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Recent progress in modelling solar radiative variability on centennial timescales

Paul Charbonneau Département de Physique, Université de Montréal

1.Solar radiative variability2.Solar activity and the magnetic cycle3.Long-term reconstructions of TSI/SSI 4.Simulated magnetic cycles5.Magnetic modulation of convection6.What is next…

Collaborators: Piotr Smolarkiewicz, Mihai Ghizaru, Dario Passos,Antoine Strugarek, Jean-François Cossette, Patrice Beaudoin, CassandraBolduc, Amélie Bouchat, Caroline Dubé, Nicolas Lawson, Étienne Racine, Corinne Simard, Gustavo Guerrero, Roxane Barnabé, Zbigniew Piotrowski

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The ones who did the real work

Cassandra BolducPhD turned in November 2014Co-Advisor Michel Bourqui, ex. McGill/AOSNow postdoc at PMOD/Davos, Switzerland

Jean-François CossettePhD granted November 2014Now Hale postdoctoral Fellow at the University of Colorado/Boulder, U.S.A.

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Solar/stellar magnetism19/11/2014, along HWY 40 into Montréal

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The solar constant (1)

Definition: Wavelength-integrated electromagnetic energy illuminating one square meter of Earth’s upper atmosphere, at a Sun-Earth distance of one astronomical unit (149598500 km).

Now called Total Solar Irradiance (TSI)

TSI = 1362 +/- 4 Watt / m2

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The solar constant (2)

Claude Pouillet (1790-1868)

1838: IST ~ 690 W/m2

John Herschel (1792-1871)

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The solar constant (3)

1881, Mt Whitney, CA: TSI=2903 W/m2 !!

Samuel Pierpont Langley (1834-1906)

(Invented the bolometer)

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The total solar irradiance (1)

(Invented the bolometer)

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The total solar irradiance (2)

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Min/max change in Earth’sequilibrium temperature: 0.04oC

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The solar spectral irradiance

From UV to X-Rays, variability increases a lot with decreasing wavelength;However, the bulk of electromagnetic energy at these wavelengths is absorbed very high in the Earth’s atmosphere (stratosphere and higher).The UV (120-400nm) accounts for 1% of the TSI, but 14% of its variability.

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Solar/stellar magnetism

« If the sun did not have a magnetic field, it would be as boring a star asmost astronomers believe it to be »

(Attributed to R.B. Leighton)

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Solar ac SoHO/LASCO C-3 tivity

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Solar activity

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Sunspots (1)

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Harriot, Fabricius, Galileo, Scheiner…

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The sunspot cycle (1)

Discovered in 1843 by an amateur astronomer, after 17 yearsof nearly continuous sunspot observations.

HeinrichSchwabe

Rudolf Wolf

The sunspot cycle has a period of approximately 11 years,and its amplitude shows large cycle-to-cycle fluctuations,as well as extended episodes of apparent halt..

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Sunspots (2)

G.E. Hale, F. Ellerman, S.B. Nicholson, and A.H. Joy,The Astrophysical Journal, 49,153-178, (1919)

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The sunspot cycle (2)

2001, cycle peak Magnetogram

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The solar magnetic cycle

The solar magnetic cycle has a period of ~22 yr, but solar activity does not care about magnetic polarity, so that solar activity cycles on a ~11 yr period

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Solar activity

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Solar internal structure

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Two schools of thoughts

1. All TSI variation on all relevant timescales are due to varying surface coverage of magnetic features (spots, faculae, network, etc.). Strongest evidence: reconstructions based on photospheric data can reproduce 95% of observed variance.

2. Some TSI variations on timescales decadal and longer originate from deep inside the sun (changes in solar radius, photospheric temperature gradient, magnetic modulation of convective energy flux, etc.). Strongest evidence: cyclic modulation of p-mode frequencies.

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Semi-empirical reconstructions of total and spectral solar irradiances

[ with C. Bolduc, and a lot of other people…]

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Fragmentation …

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… and erosion

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A fragmentation-based model[ Crouch et al. 2008, ApJ, 677, 723 ]

A Monte Carlo simulation of surface magnetic flux evolution:

1. Spots of surface area A are injected on a computational « solar disk » (data from Royal Greenwich Obs.)2. Emergences on backside treated statistically 3. Spots fragment randomly, and erode at their perimeter 4. These processes of fragmentation/erosion continue until only elementary magnetic flux tubes are left; these disappear randomly5. The resulting distribution of surface features N(A;t) is convolved with a contrast function, including limb darkening, to yield a TSI time series.

