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Spring Term Astrophysics Stellar Physics Dr P.A. Hatherly Modules: PH2006, PH3811 Topics to be Covered: Properties of Stars – Distances, velocities, dimensions, masses, temperatures, luminosities. Stellar Interiors – Pressures and temperatures, compositions, power sources. Life-cycles of Stars – Star formation, evolution and death. Resources Available Recommended Texts: – “Universe” (4th or 5th edition, W.J. Kaufmann) – "The Physics of Stars" (2nd edition, A.C. Phillips) IT – CD-ROMS on Departmental PCs – Unit Website Navigate via physicsnet at http://www.rdg.ac.uk/physicsnet/ Unit Structure 14 Lectures/presentations – Weeks 4 and 8 for private study 6 Workshops/discussion sessions – Week 1 - no workshop 2 assessed problem worksheets and 1 formal examination Lecture Calendar Sun Mon Tue Wed Thu Fri Sat Week 1 17 15 16 14 13 12 11 Jan 2 24 22 23 21 20 19 18 3 31 29 30 28 27 26 25 4 7 6 5 4 3 2 1 Feb 5 14 12 13 11 10 9 8 6 21 19 20 18 17 16 15 7 28 26 27 25 24 23 22 8 29 8 6 5 4 3 2 1 March 9 13 11 12 10 9 8 7 10 20 18 19 17 16 15 14 Key: Lecture 9-11 Lecture 9-11, Workshop 11-12 Open discussion and revision 9-12 Private Study Release Assessment 1 on 26th January Return Assessment 1 on 11th February Release Assessment 2 on 23rd February Return Assessment 2 on 10th March All Lectures in the Gordon Theatre, Engineering All Workshops in 131, Physics All Assessments to be returned to the School Office (Room 217, Physics) by 13:00 on the due date Assessment Continuous Assessment – Selected problems set in weeks 3 and 7 Posted on website on 26th January and 23rd February – Answers returned in weeks 5 and 9 To the School Office by 1pm, 11th February and 10th March – Results/feedback in weeks 6 and 10 Results posted on website and problems discussed in the following workshop – Contribution: 40% Assessment Formal Examination – 2 hour paper in Summer – Contribution: 60% Assumed Knowledge: Classical Mechanics and Optics – Part 1 Thermodynamics and Statistical Mechanics – In progress Atomic and Molecular Physics – Simple quantum ideas, in progress Ideas from Observational Astronomy – (useful, but not essential) Distances of Stars Stellar Parallax d p 1 AU Distances of Stars The angle subtended, p, is simply given by: p = 1/d (with d in AU and p in radians) Definition: – If a star gives a parallax of 1” (1 second of arc, arcsec = 1/3600°) then the distance to the star is 1 parsec (pc) – Hence, d (pc) = 1/p (arcsec) Distances of Stars Examples: – The first star to have its parallax measured was 61 Cygni. Its parallax was 0.33”. How far away is it? – d = 1/p = 1/0.33 = 3 pc – The nearest star, Proxima Centauri is at a distance of 1.3 pc. What is its parallax? – p = 1/d = 1/1.3 = 0.77” Distances of Stars Relationship to Other Units – 1 pc = 2.06x105 AU – 1AU = 1.5x108 km \1 pc = 3.086x1013 km – Distance light travels in 1 year = 1 light year (ly) = 9.46x1012 km \1 pc = 3.26 ly Distances of Stars Limitations of Parallax – Maximum distance from ground based observations, 50 pc – Maximum from space-based observations, 500 pc – Other methods required for greater distances “Standard candles” Velocities of Stars Define: – Proper Motion: The angular velocity of a star tangential to the line of sight – Symbol, m; Units, arcsec/year – Tangential Velocity: vt ; Units km/s – related to the proper motion by: vt = 4.74md km/s (with d in pc) Velocities of Stars Define: – Radial Velocity: The velocity of the star along the line of sight. – Symbol, vr ; Units, km/s – Note a negative radial velocity means a star is approaching us Velocities of Stars vt Example: vs q vr – Barnard’s Star (distance, 1.82 pc) – Proper motion = 10.32 arcsec/year – Tangential velocity = 89.1 km/s – Radial velocity = -111 km/s – Speed vs = (vr2 + vt2)1/2 = 142.3 km/s – Angle to line of sight q = tan-1(vt /vr ) = -38.75° Velocities of Stars Measurement of Velocities – Proper motion - straightforward observation, maybe over many years, of the position of a star – Radial velocity - Use Doppler Effect Red shift - vr positive No shift - vr zero Blue shift - vr negative Velocities of Stars Example: – Barnard’s Star - 10.32 arcsec/year is easy to measure (= 0.6% angular diameter of full moon) – Doppler shift due to vr Dn/n = vr /c = -0.04% Stellar Magnitude Scale A logarithmic scale, defined such that a difference of magnitude of 5 corresponds to a change in intensity of 100 Smaller magnitudes mean brighter stars – e.g., a magnitude 0 star is 100x brighter than magnitude 5 Stellar Magnitude Scale Relative Intensities (mag. 0 = 1) Magnitude -2 -1 0 1 2 3 4 5 Relative