High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR)

The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Researchunder sponsorship of the National Science Foundation. An Equal Opportunity/Affirmative Action Employer.

Processes that Cause Solar

Irradiance Variability

Mark MieschHAO/NCAR

2008 SORCE Science MeetingSanta Fe, NMFeb 5-7, 2008

! Solar Convection! Structure of Giant Cells

! DR, MC, and mean thermal variations

! Solar Magnetism! Elements of the Solar Dynamo! Tachocline Instabilities! The Activity Cycle

! Summary

Outline ultimate vs proximate causes

ASH

radial velocity, r = 0.98R

Miesch, Brun, DeRosa & Toomre (2008)

Giant Cells

temperature, r = 0.98R

Miesch, Brun, DeRosa & Toomre (2008)

Solar Cyclones pdf

Solar Cyclones pdf

Structure and Evolution of Giant Cells 7

Fig. 4.— Radial velocity vr at four horizontal levels (a) 0.98R, (b) 0.92R, (c) 0.85R, and (d) 0.71R. The color table is as in Fig. 1, withthe range indicated in each frame. Each image is an orthographic projection with the north pole tilted 35! toward the line of sight. Thedotted line indicates the solar radius r = R.

Fig. 5.— The enstrophy (!2, where ! = !"v) shown for a 45!

! 45! patch in latitude (10!-55!) and longitude at (a) r = 0.98Rand (b) r = 0.85R. The color table is as in Fig. 1 but here scaledlogarithmically. Ranges shown are (a) 10"12 to 10"7 s"2 and (b)10"13 to 10"8 s"2.

coupling to the tachocline which is only crudely incorpo-rated into this model through our lower boundary con-ditions (Miesch et al. 2006). For example, perhaps thetachocline is thinner, and the associated entropy varia-tion correspondingly larger, than what we have imposed(§2). More laminar models have more viscous di!usionbut they also have larger Reynolds stresses so many areable to maintain a stronger di!erential rotation, somewith conical angular velocity contours as in the Sun (El-liott et al. 2000; Brun & Toomre 2002; Miesch et al.2006). A more complete understanding of how the highlyturbulent solar convection zone maintains such a largeangular velocity contrast requires further study.

At latitudes above 30! the angular velocity increasesby about 4-8 nHz (1-2%) just below the outer boundary(r = 0.95R-0.98R). This is reminiscent of the subsurfaceshear layer inferred from helioseismology but its sense isopposite; in the Sun the angular velocity gradient is nega-tive from r = 0.95R to the photosphere (Thompson et al.2003). This discrepancy likely arises from our impenetra-ble, stress-free, constant-flux boundary conditions at theouter surface of our computational domain, r = 0.98R.In the Sun, giant-cell convection must couple in some wayto the supergranulation and granulation which dominatesin the near-surface layers. Such motions cannot presentlybe resolved in a global three-dimensional simulation andinvolve physical processes such as radiative transfer andionization which lie beyond the scope of our model.

The meridional circulation is dominated by a singlecell in each hemisphere, with poleward flow in the up-per convection zone and equatorward flow in the lowerconvection zone (Fig. 6c). At a latitude of 30!, the tran-sition between poleward and equatorward flows occursat r ! 0.84-0.85 R. These cells extend from the equa-tor to latitudes of about 60!. The sense (poleward) andamplitude (15-20 m s"1), of the flow in the upper con-vection zone is comparable to meridional flow speeds in-ferred from local helioseismology and surface measure-ments (Komm et al. 1993; Hathaway 1996; Braun &Fan 1998; Haber et al. 2002; Zhao & Kosovichev 2004;Gonzalez-Hernandez et al. 2006). The equatorward flowin the lower convection zone peaks at r ! 0.75R with anamplitude of 5-10 m s"1.

Near the upper and lower boundaries there are thincounter cells where the latitudinal velocity "v!# reverses.The presence of these cells is likely sensitive to the bound-

Structure and Evolution of Giant Cells 7

Fig. 4.— Radial velocity vr at four horizontal levels (a) 0.98R, (b) 0.92R, (c) 0.85R, and (d) 0.71R. The color table is as in Fig. 1, withthe range indicated in each frame. Each image is an orthographic projection with the north pole tilted 35! toward the line of sight. Thedotted line indicates the solar radius r = R.

Fig. 5.— The enstrophy (!2, where ! = !"v) shown for a 45!

