Download Astronomical Spectra

Astronomical Spectroscopy and
Lab
2012년 2학기
3345.504
교수 : 이 상각 [email protected]
19동 317 호
880-6627
조교 : 박근홍 [email protected]
Course Overview
• Lectures on
• Astronomical Spectrographs
• Atomic and Molecular Spectra.
• Line formation & broadening in stellar
atmosphere
• Astronomical Spectra
• Stellar Element Abundances
Course Overview
• Practical Excersise : BOES spectra
reduction and analysis
• 1. Reduction of raw high resolution
spectral data (BOES data).
• 2. Determination of stellar atmospheric
parameters ( Teff, log g, and [Fe/H])
• 3. Detailed analysis of elemental
abundances
Course Overview
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Student Presentation topics on Astronomical spectra:
- White dwarf spectra and Atmospheres
- M, L, T, Y brown dwarfs
- Metal Poor Stars
- Pulsating stars and Astroseismology
- Wolf-Rayet stars
- AGB stars and Post-AGB stars
- Chemically Peculiar Stars
- Pre-main Sequence Stars : T Tauri stars and
Herbig Ae/Be Stars
• - Be stars
• - Blue & Red luminous Supergiants
References
• The Observation and analysis of stellar
photospheres : D. F. Gray
• Interpreting Astronomical Spectra : D. Emerson
• Stellar Spectral Classification : R. G. Gray and C. J.
Corbally
• Optical Astronomical Spectroscopy : C. R. Kitchin
• Astronomical Spectroscopy : J. Tennyson
Other Useful References
• Astrophysical Quantities
• Holweger & Mueller 1974, Solar Physics, 39, 19 – Standard Model
• MARCS model grid (Bell et al., A&AS, 1976, 23, 37)
• Kurucz (1979) models – ApJ Suppl., 40, 1
• Solar composition – "THE SOLAR CHEMICAL COMPOSITION " by
Asplund, Grevesse & Sauval in "Cosmic abundances as records of
stellar evolution and nucleosynthesis", eds. F. N. Bash & T. G. Barnes,
ASP conf. series, in press: see also Grevesse & Sauval 1998, Space
Science Reviews, 85, 161 or Anders & Grevesse 1989, Geochem. &
Cosmochim. Acta, 53, 197
• Solar gf values – Thevenin 1989 (A&AS, 77, 137) and 1990 (A&AS, 82,
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Bagnulo, S., Jehin, E., Ledoux, C., Cabanac, R., Melo, C., Gilmozzi, R.,
and the ESO Paranal Science Operations Team, 2003, Messenger, 114,
10
http://www.sc.eso.org/santiago/uvespop
Kurucz, R. L. 1994, "Solar Abundance Model Atmospheres for 1, 2, 4, 8
km/s", Kurucz CD-ROM No. 13, Cambridge, Mass.
http://kurucz.harvard.edu/grids.html
Kurucz, R. L., and Bell, B., 1995, Kurucz CD-ROM No. 23, Cambridge
Mass.
http://kurucz.harvard.edu/linelists.html
Smith, P. L., Heise, C., Esmond, J. R., and Kurucz, R. L. 1996, "On-Line
Atomic and Molecular Data for Astronomy", in UV and X-ray
Spectroscopy of Astrophysical and Laboratory Plasmas, K. Yamashita
and T. Watanabe, eds., Universal Academy Press, Tokyo, 513
http://www.pmp.uni-hannover.de/cgi-bin/ssi/test/kurucz/sekur.html
Kupka, F., Piskunov, N. E., Ryabchikova, T. A., Stemples, H. C., Weiss,
W. W. 1999, A&AS 139, 119
http://www.astro.uu.se/~vald/php/vald.php
http://vald.astro.univie.ac.at/~vald/php/vald.php
http://vald.inasan.ru/~vald/php/vald.php
• http://spectra.freeshell.org/spectroweb.html
The Interactive Database of Spectral Standard Star Atlases
Astronomical Spectra
Coronal density : 108 m-3 (102cm-3), 107k
Stellar Atmosphere :
(Log g for the Earth is 3.0 (103 cm/s2)
Log g for the Sun is 4.4 (2.7 x 104 cm/s2)
Log g for a white dwarf is 8
Log g for a supergiant is ~0)
Gaseous nebulae(photoionized): 109 m-3, 104 K
Molecular cloud : few tens K
Atomic and Molecular Spectra
• Atomic spectra :
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Hydrogen and Hydrogen like atoms
Metalic atoms
Schrodinger Equation
Pauli Exclusion Principle
LS Coupling & jj Coupling
• Molecular spectra :
• Diatomic molecular spectra
Line broadening
• There are two basic line broadening
mechanisms; instrumental and intrinsic :
• Instrumental Broadening
– The first is due to finite spectroscopic
resolution and can be controlled by the
researcher. Often higher resolution can be
achieved by larger gratings or coarse
gratings operated in higher order or longer
path lengths for fourier transform
spectrometers.
