Massive-Star Magnetospheres: Now in 3-D!

Transcription

1 Massive-Star Magnetospheres: Now in 3-D! Principal Investigator : Richard Townsend, University of Wisconsin-Madison Co-Investigator : Asif ud-doula, Penn State Worthington-Scranton Collaborator : Stanley Owocki, University of Delaware Graduate Student : Nicholas Hill, University of Wisconsin-Madison Contents 1 Introduction 3 2 Background The Incidence of Magnetic Fields in Massive Stars Interactions Between Field and Wind Origins and Evolutionary Impact of Magnetic Fields Recent Relevant Research by Project Team MHD Models of Massive-Star Magnetospheres The Strong-Field Limit: RRM and RFHD Rotation and Angular Momentum Loss Proposed Research Overview D MHD Models of Massive-Star Magnetospheres The Strong-Field Limit: Arbitrary RFHD The Link with Observations Logistics Project Team & Responsibilities Work Plan Summary of Project Strengths Intellectual Merits Impact on NASA s Mission A References 15 B Biographical Sketches 18 B.1 PI Richard Townsend B.2 Co-I Asif ud-doula C Current & Pending Support 21 C.1 PI Richard Townsend C.2 Co-I Asif ud-doula

2 D Budget Justification 22 D.1 Budget Narrative D.2 Personnel and Work Effort D.3 Project Facilities D.4 Budget Details

3 1 Introduction The first decade of the 21 st Century has witnessed enormous strides in our understanding of the incidence, properties and impact of magnetic fields in massive (M 5 M ) main-sequence stars. For the better part of the preceding century, these stars were presumed on observational grounds to be non-magnetic, due to the lack of any direct or indirect field detections. Moreover, the absence a sub-photospheric convection zone to serve as a field-generating dynamo (as found, for instance, in lower-mass stars) lent additional, theoretical support to this presumption. However, cracks appeared in this narrative in the late 1970s, with the photopolarimetric detection of kilogauss-strength, ordered (typically dipole) fields in a handful of B-type stars noted previously for their anomalous helium abundances. Over the intervening years, these cracks have been appreciably widened by new spectropolarimetric instrumentation enabling the detection of fields in a significant number of O- and B-type stars. Indirect detection methods have also proven productive: in tandem with theoretical models predicting X-ray emission from magnetically channeled wind shocks, ROSAT and Chandra observations have played a role in the discovery of new magnetic massive stars, including the first-known magnetic O star. These successes have sparked interest in the magnetospheres of massive stars the circumstellar environments where magnetic field and radiation-driven wind interact strongly with one another. These magnetospheres represent ideal laboratories for studying the physics of magnetized plasmas under extreme conditions. However, they can also govern the evolution and eventual fate of their host star, by amplifying angular momentum loss in the wind. Thus, their impact can be farreaching, extending even into the stellar grave to set rotation rates of young pulsars. Initial progress in understanding massive-star magnetospheres has been very encouraging. However, models so far have been restricted to two-dimensional axisymmetric configurations, with three-dimensional configurations possible only in special cases having strong fields and simple topologies. For a number of reasons that we shall discuss below, these restrictions are limiting further progress. We therefore propose to develop completely general three-dimensional models for the magnetospheres of massive stars, on the one hand to understand the observational properties of these magnetospheres and exploit them as plasma-physics laboratories, and on the other to gain a comprehensive understanding of how the magnetospheres contribute toward the evolution of their host star. ( 4). The project reunites a strong team with a proven track record in the theory and modeling of massive-star magnetospheres: Principal Investigator Richard Townsend (University of Wisconsin-Madison), Co-Investigator Asif ud-doula (Penn State Worthington-Scranton), and Collaborator Stanley Owocki (University of Delaware). These researchers will be joined by Nicholas Hill, a Graduate Student studying at UW-Madison under Townsend. To establish the necessary scientific and technical context for the project, we begin by reviewing the background to magnetic fields and magnetospheres of massive stars ( 2), and discussing recent relevant contributions to these respective fields by the project team ( 3). 2 Background 2.1 The Incidence of Magnetic Fields in Massive Stars Landstreet & Borra (1978) were the first to discover a magnetic field in a massive star, with the photopolarimetric detection of a 10 kg oblique 1 dipolar field in the B2Vp helium-strong star σ Ori E. Subsequent studies (e.g., Borra & Landstreet, 1979; Bohlender et al., 1987, and references therein) revealed the presence of similar fields in other helium-strong and helium-weak stars, supporting the 1 i.e., β > 0, where the magnetic obliquity β is the angle between rotational and magnetic axes. 3

4 Figure 1: Reconstruction of the closed-loop magnetic topology of τ Sco, based on source-surface extrapolations from spectropolarimetric measurements of the photospheric field strength (from Donati et al., 2006). hypothesis that these Bp (chemically peculiar B-type) stars represent a high-temperature extension of the magnetic Ap-star phenomenon. The detection of fields in other types of massive star, in particular those that don t exhibit obvious chemical peculiarity, had to await the construction of modern instruments capable of detecting the 0.1% circular polarization signature of the Zeeman effect in metal lines. Highlights have included the discovery of a 1.1 kg oblique-dipole field on the O6.5V star θ 1 Ori C, the ionizing source of the Orion Nebula Cluster (ONC) and the first known-magnetic O star (Wade et al., 2006); the detailed mapping of the surprisingly complex field topology of the B0.2V star τ Sco (Donati et al., 2006, see also Fig. 1); and the discovery of a dipole field on the archetypal massive pulsating star β Cephei (Henrichs et al., 2000). Most recently, an international consortium of over 50 researchers has been awarded 640 hours of Large Programme time at the Canada-France-Hawaii Telescope, to search for and characterize magnetic fields in massive stars using the ESPaDOnS spectropolarimeter. This ongoing MiMeS 2 collaboration (see Wade et al., 2009) has so far led to the discovery of fields in two additional O-type stars (HD Grunhut et al., 2009; HD 108 Martins et al., 2010), bringing the current total to five; the discovery of a field in the B2Vp star HR 7355 (Oksala et al., 2010), which with a period of only half a day exhibits the most extreme rotation of all magnetic massive stars; the discovery of fields in 9 other B-type stars; and the more-detailed characterization of a number of massive stars already known to be magnetic. All four team members of the present proposal ( 5) are closely involved in the MiMeS collaboration, with PI Townsend serving on the steering committee. 2.2 Interactions Between Field and Wind It is notable that θ 1 Ori C, the archetype for magnetic O-type stars, was hypothesized to harbor a magnetic field well before a secure field detection was achieved. To explain the periodic X-ray emission seen in Einstein and ROSAT observations of the star (see Gagne et al., 1997, also Fig. 2), Babel & Montmerle (1997b,a) advanced a seminal magnetically channeled wind shock (MCWS) narrative: radiation-driven wind streams flowing up from opposing footpoints of closed magnetic loops collide, and are shock-heated to temperatures where thermal X-ray emission becomes significant. This idea has been extensively tested by Co-I ud-doula and Collaborator Owocki, who conducted 2 Magnetism in Massive Stars 4

