Magnetic O-Stars

Alexa Hart University of Denver Department of Physics and Astronomy Advanced Electromagnetism II May 21, 2008

1 Introduction

Solar studies revealed long ago that stars can harbor magnetic fields, and that those magnetic fields can be strong enough to significantly influence fundamental stellar properties. Models have predicted that magnetic fields can effect stellar mass loss, convection, angular momentum and much more. Thus, the evolutionary track of a star can depend sensitively on its magnetic field. The origin of such magnetic fields is unknown; one theory claims they are a result of a dynamo process happening within the star due to convection (like the Sun’s), while the other identifies them as condensed ”fossils” of the molecular clouds from which they formed. Until recently, astronomers have not had the instrumentation necessary to detect any but the very strongest stellar magnetic fields, so although they are known to be important, magnetic effects have been largely ignored. Within the last decade, improvements to detection techniques and instrumentation have provided astronomers the opportunity to measure the weaker magnetic fields of hot, massive O-Stars. These observations have shown surprising agreement with a model developed for a very different type of star, one that is called ”chemically peculiar.” The model, developed by Babel and Montmerle (1997), predicts an off-axis dipolar magnetic field, with magnetically confined winds resulting in the creation of a decretion disk at the magnetic equator.

2 Background 2.1 The Zeeman Effect All measurements of stellar magnetic fields exploit an phenomenon called Zeeman splitting. In the absence of a magnetic field, all quantum states with a common quantum number n have the same energy. However, if a magnetic field is applied, then the magnetic moments associated with spin and angular momentum will precess around the direction of the applied field according to their magnitude and orientation. The Hamiltonian describing the interaction with the magnetic field is

0 H = −(~µl + ~µs) · B~ ext (1)

e ~ e ~ Where ~µl = − 2m L and ~µs = − m S, S~ being the spin angular momentum and L~ the orbital angular momentum. Therefore e H0 = (L~ + 2S~) · B~ (2) 2m ext Thus the spectral line from a particular transition in these particles will separate into several discrete wavelengths, the number of which is determined by the degeneracy of the inital state. Thus if l = 1, then the line will split into three discrete lines, one each for ml = -1, 0 and 1. Further, the precession for the ml = 1 will precess in the opposite direction to the ml = −1 state, thereby emitting circularly polarized light with positive and negative helicity, respectively (see Griﬃths (1995) for a full derivation). These wavelength shifts correspond to a change in the energy levels, expressed (in the weak ﬁeld limit) for an external applied

ﬁeld B~ ext = Bzˆ,

∆E = µBgjBextmj (3)

1 −9 Where µB = 5.788 × 10 ev/G is the Bohr Magneton, mj is the magnetic quantum number associated with the total angular momentum, and gj is the Lande g-factor, deﬁned by j(j + 1) − l(l + 1) + 3/4 g = 1 + (4) j 2j(j + 1)

Here we have made the assumption that the applied B-ﬁeld Bext << Binternal is small compared to the internal B-ﬁeld due to spin-orbit coupling. For Hydrogen, Binternal ≈ 10, 000 Gauss, and thus this is a safe assumption for the atmospheres of most stars, which have Bexternal ≈ 1, 000 G.

2.2 Magnetohydrodynamics The atmospheres and winds of OB stars are composed of ionized gas, and thus are considered a highly con- ductive plasma, governed in a simpliﬁed model by the theory of magnetohydrodynamics, essentially Maxwell’s equations coupled with ﬂuid dynamics:

∇ × B~ = µJ~ J~ = σ(E~ + ~v × B~ ) ∇ · B~ = 0 ~ ∂B~ ∂~v ~ ~ ∇ × E = − ∂t ρ ∂t + ρ(~v· ∇)~v = −∇p + J × B p = 2ρRT The main point here is that in a plasma, flow is restricted to move along the magnetic field lines: the plasma and the B-field are ”locked” together (see Hood (1998) for a full discussion). This coupling causes many observable phenomena, including confinement of stellar winds by the magnetic fields, and magnetic braking, a slowing of the stellar rotation rate due to the co-rotation of the ionized outer layers and winds.

2.3 A Physical Barrier The speed of sound is not just a limit to how fast sound waves can travel in a medium; all waves that are physical in nature have this same limitation. When a pressure wave in a plasma is accelerated to the speed of sound, it suddenly trips over itself, causing a shock front, or a discontinuity in temperature and pressure, to develop. After material has been processed through a shock front, it will emit X-ray radiation.

3 Stellar magnetic ﬁeld detection methods

All methods astronomers have developed to detect magnetic fields exploit the Zeeman effect. If a star has a very small rotation and a strong magnetic field, the discrete spectral lines (for different values of ml) can be distinguished with a spectrometer, and thus the magnetic field measured directly by use of Equation (3) with E = hc/λ. More frequently, however, rotational doppler effects blur the discrete wavelegths associated with the splitting so that they will all be contained in one broad spectral line.