Line formation and broadening
in stellar atmosphere
• Intrinsic Broadening
– The second is fundamental line broadening
which can be caused by at least three
factors:
• Doppler Broadening
– Related to special relativity: Motion components of a
particle along the line of sight causes a shift in
radiation frequency. Since particles generally have a
distribution of velocities, this creates a gaussian
blurring in the spectral lines.
Line formation and broadening
in stellar atmosphere
• Lifetime Broadening = Natural Broadening
– Quantum mechanical in origin : Allowed transitions
have a short lifetime and this translates to some
uncertainty in the frequency of atomic oscillators
creating a Lorentzian line profile.
Line broadening in stellar
atmosphere
• Density Broadening = Pressure Broadening
– Combination of quantum mechanical and
electromagnetic effects: Ions are bombarded by
transient electric and magnetic fields of high speed
electrons zipping nearby, these electric fields split and
shift the energy levels. This constant perturbation
within the plasma environment depends most strongly
on density and causes strong line broadening in higher
density plasmas. Temperature, ionization level and the
particular quantum transition involved also plays a role.
Line broadening
• In most thin plasmas one sees a combination of
Doppler and Lorenztian broadening called Voigt
profiles. The Lorentzian component affects mostly
the low intensity 'wings' of the emission lines so line
profiles can be approximated as gaussians,
especially considering the dynamic range limitations
of computer screens. Most of the time spectra taken
by researchers do not fully resolve the intrinsic line
profile so the lines are broadened mainly by
instrumental imperfection
Stellar Element Abundances
• Model Atmosphere
 Stellar parameters = Teff, log g,
[Fe/H], vt (micro-turbulent velocity)
• Curve of growth
•  weak lines : EW ~ abundance
Astronomical Spectrographs
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Basic Spectrograph Optics
Objective Prism Spectrographs
Slit Spectrographs
Echelle Spectrographs
BOES (Bohyun Mountain Observatory
Echelle spectrographs)
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09/04 :
09/06 :
09/11 :
09/13 :
09/18 :
09/20 :
09/25 ;
09/27 :
10/02 :
10/04 :
10/09 :
10/11 :
10/16 :
introduction of course
Astronomical Spectra
Atomic Spectra 1
Atomic Spectra 2
Molecular Spectra 1
Molecular Spectra 2
Line Formation and Broadening 1
Line Formation and Broadening 2
Line Formation and Broadening 3
Line Formation and Broadening 4
Abundance Determination
Astronomical spectrograph 1
Astronomical Spectrograph 2
• 10/18 : Midterm Examination
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10/23 :
10/25 :
10/30 :
11/01 :
11/06 :
11/08 :
11/13 :
11/15 :
11/20 :
11/22 :
11/27 :
11/29 :
12/04 :
12/06 :
Astronomical spectrograph 3 (CCD)
BOES data Reduction 1.
BOES Data Reduction 2
BOES data Analysis : TAME
BOES data Analysis : Stellar Parameters
BOES data Analysis : Abundance Determination
Presentation of the Student’s Abundance Determination 1
Presentation of the Student’s Abundance Determination 2
Presentation of the Student’s Abundance Determination 3
Student Presentation on Astronomical Spectra 1
Student Presentation on Astronomical Spectra 2
Student Presentation on Astronomical Spectra 3
IGRINS : High Resolution NIR spectrograph
What Sciences can be done with IGRINS?