! 45! patch in latitude (10!-55!) and longitude at (a) r = 0.98Rand (b) r = 0.85R. The color table is as in Fig. 1 but here scaledlogarithmically. Ranges shown are (a) 10"12 to 10"7 s"2 and (b)10"13 to 10"8 s"2.

coupling to the tachocline which is only crudely incorpo-rated into this model through our lower boundary con-ditions (Miesch et al. 2006). For example, perhaps thetachocline is thinner, and the associated entropy varia-tion correspondingly larger, than what we have imposed(§2). More laminar models have more viscous di!usionbut they also have larger Reynolds stresses so many areable to maintain a stronger di!erential rotation, somewith conical angular velocity contours as in the Sun (El-liott et al. 2000; Brun & Toomre 2002; Miesch et al.2006). A more complete understanding of how the highlyturbulent solar convection zone maintains such a largeangular velocity contrast requires further study.

At latitudes above 30! the angular velocity increasesby about 4-8 nHz (1-2%) just below the outer boundary(r = 0.95R-0.98R). This is reminiscent of the subsurfaceshear layer inferred from helioseismology but its sense isopposite; in the Sun the angular velocity gradient is nega-tive from r = 0.95R to the photosphere (Thompson et al.2003). This discrepancy likely arises from our impenetra-ble, stress-free, constant-flux boundary conditions at theouter surface of our computational domain, r = 0.98R.In the Sun, giant-cell convection must couple in some wayto the supergranulation and granulation which dominatesin the near-surface layers. Such motions cannot presentlybe resolved in a global three-dimensional simulation andinvolve physical processes such as radiative transfer andionization which lie beyond the scope of our model.

The meridional circulation is dominated by a singlecell in each hemisphere, with poleward flow in the up-per convection zone and equatorward flow in the lowerconvection zone (Fig. 6c). At a latitude of 30!, the tran-sition between poleward and equatorward flows occursat r ! 0.84-0.85 R. These cells extend from the equa-tor to latitudes of about 60!. The sense (poleward) andamplitude (15-20 m s"1), of the flow in the upper con-vection zone is comparable to meridional flow speeds in-ferred from local helioseismology and surface measure-ments (Komm et al. 1993; Hathaway 1996; Braun &Fan 1998; Haber et al. 2002; Zhao & Kosovichev 2004;Gonzalez-Hernandez et al. 2006). The equatorward flowin the lower convection zone peaks at r ! 0.75R with anamplitude of 5-10 m s"1.

Near the upper and lower boundaries there are thincounter cells where the latitudinal velocity "v!# reverses.The presence of these cells is likely sensitive to the bound-

Structure and Evolution of Giant Cells 7

Fig. 4.— Radial velocity vr at four horizontal levels (a) 0.98R, (b) 0.92R, (c) 0.85R, and (d) 0.71R. The color table is as in Fig. 1, withthe range indicated in each frame. Each image is an orthographic projection with the north pole tilted 35! toward the line of sight. Thedotted line indicates the solar radius r = R.

Fig. 5.— The enstrophy (!2, where ! = !"v) shown for a 45!

! 45! patch in latitude (10!-55!) and longitude at (a) r = 0.98Rand (b) r = 0.85R. The color table is as in Fig. 1 but here scaledlogarithmically. Ranges shown are (a) 10"12 to 10"7 s"2 and (b)10"13 to 10"8 s"2.

coupling to the tachocline which is only crudely incorpo-rated into this model through our lower boundary con-ditions (Miesch et al. 2006). For example, perhaps thetachocline is thinner, and the associated entropy varia-tion correspondingly larger, than what we have imposed(§2). More laminar models have more viscous di!usionbut they also have larger Reynolds stresses so many areable to maintain a stronger di!erential rotation, somewith conical angular velocity contours as in the Sun (El-liott et al. 2000; Brun & Toomre 2002; Miesch et al.2006). A more complete understanding of how the highlyturbulent solar convection zone maintains such a largeangular velocity contrast requires further study.

At latitudes above 30! the angular velocity increasesby about 4-8 nHz (1-2%) just below the outer boundary(r = 0.95R-0.98R). This is reminiscent of the subsurfaceshear layer inferred from helioseismology but its sense isopposite; in the Sun the angular velocity gradient is nega-tive from r = 0.95R to the photosphere (Thompson et al.2003). This discrepancy likely arises from our impenetra-ble, stress-free, constant-flux boundary conditions at theouter surface of our computational domain, r = 0.98R.In the Sun, giant-cell convection must couple in some wayto the supergranulation and granulation which dominatesin the near-surface layers. Such motions cannot presentlybe resolved in a global three-dimensional simulation andinvolve physical processes such as radiative transfer andionization which lie beyond the scope of our model.

