What we have, and what we are missing

1. Essential Observations for Stellar Dynamos What we have, and what we are missing Steve Saar (CfA/SAO)

2. Observations of Stellar Magnetic Variability • Ideally would like high res. vector B! But… • difficult observations, tricky analysis (various ZDI) • results typically low S/N, low spatial res. heavily averaged down B 0. • Still, of use! Only way to see polarity changes… So, typically use proxies for B….

3. Observations of Magnetic Proxies • Photometry: • observe net differences in light – sum of spots and faculae/plage. (Trick is to disentangle their effects, understand minimum level) • Ca II HK: • totalchromospheric signal (need to calibrate away photospheric background, non-magnetic emission) X-rays: • Not enough data typically… and flares complicate more, but pure B Need long duration (decade+) data with decent coverage

4. Ca II HK data • see clear cycles, not-so-clear cycles, multiple cycles, chaotic variability, constant emission, trends… • some calibration issues tho, at low S…

5. Get: • cycle period Pcyc • cycle amplitude Acyc Also: • rotation period Prot(multiple times, most usefully!) • active longitudes • multiple Pcyc(younger stars) • polarity (with ZDI, but few stars, short timeseries) • intermittency (cycle on/off) • pseudo-”butterfly” diagrams (Prot vs FHK over Pcyc ) • background level (turbulent dynamo?)

6. Ca II HK vs.photometry • AHKvsAphot to see dominance of bright B (plage/faculae) like Sun (positive corr.)dominance of dark B (spots) in more active stars (negative corr.) Lockwood, Radick et al

7. pseudo-Butterfly diagrams: Prot vs. SHK • See evolution of Prot over the cycle… gets at differential rotation and active latitude migration, which leads to… Donahue 1996 Donahue & Baiunas 1992

8. Looking under the hood: What makes a dynamo tick? Mean-field αΩ Dynamo number: D ~ αΔΩ R3 /η2 R is easy enough, but the others? Start with differential rotation ΔΩ, can get from: • changes in Prot • Doppler imaging (spots; high vsini) • ZDI (B in plage; high vsini) • line shape (GK, high vsini) Note: this is Surface DR… good enough?

9. SDR vs. rotation (pre Keper) Key: X=F +=G =K diamond=M boxed=DI large=HK Saar 2009,2011 ∆Ω ~ Ω0.64 =0.25 dex for Ω < 10 d-1 ∆Ω tends to decline for Ω > 10 d-1, , mass dependence (Barnes) ∆Ω does not continue to increase(!) (at least not for all masses)

10. SDR vs. rotation: Rossby number Key: X=F +=G =K diamond=M boxed=DI * Saar 2009,2011 Fitsare to maximum ∆Ω seen in single dwarfs, F5 and later. For Ro-1 < 90, ∆Ω ~ Ro-1.0 =0.24 dex For Ro-1 > 90, ∆Ω ~ Ro1.3 =0.30 dex

11. Interestingly, If you aren’t choosy… (Barnes et al 2005; Rheinhold et al 2013) If you don’t screen out binaries, early F stars, evolved stars: Lose most Ω dependence, retain some Teff dependence. Which is right? Know your stars! Many evolved stars & binaries

12. What makes a dynamo tick? II. Mean-field αΩ Dynamo number again: D ~ αΔΩ R3 /η2 What about α? What is it exactly? α ~ τc/3 < u’ ∨ xu’> Proportional to averaged small-scale kinetic helicity – we can estimate convective velocities, but what about twist? Dimensionally, sometimes estimated from α~ LΩ . Is this good enough??

13. What makes a dynamo tick? III. Mean-field αΩ Dynamo number again: D ~ αΔΩ R3 /η2 What about η? What is it exactly? η ~ τc/3 < u’ u’> Proportional to averaged small-scale velocity fluctuation – turbulent diffusivity; get from: • Kepler flicker (Bastien et al 2013) ? • Erodes AR – get from AR decay timescales? Dimensionally, sometimes estimated from α~ Lv . Is this good enough??

14. Lx/Lbol vs. Rotation (Rossby number) Key: diamond=phot box=HK Circle=DI Size~ Lx/Lbol ~Ro-2.3 =0.27 dex for Ro-1 < 80 Lx/Lbol ~ 10-3for Ro-1 > 80, saturation saturated Lx/Lbol begins just where ∆Ω(Ro) peaks!