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From surface magnetism to TSI[ Crouch et al. 2008, ApJ, 677, 723; Bolduc et al. 2015, ApJ, submitted ]

A four-component model: quiet sun, spots, faculae, network:

Irradiance deficit due to « spots  » :

Irradiance excess due to « faculae » and « network » :

(Chapman & Meyer 1986)

(Lean et al. 1998; Brandt et al. 1994)

Quiet Sun modulation from F10.7 radio flux :

(Tapping et al. 2007)

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Genetic algorithms

A class of optimization methods inspired by biologial evolution, particularlyappropriate for complex, partly stochastic multimodal optimization tasks.

Breed new generation from selected best

Select best members of the population

Compute fitness of new population members

Initialisation: construct a population of random solution; compute their fitness

Fittest solution good enough? END!NO YES

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TSI reconstructions (1)[ Bolduc et al. 2015, ApJ, submitted ]

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TSI reconstructions (2)[ Bolduc et al. 2015, ApJ, submitted ]

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TSI reconstructions (3)[ Bolduc et al. 2015, ApJ, submitted ]

Reconstructions going back centuries or millennia take the models far out of their calibration regimes : extrapolation is dangerous !

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Magnetically-mediated cyclic modulation of convective energy transport

[ with J.-F. Cossette, P. Smolarkiewicz, M. Ghizaru ]

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The MHD equations

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EULAG-MHD[ Smolarkiewicz & Charbonneau, J. Comput. Phys. 236, 608-623 (2013) ]

EULAG: a robust, general solver for multiscale geophysical flows

EULAG-MHD: MHD generalization of above; developed mostlyat UdeM in close collaboration with Piotr Smolarkiewicz

Core advection scheme: MPDATA, a minimally dissipativeiterative upwind NFT scheme; equivalent to a dynamical, adaptivesubgrid model.

Thermal forcing of convection via volumetric Newtonian cooling termin energy equation, pushing reference adiabatic profile towards avery slightly superadiabatic ambiant profile

Strongly stable stratification in fluid layers underlying convecting layers.

Model can operate as LES or ILES

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Simulation design

Simulate anelastic convection in thick,rotating and unstably stratified fluid shellof electrically conducting fluid, overlayinga stably stratified fluid shell.

Recent such simulations manage to reachRe, Rm ~102-103, at best; a long way fromthe solar/stellar parameter regime.

Throughout the bulk of the convectinglayers, convection is influenced byrotation, leading to alignment of convective cells parallel to the rotation axis.

Stratification leads to downward pumpingof the magnetic field throughout the convecting layers.

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Rotation and differential rotation (1)

Vertical (radial) flow velocity, in Mollweide projection[ from Guerrero et al. 2013, Astrophys. J., 779, 176 ]

No rotation Rotation at solar rate

This is stratified, rotating turbulence !

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MHD simulation of global dynamos [ Ghizaru et al. 2010, ApJL, 715, L133 ]

Electromagnetic induction by internal flows is the engine powering the solarmagnetic cycle. The challenge is to produce a magnetic field well-structuredon spatial and temporal scales much larger/longer than those associatedwith convection itself. This is the magnetic self-organisation problem.

Temperature perturbation Radial flow component Radial magnetic field component

http://www.astro.umontreal.ca/~paulchar/grps > Que faisons nous > Simulations MHD

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Simulated magnetic cycles (1)

Large-scale organisation of the magnetic field takes place primarily at and immediately below the base of the convecting fluid layers

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Magnetic modulation of convective energy transport in EULAG-MHD simulation

[ Cossette et al. 2013, ApJL, 777, L29 ]

The simulation is more « luminous » at magnetic cyclemaximum, by a solar-like 0.2% Lsol !

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How to modulate convective energy transport

1. Lorentz force modulates convective velocity ur ;2. Change in magnitude of temperature perturbations;3. Change in degree of correlation between the two; 4. Change in latitudinal distribution of F .5. All of above ? And/or something else … ?

Temperature deviation from horizontal mean

Vertical flow speed

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Spatiotemporal variabilityof the convective flux

[ Cossette et al. 2013, ApJL, 777, L29 ]Zonally-averaged toroidal field and convective flux at r/R=0.87

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Pinning it down…[ Cossette et al. 2013, ApJL,

777, L29 ]

Differences are in the tailsof the flux distributions: hotspots are enhanced, turbulententrainment is suppressed.

The strongest (anti)correlationswith the magnetic cycle arefor the negative convectivefluxes.

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Small (multi)periodic signal in temperature[ Beaudoin et al. 2015, in prep. ]

95% confidence

Foukal et al. 2006, Nature 443, 161-166: this cannot produce TSI variations !

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Convection is NOT diffusion !

1. The Newtonian diffusive heat flux is proportional to the temperature gradient; the heat flux is entirely determined by local conditions.

2. The convective heat flux is proportional to temperature at point of origin of upflows and downflows; for strongly turbulent convection, these flow structures can cross many scale heights; the heat flux is strongly non-local.

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Convection is NOT diffusion !

