1. Recent progress in modelling solar radiative variability on centennial timescales Paul Charbonneau Département de Physique, Université de Montréal
Solar radiative variability
Solar activity and the magnetic cycle
Long-term reconstructions of TSI/SSI
Simulated magnetic cycles
Magnetic modulation of convection
What is next…
Collaborators: Piotr Smolarkiewicz, Mihai Ghizaru, Dario Passos,
Antoine Strugarek, Jean-François Cossette, Patrice Beaudoin, Cassandra
Bolduc, Amélie Bouchat, Caroline Dubé, Nicolas Lawson, Étienne Racine,
Corinne Simard, Gustavo Guerrero, Roxane Barnabé, Zbigniew Piotrowski
McGill AOS 19/01/2015

2. The ones who did the real work
Jean-François Cossette
PhD granted November 2014
Now Hale postdoctoral Fellow at the University of Colorado/Boulder, U.S.A.
Cassandra Bolduc
PhD turned in November 2014
Co-Advisor Michel Bourqui, ex. McGill/AOS
Now postdoc at PMOD/Davos, Switzerland
McGill AOS 19/01/2015

3. Solar/stellar magnetism
19/11/2014, along HWY 40 into Montréal
McGill AOS 19/01/2015

4. TSI = 1362 +/- 4 Watt / m2 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
( km).
Now called Total Solar Irradiance (TSI)
TSI = /- 4 Watt / m2
McGill AOS 19/01/2015

5. The solar constant (2) 1838: IST ~ 690 W/m2 John Herschel (1792-1871)
Claude Pouillet ( )
McGill AOS 19/01/2015

6. The solar constant (3) 1881, Mt Whitney, CA: TSI=2903 W/m2 !!
Samuel Pierpont Langley ( )
(Invented the bolometer)
McGill AOS 19/01/2015

7. The total solar irradiance (1)
(Invented the bolometer)
McGill AOS 19/01/2015

8. The total solar irradiance (2)
Min/max change in Earth’s
equilibrium temperature: 0.04oC
McGill AOS 19/01/2015

9. The solar spectral irradiance
Plot by J. Lean, NRL, courtesy NASA
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 ( nm) accounts for 1% of the TSI, but 14% of its variability.
McGill AOS 19/01/2015

10. Solar/stellar magnetism
« If the sun did not have a magnetic
field, it would be as boring a star as
most astronomers believe it to be »
(Attributed to R.B. Leighton)
McGill AOS 19/01/2015

11. Solar ac SoHO/LASCO C-3 tivity
SoHO/EIT 19.5 nm
McGill AOS 19/01/2015

12. Solar activity
SoHO/LASCO C-3
McGill AOS 19/01/2015

13. Sunspots (1)
SDO / HMI Continuum
McGill AOS 19/01/2015

14. Harriot, Fabricius, Galileo, Scheiner…
McGill AOS 19/01/2015

15. The sunspot cycle (1) Heinrich Schwabe
Discovered in 1843 by an amateur astronomer, after 17 years
of nearly continuous sunspot observations.
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..
Rudolf Wolf
McGill AOS 19/01/2015

16. Sunspots (2) G.E. Hale, F. Ellerman, S.B. Nicholson, and A.H. Joy,
The Astrophysical Journal, 49, , (1919)
McGill AOS 19/01/2015

17. The sunspot cycle (2) 2001, cycle peak Magnetogram
McGill AOS 19/01/2015

18. 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
McGill AOS 19/01/2015

19. Solar activity
McGill AOS 19/01/2015

20. Solar internal structure
McGill AOS 19/01/2015

21. Two schools of thoughts
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.
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.
McGill AOS 19/01/2015

22. Semi-empirical reconstructions of total and spectral solar irradiances [ with C. Bolduc, and a lot of other people…]
McGill AOS 19/01/2015

23. Fragmentation …
McGill AOS 19/01/2015

24. … and erosion
McGill AOS 19/01/2015

25. A fragmentation-based model [ Crouch et al. 2008, ApJ, 677, 723 ]
A Monte Carlo simulation of surface magnetic flux evolution:
Spots of surface area A are injected on a computational
« solar disk » (data from Royal Greenwich Obs.)
Emergences on backside treated statistically
Spots fragment randomly, and erode at their perimeter
These processes of fragmentation/erosion continue until
only elementary magnetic flux tubes are left;
these disappear randomly
The resulting distribution of surface features N(A;t)
is convolved with a contrast function, including limb
darkening, to yield a TSI time series.
McGill AOS 19/01/2015

