6. Stellar spectra. excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H -

Size: px
Start display at page:

Download "6. Stellar spectra. excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H -"

Transcription

1 6. Stellar spectra excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H - 1

2 Occupation numbers: LTE case Absorption coefficient: = n i calculation of occupation numbers needed LTE each volume element in thermodynamic equilibrium at temperature T(r) hypothesis: electron-ion collisions adjust equilibrium difficulty: interaction with non-local photons LTE is valid if effect of photons is small or radiation field is described by Planck function at T(r) otherwise: non-lte 2

3 Excitation in LTE Boltzmann excitation equation n ij : number density of atoms in excited level i of ionization stage j (ground level: i=1 neutral: j=0) g ij : statistical weight of level i = number of degenerate states E ij excitation energy relative to ground state g ij = 2i 2 for hydrogen = (2S+1) (2L+1) in L-S coupling log n ij =log g ij E ij (ev) 5040 n 1j g 1j T The fraction relative to the total number of atoms of in ionization stage j is n ij n j = g ij U j (T) e E ij/kt U j (T )= X i g ij e E ij/kt U j (T) is called the partition function 3

4 Ionization in LTE: Saha s formula Generalize Boltzmann equation for ratio of two contiguous ionic species j and j+1 Consider ionization process j j+1 initial state: final state: n 1j & statistical weight g 1j n 1j+1 + free electron & statistical weight g 1j+1 g El n 1j+1 (v) dx dy dz dp x dp y dp z R R n1j+1 (v)dv d 3 p = n 1j+1 number of ions in groundstate with free electron with velocity in (v,v+dv) in phase space g El : volume in phase space normalized to smallest possible volume (h 3 ) for electron: g El =2 dx dy dz dp x dp y dp z h 3 2 spin orientations R dx dy dz = R dv = V =1/ne dp x dp y dp z =4πp 2 dp =4πm 3 v 2 dv 4

5 Ionization: Saha s formula n 1j+1 (v) dv dp x dp y dp z = g 1j+1 g El e (E 1 j + 2 mv 2 )/kt n 1j g 1j using Boltzmann formula n 1j+1 (v) dv dp x dp y dp z = g 1j+1 2dV dp x dp y dp z e [E j+ 1 n 1j g 1j h 3 2m (p 2 x +p2 y +p2 z )]/kt Sum over all final states: integrate over all phase space n 1j+1 = n 1j g 1j+1 g 1j 2 V h 3 e E j/kt Z Z Z e 1 2mkT (p2 x +p2 y +p2 z ) dp x dp y dp z Z e x2 dx = π (2πmkT ) 3/ 2 Saha 1920 n 1j+1 n e n 1j =2 g 1j+1 g 1j µ 2π mkt h 2 3/ 2 e E j kt - ionization falls with n e (recombinations) - ionization grows with T 5

6 Ionization: Saha s formula Generalize for arbitrary levels (not just ground state): n j = X n ij n j+1 = i=1 X i=1 n ij+1 n ij+1 = n 1j+1 g ij+1 g 1j+1 e E ij+1/kt using Boltzmann s equation n j+1 = n 1j+1 g 1j+1 X g ij+1 e E ij+1/kt i=1 U j+1 (T) : partition function also n j = n 1j g 1j U j (T) n j+1 n e n j =2 U j+1(t) U j (T) µ 2πmkT h 2 3/2 e E j kt 6

7 Ionization: Saha s formula Using electron pressure P e instead of n e (P e = n e kt) n j+1 n j P e =2 U j+1(t) U j (T) µ 2πm h 2 3/ 2 (kt) 5/2 e E j kt which can be written as: n log j+1 U 10 = log 10 P e +log j+1 (T ) 10 n j U j (T ) +2.5log 10 T 5040 T E j with P e in dyne/cm 2 and E j in ev 7

8 Ionization: Saha s formula Example: H at P e = 10 dyne/cm 2 (~ solar pressure at T = T eff ) T (K) n(h + ) / n(h) n(h) /[n(h) + n(h + )] n(h + ) /[n(h) + n(h + )] 4, E E-9 6, E E-3 8, E , E , E , E , E E H fractional ionization H I H II Temperature

9 On the partition function Partition function for neutral H atom E i0 E ion = 13.6 ev U 0 (T)= X g i0 e E i0/kt i=1 g i0 = 2i 2 U 0 (T ) 2 e E ion /kt infinite number of levels partition function diverges! reason: Hydrogen atom level structure X i 2 calculated as if it were alone in the universe not realistic cut-off needed i=1 divergent idea: orbit radius r = a 0 i 2 (i is main quantum number) there must be a max i corresponding to the finite spatial extent of atom r max 4π 3 r3 max = 1 N = 4π 3 (r 0i 2 max) 3 i max introduces a pressure dependence of U 9

10 An example: pure hydrogen atmosphere in LTE Temperature T and total particle density N given: calculate n e, n p, n i From Saha s equation and n e = n p (only for pure H plasma): (T) 10

11 The LTE occupation number n i * From Saha s equation: n 1j+1 n e n 1j =2 g 1j+1 g 1j µ 2πmkT h 2 3/2 e E j kt n 1j = n 1j+1 n e g 1j 1 g 1j+1 2 µ h 2 2πmkT 3/2 e E j kt + Boltzmann: n i := n ij = n 1j+1 n e g ij 1 g 1j+1 2 n ij n 1j = g ij g 1j µ h 2 2πmkT e E 1i/kT 3/2 e E ij kt in LTE we can express the bound level occupation numbers as a function of T, n e and the ground-state occupation number of the next higher ionization stage. Note n i * is the occupation number used to calculate bf-stimulated and bfspontaneous emission 11

12 Stellar classification and temperature: application of Saha and Boltzmann formulae temperature (spectral type) & pressure (luminosity class) variations + chemical abundance changes. Qualitative plot of strength of observed Line features as a function of spectral type 12

13 Stellar classification and temperature: application of Saha and Boltzmann formulae The pioneers of stellar spectroscopy 13

