Stellar Magnetic Fields and Signatures of Heating Jeffrey Linsky JILA, University of Colorado and National Institute of Standards and Technology (NIST) Boulder Colorado USA COSPAR Session D2.2/E3.2 Beijing China 17 July 2006

Important questions concerning magnetic fields and heating What can be learned empirically about stellar magnetic fields and large-scale structure? Are there useful scaling laws that relate magnetic properties to heating? Are there thresholds where the magnetic structure and heating change character? Are active stars scaled up versions of the Sun? What is the most useful independent variable for relating magnetic fields to heating?

Measuring magnetic fields using Zeeman line broadening (unpolarized light): Assumptions Excess broadening of high Landé g factor lines compared to low Landé g factor lines measures the unsigned magnetic field (B) and filling factor (f) in the photosphere. Magnetic regions are assumed to have a single value of B (or a few values) and nonmagnetic regions have B=0. Field are lines oriented radially in the photosphere. Thermal structure of the magnetic and nonmagnetic regions is assumed to be the same. [Unlikely to be true. Leads to errors in f but not in B.] This technique avoids severe cancellation. [At solar maximum, the net polarization signal would give B=2 G amplitude.] Best to observe in the IR because λ B / λ D ~ λ. For large B see the Zeeman spliting. For small B see only broadening.

Zeeman broadening of the T Tauri star TW Hya (K7) assuming 4 regions of different B (From Valenti and Johns-Krull (2001))

Zeeman broadening of the flare star EV Lac (from Johns-Krull and Valenti (1996)). Bf=2.3 kG

Magnetic parameters and relations (Valenti and Johns-Krull ASP 248, 179(2001)) Equipartition (magnetic pressure = gas pressure): B² eq =8πP g. B/B eq ≈1 for normal dwarfs but larger for very active stars (starspots?) [Wilson depression] f small for inactive, slowly rotating stars but large for rapid rotators. Magnetic coverage “saturation” (f≈1) when P<1 day. Bf ≈ (1.5kG)(0.01) ≈ 15G for Sun to (4kG)(1.0) ≈ 4 kG for very active stars (a factor of 270 in magnetic flux).

Activity “saturation” (measured by UV or X-ray emission) is related to the Rossby number R o = P rot /т conv (from Sterzik and Schmitt (1997))

Other methods for determining that stars have magnetic fields Radio emission [gyroresonance (T ≈ 10^7 K), gyrosynchrotron (T>10^9 K), or coherent (T>10^12 K)] Channeled flows (accretion from disk to star) Very strong X-ray and UV emission lines Starspots (rotational modulation signal) Flares (radio to gamma rays) Stellar cycles (UV and X-ray)

Maps of H I density in the astrospheres of stars due to interaction of the ISM and stellar wind (Wood et al. ApJ, 628, L143 (2005))

Blue side of Lyα absorption showing effects of increasing mass loss (Wood et al ApJ 628 (2005))

Stellar wind mass flux vs. activity (measured by X-ray surface flux) Wood et al. ApJL 628, L146 (2005). From analysis of Lyman-α astrospheric absorption. Power law correlation until F x = 8x10^5, then a sharp drop. ε Eri: P rot ≈ 11.7 days, f ≈ 0.1. ξ Boo A: P rot =6.43 days, f≈0.2. Transition corresponds to activity level where polar spots become prominent. Large-scale magnetic geometry changes from solar- like (isolated active regions) to a more dipolar-like field with f ≈ 0.1 and a torroidal component.

Simulations of photospheric magnetic fields for a sun-like star with different rotational periods (activity levels) Schrijver & Title ApJ 551, 1099 (2001). Models with solar parameters (granulation, supergranulation, meridional flow, differential rotation, 11 year cycle, etc.) Only change is number of magnetic bipoles emerging per day: A 0 =1 (Sun) to 30 (active). When A 0 =30, Bf≈10xsolar max, P rot ≈6 days. For A 0 =30 model, magnetic flux densities near pole would make large spot areas (opening angle 25 degrees, B≈2 kG, and f ≈1. Rings of opposite magnetic polarity near pole could easily produce large prominences, flares, and coronal mass ejections. These phenomena observed on AB Dor (Collier Cameron, Donati, Hussain, Jardine).

