Probing the Sun in 3D

Karen Harvey Prize LectureBoulder 2009

Laurent GizonLaurent GizonMax Planck Institute for Max Planck Institute for Solar System Research, Solar System Research, & Goettingen University, & Goettingen University, GermanyGermany

Thanks

Tom Duvall Aaron Birch Sami Solanki

Phil Scherrer

This presentation uses material from: Robert Cameron, Jason Jackiewicz,

Hannah Schunker

Outline

Helioseismology: IntroductionHelioseismology: Introduction Why look inside the Sun?Why look inside the Sun? Solar oscillationsSolar oscillations Local helioseismologyLocal helioseismology

Probing flows Probing flows Probing magnetic activityProbing magnetic activity

Why look inside the Sun?

Test the theory of stellar structure and evolutionTest the theory of stellar structure and evolution Study effects beyond the standard solar model: Study effects beyond the standard solar model:

Convection, rotation, etc.Convection, rotation, etc.

Everything above the surface is driven by what is Everything above the surface is driven by what is happening inside!happening inside!

Why does the Sun have a magnetic field?Why does the Sun have a magnetic field? Solar Dynamo: large-scale flows, 11-yr variationsSolar Dynamo: large-scale flows, 11-yr variations

Can we see solar active regions before they emerge at Can we see solar active regions before they emerge at the surface?the surface?

Solar oscillations•The Sun is filled with internal acoustic waves with periods near 5 min (freq. near 3 mHz).

•Waves are excited by near-surface turbulent convection.

•Surface motions (Doppler shifts) are a few 100 m/s, superimposed on the 2 km/s solar rotation.

Velocity images (1 min cadence, mean image subtracted)measured with MDI on the SOHO spacecraft

Power spectrum of solar oscillations

p modes: pressure wavesf modes: surface-gravity waves

Power spectrum of solar oscillations

depths < 200 Mm

depths < 20 Mm

Global helioseismology Measurement and

inversion of the frequencies of the global modes of resonance (many thousands of individual modes are resolved in freq space)

Among the most precise measurements in astrophysics.

internal structure and rotation as a function of radius and latitude (2D).

Global helioseismology

red is faster (P=26 days) blue is slower (P=35 days)Schou et al. (1997)

•Frequencies of the normal modes of oscillations are Doppler shifted by rotation

•Differential rotation in the convective envelope.•Uniform rotation in the radiative interior.•very small temporal changes connected to the solar cycle

Example: Internal rotation

Local helioseismology

A set of techniques to interpret the A set of techniques to interpret the full wavefield at the solar surface, not full wavefield at the solar surface, not just the frequencies of the waves. just the frequencies of the waves.

The goal is to retrieve 3D vector The goal is to retrieve 3D vector flows and 3D structural flows and 3D structural inhomogeneities.inhomogeneities.

Local Helioseismology

T Duvall

F Hill

C Lindsey

M Woodard

D Braun

Time-distance helioseismology

A technique to A technique to measure the time it measure the time it takes for waves to takes for waves to propagate between propagate between any two point (A,B) any two point (A,B) on the surface on the surface through the interiorthrough the interior

Seismic traveltimes Seismic traveltimes contain information contain information about the local about the local properties of the properties of the mediummedium A

B

.

.

>t+

t-

>

c

U

Time-distance helioseismology

Mean travel times are Mean travel times are sensitive to wave-sensitive to wave-speed perturbationsspeed perturbations

Differences between the A→B and B→A directions arise from bulk motion along the path.

Travel-time differences Travel-time differences are sensitive to flowsare sensitive to flows

A

B

.

.

