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3.2 Spectra and Spectral Classification 3.2.1 Temperature Temperature is usually measured by comparing the radiation of a star with that of a blackbody. Effective temperature Teff : T. of a blackbody with the same total flux density as the star σ Teff4 = Φ (Stefan-Boltzmann law) where Φ = Φ(R) is the total (bolometric) flux density at the surface of the star. At a distance r from the star, we measure the flux density Φ(r). Φ(R) r 2 As Φ~ r -2 , we have =( ) Φ(r) R i.e. Φ(R) = Φ(r)/δ2 where δ = R/r is the angular radius of the star In order to estimate Teff , we have to measure ● the total flux density (at all wavelengths; difficult particularly in the UV) ● the angular radius of the stars (difficult; see later) This is possible only for a small number of stars. 3.2 Spectra and Spectral Classification With Teff , the luminosity can be expressed as L = 4π R 2 Φ(R) = 4π R 2 σTeff4 Or for the absolute magnitude M ~ log R + 4 log T eff This relation provides an interesting interpretation of the colour-magnitude diagram from Sect. 3.1.4: ● A constant B-V corresponds to a constant T Different M at the same B-V must therefore reflect different radii R (brighter stars must be larger than fainter stars of the same T) Giants MV ● Supergiants Mai nS equ enc e White Dwarfs B-V 3.2 Spectra and Spectral Classification Other temperature definitions Colour temperature T c : T. of a blackbody that has the same colour index as the star. As the colour index m1 - m 2 = -2.5 log[Φ(λ1)/Φ(λ 2)], the ratio of the flux densities at two wavelengths have to be the same. Φ(λ 1 ) Bλ1(Tc) = Φ(λ 2 ) Bλ2(Tc) and therewith m 1 - m 2 = -2.5 log Bλ1(Tc ) Bλ2(Tc ) hc λ 5 = -2.5 log (λ1 ) +2.5 2 kTc ( 1λ1 - 1λ2 ) log e for the Wien approximation for the optical part of the spectrum (provided that T is not too high). m 1- m 2 = a + b i.e. a simple relation between T and colour index Tc Wien temperature: T. from Wien's displacement law Brightness temperature: T. of a blackbody with the same flux density at some wavelength Kinetic temperature: related to the average speed of the gas particles Ionization temperature: T. necessary for ionizing the gas Remark: Since the stars are not exactly blackbodies, the values for the different temperatures are not exactly the same. 3.2 Spectra and Spectral Classification 3.2.2 Spectroscopy of stars (a) Low-resolution spectroscopy ● ● ● Simplest version: objective prism spectroscopy (slitless) Advantages: - easy to realize - large number of spectra simultaneously Disadvantages: - low spectral resolution - spectra overlap - strong influence of sky background Detector Main mirror Objective prism spectrum exposure of the Hyades star cluster. The telescope was slightly moved perpendicular to the dispersion direction in order to increaase the width of the spectrum. 3.2 Spectra and Spectral Classification 3.2.2 Spectroscopy of stars (b) High-resolution spectroscopy ● ● Light from telescope Collimating mirror Entrance slit Slit spectrograph with diffraction grating Spectral resolution A =λ/dλ depends on - resolution of the grating (number of grooves) - resolution of detector (pixel size) - width of the entrance slit … must be optimized Diffraction grating Camera mirror Computer High-resolution solar spectrum. The combination of high resolution and wide wavelength coverage results in a linear spectrum that would be much too wide to be registered on a single detector. Therefore the spectrum is „folded“ so that different wavelength intervals are one upon the other. Detector (CCD) 3.2 Spectra and Spectral Classification 3.2.2 Spectroscopy of stars (c) Emission- and absorption spectra Hot, dense source (solid body, opt. dense gas) continuum spectrum (without lines) Hot, optically thin gas Continuum source plus hot, optically thin gas emission line spectrum (no continuum) absorption line spectrum (with continuum) 3.2 Spectra and Spectral Classification 3.2.2 Spectroscopy of