IAO 2022, Практически тур — Задача 13. Differential rotation of the Sun

II International Remote Astronomy Olympiad — Practical round · 15 октомври 2022 г.

Practical round. Problems to solve

II International Remote Astronomy Olympiad. Matera, Italy, 15–24 October 2022.

Note: problems for Group α — 13, 14, for Group β — 14, 15, for Group γ — 13, 14, 15.

Source notes and availability

The file contains three independent tasks and all tabulated data, theoretical curves and a blank plotting grid. Its fourth page repeats tasks14 and15; this does not create new tasks. The sunspot dates are printed as October2018 and retained. The star table uses labels A–I,L,M as printed. The isochrone diagram numbers its curves but provides no numerical age key, although task15 asks for an age. No matching official solutions or additional reference files were found in the complete same-year archive catalogue.

Условие

The Sun is characterized by a differential rotation, i.e. the angular velocity decreases with increased latitude.

When the weather conditions permit, daily observations of the photosphere are carried out at the INAF–Catania Solar Telescope by a Cooke refractor (150 mm / 2230 mm). These observations allow us to measure the location of the barycenter of the sunspot groups visible on the solar disc.

In the tables 13.1. – 13.4. (see supplement materials) we report the National Oceanographic and Atmospheric Administration (NOAA) sunspot group numbers (NOAA Nr.), which identify each group, and the corresponding longitudes ($\lambda$, in degrees) and latitudes ($\varphi$, in degrees) for some available observation days.

13.1 Assuming that the observations have been done every day at 08:30 UT and using the sunspot groups as traces for the solar rotation, build the graph containing the average rotation velocity (degree/day) vs latitude for the following North latitudes: 08N, 16N, 20N and 28N.

13.2 Analogously, build a similar graph for the Southern hemisphere using the following latitudes: 06S, 10S, 18S and 27S.

13.3 Assume that the differential rotation of the Sun may be described by a simple linear regression between the velocity (V) and the latitude (L):

with B angular coefficient and A constant term, respectively. Determine the slopes of the linear regression for both hemispheres by the best fit method.

13.4 How much is rotational velocity at the equator if you use only the sunspot groups observed in the southern hemisphere?

13.5 In which hemisphere the rotational velocity varies faster with the latitudes? (Answer “N” for Northern hemisphere or “S” for Southern one.) Prove your answer by numerical values obtained in your calculations).

13.1. 01.10.2018.

NOAA Nr.	$\varphi$	$\lambda$
12192	03 N	18 E
12193	08 N	02 E
12194	12 S	45 E
12195	16 N	37 E
12197	06 S	35 E
12198	10 S	18 E
12199	20 N	47E
12200	18 S	02 W
12201	27 S	12 W
12202	28 N	05 E

13.2. 02.10.2018.

NOAA Nr.	$\varphi$	$\lambda$
12192	03 N	04 E
12193	08 N	12 W
12194	12 S	32 E
12195	16 N	23 E
12197	06 S	20 E
12198	10 S	04 E
12199	20 N	34 E
12200	18 S	11 W
12201	27 S	23 W
12202	28 N	07 W

13.3. 03.10.2018.

NOAA Nr.	$\varphi$	$\lambda$
12192	03 N	11 W
12193	08 N	26 W
12194	12 S	18 E
12195	16 N	09 E
12197	06 S	05 E
12198	10 S	11 W
12199	20 N	21 E
12200	18 S	23 W
12201	27 S	35 W
12202	28 N	20 W

13.4. 05.10.2018.

NOAA Nr.	$\varphi$	$\lambda$
12192	03 N	40 W
12193	08 N	55 W
12194	12 S	10 W
12195	16 N	16 W
12197	06 S	24 W
12198	10 S	39 W
12199	20 N	06 W
12200	18 S	48 W
12201	27 S	59 W
12202	28 N	44 W

Решение

Теми и трудност

Трудност: неоценена.

Слънчева система · Слънце

Предпоставки: Разширена олимпиадна подготовка

---

Оригинал в Архива: prac-IRAO2022.pdf