Circular Polarization in Magnetized Wind Recombination Lines

1. Circular Polarization in Magnetized Wind Recombination Lines Kenneth Gayley Univ. of Iowa

2. Why wonder if hot-starwinds have B fields? • the solar analogy • impact on star formation • transport of angular momentum • circumstellar and wind dynamics • end stages: SN, GRB

3. Why hot-star winds shouldnot have B fields • lack of large surface convection zones • often fast rotators with strong winds • radii of order 10 times solar, diluting B

4. Why hot-star winds shouldhave B fields • fossil fields (global?) • buoyant above core convective zone • shear instabilities near surface • X-rays (from confined coronae?) • equipartition with wind energy (~100 G)

5. Why hot-star windsdo have B fields • observed in young Ae/Be stars • observed in chemically odd Ap/Bp stars • explain line profiles from sigma Ori E • hot stars certainly have bright E&M

6. Rigidly rotating magnetospheremodel for sigma Ori E Line emitting plasma is confined and forced to corotate with the tilted dipole field. Model by Townsend and Owocki (2004).

7. Scales of the magneticfield in time and space • global configurations (dipole or radial) • rotational modulation of starspots • small-scale loops and CIRs–- X-rays? • microscopic and stochastic (E&M)

8. Scales of the magneticfield in time and space • global configurations (dipole or radial) • rotational modulation of starspots • small-scale loops and CIRs–- X-rays? • microscopic and stochastic (E&M) -- B fields propagate E fields to Earth

9. Scales of the magneticfield in time and space • global configurations (dipole or radial) • rotational modulation of starspots • small-scale loops and CIRs–- X-rays? • microscopic and stochastic (E&M) -- B fields propagate E fields to Earth -- B fields drive the wind (classically)

10. How do B fields (classically) drive a hot-star wind? • typical O-star stochastic B is ~ 100 G • stochastic E is the same (E&M) • both stochastic, but correlated tightly -- E field jiggles, Lorentz force drives -- Lorentz force is mostly on bound e

11. How stochastic (E&M) B fields drive free electrons Radiative reaction causes the damping that allows the E field to do work against the velocity, requiring a phase angle that in turn creates a Lorentz force that drives the wind

12. How stochastic (E&M) B fieldsdrive bound electrons When there is an elastic binding force, driving at the resonant frequency allows the binding force to provide the circular acceleration, leaving the E force free to do work in phase with v, creating a huge v and a huge outward Lorentz force

13. How a constant shifts the resonance frequency At resonance, v is perpendicular to the binding force, so the Lorentz force of the constant alters the binding force and changes the resonant frequency by half the cyclotron frequency (classically)

14. Summary of how B fields yield Zeeman shifts • the Lorentz force from a radial B helps/hinders the atomic binding • the effect alters the binding resonance frequency, similar to how motion gives a Doppler shift • the classical shift is half the cyclotron frequency • shift is ~1 km/s at 1000 G

15. The problem with magnetic detection in wind lines • cancellation of circular polarization due to Doppler mixing yields B/v residual • surviving signal is ~ 0.1% for B in 100 G and v in 100 km/s • winds are where the v is higher and B is lower than at the surface • if the lines go effectively thick, they will form too far out, and I(x) will swamp V(x)

16. The value of magnetic detection in winds • WR stars: we see only the wind • B field effects in winds: X-ray generation • torque and spindown happens in the wind • as with MDI of surface fields, spectral resolution gives spatial information • unlike MDI, radial information allows non-potential field extrapolation

17. Current and Planned Observationsof B Fields in Massive Stars Tau Sco mapped with ESPaDOnS The MiMeS project: the search for magnetic massive stars

18. “Heartbeat” polarization for radial B proportional to v

19. % Circular polarization for 100G at 100 km/s (effectively thin lines, homogeneous expansion, split monopole field)

20. Polarization affects: • formation depth (“gradient effect”) • width of radial bin (“stretching effect”) • angle to the radial (“angle effect”) • shape/size of resonance zone (“morphing effect”)

21. What are the signatures of radially swept fields? • V(x) is antisymmetric if stellar-disk effects are small, i.e., for strong emission lines • Thin lines give V(x) signal that integrates to zero on each side of the profile • radial B fields mimic a change in the velocity law: I(x+) = [1-B/v] I( [1-B/v]x ) • then V(x) ~ B/v times [I(x) + xI’(x)] • “heartbeat” waveform helps distinguish signal from noise