14 The pioneers of stellar spectroscopy at work 14

15 Annie Jump Cannon 15

16 Annie Jump Cannon 16

17 Stellar classification Type O Approximate Surface Temperature > 25,000 K B 11,000-25,000 Main Characteristics Singly ionized helium lines either in emission or absorption. Strong ultraviolet continuum. He I 4471/He II 4541 increases with type. H and He lines weaken with increasing luminosity. H weak, He I, He II, C III, N III, O III, Si IV. Neutral helium lines in absorption (max at B2). H lines increase with type. Ca II K starts at B8. H and He lines weaken with increasing luminosity. C II, N II, O II, Si II-III-IV, Mg II, Fe III. A 7,500-11,000 Hydrogen lines at maximum strength for A0 stars, decreasing thereafter. Neutral metals stronger. Fe II prominent A0-A5. H and He lines weaken with increasing luminosity. O I, Si II, Mg II, Ca II, Ti II, Mn I, Fe I-II. F 6,000-7,500 G 5,000-6,000 Metallic lines become noticeable. G-band starts at F2. H lines decrease. CN 4200 increases with luminosity. Ca II, Cr I-II, Fe I-II, Sr II. Solar-type spectra. Absorption lines of neutral metallic atoms and ions (e.g. onceionized calcium) grow in strength. CN 4200 increases with luminosity. K 3,500-5,000 Metallic lines dominate, H weak. Weak blue continuum. CN 4200, Sr II 4077 increase with luminosity. Ca I-II. M < 3,500 Molecular bands of titanium oxide TiO noticeable. CN 4200, Sr II 4077 increase with luminosity. Neutral metals. 17

18 online Gray atlas at NED nedwww.ipac.caltech.edu/level5/gray/frames.html Stellar classification 18

19 Stellar classification ionization (I.P. 25 ev) The spectral type can be judged easily by the ratio of the strengths of lines of He I to He II; He I tends to increase in strength with decreasing temperature while He II decreases in strength. The ratio He I 4471 to He II 4542 shows this trend clearly. The definition of the break between the O-type stars and the B-type stars is the absence of lines of ionized helium (He II) in the spectra of B-type stars. The lines of He I pass through a maximum at approximately B2, and then decrease in strength towards later (cooler) types. A useful ratio to judge the spectral type is the ratio of He I 4471/Mg II A DIGITAL SPECTRAL CLASSIFICATION ATLAS R. O. Gray 19

20 O-star spectral types 20

21 B0Ia SiIV SiIII B-star spectral types B0.5Ia B1Ia B1.5Ia SiII B2Ia B3Ia B5Ia B8Ia B9Ia 21

22 Stellar classification (I.P. 6 ev) H & K strongest T high enough for single ionization, but not further 22

23 Stellar classification Balmer lines indicate stellar luminosity Gravity atmospheric density line broadening Are the ionization levels for different elements observed in a given spectral type consistent with a single temperature? Spectral class O B A-M ion and ionization potential He II C III N III O III Si IV HII C II N II O II Si III Fe III Mg II Ca II Ti II Cr II Si II Fe II

24 Cecilia Payne-Gaposchkin 24

25 Stellar classification Saha s equation stellar classification (C. Payne s thesis, Harvard 1925) The strengths of selected lines along the spectral sequence. variations of observed line strengths with spectral type in the Harvard sequence. Saha-Boltzmann predictions of the fractional concentration N r,s /N of the lower level of the lines indicated in the upper panel against temperature T (given in units of 1000 K along the top). The pressure was taken constant at P e = N e k T = 131 dyne cm -2. The T-axis is adjusted to the abscissa of the upper diagram in order to obtain a correspondence between the observed and computed peaks. 25

26 Cecilia Payne-Gaposchkin 26

27 Stellar continua: opacity sources 27

28 Stellar continua: the Balmer jump From the ground we can measure part of Balmer ( < 3646 A) and Bracket ( > 8207 A) continua, and complete Paschen continuum ( A) Provide information on T, P. Spectrophotometric measurements in UV (hot stars), visible and IR (cool stars) ionization changes are reflected in changes in the continuum flux for > (Balmer limit) no n=2 b-f transitions possible drop in absorption atmosphere is more transparent observed flux comes from deeper hotter layers higher flux BALMER JUMP Balmer discontinuity (when H^- absorption is negligible T > 9000 K) = κ bf (> 3650) κ bf (< 3650) = κ bf (n =3)+... κ bf (n =2)+κ bf (n =3)+... ' κbf (n =3) κ bf (n =2) 28

29 Stellar continua: the Balmer jump from κ bf = σ bf n N n σ bf n 1 n 5 ν 3 and Boltzmann s equation N n N tot g n U n e E n/kt = n 2 N tot e E n/kt κ bf 1 n 3 e E n/kt κ bf (> 3650) κ bf (< 3650) ' 8 27 e (E 3 E 2 ) /kt e.g at T = 5,000 K at T = 10,000 K if b-f transitions dominate continuous opacity the Balmer discontinuity increases with decreasing T measure T from Balmer jump 29

30 Stellar continua: H - apply Saha s equation to H - (H - is the atom and H 0 is the ion ) N(H 0 ) n e N(H ) = T 3/2 e 8753/T N(H 0 ) log 10 N(H ) = log 10 P e +2.5log 10 T 5040 T under solar conditions: N(H - ) / N(H 0 ) ' E I at the same time: N 2 / N(H 0 ) ' N 3 / N(H 0 ) ' (Paschen continuum) N(H - )/ N(H 0 ): > N 3 / N(H 0 ): b-f from H - more important than H b-f in the visible 30

31 Stellar continua at solar T H - b-f dominates from Balmer limit up to H - threshold (16500 A). H 0 b-f dominates in the visible for T > 7,500 K. Balmer jump smaller than in the case of pure H 0 absorption: instead of increasing at low T, decreases as H - absorption increases Max of Balmer jump: 10,000 K (A0 type) H - opacity n e higher in dwarfs than supergiants Balmer jump sensitive to both T and P e in A-F stars 31