26. From surface magnetism to TSI [ Crouch et al
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  » :
(Lean et al. 1998; Brandt et al. 1994)
Irradiance excess due to « faculae » and « network » :
(Chapman & Meyer 1986)
Quiet Sun modulation from F10.7 radio flux :
(Tapping et al. 2007)
McGill AOS 19/01/2015

27. Genetic algorithms
A class of optimization methods inspired by biologial evolution, particularly
appropriate for complex, partly stochastic multimodal optimization tasks.
Initialisation: construct a population of random solution; compute their fitness
Select best members of the population
Breed new generation from selected best
Compute fitness of new population members
Fittest solution good enough?
END! NO
YES
McGill AOS 19/01/2015

28. TSI reconstructions (1) [ Bolduc et al. 2015, ApJ, submitted ]
McGill AOS 19/01/2015

29. TSI reconstructions (2) [ Bolduc et al. 2015, ApJ, submitted ]
McGill AOS 19/01/2015

30. 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 !
McGill AOS 19/01/2015

31. Magnetically-mediated cyclic modulation of convective energy transport [ with J.-F. Cossette, P. Smolarkiewicz, M. Ghizaru ]
McGill AOS 19/01/2015

32. The MHD equations
McGill AOS 19/01/2015

33. EULAG-MHD [ Smolarkiewicz & Charbonneau, J. Comput. Phys
EULAG: a robust, general solver for multiscale geophysical flows
EULAG-MHD: MHD generalization of above; developed mostly
at UdeM in close collaboration with Piotr Smolarkiewicz
Core advection scheme: MPDATA, a minimally dissipative
iterative upwind NFT scheme; equivalent to a dynamical, adaptive
subgrid model.
Thermal forcing of convection via volumetric Newtonian cooling term
in energy equation, pushing reference adiabatic profile towards a
very slightly superadiabatic ambiant profile
Strongly stable stratification in fluid layers underlying convecting layers.
Model can operate as LES or ILES
McGill AOS 19/01/2015

34. Simulation design Simulate anelastic convection in thick,
rotating and unstably stratified fluid shell
of electrically conducting fluid, overlaying
a stably stratified fluid shell.
Recent such simulations manage to reach
Re, Rm ~ , at best; a long way from
the solar/stellar parameter regime.
Throughout the bulk of the convecting
layers, convection is influenced by
rotation, leading to alignment of
convective cells parallel to the rotation axis.
Stratification leads to downward pumping
of the magnetic field throughout the
convecting layers.
McGill AOS 19/01/2015

35. Rotation and differential rotation (1)
No rotation
Rotation at solar rate
This is stratified, rotating turbulence !
Vertical (radial) flow velocity, in Mollweide projection
[ from Guerrero et al. 2013, Astrophys. J., 779, 176 ]
McGill AOS 19/01/2015

36. MHD simulation of global dynamos [ Ghizaru et al
MHD simulation of global dynamos [ Ghizaru et al. 2010, ApJL, 715, L133 ]
Temperature perturbation
Radial flow component
Radial magnetic field component
> Que faisons nous > Simulations MHD
Electromagnetic induction by internal flows is the engine powering the solar
magnetic cycle. The challenge is to produce a magnetic field well-structured
on spatial and temporal scales much larger/longer than those associated
with convection itself. This is the magnetic self-organisation problem.
McGill AOS 19/01/2015

37. 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
McGill AOS 19/01/2015

38. Magnetic modulation of convective energy transport in EULAG-MHD simulation [ Cossette et al. 2013, ApJL, 777, L29 ]
The simulation is more « luminous » at magnetic cycle
maximum, by a solar-like 0.2% Lsol !
McGill AOS 19/01/2015

39. How to modulate convective energy transport
Vertical flow speed
Temperature deviation from horizontal mean
Lorentz force modulates convective velocity ur ;
Change in magnitude of temperature perturbations;
Change in degree of correlation between the two;
Change in latitudinal distribution of F .
All of above ? And/or something else … ?
McGill AOS 19/01/2015

40. Spatiotemporal variability of the convective flux [ Cossette et al
Spatiotemporal variability of the convective flux [ Cossette et al. 2013, ApJL, 777, L29 ]
Zonally-averaged toroidal field and convective flux at r/R=0.87
McGill AOS 19/01/2015

