1. STARS Structure & Evolution Lecture No. 1: Properties & Structure Iwan P. Williams 2013

2. LUMINOSITY L is the Total Power emitted by a star. This is the fundamental property of the star we need to know in order to test stellar theory with observations. In SI units it would be measured in Watts.

3. The MeasuredFlux, (Brightness) Fat the Earth a distance D from the Star In SI units,Watts m-2 D

4. Stellar Magnitudes The eye responds to the log of the brightness Define magnitude= -2.5 log10 F + const (Choice of 2.5 and const made to agree best with Ptolemy’s classification. Sirius: -1.4 magnitude star, Vega: +0.03 magnitude star)

5. Examples of apparent magnitudes

6. Apparent magnitudem (confusingly, what we actually observe) for star at its actual distanceD Absolute MagnitudeM at 10 pc If same star at distance10 pc

7. Subtracting the two equations, we get

8. The black body relationship gives F= sT4, While Wien’s law gives lmax= (2.9x106)/T nm

9. U 365 nm B 440 nm V 550 nm R 700 nm --------------------------------------- I 900 nm = 0.90 m J 1650 nm = 1.25 m H 1250 nm = 1.65 m K 2200 nm = 2.20 m --------------------------------------- L' 3800 nm = 3.80 m M' 4700 nm = 4.70 m --------------------------------------- N 10200 nm = 10.20 m Q 21000 nm = 21.00 m Traditionally, UBV filters were used but now are supplemented with 8 IR filters

10. H SUN, by mass: H: X = 73% He: Y = 25% ‘metals’ Z = 2% He C, N, O Fe

11. The Main Spectral Classes

12. log (T) = (14.551 – (B – V) )/ 3.684

13. HR diagram of 41,453 stars using distances measured by the Hipparchos satellite p=0.001" or D=1000pc

14. Measuring Radius R Two obvious ways • Directly: imaging or interferometry • (but this is restricted to nearby large stars e.g. Betelgeuse) • From LandT :

15. The Sun’s Radius Directly from imaging R= 6.96108 m = 109 Rearth Mercury’s orbit = 83 R Earth’s orbit = 1 AU = 1.4961011 m = 215 R

16. From the H-R Diagram log10 L 100 Rsun 10 Rsun 1 Rsun 0.1 Rsun log10 T

17. Stellar Sizes vary widely Betelgeuse 300 R to Sirius B 0.01 R ~REarth

18. Mass of stars • This can only be obtained directly from binary systems, essentially the same technology as for finding extra-solar planets • With a theory for stellar structure, this could be inferred from the HR diagram.

19. Sirius B M= 1.02M T = 27,000 K R = 6000 km Average Density:  = 3106 water g = 0.5 106g An 80 kg (13 stone) person would weigh 40106 kg

20. Masses of stars on the MS 0.2 to 20 M Most massive known 120 M SUN

21. Flux F D D L=4πD2F Orbiting Binary stars A summary of the methodology for finding properties of stars Mass (M)

22. Luminosity MASS

24. The ENERGY source of SUN. The efficiency of chemical processes is no better than f ~ 10-9 per unit mass. Nuclear H fusion is much more efficient: f = 0.007 per unit mass

25. Stellar Lifetimes on MS • Observation for MS: • Therefore the • MS lifetime is: Which gives a MS lifetime decreasing rapidly with mass:

26. Estimating internal pressure (Pc is the central pressure) . R/2 R/2 condition for hydrostatic equilibrium: M/2 M/2 Outward Gas Pressure here ~ Pc = Gravity Inpull FORCE AREA P=

27. IDEAL GAS  = 8.31×103 J kg-1 K-1 M = Star’s Mass R = Star’s Radius i.e. gravity balanced by gas pressure But for hydrostatic equilibrium, This is >> 13.6 eV, the ionization energy of an H atom & of any other atom!

28. Typical core values from solar models:

29. The equations of stellar structure , the essential physical laws governing structure of a star: Hydrostatic Equilibrium Mass in r (1) & (2) state that the gravitaty is balanced by the internal pressure forces; Energy Generation (4) Radiation or Convection Energy Transport (3) equates the energy generated by nuclear fusion to energy flowing outwards, (4) states how this flow is achieved. Unknowns: L(r), (r), T(r)