, S. D., & Shipman, R. F. 2003, ApJS, 147, 379 CHAPTER 4. SPECTRAL DETERMINATION OF GEOMETRY 82

Soker, N. 2006, ApJ, 645, L57

Surendiranath, R., Parthasarathy, M., & Varghese, B. A. 2002, Ap&SS, 281, 751

Th´evenin, F., Parthasarathy, M., & Jasniewicz, G. 2000, A&A, 359, 138

Ueta, T., Meixner, M., & Bobrowsky, M. 2000, ApJ, 528, 861 van der Veen, W. E. C. J., Waters, L. B. F. M., Trams, N. R., & Matthews, H. E. 1994, A&A, 285, 551

Wasserburg, G. J., Boothroyd, A. I., & Sackmann, I.-J. 1995, ApJ, 447, L37

Wiscombe, W. J. 1979, Mie Scattering Calculations: Advances in Technique and Fast, Vector-Speed Computer Codes, NCAR T/N-40+STR (Boulder: NCAR)

Zacs, L., Klochkova, V. G., Panchuk, V. E., & Spelmanis, R. 1996, MNRAS, 282, 1171

Ziurys, L. M., Milam, S. N., Apponi, A. J., & Woolf, N. J. 2007, Nature, 447, 1094

Zuckerman, B., & Dyck, H. M. 1986, ApJ, 311, 345 83

Chapter 5

The Formation of Crystalline Dust in AGB Winds from Binary Induced Spiral Shocks

5.1 Abstract1

As stars evolve along the Asymptotic Giant Branch, strong winds are driven from the outer envelope. These winds form a shell, which may ultimately become a planetary nebula. Many planetary nebulae are highly asymmetric, hinting at the presence of a binary companion. Some post-Asymptotic Giant Branch objects are surrounded by tori of crystalline dust, but there is no generally accepted mechanism for annealing the amorphous grains in the wind to crystals. Here, we show wind shaping by a binary companion provides a possible mechanism for forming crystalline dust in the orbital plane.

5.2 Introduction

During the Asymptotic Giant Branch (AGB) phase, strong winds are driven from the outer envelope. After ∼ 105 yrs, the AGB envelope is expelled resulting in a proto-white dwarf surrounded by a circumstellar nebula. As the hotter core of the

1Originally published as Edgar, Nordhaus, Blackman & Frank 2008 ApJL 675, 101 CHAPTER 5. CRYSTALLINE DUST FORMATION IN AGB WINDS 84 star is unveiled, the nebula ionizes and becomes a planetary nebula (PN). Most PNe are highly asymmetric, displaying complex morphological structures such as disks and bipolar jets (e.g. Balick and Frank 2002, and references therein). The engine driving the asymmetry is thought to begin during the AGB phase or shortly thereafter in the post-AGB phase. A binary companion may be responsible for shaping the nebula. Recent work suggests that a binary interaction may required to form a PN (Soker 2006; Moe & De Marco 2006; Nordhaus et al. 2007). The formation of equatorial tori, collimated bipolar jets and circumstellar disks may be a consequence of additional energy and angular momentum supplied by the binary companion either through a common envelope phase or by directly shaping the AGB wind (Nordhaus and Blackman 2006; Nordhaus et al. 2007; Blackman et al. 2001). A binary can also process the wide variety of dust species present in AGB winds (Waters 2004). Most of the grains are amorphous, with crystalline silicates also seen at 10-20% abundance from stars with particularly high mass loss rates (Kemper et al. 2001; Suh 2002). Observations of a number of post-AGB systems reveal SEDs consistent with a torus of crystalline dust at large radius. A number of papers have suggested that this dust lies in a Keplerian circumbinary disc (Molster et al. 1999; de Ruyter et al. 2006; Van Winckel et al. 2006; Gielen and Van Winckel 2007; Deroo et al. 2007). However, a velocity curve has only been obtained for one system, the ‘Red Rectangle’ (Bujarrabal et al. 2005), and this system still contains features difficult to interpret. Soker (2000) noted that there are serious difficulties in transforming a spherical AGB wind into a circumbinary disc, both in terms of the angular momentum supply and transfer mechanism. The origin of the crystallinity is also not clear. Molster et al. (1999) suggested that some form of low temperature annealing might occur, while Tielens et al. (1998) contend that pre-existing crystalline grains are amorphised by iron diffusion. Here, we discuss an alternative means of reproducing observed dust tori: annealing in shocks induced by a binary companion. We will show that the shock temperatures can be sufficient to anneal the grains with the shock lying in the orbital plane. Shock heating has been proposed before (Nakamoto and Miura 2003), but without a possible mechanism. CHAPTER 5. CRYSTALLINE DUST FORMATION IN AGB WINDS 85

