Solar Irradiance, Diameter, Shape, and Activity

J.R. Kuhn, Institute for Astronomy, University of Hawaii

Rock BushMarcelo EmilioIsabelle SchollPhil Scherrer

GONG10, June 2010

What can we learn about thesolar cycle from precise“global” measurements?

…since 2002

• A solar cycle of MDI; HMI debuts

• More than a solar cycle of helioseismic measurements

• COROT, “night-time solar physics”

Global solar properties

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TBc

TRL

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Luminosity and irradianceLuminosity, radius, tempFrequency, magnetic field, temperature

‘Even’ m-dependent frequency splittings

Is solar the irradiance change primarily luminosity change?

Frequencies and F10.7

Broomhall et al. 2009

Even coefficient frequency splittings

Splitting coefficient temporal variability qualitatively describes surface magnetism changes

Its hard to change the solar surface temperature by changing solar luminosity

The solar limb is largely fixed by rapid opacity decline

“few km” thick transitionfrom opaque to transparent

90.5 TH

Solar radius, past results from under the atmosphere….

A fluctuating solar radius is seen from the ground

• 76 yr fluctuation with 0.2 arcsec half-amplitude

• 11 yr fluctuation, smallest sun at peak in sunspot number with 0.1 arcsec half-amplitude

76 yrs

Solar astrometry: Is the Sun shrinking?

• 0.05 – 0.2 arcsec/century

Gilliland, 1981

Limb astrometry from Space

drAngle of arrival fluctuations define dr

dIPhotometric gain uncertainty (flatfielding) defines dr

In practice limb isn’t knife edge, spacecraft pointing jitter is about 0.01 pixel (and correlated!),long term stability limitations are due to optics thermal drifts [(MDI) 1px=2”]

mas 0.4r pixels limb 3000

mas 20 dr intensity rms 1%

:MDI

s 45r pixels limb 12000

mas 5 dr intensity rms 1%

4K4K x :HMI

NB: Telescope diffraction limit has verylittle to do with astrometric accuracy

Limb Astrometry Systematic Errors

• Spacecraft pointing jitter (not limiting)– “coherent”

– MDI, 0.02 arcsec

• Optical errors (limiting) – Temporal stability

• Thermal changes, dimensional stability, index changes

– Spatial changes• Field focus variations

– Two orders of magnitude larger than solar signals (MDI, 0.5arcsec)

– “Roll” calibration essential

• MDI approach– Measure and calibrate all aspects of instrument

– PROVEN: Shape measurements essentially achieved photometric precision (i.e. oblateness/hexadecapole uncertainty 0.5 mas in 12 images)

HMI Solar Limb Astrometry • What Limb Astrometry from HMI?

– The solar radius– The solar radius variations with time (and oscillations)– The solar radius variations with central angle (shape, and oscillations)

• Why Do This With HMI?– Can’t be done on the ground with HMI accuracy (in some cases by two orders

of magnitude)– HMI will surpass MDI astrometric accuracy by at least one order of magnitude– These are difficult measurements, no other space experiment addresses the same

technical issues and no other space experiment reproduces the HMI astrometric approach

• What are the pressing questions?– Does the solar radius change (at all) with solar cycle?

• Knowledge of radius changes and irradiance or luminosity changes constrains the solar cycle mechanisms… a long debated problem

– What is the Sun’s shape and is this consistent with solar system limits on its gravitational potential and the internal rotation rate?

– Limb Oscillations (p-modes, g-modes, r-modes) dispersion relation information has yet to be carefully measured and interpreted

Satellite limb profiles

MDI Raw Radius Data

Calibrated MDI astrometry systematics

Front window: 6C gradient 1.5km focal length 0.84” Primary lens: 10C temperature focal shift -0.2”OSS expansion: 10C temperature change expansion 0.75”

Instrument changes

The solar radius change…

The solar radius over time

km

No solar cycle radius changes!