6. Stellar spectra. excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H -

6. Stellar spectra. excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H - 6. Stellar spectra excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H - 1 Occupation numbers: LTE case Absorption coefficient: = n i calculation of occupation numbers

More information

6. Stellar spectra. excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H -

6. Stellar spectra. excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H - 6. Stellar spectra excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H - 1 Occupation numbers: LTE case Absorption coefficient: κ ν = n i σ ν$ à calculation of occupation

More information

The Classification of Stellar Spectra Chapter 8

The Classification of Stellar Spectra Chapter 8 The Classification of Stellar Spectra Chapter 8 Star Clusters in the Large Magellanic Cloud http://www.seds.org/hst/ NGC850.html The Classification of Stellar Spectra Classification scheme developed before

More information

Stellar Spectra ASTR 2120 Sarazin. Solar Spectrum

Stellar Spectra ASTR 2120 Sarazin. Solar Spectrum Stellar Spectra ASTR 2120 Sarazin Solar Spectrum Solar Prominence Sep. 14, 1999 Solar Activity Due to rotation, convection, and magnetic field (Section 7.2 review) Charged Particles in Magnetic Fields

More information

(c) Sketch the ratio of electron to gas pressure for main sequence stars versus effective temperature. [1.5]

(c) Sketch the ratio of electron to gas pressure for main sequence stars versus effective temperature. [1.5] 1. (a) The Saha equation may be written in the form N + n e N = C u+ u T 3/2 exp ( ) χ kt where C = 4.83 1 21 m 3. Discuss its importance in the study of stellar atmospheres. Carefully explain the meaning

More information

7. Non-LTE basic concepts

7. Non-LTE basic concepts 7. Non-LTE basic concepts LTE vs NLTE occupation numbers rate equation transition probabilities: collisional and radiative examples: hot stars, A supergiants 1 Equilibrium: LTE vs NLTE LTE each volume

More information

Stellar Astrophysics: The Classification of Stellar Spectra

Stellar Astrophysics: The Classification of Stellar Spectra Stellar Astrophysics: The Classification of Stellar Spectra Temperature and Color The intensity of light emitted by three hypothetical stars is plotted against wavelength The range of visible wavelengths

More information

Quantum Mechanics and Stellar Spectroscopy.

Quantum Mechanics and Stellar Spectroscopy. Quantum Mechanics and Stellar Spectroscopy http://apod.nasa.gov/apod/ Recall the electric force. Like gravity it is a 1/r 2 force/ That is: F elec = Z 1 Z 2 e2 r 2 where Z 1 and Z 2 are the (integer) numbers

More information

Lecture 4: Absorption and emission lines

Lecture 4: Absorption and emission lines Lecture 4: Absorption and emission lines Senior Astrophysics 2018-03-13 Senior Astrophysics () Lecture 4: Absorption and emission lines 2018-03-13 1 / 35 Outline 1 Absorption and emission line spectra

More information

Stars - spectral types

Stars - spectral types Stars - spectral types 1901: Led by Annie Jump Cannon, Harvard astronomers looked at the spectra of >200,000 stars. Classified them as A, B, C etc. Cannon rearranged them into OBAFGKM based on how lines

More information

The Stellar Opacity. F ν = D U = 1 3 vl n = 1 3. and that, when integrated over all energies,

The Stellar Opacity. F ν = D U = 1 3 vl n = 1 3. and that, when integrated over all energies, The Stellar Opacity The mean absorption coefficient, κ, is not a constant; it is dependent on frequency, and is therefore frequently written as κ ν. Inside a star, several different sources of opacity

More information

7. Non-LTE basic concepts

7. Non-LTE basic concepts 7. Non-LTE basic concepts LTE vs NLTE occupation numbers rate equation transition probabilities: collisional and radiative examples: hot stars, A supergiants 10/13/2003 Spring 2016 LTE LTE vs NLTE each

More information

FIA0221: Taller de Astronomía II. Lecture 14 Spectral Classification of Stars

FIA0221: Taller de Astronomía II. Lecture 14 Spectral Classification of Stars FIA0221: Taller de Astronomía II Lecture 14 Spectral Classification of Stars Spectral types along the stellar CMD. Oh, Be A Fine Girl Kiss Me! Classification of Stellar spectra: The MK system: strong He+

More information

Spectral Line Intensities - Boltzmann, Saha Eqs.

Spectral Line Intensities - Boltzmann, Saha Eqs. Spectral Line Intensities - Boltzmann, Saha Eqs. Absorption in a line depends on: - number of absorbers along the line-of-sight, and -their cross section(s). Absorp. n a σl, where n a is the number of

More information

Chapter 3C. 3-4C. Ionization

Chapter 3C. 3-4C. Ionization Chapter 3C The excitation ratio N B /N A increases as the excitation potential get smaller. Also, as T increases, the higher energy levels become more populated. One should see that as T goes to infinity,

More information

Temperature, Blackbodies & Basic Spectral Characteristics.

Temperature, Blackbodies & Basic Spectral Characteristics. Temperature, Blackbodies & Basic Spectral Characteristics. Things that have one primary temperature but also exhibit a range of temperatures are known in physics as blackbodies. They radiate energy thermally.

