1. The electromagnetic spectrum Characteristics of stars The HR diagram Starlight

2. 1663: Newton buys an astrology book and a glass prism at Sturbridge fair 1666: in Woolsthorpe family manor, Newton discovers that the prism decomposes solar light in the same colors as the rainbow → shows that white light is composed of different colors He postulates that each monochromatic radiation is composed of particles → photons That hypothesis will be abandoned until the 20 th Century, with the discovery that light presents both wave and particle aspects The electromagnetic spectrum

3. Invisible light Around 1800, Herschel discovers infrared radiation and Ritter ultraviolet radiation Scientists progressively realize that visible radiation represents only a tiny part of the electromagnetic spectrum, corresponding to freaquencies detected by the human eye The visible part of the spectrum corresponds to: maximum of solar emission excellent transparency of Earth atmosphere → natural selection (Darwin) The electromagnetic spectrum - 2 HerschelRitter

4. Spectral domains Historical – also correspond to different processes Frequency ν – wavelength λ: Velocity of light: c = 3 × 10 8 m/s Energy: Planck constant: h = 6.63 × 10 −34 J·s The electromagnetic spectrum - 3

5. The black body (1) Perfectly absorbing body → only radiation emitted by the objet, because of its temperature, is detected (no reflexion) Hotter body → emission peak λ max at higher frequency Wien’s displacement law: C ≈ 3 × 10 −3 m·K ≈ 3000 μm·K Examples: Sun: T ≈ 5800 K → λ max ≈ 0.5 μm Earth: T ≈ 300 K → λ max ≈ 10 μm The electromagnetic spectrum - 4

6. The black body (2) Stefan-Boltzmann’s law: Total flux = total energy emitted per unit surface and time Stefan’s constant: σ ≈ 5.7 × 10 −8 W·m −2 K −4 Planck’s law: Emitted flux per unit frequency: Jozef Stefan The electromagnetic spectrum - 5

7. The black body (3) Planck’s law: Emitted flux per unit wavelength: Or: c 1 ≈ 3.7 × 10 −16 J·m 2 s −2 c 2 ≈ 0.0144 m·K Conservation of energy → Max Planck The electromagnetic spectrum - 6

8. Types of spectra Light bulb → continuum spectrum Hot gas → emission lines (1) Cool gas in front of light bulb → continuum + absorption lines (2) E e–e– e–e– (1)(2) The electromagnetic spectrum - 7

9. Stellar spectra Generally: continuum + absorption lines Stellar interior very hot and opaque → continuum spectrum Outer layers more transparent and cooler → absorption lines Characteristics of stars Remark: Astronomers often measure wavelength in Angström (Å) 1 Å = 10 −10 m = 0.1 nm

10. Spectral types Classification according to spectrum (ex : strangth of hydrogen lines) → O B A F G K M sequence (Oh be a fine girl kiss me…) Characteristics of stars - 2

11. Appearance of stellar spectra Spectrum appearance depends on gas properties: temperature pressure chemical composition Temperature is the dominant factor → spectral types correspond to a classification according to température of outer layers (stellar atmosphere) Remarks: stellar is not a precisely defined concept as gas pressure gradually increases with depth spectral types are divided into sub-types (0 to 9) → ex: A0, G2 Characteristics of stars - 3

12. Effective temperature Surface température is not a well defined concept → one introduces effective temperature T eff T eff = temperature of a black body emitting the same flux as the star Bolometric luminosity L bol = total energy emitted by unit of time (power) (R = radius of the star) Characteristics of stars - 4

13. Influence of distance Radiation emitted by the star is spread over a sphere of radius R If d is the distance between the star and the observer, the same energy is spread over a sphere of radius d (→ surface 4πd 2 ) Conservation of energy → geometrical dilution: R d Characteristics of stars - 5

14. Distance to stars Distances of nearby stars can be obtained by triangulation Motion of Earth around the Sun allows to measure parallax In the course of a year, a nearby star seems to move with respect to background stars along an ellipse of semi major axis: a d θ 1 parsec = distance of a star whose parallax θ = 1″ 1 parsec (pc) = 1 UA × n r of seconds / radian 1 pc = 206265 UA ≈ 3.26 light-years (L.Y.) ≈ 3 × 10 16 m Characteristics of stars - 6

15. Stars in the solar neighborhood Larger parallaxes < 1″ → d > 1 pc 117 stars known at less than 20 L.Y. (in 2006) Mean distance 3D sketch of solar neighborhood Characteristics of stars - 7

