using sunspot demographics to probe the small- scale vs...
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Using Sunspot Demographics to Probe the Small-Scale vs. Global Components of the Dynamo
Andrés Muñoz-Jaramillo www.solardynamo.org
Funded by: Jack Eddy Fellowship of NASA - Living a Star
Contract SP02H1701R from Lockheed-Martin to the SAO NSF REU program
• Equatorward migration of active latitudes.
• Poleward migration of their decayed diffuse field
• Polar field reversal at the maximum of the cycle.
Image by David Hathaway
Bipolar Magnetic Regions and The Global Component of the Dynamo
Bipolar magnetic regions (BMRs) are believed to be the photospheric signature of buoyant emergent flux-tubes
Weber, Fan, & Miesch (2011)
Fan (2008)
Jouve, Brun, & Aulanier (2013)
Nelson et al. (2014)
Bipolar Magnetic Regions and The Global Component of the Dynamo
Bipolar magnetic regions (BMRs) are believed to be the photospheric signature of buoyant emergent flux-tubes
Bipolar Magnetic Regions and The Global Component of the Dynamo
These flux tubes originate from large-scale belts of toroidal field inside the convection zone.
Brown et al. (2010)
Racine et al. (2011)
Quiet-Sun Magnetism and the Small-Scale Component of the Dynamo
Driven by the interaction of turbulent convection and magnetic fields and it can be observed all through the photosphere (including at solar
minimum)
Image by I. Kitiashvili
Rempel (2014)
Image by R. Stein
Typical length-scales match those of convection
Are these two different dynamos? The large-scale structures from which BMRs originate arise through the
dynamic organization of small-scale magnetic fields.
There is only one solar dynamo and it operates all through the convection zone.
WHY DO WE WANT TO UNDERSTAND THE GLOBAL AND SMALL-SCALE COMPONENTS OF THE DYNAMO? One of the reasons
• The solar cycle modulates a wide array of geoeffective quantities: – Solar Wind
Finding the solar magnetic baseline
Image taken from ESA
• The solar cycle modulates a wide array of geoeffective quantities: – Solar Wind. – Solar Irradiance.
Finding the solar magnetic baseline
Credit: SOHO/NASA/ESA
• The solar cycle modulates a wide array of geoeffective quantities: – Solar Wind. – Solar Irradiance. – Flare and CME rate.
Finding the solar magnetic baseline
Aschwanden & Freeland 2012 Owens & Lockwood 2012
• The solar cycle modulates a wide array of geoeffective quantities: – Solar Wind. – Solar Irradiance. – Flare and CME rate. – Cosmic ray flux
Finding the solar magnetic baseline
Bazilevskaya et al. 2014
• The solar cycle modulates a wide array of geoeffective quantities: – Solar Wind. – Solar Irradiance. – Flare and CME rate. – Cosmic ray flux
• If emergence of BMRs stops (like during the Maunder Minimum), what happens to these quantities?
What is the basal level of solar magnetism?
Finding the solar magnetic baseline
Sunspots are the optical signature of the presence of magnetic fields
SDO Sunspot Groups
MDI Sunspot Umbrae
SDO Sunspot Umbrae
Sunspot area is a good proxy for magnetic flux.
We have good sunspot databases spanning nearly 140 years.
Our Data • Sunspot Group Area:
– Royal Greenwich Observatory (RGO). 1874 - 1976. – Solar Observing Optical Network (SOON). 1985 - present. – Pulkovo’s catalogue of solar activity (PCSA). 1938 - 1991. – Kislovodsk Mountain Astronomical Station (KMAS). 1954 - present. – SDO/HMI. 2010 - present.
• Sunspot Area: – SOHO/MDI Umbral. 1996 - 2010. – SDO/HMI Umbral. 2010 - present. – San Fernando Observatory (SFO). 1983 - present.
• Bipolar Magnetic Region Flux: – KPVT. 1976 - 1986. – SOHO/MDI. 1996 - 2010. – KPVT/SOLIS. 1996 - present.
• Structures near the lower detection threshold suffer from a host of issues that can potentially distort our statistical analysis.
Data Truncation
• To avoid this issues, we impose a truncation limit one order of magnitude above the minimum size of detection.
Data Truncation
• To avoid this issues, we impose a truncation limit one order of magnitude above the minimum size of detection.
Data Truncation
Only data inside dark areas is included in our fits and analysis, light areas are shown for visual reference.
Population Pyramids Powerful tool for understanding the makeup and history of a population
Colombia 2015
China 2015
Source: http://populationpyramid.net/
Population Pyramids Powerful tool for understanding the makeup and history of a population
China 2015
Great Leap Forward (1958-1960)
One Child Policy (1980)
Pre One Child Policy echo
One Child Policy Relaxation (2013)
Source: http://populationpyramid.net/
Population Pyramids Powerful tool for understanding the makeup and history of a population
Empirical distribution of area/flux, normalized so that it becomes a
probability density function (PDF)
AREA AND FLUX DISTRIBUTION
Muñoz-Jaramillo et al., ApJ, 800:48, 2015 In collaboration with Ryan Senkpeil, John Windmueller, Ernest Amouzou, Dana Longcope, Andrey Tlatov, Yury Nagovitsyn, Alexei Pevtsov, Gary Chapman, Angela Cookson, Anthony Yeates, Fraser Watson, Laura Balmaceda, Piet Martens, & Ed DeLuca
Which distribution to use?