Zeeman-Doppler imaging of AB Dor (Donati et al. 1999) K0 V, Myr, P rot =0.51 d. ZDI with Stokes I and V. Spots mostly at pole (area 9%, B=400 G, f=0.5). Radial field (Bf>1 kG) in regions of opposite polarity. Azimuthal field (Bf>1 kG). Belt surrounding rotational pole at deg. (Also HR 1099) Differential rotation like Sun (equator faster than pole). Evidence for a distributed magnetic dynamo in the convective zone. Log F x = 8.0 (very active).

AB Dor: prominences and magnetic geometry Time drifts of absorption features across disk indicate 16 “slingshot” prominences (Donati et al 1999). 4 prominences seen twice show magnetically enforced corotation with photosphere. Absorbing gas at R star. (corotation radius ≈3 R star ) Anchored at high latitude. Lifetimes short in indicating reorganization of coronal magnetic fields.

Nonpotential magnetic field of young rapid rotator AB Dor (Hussain et al. ApJ 575, 1078 (2002)) ZDI analysis with a code that includes nonpotential fields. Free energy 14% of potential field in corona (20% at base). Nonpotential component of azimuthal field (right) due to electric currents in polar spot penumbra (70-80 deg latitude). Predicts large slingshot prominences with high latitude footpoints (mixed polarity). Consistent with flares and strong X-ray emission from polar regions of rapid rotators (e.g., 44i Boo, Algol).

Magnetic field structure of the moderately active star ξ Boo A (Petit et al. MNRAS 361 (2005)) G8 V star: P rot =6.43 days, log f X =6.1 (just to the right of the wind/X-ray boundary. Stokes I and V spectrophotometry Large-scale dipole component: B p ~40 G inclined ~35° to rotational pole. Large-scale torroidal component: B t ~120 G probably surrounding the magnetic pole. Small scale magnetic structure unresolved. Large-scale magnetic structure is very different from the Sun. Rotation 4 times faster than Sun.

Coronal activity regimes based on stars in clusters (Pleiades, IC 2602, IC 2391, α Persei, Hyades and the field) (Randich ASP 198, 401 (2000)) R o = P rot /т c (Rossby number) Linear regime: log R 0 = +0.6 to -0.8 (for sun-like stars P rot = 50 to 2 days). Saturation regime: log R 0 = -0.8 to -2.0 (P rot = 2 to 0.1 days). Supersaturation regime: log R 0 < Sun: log R 0 = +0.6

Theoretical chromosphere models of K2 dwarfs with two components (nonmagnetic regions heated by acoustic waves and magnetic flux tubes heated by longitudinal MHD waves). B 0 =2100 G, f 0 determined empirically from P rot. Increasing f 0 means less flux tube spreading with height, stronger shocks and more chromospheric heating. (Cuntz et al. ApJ 522, 1053 (1999)). Relation of Ca II emission to P rot from theoretical models is consistent with observations.

The effects of rotation on magnetic fields, heating, and coronal magnetic structures for solar mass stars P rot (days) Log f X ffB(G) Log R 0 A 0 Comments Quiet Sun, few active regions Change in wind vs. X-ray plot Azimuthal polar belt. Polar spots ? Saturation begins (log L X /L bol = -3) ? AB Dor. Coronal free energy 14%

Conclusions and suggestions for future research on “Magnetic coupling in solar and stellar atmospheres” Active stars are not scaled-up Suns. Their magnetic properties are qualitatively different. Rotation (not age) controls the input rate of magnetic bipoles (A 0 ) which controls the magnetic geometry and magnetic energy input, f X ~A 0. Magnetic field filling factor controls the spreading of flux tubes in the chromosphere and thus wave heating. Magnetic field geometry and filling factor in the corona likely control the wind, X-ray emission, flaring, etc. Important thresholds: log f X =5.9, 7.7 (P rot ≈ 12, ≈ 2 days). Saturation is unexplained but may involves negative feedback of the magnetic field on the internal velocities that amplify the field via the dynamo mechanism.