16. Nearest stars The 117 stars at less than 20 L.Y., by spectral type: OBAFGKMbr.dw.w.dw. 002161678 8 6 Our nearest neighbors: The Sun(G2)8 light-minutes Proxima Centauri(K5)4.2 L.Y. Alpha Centauri A(G2)4.4 L.Y. Alpha Centauri B(K0)4.4 L.Y. Barnard star(M5)5.9 L.Y. Characteristics of stars - 8

17. Magnitudes Hipparcos classified the naked-eye stars according to their apparent brightness, from 1 st magnitude – brightest ones – to 6 th – faintest ones Eye sensitivity follows a logarithmic law To stick as much as possible to Hipparcos system, astronomers defined the apparent magnitude of a star: Sirius :m = –1.5Vega :m = 0.0 Canopus :m = –0.7Capella :m = 0.0 Arcturus :m = –0.1Rigel :m = 0.1 Characteristics of stars - 9

18. Absolute magnitude and distance modulus Apparent magnitude is not an intrinsic property of a star as it depends on its distance R is generally unknown → one defines absolute magnitude M M = apparent magnitude the star would have at a distance of 10 pc Distance modulus: Characteristics of stars – 10

19. Photometry In modern astronomy, on always observe through filters which transmit only part of the electromagnetic spectrum → measurement of flux received in a given spectral band → the choice of filters determine the photometric system → a magnitude is always given with reference to a filter Ex : m B, m V, M B, M V,… The additive constant C t is fixed with reference to standard stars ex: m i (Vega) = 0 in all filters Transmission curves of UBVRI filters Characteristics of stars – 11

20. Colours To quantify the colour of a star (or another celestial body), colour indices are defined Ex: m B –m V = M B –M V independent of distance as geometric dilution does not depend on wavelength Colour indices are written B–V, V–R, etc… Remark: they are intrinsic properties of stars if nothing modifies the spectrum in between source and observer (ex: absorption by dust) Characteristics of stars – 12 Transmission curves of UBVRI filters

21. Spectral types and colours Different effective temperatures correspond to: different spectral types different colours → relation between spectral type and colour of a star approximative since both depend on other parameters f (ex. pressure and chemical composition) OBAFGKM Spectral type 0.0 0.5 1.0 1.5 B–V Characteristics of stars – 13

22. Around 1910, Ejnar Hertzsprung and Henry Norris Russell plot stars in an `absolute magnitude – spectral type´ diagram The HR diagram They realize that stars do not appear at random but into specific areas: most stars are located along the main sequence a minority appear in the red giant area a few are located in the white dwarf region OBAFGKM Spectral type +10 +5 0 −5−5 MVMV main sequence red giants white dwarfs

23. The theoretical HR diagram absolute magnitude ↔ luminosity in spectral band considered spectral type ↔ effective temperature The HR diagram - 2 → theoreticians use a theoretical HR diagram in which bolometric luminosity is plotted as a function of effective temperature (in logarithmic scale) log L bol log T eff

24. Influence of radius → straight lines of constant radius in HR diagram stars located to the upper right of the main sequence are giants and supergiants main sequence stars are generally called dwarfs stars located below the main sequence are subdwarfs and white dwarfs log (L/L ) log (T eff /T eff, ) 0.00.51.0 +4 +2 −2−2 0 R 10R 100R The HR diagram - 3

25. Luminosity classes Beside spectral types, luminosity classes have been introduced For a givan T eff, a ≠ luminosity corresponds to a ≠ radius Classes : I, II : supergiants III : giants IV : subgiants V : dwarfs Ex :Sun: G2V Canopus: F0II The HR diagram - 4

26. The colour-magnitude diagram If stars belong to a same cluster → they are approximately at the same distance → we can use apparent magnitude instead of absolute magnitude A colour index is often use to measure T eff (more easily obtained than a spectrum) → the observational HR diagram is often a colour-magnitude diagram V V−RV−R E. Hertzsprung H.N. Russell The HR diagram - 5

27. Colour-magnitude diagram of a globular cluster Very useful tool to study stellar evolution Sample of stars at: same distance same age same chemical composition different masses → study stellar evolution Colour-magnitude diagram of M13 cluster The HR diagram - 6

28. Colour-magnitude diagram of nearby stars Parallaxes determined by Hipparcos satellite (most accurate to date) majority of dwarfs (on main sequence) minority of giants a few subdwarfs a few white dwarfs c-m diagram of nearby stars The HR diagram - 7