Essential Observations for
Stellar Dynamos
What we have, and what we
are missing
Steve Saar (CfA/SAO)
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….
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:
 total chromospheric signal (need to calibrate away photospheric
background, non-magnetic emission)
X-rays:

Not enough data typically… and flares complicate more, but
pure B
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
Lockwood, Radick et al
 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.)
pseudo-Butterfly diagrams: Prot vs. SHK
Donahue 1996
Donahue & Baiunas 1992
 See evolution of Prot over the cycle… gets at differential
rotation and active latitude migration, which leads to…
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
SDR vs. rotation (pre Keper)
Key:
X=F
+=G
=K
diamond=M
boxed=DI
large=HK
∆Ω ~ Ω
0.64
 =0.25 dex for Ω < 10
d-1
Saar 2009,2011
∆Ω tends to decline for Ω > 10 d-1, , mass dependence (Barnes)
 ∆Ω does not continue to increase(!) (at least not for all
SDR vs. rotation: Rossby number
Key:
X=F
+=G
=K
diamond=M
*
boxed=DI
Saar 2009,2011
Fits are to maximum ∆Ω seen in single dwarfs, F5 and later.
For Ro-1 < 90,
For Ro-1 > 90,
 =0.24 dex
 =0.30 dex
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
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:
(Bastien et al 2013) ?

Erodes AR – get from
?
Dimensionally, sometimes estimated from α ~ Lv .
Is this good enough??
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 ~ 10-3
for Ro-1 > 80, saturation
!
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” rotationactivity 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
log R’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)…
box = dwarf; + = evolved
log M/H
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
HK/SHK (%)
MM
•Sample:
<Teff> = 5610 ± 379 K
<[M/H]> = -0.015 ± 0.228
(but a low activity bias!)
box = dwarf; + = evolved
log R’HK
# years obs.: 4,5,6,7
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)
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)
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”!)
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 !
The Evolution of SDR (combined view)
Arrow of time:
∆Ω - Ro
Lx/Lbol (B) - ∆Ω
Lx/Lbol - Ro
∆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.
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
SDR vs. age (from gyrochronology)
Key:
diam.=phot
box=HK
circle=DI
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”(?)
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?
(so when does he start talking about…)
Stellar Activity Cycles
The SDR results help guide how best to explore cycle
properties. Previously (Saar & Brandenburg 2001)….
Single dwarfs
+ binaries,
evolved stars
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 secondary
Pcyc (smaller
connected
symbols) lie
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?
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/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.
Ro<<0.1 poloidal/axisym.
Ro ~0.1-2 toroidal/non.-axisym.
Ro>2 poloidal/axisymmetric
Three dynamo modes?
Three regimes?
Main Pcyc: AHK ~ Ro0.3
Pcyc(2nd): AHK ~ Ro-0.4
Transfer of energy to higher
order modes as Ro-1 increases?
Size ~ B
Round/star – axisymmetry
Red/blue – poloidal/toroidal
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. Nonaxisymmetric 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 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
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
Key:
X=F
I branch
@
various
ages
+=G
=K
=M
box=DI
bold=FTLP
large=HK
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.
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…
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
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-activityage 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
•
Magnetic Cycles IV. Bright or
Look at the sign of the A
-Dark?
A
relation (Radick ea 1998, Lockwood
ea 2007)
HK
pho
•
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
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 Maunderlike minima are rare.
Is the Sun an oddball for having magnetic minima?
Important for Climate, dynamos, Sun-in-time evolution
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? II
Do 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
log R’HK
•Flat log R’HK<-5.1 MM
level inappropriate
• Instead, look for MM
stars near bottom
dwarf R’HK boundary
log M/H
+ = 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.
HK/SHK (%)
MM
•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
log R’HK
*= dwarf; += evolved
Are Maunder-like minima rare? IV
Answer(?): 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 Xrays 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
Data: seasonally averaged HK,photometric RMS (includes active
longitude flip-flops, some AR growth/decay)
•
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(shortterm)1.31
SDR vs. rotation II: Rossby Number
Key:
X=F
+=G
=K
=M
box=DI
bold=FTLP
large=HK
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
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?