Investigating the Role of Magnetic Fields in Binary Star Formation Justin Kang Spring 2019 In partial fulfillment of the requirements for graduation with the Dean’s Scholars Honors Degree in Astronomy Supervisor: Stella Offner Second Reader: Richard Fitzpatrick Departmental Reader: Greg Sitz ABSTRACT The initial conditions in pre-stellar cores that lead to single versus binary star systems are debated. The role of magnetic fields, in particular, is uncertain. Observations from the Atacama Large Millimeter/sub-millimeter Array telescope (ALMA), which can probe the polarization of thermal emission from dust within star-forming dense cores, suggests that the environments single star systems form in are most similar to those of weakly-magnetized simulations. In this weak-field case, the magnetic field is weak relative to the turbulent pressure and gas pressure; turbulence shapes the material that forms the protostar. However, no such comparison has been conducted for the environments of binary star systems. We expect these systems to be different as the binary companion will interact with the system through mechanisms such as radiation, accretion, and dynamics. In order to compare the outcomes of these two systems, we analyze a simulation of a turbulent, star-forming molecular cloud with moderate-strength magnetic fields. To remain comparable to observations, we model the propagation of the simulation’s emission. We also introduce various physics, such as scattering, absorption, and emission processes of the dust and gas. By accounting for effects such as noise and instrumental resolution, we generate "synthetic observations" of the dust polarization that are comparable to ALMA’s real observations. We then compare the polarization properties between cores forming single and multiple stars to predict what real observable differences may exist. Comparing the synthetic observations with visualizations of the simulation, we gain physical insight into the role of magnetic fields in star-forming regions. Keywords: star formation — magnetic fields — simulations 2 1. INTRODUCTION 1.1. Star formation Stars form in cold, dense, molecular clouds. Known as giant molecular clouds (GMCs), these structures have masses of roughly 103 107 M ,rangeinsizefrom 10 100 parsecs, have − ⇠ − temperatures of 10 K, and are composed primarily of molecular hydrogen (Dobbs et al. 2014). ⇠ It is commonly believed that most clouds are approximately in virial equilibrium. This state is well-described by the virial theorem: 1 1 d 2 I¨ =2(T TS)+B + W (⇢vr ) dS, (1) 2 − − 2 dt · ZS where 1 3 T = ⇢v2 + P dV, (2) 2 2 ZV ✓ ◆ TS = r ⇧ dS, (3) · · ZS 1 2 B = B dV + r TM dS, (4) 8⇡ · · ZV ZS W = ⇢r φdV. (5) − ·r ZV Physically, I is the cloud moment of inertia, T the turbulent and thermal kinetic energy of the cloud, TS the pressure energy at the cloud surface, B the difference between the internal magnetic pressure and surface magnetic pressure and tension, and W the gravitational binding energy. The final integral represents the rate of change of momentum flux across the surface. For simplification, here we assume that the cloud is not accreting or losing any mass, and not in an external potential (Goldbaum et al. 2011; Krumholz 2017). Looking at the virial theorem, I¨ gives the rate of change of the cloud’s expansion or contraction. If I<¨ 0,thecloudcollapsesonitself.IfI¨ =0,thenitneithercontractsnotexpands,andisin virial equilibrium (Krumholz 2017). Thus we see that clouds have thermal, turbulent, and magnetic support against collapse due to gravity. Instabilities, caused by external factors such as supernovae, can drive overdensities in the cloud, causing those beyond the Jeans mass to gravitationally collapse 3 and form clumps (Krumholz 2017). As the density increases, they become pre-stellar cores. Once the density in these cores gets high enough to fuse hydrogen, a protostar will form. Protostars are often categorized into different "classes" as they evolve; to focus on the star formation process, we focus on the first two, class 0 and class I. In the class 0 stage (the first stage of a protostar), there is a central protostar still embedded in an envelope of gas. The protostar will accrete a significant, if not amajorityofitsmassduringthisstage.IntheclassIstage,therearerelativelyevolvedprotostars, that have both protostellar disks and envelopes (André, Ward-Thompson, & Barsony 2000). 