5 05 h 38 m 48 s 05 h 38 m 46 s 05 h 38 m 44 s Sigma Ori E D IRS1 Sigma Ori AB C (a) Figure 2: Chandra images showing X-ray emission from massive-star magnetospheres. (a) The Trapezium cluster at the heart of the ONC, color-keyed by spectral hardness; the bright source at image center is θ 1 Ori C, which although quite hard appears white instead of blue due to pile-up (from the Chandra Orion Ultra-deep Project; see Getman et al., 2005). (b) The σ Orionis cluster, with the various components labeled; note how σ Ori D, having the same B2V spectral type as σ Ori E but no magnetic field, is not detected (from Skinner et al., 2008). (b) the first magnetohydrodynamical (MHD) simulations of the wind-field interaction in massive stars (ud-doula & Owocki, 2002; Owocki & ud-doula, 2004). As we discuss in greater detail in 3.1, these simulations confirm the general MCWS paradigm, and in particular are able to reproduce the X-ray observations of θ 1 Ori C. The MCWS paradigm served to formalise previous notions that magnetic massive stars are surrounded by a magnetosphere, where the field channels and confines wind plasma. The original conception of a massive-star magnetosphere dates back to the discovery of a field in σ Ori E by Landstreet & Borra (1978); these authors commented that the star s distinctive photometric and Hα variations could be explained by an oblique-rotator model in which hot gas is trapped in a magnetosphere above the magnetic equator. With later observations by IUE revealing corresponding modulation in the star s UV resonance lines (Shore & Adelman, 1981), with the discovery of periodic non-thermal radio emission indicative of high-energy plasma processes (Drake et al., 1987), and with the detection of (possibly periodic) X-ray emission by ROSAT, XMM-Newton and Chandra (Skinner et al., 2008, and references therein; see also Fig. 2), this star has become a poster child for the wind-field interaction. The observational signatures of wind-field interactions are seen in a number of other magnetic massive stars (see, e.g. Pedersen & Thomsen, 1977; Shore & Brown, 1990). Thus, as was the case originally with θ 1 Ori C, the presence of a magnetic field can often be inferred indirectly from these signatures, paving the way for efficient target selection in spectropolarimetric surveys. Such an approach motivated the discovery of a field in β Cephei from its UV variability (see Henrichs & et al., 1993, also, Fig. 3(a)), HR 7355 from its Hα emission (see Rivinius et al., 2008, also, Fig. 5), and NU Ori and LP Ori from their X-ray emission (see Petit et al., 2008). Clearly, then, there is much to be gained from modeling massive-star magnetospheres and their associated observational signatures. 5

6 nisation stage is ud & Rothenflug se ions is thought cise origin of the served for many B1IV star β Cep, well and which ic poles (almost) ld of β Cep ep (HD , 12 day period in (1972). Henrichs as the rotational to a co-rotating as confirmed by chs et al. (2000, mary star but from the close companion which is in a 90 year 120 orbit and which has been regularly observed by speckle interferometry. B long (G) EW(C IV) [ 700, 800]km/s P= (11) days T min = (6) IUE , 81 spectra TBL , 48 spectra UV phase C IV doublet at d measurements Fig. 1. The EW of the C(a) IV doublet of β Cep as a function of rotational (b) days are shown phase for a rotation period of days (top) and the magnetic Figure 3: Observational signatures of magnetospheres. (a) Variations in the EW of the Civ restom). Figure doublet taken offrom β Cephei Henrichs(top), et al. (2005). shown together with the variations in the mean longitudinal field measurement from folded with the same period (bot- and maximumonance um C IV EW andstrength of the star s (subsequently-discovered) magnetic field (from Henrichs & et al., 1993). (b) ximum C IV EW. the Strömgren u-band light curve of σ Ori E, revealing the eclipse-like dimmings that occur when le magnetic field its two magnetospheric clouds transit in front of the star. The solid line indicates the predictions flow, but which of the 3. Line RRMprofile model calculations (from Townsend using et SEI al., 2005). ii. As a result the uator until it bene would expect2.3imation Origins is oftenand used. Evolutionary The great advantage Impact of thisof method Magnetic is 125 Fields In radiation transfer of line driven winds, the Sobolev approx- n in the magnetic that it allows for estimation of important parameters, such etic poles. Asas mentioned optical depth, in 1, based massive on the local starsphysical do notconditions harbor the only. same convection-driven dynamo responsible lity of the mag-fotion axis and thesomewhat imation isuncertain. used twospruit different (2002) contexts. has First proposed to calculate a mechanism the in which a toroidal-field instability field Forgeneration the calculation in low-mass of the linestars. profiles Inthe fact, Sobolev the origin approx- of magnetic fields in massive stars remains discovered by Tayler (1973) generates a poloidal field, which is then stretched and amplified by differential rotation. This Tayler-Spruit dynamo has been incorporated in stellar evolution calculations by a number of authors (e.g., Maeder & Meynet, 2003; Mullan & MacDonald, 2005; Heger et al., 2005). Problematically, however, the fields predicted by this dynamo are expected to scale with rotation rate and exhibit temporal variability; whereas observations of massive magnetic stars reveal fields which appear stable over decades, and moreover show no clear correlation with rotation (Donati & Landstreet, 2009, and references therein). An alternative hypothesis, more consistent with the observations, is that the fields are fossil remnants from stars pre-main sequence phase (see, e.g., Aurière et al., 2007; Alecian et al., 2008). With slow decay timescales, these fossil fields are expected to outlast the lifetime of the host star. Despite the continuing debate concerning their origin, a consensus is emerging over the impact magnetic fields can exert on the structure and evolution of a massive star. Even a weak field suffices to enhance the internal transport of angular momentum to a point where near-uniform rotation ensues during the main-sequence (MS) phase (e.g., Maeder & Meynet, 2004). This uniform rotation causes fast, thermally-driven meridional circulation currents, which on the one hand bring CNOprocessed elements up to the surface, and on the other mix fresh hydrogen fuel into the core, prolonging the star s lifetime (Maeder & Meynet, 2005). During the subsequent post-ms evolution toward the red supergiant phase, rapid envelope expansion greatly increases the star s moment of inertia, leading to rotational braking of both envelope and core. Heger et al. (2005) have argued 6

