What we have, and what we are missing - PowerPoint Presentation

Slide1

What we have, and what we are missing

Steve Saar (CfA/SAO)

Essential Observations for Stellar Dynamos

Slide2

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…

Slide3

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

)

Slide4

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…

Slide5

Get:

cycle period

Pcyccycle amplitude Acyc Also:

rotation period P

rot

(multiple times, most usefully!)

active longitudes

multiple

P

cyc

(younger stars)

polarity (with ZDI, but few stars, short

timeseries

)

intermittency (cycle on/off)

pseudo-”butterfly” diagrams (P

rot

vs

F

HK

over

P

cyc

)

background level (turbulent dynamo?)

Slide6

Ca II HK

vs.photometry

AHK vs

A

phot

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

Slide7

pseudo-Butterfly diagrams: P

rot vs. SHK

See evolution of Prot over the cycle… gets at differential rotation and active latitude migration, which leads to…

Donahue &

Baiunas

1992

Donahue 1996

Slide8

Looking under the hood: What makes a dynamo tick?

Mean-field

αΩ Dynamo number: D ~

α

ΔΩ

R

3

/η

2

R is easy enough, but the others?

Start with differential rotation

ΔΩ

,

can get from:

changes in P

rot

Doppler imaging (spots; high

vsini

)

ZDI (B in

plage

; high

vsini

)

line shape (GK, high

vsini

)

Note: this is Surface DR… good enough?

Slide9

SDR vs.

rotation (pre Keper)

∆Ω ~ Ω

0.64



=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=DIlarge=HK

Saar 2009,2011

Slide10

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 ~

Ro

1.3



=0.30

dex

Key:

X=F

+=G



=K

diamond=M

boxed=DI

*

Saar 2009,2011

Slide11

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

T

eff

dependence.

Which is right? Know your stars!

Many evolved stars & binaries

Slide12

What makes a dynamo tick? II.

Mean-field

αΩ Dynamo number again: D ~

α

ΔΩ

R

3

/η

2

What about

α

? What

is

it exactly?

α

~ τ

c

/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??

Slide13

What makes a dynamo tick? III.

Mean-field

αΩ Dynamo number again: D ~

α

ΔΩ

R

3

/η

2

What about

η

? What

is

it exactly?

η

~ τ

c

/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??

Slide14

L

x/Lbol vs. Rotation (Rossby number)

L

x

/

L

bol

~

Ro

-

2.3



=0.27

dex

for Ro

-1

< 80

L

x

/

L

bol

~ 10

-3

for Ro

-1

>

80

, saturation

saturated Lx/Lbol

begins just where

∆Ω(Ro)

peaks

!

Key:

diamond=phot

b

ox=

HK

Circle=

DI

Size~



Slide15

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….

Slide16

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!…

Slide17

Slide18

Slide19

Slide20

Slide21

Slide22

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)

Slide23

New definition for MGM candidates:

Dwarf star

, confirmed by high res. spectral fit (

T

eff

, 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’

HK

box = dwarf; + = evolved

Slide24

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 S

HK

≤ 2%).

These are our new magnetic grand minimum candidates

.

MGM candidates: ~8% of sample dwarfs

Sample:

<T

eff

>

= 5610 ± 379 K

<[M/H]>

= -0.015 ± 0.228

(but a low activity bias!)

box

=

dwarf; + = evolved

# years obs.:

4

,

5

,

6

,

7log R’

HK



HK

/S

HK (%)

MM

Slide25

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) (

T

eff

,

d

CZ

dep.

i

nto



c

)

For Ro

-1

<

90

,

∆Ω ~ Ro

-0.90



=0.24

dexFor Ro-1 > 90, ∆Ω ~ Ro1.31



=0.30

dex

(

fit to maximum ∆Ω seen)

Key:

X=F

+=G



=K

diamond=M

boxed=DI

*

Slide26

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

Slide27

SDR vs. L

x/Lbol (proxy for B, dynamo)

Key:white =

dMe

circle=DI

box=HK

diamond=

phot

.

