Atomic Spectra in Astrophysics

Transcription

1 Atomic Spectra in Astrophysics Potsdam University : Wi : Dr. Lidia Oskinova lida@astro.physik.uni-potsdam.de

2 Purpose of this course 01 The information about cosmic objects is almost exclusevly by their light Which parmateres of light can be measured? Spectroscopy - most detailed information about physical properties of the object Requerement: be familiar with the basics of qunatum mechanics

3 Content 02 Historical overview Emission and absorption - transition probabilities Radiative transfer, optical depth Hydrogen spectra: wave functions, quantum numbers, selection rules Complex atoms: LS coupling, jj coupling Stellar spectra: classification, models Polarization: linear: scattering, circular: Zeeman, magnetic fields Nebular spectra Intergalactic absorption line spectra: Curve-of-growth Lines from stellar winds: Sobolev approximation, P-Cygni profiles Optical spectroscopy: long-slit, echelle, multi-object, integral field UV spectroscopy: instruments, objects X-ray spectroscopy: instruments, line profiles IR spectroscopy: instruments, diagnostics mm spectroscopy: instruments, diagnostics

4 We will never know how to study by any means the chemical composition of stars - Auguste Comte (1835) 03

5 Descartes: rainbow colors are reflections of the white light. Newton: White light is 04a made up from the colours of the rainbow. Experiment: white light prism rainbow prism again back to white. Thomas Melvill 1752, putting different substances in flames differently patterned spectra s, Herschel: spectra are excellent to detect small quantities of an element in a powder put into a flame. William Wollaston (1802): the solar spectrum has tiny gaps. Joseph von Fraunhofer (1814) älmost countless number" of lines in solar spectrum. Foucault (1849) a substance which emitted light at the D line frequency, also absorbs light at that frequency. Sir George Stokes -- the phenomenon of resonance. Anders Angstrom 1853 observed and measured the spectrum of hydrogen. Bunsen and Kirchhoff systematic investigation of spectra ( , in Heidelberg). Thousands of spectral lines measured. New elements, rubidium and cesium, spectroscopically discovered. The method was used to find fifteen more new elements before the end of the century. In 1869, Joseph Lockyer studied the spectra of solar prominences (in eclipses). Discovery of helium. Johann Balmer (1860s), a school teacher, found a formula to describe the lines measured by Angstrem. Rydberg (1888) generalisation of Balmer Fowler, University of Virginia

6 In 1814 Joseph von Fraunhofer ( ) obtained solar spectrum

7 Besides rainbow colors: many dark lines Dark lines: Fraunhofer catalogued wavelengths and gave letters Sodium D-lines are still in use today Fraunhofer observed Betelgeuse - different pattern of dark lines he concluded that this is because of different composition Lines A & B in solar spectrum - telluric molecular oxygen

8 Kirchoff-Bunsen experiments (1859) Colors of metals burnt in flanes: sodium - Fraunhofer D-lines Each chemical element has a unique signature of emission line Emission and absorption lines (dark and bright) are the same for the same element Explanation XX century qunatum mechanics

9 07 Types of Astronomical Spectra: Emission and absorption spectrum Absorption: cooler material in front of hotter material emitting light in suitable wavelength range Emission: requires atoms or ions in an excited state Stars, emission nebulae, galaxies, quasars

10 Stars 08 Stellar photosphere is blackbody with T eff. Absorption lines formed in cooler atmosphere.

11 Emission nebulae 09 Emission is formed in optically thin nebular gas. There is no source of cintinous radiation (like bb) behind the nebular

12 Galaxies Composite spectrum of billions of stars and nebulae 10

13 Quasars 11 Lα-line is redshifted 1+z=λ observed /λ lab QSO provides background light source Absoption lines on different z i from foregraound nebulae and galaxies

14 Information potential of spectroscopy Composition. each chemical element leaves own fingerprint Temperature. fom the degree of exitation of atoms and ions Abundances. from line strength Motion. Doppler shift & Rotation : line profiles 12 Pressure. Line broadening v c = λ λ Magnetic field. Line splitting For each atop or ion one needs to know: Spectral lines (often used are Grotrian diagrams) Its energy level structure Intrinsic line strength The rest wavelengths

15 Radiation. Matter. Interactions of radiation with matter. 13 Radiation Radiation: ensemble of photons moving with c. A photon is characterized by: 1) Energy E=hu, h= erg/s 2) Spatial coordinates r. 3) Angular coordinates describing the direction of propagation ω. Consider photons with ν - ν+dν, located close to r and propagating within solid angle dω. Intensity is the energy transferred by these photons across a normal area dσ I ν (r,ω)dνdσdω

16 Matter in thermodynamic equilibrium 14 Velocities of particles are distributed according to the Maxwell law (electrons as well as ions). dn i = n i 4π m 3 (2πmkT) 3/2 e mv2 2kT v 2 dv The distribution of level populations in the ions: Boltzmann law Ionization stages: Saha law n i n 1 = g i g 1 e hν 1i kt n n + e n 1 = g+ 2(2πm e kt) 3/2 g 1 e hν 1c h 3 kt Radiation intensity: Plank-law with the same temperature as in Maxwell, Saha, and Boltzmann laws. B ν (T)= 2hν3 c 2 (e hν kt 1) 1 Local thermodynamic equilibrium (LTE) at each point conditions (1)-(3) are satisfied, but I ν can be different

