[Paper Review] The solar magnetic field since 1700: I. Characteristics of sunspot group emergence and reconstruction of the butterfly diagram

Jie Jiang, R. H. Cameron+2 more|arXiv (Cornell University)|Feb 7, 2011

Solar and Space Plasma Dynamics31 references54 citations

TL;DR

This paper reconstructs the solar butterfly diagram from 1700 onward using semi-synthetic sunspot group data derived from statistical correlations between sunspot group properties—such as latitude, area, tilt angle, and longitude—and the group sunspot number ($R_G$). By modeling these correlations, the authors generate time-resolved, statistically consistent reconstructions of sunspot emergence, enabling long-term studies of the Sun's magnetic field evolution, particularly for flux transport and irradiance modeling.

ABSTRACT

We use the historic record of sunspot groups compiled by the Royal Greenwich Observatory together with the sunspot number to derive the statistical properties of sunspot group emergence in dependence of cycle phase and strength. In particular we discuss the latitude, longitude, area and tilt angle of sunspot groups as functions of the cycle strength and of time during the solar cycle. Using these empirical characteristics the time-latitude diagram of sunspot group emergence (butterfly diagram) is reconstructed from 1700 onward on the basis of the Wolf and group sunspot numbers. This reconstruction will be useful in studies of the long-term evolution of the Sun's magnetic field.

Motivation & Objective

• To reconstruct the long-term evolution of the solar butterfly diagram from 1700 onward using only sunspot number data.
• To model the statistical relationships between sunspot group emergence characteristics (latitude, area, tilt, longitude) and solar cycle properties (phase, strength).
• To generate semi-synthetic datasets of sunspot group emergence for use in long-term solar magnetic field modeling.
• To enable Monte Carlo-style studies of solar open flux, polar field evolution, and irradiance variations over centuries.

Proposed method

• Use the group sunspot number ($R_G$) as the time base for reconstructing sunspot group emergence from 1700 onward.
• Establish empirical correlations between $R_G$-derived cycle parameters (strength, phase) and sunspot group properties (latitude, area, tilt, longitude) using RGO, MWO, and Kodaikanal datasets.
• Model the mean emergence latitude as a second-order polynomial function of cycle phase, with cycle strength-dependent amplitude.
• Simulate sunspot group areas using a power-law for small groups and a log-normal distribution for large groups, with mean area increasing during cycle maxima.
• Incorporate tilt angle statistics and longitude distribution based on observed correlations with cycle strength and phase.
• Generate semi-synthetic butterfly diagrams by drawing random realizations from the derived statistical distributions, conditioned on $R_G$ and $R_Z$ time series.

Experimental results

Research questions

• RQ1 How do the mean emergence latitude and latitudinal spread of sunspot groups vary with solar cycle phase and strength?
• RQ2 What is the statistical relationship between sunspot group area distribution and cycle phase or cycle strength?
• RQ3 How do tilt angles and longitudinal distributions of sunspot groups correlate with cycle parameters?
• RQ4 To what extent can the butterfly diagram be reconstructed from $R_G$ alone using empirical correlations?
• RQ5 How do differences between $R_G$ and $R_Z$ affect the reconstructed butterfly diagrams before 1874?

Key findings

• The mean emergence latitude of sunspot groups follows a second-order polynomial in cycle phase, with stronger cycles showing higher mean latitudes.
• The ratio of latitudinal spread to mean emergence latitude varies systematically with cycle phase, indicating a non-uniform distribution of activity across the solar disk.
• Sunspot group area distributions are consistent across cycles, with a power-law dependence for small groups and a log-normal profile for large groups.
• Mean sunspot group areas are significantly larger during cycle maxima, especially in strong cycles.
• Sunspot nests—clusters of groups—play a prominent role during cycle maxima, contributing to the observed peak in group numbers.
• Reconstructed butterfly diagrams based on $R_G$ and $R_Z$ show small but cycle-dependent differences in mean latitude and emergence pattern prior to 1874, reflecting discrepancies between the two sunspot number series.