L

x

/

L

bol

~

∆Ω

1.36



=0.48

dex

for

L

x

/

L

bol

< 6x10

-4

(

Ω

< 10 d

-1

) Lx/L

bol

~ 10

-3

(for Ω > 10 d-1), saturation - for all ∆Ω !



Lx

/

L

bol

(and B?) a

maximum,

independent

of

∆Ω !

Slide28

SDR vs. L

x/Lbol (

The Answer is “7”!)

L

x

/L

bol

~

∆Ω

1.36



=0.48 dex for

L

x

/L

bol

< 6x10

-4

(

Ω

< 10 d

-1

)

L

x

/L

bol

~ 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

.

Slide29

The Evolution of SDR (combined view)

Initially:

∆Ω

~ Ro

+1.3

while

L

x

/L

bol

~

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. L

x

/

L

bol

is steady during the initial

∆Ω

increase, but decays once

∆

Ω

reaches a maximum

and

begins to decrease.

Arrow of time:

∆Ω

- Ro

L

x

/L

bol

(B) -

∆Ω

L

x

/L

bol

- Ro

Slide30

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=HKcircle=DI

Slide31

Starspot

amplitudes/distributions

Combine V band spot amplitudes Aspot for >1200 cluster/field single dwarfs

Maximum, mean

A

spot

and distribution all useful.

Connect

A

spot,max

: is there a “wedge” removed (

green

)?

Slide32

Starspot

amplitudes/distributions. II.

Simple models can work:Aspot,max ~ Ro-0.7 < A

max

(2 –

e

βRo

) (no “wedge” missing; dashed)

A

spot,max

~ [Ro

-0.7

< A

max

(2 –

e

βRo

)] -

DR(Ro

-1) (

“wedge”

gone; solid)

Increased shearing/decay of spots due to DR may explain drop in

A

spot,max

Data at high

A

spot

,

a bit sparse though…

Slide33

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(A

spot

) saturates at Ro

-1

> ~60, small drop around Ro

-1

~ 100?

A

spot,max

binned, shows sharp drop at

Ro

-1

~ 100, continued rise for larger Ro

-1

Slide34

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

A

spot

also rises, drops sharply to ~0 (~Gaussian) Ro

-1

> 100 (diamonds).

A

spot,max

,

A

spot

skewness

, and kurtosis all show sharp breaks at Ro

-1

~ 100, at the

A

spot

“wedge”, where DR slope changes sign and X-rays (and magnetic flux?) saturate. Coincidence?

Slide35

Stellar Activity Cycles

The

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

Slide36

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

P

cyc

(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….

Slide37

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 P

cyc

(2nd) (connected to main

Pcyc by vertical dotted)…

But secondary cycles are key here, bands are fairly wide –

Are

P

cyc

(2nd) true cycles (polarity reversing) or just amplitude modulations?

Or just a modulation on the main cycle?

Slide38

Are secondary

Pcyc

true cycles?

P

cyc

(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

P

cyc

(2nd),

A

HK,

have quite different behavior with rotation, suggesting a distinct phenomenon (Moss et al. 2008)

=

different cycle mode?

Main

P

cyc

:

A

HK

~ Ro

0.3

P

cyc

(2nd):

A

HK

~ Ro

-0.4

Transfer of energy to higher order modes as Ro

-1

increases?

Slide39

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?

Main

P

cyc

:

A

HK

~ Ro

0.3

P

cyc

(2nd):

A

HK

~ Ro

-0.4

Transfer of energy to higher order modes as Ro

-1

increases?

Size ~ B

Round/star –

axisymmetry

Red/blue –

poloidal/toroidal

Ro<<0.1

poloidal/axisym

.

Ro ~0.1-2

toroidal/non.-axisym

.

Ro>2

poloidal/axisymmetric

Three regimes?