1.2. Binary star formation To understand the importance of binary star formation, we must understand the importance of binary stars. From observational surveys, we find that the companion frequency, or the average number of companions per observed target, is 36.9 5.2% for class I protostars, and possibly less for ± class 0 protostars (Duchêne & Kraus 2013). Due to the limited sample size of class 0 protostars, the companion frequency for these is less certain. However, other sources suggest that nearly all stars form in binary systems (Reipurth et al. 2014). When we look at main-sequence field stars (opposed to those in clusters), we find that the multiplicity frequency, or the fraction of multiple systems in apopulation,is44 2% for solar-mass stars, and 80% for O-type stars (masses 15 100 times ± ≥ ⇠ − greater than the Sun) (Duchêne & Kraus 2013). Thus we see that binary systems are extremely common. Because these systems are so common, it is important to understand how they form. One of the widely accepted mechanisms of binary star formation is core fragmentation (Bonnell &Bate 1994). During the collapse of the initial core mentioned in Section 1.1,thecorecanbreak apart into fragments, which can then also collapse. If these collapsing fragments can get dense enough for hydrogen to fuse, then they will also form stars. Although there are other mechanisms of binary star formation, such as disk fragmentation, core fragmentation is the mechanism that we will consider for the remainder of this thesis. In the case of binary systems, dynamics and competing processes between the partners, such as accretion and radiation, will complicate the micro-physics of the formation process (Reipurth et al. 2014). One example of this is the role of magnetic fields in the binary star formation process. 4 1.3. Magnetic fields As we described in Equation 1,themagneticfieldinitiallyprovidesthecloudsupportagainst collapse. However, the role of the magnetic field post-collapse remains unclear. In the "strong-field" mode of star formation, gravitational collapse is regulated by a strong, ordered magnetic field, and during, the collapse, the strongly magnetized dense gas is predicted to pinch the magnetic field into an hourglass shape (Fiedler & Mouschovias 1993). To test this theory, Hull et al. (2017)used ALMA to observe the magnetic field morphology of a class 0 protostar in the Serpens star-forming region. For comparison, they also ran four ideal magnetohydrodynamic (MHD) simulations using the AREPO code (Springel 2010), with magnetic field strengths ranging from weak to strong (relative to the turbulent and kinetic energy). Based on their visual and statistical comparisons, Hull et al. (2017)determinedthattheirobservationsweremostsimilartoweakly-magnetizedsimulations.In their observations they observed neither the hourglass morphology nor a consistency with a large-scale magnetic field. From their simulations, they found that for the weak-field case, turbulence shapes the magnetic field on small scales, and the density and magnetic field orientation are randomly aligned. However, no such analysis has been conducted for forming binary systems. Since no observations of protostellar cores have been confirmed to contain forming binary stars, we conduct a theoretical study of these systems. 1.4. Observing magnetic fields There are several ways of observing magnetic fields. The Zeeman effect directly gives the direction and strength of the field, but only the component along the line of sight (Crutcher 2009). The polarization of molecular line emissions gives kinematic information and the magnetic field structure (Goldreich & Kylapis 1981). The final method, the polarization of thermal dust emission, probes the magnetic field morphology in the plane of the sky but gives no strength information (Crutcher 2012). This third mechanism is what ALMA observes and Hull et al. (2017) used, and the mechanism we will use in our analysis. The polarization of dust emission is generated in two ways: background-starlight polarization and thermal dust emission. The former comes from stellar absorption of background 5 Figure 1. The Stokes parameters Q, U,andV ; taken from Collett (2005). Here Q SL(H/V)P, U SL 45P, ⌘ ⌘ ± and V S . ⌘ (R/L)CP starlight, and emits in the optical and infrared. In the high-density regions of GMCs, the extinction is too great for stellar absorption to occur. Thus the primary mechanism of polarization in GMCs is thermal dust emission. Here radiative alignment torque from the magnetic field causes spinning dust grains to align with their long axes perpendicular to the field (Hoang & Lazarian 2009). This emission is then polarized perpendicular to the magnetic field; thus we can synthesize the magnetic field morphology by applying a 90° rotation (with 180° ambiguity). To describe the polarization, we make use of the Stokes I, Q, U,andV parameters (Collett 2005). These are derived from the time average of the instantaneous polarization ellipse. I describes the total intensity of the light, Q the degree of horizontal and diagonal linear polarization, U the degree of diagonal linear polarization, and V the circular polarization. These are visualized in Figure 1. For our analysis, we ignore the V parameter because the signal-to-noise ratio from circular polarization has not been significant in observations. From the remaining parameters, we can derive a few useful properties. The polarization intensity is given by P = Q2 + U 2,andthepolarization p 6 fraction, or the fraction of intensity coming from polarized emission, is given by 2 2 Pfrac = P/I = Q + U /I. (6) p Finally, the polarization angle is given by ✓ = 1/2 arctan (U/Q). The polarization angle gives the direction of the thermal dust emission, and subsequently the morphology of the magnetic field.