Time series analysis methods in vivo and silico

1. Nigul Olspert Aalto University ICS nigul.olspert@aalto.fi Time series analysis methods in vivo and silico

2. Outline • General goals • In vivo (datasets of the Sun and other stars) • In silico (datasets from DNS simulations) • Statistical methods • Carrier fit method • Frequency dependent correlation method • Method of time delays • Case study of a young solar analogue LQ Hya with CF method

3. General goals (in vivo) • Analysis of solar and stellar datasets with the statistical method toolbox • Long-term data sets of solar activity tracers (TSI, sunspots, flares, CMEs, coronal holes, extreme events) to form as accurate as possible understanding of the toroidal and poloidal phases of the solar dynamo • Long-term data sets of stellar activity tracers (photometry, spectroscopy, spectropolarimetry) to quantitatively characterize the magnetic activity in young solar analogues

4. General goals (in silico) • Analysis of solar-like solutions from simulations • Relating in silico statistical properties to observable ones • Refining the models accordingly • Studying different dynamo paradigms

5. General goals (in silico) • Analysis of young sun solutions • Characterization of dynamo modes and the nature of stellar cycles • Study of the processes causing time-dependent behavior (such as Maunder minimum)

6. Carrier fit method • Suitable for analyzing time series in which a fast clocking frequency (such as the rotation of the star) is modulated with a slower process (such as the stellar activity cycle) • Benefits • Applicable for data with gaps • Small number of free parameters • Informative visualization technique via colored phase diagrams with normalized amplitudes • Enables to detect • Active longitudes (azimuthal dynamo wave) • Phase shifts and flip-flops

7. Frequency dependent correlation method • More general than linear correlation techniques • Two variables may be uncorrelated in one frequency band but correlated/anticorrelated in other band • Model is built using successive smooth and clip operations • Possible applications • Find dependencies between different solar proxies like TSI (or flares) and sunspot areas • Predicting/hindcasting

8. Method of time delays • Problem setting • Physical variable observed through multiple channels • Possible application • Time delays between measurements done in different stations of magnetometer network • Useful for estimating spatial distributions of magnetic storm events • Time delays can be estimated from • Methods based on cross-correlation • Dispersion spectra • Interpolation based methods (to fill the gaps in data)

9. Current study of LQ Hya • Young solar analogue • K2-dwarf, age 35−55 Myr, strong Hα and Ca II H&K emission • Previous period estimates vary around 1d.6

10. Current study of LQ Hya • Nonaxisymmetric spot distribution • Large spots/spot groups • Coherence time of the nonaxisymmetric structures is an order of magnitude longer than that one of the Sun • Future tasks • Find optimal period using CF method • Compare with results from Doppler imaging Zeeman-Doppler imaging