SUN COURSE - SLIDE SHOW 1

For Centuries We Have Worshipped the Sun E.g., Greece -- Sun God: "Helios"

1. Of great mathematical interest in own right 2. Influence on Earth 3. Important for Astronomy -- fundamental cosmic processes -- the only star can see closely Many basic properties still a mystery 4. For me... Why Study the Sun ? So Sun is 1 of liveliest branches of mathematics Many research students attracted…

Why Does an Applied Mathematician Study the Sun ? Traditionally, close link A.M./Astron e.g., James Gregory ( ) Co-founder of Calculus Invented Reflecting Telescope

James Gregory Elected FRS 1668 (age 30) Lined up telescope along north-south line. Early pendulum clock Appointed 1st regius prof maths in St A 1668 (recommendation of Newton) Given Upper Hall of University Library as place of work

Wanted use St Rule's tower for observations: picture (1680) But left in 1674 with words: "The affairs of the Observatory of St Andrews were in such a bad condition, the reason of which was, a prejudice the masters of the University did take at the mathematics. After this, my salary was also kept back from me, and scholars of most eminent rank were violently kept from me, contrary to their own wills, the masters persuading them that their brains were not able to endure it."

James Gregory : - wrote 1st text book on Calculus - discovered: -- General Binomial theorem -- Taylor expansions -- Ratio test for convergence of a series -- Series for sin x and tan x -- Integral of log x and sec x -- Differentiation is inverse to Integration -- How to use Change of Variable in integration

Solar Vital Statistics Ball of gas held together by gravity ? R = 10; 100; 1000 R E Radius 700 Mm (1Mm = 1000 km) = 100 x Earth ? Age = 1000 y; 1,000,000 y; 1,000,000,000y Age billion years (1b = 1000 million) ? Chemical composition 91% H, 8.9% He, + minor elements (O, C, N, Fe...) ? Mean distance from Earth93 million miles = 215 R o

Interior --> Core, Convection zone Atmosphere --> Photosphere, Chromosphere, Corona 1. Overall Structure

Core -- Energy is Generated Temperature = 15 million K Pressure 200 billion times atmospheric pressure Natural fusion reactor [-- but Gentle]

Convection Zone - turbulent motions Top - visible surface of Sun: PHOTOSPHERE ("Light")

Temperature = 6000 K Sunspots -- in pairs (why ?) Rotates -- not like solid ball -- Equator 26 days -- Poles 37 days Close-up : Covered with turbulent convection cells -- "Granulation" Same as porridge or mackerel sky 2. Photosphere

Covered with turbulent convection cells: “Granulation” (1 Mm) “Supergranulation” (15 Mm) Photosphere

Amazing images at from La Palma this year

In close- up: points, flowers, ribbons (created by magnetic fields)

3. SUNS POTS

Sunspots Existence known since 350 BC (Greece), 28 BC (China) In West, no ref until 850 AD; Galileo (1611) Site strong B. Umbra Penumbra Flux tube - ?? Model

Dark because Cool 1600K cooler than photo. ?? Why cool

LATEST IDEAS on NATURE of SUNSPOTS Introduction Observed over 2000 years Hale (1908): strong B (3000G cf mean q Sun 3G) Outside sunspots: strong small-scale convn (gran, 1 Mm) + weak larger-scale convn (supergran, 15 Mm) Umbra - (15 Mm, B strong, vertical) dark -- cool, inhibition of convection

Penumbra (40 Mm, B intermed, inclined) radial light/dark filaments

NEW THEORY - Weiss et al (2004)

Scharmer et al (2004) New Swedish Solar Telescope on La Palma (Canaries)

Stunning Image (Swedish telescope, La Palma) Penumbral structure created by B Close-up of penumbra -> new surprises:

Points moving along lanes; Bright flows in/out; Strange dark cores