stars (d) Components of stellar spectra ● ● ● Section of a CCD exposure of a spectrum Continuum Absorption lines from various chemical elements (Emission lines in rare cases only) Wavelength calibrated tracing of the spectrum Equivalent width Wλ : measure of the strength of a spectral line relative to the continuum Φ Wλ Φc = ∫ Φ(λ) dλ [Å] line continuum Φc Def.: Equivalent width of an absorption line = width of a rectangular and absolutely dark spectral region with the hight of the local continuum and the total flux equal to the total flux of the line λ 0 Wλ (Note that stellar absorption lines are usually not completely dark, even in the line cores.) 3.2 Spectra and Spectral Classification 3.2.3 Spectral classification of stars (e) Spectral sequence – early versions ● ● ● ● Photographic objective prism spectra available at the end of 19th century Different types of spectra with different complexity First classifications according the strengths of the lines that occur in nearly all spectra Later found that these are the lines of the hydrogen atom (H) 3.2 Spectra and Spectral Classification 3.2.3 Spectral classification of stars Partucularly simple spectrum for Vega regular series of absorption lines = Balmer series of the H atom (Hα, Hβ, Hγ, ...) Transition between two energy states of the H atom, n1 and n 2 , corresponds to a photon wavelength λ with 1 = R (1 - 1 ) λ n 12 n 22 R: Rydberg constant (Balmer-Rydberg formula) ● ● Early classification set spectra of this type = type A Continued with B,C,D,E,... according to decreasing strength of the Balmer lines 3.2 Spectra and Spectral Classification (f) Spectral classification – Harvard Sequenz ● ● ● ● ● ● Edward C. Pickering (1846-1919) Annie J. Cannon (1863-1941) By World War I, photographic objective prism spectra of more than 250 000 stars for the Henry-Draper (HD) Catalogue A. J. Cannon and her team provided classifications for 225 300 spectra in only 4 years New classification scheme based on all prominent lines instead of Balmer lines only → ABC types re-ordered Cannon realized that T is the principal distinguishing feature New system: O – B – A – F – G – K – M – L („Oh Be A Fine Girl Kiss Me“) With fine structure of 10 subclasses: A0,...,A9,B0,....,B9,... Temperature sequence Remark: type L was added only recently Harvard Observatory College (1913): A. J. Cannon and her team of Ladies at Harvard working for years on the classification of steller spectra. In 1897 Cannon was hired by Pickering to classify the spectra of stars of the southern hemisphere. Cannon and her team classified stars at an average rate of 5,000 spectra per month, up to three per minute. 3.2 Spectra and Spectral Classification (f) Spectral classification – Harvard Sequenz: example spectra M4 F6 M7 M3 F9 O5 O7 G1 M0 G6 M4e B3 B6 G9 M6 M2 A2 K4 A6 A8 K5 M5 K7 A9 4000 6000 Wavelength (Å) 8000 Hot stars (>10000K) ● continuum rising into the blue and UV ● steady increase of H Balmer lines 4000 6000 Wavelength (Å) 8000 F6-K5 (7000-4000K) ● Center of continuum shifts to longer λ ● Balmer lines weaker ● Metallic lines 4000 6000 Wavelength (Å) 8000 Cool stars (<4000K) ● Center of continuum shifts to longer λ ● Metallic lines ● Molecular bands Credit: University of Oregon (Department of Physics), Silva & Cornell (1992), Astrophysical Journal 4000 6000 Wavelength (Å) 8000 Very cool stars ● Center of continuum shifts to near IR ● Vera strong molecular bands 3.2 Spectra and Spectral Classification (f) Spectral classification – Harvard Sequenz: compact version 400 nm He II (strong) Hydrogen 650 nm O 30 000 K Helium He I, H 20 000 K B Helium H (very strong), CaII (weak) Calcium 10 000 K A Calcium H (strong), CaII, Fe (weak) Iron F 7 000 K Iron Oxygen Magnesium CaII, neutral metals (strong), H (moderately), neutral metals G CaII, neutral metals (maximum) K 4 000 K Strong molecular bands (TiO) M 3 000 K 6 000 K Oxygen Many molecules Credit: 2005 Pearson Prentice Hall, Inc. 3.2 Spectra Excurs: and