Energy Transport and Structure of the Solar Convection Zone

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Energy Transport and Structure of the Solar
Convection Zone

• James Armstrong
• University of Hawaii Manoa
• 5/25/2004
• Ph.D. Oral Examination

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Introduction

• Magnetic Solar Cycle
• Solar Irradiance Cycle
• Structural changes
• Surface features
• How do proxy models work?

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Introduction

• Observations
• PSPT
• Red, Blue, and CaIIK
• MDI
• Used as a check
• Faculae
• Bright wall model
• Comparison to proxy models

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Introduction

• Sunspot bright rings
• Simple resistor model
• 2D diffusive model
• Bright ring observations
• Temperature Profiles
• How much energy do they radiate?
• Facular regions
• PSF and other corrections
• Discussion and Conclusions

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Note For Convenience

• Ill often refer to pixels or regions as being
  bright. This should be taken to mean
  bolometrically bright.
• I will often also use µ. µ is the cosine of the
  viewing angle.

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Magnetic Solar Cycle

• Roughly periodic with period of 11 years.
• Sunspots appear at higher latitudes early in the
  cycle and lower in the cycle.
• Magnetic field flips from one cycle to the next.

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Magnetic Solar Cycle

• Solar magnetic field begins with a poloidal field
• Poloidal field is wound up generating a torroidal
  field
• Magnetic field rises and recycled

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Solar Irradiance

• Solar irradiance changes by 0.1 over the solar
  cycle.
• This is correlated with the solar magnetic cycle.
• Short term variability is large.

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Irradiance vs. Luminosity

• Irradiance
• Amount of energy radiated in a particular
  direction e.g. toward earth
• Luminosity
• The total energy radiated by the sun
• They are not the same!
• Changes in irradiance does not imply changes in
  luminosity.

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Irradiance vs. Luminosity
Solar irradiance cycle is caused by the time
average of irradiance.
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Why? Two explanations

• Solar irradiance cycle is driven by structural
  changes in the solar interior.
• Solar irradiance cycle is driven by surface
  features.

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Deeper Structure Changes

• Magnetic fields generated at or near base of
  convection zone
• Magnetic fields lead to changes in the solar
  structure
• This leads to observed solar irradiance changes

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Surface Features

• Magnetic fields cause holes.
• Facular regions appear bright.
• Due to suppression of convective motion sunspots
  appear dark.
• Use average area of bright and dark features to
  predict the irradiance.

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Proxy Models

• Faculae are bright and increase solar irradiance
• Sunspots are dark and decrease solar irradiance
• Assumes that the quiet sun doesnt change

Predict about 95 of irradiance variability
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Proxy Models How do they work?

• Create a proxy model with known properties and
  compare.
• Include an underlying irradiance cycle.
• Sunspots and faculae have equal contributions.

• Linear regression performed without underlying
  irradiance cycle.

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Comparison

• Real proxy models have an R of 95
• Simulated proxy models have an 94
• Didnt include the underlying solar cycle
• Only had two independent variables
• Adding an independent variable which is random
  noise increased R to 95
• Over estimated contributions from faculae
• Under estimated contributions for sunspots

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Observations

• Precision Solar Photometric Telescope (PSPT)
• Located on Mauna Loa
• Seeing Limited Observations
• Pixels of 1
• Photometry of 0.1
• Three bands
• Red 606.7 607.2 nm
• Blue 409.3 409.6
• CaIIK 393.1 393.4 nm

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Red and Blue ? Temperature
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CaIIK Traces Magnetic Field
Other Facular studies compute line of sight
magnetic field by dividing by m.
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Faculae - The Hot Wall Model

• Magnetic fields provide pressure support.
• Pressure equilibrium implies lower density.
• Lower density leads to lower opacity providing an
  energy shunt a preferred route for energy to
  emerge from the solar surface.

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Properties of Faculae

• Faculae redistribute the angular surface
  irradiance.
• Represent a local increase in the radiated
  energy.
• Stronger faculae appear dark at disk center.