The meridional circulation is dominated by a singlecell in each hemisphere, with poleward flow in the up-per convection zone and equatorward flow in the lowerconvection zone (Fig. 6c). At a latitude of 30!, the tran-sition between poleward and equatorward flows occursat r ! 0.84-0.85 R. These cells extend from the equa-tor to latitudes of about 60!. The sense (poleward) andamplitude (15-20 m s"1), of the flow in the upper con-vection zone is comparable to meridional flow speeds in-ferred from local helioseismology and surface measure-ments (Komm et al. 1993; Hathaway 1996; Braun &Fan 1998; Haber et al. 2002; Zhao & Kosovichev 2004;Gonzalez-Hernandez et al. 2006). The equatorward flowin the lower convection zone peaks at r ! 0.75R with anamplitude of 5-10 m s"1.

Near the upper and lower boundaries there are thincounter cells where the latitudinal velocity "v!# reverses.The presence of these cells is likely sensitive to the bound-

Structure and Evolution of Giant Cells 7

Fig. 4.— Radial velocity vr at four horizontal levels (a) 0.98R, (b) 0.92R, (c) 0.85R, and (d) 0.71R. The color table is as in Fig. 1, withthe range indicated in each frame. Each image is an orthographic projection with the north pole tilted 35! toward the line of sight. Thedotted line indicates the solar radius r = R.

Fig. 5.— The enstrophy (!2, where ! = !"v) shown for a 45!

! 45! patch in latitude (10!-55!) and longitude at (a) r = 0.98Rand (b) r = 0.85R. The color table is as in Fig. 1 but here scaledlogarithmically. Ranges shown are (a) 10"12 to 10"7 s"2 and (b)10"13 to 10"8 s"2.

coupling to the tachocline which is only crudely incorpo-rated into this model through our lower boundary con-ditions (Miesch et al. 2006). For example, perhaps thetachocline is thinner, and the associated entropy varia-tion correspondingly larger, than what we have imposed(§2). More laminar models have more viscous di!usionbut they also have larger Reynolds stresses so many areable to maintain a stronger di!erential rotation, somewith conical angular velocity contours as in the Sun (El-liott et al. 2000; Brun & Toomre 2002; Miesch et al.2006). A more complete understanding of how the highlyturbulent solar convection zone maintains such a largeangular velocity contrast requires further study.

At latitudes above 30! the angular velocity increasesby about 4-8 nHz (1-2%) just below the outer boundary(r = 0.95R-0.98R). This is reminiscent of the subsurfaceshear layer inferred from helioseismology but its sense isopposite; in the Sun the angular velocity gradient is nega-tive from r = 0.95R to the photosphere (Thompson et al.2003). This discrepancy likely arises from our impenetra-ble, stress-free, constant-flux boundary conditions at theouter surface of our computational domain, r = 0.98R.In the Sun, giant-cell convection must couple in some wayto the supergranulation and granulation which dominatesin the near-surface layers. Such motions cannot presentlybe resolved in a global three-dimensional simulation andinvolve physical processes such as radiative transfer andionization which lie beyond the scope of our model.

The meridional circulation is dominated by a singlecell in each hemisphere, with poleward flow in the up-per convection zone and equatorward flow in the lowerconvection zone (Fig. 6c). At a latitude of 30!, the tran-sition between poleward and equatorward flows occursat r ! 0.84-0.85 R. These cells extend from the equa-tor to latitudes of about 60!. The sense (poleward) andamplitude (15-20 m s"1), of the flow in the upper con-vection zone is comparable to meridional flow speeds in-ferred from local helioseismology and surface measure-ments (Komm et al. 1993; Hathaway 1996; Braun &Fan 1998; Haber et al. 2002; Zhao & Kosovichev 2004;Gonzalez-Hernandez et al. 2006). The equatorward flowin the lower convection zone peaks at r ! 0.75R with anamplitude of 5-10 m s"1.

Near the upper and lower boundaries there are thincounter cells where the latitudinal velocity "v!# reverses.The presence of these cells is likely sensitive to the bound-

North-South (NS) Downflow Lanes

Prograde propagation: traveling convective modes

thermal, magnetic signatures?

Might NS Downflow Lanes Imprint through to the Corona?

Courtesy J. Luhmann (SSL): Mt. WIlson data

Courtesy A. Norton (NSO): GONG dataCourtesy NASA; SOHO EIT/UVCS data

Courtesy NASA: Skylab data

Maintenance of Mean Flows: Dynamical balances!