More information

Atomic Physics 3 ASTR 2110 Sarazin

Atomic Physics 3 ASTR 2110 Sarazin Atomic Physics 3 ASTR 2110 Sarazin Homework #5 Due Wednesday, October 4 due to fall break Test #1 Monday, October 9, 11-11:50 am Ruffner G006 (classroom) You may not consult the text, your notes, or any

More information

11.1 Local Thermodynamic Equilibrium. 1. the electron and ion velocity distributions are Maxwellian,

11.1 Local Thermodynamic Equilibrium. 1. the electron and ion velocity distributions are Maxwellian, Section 11 LTE Basic treatments of stellar atmospheres adopt, as a starting point, the assumptions of Local Thermodynamic Equilibrium (LTE), and hydrostatic equilibrium. The former deals with the microscopic

More information

Family of stars. Fred Sarazin Physics Department, Colorado School of Mines. PHGN324: Family of stars

Family of stars. Fred Sarazin Physics Department, Colorado School of Mines. PHGN324: Family of stars Family of stars Reminder: the stellar magnitude scale In the 1900 s, the magnitude scale was defined as follows: a difference of 5 in magnitude corresponds to a change of a factor 100 in brightness. Dm

More information

2. Stellar atmospheres: Structure

2. Stellar atmospheres: Structure 2. Stellar atmospheres: Structure 2.1. Assumptions Plane-parallel geometry Hydrostatic equilibrium, i.e. o no large-scale accelerations comparable to surface gravity o no dynamically significant mass loss

More information

THE OBSERVATION AND ANALYSIS OF STELLAR PHOTOSPHERES

THE OBSERVATION AND ANALYSIS OF STELLAR PHOTOSPHERES THE OBSERVATION AND ANALYSIS OF STELLAR PHOTOSPHERES DAVID F. GRAY University of Western Ontario, London, Ontario, Canada CAMBRIDGE UNIVERSITY PRESS Contents Preface to the first edition Preface to the

More information

SISD Training Lectures in Spectroscopy

SISD Training Lectures in Spectroscopy SISD Training Lectures in Spectroscopy Anatomy of a Spectrum Visual Spectrum of the Sun Blue Spectrum of the Sun Morphological Features in Spectra λ 2 Line Flux = Fλ dλ λ1 (Units: erg s -1 cm -2 ) Continuum

More information

Opacity. requirement (aim): radiative equilibrium: near surface: Opacity

Opacity. requirement (aim): radiative equilibrium: near surface: Opacity (Gray) Diffusion approximation to radiative transport: (assumes isotropy valid only in the deep stellar interior) - opacity is a function of frequency (wave length ). - aim: to reduce the (rather complex)

More information

A Stellar Spectra 3. Stars shine at night (during the day too!). A star is a self-luminous sphere of gas. Stars are held together by gravity.

A Stellar Spectra 3. Stars shine at night (during the day too!). A star is a self-luminous sphere of gas. Stars are held together by gravity. Stellar Spectra Relativity and Astrophysics Lecture 12 Terry Herter Outline What is a star? Stellar Spectra Kirchhoff s Laws Spectral Classification Spectral Types: O B A F G K M L T Stellar Photometry

More information

CHAPTER 22. Astrophysical Gases

CHAPTER 22. Astrophysical Gases CHAPTER 22 Astrophysical Gases Most of the baryonic matter in the Universe is in a gaseous state, made up of 75% Hydrogen (H), 25% Helium (He) and only small amounts of other elements (called metals ).

More information

The Sun and the Stars

The Sun and the Stars Classification of stellar spectra Potted History : 1802 William Wallaston showed that the spectrum of the sun is not simply a continuous spectrum, but is broken up by a series of dark lines (absorption

More information

2. Basic Assumptions for Stellar Atmospheres

2. Basic Assumptions for Stellar Atmospheres 2. Basic Assumptions for Stellar Atmospheres 1. geometry, stationarity 2. conservation of momentum, mass 3. conservation of energy 4. Local Thermodynamic Equilibrium 1 1. Geometry Stars as gaseous spheres!

More information

ASTR-1010: Astronomy I Course Notes Section IV

ASTR-1010: Astronomy I Course Notes Section IV ASTR-1010: Astronomy I Course Notes Section IV Dr. Donald G. Luttermoser Department of Physics and Astronomy East Tennessee State University Edition 2.0 Abstract These class notes are designed for use

More information

Substellar Atmospheres II. Dust, Clouds, Meteorology. PHY 688, Lecture 19 Mar 11, 2009

Substellar Atmospheres II. Dust, Clouds, Meteorology. PHY 688, Lecture 19 Mar 11, 2009 Substellar Atmospheres II. Dust, Clouds, Meteorology PHY 688, Lecture 19 Mar 11, 2009 Outline Review of previous lecture substellar atmospheres: opacity, LTE, chemical species, metallicity Dust, Clouds,

More information

Sun. Sirius. Tuesday, February 21, 2012

Sun. Sirius. Tuesday, February 21, 2012 Spectral Classification of Stars Sun Sirius Stellar Classification Spectral Lines H Fe Na H Ca H Spectral Classification of Stars Timeline: 1890s Edward C. Pickering (1846-1919) and Williamina P. Fleming

More information

PHYS 231 Lecture Notes Week 3

PHYS 231 Lecture Notes Week 3 PHYS 231 Lecture Notes Week 3 Reading from Maoz (2 nd edition): Chapter 2, Sec. 3.1, 3.2 A lot of the material presented in class this week is well covered in Maoz, and we simply reference the book, with

More information

Ay Fall 2004 Lecture 6 (given by Tony Travouillon)

Ay Fall 2004 Lecture 6 (given by Tony Travouillon) Ay 122 - Fall 2004 Lecture 6 (given by Tony Travouillon) Stellar atmospheres, classification of stellar spectra (Many slides c/o Phil Armitage) Formation of spectral lines: 1.excitation Two key questions:

More information

3. Stellar Atmospheres: Opacities

3. Stellar Atmospheres: Opacities 3. Stellar Atmospheres: Opacities 3.1. Continuum opacity The removal of energy from a beam of photons as it passes through matter is governed by o line absorption (bound-bound) o photoelectric absorption

More information

Spectral Line Shapes. Line Contributions

Spectral Line Shapes. Line Contributions Spectral Line Shapes Line Contributions The spectral line is termed optically thin because there is no wavelength at which the radiant flux has been completely blocked. The opacity of the stellar material

More information

! p. 1. Observations. 1.1 Parameters

! p. 1. Observations. 1.1 Parameters 1 Observations 11 Parameters - Distance d : measured by triangulation (parallax method), or the amount that the star has dimmed (if it s the same type of star as the Sun ) - Brightness or flux f : energy