7 128 J. Babel & T. Montmerle: X-ray emission from Ap-Bp stars log(t) 80 ksec Fig. 7. Schematic view of the (a) model proposed for the X-ray emission (b) Figure from IQ 4: Aur (a)(see A cartoon text). sketch of the MCWS paradigm, showing the field lines and distribution of X-ray-emitting plasma in a (northern-hemisphere) meridional slice through a dipole-field magnetosphere and a(from fixed value Babel for& L tags Montmerle, a dipolar magnetic 1997b) field (b) Aline. snapshot At the from a 2-D MHD simulation of θ 1 Ori C, showing magnetic thequator field L lines = r/r and. The thepower logarithm released ofatthe magnetic plasma temperature in a corresponding meridional slice equator, (but Pwith eq sh, isboth thus hemispheres shown). P eq 1 Fig. 8. a Total power released at the shock by unit surface as a function sh =2R2 2 ρ w,eqvw,eq2πl 3 dl. (3) of distance for a shockfront in the magnetic equatorial plane. The solid that this core braking helps to explain the low rotation rates line isof foryoung a computation pulsars; taking however, into account theyofalso the whole magnetic note that a slowly rotating core is incompatible with the favored where the integration is carried out between L = 1 and the field geometry. collapsar The dotted model line(e.g., is for an MacFadyen effect of the magnetic field & Woosley, last closed shell 1999) L A for = rlong-soft A /R. Wegamma-ray define here Lbursts. only through the conservation of flux between the envelope and the A as the locus insothe far, magnetic studiesequatorial of the evolutionary plane where equipartition impact of magnetic between fields wind. The have vertical focused bar indicates largely theon wind-limit the internal (see Fig. 5). b Same as in a but for the temperature reached at the shockfront for a shock in redistribution the magnetic field of angular and the gas momentum. is met. Density However, and velocity the are loss of angular momentum in wind outflows the equatorial plane. cantaken alsoat bethesignificant, magnetic equator especially from the when wind amplified computation by aofmagnetic field. This point has been vividly underscored Sect The infactor recent of 2years beforeby the integral the direct in Eq. measurement 3 refers to the of spin-down in the Bp stars HD (Mikulášek two magnetic hemispheres. The power released per unit surface, w eq al., 2008), HR 7355 (Mikulášek et al., 2010), Theand temperature the archetype is plottedσ asori a function E (Townsend of L in Fig. 8. We find sh, in the equatorial plane as a function of the distance L in the et al., 2010). These are quite remarkable results; although that the magnetic temperature braking lies inisthe inferred range 3 in 10 lowmass K disk is shown in Fig. 8.a for two hypotheses. (1) If we consider the stars whole from limiting observed effect of correlations the magnetic field between geometry rotation on the and for age L>1.6. (see Bouvier, We note that 2009, higher and temperatures references are reached in the computations which include the whole effect of magnetic therein), wind (see it Sect. has never 3.2), we been observe measured that all the in energy a single, is dissipated individual object. We revisit this topic of magnetic confinement. This is linked to the divergence of magnetic field breaking further than in 3.3. L =1.6, with a maximum of w eq sh around L =2.1. lines which increases the wind velocity with respect to the nonmagnetic case (see Fig. 6). No energy is deposited for L < 1.6, as this region corresponds to λ > λ lim (see Fig. 6). For this model we obtain P eq sh = Recent 30 erg.s 1, with Relevant 75% of the total Research luminosity being byreleased Project Team 3.1for L<6.5. MHD (2) Models We alsoof showmassive-star in Fig. 8 a simplemagnetospheres case, where 4.2. The post-shock region the velocity law is taken from spherically symmetric models and Over where thewe past makedecade, the approximation MHD simulations that the magnetic pioneered field has by noco-i We ud-doula can first get have an order-of-magnitude been a prime driver estimate of of the size of effects on the wind structure except through the conservation of the postshock region by assuming that the postshock matter theoretical progress in understanding massive-star magnetospheres (see ud-doula & Owocki, 2002; mass between the stellar envelope and the magnetic field lines is in pressure equilibrium with the wind ram pressure, so that ud-doula, 2003; Owocki & ud-doula, 2004; ud-doula et al., (see. Sect. 3.2). In this case, a much larger energy is deposited in N 2006, psh k B T 2008, psh ρ2009). w vw 2 = pthese ram, with simulations, N psh the number density implemented using the zeus-2d code (Stone & Norman, the disk for L<2.5. The total power released is, however, not of particles, 1992a,b), andhave by making focused the approximation so far on the for the postshock axisymmetric much increased radiation-driven and is wind erg.s 1 outflow. From the from Rankine- stars harboring domain of acylindrical dipole magnetic homegeneous field. region. A key We furthermore result Hugoniot fromjump earlyrelations papersinis thethat case the of a strong effectadiabatic of the field shockonassume the wind that varies, T psh = Tfrom sh, where star Tto sh star, is given with by Eq. 4. In this wind (Mach magnetic numberconfinement 1), and for aparameter ratio of specific heats γ =5/3, case, the power emitted by the postshock region, Ppsh em, is given the temperature at the shock front is given by by T sh =0.188 µm η p B2 eqr 2 ; (1) vw 2 = K[v w /(100km s 1 )] Ṁv 2, (4) Ppsh em πr 2 k L 2 h psh n 2 ep (T ) (5) B with equatorial surface field strength B where the mean molecular weight of the gas eq, stellar radius R is µ =0.5for an where, mass-loss rate Ṁ and wind terminal h psh is the height of the postshock region above the disk, speed ionised v H, this gas and parameter m p is the proton characterizes mass. We first the assume ratio a of shock magnetic-to-kinetic P (T ) is the cooling energy function. density Let in us the now flow, consider an empty at the magnetic equator so that the preshock velocity v w = v w,eq. magnetosphere at t o. If we now switch on the radiation driven 7

