What we have, and what we

are missing

Steve Saar (CfA/SAO)

Essential Observations for Stellar Dynamos

Observations of Stellar Magnetic Variability

So, typically use proxies for B….

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…

Observations of Magnetic Proxies

X-rays: Not enough data typically… and flares complicate more, but pure B

Need long duration (decade+) data with decent coverage

Photometry: observe net differences in light – sum of spots and

faculae/plage. (Trick is to disentangle their effects, understand minimum level)

Ca II HK: total chromospheric signal (need to calibrate away photospheric

background, non-magnetic emission)

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…

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?)

Ca II HK vs.photometry

AHK vs Aphot 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

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 & Baiunas 1992Donahue 1996

Looking under the hood: What makes a dynamo tick?

Mean-field αΩ Dynamo number:

D ~ α ΔΩ 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?

SDR vs. rotation (pre Keper)

∆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)

Key:X=F

+=G

=K

diamond=M

boxed=DI

large=HK

Saar 2009,2011

SDR vs. rotation: Rossby number

Fits are 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

Key:X=F

+=G

=K

diamond=M

boxed=DI*

Saar 2009,2011

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

What makes a dynamo tick? II.Mean-field αΩ Dynamo number again:

D ~ α ΔΩ R3 /η2

What about α ? What is it exactly?

α ~ τc/3 < u’ ∨ x u’>

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??

What makes a dynamo tick? III.Mean-field αΩ Dynamo number again:

D ~ α ΔΩ 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??

Lx/Lbol vs. Rotation (Rossby number)

Lx/Lbol ~ Ro -2.3 =0.27 dex for Ro-1 < 80 Lx/Lbol ~ 10-3 for Ro-1 > 80, saturation saturated Lx/Lbol begins just where ∆Ω(Ro) peaks!

Key:diamond=phot

box=HK

Circle=DI

Size~

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….

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!…

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-Vitense etal 05)

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’HK to 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 M/H

log

R’ H

K

box = dwarf; + = evolved

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. RMS of 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!)

box = dwarf; + = evolved

# years obs.: 4,5,6,7log R’HK

HK/S

HK (

%)

MM

SDR vs. rotation: Rossby number

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)

Key:X=F

+=G

=K

diamond=M

boxed=DI*

What about ΔΩ and magnetic flux itself?

Should work… (Pevtsov et al 2003; TTauris excepted)

Not enough B measurements so use X-ray emission as a proxy

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 !

SDR vs. Lx/Lbol (The Answer is “7”!)

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 !

Key:white = dMe

circle=DI

box=HK

diamond= phot.

The Evolution of SDR (combined view)

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

∆Ω increases to a maximum as Ω declines, then decreases. Lx/Lbol is steady during the initial ∆Ω increase, but decays once ∆Ω reaches a maximum and begins to decrease.

Arrow of time:

∆Ω - Ro Lx/Lbol (B) - ∆Ω Lx/Lbol - Ro

SDR vs. age (from gyrochronology)

For Ro-1 < 80, ∆Ω ~ t -0.46 =0.27 dex standard 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 the tachocline/shear dynamo “takes over”(?)

Key:diam.=phot

box=HK

circle=DI

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)?

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…

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 at Ro-1 ~ 100, continued rise for larger Ro-1

Starspot amplitudes/distributions. IV. Higher order moments:Skewness Aspot 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 , Aspot skewness, 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?

Stellar Activity CyclesThe SDR results help guide how best to explore cycle properties. Previously (Saar & Brandenburg 2001)….

(so when does he start talking about…)

Single dwarfs

+ binaries, evolved stars

Activity Cycles I. Cycle Period

Nothing obvious at first….

• cyc ~ 0.0 ? (vis Barnes et al SDR? See also Olah et al 2009: cyc/Ω ~ -1)

• But consider where secondary Pcyc (smaller connected symbols) lie

(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….

Activity Cycles II. Cycle Period

• 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 ?

Consider Pcyc(2nd) (connected to main Pcyc by vertical dotted)…

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?

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?

Magnetic Fields/GeometriesHow 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?

Main Pcyc: AHK ~ Ro0.3

Pcyc(2nd): AHK ~ Ro-0.4

Transfer of energy to higher order modes as Ro-1 increases?

Size ~ BRound/star – axisymmetryRed/blue – poloidal/toroidal

Ro<<0.1 poloidal/axisym.Ro ~0.1-2 toroidal/non.-axisym.Ro>2 poloidal/axisymmetric

Three regimes?

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

Some side implicationsConvective 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

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, cyc shows 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!

What’s up? Check color - Prot diagram

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.

Key:X=F

+=G

=K

=M

box=DI

bold=FTLP

large=HK

I branch @ various ages

C branch @ various ages

Activity Cycles IIb. Cycle Period

• 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…

Try Rossby number & non-dim. cycle freq. (vis. Brandenburg etal. 1998)

Activity Cycles IIc. Cycle Period

• 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

OR… surrender to a lack of dependence! Fits not as good though…

Magnetic Cycles III. Amplitudes• Ca II HK = plage/network data: Max Acyc increases with B-V, peaks in mid K (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)

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.

Magnetic Cycles IV. Bright or Dark?• Look at the sign of the AHK - Apho relation (Radick ea 1998,

Lockwood ea 2007)

• Positive for low R’HK stars (vis Sun) - more activity = brighter plage/network dom.

