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We propose an efficient numerical method for solving a non-linear ordinary differential equation describing the stellar structure of the slowly rotating polytropic fluid sphere. The Ramanujan’s method i.e. an iterative method has been used to determine the roots of the obtained series through special function as it gives the accurate numerical results to the series solution as any other computational methods. Therefore, it can be used as an application to astrophysics and astronomy. The numerical results are presented for values of the polytropic index n= 0.0(0.1) to 2.0.

This paper examines long-term (more than four solar cycles) temporal and spatial fluctuations in the solar rotation by investigating radio-emission escapes from various layers of the solar atmosphere during the years 1967–2010. The flux modulation approach can also be used to investigate variations in solar rotation, which is a contentious topic in solar physics. This study makes use of a time-series of radio flux data at various frequencies (245–15 400 MHz) obtained at Sagamore Hill Solar Radio Observatory in Massachusetts, USA, and at other observatories from 1967 to 2010. The periodicity present in the temporal variation of the time-series is estimated through a Lomb–Scargle periodogram. The rotation period estimated for five radio emissions (606, 1415, and 2695 MHz from the corona, and 4995 and 8800 MHz from the transition region) through a statistical approach shows continuous temporal and spatial variations throughout the years. The smoothed rotation period shows the presence of periodic ∼22-yr and ∼11-yr components. The 22-yr component could be linked to the reversal of the solar magnetic field (Hale) cycle, while the 11-yr component is most likely related to the sunspot (Schwabe) cycle. In addition to these two components, random components are also prominently present in the analysed data. The cross-correlation between the sunspot number and the rotation period obtained shows a strong correlation with the 11-yr Schwabe and 22-yr Hale cycle. The corona rotates faster or slower than the transition region in different epochs. The alternation of the faster rotation speed between the corona and transition region also follows the 22-yr cycle.

The present work is an effort to investigate possible radial variations in the solar coronal rotation by analyzing the solar radio emission data at 15 different frequencies (275-1755 MHz) for the period starting from July 1994 to May 1999. We used a time series of disk-integrated radio flux recorded daily at these frequencies through radio telescopes situated at Astronomical Observatory of the Jagellonian University in Cracow. The different frequency radiation originates from different heights in the solar corona. Existing models, indicate its origin at the height range from nearly $\sim12,000$ km (for emission at 275 MHz), below up to $\sim2,400$ km (for emission at 1755 MHz). There are some data gaps in the time series used for the study, so we used statistical analysis using the Lomb-Scargle Periodogram (LSP). This method has successfully estimated the periodicity present in time series even with such data gaps. The rotation period estimated through LSP shows variation in rotation period, which is compared with the earlier reported estimate using auto correlation technique. The present study indicates some similarity as well as contradiction with studies reported earlier. The radial and temporal variation in solar rotation period are presented and discussed for the whole period analyzed., 6 pages, 6 figures

Solar rotation is still one of the unresolved concern of solar physics. We performed time series analysis on the bins formed on equally separated latitude regions on the soft X-ray images. These images are observed with the X-ray telescope (XRT) on board the Hinode satellite. The flux modulation method traces the passage of X-ray feature over the solar disc and statistical analysis of the time series data of the SXR images (one per day) for the period extends from year 2015 to 2017 gives the coronal rotation period as a function of latitude. The investigation provided quite systematic information of the solar rotation and its variability.