The Sun Chapter 7:

General Properties Average star Absolute visual magnitude = 4.83 (magnitude if it were at a distance of 32.6 light years) Central temperature = 15 million 0 K 333,000 times Earth’s mass 109 times Earth’s diameter Consists entirely of gas (av. density = 1.4 g/cm 3 ) Only appears so bright because it is so close. Spectral type G2 Surface temperature = K

Energy Production Energy generation in the sun (and all other stars): Nuclear Fusion = fusing together 2 or more lighter nuclei to produce heavier ones Nuclear fusion can produce energy up to the production of iron. For elements heavier than iron, energy is gained by nuclear fission. Binding energy due to strong force = on short range, strongest of the 4 known forces: electromagnetic, weak, strong, gravitational

Energy generation in the Sun: The Proton-Proton Chain Basic reaction: 4 1 H → 4 He + energy 4 protons have 0.048* kg (= 0.7 %) more mass than 4 He.  Energy gain =  m*c 2 = 0.43* J per reaction. Need large proton speed (  high temperature) to overcome Coulomb barrier (electromagnetic repulsion between protons). Sun needs reactions, transforming 5 million tons of mass into energy every second, to resist its own gravity. T ≥ K = 10 million 0 K

The Solar Interior In the outer regions, energy is transported via convection. (→ granulation) In the inner regions, energy is transported outward through radiation. In the center, energy is produced via nuclear fusion.

The Solar Neutrino Problem The solar interior can not be observed directly because it is highly opaque to radiation. But neutrinos can penetrate huge amounts of material without being absorbed. Davis solar neutrino experiment Early solar neutrino experiments detected a much lower flux of neutrinos than expected (→ the “solar neutrino problem”). Recent results have proven that neutrinos change (“oscillate”) between different types (“flavours”), thus solving the solar neutrino problem.

Sun Spots Cooler regions of the photosphere (T ≈ 4240 K). Only appear dark against the bright sun; would still be brighter than the full moon when placed on the night sky!

The Solar Cycle 11-year cycle Reversal of magnetic polarity After 11 years, North/South order of leading/trailing sun spots is reversed => Total solar cycle = 22 years The Maunder Butterfly Diagram Sun spot cycle starts out with spots at higher latitudes on the sun. Evolve to lower latitudes (towards the equator) throughout the cycle.

The Maunder Minimum Period from ~ 1645 to 1715, with very few sunspots Coincides with a period of colder-than-usual winters

Sun Spots and Magnetic Fields Magnetic field in sun spots is about 1000 times stronger than average. In sun spots, magnetic field lines emerge out of the photosphere. Magnetic North Poles Magnetic South Poles

Magnetic Field Lines Magnetic North Pole Magnetic South Pole Magnetic Field Lines

Magnetic Fields in Sun Spots Magnetic fields on the photosphere can be measured through the Zeeman effect. → Sun Spots are related to magnetic activity on the photosphere.

Solar Activity Observations at ultraviolet and X-ray wavelengths reveal that sunspots are regions of enhanced activity.

The Sun’s Magnetic Dynamo The sun rotates faster at the equator than near the poles. This differential rotation might be responsible for magnetic activity of the sun.

Magnetic Loops Magnetic field lines

The Sun’s Magnetic Cycle After 11 years, the magnetic field pattern becomes so complex that the field structure is re-arranged. → New magnetic field structure is similar to the original one, but reversed! → New 11-year cycle starts with reversed magnetic-field orientation

Prominences Looped Prominences: gas ejected from the sun’s photosphere, flowing along magnetic loops Relatively cool gas (60,000 – 80,000 o K) May be seen as dark filaments against the bright background of the photosphere

Eruptive Prominences (Ultraviolet image) Extreme events (solar flares) can significantly influence Earth’s magnetic field structure and cause northern lights (aurora borealis).

Aurora Borealis Sound waves produced by a solar flare ~ 5 minutes Ring of aurorae around the north magnetic pole

Coronal Holes X-ray images of the sun reveal coronal holes. These arise at the foot points of open field lines and are the origin of the solar wind.

The Family of Stars Chapter 8:

We already know how to determine a star’s surface temperature chemical composition surface density In this chapter, we will learn how we can determine its distance luminosity radius mass and how all the different types of stars make up the big family of stars. Motivation

Distances to Stars Trigonometric Parallax: A star appears slightly shifted from different positions of the Earth on its orbit. The further away the star is (larger d), the smaller the parallax angle p. d = __ p 1 d in parsec (pc) p in arc seconds 1 pc = 3.26 LY

The Trigonometric Parallax Example: Nearest star,  Centauri, has a parallax of p = 0.76 arc seconds d = 1/p = 1.3 pc = 4.3 LY The Limit of the Trigonometric Parallax Method: With ground-based telescopes, we can measure parallaxes p ≥ 0.02 arc sec => d ≤ 50 pc => This method does not work for stars further away than 50 pc.

Intrinsic Brightness / Absolute Magnitude The more distant a light source is, the fainter it appears. The same amount of light falls onto a smaller area at distance 1 than at distance 2 => smaller apparent brightness Area increases as square of distance => apparent brightness decreases as inverse of distance squared

Intrinsic Brightness / Absolute Magnitude The flux received from the light is proportional to its intrinsic brightness or luminosity (L) and inversely proportional to the square of the distance (d): F ~ L __ d2d2 Star A Star B Earth Both stars may appear equally bright, although star A is intrinsically much brighter than star B.

Distance and Intrinsic Brightness Betelgeuse Rigel Example: App. Magn. m V = 0.41 Recall: Magn. Diff.Intensity Ratio *2.512 = (2.512) 2 = 6.31 …… 5(2.512) 5 = 100 App. Magn. m V = 0.14 For a magnitude difference of 0.41 – 0.14 = 0.27, we find a flux ratio of (2.512) 0.27 = 1.28

Distance and Intrinsic Brightness Betelgeuse Rigel Rigel appears 1.28 times brighter than Betelgeuse. Thus, Rigel is actually (intrinsically) 1.28*(1.6) 2 = 3.3 times brighter than Betelgeuse. But, Rigel is 1.6 times further away than Betelgeuse.

Absolute Magnitude To characterize a star’s intrinsic brightness or luminosity, we define the Absolute Magnitude (M V ): Absolute Magnitude M V = Magnitude that a star would have if it were at a distance of 10 pc.

Absolute Magnitude Betelgeuse Rigel BetelgeuseRigel mVmV MVMV d152 pc244 pc Back to our example of Betelgeuse and Rigel: Difference in absolute magnitudes: 6.8 – 5.5 = 1.3 => Luminosity ratio = (2.512) 1.3 = 3.3