5.3 Numerical Study

Our code is based on the Flash code of Fryxell et al. (2000), an adaptive mesh refine- ment (AMR) code based around a Piecewise-Parabolic Method (PPM) hydrodynamics solver.2.Forthiswork,weuseFlash in cartesian co-ordinates. We have added a simple nbody solver, to model the binary. The wind is modelled by resetting all grid cells within a distance rwind of the primary to a density ρwind,atemperatureTwind, and a radial velocity of vwind with respect to the primary. This does not model the full physics driving the wind. However, so long as all the driving occurs within the orbit of the secondary, the details cannot affect our results. The gravitational effect of the bodies is subject to softening. The softening length for the primary is less than rwind; that of the secondary is chosen to be smaller than the expected Hoyle–Lyttleton radius (see, e.g. Edgar 2004). We do not include a jet (cf Garc´ıa-Arredondo and Frank 2004), since it is not relevant to the present study. Close to each boundary there is a damping region, where the gas density and temperature are reduced to their ambient values. We do this to ensure that waves cannot reflect from the boundaries.

We performed two sets of runs. In the ﬁrst, we used a 1 M primary, with ρwind = −14 −3 3 6 −1 13 10 gcm , Twind =10 K, vwind =3.8 × 10 cm s and rwind =2× 10 cm. The 3 second set of runs contained a 3 M primary, with Twind =2× 10 K, vwind =6.5 × 6 −1 10 cm s ,andρwind and rwind unchanged. This choice of parameters ensures that the wind can escape from the system (velocities fall to < 106 cm s−1 for material leaving the computational domain). We reﬁne the grid to ensure that rwind is always covered by 8 grid cells, while the secondary’s Hoyle–Lyttleton radius is always covered by 4 grid cells. The gas is assumed to be adiabatic, with γ =4/3, a reasonable intermediate value.

5.4 Results

We first consider a 1 M primary, a 0.25 M secondary and an orbital semi-major axis of 6 AU. Most observed post-AGB binaries orbits are smaller. However, we are modelling the early AGB phase, and Theuns et al. (1996) showed that the outflowing wind offers an excellent mechanism for shrinking the binary’s orbit (although we do

2The source code is available at http://ﬂash.uchicago.edu/ CHAPTER 5. CRYSTALLINE DUST FORMATION IN AGB WINDS 86

Figure 5.1 Volumetric density renderings of the wind emitted by a 1 M primary, with a0.25 M secondary in a 6 AU orbit. The view along the z axis is shown on the left, that along the x axis on the right. The binary orbits in the z =0plane not permit this in the current runs). The Hoyle–Lyttleton radius of the secondary approximately 4.5×1012 cm. Since we require at least four grid cells across the Hoyle– Lyttleton radius, our grid resolution is just over 1012 cm near the planet’s orbit. In Figure 5.1, we show the gas density of the system along two axes. The spiral structure along the z axis is remarkably similar to that noted by Mauron and Huggins (2006) in AFGL 3068, albeit on a diﬀerent scale. The structure is also similar to that noted by Theuns and Jorissen (1993) and Mastrodemos and Morris (1999). Figure 5.2 shows the temperature structure of the spiral. Temperatures exceeding 1000 K are generated in a region ∼ 1013 cm thick. This region is well resolved by our grid. We ran a second numerical experiment, identical except for increasing the softening length of the secondary to a value substantially larger than the Hoyle–Lyttleton radius. This isolated the eﬀect of the secondary from the orbital motion of the binary. The overall density structure was little changed, but the temperatures in the spiral dropped dramatically. Therefore the orbital ‘recoil’ of the primary is responsible for the macroscopic density structures, in support of the ‘piston’ model of He (2007).3

3Compare especially their Figure 4 to our Figure 5.1 CHAPTER 5. CRYSTALLINE DUST FORMATION IN AGB WINDS 87

However, the local deflection of the flow by the secondary drives the shock formation, and associated increase in temperature. In a third numerical experiment, we increased the binary separation to 10 AU, but kept all the other parameters the same as the first. The flow was similar to the first numerical experiment, with a slightly reduced peak temperature in the shock. We also performed a fourth numerical experiment, identical to the first except for a 100 MJ secondary (making a q =0.095 binary). The spiral density structure was retained, but found that the peak temperature was slightly lower, and spread over a smaller volume. Finally, we performed a set of runs for a system with a 3 M primary, and found similar behaviour. When vwind was increased to ensure that the wind could escape, the shock temperatures were higher.

