Atomic Spectra in AstrophysicsAtomic Spectra in Astrophysics

Potsdam University : Wi 2016-17 : Dr. Lidia Oskinovalida@astro.physik.uni-potsdam.de

01Purpose of this course

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

02Content

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

03

‘‘We will never know how to study by any means the chemicalcomposition of stars’’ - Auguste Comte (1835)

04a Descartes: rainbow colors are reflections of the white light. Newton: White light ismade 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 patternedspectra. 1820’s, Herschel: spectra are excellent to detect small quantities of anelement in a powder put into a flame.

William Wollaston (1802): the solar spectrum has tiny gaps. Joseph von Fraunhofer(1814) almost countless number" of lines in solar spectrum.

Foucault (1849) a substance which emitted light at the D line frequency, alsoabsorbs 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 (1855 ... 1863, inHeidelberg). Thousands of spectral lines measured. New elements, rubidium andcesium, spectroscopically discovered. The method was used to find fifteen more newelements 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 linesmeasured by Angstrem. Rydberg (1888) generalisation of Balmer formula.

@Michael Fowler, University of Virginia

In 1814 Joseph von Fraunhofer (1787-1826) obtained solar spectrum

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

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

07Types 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

08Stars

Stellar photosphere is blackbody with Teff . Absorption lines formed in cooler

atmosphere.

09Emission nebulae

Emission is formed in optically thin nebular gas. There is no source of cintinous

radiation (like bb) behind the nebular

10Galaxies Composite spectrum of billions of stars and nebulae

11Quasars

Lα-line is redshifted

1+z=λobserved /λ lab

QSO provides background light

source

Absoption lines on different zi from

foregraound nebulae and galaxies

12Information 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

vc=∆λλ

Pressure. Line broadening

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

Responce to magnetic field

13Radiation. Matter. Interactions of radiation with matter.

RadiationRadiation: ensemble of photons moving with c. A photon is characterized by:

1) Energy E=hu, h=6.6 10-27 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

Iν (r,ω)dνdσdω

14Matter in thermodynamic equilibrium

Velocities of particles are distributed according to the Maxwell law (electrons

as well as ions).

dni = ni4πm3

(2πmkT )3/2 e−mv2

2kT v2dv

The distribution of level populations in the ions: Boltzmann law

ni

n1=

gi

g1e−

hν1ikT

Ionization stages: Saha law

nen+

n1=

g+

g1

2(2πmekT )3/2

h3 e−hν1ckT

Radiation intensity: Plank-law with the same temperature as in Maxwell, Saha,

and Boltzmann laws. Bν(T ) = 2hν3

c2 (ehνkT − 1)−1

Local thermodynamic equilibrium (LTE) at each point conditions (1)-(3) are

satisfied, but Iν can be different

15Absorption coefficient kik

Number of photoexcitations can be expressed via absorption

coefficient kik . Lets Iν intensity of radiation in line i k

Number of photoexcitations by radiation between ν-ν+dν per time

per V per dω 1hν

Iνkik(ν)nidνdω

For isotropical velocity distribution, we can integrate over ν and

ω, then number of photoexcitation per 1 s per 1 cm3 is

ni

∫ ∞0

kik(ν)dνhν

∫

Iνdω = 4πni

∫ ∞o

kik(ν)Jνdνhν

Absorption coefficient kik(ν) has sharp maximum at the line

center. If J(ν) doesn’t change much in the line and can be written

as Jik thenni

4πhνik

Jik

∫ ∞0

kik(ν)dν ≡ niBik Jik

16Optical depth

Lets neglect depence of the absorption coefficient on frequency

within the line.

Number of photoexcitations is described by absorption

coefficient kik

τik =

∫

nikkikdz

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 Iik = I0e−τik

17Emission: an atom in excited state can emit a photon.

ni and nj level populations,

as before Jν =1

4π

∫

Iνdω average intensity. At this point we

assume that Jν = Jik independent of friquency within the line

Spontaneous transitions k i: nkAki

Induced transitions k i: nkBki Jik

Photoexcitations i k: niBik Jik

Aki [s−1], Bki [s−1erg−1cm2], Bik - Einstein coefficients

Aki =2hν

ik3

c2 Bki, Bki =gi

gkBik

Oscillator strength: Aki =gi

gk

8π2e2ν2ik

mec3 fik

There are numerous compilaitons of oscillator strengths that are

routinely used for computing model spectra.

18Collisional excitation and de-excitation

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 de-

excite 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: ni ne Cik

Number of de-excitations per V per time k i: nk ne Cki

Cik =

∫ ∞v(i,k)

qikv f (v)dv , where vik :mev

2ik

2= hνik

and Cik =gk

gie−

hνikkTe Cki and qik collisonal excitation cross-section

19Units

Frequincy [Hz] directly proportional to energy E=hν

Astronomers tend to use wavelength: µm, nm, Ao

(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 cR

gives velocity resolution. E.g. R=30000

can resolve velocity 10 km/s

Relation λ = cν

. Doppler shift from the rest

wavelenght λ0 is given by vr = c∆λλ0

.

Different physical processat different spectralregions. Examples?

Thermal process, whichwavelengths? Examples?

Ground basedAtmosphere is mearlytransparent.. at which λ?However, the spectra arealways affected by telluriclines.

Space based Not affectedby atmosphere, but stillsuffering absorption in theISM. At which λ? Why?

Hydrogen Atom

Direct observation of H electron orbital (Stodolna et al. 2013, Phys. Rev. Lett.110, 213001)

22The Schrodinger Equation of H-like atom

The Hamiltonian operator of H-like system

H = −~2

2µ∇2 − Ze2

4πǫ0rAtomic Units Electron mass, me =1.66 10-27 kg

Electron charge, e=1.6 10H19 C

Bohr radius, a0 = 4πǫ0~2

me2 = 5.29 10-11 m

Dirack constant, h/2π = 1 a.u.

H = − 12µ∇2 − Z

r

For a system with energy E and wavefunction ψ: Hψ = Eψ

For H-like atom[

− 12µ∇2 − Z

r− E]

ψ(~r) = 0

23Wavefunctions and separating the variables

Reduced mass: µ = m1m2

m1+m2

Coordinates ~r = (r, θ, φ)

For H-like atoms one can solve

Schrodinger eq. analytically by

separating the variables.

ψ(r, θ, φ) = Rnl(r)Ylm(θ, φ)

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 ml =-l, -l+1,..l-1, l (2l+1 values)

and spin quantum number ms =+1/2,-1/2

24Quantum numbers

n determines the energy of the atom

l describes the electron angular momentum: ~[l(l + 1)]1/2

0 1 2 3 4 5 6 7 ...

s p d f g h i k l ... ml 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 .

Electron spin is 1/2 for H-like atoms angular moment √

3/2~

sz projection of spin angular momentum. It can have s, -s+1,...,s-

1, s values. For one electron system only -1/2, +1/2.

A state isdetermined by nlquantumnumbers.

1s ground state2s, 2p first exited3s, 3p, 3d

Each nlconfiguration is2(2l+1)-folddegenerate