17 Absorption coefficient k ik 15 Number of photoexcitations can be expressed via absorption coefficient k ik. Lets I ν intensity of radiation in line i Number of photoexcitations by radiation between ν-ν+dν per time per V per dω 1 I hν νk ik (ν)n i dνdω For isotropical velocity distribution, we can integrate over ν and ω, then number of photoexcitation per 1 s per 1 cm 3 is n i 0 k ik (ν) dν hν Iν dω=4πn i o k ik (ν)j ν dν hν Absorption coefficient k ik (ν) has sharp maximum at the line center. If J(ν) doesn t change much in the line and can be written as J ik then n i 4π hν ik J ik 0 k ik (ν)dν n i B ik J ik k

18 Optical depth 16 Lets neglect depence of the absorption coefficient on frequency within the line. Number of photoexcitations is described by absorption coefficient k ik τ ik= n ikk ikdz When τ 1 the medium is optically thick, when τ 1 it is optically thin Optical depth: thickness of the layer measured in the mean photon free paths. For monochromatic light and in case of pure absorption one can write I ik = I 0 e τ ik

19 Emission: an atom in excited state can emit a photon. 17 n i and n j level populations, as before J ν = 1 Iν dω 4π average intensity. At this point we assume that J ν = J ik independent of friquency within the line Spontaneous transitions k i: n k A ki Induced transitions k i: n k B ki J ik Photoexcitations i k: n i B ik J ik A ki [s 1 ], B ki [s 1 erg 1 cm 2 ], B ik - Einstein coefficients A ki = 2hν ik 3 c 2 B ki, B ki = g i g k B ik Oscillator strength: A ki = g i g k 8π 2 e 2 ν 2 ik m e c 3 f ik There are numerous compilaitons of oscillator strengths that are routinely used for computing model spectra.

20 Collisional excitation and de-excitation 18 Elastic collisions: do not change inner state of the particles. Establish Maxwell distribution. Holds well for atoms in ground state and electrons because of large cross-sectons. Atoms in excited state: short-life times. If densities are small, an atom can deexcite before collision. Large deviation from Maxwellian distribution is likely. Unelastic collisions excitation/ionization or de-excitaiton/recombination. Most common in astrophysics electron-atom collisions. Number of excitations per V per time i k: n i n e C ik Number of de-excitations per V per time k i: n k n e C ki C ik = v(i,k) q ikv f (v)dv, wherev ik : m ev 2 ik 2 = hν ik and C ik = g k g i e hν ik kte C ki and q ik collisonal excitation cross-section

21 Units 19 Frequincy [Hz] directly proportional to energy E=hν Astronomers tend to use wavelength: µm, nm, A o (10-4, 10-7, 10-8 cm) Spectrographs work naturaly in wavelength. The resolving power of the spectrograph is R= λ λ, where λ is the smallest wavelength difference that can be resolved. The ratio c R can resolve velocity 10 km/s Relation λ= c ν gives velocity resolution. E.g. R= Doppler shift from the rest wavelenght λ 0 is given by v r = c λ λ 0.

22 Different physical process at different spectral regions. Examples? Thermal process, which wavelengths? Examples? Ground based Atmosphere is mearly transparent.. at which λ? However, the spectra are always affected by telluric lines. Space based Not affected by atmosphere, but still suffering absorption in the ISM. At which λ? Why?

23 Hydrogen Atom Direct observation of H electron orbital (Stodolna et al. 2013, Phys. Rev. Lett. 110, )

24 The Schrödinger Equation of H-like atom 22 The Hamiltonian operator of H-like system Atomic Units Electron mass, m e = Ĥ= 2 2µ 2 Ze2 4πǫ 0 r kg Electron charge, e=1.6 10H19 C Bohr radius, a 0 = 4πǫ 0 2 me 2 = m Dirack constant, h/2π = 1 a.u. Ĥ= 1 2µ 2 Z r For a system with energy E and wavefunction ψ: Ĥψ=Eψ For H-like atom[ 1 2µ 2 Z r E] ψ( r)=0

25 Wavefunctions and separating the variables 23 Reduced mass: µ= m 1m 2 m 1 +m 2 Coordinates r=(r,θ,φ) ψ(r,θ,φ)=r nl (r)y lm (θ,φ) For H-like atoms one can solve Schrödinger eq. analytically by separating the variables. Radial solutions - Laguerre polinomials Angular solutions - spherical harmonics R(r) solutions exists only if main quantum number n=1,2,..., Y(τ,ψ): orbital quantum number l = 0,1,2,..., n-1 and magnetic quantum number m l =-l, -l+1,..l-1, l (2l+1 values) and spin quantum number m s =+1/2,-1/2

26 Quantum numbers 24 n determines the energy of the atom l describes the electron angular momentum: [l(l+1)] 1/ s p d f g h i k l... m l the magnetic quntum number: determines level splitting in the presence of magnetic field. m is the projec angular momentum on the z-axis s spin. The electron angular momentum is [s(s+1)] 1/2. for H-like atoms angular moment 3/2 Electron spin is 1/2 s z projection of spin angular momentum. It can have s, -s+1,...,s- 1, s values. For one electron system only -1/2, +1/2.

27 A state is determined by nl quantum numbers. 1s ground state 2s, 2p first exited 3s, 3p, 3d Each nl configuration is 2(2l+1)-fold degenerate