8 and indicates whether the wind is appreciably confined by the field (η 1), or whether it remains to a large degree unaffected (η 1). MHD simulations at η = 10 have confirmed the basic MCWS paradigm advanced by Babel & Montmerle (1997b,a): wind streams from opposing footpoints of closed magnetic loops collide at the magnetic equator, and are shock-heated to temperatures where X-ray emission becomes significant (see Fig. 4). Initial modeling of this emission (see Gagné et al., 2005) reveals an encouraging degree of agreement with the X-ray spectra of θ 1 Ori C (η 10) obtained by ROSAT and Chandra, thereby supporting the star s status as an MCWS X-ray prototype. Attempts at reproducing other observables have proven rather more difficult. Models for UV resonance lines predict that equivalent widths (EWs) should be largest when a star is viewed magnetic pole-on, and weakest when the star is equator-on (see ud-doula, 2008). However, FUSE spectra of θ 1 Ori C (which fortuitously alternates between pole-on and equator-on aspects over its 15 d-day rotation cycle) reveal exactly the opposite behavior in the Civ resonance doublet and other UV lines. This is not a peculiarity of this specific star; Shore & Brown (1990) have observed similar behavior in almost all of the Bp stars in their sample, and as Fig. 3(a) clearly shows β Cephei also has backward Civ variations. We plan to address these discrepancies as part of our proposed activities to link models with observations (see 4.4). A further open issue stems from the axisymmetric nature of the zeus-2d MHD simulations. These simulations reveal that magnetospheric plasma flows are often highly structured for instance, showing large, sinuous density enhancements when cooled post-shock plasma falls back down to the stellar surface (see ud-doula & Owocki, 2002, their Fig. 4). With the (artificial) imposition of symmetry in the azimuthal direction, these enhancements extend all the way around the star, and therefore make an overly-large contribution to diagnostics such as Hα emission. In reality, of course, the azimuthal extent of any flow structures will be limited by spontaneous symmetry breaking. A prime motivation for bringing the MHD simulations into 3-D ( 4.2) is to discover the mechanisms responsible for establishing the characteristic azimuthal scale of flow structures. 3.2 The Strong-Field Limit: RRM and RFHD Toward large values of η, MHD simulations are computationally expensive because the numerical timestep required required to ensure stability (via the usual Courant condition) becomes very short. Indeed, for stars like σ Ori E (η 10 6 ), the timestep is so short that MHD simulations are in practice impossible. PI Townsend has led the development of a family of models to handle such cases, based on the recognition that as η the magnetic field behaves as if it were essentially rigid. The Rigidly Rotating Magnetosphere (RRM) model (Townsend & Owocki, 2005) considers the fate of post-shock plasma in this rigid-field limit, as it radiatively cools back down to nearphotospheric temperatures. If the star rotates slowly, then the cooled plasma eventually slides back down to the surface along field lines (as already noted above for the MHD simulations of θ 1 Ori C). However, with sufficiently rapid rotation, the outward centrifugal acceleration arising from enforced co-rotation can exceed the inward pull of gravity, allowing the plasma instead to settle into stable magnetohydrostatic equilibrium near the tops of closed magnetic loops. The RRM model provides a semi-analytical prescription for the 3-D distribution of this centrifugally supported plasma, based on the behavior of the effective (gravitational plus centrifugal) potential along each separate field line. Broadly speaking, for a rotation-aligned dipole field this distribution is an equatorial disk with a central hole, whereas for oblique-dipole fields it takes the form of a pair of clouds, suspended above the intersections between magnetic and rotational equators (see the optical/uv panel of Fig. 6). 8