• W = dr/r / dL/L < 2 x 10-2

– Solar cycle luminosity is much smaller than irradiance change

– Solar asphericity and 2D atmosphere structure dominates dR and dL

– Solar cycle frequency changes not due primarily to changing geometry (s)

• Some models can predict small W, c.f. Mullan et al. 2007 (although H- opacity effects on ‘radius’ ignored? )

Asphericity and solar shape• Are solar cycle irradiance variations due to

redistribution of emergent solar luminosity?– Latitudinal variation, dR(μ)/R– MDI and HMI solar shape measurements

Modern ground-based solar shape measurements

Limb astrometry, MDI

6-50 pixel annulus))(1))((()( rIrI

480pix

MDI: 1.96” pixelHMI: 0.5” pix

HMI raw shape and limb photometry

See GONG10 Bush et al. poster

equator

pole

Rolling HMI separates solar shape from optical distortion

cos2θ

cos3θ

cos4θ

cos5θ

Satellite roll angle

MDI and HMI sun during some rolls has no magnetic activity

MDI: March 1997 HMI: April 9 2010 HMI: April 16 2010

MDI: Nov. 2009MDI roll in 2001 available, but active sun

HMI roll available every 6 months

Oblateness from 1997-2010MDI and HMI observations without magnetic corrections

1997 MDI 2009 MDI

2010a HMI 2010b HMI

MDI Solar minimum (1997) and maximum (2001) roll data

MDI limb shape analysis, magnetic contamination – e.g. 2001

• Magnetic contamination increases limb brightness, decreases limb radius

• Note scale: 40mas radius decrease, 0.01 intensity increase

After accounting for magnetic activity, the limb shape is still variable

Active latitutes:If we missed magneticcontributions, oblatenesswould be even larger!

Solar oblateness isn’t constant

But note: Fivian et al. 2007 from RHESSI claim 2006 oblateness is surface value

MDI and HMISolar shape data

RHESSI photometry technique

Fivian, Hudson, Lin, 2007

Oblateness coefficient variability from RHESSI

Helioseismic splittings also sample solar shape

• These are tiny shape variations, 2001 to 2010 Req-Rpole change is about 2.5km, smaller than our limits on the solar cycle mean radius variation

• Helioseismic “oblateness” (the “even” frequency splitting coefficients) are anticorrelated with geometric oblateness

• Acoustic (interior) atmosphere non-homologously expanding with respect to “surface” (Kosovichev, Lefebvre 1995, 1996)

• Oblateness changes are too small to account for even coefficient variations (and opposite in sign)

The solar brightness, ground, MDI, HMIGround Oblateness Measurements

HMI

MDI

Solar cycle acoustic changes

• Primarily NOT geometric effects (in mean frequencies or splittings)

• The solar atmosphere change with cycle is not well described by any 1-dimensional model (either magnetic or thermal)

• Diffuse, unresolved, magnetic flux and surface brightness is needed

“Superficial” vs. “seeing the tachocline”

• Tough problem: “everything” is correlated with possibly complex causal connections (cf. Basu et al. 2009 “hints of tachocline” visible in helioseismic time dependence)

• Magnetic vs. “thermal”

Deep origins of magnetized plasma must carry excess entropy to surface

ConvectionZone

RadiativeZone

Tachocline region

Photosphere

Over a solar cycle magnetized fluid over 11yrincreases entropy by 0.1% at base of SCZ

Radiative flux through magnetizedfluid sees lower opacity and increasedentropy relative to non-magnetized fluid

Solar cycle magnetic fields

Magnetized fluidis “hotter”

dzdTT

lCp

216

3

Thermal “antishadows”

Temperature gradient enhancedstable stratification becomes unstable

Alternatively, vertical surface B fields decrease vertical “irradiance”

The integrated disk brightness change due to bright faculae is 38% of the faint faculae

NB: cf. Ken Topka facular contrast results

“Bright” faculae are dark, at any wavelength neardisk center

Data from the Precision Photometric SolarTelescope

Continuum contrast vs. vertical orientation and CaK contrast

Magnetic fields and irradiance

Fast and slow B vs. irradiance

Fast variations: B increases “I” Slow variations: B decreases I

Frequency variations are not determined simply by solar activity

(from Broomhall et al. 2009)

Global photometric timeseries analysis

• Solar and stellar observations converge studies of resolved stellar magnetic

atmospheres are happening: Night-time solar physics

Spots and faculae may produce only a tiny luminosity pertubation (flux

redistribution)

dI

time

Use solar rotation to describe angular variation in active region or spot “irradiance” … luminosity