15. What makes a dynamo tick? Other items of importance… Stars spin down due to magnetic torque in the stellar wind Spin down in turn effects dynamo B generation, so… Need to know mass loss (or have a good model for it) Data is sparse…. (Wood et al 2005, etc) Helicity losses too (Brandenburg, etc)? maybe from CME rates but almost no data….

16. What makes a dynamo tick? Other items of importance. II • What drives intermittency (Magnetic grand minima?) - mostly older stars (>1 Gyr), CZ depth dependence? • What are the secondary cycles? • Importance of meridional flows… • How does the spatial distribution of activity evolve? • How does the presence of a binary affect things? … and I’m probably forgetting your favorite!…

22. Revisit - Data to Use:Be a bit more picky! Any good quality SDR measurement, but only from • Dwarf stars: avoid evolutionary/structural issues • Single stars (or effectively so): avoid tidal effects • Stars ~F5 and cooler: drop stars with thinner CZ which do not follow the “standard” rotation-activity relationships (Walter 87, Bohm-Vitenseetal 05)

23. New definition for MGM candidates: • Dwarf star, confirmed by high res. spectral fit (Teff , log g) • Low activity: d log R’HK < -5.12 - 0.21 log M/H + dR’HK • Low variability: RMS R’HK variation < 2% (adjust dR’HKto keep optimize separation of potential MGM candidates). Stay flat for > 4 years (> solar minimum) d log R’HK ~ 0.06 gives good results (dashed line, see next slide)… log R’HK box = dwarf; + = evolved log M/H

24. Are Maunder-like minima rare? III Dwarfs within d log R’HK ≤0.06 (15%) of R’HK(M/H) boundary show low variability (fract. RMSof SHK ≤ 2%). These are our new magnetic grand minimum candidates. • MGM candidates: ~8% of sample dwarfs • Sample: <Teff> = 5610 ± 379 K <[M/H]> = -0.015 ± 0.228 • (but a low activity bias!) MM HK/SHK (%) box = dwarf; + = evolved # years obs.: 4,5,6,7 log R’HK

25. SDR vs. rotation: Rossby number Key: X=F +=G =K diamond=M boxed=DI * Fits improved if local c is used for ∆Ω(Ω) increasing, global c for∆Ω(Ω) decreasing (from Y-C Kim) (Teff, dCZ dep. into c) For Ro-1 < 90, ∆Ω ~ Ro-0.90 =0.24 dex For Ro-1 > 90, ∆Ω ~ Ro1.31 =0.30 dex (fit to maximum ∆Ω seen)

26. What about ΔΩ and magnetic flux itself? Not enough B measurements so use X-ray emission as a proxy Should work… (Pevtsov et al 2003; TTauris excepted)

27. SDR vs. Lx/Lbol (proxy for B, dynamo) Key: white = dMe circle=DI box=HK diamond= phot. Lx/Lbol ~ ∆Ω1.36 =0.48 dex for Lx/Lbol < 6x10-4 (Ω < 10 d-1) Lx/Lbol ~ 10-3 (for Ω > 10 d-1), saturation - for all∆Ω ! Lx/Lbol (and B?) a maximum,independent of ∆Ω !

28. SDR vs. Lx/Lbol(The Answer is “7”!) Key: white = dMe circle=DI box=HK diamond= phot. Lx/Lbol ~ ∆Ω1.36 =0.48 dex for Lx/Lbol < 6x10-4 (Ω < 10 d-1) Lx/Lbol ~ 10-3 (for Ω > 10 d-1), saturation - for all∆Ω !  Lx/Lbol (and B?) a maximum,independent of ∆Ω !

29. The Evolution of SDR (combined view) Arrow of time: ∆Ω - Ro Lx/Lbol (B) - ∆Ω Lx/Lbol - Ro ∆Ω increases to a maximum as Ωdeclines, then decreases. Lx/Lbol is steady during the initial ∆Ωincrease, but decays once ∆Ω reaches a maximum and begins to decrease. Initially: ∆Ω~ Ro +1.3 while Lx/Lbol ~10-3(saturated activity)Then ∆Ω ~ Ro -0.9 after Ro-1 ~ 80 or Ω < 10 d-1

30. SDR vs. age (from gyrochronology) Key: diam.=phot box=HK circle=DI For Ro-1 < 80, ∆Ω ~ t-0.46=0.27 dexstandard Ω spindown For younger stars, ∆Ω increases to this level, F stars by ~30 Myr, G stars by ~60 Myr, early K by ~120 Myr, late M by ~1 Gyr. = the age when thetachocline/shear dynamo “takes over”(?)

