3PS Physics of

Ben Murdin Books

A The Physics of Stars @ A.C. Phillips, 1994, John Wiley & Sons, ISBN 0-471-94155-7 A An Introduction to the theory of Stellar Structure and Evolution @ D. Prialnik, 2000, Cambridge University Press, ISBN 0-521-65937-X A An Introduction to Modern Astrophysics @ B.W. Carroll and D.A. Ostlie, 1996, Addison-Wesley, ISBN 0-201-54730-9 A The Stars: Their Structure and Evolution @ R.J. Tayler, 1994, Cambridge University Press, ISBN 0-521-45885-4 Pbk Assessment

A There will be Physics of Stars coursework assignments worth 30% of the whole module, in which you will be required to make calculations of the structure for a chosen for you at random. A The exam (70%) will be a standard 3 out of 4. Syllabus

A Everything is examinable! A Notes: @ Equations in solid boxes are essential and should be memorised (some you should know already!), e.g.

P = nkBT @ Equations in dashed boxes are very important but I would give in exam, you should know what terms mean, e.g. π 3 ⎛ k T ⎞ ⎛ μ ⎞ B ⎜ ⎟ n = 8 gs ⎜ ⎟ exp⎜ ⎟ ⎝ hc ⎠ ⎝ kBT ⎠ Burning questions!

A What is a Star? A In other courses: A Other Questions @ What is the energy source? @ How big? @ What can we measure? @ How hot? @ How dense? @ How bright? @ How old? @ What colour? @ How are they born? @ How do they die? Overview

A Astronomical Measurements @ Spectra @ Mass @ Distance @ @ Radius @ Chemical composition @ Neutrinos A Astrophysical Relationships @ The Hertzprung-Russell Diagram @ Mass-Luminosity Relationship A Course Aims: @ To develop a model which explains the above relationships and: @ Predicts the birth, evolution and death of stars. Core concept

A A star is a complex negative feedback system in which: @ Gravity tries to reduce the energy of the system @ If the energy can’t all escape, some gravitational energy is converted into heat @ The heat triggers exothermic thermonuclear burning @ The hot gas expands against gravity @ Energy Balance Implies: ? rate of radiation = rate of gravitational energy loss + nuclear power generation ? All three terms are functions of the variables pressure P, density ρ, temperature T, heat flow L The Sun – our closest star

A Spectrum: Yellow 30 A Mass M~ = 1.99 x 10 kg A Sun-Earth mean distance = 1 Astronomical Unit (A.U.) = 1.50 x 1011m 26 A Luminosity L~ = 3.83 x 10 W 8 A Radius R~ = 6.96 x 10 m A Composition of the Sun @ Observational data: spectrum of solar surface, meteorites @ Similar to typical composition in the universe:

@ Hydrogen X1 ~70% by mass, helium X4~30% @ Heavier elements XZ~1-2% ? O, C, N, Ne, Fe, … in order of abundance A Age of the Sun @ Only known indirectly: radioactive dating of rocks; @ computed evolutionary models of the Sun.~ 4.6 x 109 Luminosity

A @ System dates from Hipparchus of Rhodes (300BC), now quantified as [factor 100 less in flux = 5 steps up in magnitude]

m1 – m2 = - 2.5 log10 (f1/f2 )

A Absolute Bolometric Magnitude @ needs distance because Flux f=L/4πd2 @ Define: = apparent magnitude for stars at 10pc away Mbol = m - 5log(d/10pc) (subs L1=L2, d1=10pc, m1=Mbol) @ If the Sun were 10pc away, it would have apparent magnitude +4.72 M = -2.5 log (L/L ) + 4.72 @ Therefore bol 10 ¤ Luminosity

A Luminosity Temperature (Stefan-Boltzmann) Law @ needs radius −8 -2 -4 π 2 4 @ σ= 5.670 400×10 Wm K L = 4 R σTe @ => Te~ = 5770K

A Using scaling rules: 2 4 L ⎛ R ⎞ ⎛ Te ⎞ = ⎜ ⎟ ⎜ ⎟ LO ⎝ RO ⎠ ⎝ TeO ⎠

A Homework: Check value of Te.How long does a kettle take to boil in the desert? How close to a light-bulb should you hold your hand to feel as warm as the Sun? Black body spectra