5.5 Discussion

Our numerical experiments suggest a mechanism for producing a torus of crystalline dust around an AGB binary: amorphous dust grains are annealed in the gas shocked by the secondary. As the outward motion of the spiral shock slows, the arms will merge and appear as a torus.

5.5.1 Grain Annealing

There are a number of important scales which must be assessed to determine whether such annealing can occur. First are the shock velocities. Examining the output of our Flash runs, we find that the velocities are always ∼ 106 cm s−1. Pre-shock, the velocities can be a factor of a few higher. Post-shock, the velocities can be a factor of a few lower. In our calculations, the velocity is mainly radial, so the crossing time of the high temperature region (1012 cm or so in radial extent in the midplane) is ∼ 106 s. Next is the stopping distance of grains by gas. Calculating the distance required for a grain to sweep up its own mass of gas, we find lstop =(4ρdustadust) / (3ρ)For 11 expected gas densities and dust sizes, lstop ∼ 1.3 × 10 cm, which is sufficiently small to ensure that gas and dust are dynamically coupled; dust grains will not be blown out by radiation pressure. Note that lstop is somewhat smaller than the numerical resolution. The stopping timescale will be similar to the time required to heat the CHAPTER 5. CRYSTALLINE DUST FORMATION IN AGB WINDS 88

Figure 5.2 Temperature structure of the wind emitted by a 1 M primary, with a

0.25 M secondary in a 6 AU orbit CHAPTER 5. CRYSTALLINE DUST FORMATION IN AGB WINDS 89

5 dust grains by collisions. This is given by theat = lstop/v ≈ 1.3 × 10 s. In making the above argument, we have assumed that the frictional heating of the grains can overcome their radiative cooling. Since the radiative loss rate can be quite high, this might not be a valid assumption. Hallenbeck et al. (2000) studied the annealing of silicate grains as a function of temperature. The process is controlled by the Boltzmann equation, with the rate ∝ exp {−E/kB T }. If temperatures exceeding 1067 K were reached, the amorphous grains would anneal to crystals on times tanneal ≈ 280 s. At lower temperatures annealing stalled for around 35 h, after an initial burst of crystallisation. Harker and Desch (2002) applied this to spiral shocks in proto-planetary discs induced by gravitational instabilities, concluding that annealing would be possible. The final timescale is that of cooling. We have used a simple adiabatic equation of state for the gas. In reality, the gas will be able to cool through a forest of molecular line transitions. Computing these accurately is complicated. To make an estimate, we use the cooling curves of Schirrmacher et al. (2003), who considered the wind of a pulsating star. Using figure 4 of their work, we find tcool =(3kB T ) / 2mH Qˆrad . Using the value of the cooling function for a temperature of 1100 K and a density of −15 −3 5 10 gcm , we find tcool ≈ 1.4 × 10 s.

What are the implications for grain annealing? First, tanneal is so short compared to the other timescales that, so long as temperatures in excess of 1067 K are reached, we can assume that annealing is instantaneous. If we could neglect post-shock cooling of the gas, then the crossing time for the whole shock is so long that annealing should occur even if the shock temperature is only 1067 K. However, cooling is likely to be signiﬁcant, so successful annealing requires theat

Note that Qˆrad is approximately proportional to density, so this ratio is fairly insensi- tive to ρ. Smaller grains will heat (and hence anneal) faster. We calculated theat for 1 µm grains, we expect the actual grains to be smaller, perhaps as small as 0.1 µm, making the heating time an order of magnitude less. Such grains would anneal easily - CHAPTER 5. CRYSTALLINE DUST FORMATION IN AGB WINDS 90 particularly since each grain trajectory will encounter the spiral shock multiple times.

5.5.2 Shock Temperature Scaling

We now estimate how the shock temperature of the gas scales with the system parameters. The problem may be split into two parts: the wind from the primary may be modelled as a spherical Bondi wind (see, e.g. chapter 2 of Frank et al. 2002). A shock is then induced in this wind by the secondary. An important parameter in a Bondi wind is the sonic radius. This occurs at GM r = 2 . In our winds T ∼ 1000 K or less, implying that the sonic radius will s 2cs(rs) be outside the orbit of the secondary. Since we construct our initial conditions to be escaping and supersonic, our wind solution should always be supersonic (the Type 4 solutions of Frank et al.). Since the Bondi solution itself is not analytically available, we shall assume that the Mach number of the flow remains constant and that the wind velocity remains close to the escape velocity. Both assumptions are correct for highly supersonic Bondi flows. The flow then shocks as it passes the secondary. However, the Mach number of the shock is not Mlaunch, since we must add in the orbital motion of the companion to obtain the total relative velocity of the gas. This is comparatively straightforward, √ since the velocity of a body in a circular orbit is a factor 2 smaller than the escape 2 2 velocity. This implies that M ≈ 1.5Mlaunch. Combining these, we find