31. Starspot amplitudes/distributions Combine V band spot amplitudes Aspot for >1200 cluster/field single dwarfs Maximum, mean Aspot and distribution all useful. Connect Aspot,max: is there a “wedge” removed (green)?

32. Starspot amplitudes/distributions. II. Simple models can work: Aspot,max ~ Ro-0.7 < Amax(2 – eβRo ) (no “wedge” missing; dashed) Aspot,max ~ [Ro-0.7 < Amax(2 – eβRo )] - DR(Ro-1) (“wedge”gone; solid) Increased shearing/decay of spots due to DR may explain drop in Aspot,max Data at high Aspot, a bit sparse though…

33. Starspot amplitudes/distributions. III. 12 bins of 100 stars each; look at moments of distribution: Mean <Aspot> saturates at Ro-1 > ~60 (boxes) RMS σ(Aspot) saturates at Ro-1 > ~60, small drop around Ro-1 ~ 100? Aspot,max binned,shows sharp drop atRo-1 ~ 100, continued rise for larger Ro-1

34. Starspot amplitudes/distributions. IV. Higher order moments: SkewnessAspot dist. generally rises, sharp break to lower values (more symmetric dist.) at Ro-1 ~100 (boxes) Excess kurtosis Aspot also rises, drops sharply to ~0 (~Gaussian) Ro-1 > 100 (diamonds). Aspot,max , Aspotskewness, and kurtosis all show sharp breaks at Ro-1 ~ 100, at the Aspot “wedge”, where DR slope changes sign and X-rays (and magnetic flux?) saturate. Coincidence?

35. (so when does he start talking about…) Stellar Activity Cycles TheSDR results help guide how best to explore cycle properties. Previously (Saar & Brandenburg 2001)…. Single dwarfs + binaries, evolved stars

36. Activity Cycles I. Cycle Period (Work in progress….) Backtrack from Saar & Brandenburg (99,01), use only single dwarfs (vis SDR!) Update data with Frick et al (2004), Messina & Guinan (2001), plus…. Nothing obvious at first…. • cyc ~ 0.0 ? (vis Barnes et al SDR? See also Olah et al 2009: cyc/Ω ~ -1) • But consider where secondaryPcyc(smaller connected symbols) lie

37. Activity Cycles II. Cycle Period Consider Pcyc(2nd) (connected to main Pcyc by vertical dotted)… • 2 or 3 bands, separated by factors of 4, each with cyc ~ 1.3 • Possible break at  ~ 10 x solar - the same point where  slope changes…. • Multimode dynamo, quantized cyc steps with change in behavior with  at high ? But secondary cycles are key here, bands are fairly wide – Are Pcyc(2nd) true cycles (polarity reversing) or just amplitude modulations? Or just a modulation on the main cycle?

38. Are secondary Pcyc true cycles? Pcyc(2nd) are often shorter than primary cycle, sometimes just a few (2-6) years. Short, polarity reversing cycles are seen in a few stars: tau Boo (F9V; Donati et al 2008), HD 190771 (G5V; Petit et al 2009) Also: Fractional cycle amplitudes seen in HK of Pcyc(2nd), AHK, have quite different behavior with rotation, suggesting a distinct phenomenon (Moss et al. 2008) = different cycle mode? Main Pcyc: AHK ~ Ro0.3 Pcyc(2nd): AHK ~ Ro-0.4 Transfer of energy to higher order modes as Ro-1 increases?

39. Magnetic Fields/Geometries How does this all inform recent (ZDI) results on magnetic field strengths/geometries? Ro ~ 0.1 (below) is ~saturation: DR drops off to both sides. Three dynamo modes? Ro<<0.1 poloidal/axisym. Ro ~0.1-2 toroidal/non.-axisym. Ro>2 poloidal/axisymmetric Three regimes? Size ~ B Round/star – axisymmetry Red/blue – poloidal/toroidal Main Pcyc: AHK ~ Ro0.3 Pcyc(2nd): AHK ~ Ro-0.4 Transfer of energy to higher order modes as Ro-1 increases?