• Negative in high R’HK stars - more activity = fainter spot dominated

(Exceptions are either evolved, or low significance)

• Correlation sign change seen in Sun in most active cycles too! (Foukal 1997)

Magnetic Cycles V. Connection to DR? Compare cycle and SDR data - again, only single dwarfs

(red are saturated, >DR break).

Nothing so clear here….

Magnetic Cycles V. Connection to DR?

• Messina & Guinan (2003) found (13 stars) branches with

cyc ~ Aiexp(-0.055/)• Need to look at this with the larger dataset! Another

connection to multimodes?

Long-term variations: minima

Is the Sun an oddball for having magnetic minima?

Important for Climate, dynamos, Sun-in-time evolution

The Sun clearly has magnetic Grand minima (and maxima) but their existence in other cool stars has been questioned recently (Wright 2004).

Wright found few low activity (log R’HK <-5.1) stars within ∆Mv = 1 of the Main sequence (log M/H= 0). He concluded that truly solar-like stars in Maunder-like minima are rare.

Answer: yes and no….

Are Maunder-like minima rare? Problem: Wright’s use of ∆Mv confuses evolution and metallicity (M/H) differences. Cleanly separate dwarfs by using spectroscopically determined Teff and log g values (Valenti & Fischer 2005).

When you do this, dwarfs may be separated independent of their M/H.

Teff - log g pic

Are Maunder-like minima rare? IIDo this and minimum activity (R’HK) in dwarfs is (apparently) a strongly decreasing function of metallicity M/H! Trend should be flat or even reversed (SHK=Ccore/Ccont; Ccore ~ same, Ccont at low M/H)

• Likely there is an HK calibration problem

• Flat log R’HK<-5.1 MM level inappropriate

• Instead, look for MM stars near bottom dwarf R’HK boundary

log M/H

log

R’ HK

+ = dwarf, x = evolved

Are Maunder-like minima rare? III

Dwarfs within log R’HK ≤0.06 (~+15%) of R’HK(M/H) boundary show minimal variability (HK/SHK ≤ 2%).

These are our new Maunder minimum star candidates.

• MM candidates: Teff = 5730 ± 271 K [M/H] = -0.015 ± 0.400 6.1% of sample dwarfs

• Sample: Teff = 5610 ± 379 K [M/H] = -0.015 ± 0.228

• MMs have narrower Teff but wider M/H distribution*= dwarf; += evolved

log R’HK

HK/S

HK (

%)

MM

Are Maunder-like minima rare? IVAnswer(?): No, ~8% of G dwarfs in sample are MM candidates. But

only ~1% of K dwarfs and ~3% of F dwarfs (all F8-9) are candidates. • Consistent with number of “flat activity” stars in solar-age M67 (Giampapa et

al 2006) if binaries excluded.

• No MM candidates in Teff gap 5100-5600 K (~K1 to G5), few cooler.

• MM candidates more frequent in low and high metallicities.

About the new Maunder-like candidates. • Mostly G5-F9 stars. All metallicities, but low and high M/H favored.

• About 8% of G dwarfs in Wright et al (2004) sample with HK are candidates. Sample is biased to low activity, tho!

• This is consistent with number of “flat activity” stars in solar-age M67 (Giampapa et al 2006) if binaries/outliers excluded.

• None of the MM candidates in the Wright et al sample has been detected in X-rays to date.

• Statistics are meager, but MM candidates in the Wilson cycle sample are consistent with being drawn from the same Ro-1 (~dynamo number) distribution of non-candidate dwarfs, if non-MMs are restricted to ages > 2 Gyr. MM candidates are rotationally indistinguishable from older (>2 Gyr), variable dwarfs. They are capable of cycles, but don’t have them now.

• Sun is not odd. Possibly all older early-mid G stars have some Maunder-like episodes. Young Sun did not.

Magnetic Cycles. RMS variation

• HK(long-term) ~ (F’HK/Fbol)1.15 (using Lockwood ea 2007)

• pho(long-term) ~ (F’HK/Fbol)1.85 (using Lockwood ea 2007)

• So pho(long-term) ~ HK(long-term)1.61

• And: pho(long-term) ~ pho(short-term)1.14 ; HK(long-term) ~ HK(short-term)1.31

Data: seasonally averaged HK,photometric RMS (includes active longitude flip-flops, some AR growth/decay)

SDR vs. rotation II: Rossby Number

Fits improved at high Ω if Ro-1 = c Ω is used (here from Gunn et al.)… mass dependence removed for GK stars.

For Ro-1 < 60, ∆Ω ~ Ro-0.85 =0.26 dex For Ro-1 > 60, ∆Ω ~ Ro1.31 =0.21 dex a clear decrease with Ro-1

Key:X=F

+=G

=K

=M

box=DI

bold=FTLP

large=HK

Some next steps… Repeat analysis for binaries: how does an external

gravity field affect SDR and dynamo action? Effect of mass ratio, eccentricity?

Repeat analysis for PMS stars: evolving convective dynamos, core radiative zone appears, when/how does SDR turn on? With what effect?

Repeat for evolved stars; deeper CZs - differences?

Look in more detail at connection between SDR and cycle properties (Pcyc, Acyc, multiple cycles, irregular variation)

Push the best models to higher Ω - is an SDR decline seen? When do tachoclines become less effective?

SDR in clusters - distributions/diversity as a function of mass at fixed age/metallicity