T/4

Full-disk observations show flux redistribution

(data high-pass filtered with 60dmoving-mean)

Regardless of phase of the solar cycle (min-to-max) the irradiance autocorrelation shows clear evidence that active regions (faculaea nd sunspots) redistribute flux. Low temporal frequency signal shows evidence of additional luminosity signal

CoRoT Photometry – stay tuned

Conclusions

• Very precise global solar measurements are important for understanding the solar cycle

• Solar cycle helioseismic effects are primarily thermal or magnetic sound speed effects (not geometry)

• One-dimensional models don’t convincingly account for cycle variations heterogenous, unresolved (mixed) magnetic field effects are required

Magnetized plasma from RZ is hotter

/cm]G -[yr / 10

/16

3

2212

2

Bl

dzdTT

lCp

BP6MG, lPP3E5cm3E5cm

At the top of the radiative zone...

Tachocline shear layer unresolved helioseismically,lO 0.018R (Schatzman et al. 2000)

10 yr/ 11 :amplitude cycle luminosity -3

cm]-[Mx/G 5E10

1996)(Parker 10 flux, azimuthal Total10

23

Bl

Mx

Tachocline region

l

A useful solar cycle model must connect and explain all of these observations, none exists yet

Surface brightnesschanges

Helioseismic changes

Irradiancechanges

• What was the question?

• Boundaries are great

• “Superficialist” problems

• Listening to the data

• Clocks

Driving the Solar Cycle

Irradiance changes

This plot shows the residual from the 150d moving means.

+0.1W/m^2/G -0.2W/m^2/G

The slow variations using 30d averages are plotted here

Helioseismic asphericity

(Vorontsov, 2002)

(Antia et al. 2001)

26 nHz/G

140 nHz/K

(1989)

Irradiance/luminosity change

• Suppose 4DT/T = DI/I, so 0.1W/m^2/G implies 0.1 K/G solar cycle change

• If magnetic field causes thermal stratification change and frequency shifts then 26/140 K/G = 0.18 K/G

The tachocline: Where luminosity perturbations come

from?

ConvectionZone

RadiativeZone

Tachocline region

Photosphere

Over a solar cycle magnetized fluid over 11yrincreases entropy by 0.1% at base of SCZ

Radiative flux through magnetizedfluid sees lower opacity and increasedentropy relative to non-magnetized fluid

Solar cycle magnetic fields

Magnetized fluidis “hotter”

dzdTT

lCp

216

3

Thermal “antishadows”

Temperature gradient enhancedstable stratification becomes unstable

Magnetized plasma from RZ is hotter

/cm]G -[yr / 10

/16

3

2212

2

Bl

dzdTT

lCp

BP6MG, lPP3E5cm3E5cm

At the top of the radiative zone...

Tachocline shear layer unresolved helioseismically,lO 0.018R (Schatzman et al. 2000)

10 yr/ 11 :amplitude cycle luminosity -3

cm]-[Mx/G 5E10

1996)(Parker 10 flux, azimuthal Total10

23

Bl

Mx

Tachocline region

l

More numbers...

1500G)-500 give B (IR500G B then

10)/(B/B ifWhat

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if

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if

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cm10

cm/s10dz

dvG GBdtdB

fields?such regenerateport flux trans and

rotation aldifferentiCan

yr

• During the solar cycle a thin layer of magnetized plasma at the top of the radiative zone is eroded away from above by convective penetration, brought on by this radiative instability. This “relaxation oscillator” could be characterized by the condition on B that leads to instability and the higher enthalpy per magnetic energy density.

• Observable: Flux which originates from the RZ must have a higher enthalpy/magnetic energy density than magnetized fluid generated by CZ or photospheric mechanisms.