More information

Stars: some basic characteristics

Stars: some basic characteristics Stars: some basic characteristics Stars! How bright are they? How massive are they? What are the different types? How long do they live? How hot are they? Stellar brightness and luminosity The apparent

More information

Stellar atmospheres: an overview

Stellar atmospheres: an overview Stellar atmospheres: an overview Core M = 2x10 33 g R = 7x10 10 cm 50 M o 20 R o L = 4x10 33 erg/s 10 6 L o 10 4 (PN) 10 6 (HII) 10 12 (QSO) L o Photosphere Envelope Chromosphere/Corona R = 200 km ~ 3x10

More information

Spectral Classification of Stars

Spectral Classification of Stars Sun Sirius Stellar Classification Spectral Lines CaH H Fe Na H Timeline: Edward C. Pickering (1846-1919) and Williamina P. Fleming 1890s (1857-1911) label spectra alphabetically according to strength of

More information

Energy transport: convection

Energy transport: convection Outline Introduction: Modern astronomy and the power of quantitative spectroscopy Basic assumptions for classic stellar atmospheres: geometry, hydrostatic equilibrium, conservation of momentum-mass-energy,

More information

Lecture 2: Formation of a Stellar Spectrum

Lecture 2: Formation of a Stellar Spectrum Abundances and Kinematics from High- Resolution Spectroscopic Surveys Lecture 2: Formation of a Stellar Spectrum Eline Tolstoy Kapteyn Astronomical Institute, University of Groningen I have a spectrum:

More information

Substellar Atmospheres. PHY 688, Lecture 18 Mar 9, 2009

Substellar Atmospheres. PHY 688, Lecture 18 Mar 9, 2009 Substellar Atmospheres PHY 688, Lecture 18 Mar 9, 2009 Outline Review of previous lecture the Kepler mission launched successfully results P < 1 month planets by September 09 giant planet interiors comparison

More information

Atomic Physics ASTR 2110 Sarazin

Atomic Physics ASTR 2110 Sarazin Atomic Physics ASTR 2110 Sarazin Homework #5 Due Wednesday, October 4 due to fall break Test #1 Monday, October 9, 11-11:50 am Ruffner G006 (classroom) You may not consult the text, your notes, or any

More information

FYI: Spectral Classification & Stellar Spectra. 1. Read FYI: Spectral Classification A Look Back and FYI: Stellar Spectra What s in a Star?

FYI: Spectral Classification & Stellar Spectra. 1. Read FYI: Spectral Classification A Look Back and FYI: Stellar Spectra What s in a Star? FYI: Spectral Classification & Stellar Spectra E3:R1 1. Read FYI: Spectral Classification A Look Back and FYI: Stellar Spectra What s in a Star? As you read use the spaces below to write down any information

More information

Astronomy 110 Homework #07 Assigned: 03/06/2007 Due: 03/13/2007. Name: (Answer Key)

Astronomy 110 Homework #07 Assigned: 03/06/2007 Due: 03/13/2007. Name: (Answer Key) Astronomy 110 Homework #07 Assigned: 03/06/2007 Due: 03/13/2007 Name: (Answer Key) Directions: Listed below are twenty (20) multiple-choice questions based on the material covered by the lectures thus

More information

Chapter 2: Equation of State

Chapter 2: Equation of State Introduction Chapter 2: Equation of State The Local Thermodynamic Equilibrium The Distribution Function Black Body Radiation Fermi-Dirac EoS The Complete Degenerate Gas Application to White Dwarfs Temperature

More information

Stars AS4023: Stellar Atmospheres (13) Stellar Structure & Interiors (11)

Stars AS4023: Stellar Atmospheres (13) Stellar Structure & Interiors (11) Stars AS4023: Stellar Atmospheres (13) Stellar Structure & Interiors (11) Kenneth Wood, Room 316 kw25@st-andrews.ac.uk http://www-star.st-and.ac.uk/~kw25 What is a Stellar Atmosphere? Transition from dense

More information

Equilibrium Properties of Matter and Radiation

Equilibrium Properties of Matter and Radiation Equilibrium Properties of Matter and Radiation Temperature What is it? A measure of internal energy in a system. Measure from (1) velocities of atoms/molecules () population of excited/ionized states (3)

More information

2. Basic assumptions for stellar atmospheres

2. Basic assumptions for stellar atmospheres . Basic assumptions for stellar atmospheres 1. geometry, stationarity. conservation of momentum, mass 3. conservation of energy 4. Local Thermodynamic Equilibrium 1 1. Geometry Stars as gaseous spheres

More information

6. Interstellar Medium. Emission nebulae are diffuse patches of emission surrounding hot O and

6. Interstellar Medium. Emission nebulae are diffuse patches of emission surrounding hot O and 6-1 6. Interstellar Medium 6.1 Nebulae Emission nebulae are diffuse patches of emission surrounding hot O and early B-type stars. Gas is ionized and heated by radiation from the parent stars. In size,

More information

Parallax: Space Observatories. Stars, Galaxies & the Universe Announcements. Stars, Galaxies & Universe Lecture #7 Outline

Parallax: Space Observatories. Stars, Galaxies & the Universe Announcements. Stars, Galaxies & Universe Lecture #7 Outline Stars, Galaxies & the Universe Announcements HW#4: posted Thursday; due Monday (9/20) Reading Quiz on Ch. 16.5 Monday (9/20) Exam #1 (Next Wednesday 9/22) In class (50 minutes) first 20 minutes: review

More information

The Physics of Light, part 2. Astronomy 111

The Physics of Light, part 2. Astronomy 111 Lecture 7: The Physics of Light, part 2 Astronomy 111 Spectra Twinkle, twinkle, little star, How I wonder what you are. Every type of atom, ion, and molecule has a unique spectrum Ion: an atom with electrons