9 Figure 5: Dynamical Hα spectra of σ Ori E, showing the variations relative to the photospheric profile over two rotation cycles; white indicates emission, and black absorption. The left-hand panel is based on echelle observations of the star, while the right-hand panel comes from an RRM model (from Townsend et al., 2005). The RRM model has been remarkably successful in explaining the variable Hα emission of σ Ori E (see Fig. 5), which had long been known to harbor a pair of circumstellar clouds at the equatorial intersections (e.g., Landstreet & Borra, 1978). It seems a promising candidate for explaining similar emission reported in other magnetic B-type stars, in particular HR 7355 (Rivinius et al., 2008) and δ Ori C (Leone et al., 2010). More generally, the model has established a unified framework for interpreting the photometric variations of other strong-field stars, as arising when magnetospheric clouds transit in front of the star (Townsend, 2008, also Fig. 3(b)). As a successor to the RRM model, the Rigid Field Hydrodynamics (RFHD) model was developed to simulate the dynamical and energetic processes at work in magnetospheres in the rigid-field limit (see Townsend et al., 2007). The time-dependent flow along each individual field line is now simulated using a 1-D hydrodynamical code; by piecing together independent simulations of many different field lines (typically, 2,000 3,000), a 3-D dynamical picture of a star s magnetosphere can be constructed at a fraction of the computational cost of an equivalent MHD simulation. RFHD simulations confirm the basic disk or cloud configurations predicted by the RRM model. In addition, they reveal the shock-heated plasma formed as wind streams plow into these structures (see panels (b) and (c) of Fig. 6), meaning that they can be used to predict the X-ray emission (and other wind-related observables) of magnetospheres in the strong-field limit. To this end, PI Townsend and Grad Student Hill have been further developing the RFHD code to incorporate energy transport by thermal conduction, which has been neglected in previous studies. Panel (d) of Fig. 6 highlights how conduction serves to truncate emission above , K, by drawing thermal energy away from the hottest regions. Other novel results in the updated RFHD code include the appearance of siphon flows, where a continuous, supersonic wind stream flows from one footpoint of a closed magnetic loop to the other, passing through a shock just before it reaches the stellar surface; and the occurrence of corona-like configurations, where a magnetic loop becomes entirely filled with hot ( 10 7 K), low-density plasma in hydrostatic equilibrium. The lessons being learned from this research (to appear in a forthcoming paper) will help guide our implementation of cooling and conduction in the planned 3-D MHD code ( 4.2). 9

10 Figure 6: Snapshots from an RFHD model of σ Ori E, showing the spatial distribution of magnetospheric emission measure in three different temperature bins: optical (T < 10 6 K), soft X-ray (10 6 K < T < 10 7 K) and hard X-ray (T > 10 7 K). The plot on the right shows the corresponding differential emission measure, for models with (thin) and without (thick) thermal conduction. A powerful aspect of both RRM and RFHD models is that they are in principle applicable to arbitrary field topologies, not just the oblique dipole configurations considered so far. Thus, for instance, they could be used to model the magnetosphere of HD 37776, which harbors a quadrupole field (Thompson & Landstreet, 1985). As part of our proposed research, we plan to make the necessary enhancements to the RFHD code to implement this arbitrary-field capability ( 4.3). 3.3 Rotation and Angular Momentum Loss The project team has recently extended the MHD simulations to stars having (dynamically significant) field-aligned rotation (see ud-doula et al., 2006, 2008, 2009). Toward larger values of the confinement parameter η, the simulations reveal the formation of a co-rotating equatorial disk, with a structure similar to that predicted by RRM and RFHD models. At its outer edge, corresponding to the Alfvén radius R A η 1/4 R, material in the disk is continually drawn outward by the centrifugal force, until the field lines threading it reconnect and eject plasma from the magnetosphere. Such centrifugal breakout episodes, with the consequent release of magnetic energy, may explain the episodic X-ray flares seen in σ Ori E (see ud-doula et al., 2006; Mullan, 2009). They also represent a mechanism for mass loss from a co-rotating magnetosphere a process not fully considered in the RRM and RFHD models, because the rigid-field assumption formally places the Alfvén radius at infinity. Townsend & Owocki (2005) have presented a simple analysis of the magnetospheric mass limits established by centrifugal breakout; however, these are around two orders of magnitude larger than the observed/inferred masses of Bp-star magnetospheres. To address this discrepancy, one of the goals of our proposed 3-D MHD simulations ( 4.2) is to examine how centrifugal breakout changes when we add the third dimension (for instance, due to differences in the way magnetic reconnection operates); and, moreover, to search for other modes of magnetospheric mass loss. A parallel focus of the recent MHD simulations has been the loss of angular momentum from magnetic massive stars. This problem has been almost completely ignored in the literature, due to an overwhelming emphasis on magnetic braking caused by the pressure driven winds found in low-mass stars, as opposed to the radiation driven winds characteristic to massive stars. The simulations reveal that the braking timescale for a star with an aligned-dipole field follows the scaling τ brake τ mass η 1/2, where τ mass is the mass-loss timescale (see ud-doula et al., 2009). The application of this scaling to σ Ori E predicts τ brake 1.4 Myr, which is in remarkable agreement with directly measured τ brake = 1.34 Myr (Townsend et al., 2010). 10

11 This latter result is very encouraging, but comes with a number of caveats not the least being that σ Ori E harbors an oblique-dipole field, not the aligned dipole assumed in the simulations. A key goal of the 3-D MHD simulations ( 4.2) will therefore be to explore how differing magnetic topologies influence the rate of angular momentum loss. 4 Proposed Research 4.1 Overview From the review of the project team s recent research activities ( 3), there emerges a clear message: Further progress in understanding the dynamics, energetics and evolutionary impact of massive-star magnetospheres requires the transition to fully 3-dimensional models. Our proposed three-year research program, comprising a combination of code development, simulation, confrontation with observations and theoretical work, has the primary goal of achieving this transition D MHD Models of Massive-Star Magnetospheres In the preceding sections, we enumerate a number of important reasons why future MHD simulations of massive-star magnetospheres should be conducted in 3-D. To recapitulate, 3-D simulations will permit spontaneous symmetry breaking in the azimuthal direction, allowing us to quantify the characteristic scale of azimuthal structures, and investigate the mechanisms responsible for establishing this scale; they will provide a closer-to-physical picture of processes, such as magnetic reconnection during centrifugal breakout, that influence the mass and energy evolution of magnetospheres; they will enable consideration of field topologies more complex than the rotation-axis-aligned dipoles considered so far in particular, oblique dipoles, quadrupoles, and even cases such as in Fig. 1; they will allow us to generalize our studies of magnetospheric X-ray emission, optical and UV variability, mass and angular momentum loss to stars harboring these more-complex field topologies. With these points as our guiding motivation, our first step will be to develop an MHD code. Not wishing to reinvent the wheel, we plan to modify one of the existing freely available 3-D codes. To simplify implementation of the stellar-surface boundary, we restrict ourselves to codes that support a spherical-polar coordinate system; at the time of writing, the candidates are amrvac (Nool & Keppens, 2002), pluto (Mignone et al., 2007), and astrobear (Cunningham et al., 2009). The project team has already contacted the respective authors of these codes, to confirm that they have the necessary capabilities (in particular, support for execution on parallel computer architectures). In the initial stages of the project, we will evaluate the candidate MHD codes to decide which is best suited to our purpose. Then, the adopted code will be modified as follows: (i). Flow boundary conditions will be imposed to allow outflow and inflow at the stellar surface, and outflow at the grid edge. The field imposed at the stellar surface will be consistent with the chosen magnetic topology. 11