Tang et al. (1984) Schrijver et al. (1997)
Bogdan et al. (1988) Baumann & Solanki (2005) Zhang et al. (2010) Schad & Penn (2010)
Parnell (2002) Zharkov et al. (2005) Meunier (2003) Hagenaar et al. (2003) Parnell et al. (2009)
Power Law Log-Normal Weibull
Exponential
Composite Distributions Kuklin (1980) Harvey & Zwaan (1993) Jiang et al. (2011) Nagovitsyn et al. (2012)
Which distribution to use? • We fitted all our 11 databases with these four distributions
(power-law, log-normal, Weibull, and exponential).
• We applied a quantitative model selection criterion called Akaike’s Information Criterion (AIC; Akaike 1983):
• In AIC, the model’s log-likelihood (lk) and the fitted model’s degrees of freedom (n) are used to strike a balance between underfitting and overfitting.
( )AIC 2lk 2M n= − −
Why two distinct groups? • Databases better fitted by a Weibull (log-normal)
cover the largest (smallest) range of values.
What if different sets are sampling different sections of a single
distribution?
We tested this hypothesis by referencing all our databases to
RGO sunspot group area
Composite Fit
• A histogram using logarithmic bins shows distinct peaks (Nagovitsyn et al. (2012)
• This is visible on the empirical distribution as a change in curvature.
• We fit a composite distribution made of a Weibull and a log-normal. We find it to be the best model of all.
• Our results suggest that photospheric magnetic structures arise from two different mechanisms (global vs. small-scale components of the dynamo).
Coincidence or Evidence?
Consistence with the results of Parnell et al. (2009)
Applying six different detection algorithms on MDI/HR, MDI/FD, and SOT/NFI magnetograms, they found a power-law distribution covering more than five orders of magnitude in flux
Extrapolating outside of our data range we find the linear behavior expected of a power-law fit.
CYCLE DEPENDENCE OF SUNSPOT GROUP PROPERTIES Muñoz-Jaramillo et al., Submitted, 2015 In collaboration with Ryan Senkpeil, Dana Longcope, Andrey Tlatov, Alexei Pevtsov, Piet Martens, & Ed DeLuca
Pole
Activity Level: A New Way of Binning Data
• Cycle evolution of active regions and sunspots is normally done by comparing separate cycles or phases (minimum vs. maximum).
• This approach is sub-optimal for studying sunspot and BMR properties. Why?
Pole
Activity Level: A New Way of Binning Data
• The lifetime of an active region is but an instant compared with the cycle.
• Assumption: The global properties of a cycle are irrelevant for determining the properties of active regions. Only activity level is important.
Pole
Activity Level: A New Way of Binning Data
• The lifetime of an active region is but an instant compared with the cycle.
• Assumption: The global properties of a cycle are irrelevant for determining the properties of active regions. Only activity level is important.
Pole
Activity Level: A New Way of Binning Data
Statistical properties associated with low activity levels are observed in every cycle. Statistical properties can be different in each hemisphere.
Pole
Activity Level and the empirical distribution function
• There is a very clear dependence of the relative amount of large sunspot groups and higher activity levels.
• The Weibull-Log-Normal composite captures successfully this variation
Pole
Activity Level and the empirical distribution function
• There is a very clear dependence of the relative amount of large sunspot groups and higher activity levels.
• The Weibull-Log-Normal composite captures successfully this variation
Activity level and the analytic probability density function
( )( )2
21 ln
2( | , , , , ) 12
kx xkk xf x k c e ex
cc σµ
λλλ
µπσ
σλ
− − − − = − +
• The Weibull’s parameters are not correlated activity level (Hagenaar
et al 2003, 2008).
Scale Factor (λ) Scale Factor (k)
Activity level and the analytic probability density function
( )( )2
21 ln
2( | , , , , ) 12
kx xkk xf x k c e ex
cc σµ
λλλ
µπσ
σλ
− − − − = − +
• The Weibull’s parameters are not correlated activity level (Hagenaar
et al 2003, 2008). • The Log-Normal parameters correlate strongly with activity level
Mean (µ) Variance (σ) Proportionality (c)
Activity level and the analytic probability density function
( )( )2
21 ln
2( | , , , , ) 12
kx xkk xf x k c e ex
cc σµ
λλλ
µπσ
σλ
− − − − = − +
• The Weibull’s parameters are not correlated activity level (Hagenaar
et al 2003, 2008). • The Log-Normal parameters correlate strongly with activity level
• Cycle-dependent variations of the size-flux distribution are dictated exclusively by the large BMRs!
• Further support in favor of separate mechanisms giving rise to the Weibull and log-normal components.
Pole
Using the size-flux distribution to estimate the characteristic magnetic feature size
( )( ) ( ) ( ) ( )2
21( | ) 1 1AL
AL
kc ALE x A ec AL L
σµ
λ+ = − Γ + +
• We can calculate the expected value and variance given a particular activity level.
( )( )2
21 ln
2( | , , , , ) 12
kx xkk xf x k c e ex
cc σµ
λλλ
µπσ
σλ
− − − − = − +
Pole
Using the size-flux distribution to estimate the characteristic magnetic feature size
Structures associated with the Weibull component determine the magnetic baseline. Most hemispheric cycles reach this baseline.
Pole
The story is different from a whole sun Perspective
Only two cycles in the past 135 years has ever reached the magnetic baseline. The minimum of cycle 23 was not one of those.
Pole
• There is a hoard of untapped useful information hidden in the details of sunspot and magnetic feature statistics.
• We find that the size-flux distribution is best characterized by a composite distribution with Weibull and Log-Normal components. The log-normal associated with groups and active regions, the Weibull with pores and ephemeral regions.
• Only the statistical properties of the log-normal population, the active regions, is found to vary with the solar cycle.
• We propose that magnetic structures associated with the Weibull distribution are responsible for the solar magnetic baseline.
• This basal state has been reached simultaneously by both hemispheres only in two (out of 13) minima during the last 135 years. The minimum of cycle 23 was not one of them.