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The least you should remember from this talk

The solar magnetic cycle drives all of solar activity, including radiative variability at all wavelengths.

Solar radiative variability is strongly wavelength-dependent.

Radiative variability on short timescales is dominated by the surface coverage of various magnetic features.

On long timescales (decadal and up), deep-seated, magnetically-drivenmodulation of heat transport may play a significant role in TSI variations.

Global MHD numerical simulations now allow quantitative investigationsof these effects; but need to get closer to the surface to allow detailedcomparison to observations

There is much more to solar impacts on Earth’s atmosphere thanTSI variations.

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One crazy correlation…

Lightning data from Stringfellow 1974, Nature, 249, 332

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FIN

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The « millenium simulation »[ Passos & Charbonneau 2014, A&A, in press ]

Define a SSN proxy, measure cycle characteristics (period, amplitude…) and compare to observational record.

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Magnetic cycles (1)Zonally-averaged Bphi at r/R =0.718

Zonally-averaged Bphi at -58o latitude

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Characteristics of simulated cycles (1)[ Passos & Charbonneau 2014, A&A, in press ]

Define a SSN proxy, measure cycle characteristics (period, amplitude…) and compare to observational record.

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Characteristics of simulated cycles (2)[ Passos & Charbonneau 2014, A&A, in press ]

r = 0.957/0.947[ 0.763/0.841 ]

r = -0.465/-0.143[ 0.185/-0.117 ]

r = 0.688/0.738[ 0.322/0.451 ]

r = -0.395/-0.147[ -0.552/-0.320 ]

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Characteristics of simulated cycles (3)

Hemispheric cycle amplitude show a hint of bimodality

Usoskin et al. 2014,A&A 562, L10;

From 3000yr 14Ctime series

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Characteristics of simulated cycles (4)Hemispheric cycle amplitude show a hint of bimodality

Usoskin et al. 2014,A&A 562, L10;

From 3000yr 14Ctime series

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Rotation and differential rotation (2)

Angular velocity profiles, in meridional quadrant

Helioseismology HD simulation MHD simulation

Differential rotation in the Sun and solar-type stars is poweredby turbulent Reynolds stresses, arising from rotationally-induced

anisotropy in turbulent transport of momentum and heat

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Selected milestones

Browning et al. 2006: Demonstrate the importance of an underlying,

convectively stable fluid layer below the convection zone in producing

a large-scale magnetic component in the turbulent regime.

Brun et al. 2004: Strongly turbulent MHD simulation, producing copious

small-scale magnetic field but no large-scale magnetic component.

Glatzmaier 1984, 1985: Anelastic model including stratification, large-scale

fields with polarity reversals within a factor 2 of solar period; tendency for

poleward migration of the large-scale magnetic field.

Gilman 1983: Boussinesq MHD simulation, producing large-scale magnetic fields with polarity

reversals on yearly timescale; but non-solar large-scale organization.

Brown et al. 2010, 2011: Obtain irregular polarity reversals of thin, intense

toroidal field structure in a turbulent simulation rotating at 5X solar.

Nelson et al. 2012, 2013: Autonomous generation of buoyantly rising flux-ropes structures showing sunspot-like emergence patterns.

Ghizaru et al. 2010: Obtain regular polarity reversals of large-scale magnetic component on decadal timescales, showing many solar-like characteristics.

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FIN

Collaborators: Piotr Smolarkiewicz (NCAR), Mihai Ghizaru,

Étienne Racine (CSA), Jean-François Cossette, Patrice Beaudoin,

Nicolas Lawson, Amélie Bouchat, Corinne Simard, Caroline Dubé,

Dario Passos

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EULAG-MHDApplication to solar convection

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Rewrite (1), (2) and (3) as :

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The magnetic self-organization conundrum

How can turbulent convection, a flow with a length scale <<Rand coherence time of ~month, generate a magnetic componentwith scale ~R varying on a timescale of ~decade ??

Mechanism/Processes favoring organization on large spatial scales: 1. rotation (cyclonicity); 2. differential rotation (scale ~R); and 3. turbulent inverse cascades.

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Successes and problemsKiloGauss-strength large-scale magnetic fields, antisymmetric about

equator and undergoing regular polarity reversals on decadal timescales.

Cycle period four times too long, and strong fields concentrated

at mid-latitudes, rather than low latitudes.

Reasonably solar-like internal differential rotation, and solar-like

cyclic torsional oscillations (correct amplitude and phasing).

Internal magnetic field dominated by toroidal component and

strongly concentrated immediately beneath core-envelope interface.

Well-defined dipole moment, well-aligned with rotation axis,

but oscillating in phase with internal toroidal component.

On long timescales, tendency for hemispheric decoupling, and/or

transitions to non-axisymmetric oscillatory modes.Cyclic modulation of the convective energy flux, in phase with themagnetic cycle.