12 (ii). The radiative line force will be implemented using the standard Sobolev-approximation formalism developed by Castor et al. (1975), with the addition of corrections for the finite stellar disk (Friend & Abbott, 1986) and line-force saturation (Owocki et al., 1988). (iii). Optically thin radiative cooling will be implemented using the exact integration scheme developed by Townsend (2009), together with the cooling tables published by Gnat & Sternberg (2007). (iv). Inverse Compton cooling will be implemented using the expressions given by White & Chen (1995). (v). Thermal conduction by electrons will be implemented using the flux-limited prescription of Dalton & Balbus (1993), with the super-time-stepping acceleration algorithm described by Alexiades et al. (1996). After validating the modified code to confirm its correctness, we will begin production runs to address the questions that have so far been inaccessible to us. The following subsections outline our calculation plan, ordered by increasing computational complexity. All simulations will be undertaken on the high-performance computer cluster described in D Aligned-Dipole Fields Our first simulations will focus on magnetospheres having the same aligned-dipole fields considered in our previous 2-D MHD models. We will examine the azimuthal structures that arise from spontaneous symmetry breaking, and determine how the scale of these structures depends on parameters such as magnetic confinement parameter η and rotation rate. We will moreover investigate how the magnetic reconnection associated with centrifugal breakout behaves in three dimensions, and look for other modes of magnetospheric mass loss Oblique-Dipole Fields Next, we will undertake simulations of oblique-dipole magnetospheres. We will examine how the gross structure of a magnetosphere changes as the obliquity β is increased and, at larger values of η, the extent to which this structure reproduces the strong-field results from the RRM and RFHD models. Moreover, we will explore the effect of the obliquity on angular momentum loss from the magnetosphere, allowing us to create a new parametrization for the scaling of the braking timescale τ brake with η and β Complex Fields Our calculations will culminate with a simulation of τ Sco, representing a complex-field scenario. Using the surface field maps measured by Donati et al. (2006) to establish the inner boundary conditions, we will create the first ab initio model for star s magnetosphere, completely replacing the simple field extrapolations shown in Fig The Strong-Field Limit: Arbitrary RFHD Although non-axisymmetric field topologies will become accessible with the development of the 3-D MHD code, the strong-field limit (η 1) will still remain beyond reach. To address this issue, we plan to continue development of our rigid-field models ( 3.2), in particular extending the RFHD 12

13 code to handle completely-arbitrary field topologies. Steps to implement this arbitrary RFHD (A-RFHD) functionality are as follows: (i). The heart of the RFHD code, the vh-1 PPM code developed by J. Blondin and co-workers, will be replaced with a new 1-D code currently being written by PI Townsend. The new code is based on the Godunov method described by Stone & Gardiner (2009), whose simplicity makes it straightforward to extend with additional physics (e.g., cooling, conduction, etc.). (ii). The time evolution in the code will be unsplit, to improve the coupling between hydrodynamical and energetic processes. (iii). Dipole-specific routines will be replaced with ones that can handle arbitrary field topologies (as specified, for each field line, by a 3-D space curve and an associated scalar field strength). (iv). Support for open-field regions will be implemented, by allowing for field lines that have an outflow boundary condition imposed at one end (the other end remaining anchored to the stellar surface). The A-RFHD code will be used to model the magnetospheres of Bp stars whose fields depart from dipolar. An initial target will be the quadrupole-field case of HD However, with the the project team s close involvement in the MiMeS collaboration ( 2.1), we will soon ( 1 year from the time of writing) have access to detailed surface field maps of a number of other Bp stars, including the archetype σ Ori E. These maps will be used to reconstruct the stars 3-D fields (via multipolar expansion), thereby supplying the necessary input data to undertake detailed A-RFHD simulations. 4.4 The Link with Observations As has been the case with the project team s previous research activities ( 3), we plan to maintain a strong link between our models and the corresponding observations (past, present and future) of massive-star magnetospheres. Thus, for all simulations created using the new 3-D MHD and A-RFHD codes discussed above, we will harness our existing tools and expertise to synthesize observables such as optical light curves (e.g., Fig. 3(b)), Hα spectra (e.g., Fig. 5), and X-ray differential emission measures (e.g., Fig. 6). Where appropriate, these will be compared against corresponding datasets obtained from ground- and space-based observatories, allowing us to test and further refine our models. There are some areas where we will need to develop new tools. The near-universal occurrence of backward Civ variations in IUE and FUSE observations ( 3.1) may be a consequence of using the Sobolev-with-exact-integration (SEI; see Lamers et al., 1987) method for UV line-profile synthesis. This method is built on the assumption that the thermal velocity width of lines is much smaller than typical flow velocities the so-called Sobolev approximation, which is reasonable in a spherically expanding flow, but questionable in the near-stationary regions of a confined magnetosphere. To explore the possibility that the Sobolev approximation is the problem, we will adapt PI Townsend s fullmonte Monte-Carlo continuum radiative transfer code (Townsend, in preparation) to handle resonance-line transfer, and then apply it to synthesizing Civ line profiles for our simulation results. POLARIZATION? HIGH ENERGY PRODUCTION? 13