(1) Meridional Circulation = Reynolds stress

(2) Thermal Wind Balance (Taylor-Proudman theorem)

Coriolis-induced

tilting of convective

structures

Steady State

Neglect LF, VD

Rapid Rotation RS << CF

ideal gas

hydrostatic, adiabatic background

ConvectionDifferential

Rotation

Meridional

Circulation

Thermal

Gradients

Reynolds

stress

shear

advection

Coriolis

force

advection

buoyancy

baroclinicity

convective

heat flux

Miesch (2007)

Miesch, Brun, DeRosa & Toomre (2008)

Mean Flows and MC Variability

! Prograde equator maintained by Reynolds stresses

! Conical profile maintained by baroclinicity

! warm poles

! single-celled MC

! large MC variation

Dikpati & Gilman (2006)

Tobias et al (2001)

N. Brummell (UCSC)

solar surface

con

vecti

on

zon

eta

ch

ocli

ne

Babcock-Leighton

mechanism

Elements of The Solar Dynamo

Magnetic

buoyancy

Magnetic

Pumping

Y. Fan (2007)

Brun, Miesch & Toomre (2004)

Global-scale Turbulent Dynamos

Br

B!

Global Dynamos with a Tachocline

Pumping, amplification, organizationof toroidal magnetic fields

Browning, Miesch, Brun & Toomre (2006)

B"

!

Tachocline

Mid

convection

zone

Global Magneto-Shear Instabilities in theTachocline

! Banded Fields! Tipping Instability (m = 1)

! Gyroscopic stabilization

! Broad fields! Clam-shell Instability! Opens up until loops are N-S

Toroidal rings in the presence of latitudinal shear will tip!Miesch, Gilman &

Dikpati (2007)

Gilman & Fox (1997, 1999) Dikpati & Gilman (1999), Gilman & Dikpati (2000)

Cally et al (2003)

Expect m=1 signal in

emerging active regions!(Norton & Gilman 2005)

B! "

2D, shallow water, now 3D

Sustained Clam-shell Instability Miesch (2007)

Thompson et al (2003)

Possibly related to 1.3-year tachocline oscillations?Rotational Shear, Poloidal flux

maintained by external forcing

Quasi-periodic energy exchange

between mean toroidal field and

m=1 instability mode

#

Sustained Clam-shell Instability Miesch (2007)

Thompson et al (2003)

Possibly related to 1.3-year tachocline oscillations?Rotational Shear, Poloidal flux

maintained by external forcing

Quasi-periodic energy exchange

between mean toroidal field and

m=1 instability mode

#

Dynamo Models of the Solar Activity Cycle

! Babcock-Leighton Flux-Transport (BLFT) Models! Regions I, III

! Mechanisms A, B

! Cyclic activity due largely to MC

! Optimal for predictability! (photospheric source + time delay)

! Interface Models! Regions II, III! Mechanism C! Cyclic activity due to dynamo waves (or MC?)

! More in line with 3D MHD Simulations?

Coupling Mechanisms

A: Meridional CirculationB: Magnetic BuoyancyC: Convective Transport

axisymmetric, kinematic!B!t

= !" (v "B# "!"B) + S(r, #,B)

S(r, !,B) = !" ("B)

Surface Flux Evolution

Essential or Superficial? (Schussler 2005)

D. Hathaway (2007)

Can the tail wag the dog?

Sources of Variability

! Meridional Circulation (BLFT)

! Convective Transport! BL source term (BLFT)

! $, magnetic pumping (interface)

! Convective Field Generation! turbulent %-effect (interface)

! Lorentz-force feedbacks! %, $ quenching, thresholds

! non-kinematic models

! Flux Emergence! Nonlinear development of

tachocline instabilities! interaction with convection,

shear

Charbonneau & Dikpati (2000)

Charbonneau (2005)

Predictability?

Bushby & Tobias (2007)

Dikpati & Gilman (2006)

! Models are inherently fickle (BT07)! Stochastic modulation (linear)

! Deterministic chaos (nonlinear)

! little correlation from one cycle to the next

! But they seem to do wonders! (DG06)! linear model ! boundary forcing from observations! memory (n-1, n-2, n-3)

! Why?! Capturing essential physics?! Echoing patterns present in the data?

! overlap + amplitude/duration

correlation; (Cameron & Schussler 2007)

Time will tell...or will it?

! Latitudinal variability! Active Bands (equatorward migration)

! Warm poles (~10-3)

! Longitudinal Variability (/temporal)

! NS lanes! m=1 Tachocline instabilities

! Cycle Variations! Deterministic chaos / stochastic forcing! Memory

! Key Dynamo Questions! Where is the poloidal field generated?! How does flux destabilize and emerge?! How essential is the MC?

Summary

What causes cyclic activity?

What causes chaotic modulation?

Colleagues

Univ. of Colorado/JILA (Boulder)

Juri Toomre, Benjamin Brown, Nicholas Featherstone, Kyle Augustson

CEA Saclay (Paris)

Allan Sacha Brun

Univ. of Chicago

Matt Browning

Lockheed Martin (Palo Alto)

Marc DeRosa

HAO/NCAR (Boulder)

Matthias Rempel, Mausumi Dikpati, Peter Gilman

SORCE Science Meeting, Feb 5-7 2008