Slide40

Three Regimes(?)

Highest Ro

-1

: DR minimal,

convective/turbulent dynamo

,

poloidal

,

axisymmetric

geometry, low dependence of rotation on activity, uniform generation so

A

spot

lower.

Intermediate Ro

-1

: DR near maximum, but models (

eg

, Brown et al.) indicate

v

merid

tiny, so no flux transport/

tachocline

dynamo - B production in

CZ dynamo

with high shear =

toroidal

. Non-

axisymmetric

so high

A

spot

(when DR is low enough).

Low

Ro

-1

: DR smaller again, v

merid

higher (from models) so here lies solar-like flux-transport/

tachocline

dynamos.

Lower B production and

axi

-symmetric so

A

spot

small again.

Restores an important role for DR(Ω) in cycles, magnetic field production and geometry

Slide41

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

Slide42

Slide43

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

A

cyc

increase with increasing CZ depth

to mid-K; spot/plage ratio increases with Primary/secondary cycles show opposite A

cyc

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!

Slide44

Slide45

Slide46

What’s up? Check color - P

rot diagram

Stars with increasing/decreasing shear neatly divide into Barnes’ I branch (Skumanich law Prot

~ age

0.5

stars; interface dynamo?) and

C branch

(P

rot

~ e

age

; convective dynamo?) stars.

Key:

X=F

+=G

=K

=M

box=DI

bold=FTLP

large=HK

I branch

@ various ages

C branch

@ various ages

Slide47

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)

Slide48

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…

Slide49

Magnetic Cycles III. Amplitudes

Ca II HK = plage/network data: Max A

cyc increases with B-V, peaks in mid K (Saar & Brandenburg 2002)

(avg A

cyc

(spot) increases towards lower masses; Messina et al.)

A

cyc

decreases with Ro

-1

; A

cyc

(2nd) increases with Ro

-1

- another sign of multimode dynamo? (Moss ea 2008)

Slide50

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.

Slide51

Magnetic Cycles IV. Bright or Dark?

Look at the sign of the

AHK -

A

pho

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)

Slide52

Magnetic Cycles V. Connection to DR?

Compare cycle and SDR data - again, only single dwarfs (

red are saturated, >DR break). Nothing so clear here….

Slide53

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?

Slide54

Slide55

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

∆M

v

= 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….

Slide56

Are Maunder-like minima rare?

Problem: Wright’s use of

∆M

v

confuses evolution and metallicity (M/H) differences. Cleanly separate dwarfs by using spectroscopically determined T

eff

and log

g

values (Valenti & Fischer 2005).

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

Teff - log g pic

Slide57

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 (S

HK

=C

core

/C

cont

; C

core

~ same

,

C

cont

 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

Slide58

Are Maunder-like minima rare? III

Dwarfs within

log R’

HK

≤0.06 (~+15%) of

R’

HK

(M/H) boundary show minimal variability (

HK

/S

HK

 ≤ 2%).

These are our new Maunder minimum star candidates

.

MM candidates:

T

eff



= 5730 ± 271 K

[M/H]

= -0.015 ± 0.400 6.1% of sample dwarfs

Sample:

T

eff



= 5610 ± 379 K

[M/H]

= -0.015 ± 0.228

 MMs have

narrower

T

eff but wider M/H distribution

*= dwarf; += evolved



log R’

HK



HK/SHK (%)

MM

Slide59

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 T

eff

gap 5100-5600 K (~K1 to G5), few cooler.

MM candidates more frequent in low and high metallicities.

Slide60

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.

Slide61

Slide62

Magnetic Cycles. RMS variation



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



pho

(long-term) ~ (F’

HK

/F

bol)

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)

Slide63

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 ~ Ro

1.31



=0.21 dex



a clear

decrease

with

Ro

-1

Key:

X=F

+=G

=K

=M

box=DIbold=FTLPlarge=HK

Slide64

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

, A

cyc

, 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