>t+

t-

>

c

U

The cross-covariance functionis used to measure the travel times

T

dtttBtAtBAC0

'.)',()',(),,(

Let us call the filtered Doppler velocity (a random field).In local helioseismology, a fundamental quantity is the cross-covariance between two surface points A and B:

(min) lag, Time t

Example C(A,B,t) for f modesand a distance A-B of 10 Mm

Travel times:

t+ for waves to go from A to B

t- for waves to go from B to A

Flows break the symmetry in t

t+

A measure of how fast disturbances travel between A and B

Outline

Helioseismology: IntroductionHelioseismology: Introduction Probing flows Probing flows

Meridional circulationMeridional circulation SupergranulationSupergranulation Depth dependenceDepth dependence Helical flowsHelical flows

Probing magnetic activityProbing magnetic activity

Meridional Flow Near surface (top ~10 Mm)

Gizon & Rempel (2008)Giles (1999)

North-south travel-time differencesaveraged over longitude

~10 m/s flow from the equator to the poles near the surface

Meridional Flow

North-south travel-time differencesaveraged over longitude

10-15 m/s flow from the equator to the poles near the surface

Gizon & Rempel (2008)Gonzalez Hernandez et al. (2008)Giles (1999)

Solar cycle dependence

Local travel-time perturbations

The annulus / quadrant geometry (Duvall 1997)

ingoing – outgoing travel times horizontal divergence of flows

T=8.5 hr annulus radius is 12 MmEach frame is 370 Mm on the side

Convective flows andmotion of small magnetic features

Horizontal divergence of flow field at a depth of 1 Mm (30 Mm dominant spatial scale)

White shades: Divergent flows

Black shades:Convergent flows

Red/green:Small magnetic features measured by MDI/SOHO

Duvall & Gizon 2000

Lifetime of supergranulationThe study of the evolutionof supergranulation is made easier (helioseismic mapsare almost insensitive to theline of sight projection)

Many supergranules persist for a lot longer than 1 day

Average Lifetime ~2 days

Divergence maps 12 hr averages

Linear inverse problem in time-distance helioseismology

Given a set of travel time measurements,

Given a reference solar model (horizontally invariant),

Given functions (kernels) that give the sensitivity of travel times to small perturbations in the model (e.g. temperature, density, flows),

Solve a linear inverse problem to obtain the perturbations in e.g. temperature, density, flows with respect to the model.

Sun

u K dVtt

horizontal flows

Arrows: ux and uy at depth 1 Mm

Longuest arrow is 500 m/s

DEP

TH (M

m)

Jack

iew

icz,

Giz

on,

Birc

h (2

008)

3D vector flows

DEP

TH (M

m)

Jack

iew

icz,

Giz

on,

Birc

h (2

008)

3D vector flows

vdiv Hv hzNote that , which is good!

How deep do velocity structures persist?Coherence of flows (+noise) vs. depth

Jackiewicz, Gizon, Birch (2008)

Helical flows: Effect of rotation on convection

Gizon and Duvall (2003)

div = horizontal divergence; curl = vertical component of vorticity

Outline

Helioseismology: IntroductionHelioseismology: Introduction Probing flowsProbing flows Probing magnetic activityProbing magnetic activity

SunspotsSunspots

Sunspots How do sunspots form?How do sunspots form?

What is their subsurface What is their subsurface structure? structure?

Why are sunspots stable?Why are sunspots stable? Flows? Flows?

Do they persist deep in the Do they persist deep in the solar convection zone?solar convection zone?

What do they tell us about What do they tell us about the solar dynamo?the solar dynamo?

Parker

SOHO/MDI Sunspot in AR9787

Doppler

Intensity

Magnetic field

Little evolution over 9 days

Cross-covariance between the MDI signal averaged over a vertical line and the MDI signal at any other point in the map. Here for f modes. Gizon 2007; Cameron et al. 2008

Interaction of the solar waves with the sunspot

C(t=0 min) C(t=130 min)

Sunspot seismology

A different game:A different game: The effect of B is strong near the surfaceThe effect of B is strong near the surface We cannot linearize with respect to a quiet-Sun We cannot linearize with respect to a quiet-Sun

reference solar modelreference solar model

The only possible strategy:The only possible strategy: Numerical forward modeling of full waveformsNumerical forward modeling of full waveforms

Numerical Modeling

Numerical simulation of wave Numerical simulation of wave propagation through a general 3D propagation through a general 3D magnetized solar atmosphere magnetized solar atmosphere

Small amplitude waves: linearized ideal Small amplitude waves: linearized ideal MHD equations (+adhoc wave MHD equations (+adhoc wave damping)damping)