3.1 Spectropolarimetry When doppler effects blur individual Zeeman line profiles, the combination of a spectrometer with a po- larimeter, called a spectropolarimeter, can isolate small subsections of these spectral lines and measure the polarization over a very small wavelength range. Since the two ”wings” of a Zeeman-broadened spectral line will have opposite circular polarization, this type of measurement can be used to find the effective ∆E by measuring the ∆λ between the two extremum of circularly polarized light. This willl yield a value for the magnetic field paralell to the line of sight. Astronomers also measure the net linear polarization over a series of spectral lines and then average them to get a value for the disk integrated, transverse component of the magnetic field (perpendicular to the line of sight)(Neiner, 2007).

3.2 Spectroscopy Though individual Zeeman line profiles are not often distinct, one can still measure the broadening of the composite line profile as a result of the magnetic field. Because certain lines are much more sensitive to magnetic fields than others, astronomers can use insensitive lines as a baseline from which to measure the broadening of sensitive lines. However, this method only gives an estimate of a magnetic field because it is highly model dependent (Donati, 1998).

2 3.3 Zeeman-Doppler Imaging In general, doppler effects tend to confuse magnetic field measurements. However, in the case of fast-rotating stars, one can measure the polarization signature as it varies with rotation. These measurements, along with a stellar surface model, can be used to reconstruct complex magnetic field configurations. This is by far the most successful model to date, though it has limited applicability.

4 Application: Magnetic O Stars

O stars are very hot, luminous, and massive stars. High-energy ultraviolet radiation from these stars effi- ciently ionizes everything in their near neighborhood, including their stellar winds. Magnetic fields have been detected on only a few O stars, in part due to a lack of emission lines in their spectra. The first detection of a magnetic field on an O star, Θ1 Orionis C, was accomplished by Donati et al in 2002. A second magnetic field was detected on O star HD 191612 in 2005 (Donati et. al., 2006), and two more in 2008 (Petit et. al., 2008).

4.1 Magnetically Conﬁned Wind Model

The observations of both HD 191612 and Θ1 Orionis C are consistent with a model developed to describe a class of stars called ”chemically peculiar” Ap and Bp stars (Donati et. al., 2002). In this model, the star has a large scale dipolar field, with the axis of the magnetic dipole tilted some angle from the stellar axis of rotation. The effect of an off-axis field along with the coupling of the magnetic field lines to the plasma will create a very complex magnetic topology on the small scale, but it is still possible to discuss overall motion. The radiation pressure from the star pushes out an ionized stellar wind, and at the magnetic poles, it is free to escape. However, the stellar winds emanating from the rest of the stellar surface will be redirected by the magnetic field lines towards the magnetic equator. At the magnetic equator, the accelerated winds from the Northern and Southern hemispheres collide, creating a shock wave and a decretion disk (Babel & Montmerle, 1997). The disk and the rest of the material that has been processed through the shock will emit X-rays that are detectable from Earth. Since the magnetic axis of the star is different from its rotational axis, we are able to observe rotational modulation of several aspects of the spectrum, including x-ray emission from the disk (alternating between face-on and edge-on), measured mass loss rates (due to appearance and eclipse of magnetic pole), and wind sensitive spectral lines (called UV resonance lines). Rotational modulation of polarization signatures are also observed and relied on heavily for Zeeman-Doppler Imaging.

5 Conclusion

New spectropolarimetry detection techniques and instrumentation promise to reveal topologies of the important, and long overlooked, magnetic fields of stars. Future observations should illuminate the question of magnetic field origin, as well as the influence of magnetic fields on stellar evolution. As progressively weaker magnetic fields are detected, such as those in O-stars, stellar theory will face an important test. These observations will help us to better understand the full picure of a star’s lifetime.

6 Annotated Bibliography

Babel, J.; Montmerle, T. (1997). X-ray emission from Ap-Bp stars: a magnetically conﬁned wind-shock model for IQ Aur. A&A 322:121-138. http://adsabs.harvard.edu/abs/1997A%26A...323..121B

Description of magnetically-confined wind-shock model for Ap-Bp stars, with kilo-Gauss magnetic fields. The magnetic field of the star is considered to be dipolar (though the poles may not align with the stellar rotational axis) and unchanged by the wind. The wind is considered to be radial and radiatively driven. The magnetic field lines redirect the stellar wind towards the equator, forming a shock which dissipates the kinetic energy. The material then cools and begins to form a disk a the equator.

