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Astrophysical Lab Course Measurement of the Solar Rotation

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Astrophysical Lab Course Measurement of the Solar Rotation Astrophysical Lab Course Measurement of the solar rotation The solar rotation velocity will be measured with two different methods: A) The apparent movement of sunspots over the solar disk. For this a suitable set of sunspot images has been arranged, which has to be analyzed by a given Python script. B) The line shift of solar spectral lines due to the Doppler effect is used. Observations with the spectrograph at the solar observatory on Schauinsland will be made and analyzed. 1 Introduction In contrast to a rigid moving body the Sun rotates differential from east to west. The angular velocity of this motion depends on the heliographic latitude and the depth inside Sun’s convection zone. Its relation to the solar cycle is still a main focus in solar science. Fig. 1 shows the angular velocities of the differential rotation inside the Sun. Near the equator the upper layers of the convection zone and the lower photosphere (lower atmospheric layer with largest part of intensity of visible light) show the highest velocities with about 14 degree per day. With higher latitudes on the surface of the Sun the rotational velocity decreases, its minimum is about 10 degrees per day near the poles. In deeper layers of the convection zone the Sun rotates nearly rigid (see also [13]). At latitudes above 70 degree the velocities are hard to measure and reliable values can not be made. This originates from the fact that sunspots are rare above latitudes of 60 degree, that the Sun’s axis of rotation is tilted compared to Earths and from the difficulty of measuring and analyzing near pole data (see source [29]). Solar research is substantial, because the Sun is the next star which gives us information about differential rotation and how it relates to its properties. The curiosity about its rotation goes back to Galileo Galilei observations but had been renewed in the 1960s due to rise of differential rotational models and modern telescopes. Versuchsanleitung zum Astrophysikalischen Praktikum Messung der Sonnenrotation Die Messung der Sonnenrotation soll auf zwei verschiedene Arten durchgefuhrt¨ werden: Zum einen durch die Messung der scheinbaren Bewegung von Sonnenflecken auf der Sonnenscheibe und zum anderen anhand der Linienverschiebung solarer Spektrallinien durch den Doppler-E↵ekt. Fur¨ die Rotationsbestimmung anhand von Sonnenflecken wurde eine Routine in IDL entwickelt und ein Satz geeigneter Sonnenaufnahmen zusammengestellt. Fur¨ den spektroskopischen Versuch nutzen wir geeignete Aufbauten und das Sonnenobservatorium Schauinsland. Allgemein Die Erforschung der Rotation der Sonne, abh¨angig von der Breite und Tiefe, und der Zusam- menhang mit dem Aktivit¨atszyklus, ist bis heute ein Schwerpunkt in der Sonnenforschung. Die Sonne rotiert, vergleichbar der Erde, von Osten nach Westen, wobei verschiedene Breiten und Tiefen2 auf der Sonne verschiedeneMeasurement Winkelgeschwindigkeiten of the solar rotation besitzen. Manual AbbildungFigure 1: 1: Illustration Farbdarstellung of the differentialder di↵erentiellen rotation rate Rotationsrate as a function der of depth, Sonne in als relation Funktion to solar der Tiefe radiiund Breite and plotted berechnet against aus heliographic GONG Daten latitude ( (equatorGlobal Oscillation to the right, Network and pole to Group“) top.) zwi- ” Theschen angular 1996-1998. velocity Rot is entspricht calculated from einer GONG Winkelgeschwindigkeit (Global Oscillation bis Network zu 14, Group)5 Grad/T ag, data,blau bedeutet taken from ca. (1996 11 Grad/T to 1998). ag The. Die red gestrichelte colour at small Linie latitudes zeigt die indicates untere veloci- Grenze der tiesKonvektionszone up to 14.5 degree/day, an. and the blue colour at the poles indicate velocities below 11 degree/day. Dashed lines mark the lower margin of the convection zone. Auf die Geschwindigkeitskomponenten im Sonneninneren wird hier nicht weiter eingegangen (sie- he u.a.To Literatur measure the [13]). rotation Die withPhotosph the help¨arenschicht of the proposed der Sonne, methods die one das has uns to understand sichtbare Licht the under- aussendet, rotiertlying nahe geometry des Aquators¨ of the system mit einer Sun-Earth. Winkelgeschwindigkeit As one can easily see von in Fig. mehr 2 the als direction 14 Grad/T of rotation ag und f¨allt naheof der the Pole Earth auf and ca. the 10 SunGrad/T are alike ag ab. but Diese have different Art von velocities. Rotation The nennt Earth man takes di↵ 24erentielle hours for Rotation a (siehefull Abb. rotation 1). and the Sun needs about 25 to 32 days depending on the latitude. A full trip of the Earth around the Sun takes 365.24 days. 2 Theoretical basics 1 Although sunspots differ a lot in their appearance there