2 −1 −1 ≈ M rwind rorb Tpost-shock 1200 13 14 (5.2) 1M 2 × 10 cm 10 cm

This assumes that the wind velocity is always equal to the escape velocity. Our numerical experiments had vwind slightly larger than the escape velocity, leaving some ‘excess’ velocity which Equation 5.2 does not take into account. Consequently, Equation 5.2 is rather more sensitive to rorb than the temperatures of our numerical experiments. We emphasise that this calculation is only a rough estimate of the temperatures reached, and that we saw a wide range of temperatures in our numerical experiments. At the tip of the bow shock the temperature was much higher (this material would probably be accreted by the secondary anyway). Moving along the spiral arms, we found that the temperatures rapidly dropped to values similar to those predicted by Equation 5.2. Our numerical simulations indicate that the shock temperatures depend weakly on CHAPTER 5. CRYSTALLINE DUST FORMATION IN AGB WINDS 91 the secondary mass – two orders of magnitude in secondary mass lead to ∼ 20% change in temperature. This is not included in Equation 5.2 above, but the simulations are consistent with the much stronger predicted dependence on the primary mass. There are also two important scales for the secondary in addition to its own radius, namely the Hoyle-Lyttelon radius and the Roche radius. In our simulations and in the analytic scaling above we implicitly assume that the Hoyle–Lyttleton radius is smaller than the Roche radius. In cases where the reverse applies, we would expect an accretion disk to form close to the secondary. The shock structure and temperature may depend somewhat on the ratio of these two radii, which we have not pursued in the present work.

What limits are appropriate for Tpost-shock? As we have already mentioned, we require Tpost-shock > 1067 K for annealing to occur. However, it must not be too high, or the grains will vapourise - 2000 K is a good upper limit. Equation 5.2 then provides rough constrains on the systems which can produce crystalline dust tori. For a 1 M 14 14 13 star, we would require 0.6×10

(assuming the same rwind value).

5.5.3 Dust Formation

The dust has to form before it encounters the shock, which implies a minimum binary separation for this mechanism. de Ruyter et al. (2006) found rinner < 10 AU for all their systems, which is comparable to orbital distances we have used. In lower mass systems, the dust formation constraint is smaller, but so is the binary separation implied by Equation 5.2. Furthermore, in Figure 5.2 we see that annealing temperatures are reached on at least the second passage of the spiral arm. This means that it might even be possible for annealing to occur even if the secondary is within the dust formation radius.

5.6 Conclusion

We have demonstrated that a binary companion to an AGB star can create a torus of crystalline dust. The crystalline dust is formed by the annealing of amorphous CHAPTER 5. CRYSTALLINE DUST FORMATION IN AGB WINDS 92 grains in the spiral shock induced by the companion. Such a torus is likely to be expanding, and not in Keplerian orbit around the system. Peretto et al. (2007) found that NGC 6302 contained an expanding torus of gas. Molster & Kemper (2005) noted that high degrees of crystallinity in post-main sequence stars appear to be associated with binarity (see also Molster et al. 2001). Our model addresses only the formation of crystalline dust, not the growth of very large dust grains. We have put forth a model understanding that it may not be complete, and is a paradigm in need of further study. However, our model oﬀers a simple, physically consistent explanation for expanding tori of crystalline dust in young AGB binary systems. We have only made rough estimates of cooling and heating. We have demonstrated that the relevant timescales should permit annealing, but more work is needed. Future calculations should incorporate gas cooling. This is not straightforward, since the relevant temperatures and timescales imply non-equilibrium chemistry. There are a number of cooling curves available for a variety of gas mixtures, and care must be taken to select an appropriate one. A more careful study of the physics of dust in shocks will also be necessary (see e.g. Slavin et al. 2004, for calculations of shock processing of grains in the interstellar medium). Ideally, the dust should also be incorporated into the code as a separate, coupled component. This will permit a better estimate of the heating times of the grains.