More information

Opacity and Optical Depth

Opacity and Optical Depth Opacity and Optical Depth Absorption dominated intensity change can be written as di λ = κ λ ρ I λ ds with κ λ the absorption coefficient, or opacity The initial intensity I λ 0 of a light beam will be

More information

Assignments for Monday Oct. 22. Read Ch Do Online Exercise 10 ("H-R Diagram" tutorial)

Assignments for Monday Oct. 22. Read Ch Do Online Exercise 10 (H-R Diagram tutorial) Assignments for Monday Oct. 22 Read Ch. 13 + Do Online Exercise 10 ("H-R Diagram" tutorial) Luminosity passing through each sphere is the same. Area of sphere: 4π(radius) 2 Divide luminosity by area to

More information

Review of Star Intro. PHYSICS 162 Lecture 7a 1

Review of Star Intro. PHYSICS 162 Lecture 7a 1 Review of Star Intro Parallax - geometric method of determining star distance Absolute and apparent luminosity. Temperature Spectrum: What characterizes the star s surface Is related to its temperature

More information

Exam 1 will cover. The Day of the Exam. Astronomy Picture of the Day: Today s Class: Measuring temperatures of stars

Exam 1 will cover. The Day of the Exam. Astronomy Picture of the Day: Today s Class: Measuring temperatures of stars September 25, 2013 Reading: Chapter 15, section 15.1. Exam 1 next class! Review Session tomorrow night, Sep. 26, at 7 pm in Duane G2B47. Naked eye observing session tonight at 8 pm. Volunteers for Astronomy

More information

Plasma Spectroscopy Inferences from Line Emission

Plasma Spectroscopy Inferences from Line Emission Plasma Spectroscopy Inferences from Line Emission Ø From line λ, can determine element, ionization state, and energy levels involved Ø From line shape, can determine bulk and thermal velocity and often

More information

Interstellar Astrophysics Summary notes: Part 2

Interstellar Astrophysics Summary notes: Part 2 Interstellar Astrophysics Summary notes: Part 2 Dr. Paul M. Woods The main reference source for this section of the course is Chapter 5 in the Dyson and Williams (The Physics of the Interstellar Medium)

More information

2. Basic assumptions for stellar atmospheres

2. Basic assumptions for stellar atmospheres . Basic assumptions for stellar atmospheres 1. geometry, stationarity. conservation of momentum, mass 3. conservation of energy 4. Local Thermodynamic Equilibrium 1 1. Geometry Stars as gaseous spheres

More information

WINDS OF HOT MASSIVE STARS III Lecture: Quantitative spectroscopy of winds of hot massive stars

WINDS OF HOT MASSIVE STARS III Lecture: Quantitative spectroscopy of winds of hot massive stars WINDS OF HOT MASSIVE STARS III Lecture: Quantitative spectroscopy of winds of hot massive stars 1 Brankica Šurlan 1 Astronomical Institute Ondřejov Selected Topics in Astrophysics Faculty of Mathematics

More information

Lecture 6: Continuum Opacity and Stellar Atmospheres

Lecture 6: Continuum Opacity and Stellar Atmospheres Lecture 6: Continuum Opacity and Stellar Atmospheres To make progress in modeling and understanding stellar atmospheres beyond the gray atmosphere, it is necessary to consider the real interactions between

More information

ASTRONOMY AND ASTROPHYSICS Theoretical X-ray spectra of hot H-rich white dwarfs. Impact of new partition functions of iron, Fe V through Fe VII

ASTRONOMY AND ASTROPHYSICS Theoretical X-ray spectra of hot H-rich white dwarfs. Impact of new partition functions of iron, Fe V through Fe VII Astron. Astrophys. 343, 531 535 (1999) ASTRONOMY AND ASTROPHYSICS Theoretical X-ray spectra of hot H-rich white dwarfs. Impact of new partition functions of iron, Fe V through Fe VII J. Madej 1, J. Halenka

More information

Theory of optically thin emission line spectroscopy

Theory of optically thin emission line spectroscopy Theory of optically thin emission line spectroscopy 1 Important definitions In general the spectrum of a source consists of a continuum and several line components. Processes which give raise to the continuous

More information

3/26/2018. Atoms Light and Spectra. Topics For Today s Class. Reminder. Topics For Today s Class. The Atom. Phys1403 Stars and Galaxies

3/26/2018. Atoms Light and Spectra. Topics For Today s Class. Reminder. Topics For Today s Class. The Atom. Phys1403 Stars and Galaxies Foundations of Astronomy 13e Seeds Foundations of Astronomy 13e Seeds Phys1403 Stars and Galaxies Instructor: Dr. Goderya Chapter 7 Atoms Light and Spectra Reminder Homework for Chapter 5, 6 and 7 is posted

More information

Chapter 6. Atoms and Starlight

Chapter 6. Atoms and Starlight Chapter 6 Atoms and Starlight What is light? Light is an electromagnetic wave. Wavelength and Frequency wavelength frequency = speed of light = constant Particles of Light Particles of light are called

More information

Lec 3. Radiative Processes and HII Regions

Lec 3. Radiative Processes and HII Regions Lec 3. Radiative Processes and HII Regions 1. Photoionization 2. Recombination 3. Photoionization-Recombination Equilibrium 4. Heating & Cooling of HII Regions 5. Strömgren Theory (for Hydrogen) 6. The

More information

2. Basic assumptions for stellar atmospheres

2. Basic assumptions for stellar atmospheres . Basic assumptions for stellar atmospheres 1. geometry, stationarity. conservation of momentum, mass 3. conservation of energy 4. Local Thermodynamic Equilibrium 1 1. Geometry Stars as gaseous spheres

More information

Photoionized Gas Ionization Equilibrium

Photoionized Gas Ionization Equilibrium Photoionized Gas Ionization Equilibrium Ionization Recombination H nebulae - case A and B Strömgren spheres H + He nebulae Heavy elements, dielectronic recombination Ionization structure 1 Ionization Equilibrium

