Work Experience July 2016 - Peter Ward and Cathal Murphy:

Two projects 1. Sunspot cycle variations and 2. Oscillation in lightcurve of a star. Method used is wavelet analysis.




Project 1: sunspot cycle variation

Sunspots are regions on the Sun's surface which appear noticeably darker than the surrounding area. The average temperature of the sun is approximately 5500deg Celsius, wheras on a sunspot the temperature is significantly lower but still only go as low as roughly 3500deg C. Sunspots come in a great variety of sizes on average, approximately 50000 miles in diameter (median). They are believed to be caused by activity in the Sun's very powerful magnetic field and more and larger ones are present during the solar maximum, the peak of magnetic activity during the solar cycle, which generally lasts 11 years, and large flares and phenomena like Coronal mass ejection.

Our project was about finding patterns in the changes of sunspots appearence on the sun during the solar cycle. So we analysed at what latitude, on the sun, the sunspot appeared at over a large number of days in particurlarly analysing it over the solar cycle shown (which lasted a bit longer than usual, 12.6 years) to see if some sort of variations occurred and seeing if those found were of any significance.



Butterfly diagram
Fig.1- butterfly diagram. (click on image to enlarge)

We used sunspot latitude verus time (fig. 1) between 1995 to 2015, and applied Fourier transformation(FT) algorithm to find most probable time periods. In order to apply this method we used 'Wavelet' analysis code. The power of the output gives maximum probability



Butterfly diagram
Fig. 2-Power Vs days. The peaks are at roughly 60 days, north peaks before south ~4 days


Butterfly diagram
Fig. 3 -Power Vs days. The peaks are at roughly 30 days, north peaks after south ~2 days




Project 2: Oscillations in light curves of a star

We studied a sample time series of a stellar flare. Here we see a long term trend in the data because of the flare and we wanted to investigate the short term periods. The First step before applying FT was to detrend the data then we applied the same method to find a power spectrum. In this case confidence or significance levels corresponding to various time periods.



wps
Fig1. - De-trended data. (click on image to enlarge)


wps
Fig2. - 3-D Representation of wavelet power spectrum .


wps
(click on image to enlarge) Fig3. - Noise spectrum with confidence levels (0,5%,10%,20%,30%,40%,50%,60%,70%,80%,90%,100%.). The various contours would signify probability of an occurrence of a time period. (red indcates most probable and black the least). This is a relation between Fourier periods (s in logarithmic scale) and time (s). The cross-hatched region is called COI which denotes errors that arise due to FT.




Physics of the analysis

Project 1: sunspot cycle variation

We focussed on short term appearences of the sunspots. We first noticed the trend along ~9.5 years. So we decided to study variations within that time frame taking northern and southern hemisphere separately. But we found that it was skewing the data. So we tried the FT over average length of the Solar cycle (SC). We still found that the data didnt provide any meaningful results.

We then found out that this particular SC was for 12.6 years, and performed wavelet analysis on the data. This showed periodicities at 30 days, 60 days and 100 days. But since we were interested in short term variation we then filtered the analysis for 30 days and 60 days. At 30 days we see that the leading hemisphere is lagging at 60 days. This is because the emergence of Sunspots is blocked by already present layer of dense magnetic fluxes. Thus new sunpots would appear later in one hemisphere than the other. This affects the dynamo process of the SC, and leads to asymmetries. These asymmetries may lead to weaker SCs.



Project 2: Oscillations in light curves of a star

Upon applying the similar wavelet analysis. We find that there are possible periodicity at 40s (90 to 100% confidence). We discussed causes of these periodicities. These could be due to the following : 1.) Planets - When planet goes in front of the parent star. But this would take at least days. 2.) Sunspots - Assuming the star is Sunlike, the we would expect sunpots to vary every 30 days. Thus this cannot be possible cause. 3.) Other eruptions like Coronal mass ejections (CMEs), prominences and so on. These would last for few days again. So we rule this out. 4.) Flares - These would last for days but we see variations in short periods of time. These variations could be due to fluctuating plasma during the eruption. As this plasma is along a flux tube, such periodicities can be related to high-frequency waves.







Last Revised: 2016 August 3rd