A Black-body (Planck) curve @ Wein’s Law:

λmax~290nm x (10,000K /T) A Colour Index F2 class @ Choose different wavelengths:

? λU~365nm (UV) λB~440nm (Blue) λV~548nm (Vis) @ take photographs of star field G2 class with blue and visible filters to get absolute magnitudes at K5 class these wavlengths (labelled B and V) @ Colour index B-V (etc) is directly related to Temperature Absorption Spectra

A Absorption lines: Lyman Balmer @ wavelengths - Chemical composition (of surface) ∞ @ relative strengths - Temperature 4 ? Specific lines are only present if 3 atoms (molecules) have: > correct degree of ionization: 2 too hot = ionized Hα Hβ > plenty of electrons in correct Hγ ... levels: too cold = electrons only in ground state (UV, X- ray lines) 1 A I.e. Spectral Types Sun luminosity spectrum

A The sun is a G2 star. A Planck peak in yellow A Balmer lines weak, Ca II strongish A spectral lines strength - spectral types Spectral Types

A O @ <50,000K, He II A B @ <25,000K, He I A A @ <11,000K, H I (Balmer) A F @ <7,600K, H I, Ca II A G @ <6,000K, Ca II A K @ <5,100K, Ca II A M @ <3,600K, Ca II, Ca I, TiO •Spectral classifications also subdivided from 0-9 (0 is bluest/hottest) •Classifications are very nearly logarithmic in T (2 steps ~ factor 2 in T) Spectral plate classification

Hδ Hγ Hβ Hα O6.5 35,000 B0 22,000 B6 16,400 A1 10,800 A5 8,600 F0 7,200 F5 6,500 G0 5,900 G5 5,600 K0 5,200 K5 4,400 M0 3,700 M5 3,500K

CH Fe I Na I 4000 5000 6000 7000 Å The Hertzsprung-Russell Diagram

A Luminosity and surface temperature are NOT independent Pleiades (Seven Sisters, M45)

the Pleiades is one of the brightest and most easily visible open clusters on the sky. The Pleiades is about 70Myr old, contains over 3000 stars, is about 400 light years away, and only 13 light years across. Quite evident in the above photograph is the blue reflection that surrounds the bright cluster stars. HR diagram for Pleiades (NGC 4755)

The bright central star Kappa Crucis is red, in contrast to the many blue stars that surround it. The cluster contains just over 100 stars, and is about 10 million years old. The Jewel Box lies about 7500 light- years away. Wild Duck (M11)

The , M11, contains thousands of stars and is just over five thousand light years distant. The stars in this cluster all formed together about 250 million years ago. The Hertzsprung-Russell Diagram

A 22000 stars from Hipparcos Catalogue + 1000 red and white dwarfs from the Gliese Catalogue A Approximately 90% of stars lie on Main Sequence A Note vertical scale is @ absolute magnitude decreasing upwards @ Or logarithmic luminosity increasing upwards A Note horizontal scale is @ logarithmic temp increasing left, @ or B-V colour index increasing linearly to right, @ or spectral classification from left to right The Hertzsprung-Russell Diagram H-R Diagrams of clusters

A Clusters offer stars with similar composition and age, but differing mass. A The first diagram is of a cluster which is only 1 million years old. The cool K & M stars have not yet settled down onto the main sequence; they are still contracting protostars, and have not yet ignited hydrogen fusion in their cores. On the other hand, the hottest O star has already been converted to a red supergiant. A The next diagram is of a cluster which is 100 million years old. The main sequence lifetime of a 6 solar mass star is 100 million years, so stars with M = 6 Msun (L = 530 Lsun, spectral type A) are just turning off the main sequence A The final diagram is of a cluster which is 10 billion years old. The main sequence lifetime of a 1 solar mass star is 10 billion years, so stars with M = 1 Msun (L = 1 Lsun, spectral type G) are just turning off the main sequence. Mass-Luminosity diagram

A Mass and Luminosity are not independent either A there is an approximate power law called the Mass-Luminosity Relation

A L∝Mn

A where n is about 3 or 4