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Comparison of Faculae to Hot Wall Models

• We can relate the temperature at the base of the
  flux tube to the surface temperature

Tw/T97

• Walls are hot, but surrounding down flows are
  cold.

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Comparison of Observations to Proxy Models
Now we can use conversion factor.
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Comparison of Observations to Proxy Models
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Sunspot Bright Rings

• Sunspots inhibit energy transport in the
  convection zone
• Heat will build up at the bottom of the sunspot
• This excess heat flows around the sunspot
  increasing temperature of neighboring solar
  surface

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Simple Resistor Model
Perturbed temperature solution generated from
effective source at base of sunspot with an
effective luminosity of F
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Diffusion Model

• 2D diffusion model of sunspots

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Diffusion Model

• 2D diffusion model of sunspots
• Sunspot blocks all energy transport
• Conductivity derived from analytic mixing length
  and numerical simulation results
• Equilibrium conditions computed

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Conductivity
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2D Diffusion Model
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Predicted Temperature Profiles
MLT Conductivities
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Predicted Temperature Profiles
Numerical Conductivities
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Observations
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MDI

• Michaelson Doppler imager aboard SOHO
• 2 pixels
• Lower Photometry
• Not designed for photometry
• Used as a check

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Calculating the Luminosity
Observe sunspot brightness as it crosses the
solar disk to compute 3D irradiance profile.
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Observational Results
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Energy Reradiated
Sunspot in 1 in 2 in 3
8263 22 32 34
8640 6 12 21
8525 12 35 65
8706 15 38 69
But Models predict 2 or less!
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Diffusion Doesnt Work

• Mixing length or anisotropic diffusion
  conductivities dont explain bright ring data
• Correlated flows over scales much larger than a
  density scale height seem to be required
• Faculae or CaIIK bright pixels are puzzling --
  important local perturbations to heat flow?

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What about Faculae?

• Faculae redistribute energy
• May represent increase in energy
• Are probably in all sunspot rings
• Should be corrected for?

• Try excluding them from computation.

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Bright Rings - Filtered

• Removing the bright CaIIK regions

Sunspot in 1 in 2 in 3
8263 -5.0 -5.5 -10
8640 -1.3 -3.3 -8
8525 -0.4 -1.2 -6.2
8706 -0.2 -2.0 -5.3
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What Happened?
Scattered light ?
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Scattered Light

• Scattering of light causes a slight dark ring
  around the sunspot.
• Compute the PSF and correct.

• Due to remaining defects, compute forward problem
• Bright are rings missing.

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Bright Ring Faculae Are Different

• Faculae in bright rings are fainter than in quiet
  sun.
• Correction implies a bright ring which
  reradiates 10 of energy blocked.

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Comparison of Observations to Proxy Models
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Plausibility Check

• We see large changes in solar irradiance
  associated with sunspots and faculae.
• Other evidence indicates that sunspots and
  faculae dont have a large effect on solar
  irradiance
• Conflict is resolved by considering a complete
  disk crossing.

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Plausibility Check

• Most of the energy reradiated by bright rings are
  associated with magnetic fields.
• (They are facular in nature)
• Faculae are darker at disk center.
• Sunspots are darker at disk center.
• Sunspots bright ring must be darker at disk
  center.

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Conclusions

• Facular regions
• Redistribute radiated energy.
• Act as a local increase in energy budget.
• Might not represent an increase in solar
  irradiance.
• Proxy models overestimate the contributions of
  facular regions.
• They are hiding something.

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Conclusions

• Sunspot bright rings reradiate at least 40 of
  energy blocked by sunspots.
• The excess energy radiated by bright rings is
  preferentially channeled through CaIIK bright
  regions.
• After correction for scattered light, no bright
  ring remains, but facular regions imply that 10
  of energy is reradiated

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Conclusions

• Energy transport in the solar convection zone is
  not diffusive.
• Diffusion models predict that less than 1 of the
  energy blocked by a sunspot is reradiated.
• Faculae must represent an energy increase.
• Diffusion models predict that they dont.
• This represents a contradiction.
• Energy is transported by large scale bulk
  motions.
• In small features, radiative transfer is
  important.

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Questions?