14 5 Logistics 5.1 Project Team & Responsibilities To meet the challenges presented by the proposed activities, the project will reunite a team with an established track record of cutting-edge research in the field of magnetic massive stars: PI Richard Townsend is an expert on massive stars in the strong-field limit. Serving as PI of a NASA Long-Term Space Astrophysics award 3, he spearheaded the development of the RRM and RFHD models. In addition to his overall task of coordinating the project, he will draw on his extensive experience in spectroscopic and photometric modeling to synthesize observables for the simulations undertaken by the other team members ( 4.4). In his capacity as doctoral adviser, he will also be assisting Grad Student Hill in his code development and simulation tasks. Co-I ud-doula was the first to develop MHD simulations of massive-star magnetospheres, and his subsequent research activities have cemented his position as the top magnetohydrodynamicist in the field. He will take responsibility for development and testing of the 3-D MHD code ( 4.2), and serve in an advisory role during the planned simulations ( ). Collaborator Owocki is an acknowledged world leader in the theory of radiatively driven winds of massive stars. As the doctoral adviser of ud-doula and the postdoctoral adviser of Townsend, he was the inspirational force behind the team s initial foray in the study of magnetospheres. He has been deeply involved in all subsequent research activities, and will contributing toward all theoretical aspects of the project. Graduate Student Hill has an undergraduate (REU) background in solar physics, studying coronal mass ejections and magnetic reconnection. He has been working for the past year under the tutelage of Townsend, to incorporate energy transport by thermal conduction in the RFHD code. His activities, forming the core of his doctoral thesis work, will be to undertake the 3-D MHD simulations ( ), and to develop and apply the A-RFHD code ( 4.3). 5.2 Work Plan With the caveat that the most fruitful research often comes from following interesting new avenues arising from intermediate results, we offer the following general outline of our time plan for carrying out the proposed research: Year 1 Set up MHD code; Set up A-RFHD code; Monte Carlo Year 2 Dipole-Field MHD; HD Year 3 Tau Sco MHD; MiMeS Bp 6 Summary of Project Strengths 6.1 Intellectual Merits 6.2 Impact on NASA s Mission 3 NNG05GC36G; see B.1 14

15 A References Alecian, E., Wade, G. A., Catala, C., Folsom, C., Grunhut, J., Donati, J., Petit, P., Bagnulo, S., Marsden, S. C., Ramirez Velez, J. C., Landstreet, J. D., Boehm, T., Bouret, J., Silvester, J., 2008, Contributions of the Astronomical Observatory Skalnate Pleso, 38, 235 Alexiades, V., Amiez, G., Gremaud, P., 1996, Com. Num. Meth. Eng, 12, 12 Aurière, M., Wade, G. A., Silvester, J., Lignières, F., Bagnulo, S., Bale, K., Dintrans, B., Donati, J. F., Folsom, C. P., Gruberbauer, M., Hui Bon Hoa, A., Jeffers, S., Johnson, N., Landstreet, J. D., Lèbre, A., Lueftinger, T., Marsden, S., Mouillet, D., Naseri, S., Paletou, F., Petit, P., Power, J., Rincon, F., Strasser, S., Toqué, N., 2007, A&A, 475, 1053 Babel, J., Montmerle, T., 1997a, ApJ, 485, L29, 1997b, A&A, 323, 121 Bohlender, D. A., Landstreet, J. D., Brown, D. N., Thompson, I. B., 1987, ApJ, 323, 325 Borra, E. F., Landstreet, J. D., 1979, ApJ, 228, 809 Bouvier, J., 2009, in EAS Publications Series, Vol. 39, Stellar Magnetism, Neiner, C., Zahn, J.-P., eds., 199 Castor, J. I., Abbott, D. C., Klein, R. I., 1975, ApJ, 195, 157 Cunningham, A. J., Frank, A., Varnière, P., Mitran, S., Jones, T. W., 2009, ApJS, 182, 519 Dalton, W. W., Balbus, S. A., 1993, ApJ, 404, 625 Donati, J., Howarth, I. D., Jardine, M. M., Petit, P., Catala, C., Landstreet, J. D., Bouret, J., Alecian, E., Barnes, J. R., Forveille, T., Paletou, F., Manset, N., 2006, MNRAS, 370, 629 Donati, J., Landstreet, J. D., 2009, Ann. Rev. Astron. Astrophys., 47, 333 Drake, S. A., Abbott, D. C., Bastian, T. S., Bieging, J. H., Churchwell, E., Dulk, G., Linsky, J. L., 1987, ApJ, 322, 902 Friend, D. B., Abbott, D. C., 1986, ApJ, 311, 701 Gagne, M., Caillault, J., Stauffer, J. R., Linsky, J. L., 1997, ApJ, 478, L87 Gagné, M., Oksala, M. E., Cohen, D. H., Tonnesen, S. K., ud-doula, A., Owocki, S. P., Townsend, R. H. D., MacFarlane, J. J., 2005, ApJ, 628, 986 Getman, K. V., Flaccomio, E., Broos, P. S., Grosso, N., Tsujimoto, M., Townsley, L., Garmire, G. P., Kastner, J., Li, J., Harnden Jr., F. R., Wolk, S., Murray, S. S., Lada, C. J., Muench, A. A., McCaughrean, M. J., Meeus, G., Damiani, F., Micela, G., Sciortino, S., Bally, J., Hillenbrand, L. A., Herbst, W., Preibisch, T., Feigelson, E. D., 2005, ApJS, 160, 319 Gnat, O., Sternberg, A., 2007, ApJS, 168, 213 Grunhut, J. H., Wade, G. A., Marcolino, W. L. F., Petit, V., Henrichs, H. F., Cohen, D. H., Alecian, E., Bohlender, D., Bouret, J., Kochukhov, O., Neiner, C., St-Louis, N., Townsend, R. H. D., 2009, MNRAS, 400, L94 Heger, A., Woosley, S. E., Spruit, H. C., 2005, ApJ, 626, 350 Henrichs, H. F., de Jong, J. A., Donati, J., Catala, C., Wade, G. A., Shorlin, S. L. S., Veen, P. M., Nichols, J. S., Kaper, L., 2000, in The Be Phenomenon in Early-Type Stars, Smith, M. A., Henrichs, H. F., Fabregat, J., eds., Proc. IAU Colloq. 175, 324 Henrichs, H. F., et al., 1993, in New Perspectives on Stellar Pulsation and Pulsating Variable Stars, Nemec, J. M., Matthews, J. M., eds., Proc. IAU Colloq. 139, 186 Lamers, H. J. G. L. M., Cerruti-Sola, M., Perinotto, M., 1987, ApJ, 314, 726 Landstreet, J. D., Borra, E. F., 1978, ApJ, 224, L5 Leone, F., Bohlender, D. A., Bolton, C. T., Buemi, C., Catanzaro, G., Hill, G. M., Stift, M. J., 2010, MNRAS, 401, 2739 MacFadyen, A. I., Woosley, S. E., 1999, ApJ, 524,