40. Three Regimes(?) Highest Ro-1: DR minimal, convective/turbulent dynamo, poloidal, axisymmetric geometry, low dependence of rotation on activity, uniform generation so Aspot lower. Intermediate Ro-1: DR near maximum, but models (eg, Brown et al.) indicate vmerid tiny, so no flux transport/tachocline dynamo - B production in CZ dynamo with high shear = toroidal. Non-axisymmetric so high Aspot (when DR is low enough). Low Ro-1: DR smaller again, vmerid higher (from models) so here lies solar-like flux-transport/tachocline dynamos. Lower B production and axi-symmetric so Aspot small again. Restores an important role for DR(Ω) in cycles, magnetic field production and geometry

41. Some side implications • Convective dynamo in rapidly rotating stars could explain (see also Donati et al …): • Low latitude spots (should be high latitude/polar if arising from tachocline dynamo) • Reduced activity changes with Ω on saturation branch • Reduced spindown rate in younger stars • Gradual convective> shear/tachocline dynamo transition could explain lack of activity break in mid M stars

43. Quick Summary • SDR increases as ~Ro-1 for low , but… • It drops at high ! Stars can have strong B and cycles with little  • Suggestion of dominance change convective dynamos – full CZ dynamos at highest  - tachocline driven at lower  • Cycle period relations more complex/less clear, cycshows evidence for quantized relations with  - some stars show multiple cyc …. Evidence for multimode dynamos? • Amplitudes Acyc increase with increasing CZ depth to mid-K; spot/plage ratio increases with  • Primary/secondary cycles show opposite Acyc trends with ; are secondary cycles different in some way? (not true cycles? Quadrupoles?) • SDR - cyc relations may also show multiple modes… needs more work A loud cry of help!! to theorists out there!

46. What’s up? Check color - Prot diagram Key: X=F +=G =K =M box=DI bold=FTLP large=HK I branch @ various ages C branch @ various ages Stars with increasing/decreasing shear neatly divide into Barnes’ I branch (Skumanich law Prot ~ age0.5 stars; interface dynamo?) and C branch (Prot ~ eage ; convective dynamo?) stars.

47. Activity Cycles IIb. Cycle Period Try Rossby number & non-dim. cycle freq. (vis. Brandenburg etal. 1998) • 2 or 3 bands, separated by factors of ~4, but slopes vary a bit cyc/ ~ Ro-A,B,C • Possible break at Ro-1 ~ 60 - the same point where  slope changes…. • Multimode dynamo, quantization(?) of cyc steps less clear here…

48. Activity Cycles IIc. Cycle Period OR… surrender to a lack of dependence! Fits not as good though… • 2 bands, separated by factor of ~4, cyc/ ~ Ro+1 (ie, no dependence) • Simpler, but many stars are poorly fit. Possible break at Ro-1 ~ 60 - the same point where  slope changes…. • But again, some suggestion of multimode dynamo/quantization(?) of cyc

49. Magnetic Cycles III. Amplitudes • Ca II HK = plage/network data: Max Acyc increases with B-V, peaksin midK (Saar & Brandenburg 2002) (avg Acyc(spot) increases towards lower masses; Messina et al.) • Acyc decreases with Ro-1; Acyc(2nd) increases with Ro-1 - another sign of multimode dynamo? (Moss ea 2008)

50. Summary: Two SDR regimes! • ∆Ω increases with Ω at low Ω: standard rotation-activity-age relations, Barnes’ I branch - solar-like tachocline/interface and/or CZ αΩ dynamo (local c best) • ∆Ω decreases with Ω at high Ω: saturated activity, shear dynamo less effective, Barnes’ C branch - so… convective/turbulent dynamo? (global c best) Evolutionary scenario: starting with low ∆Ω and high Ω and a convective dynamo, stars spin down gradually increasing ∆Ω until ∆Ω is large enough to “take over” (at ~60 Myr in G stars, ~120 Myr in early K, ~ 1 Gyr late M). Activity steady. Thereafter, the tachocline/shear/CZ dynamo is more dominant for spindown, and magnetic activity decreases.