Solar Irradiance, Diameter, Shape, and Activity
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Solar Irradiance, Diameter, Shape, and Activity J.R. Kuhn, Institute for Astronomy, University of Hawaii Rock Bush Marcelo Emilio Isabelle Scholl Phil Scherrer. GONG10, June 2010. What can we learn about the solar cycle from precise “global” measurements?. …since 2002.

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Solar Irradiance, Diameter, Shape, and ActivityJ.R. Kuhn, Institute for Astronomy, University of HawaiiRock BushMarcelo EmilioIsabelle SchollPhil Scherrer

GONG10, June 2010


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


Since 2002
…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
Global solar properties

Luminosity and irradiance

Luminosity, radius, temp

Frequency, magnetic field,

temperature

‘Even’ m-dependent frequency splittings



Frequencies and f10 7
Frequencies and F10.7

Broomhall et al. 2009


Even coefficient frequency splittings
Even coefficient frequency splittings

Splitting coefficient temporal variability qualitatively describes surface magnetism

changes



The solar limb is largely fixed by rapid opacity decline
The solar limb is largely fixed by rapid opacity decline solar luminosity

“few km” thick transition

from opaque to transparent



A fluctuating solar radius is seen from the ground
A fluctuating solar radius is seen from the ground solar luminosity

  • 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
Solar astrometry: Is the Sun shrinking? solar luminosity

  • 0.05 – 0.2 arcsec/century

Gilliland, 1981


Limb astrometry from space
Limb astrometry from Space solar luminosity

NB: Telescope diffraction limit has very

little to do with astrometric accuracy

dr

Angle of arrival fluctuations define dr

dI

Photometric 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”]


Limb astrometry systematic errors
Limb Astrometry Systematic Errors solar luminosity

  • 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
HMI Solar Limb Astrometry solar luminosity

  • 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
Satellite limb profiles solar luminosity


Mdi raw radius data
MDI Raw Radius Data solar luminosity


Calibrated mdi astrometry systematics
Calibrated MDI astrometry systematics solar luminosity

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
Instrument changes solar luminosity


The solar radius change
The solar radius change… solar luminosity


The solar radius over time
The solar radius over time solar luminosity

km


No solar cycle radius changes
No solar cycle radius changes! solar luminosity

  • 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
Asphericity and solar shape solar luminosity

  • 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
Limb astrometry, MDI solar luminosity

6-50 pixel annulus

480pix

MDI: 1.96” pixel

HMI: 0.5” pix


Hmi raw shape and limb photometry
HMI raw shape and limb photometry solar luminosity

pole

equator

See GONG10 Bush et al. poster


Rolling hmi separates solar shape from optical distortion
Rolling HMI separates solar shape from optical distortion solar luminosity

Satellite roll angle 

cos2θ

cos3θ

cos4θ

cos5θ


Mdi and hmi sun during some rolls has no magnetic activity
MDI and HMI sun during some rolls has no magnetic activity solar luminosity

MDI: March 1997

HMI: April 9 2010

HMI: April 16 2010

MDI roll in 2001 available, but active sun

HMI roll available every 6 months

MDI: Nov. 2009


Oblateness from 1997 2010
Oblateness from 1997-2010 solar luminosity

MDI and HMI observations without magnetic corrections

1997 MDI

2009 MDI

2010a HMI

2010b HMI



Mdi limb shape analysis magnetic contamination e g 2001
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
After accounting for magnetic activity, the limb shape is still variable

Active latitutes:

If we missed magnetic

contributions, oblateness

would be even larger!


Solar oblateness isn t constant
Solar oblateness isn’t constant still variable

MDI and HMI

Solar shape data

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


Rhessi photometry technique
RHESSI photometry technique still variable

Fivian, Hudson, Lin, 2007



Helioseismic splittings also sample solar shape
Helioseismic splittings also sample solar shape still variable

  • 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 hmi
The solar brightness, ground, MDI, HMI still variable

Ground Oblateness Measurements

HMI

MDI


Solar cycle acoustic changes
Solar cycle acoustic changes still variable

  • 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
“Superficial” vs. “seeing the tachocline” still variable

  • 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
Deep origins of magnetized plasma must carry excess entropy to surface

Magnetized fluid

is “hotter”

Photosphere

Thermal “antishadows”

Solar cycle magnetic fields

Convection

Zone

Temperature gradient enhanced

stable stratification becomes unstable

Tachocline region

Radiative

Zone

Radiative flux through magnetized

fluid sees lower opacity and increased

entropy relative to non-magnetized fluid

Over a solar cycle magnetized fluid over 11yr

increases entropy by 0.1% at base of SCZ


Alternatively vertical surface b fields decrease vertical irradiance
Alternatively, vertical surface B fields to surfacedecrease vertical “irradiance”

Continuum contrast vs. vertical orientation and CaK contrast

The integrated disk brightness change due to

bright faculae is 38% of the

faint faculae

“Bright” faculae are dark, at any wavelength near

disk center

Data from the Precision Photometric Solar

Telescope

NB: cf. Ken Topka facular contrast results



Fast and slow b vs irradiance
Fast and slow B vs. irradiance to surface

Fast variations: B increases “I”

Slow variations: B decreases I


Frequency variations are not determined simply by solar activity
Frequency variations are not determined simply by solar activity

(from Broomhall et al. 2009)


Global photometric timeseries analysis
Global photometric timeseries analysis activity

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

T/4

dI

time

Use solar rotation to describe angular variation in active region or spot

“irradiance” … luminosity


Full disk observations show flux redistribution
Full-disk observations show flux redistribution pertubation (flux redistribution)

(data high-pass filtered with 60d

moving-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
CoRoT Photometry – stay tuned pertubation (flux redistribution)


Conclusions
Conclusions pertubation (flux redistribution)

  • 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
Magnetized plasma from RZ is hotter pertubation (flux redistribution)

At the top of the radiative zone...