16 Maeder, A., Meynet, G., 2003, A&A, 411, 543, 2004, A&A, 422, 225, 2005, A&A, 440, 1041 Martins, F., Donati, J., Marcolino, W. L. F., Bouret, J., Wade, G. A., Escolano, C., Howarth, I. D., 2010, MNRAS, in press; arxiv: Mignone, A., Bodo, G., Massaglia, S., Matsakos, T., Tesileanu, O., Zanni, C., Ferrari, A., 2007, ApJS, 170, 228 Mikulášek, Z., Krtička, J., Henry, G. W., de Villiers, S. N., Paunzen, E., Zejda, M., 2010, A&A, 511, L7 Mikulášek, Z., Krtička, J., Henry, G. W., Zverko, J., Žižåovský, J., Bohlender, D., Romanyuk, I. I., Janík, J., Božić, H., Korčáková, D., Zejda, M., Iliev, I. K., Škoda, P., Šlechta, M., Gráf, T., Netolický, M., Ceniga, M., 2008, A&A, 485, 585 Mullan, D. J., 2009, ApJ, 702, 759 Mullan, D. J., MacDonald, J., 2005, MNRAS, 356, 1139 Nool, N., Keppens, R., 2002, Comp. Meth. Appl. Math., 2, 92 Oksala, M. E., Wade, G. A., Marcolino, W. L. F., Grunhut, J., Bohlender, D., Manset, N., Townsend, R. H. D., 2010, MNRAS, in press; arxiv: Owocki, S. P., Castor, J. I., Rybicki, G. B., 1988, ApJ, 335, 914 Owocki, S. P., ud-doula, A., 2004, ApJ, 600, 1004 Pedersen, H., Thomsen, B., 1977, A&AS, 30, 11 Petit, V., Wade, G. A., Drissen, L., Montmerle, T., Alecian, E., 2008, MNRAS, 387, L23 Rivinius, T., Štefl, S., Townsend, R. H. D., Baade, D., 2008, A&A, 482, 255 Shore, S. N., Adelman, S. J., 1981, in Upper Main Sequence Chemically Peculiar Stars, 429 Shore, S. N., Brown, D. N., 1990, ApJ, 365, 665 Skinner, S. L., Sokal, K. R., Cohen, D. H., Gagné, M., Owocki, S. P., Townsend, R. D., 2008, ApJ, 683, 796 Spruit, H. C., 2002, A&A, 381, 923 Stone, J. M., Gardiner, T., 2009, New Astronomy, 14, 139 Stone, J. M., Norman, M. L., 1992a, ApJS, 80, 753, 1992b, ApJS, 80, 791 Tayler, R. J., 1973, MNRAS, 161, 365 Thompson, I. B., Landstreet, J. D., 1985, ApJ, 289, L9 Townsend, R. H. D., 2008, MNRAS, 389, 559, 2009, ApJS, 181, 391 Townsend, R. H. D., Oksala, M. E., Cohen, D. H., Owocki, S. P., ud-doula, A., 2010, ApJ, 714, L318 Townsend, R. H. D., Owocki, S. P., 2005, MNRAS, 357, 251 Townsend, R. H. D., Owocki, S. P., Groote, D., 2005, ApJ, 630, L81 Townsend, R. H. D., Owocki, S. P., ud-doula, A., 2007, MNRAS, 382, 139 ud-doula, A., 2003, PhD thesis, University of Delaware, 2008, in Clumping in Hot-Star Winds, W.-R. Hamann, A. Feldmeier, & L. M. Oskinova, ed., 125 ud-doula, A., Owocki, S. P., 2002, ApJ, 576, 413 ud-doula, A., Owocki, S. P., Townsend, R. H. D., 2008, MNRAS, 385, 97, 2009, MNRAS, 392, 1022 ud-doula, A., Townsend, R. H. D., Owocki, S. P., 2006, ApJ, 640, L191 Wade, G. A., Alecian, E., Bohlender, D. A., Bouret, J., Grunhut, J. H., Henrichs, H., Neiner, C., Petit, V., Louis, N. S., Aurière, M., Kochukhov, O., Silvester, J., ud-doula, A., ud-doula, 2009, 16

17 in Cosmic Magnetic Fields: From Planets, to Stars and Galaxies, Strassmeier, K. G., Kosovichev, A. G., Beckman, J., eds., Proc. IAU Symp. 259, 333 Wade, G. A., Fullerton, A. W., Donati, J., Landstreet, J. D., Petit, P., Strasser, S., 2006, A&A, 451, 195 White, R. L., Chen, W., 1995, in Wolf-Rayet stars: Binaries, Colliding Winds, Evolution, van der Hucht, K. A., Williams, P. M., eds., Proc. IAU Symp. 163,