Donati, J.-F.(1998). Surface Magnetic Fields of Non-Degenerate Stars. ESO Astrophyiscs Symposia, ”Cycli- cal Variability in Stellar Winds”. New York: Springer-Verlag. p.212. http://adsabs.harvard.edu/abs/ 1998cvsw.conf..212D

3 Review paper on the stellar magnetic field detection. Includes a summary of techniques in use, as well as a list of all types of stars for which magnetic fields had been detected (as of 1998). Also inculdes a discussion of the effect of magnetic field topologies on stellar winds, including wind confinement and decretion disks.

Donati, J.-F.; Babel, J.; Harries, J.T.; Howarth, I.D.; Petit, P.; Semel, M. (2002). The magnetic ﬁeld and wind conﬁnement of Θ1 Orionis C. MNRAS, 333:55-70. http://adsabs.harvard.edu/abs/2002MNRAS. 333...55D

Spectropolarimetric observations of Θ1 Orionis C taken with the Anglo-Australian Telescope. The observations confirm a predicted dipole B-field of 1.1 ± 0.1 kG, consistent with the model for a magnetically- confined wind-shock by Babel and Montmerle(1997). The B-field of this star is thought to be of fossil origin (vs dynamo). Additionally, they inspect all archival data sets published on Θ1 Orionis C in litera- ture to check for consistency with the magnetically confined wind-shock model and find a ”satisfactory” level of agreement, with the caveat that the mass loss rate must be reduced by a factor of five from radiatively driven wind models.

Donati, J.-F.; Howarth, I.D.; Bouret, J.-C.; Petit, P.; Catala, C.; Landstreet, J. (2006). Discovery of a strong magnetic ﬁeld on the O star HD 191612: new clues to the future of Θ1 Orionis C. MNRAS 365:L6-L10. http://adsabs.harvard.edu/abs/2006MNRAS.365L...6D

A spectropolarimeter mounted on the Canada-France-Hawaii Telescope yeilds the discovery of a strong dipolar B-field of -1.5 kG around the young Of?p star, with the magnetic poles tilted significantly with respect to the rotation axis. Based on previously measured spectral variability along with their data, they suggest an unusually slow rotation rate of 538 days, which they propose is caused by the dissipation of angular momentum in a magnetically confined wind. They discuss the various variable parameters of the star and use the magnetically confined wind-shock model to explain them, such as rotationally modulated X-ray emission and mass loss rates. Rough calculations of magnetic braking indicate that this star could be an evolved version of Θ1 Orionis C, with the magnetic field having dissipated rotational angular momentum.

Griﬃths, David J. (1995). Introduction to Quantum Mechanics. New Jersey: Prentice Hall. p. 244-246

Full derivation of Weak-Field Zeeman Splitting.

Hood, Alan (1999). The Sun: An Introduction to MHD. Online book accessed 5/10/2008. http:// www-solar.mcs.st-and.ac.uk/~alan/sun-course/solar.html In depth derivation of Magnetohydrodynamics, with applications for the Sun.

Neiner, c. (2007). Magnetic Field Measurements in OB Stars. ASP Conference Proceedings, Active OB- Stars: Laboratories for Stellar and Circumstellar Physics. Vol. 361, p.91. http://adsabs.harvard.edu/ abs/2007ASPC..361...91N

Review paper summarizing detection methods for stellar magnetic fields. Neiner lists all instruments currently in use for the purpose of detection. He discusses types of OB stars and summarizes current theory regarding the magnetic fields of each. Also included is a list of different types of OB stars, and all the searches for magnetic fields that have been conducted on each, with the statistical outcome. At the end of the paper, he lists the open questions in the field, namely magnetic field origin, an observed correlation between obliquity and rotation rate that remains unexplained, decretion disks around Be stars, and if Herbig Ae/Be stars are the progenitors of Main Sequence Ap/Bp stars.

Petit, V.; Wade, G.A.; Drissen, L.; Montmerle, T.; Alecian, E. (2008) Discovery of two magnetic massive stars in the Orion Nebula Cluster: a clue to the origin of neutron star magnetic ﬁelds? MNRAS Online Early 04/2008. http://adsabs.harvard.edu/doi/10.1111/j.1745-3933.2008.00474.x

Two new magnetic O-stars detected, HD 36982 with field strength 1.15 (+0.32, -0.2) kG, and HD 37061 with field strength 0.650 (+0.22, -0.17) kG. They claim these measurements to favor the fossil theory of origin, since these stars do not have a strong dynamo mechanism and their envelopes are largely radiative, not convective (convection is a primary source of dynamo magnetic fields.) Implications for core-collapse supernovae are discussed, in particular as a way to explaing the observed magnetic fields present in supernova-remnant neutron stars.