Acknowledgements

We acknowledge support from NSF grants AST-0406799, AST-0406823, and NASA grants ATP04-0000-0016 (NNG05GH61G) and NNG04GM12G. This work is supported in part by the U.S. Department of Energy under Grant No. B523820 to the Center for Astrophysical Thermonuclear Flashes at the University of Chicago. The computations presented here were performed using time granted through TeraGrid under project TG-AST070018T. We are grateful to Garrelt Mellema, for helpful comments about gas cooling CHAPTER 5. CRYSTALLINE DUST FORMATION IN AGB WINDS 93

References

Balick, B. and Frank, A.: 2002, ARA&A 40, 439

Blackman, E. G., Frank, A., and Welch, C.: 2001, ApJ 546, 288

Bujarrabal, V., Castro-Carrizo, A., Alcolea, J., & Neri, R. 2005, A&A, 441, 1031

De Marco, O. and Moe, M.: 2005, in R. Szczerba, G. Stasinska, and S. K. Gorny (eds.), Planetary Nebulae as Astronomical Tools, Vol. 804 of American Institute of Physics Conference Series, pp 169–172

Deroo, P. and Van Winckel, H.: 2007, Baltic Astronomy 16, 145

Deroo, P., van Winckel, H., Verhoelst, T., Min, M., Reyniers, M., & Waters, L. B. F. M. 2007, A&A, 467, 1093 de Ruyter, S., van Winckel, H., Maas, T., Lloyd Evans, T., Waters, L. B. F. M., & Dejonghe, H. 2006, A&A, 448, 641

Edgar, R.: 2004, New Astronomy Review 48, 843

Frank, J., King, A., and Raine, D. J.: 2002, Accretion Power in Astrophysics: Third Edition, Cambridge University Press

Fryxell, B., Olson, K., Ricker, P., Timmes, F. X., Zingale, M., Lamb, D. Q., MacNeice, P., Rosner, R., Truran, J. W., and Tufo, H.: 2000, ApJS 131, 273

Garc´ıa-Arredondo, F. and Frank, A.: 2004, ApJ 600, 992

Gielen, C. and Van Winckel, H.: 2007, Baltic Astronomy 16, 148

Hallenbeck, S. L., Nuth, III, J. A., and Nelson, R. N.: 2000, ApJ 535, 247

Harker, D. E. and Desch, S. J.: 2002, ApJ 565, L109

He, J. H.: 2007, A&A 467, 1081

Kemper, F., Waters, L. B. F. M., de Koter, A., and Tielens, A. G. G. M.: 2001, A&A 369, 132 CHAPTER 5. CRYSTALLINE DUST FORMATION IN AGB WINDS 94

Mastrodemos, N. and Morris, M.: 1999, ApJ 523, 357

Mauron, N. and Huggins, P. J.: 2006, A&A 452, 257

Molster, F. J., et al. 1999, Nature, 401, 563

Molster, F. J., Yamamura, I., Waters, L. B. F., Nyman, L.-A.,˚ K¨auﬂ, H.-U., de Jong, T., & Loup, C. 2001, A&A, 366, 923

Molster, F., & Kemper, C. 2005, Space Science Reviews, 119, 3

Nakamoto, T. and Miura, H.: 2003, in Astrophysics of Dust

Nordhaus, J. and Blackman, E. G.: 2006, MNRAS 370, 2004

Nordhaus, J., Blackman, E. G., and Frank, A.: 2007, MNRAS 376, 599

Peretto, N., Fuller, G., Zijlstra, A., & Patel, N. 2007, A&A, 473, 207

Schirrmacher, V., Woitke, P., and Sedlmayr, E.: 2003, A&A 404, 267

Slavin, J. D., Jones, A. P., & Tielens, A. G. G. M. 2004, ApJ, 614, 796

Soker, N. 2000, MNRAS, 312, 217

Soker, N.: 2006, ApJ 645,L57

Sorensen, P. and Pollacco, D.: 2004, in M. Meixner, J. H. Kastner, B. Balick, and N. Soker (eds.), Asymmetrical Planetary Nebulae III: Winds, Structure and the Thunderbird, Vol. 313 of Astronomical Society of the Paciﬁc Conference Series,p. 515

Suh, K.-W.: 2002, MNRAS 332, 513

Theuns, T. and Jorissen, A.: 1993, MNRAS 265, 946

Theuns, T., Boﬃn, H. M. J., & Jorissen, A. 1996, MNRAS, 280, 1264

Tielens, A. G. G. M., Waters, L. B. F. M., Molster, F. J., & Justtanont, K. 1998, Ap&SS, 255, 415 CHAPTER 5. CRYSTALLINE DUST FORMATION IN AGB WINDS 95

Van Winckel, H., Lloyd Evans, T., Reyniers, M., Deroo, P., & Gielen, C. 2006, Mem- orie della Societa Astronomica Italiana, 77, 943

Waters, L. B. F. M.: 2004, in A. N. Witt, G. C. Clayton, and B. T. Draine (eds.), Astrophysics of Dust, Vol. 309 of Astronomical Society of the Paciﬁc Conference Series, pp 229–+