is a nomenclature for their structure. Fig. 3 shows the basic structure of sunspots, the umbra (dark area with highest magnetic field), the penumbra (filament like structures with tilted magnetic tubes) and pores (small structures without surrounding penumbra). To measure the solar rotation, by studying the motion of sunspots across the solar disk, it is important to get familiar with the properties of different sunspot types. During 1921 until 1982 the Mount Wilson observatory used continuum images to characterize these sunspot properties. Multiple analysis of this data have shown that sunspots of different sizes also have different angular velocities at the Sun’s surface. In Fig. 4 one can see that the velocity of sunspots varies Astrophysical lab course Kiepenheuer-Institut für Sonnenphysik, Freiburg Man kann erkennen, dass in der Abbildung keine Angaben zu Breiten > 70◦ gemacht werden. Dies liegt an der Schwierigkeit der Messung und Interpretationen der Daten an den Sonnenpolen (siehe u.a. Literatur [29]). Die Sonnenforschung ist so maßgeblich, da die Sonne der einzige Stern in unserer N¨ahe ist, der uns Aufschluss geben kann, wie di↵erentielle Rotation entsteht und mit anderen Eigenschaften der Sonne zusammenh¨angt. Das Interesse der Rotation der Sonne geht bis auf die Zeit Galilei zuruck,¨ jedoch hatten die modernen Untersuchungsmethoden einen Aufschwung in den 1960er Jahren, als man mit Versuchen begann, Modelle der di↵erentiellen Rotation zu entwerfen. Manual Measurement of the solar rotation 3 Um die Rotation anhand einer der zwei Messmethoden bestimmen zu k¨onnen, muss man zuerst die grundlegende Geometrie des Systems Sonne-Erde n¨aher betrachten (siehe Abb. 2). AbbildungFigure 2: Left: 2: Links: Suns Koordinatensystem coordinate system and auf its der yearly Sonne varying mit angles jahreszeitlichB0 and P abh. The¨angigen angles Neigungs-B and L describe the heliographic latitude and longitude. winkel B0 und P . 7:15 Right:Rechts: Illustration Schema of Erdbewegung the Earths orbit um around die Sonne: the Sun; Die the Sonne Sun is ist tilted um up 7, 15 to und◦ to die Erde the Earths rotational axis and the Earths axis is tilted by 23:5 to the ecliptic. Earth◦ and um 23, 5 gegen die Ekliptik geneigt. Sowohl die Sonne◦ als auch Erde, rotieren in die Sun rotate in◦ the same direction. Also, the Earths movement is in the same direction as thegleiche Suns Richtung. rotation (taken Auch from die Bewegung[2]). der Erde um die Sonne ist im gleichen Sinne (aus [2]). Wie man in Abbildung 2 erkennen kann, haben die Rotation der Erde, der Sonne und die Bewe- gung der Erde um die Sonne alle den gleichen Drehsinn, besitzen aber verschiedene Umlaufdauern: Die Erde rotiert mit einer Umlaufdauer von ca. 24 Stunden, die Sonne ben¨otigt zwischen 25 und 32 Tagen fur¨ eine Umdrehung. Die Erde ben¨otigt ca. 365,24 Tage fur¨ einen Umlauf um die Sonne. Grundlagen - Sonnenflecken Man unterscheidet Sonnenflecken durch ihre verschiedenen Erscheinungsbilder. Man hat sich fur¨ die Nomenklatur entschieden, die in Abbildung 3 dargestellt ist. M¨ochte man die Rotation der Sonne anhand von Sonnenflecken bestimmen, so ist es wichtig, sich vorher mit den Eigenarten verschiedener Flecken zu befassen. Das Mount Wilson Observatorium mit seiner bekannten whitelight data“ hat von 1921 bis 1982 ” SonnenfleckendatenAbbildung 3: Die Nomenklatur erhoben. der Erscheinungen in Verbindung mit Sonnenflecken (aus [4]). Figure 3: Nomenclature of phenomena related to sunspots (taken from [4]). Wiederholte Analysen der Daten ergaben, dass Flecken verschiedener Art und Gr¨oße sich verschie- de schnell bewegen. In Abbildung 4 kann man erkennen, dass die Geschwindigkeit der Flecken signifikant mit der Gr¨oße der Flecken variiert. Gr¨oßere Sonnenflecken (Typ H) rotieren bis zu 0, 4 Grad langsamer als Sonnenflecken kleinerer Gr¨oße (Typ J). Dies ist einerseits zuruckzuf¨ uhren¨ Kiepenheuer-Institut für Sonnenphysik, Freiburg Astrophysical lab course 2 Abbildung 4: Siderische Winkelgeschwindigkeit von Sonnenflecken eingeteilt in drei verschiedene Kategorien der Gr¨oße von Einzelflecken und die Fleckengruppen (aus [12]). auf die verschiedenen Tiefen der Sonnenflecken im Sonneninneren und andererseits auf den visko- sen Widerstand des sich langsamer bewegenden Plasmas der Photosph¨are. Fleckengruppen eignen sich nur bedingt fur¨ die Sonnenrotationsbestimmung, da sie sich ungleichm¨aßiger bewegen als Ein- zelflecken. Sie bewegen sich oft relativ zueinander, was die Bestimmung einer gewichteten Mitte notwendig macht. Diese Ungleichm¨aßigkeit ist auch in Abbildung 4 gut erkennbar. Desweiteren ist ihre Rotationscharakteristik ¨ahnlich der großen Einzelflecken und somit eher ungeeignet.[12] Grundlegend empfiehlt es sich, stabile Sonnenflecken kleiner bis mittlerer Gr¨oße mit einer m¨oglichst langen Lebensdauer fur¨ die Bestimmung der Sonnenrotation zu verwenden,
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