More information

V. Stars.

V. Stars. V. Stars http://sgoodwin.staff.shef.ac.uk/phy111.html 0. The local HR diagram We saw that locally we can make an HR diagram of absolute luminosity against temperature. We find a main sequence, giants and

More information

Spectroscopy Lecture 2

Spectroscopy Lecture 2 Spectroscopy Lecture 2 I. Atomic excitation and ionization II. Radiation Terms III. Absorption and emission coefficients IV. Einstein coefficients V. Black Body radiation I. Atomic excitation and ionization

More information

Stellar Spectra ASTR 2110 Sarazin. Solar Spectrum

Stellar Spectra ASTR 2110 Sarazin. Solar Spectrum Stellar Spectra ASTR 2110 Sarazin Solar Spectrum Test #1 Monday, October 9, 11-11:50 am Ruffner G006 (classroom) You may not consult the text, your notes, or any other materials or any person Bring pencils,

More information

Electromagnetic Spectra. AST443, Lecture 13 Stanimir Metchev

Electromagnetic Spectra. AST443, Lecture 13 Stanimir Metchev Electromagnetic Spectra AST443, Lecture 13 Stanimir Metchev Administrative Homework 2: problem 5.4 extension: until Mon, Nov 2 Reading: Bradt, chapter 11 Howell, chapter 6 Tenagra data: see bottom of Assignments

More information

Chapter 4. Spectroscopy. Dr. Tariq Al-Abdullah

Chapter 4. Spectroscopy. Dr. Tariq Al-Abdullah Chapter 4 Spectroscopy Dr. Tariq Al-Abdullah Learning Goals: 4.1 Spectral Lines 4.2 Atoms and Radiation 4.3 Formation of the Spectral Lines 4.4 Molecules 4.5 Spectral Line Analysis 2 DR. T. AL-ABDULLAH

More information

Astronomy 421. Lecture 14: Stellar Atmospheres III

Astronomy 421. Lecture 14: Stellar Atmospheres III Astronomy 421 Lecture 14: Stellar Atmospheres III 1 Lecture 14 - Key concepts: Spectral line widths and shapes Curve of growth 2 There exists a stronger jump, the Lyman limit, occurring at the wavelength

More information

Example: model a star using a two layer model: Radiation starts from the inner layer as blackbody radiation at temperature T in. T out.

Example: model a star using a two layer model: Radiation starts from the inner layer as blackbody radiation at temperature T in. T out. Next, consider an optically thick source: Already shown that in the interior, radiation will be described by the Planck function. Radiation escaping from the source will be modified because the temperature

More information

CDO AP Chemistry Unit 5

CDO AP Chemistry Unit 5 1. a. Calculate the wavelength of electromagnetic radiation that has a frequency of 5.56 MHz. b. Calculate the frequency of electromagnetic radiation that has a wavelength equal to 667 nm. 2. Electromagnetic

More information

Characteristic temperatures

Characteristic temperatures Characteristic temperatures Effective temperature Most sources are only roughly blackbodies (if that). So we integrate the flux over frequency and define: F = I cosθ dω d = σ T e 4 i.e. a source of effective

More information

ASTR-1020: Astronomy II Course Lecture Notes Section III

ASTR-1020: Astronomy II Course Lecture Notes Section III ASTR-1020: Astronomy II Course Lecture Notes Section III Dr. Donald G. Luttermoser East Tennessee State University Edition 4.0 Abstract These class notes are designed for use of the instructor and students

More information

Pictures of Atoms. 48 iron atoms on copper Made with a scanning tunnelling microscope

Pictures of Atoms. 48 iron atoms on copper Made with a scanning tunnelling microscope A-toms = Not Cutable Democritus 420BC popularized the theory matter was made of Atoms: Too small to be seen Indivisible Surrounded by a void Solid No internal structure Pictures of Atoms 48 iron atoms

More information

ASTR 5110 Atomic & Molecular Physics Fall Stat Mech Midterm.

ASTR 5110 Atomic & Molecular Physics Fall Stat Mech Midterm. ASTR 5110 Atomic & Molecular Physics Fall 2013. Stat Mech Midterm. This is an open book, take home, 24 hour exam. When you have finished, put your answers in the envelope provided, mark the envelope with

More information

EVOLUTION OF STARS HERTZSPRUNG-RUSSELL DIAGRAM

EVOLUTION OF STARS HERTZSPRUNG-RUSSELL DIAGRAM VISUAL PHYSICS ONLINE EVOLUTION OF STARS HERTZSPRUNG-RUSSELL DIAGRAM The total power radiated by a star is called its intrinsic luminosity L (luminosity). The apparent brightness (apparent luminosity)

More information

Lecture 3: Emission and absorption

Lecture 3: Emission and absorption Lecture 3: Emission and absorption Senior Astrophysics 2017-03-10 Senior Astrophysics Lecture 3: Emission and absorption 2017-03-10 1 / 35 Outline 1 Optical depth 2 Sources of radiation 3 Blackbody radiation

More information

Atomic Structure and Periodicity

Atomic Structure and Periodicity Atomic Structure and Periodicity Atoms and isotopes: Isotopes-#p + same for all but mass number is different b/c of # n o Average atomic mass is weighted average of all the isotopes for an element Average

More information

The Sun as a Typical Star. Stellar Spectra. Stellar Spectroscopy

The Sun as a Typical Star. Stellar Spectra. Stellar Spectroscopy Stellar Spectroscopy Resolved observa7ons of the sun allow us to look at varia7ons across the surface, but we can only look at (almost all) other stars in integrated light. In the visible, we see the photosphere

More information

Interstellar Medium Physics

Interstellar Medium Physics Physics of gas in galaxies. Two main parts: atomic processes & hydrodynamic processes. Atomic processes deal mainly with radiation Hydrodynamics is large scale dynamics of gas. Start small Radiative transfer

More information

Notes on Photoionized Regions Wednesday, January 12, 2011

Notes on Photoionized Regions Wednesday, January 12, 2011 Notes on Photoionized Regions Wednesday, January 12, 2011 CONTENTS: 1. Introduction 2. Hydrogen Nebulae A. Ionization equations B. Recombination coefficients and cross sections C. Structure of the hydrogen

More information

13.3 Spectra of Stars

13.3 Spectra of Stars 13.3 Spectra of Stars A star's spectrum depicts the energy it emits at each wavelength and is perhaps the single most important thing we can know about the star. From the spectrum we can find the star's

More information

II Light.