Ionized SpectralHelium Classification Exercise: The ionizing energy of the Helium atom is 24 eV. Therefore, the photoionization of He requires a radiation field where the typical photon energy is E = 24 eV. The temperature should be estimated. E = hν = hc/λ = 24 eV λ = 64 nm Wien's law: T W = 0.0029 K m / 64 nm = 45 000 K Note on the terminology: He I = neutral helium He II = singly ionized helium 3.2 Spectra and Spectral Classification (f) Spectral classification – Harvard Sequenz: summary Main properties ● The spectral sequence is a sequence of decreasing effective tempereture The strength of the characteristic spectral lines varies systematically along sequence Relative width of absorption lines ● 50 effective temperature [1000 K] 25 10 8 6 5 spectral type Note on the terminology: He I = neutral helium He II = singly ionized helium 3.2 Spectra and Spectral Classification (d) Luminosity classes (MK system) Are there any differences between the spectra of main sequence stars and those of giants? (see Sect. 3.2.1) Observation: compared to giants, dwarf stars have 1. broader Balmer lines 2. stronger lines of neutral metals (i.e. weaker lines of ionized metals) Theoretical explanation: ● Line strength depends not only on T, but also on the pressure P ● Giants (extended atmospheres) have lower P at the same T as dwarfs Consequence of the higher pressure in the atmospheres of dwarfs: 1. Electric field of ions in the neighbourhood of an H atoms shift the energy levels (Stark effect) → line broadening 2. Higher density → higher probability for recombinations → lines of neutral metals stronger 3.2 Spectra and Spectral Classification (d) Luminosity classes (MK system) Ia Iab, Ib II III IV V VI D (*) Bright supergiants Supergiants Bright giants Giants Subgiants Main sequense stars (dwarfs) Subdwarfs White dwarfs (*) DA, DB, DC Complete spectral classification: luminosity class plus spectral type (two-dimensonal spectral classification) e.g. G2V for the Sun, A0V for Vega, ... 3.2 Spectra and Spectral Classification 3.2.4 Hertzsprung-Russell Diagram (HRD) Diagram showing the relationship between (a) absolute magnitude or luminosity and (b) spectral type or effective temperature (sometimes also color index) That means there exist different forms of this diagram, usually ● log L versus spectral type ● log L versus log T ● M versus B-V Right: HRD for 23 000 stars for which accurate distances (relative error <10%) are known (mostly from the HIPPARCOS satellite). 3.2 Spectra and Spectral Classification 3.2.4 Hertzsprung-Russell Diagram (HRD) ● ● The HRD displays the relationship between fundamantal properties of the stars (→ key diagram for stellar structure and evolution) Stars tend to fall only in certain regions of the HRD: - main sequence (most prominent) - giants and supergiants - white dwarfs Right: Schematic HRD showing the densely populated areas as well as many of the well known stars. Diagonal lines correspond to the L-R-T based on the Stefan-Boltzmann law (Sect. 3.2.1) 3.2 Spectra and Spectral Classification HRD of the nearby stars HRD for the brightest stars HRD of the stars within about 5 pc of the Sun. The diagonal lines correspond to constant stellar radius. 100 brightest stars in the sky. This HRD is biased in favor of the most luminous stars —which appear toward the upper left. 3.2 Spectra and Spectral Classification ● ● Usually ~10 2 stars Loosely bound Concentrated toward Galactic plane Globular star cluster Apparent magnitude V ● Apparent magnitude V Open star cluster ● ● ● B-V HRD ● „Long“ MS (towards blue stars) ● MS turnoff point at small B-V ● In general, only very few giants B-V Usually ~105 stars Compact clusters Not concentrated to Galactic plane HRD ● „Short“ MS (no blue MS stars) ● MS turnoff point redder (larger B-V) ● Many giants, complex structure: SGB: sub-giant branch RGB: red giant branch AGB: asymptotic giant branch HB: horizontal branch BS: blue stragglers P-AGB: post asymptotic giant branch