22. Conclusions about magnetic fields in hot stars and winds • B fields exist and do interesting things in hot-star winds • classical pictures are useful for understanding what the fields do • observational capabilities are just now coming online: ESPaDOnS and NARVAL • signal will be weak, theory is “proof”

24. Conclusions about magnetic fields in hot stars and winds B fields exist and do interesting things in hot-star winds classical treatments are useful for understanding what the fields do observational capabilities are just now coming online: ESPaDOnS and NARVAL signal is so weak that theoretical support is crucial

25. V profile in strong but effectively thin emission lines • set by B/v in the deepest visible regions, about 0.1% for B=100 G and v=100 km/s • a radial B effectively increases/decreases the wind velocity for the two polarizations • antisymmetric V(x) globally regular B • then V(x) ~ B/v times [I(x) + xI’(x)] • “heartbeat” waveform helps distinguish signal from noise

26. Emission line profiles from spherically symmetric winds When the winds are spherically symmetric, it is helpful to take the point of view of the emitting gas, and integrate over the observers, rather than the other way around

27. Split monopole B fields allowa similar symmetry simplification In a strong wind, the B field should be radial, but the sign must reverse to avoid net flux– that would break spherical symmetry, but we can return it if the magnitude is symmetric: split monopole

28. Wind emission lines and the “big star” effect • in dense winds, like WR, the star simply looks much bigger at line frequencies • this is often how lines appear in emission • if light escapes the zone where it was born, it escapes the whole wind • the line formation is essentially a collision process, if zones are “effectively thin”

29. I(x) and V(x) / I(x) for splitmonopole with linear expansion

30. Hot Stars: live fast and die young Galactic luminosity, chemical enrichment, energetic flows, and cosmic rays are all largely due to hot, massive stars, up to a hundred times more massive and a million times more luminous than our Sun.

31. Evidence for large-scale circumsolar magnetism http://solar-heliospheric.engin.umich.edu/hjenning/Corona.html

32. Hot emission from confinedgas in solar magnetic loops

33. Convective regions in different mass stars

34. The Good News For radio: • ultra low attenuation • excellent spatial resolution • thermal free-free signatures • nonthermal diagnostics of acceleration For X-rays: • fairly low attenuation • important energy channel for hot gas • temperature-sensitive spectral lines

35. The Not-So-Good News: For radio: • uncertainty in acceleration and B fields • thermal emission is a weak energy component • density-squared sensitivity to clumping For X-rays: • self-absorption may remove some sources • trace energy channel when nearly adiabatic • again the density-squared clumping sensitivity

36. Good/Bad News for Adiabaticity Cluster outflows with are expected to be primarily adiabatic. The good news: • energy bookkeeping is made easier • gas gets hot enough to emit X-rays • high pressure resists clumping The bad news: • bulk of energy is not directly observable • radiative efficiency becomes a critical parameter which is sensitive to clumping and ionization

37. Patterns and Turbulence Importance of clumping motivates a better understanding of compression and turbulence: • Patterned compression (standing shocks, slowly propagating working surfaces) could yield geometry dependence and intermittency • Compressible turbulence involving scale-invariant perturbations gives a log-normal density profile But either way, the potential for strong clumping implies that a tiny fraction of the mass may be responsible for the observed emission

38. Density Distributions Define characteristic densities: In general:

39. Contrast with Single Filling Factor emission filling factor: mass filling factor: but for log-normal: single filling factor: and therefore: so in this case: !

40. Scaling with Filling Factor If emission measure (EM) and volume (V) are observed: one-component clumps: log-normal clumps: scales as: scales as: scales as: scales as:

41. B Fields vs. Ram Pressure • Zeeman splitting in molecular clouds gives • synchrotron emission from cluster outflows • B affects dynamics when , so when • may matter close to star where , or far from cluster core where • May explain radio filaments (Yusef-Zadeh 2003), and might also alter outflow dynamics (Ferriere, Mac Low, & Zweibel 1991)

42. Dipole Field Effects on Wind From ud-Doula & Owocki (2002)

43. Conclusions • Resonant character of nonthermal radio lets it trace particle distribution (but… relativistic tail only) • Thermal radio is a high-density diagnostic (but… is insensitive to T and oversensitive to clumping) • Thermal X-ray is a good diagnostic of both density and T for hot gas (but… is also sensitive to clumps) • Radiative efficiency is a key issue in adiabatic limit • One-component clumping factor is likely too naive • Blowouts and leaky shells reduce thermal energy and limit bubble size • B fields may affect winds close to stars and flows far from cluster, and light up nonthermal filaments