Initial value problemInitial value problem Spectral in the horizontal coordinatesSpectral in the horizontal coordinates Finite differences in the z directionFinite differences in the z direction

SLiM, Cameron et al. (2007, 2008) SLiM, Cameron et al. (2007, 2008)

Background models

Solar-like background Solar-like background atmosphereatmosphere

Stabilized against Stabilized against convective instabilitiesconvective instabilities

Quiet-Sun atmosphere Sunspot modelMonolith

Axisymmetric self-similar solution (Deinzer 1965)

B0z=3kG

Background models

Solar-like background Solar-like background atmosphereatmosphere

Stabilized against Stabilized against convective instabilitiesconvective instabilities

Quiet-Sun atmosphere Sunspot modelMonolith

Axisymmetric self-similar solution (Deinzer 1965)

B0z=3kG

Comparison with observationsP1 acoustic wave packet

P1 acoustic wave packet

Cameron, Schunker, Gizon

f p1 p2

Seismology of sunspots:

Waves speed up as they go through a sunspot (f, p1-p4)Waves speed up as they go through a sunspot (f, p1-p4) Partial conversion into slow MHD modes extracts energy Partial conversion into slow MHD modes extracts energy

from the incoming wave packets (Cally & Bogdan)from the incoming wave packets (Cally & Bogdan) The simple sunspot model that we have tested gives The simple sunspot model that we have tested gives

waveforms that are in qualitative agreement with the waveforms that are in qualitative agreement with the observations (f and p1-p4)observations (f and p1-p4)

This model sunspot is shallow (<2 Mm)This model sunspot is shallow (<2 Mm)

It should be possible to refine the solution by using linear It should be possible to refine the solution by using linear inversions around this simple model.inversions around this simple model.

Points to remember

Helioseismology has produced a considerable amount of Helioseismology has produced a considerable amount of discoveries in solar physics: rotation, convection, temporal discoveries in solar physics: rotation, convection, temporal variations, meridional circulation, etc. variations, meridional circulation, etc.

Local helioseismology, although still in development, is Local helioseismology, although still in development, is playing a key role in revealing the complex interactions playing a key role in revealing the complex interactions between internal flows and the magnetic field.between internal flows and the magnetic field.

Probing magnetic activity (and sunspots) is challenging but Probing magnetic activity (and sunspots) is challenging but feasible using numerical simulations of wave propagation.feasible using numerical simulations of wave propagation.

The fields of helio- and asteroseismology are supported by The fields of helio- and asteroseismology are supported by major space- and ground-based projects. major space- and ground-based projects.

Future projects/missions

HelioseismologyHelioseismology:: Continuation of GONG Network (Since 1995, NSF) Continuation of GONG Network (Since 1995, NSF) HMI/SDO (2009, NASA): 4k x 4k images, all the time HMI/SDO (2009, NASA): 4k x 4k images, all the time Solar Orbiter (2017, ESA) Solar Orbiter (2017, ESA)

Asteroseismology: Asteroseismology: Ground-based telescopes, e.g. VLTGround-based telescopes, e.g. VLT COROT (2007, ESA)COROT (2007, ESA) Kepler (2009, NASA)Kepler (2009, NASA) PLATO (2017, ESA) ?PLATO (2017, ESA) ? Ground-based network (SONG)Ground-based network (SONG)

The Solar Dynamics Observatory (NASA)

Launch: December 2009?Launch: December 2009? HMI: Doppler velocity for HMI: Doppler velocity for

helioseismology + vector B helioseismology + vector B AIA: multi-wavelength AIA: multi-wavelength

high-cadence imaging of high-cadence imaging of

chromosphere/coronachromosphere/corona Roughly one 4kx4k image Roughly one 4kx4k image

per second, alwaysper second, always Data flow: ~2 TB/dayData flow: ~2 TB/day

HMI data: full-disk coverage, all the time, at high spatial resolution:HMI data: full-disk coverage, all the time, at high spatial resolution:

Perfect for local helioseismology and to study the evolution of all Perfect for local helioseismology and to study the evolution of all active regions from limb to limb!active regions from limb to limb!