II Light. II Light http://sgoodwin.staff.shef.ac.uk/phy111.html 0. Light Light is the main tool we have in astronomy. We detect light from distant objects and can determine the temperature, density, composition,

More information

Problem Set 4 is due Thursday. Problem Set 5 will be out today or tomorrow. Launch Latest from MASCOT

Problem Set 4 is due Thursday. Problem Set 5 will be out today or tomorrow. Launch Latest from MASCOT 1 Problem Set 4 is due Thursday. Problem Set 5 will be out today or tomorrow. Launch Latest from MASCOT 3 Continuous Spectra: Thermal Radiation The equations below quantitatively summarize the light-emitting

More information

Properties of Stars (continued) Some Properties of Stars. What is brightness?

Properties of Stars (continued) Some Properties of Stars. What is brightness? Properties of Stars (continued) Some Properties of Stars Luminosity Temperature of the star s surface Mass Physical size 2 Chemical makeup 3 What is brightness? Apparent brightness is the energy flux (watts/m

More information

Emitted Spectrum Summary of emission processes Emissivities for emission lines: - Collisionally excited lines - Recombination cascades Emissivities

Emitted Spectrum Summary of emission processes Emissivities for emission lines: - Collisionally excited lines - Recombination cascades Emissivities Emitted Spectrum Summary of emission processes Emissivities for emission lines: - Collisionally excited lines - Recombination cascades Emissivities for continuum processes - recombination - brehmsstrahlung

More information

Section 11.5 and Problem Radiative Transfer. from. Astronomy Methods A Physical Approach to Astronomical Observations Pages , 377

Section 11.5 and Problem Radiative Transfer. from. Astronomy Methods A Physical Approach to Astronomical Observations Pages , 377 Section 11.5 and Problem 11.51 Radiative Transfer from Astronomy Methods A Physical Approach to Astronomical Observations Pages 365-375, 377 Cambridge University Press 24 by Hale Bradt Hale Bradt 24 11.5

More information

5. Atomic radiation processes

5. Atomic radiation processes 5. Atomic radiation processes Einstein coefficients for absorption and emission oscillator strength line profiles: damping profile, collisional broadening, Doppler broadening continuous absorption and

More information

Binary Stars (continued) ASTR 2120 Sarazin. γ Caeli - Binary Star System

Binary Stars (continued) ASTR 2120 Sarazin. γ Caeli - Binary Star System Binary Stars (continued) ASTR 2120 Sarazin γ Caeli - Binary Star System Visual Binaries: Types of Binary Stars Spectroscopic Binaries: Eclipsing Binaries: Periodic changes in brightness, stars block one

More information

Chapter 15 Surveying the Stars

Chapter 15 Surveying the Stars Chapter 15 Surveying the Stars 15.1 Properties of Stars Our goals for learning How do we measure stellar luminosities? How do we measure stellar temperatures? How do we measure stellar masses? How do we

More information

Gas 1: Molecular clouds

Gas 1: Molecular clouds Gas 1: Molecular clouds > 4000 known with masses ~ 10 3 to 10 5 M T ~ 10 to 25 K (cold!); number density n > 10 9 gas particles m 3 Emission bands in IR, mm, radio regions from molecules comprising H,

More information

Stars, Galaxies & the Universe Announcements. Stars, Galaxies & the Universe Observing Highlights. Stars, Galaxies & the Universe Lecture Outline

Stars, Galaxies & the Universe Announcements. Stars, Galaxies & the Universe Observing Highlights. Stars, Galaxies & the Universe Lecture Outline Stars, Galaxies & the Universe Announcements Lab Observing Trip Next week: Tues (9/28) & Thurs (9/30) let me know ASAP if you have an official conflict (class, work) - website: http://astro.physics.uiowa.edu/~clang/sgu_fall10/observing_trip.html

More information

AGN Physics of the Ionized Gas Physical conditions in the NLR Physical conditions in the BLR LINERs Emission-Line Diagnostics High-Energy Effects

AGN Physics of the Ionized Gas Physical conditions in the NLR Physical conditions in the BLR LINERs Emission-Line Diagnostics High-Energy Effects AGN Physics of the Ionized Gas Physical conditions in the NLR Physical conditions in the BLR LINERs Emission-Line Diagnostics High-Energy Effects 1 Evidence for Photoionization - continuum and Hβ luminosity

More information

Limb Darkening. Limb Darkening. Limb Darkening. Limb Darkening. Empirical Limb Darkening. Betelgeuse. At centre see hotter gas than at edges

Limb Darkening. Limb Darkening. Limb Darkening. Limb Darkening. Empirical Limb Darkening. Betelgeuse. At centre see hotter gas than at edges Limb Darkening Sun Betelgeuse Limb Darkening Stars are both redder and dimmer at the edges Sun Limb Darkening Betelgeuse Limb Darkening Can also be understood in terms of temperature within the solar photosphere.

More information

Photoionization Modelling of H II Region for Oxygen Ions

Photoionization Modelling of H II Region for Oxygen Ions Journal of Materials Science and Chemical Engineering, 2015, 3, 7-16 Published Online April 2015 in SciRes. http://www.scirp.org/journal/msce http://dx.doi.org/10.4236/msce.2015.34002 Photoionization Modelling

More information

Stars: Intro & Classification

Stars: Intro & Classification Stars: Intro & Classification Astronomy 1 Elementary Astronomy LA Mission College Spring F2015 Quotes & Cartoon of the Day The wonder is, not that the field of stars of so vast, but that man has measured

More information