Superficial two component (faculae+spots) irradiance models

• Models based on resolved CaK images or B flux have been used to “explain” irradiance

dItSItFctI spotfacbol ))(),()(),(()(

Observed time-variable irradiance

Observed time andlatitudinal facular/spot dist.(determined by proxy)

Facular/spot irradiance contrast function

.mis cosine central angle

),(),(or ),(),(

that so usedoften are proxiesCaIIK and B measure, todifficult is F

tkKtFtbBtF

Models which use a statistical fit to determine the coefficients b and k can account for 70-90% of theirradiance variability (c.f. Solanki, Lean and collaborators)

Superficial, two component faculae + spot models are empirical and imcomplete

The integrated disk brightness change due to bright faculae is 38% of the faint faculae

NB: Ken Topka substantially made this point 8 years ago!

“Bright” faculae are dark, at any wavelength neardisk center

Data from the Precision Photometric SolarTelescope

How does the convection zone transport heat?

• mixing-length diffusion conflicts

lvC

tT

CT

p

p

�

MLT convection fails to estimate SCZ conductivity

Non-mixing length theory (realistic) solar convection has highly correlatedvertical flows. The effective conductivity of the solar convection zone is farfrom mixing length theory approximations (images from Georgobiani Stein, and Kuhn)

small perturbations are diffusive butanisotropic and with conductivity muchsmaller than mixing length predictions

• Transport properties of the perturbed convection zone aren’t analogous to a “high conductivity silver slab.” Correlated flows over many density scale heights make the CZ anisotropic and not as well mixed as mixing length models predict.

Superficial models miss time dependence of irradiance componets

Spot and facular signals peak about 1 year before luminosity signal

F = 0.08E0.005 B -0.09E0.01 dB/dt

sunspot peak

Totalirradiance

Spots and faculae may produce only a tiny luminosity pertubation (flux

redistribution)

dI

time

We use solar rotation to describe angular variation in active region or spot “irradiance” … luminosity

T/4If irradianceis due to flux redistribution, its autocorelation must yield a negative “dip” at T/4=7d due to oppositesign flux enhancements between normal and near-tangentviewing angles

Full-disk observations show flux redistribution

(data high-pass filtered with 60dmoving-mean)

Regardless of phase of the solar cycle (min-to-max) the irradiance autocorrelation shows clear evidence that active regions (faculaeand sunspots) redistribute flux. Low temporal frequency signal shows evidence of additional luminosity signal. NB Frolich finds more complex behavior in VIRGO data...

Superficial models miss irradiance and luminosity

distinction

• Immediate effect of B flux appearing at low latitudes is to decrease irradiance (flux directed away from normal direction) -- this is dB/dt term of regression for I(t)

• Long term effect is from higher entropy magnetized plasma to increase solar luminosity in proportion to B flux

Superficial models miss diffuse irradiance component

Solar cycle changes

Photometry from Mt. Wilson,previous cycle implied thislimb temperature

Most of a solar cycle was obtainedfrom Mt. Wilson oblateness expt.

MDI Roll dataphotometry implythis limb temperaturedistribution

Phase properties

)](exp[)()( titAtf

Delayed Oscillator

RZ

CZ

Bf F(t) )()(

)()(

)()(

tGtFdtdF

dtdG

tFtGdtdF

dttFdttGdF

G(t)

dttFdGabs )(

dtdG

dtdG

dtdG emitabs

)( tGdGemitFlux storage and “heating” in RZ, G[a,e]Flux diffusion and winding in CZ, F[b,d]

222 :Linearized

Delayed Oscillator Output

Solar Cycle Effects

Delayed oscillator - correlateddriving amplitude and phase delayin RZ. Higher amplitudes imply

shorter periods (8%)...

Solar cycle phase regulation

• Solar cycle coherence and amplitude variability hint at a stable storage or steady flux transport process, i.e. Babcock-Leighton stochastic flux transport, not intrinsically non-linearity mechanisms

To do...

• find the complete luminosity budget of surface magnetic fields

• find B (and dB/dt) at tachocline

• determine dQ/dB from first principles

• build a relaxation delayed oscillator model for the full CZ

ConvectionZone

RadiativeZone

Tachocline region

Photosphere

Over a solar cycle magnetized fluid over 11yr increases entropy by 0.1% at base of SCZ

Radiative flux through magnetizedfluid sees lower opacity and increasedentropy relative to non-magnetized fluid

Solar cycle magnetic fields

Magnetized fluidis “hotter” Thermal “antishadows”

Temperature gradient enhanced stable stratification becomes unstable