Tachocline region

l

BP6MG, lP3E5cm

Tachocline shear layer unresolved helioseismically,

lO 0.018R (Schatzman et al. 2000)


Helioseismic changes pertubation (flux redistribution)

Irradiance

changes

Surface brightness

changes

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


  • What was the question? pertubation (flux redistribution)

  • Boundaries are great

  • “Superficialist” problems

  • Listening to the data

  • Clocks


Driving the solar cycle
Driving the Solar Cycle pertubation (flux redistribution)


Irradiance changes
Irradiance changes pertubation (flux redistribution)

+0.1W/m^2/G

-0.2W/m^2/G

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

The slow variations using 30d averages are plotted here


Helioseismic asphericity
Helioseismic asphericity pertubation (flux redistribution)

(Vorontsov, 2002)

(Antia et al. 2001)

(1989)

26 nHz/G

140 nHz/K


Irradiance luminosity change
Irradiance/luminosity change pertubation (flux redistribution)

  • 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
The tachocline: Where luminosity perturbations come from? pertubation (flux redistribution)

Magnetized fluid

is “hotter”

Photosphere

Thermal “antishadows”

Solar cycle magnetic fields

Convection

Zone

Temperature gradient enhanced

stable stratification becomes unstable

Tachocline region

Radiative

Zone

Radiative flux through magnetized

fluid sees lower opacity and increased

entropy relative to non-magnetized fluid

Over a solar cycle magnetized fluid over 11yr

increases entropy by 0.1% at base of SCZ


Magnetized plasma from rz is hotter1
Magnetized plasma from RZ is hotter pertubation (flux redistribution)

At the top of the radiative zone...

Tachocline region

l

BP6MG, lP3E5cm

Tachocline shear layer unresolved helioseismically,

lO 0.018R (Schatzman et al. 2000)


More numbers
More numbers... pertubation (flux redistribution)


  • 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
Superficial two component (faculae+spots) irradiance models 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.

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

Facular/spot irradiance

contrast function

.mis cosine central angle

Observed time-variable

irradiance

Observed time and

latitudinal facular/spot dist.

(determined by proxy)

Models which use a statistical fit to determine the coefficients b and k can account for 70-90% of the

irradiance variability (c.f. Solanki, Lean and collaborators)


Superficial two component faculae spot models are empirical and imcomplete
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

“Bright” faculae are dark, at any wavelength near

disk center

Data from the Precision Photometric Solar

Telescope

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


How does the convection zone transport heat
How does the convection zone transport heat? empirical and imcomplete

  • mixing-length diffusion conflicts


Mlt convection fails to estimate scz conductivity
MLT convection fails to estimate SCZ conductivity empirical and imcomplete

Non-mixing length theory (realistic) solar convection has highly correlated

vertical flows. The effective conductivity of the solar convection zone is far

from mixing length theory approximations (images from Georgobiani Stein,

and Kuhn)

small perturbations are diffusive but

anisotropic and with conductivity much

smaller than mixing length predictions



Superficial models miss time dependence of irradiance componets
Superficial models miss time dependence of irradiance componets

sunspot peak

Total

irradiance

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

Spot and facular signals peak

about 1 year before luminosity signal


Spots and faculae may produce only a tiny luminosity pertubation flux redistribution1
Spots and faculae may produce only a tiny luminosity pertubation (flux redistribution)

If irradianceis due to flux redistribution, its autocorelation

must yield a negative “dip” at T/4=7d due to opposite

sign flux enhancements between normal and near-tangent

viewing angles

T/4

dI

time

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


Full disk observations show flux redistribution1
Full-disk observations show flux redistribution pertubation (flux redistribution)

(data high-pass filtered with 60d

moving-mean)

Regardless of phase of the solar cycle (min-to-max) the irradiance autocorrelation shows clear evidence that active regions (faculae

and 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
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



Solar cycle changes
Solar cycle changes distinction

Photometry from Mt. Wilson,

previous cycle implied this

limb temperature

MDI Roll data

photometry imply

this limb temperature

distribution

Most of a solar cycle was obtained

from Mt. Wilson oblateness expt.


Phase properties
Phase properties distinction


Delayed oscillator
Delayed Oscillator distinction

F(t)

Bf

G(t)

Flux storage and “heating”

in RZ, G[a,e]

Flux diffusion and winding

in CZ, F[b,d]

RZ

CZ



Solar cycle effects
Solar Cycle Effects distinction

Delayed oscillator - correlated

driving amplitude and phase delay

in RZ.

Higher amplitudes imply

shorter periods (8%)...


Solar cycle phase regulation
Solar cycle phase regulation distinction

  • 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
To do... distinction

  • 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


Magnetized fluid distinction

is “hotter”

Photosphere

Thermal “antishadows”

Temperature gradient

enhanced stable stratification

becomes unstable

Solar cycle magnetic fields

Convection

Zone

Tachocline region

Radiative

Zone

Radiative flux through magnetized

fluid sees lower opacity and increased

entropy relative to non-magnetized fluid

Over a solar cycle magnetized fluid

over 11yr increases entropy by 0.1%

at base of SCZ


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