Intensity 6.3 2.152 (=1001/5) 1 0.46 0.16 0.06 0.025 0.01 Stellar Magnitude Scale Definitions: – Apparent Magnitude, m : The magnitude a star appears to be – Absolute Magnitude, M : The apparent magnitude a star would have if it were viewed from a distance of 10 pc Stellar Magnitude Scale Relationship between M and m : – (m - M ) = 5log10d - 5 d is the distance to the star in pc – The quantity (m - M ) is known as the Distance Modulus – Example: Sirius has an apparent magnitude of 1.46. It is 2.7 pc away, what is its absolute magnitude? – m = -1.46, d = 2.7 pc – M = -1.46 - 5log102.7 + 5 = 1.38 Relative Luminosities Often convenient to refer to the relative luminosities of stars. From the definition of magnitudes, if two stars have absolute magnitudes M1 and M2 , and luminosities L1 and L2 , L1 ( M2 M1 )/ 5 100 L2 Relative Luminosities Example: – The absolute magnitude of the Sun is +4.8 and that of Sirius is +1.38. What is the ratio of their luminosities? – Lsirius /L =100(4.8-1.38)/5 = 23.3 Colour Correction Careful observation of stars reveals they have a range of colours – Black-body or thermal radiation – Stefan’s Law - power per unit area P = sT 4 (T in K) – Wien’s Law lmax(nm) = 2.9x106/T Colour Corrections Examples of spectra UV Visible IR Sun Betelgeuse Sirius 0 200 400 600 800 Wavelength (nm) 1000 1200 Colour Corrections Clearly, many stars produce a large amount of light outside the visible – Observe stars through a variety of filters. – U - 300 - 400 nm – B - 380 - 550 nm – V - 500 - 650 nm Colour Corrections From the filters, we obtain: – bu, bb and bv – Ratios bv /bb and bb /bu Examples: – Sun, bv /bb = 1.77, bb /bu =1.10,T = 5800 K – Sirius, bv /bb = 1.00, bb /bu =0.95, T = 10000 K – Betelgeuse, bv /bb = 5.50, bb /bu =6.67, T = 2400 K Colour Corrections Note that: – bv /bb and bb /bu <1 with bb /bu < bv /bb hot, blue star, T >20000 K. – bv /bb and bb /bu roughly equal and ~1 cooler, white star, T ~9000 K. – bv /bb and bb /bu >1 with bb /bu > bv /bb cool, orange/red star T <4000 K. Stellar Spectra Examination of stellar spectra reveal absorption lines on the black body background – Due to neutral or ionised atoms or molecules in the stellar atmosphere – Gives composition of star, another handle on temperature and a means of classification. Stellar Spectra The spectra of stars are classified according to the scheme: OBAFGKM Increasing Temperature Each class is further divided from 0-9, with 0 being the hottest and 9 the coolest Note: This scheme can be remembered by the “traditional” mnemonic: Oh Be A Fine Girl (Guy, Gorrilla...) Kiss Me Stellar Spectra Historical Note: – Originally (19th C), classification was based on the strength of the hydrogen Balmer absorption spectrum, and ran from A to P in order of decreasing absorption – The current scheme arose as a more logical classification in terms of temperature Stellar Spectra Hg Ha Hb O B A F G K M Mg I TiO Na TiO Stellar Spectra Class Colour Temp. (x103 K) Spectral lines Examples O Blue-violet 28 – 50 Ionised atoms Pup1, Ori2 B Blue-white 10 – 28 He, some H a Vir3, b Ori4 A White 7.5 – 10 Strong H, some ionised metals a Cma5, a Lyr6 F Yellow-white 6 – 7.5 H and Can+, Fen+. a Car7, a Cmi8 G Yellow 5–6 Can+, other ionised and neutral metals Sun, a Aur9 K Orange 3.5 – 5 Neutral metals a Boo10, a Tau11 M Red-orange 2.5 – 3.5 TiO and Ca a Sco12, a Ori13 Common names: 1Naos, 2Mintaka, 3Spica, 4Rigel, 5Sirius, 6Vega, 7Canopus, 8 Procyon, 9Capella, 10Arcturus, 11Aldebaran, 12Antares, 13Betelgeuse Stellar Classification We now have two vital pieces of information: – Luminosity, via distance and magnitude – Temperature from spectroscopy Is there any correlation between these parameters? – Very important result - a plot of luminosity versus temperature (spectral class) – The Hertzprung-Russel (H-R) Diagram H-R Diagram for a number of the brightest and nearest stars The H-R Diagram Points to note: – The narrow band of stars scattered close to the solid line. – Most stars occur along this band – an indication that this is where stars spend most of their lives. For this reason, it is known as the Main Sequence. The H-R Diagram – Other regions to note are stars of high luminosity but low temperature (indicating they are large – hence the term red giant) and stars of high temperature but low luminosity (indicating small diameters, hence white dwarf ) – As we shall see, the H-R diagram is extremely useful in many aspects of stellar physics Next Lecture: Dimensions of Stars Luminosity and Spectral Class – Spectroscopic Parallax Masses of Stars – Mass-Luminosity Relationship Stellar Interiors – Hydrostatic Equilibrium