41. Convective entrainment and « hot spots »
McGill AOS 19/01/2015

42. Pinning it down… [ Cossette et al. 2013, ApJL, 777, L29 ]
Differences are in the tails
of the flux distributions: hot
spots are enhanced, turbulent
entrainment is suppressed.
The strongest (anti)correlations
with the magnetic cycle are
for the negative convective
fluxes.
McGill AOS 19/01/2015

43. Small (multi)periodic signal in temperature [ Beaudoin et al
Small (multi)periodic signal in temperature [ Beaudoin et al. 2015, in prep. ]
95% confidence
Foukal et al. 2006, Nature 443, : this cannot produce TSI variations !
McGill AOS 19/01/2015

44. Convection is NOT diffusion !
The Newtonian diffusive heat flux is proportional to the temperature gradient; the heat flux is entirely determined by local conditions.
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.
McGill AOS 19/01/2015

45. Convection is NOT diffusion !
McGill AOS 19/01/2015

46. 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-driven
modulation of heat transport may play a significant role in TSI variations.
Global MHD numerical simulations now allow quantitative investigations
of these effects; but need to get closer to the surface to allow detailed
comparison to observations
There is much more to solar impacts on Earth’s atmosphere than
TSI variations.
McGill AOS 19/01/2015

47. One crazy correlation…
Lightning data from Stringfellow 1974, Nature, 249, 332
McGill AOS 19/01/2015

48. FIN
McGill AOS 19/01/2015

49. The « millenium simulation » [ Passos & Charbonneau 2014, A&A, in press ]
Define a SSN proxy, measure cycle characteristics (period, amplitude…) and compare to observational record.
McGill AOS 19/01/2015

50. Magnetic cycles (1) Zonally-averaged Bphi at r/R =0.718
Zonally-averaged Bphi at -58o latitude
McGill AOS 19/01/2015

51. 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.
McGill AOS 19/01/2015

52. Characteristics of simulated cycles (2) [ Passos & Charbonneau 2014, A&A, in press ]
0.957/0.947
[ 0.763/0.841 ]
r =
-0.395/-0.147
[ / ]
r =
0.688/0.738
[ 0.322/0.451 ]
r =
-0.465/-0.143
[ 0.185/ ]
McGill AOS 19/01/2015

53. Characteristics of simulated cycles (3)
Hemispheric cycle amplitude show a hint of bimodality
Usoskin et al. 2014,
A&A 562, L10;
From 3000yr 14C
time series
McGill AOS 19/01/2015

54. Characteristics of simulated cycles (4)
Hemispheric cycle amplitude show a hint of bimodality
Usoskin et al. 2014,
A&A 562, L10;
From 3000yr 14C
time series
McGill AOS 19/01/2015

55. Rotation and differential rotation (2)
Helioseismology
HD simulation
MHD simulation
Angular velocity profiles, in meridional quadrant
Differential rotation in the Sun and solar-type stars is powered
by turbulent Reynolds stresses, arising from rotationally-induced
anisotropy in turbulent transport of momentum and heat
McGill AOS 19/01/2015

56. Selected milestones
Gilman 1983: Boussinesq MHD simulation, producing large-scale magnetic fields with polarity reversals on yearly timescale; but non-solar large-scale organization.
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.
Brun et al. 2004: Strongly turbulent MHD simulation, producing copious
small-scale magnetic field but no large-scale magnetic component.
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.
Brown et al. 2010, 2011: Obtain irregular polarity reversals of thin, intense
toroidal field structure in a turbulent simulation rotating at 5X solar.
Ghizaru et al. 2010: Obtain regular polarity reversals of large-scale magnetic component on decadal timescales, showing many solar-like characteristics.
Nelson et al. 2012, 2013: Autonomous generation of buoyantly rising flux-ropes structures showing sunspot-like emergence patterns.
McGill AOS 19/01/2015

57. 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
McGill AOS 19/01/2015

58. EULAG-MHD Application to solar convection
Rewrite (1), (2) and (3) as :
McGill AOS 19/01/2015

59. The magnetic self-organization conundrum
How can turbulent convection, a flow with a length scale <<R
and coherence time of ~month, generate a magnetic component
with 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.
McGill AOS 19/01/2015

60. Successes and problems
KiloGauss-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.
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.
Reasonably solar-like internal differential rotation, and solar-like
cyclic torsional oscillations (correct amplitude and phasing).
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 the
magnetic cycle.
McGill AOS 19/01/2015