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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
)](),([)/(b
l,...),s(/),(
4
),(),(
k
nl
42
scflmP
TBc
TRL
dyxIyxL
k
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
i
43/2if
if
i4
if
9
5
B10G)11(BB
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