Using Sunspot Demographics to Probe the Small- Scale vs...

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

SOLAR PHOTOSPHERIC MAGNETISM

SDO/HMI

It spans a wide variety of scales SDO/HMI

Hinode/SOT

WHERE DOES IT COME FROM?

Bipolar Magnetic Regions and The Global Component of the Dynamo

Movie by David Hathaway

• 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 (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 (BMRs) are believed to be the photospheric signature of buoyant emergent flux-tubes


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

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.


Credit: SOHO/NASA/ESA

• The solar cycle modulates a wide array of geoeffective quantities: – Solar Wind. – Solar Irradiance. – Flare and CME rate.


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


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?


OUR DATA

Sunspots are the optical signature of the presence of magnetic fields

SDO/HMI

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.

SUNSPOT DEMOGRAPHICS

Population Pyramids Powerful tool for understanding the makeup and history of a population

Colombia 2015

China 2015

Source: http://populationpyramid.net/


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/


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= − −

Single Fits Sunspot Group Area

Sunspot Area

BMR Flux

Single Fits Better Fitted by Weibull

Better Fitted by Log-Normal

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

Weibull

Log-Normal

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.

Weibull

Log-Normal

• Our results suggest that photospheric magnetic structures arise from two different mechanisms (global vs. small-scale components of the dynamo).

Coincidence or Evidence?

Transition between distributions

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


• 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


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

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)


( )( )2

21 ln

2( | , , , , ) 12


cc σµ

λλλ

µπσ

σλ

− − − − = − +


et al 2003, 2008). • The Log-Normal parameters correlate strongly with activity level

Mean (µ) Variance (σ) Proportionality (c)


( )( )2

21 ln

2( | , , , , ) 12


cc σµ

λλλ

µπσ

σλ

− − − − = − +


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.

ESTIMATING THE MAGNETIC BASELINE

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


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.

CONCLUDING REMARKS

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.

Using Sunspot Demographics to Probe the Small- Scale vs...

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