• 12/11: Final Examination
Grading
• Grading :
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Midterm & Final Exams : 50 %
BOES spectra reduction and analysis : 25%
Topic Presentation : 15%
Class Participation & Attendance : 10%
History of Stellar Atmospheres
• Cecelia Payne Gaposchkin wrote the first PhD thesis
in astronomy at Harvard
• She performed the first analysis of the composition
of the Sun (she was mostly right, except for
hydrogen).
• What method did she use?
• Note limited availability of atomic data in the 1920’s
Blackbody Equation
Planck radiation law (Planck Function)
2hν3
1
Bν(T) = ---------- --------------c2
e(hν/kT) - 1
brightness Bν(T) has units of erg s
-1
cm-2 Hz
Rayleigh-Jeans tail
-1
ster
hν << kTBν(T) ~ (2ν2/c2) kT
decreasing freq … shallow second power drop
Wien cliff
hν >> kTBν(T) ~ (2hν3/c2)e-(hν/kT)
increasing freq … steep exponential drop
-1
Blackbody Spectrum
(2ν2/c2) kT
(2hν3/c2)e-(hν/kT)
Temperature Scales
°F
°C
°K
Blackbody Spectrum and Temp
position of blackbody depends on temperature
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…so, objects of different temperatures look different
1. Wein’s Law
location of blackbody curve peak determined by temperature
… take derivative of blackbody equation
… use blackbody curve as a THERMOMETER
… Wobble Law … peak moves left/right
λ
= 2900 / T
max (in microns)
(in Kelvin)
Sun has T = 5800 K …
λ
max
= 2900 / 5800 K = 0.5 microns (or 5000 Å)
λ
max
= 2900 / 310 K = 9.4 microns
YOU have T = 310 K …
2. Stefan-Boltzmann Law
height of blackbody curve determined by temperature AND SIZE
… integrate blackbody equation over all angles and frequencies
… hotter object … more photons
… bigger object … more photons
… Size Law … peak moves up/down to more/less energy
luminous energy = surface area X energy/area
E
total
= L = 4πR2 σT4
L ~ R2 T4
( in erg s
Sun has T = 5800 K now, but when it turns into a red giant …
T drops to ~ 2900 K
… L drops by factor of 16
R increases to 100 X radius today
… L rises by factor of 10000
together
… L increases by factor of 600 … we’re COOKED!
-1)
Spectral Features: Light and
Matter
atoms are made up of particles
protons, neutrons, electrons
H is simplest
He is next
C is # 6
neutral)
… 1 proton, 1 electron (if neutral)
… 2 protons, 2 neutrons, 2 electrons (if neutral)
… 6 protons, 6 neutrons, 6 electrons (if
# protons DEFINES the element
Bohr Atom is a model that explains interaction of light and atoms
invokes particle nature of photons
 discrete amounts of energy are needed for
absorption/emission
 e¯ orbitals at specific energy levels
Bohr Atom
energy
levels
electron options
once excited by photon, electron has options …
1. re-emits
2. cascades
3. ionized
Atoms are easy, Molecules …
molecules are made up of more than one atom
each atom provides options
absorption + rotation + vibration
He (easy) ………….. C (not bad)
CO (ugh!) 
H atom vs. H2 molecule
Link to Spectroscopy
each atom/isotope/molecule has a fingerprint
a combination of atomic fingerprints is emitted by each object
a galaxy, a star, a planet, or YOU emit a complicated spectrum
Spectrum of the Sun
Emission and Absorption
Creation of Spectra
Four Types of Spectra
1. CONTINUOUS spectrum = BLACKBODY spectrum
atoms are wiggling … photons emitted … light bulb, Sun (sort of)
2. ABSORPTION spectrum
atoms catching photons … see dark lines … He in Sun, Earth CO2
3. EMISSION spectrum
atoms pitching photons … see bright lines … aurorae, meteors
4. REFLECTION spectrum
combination of catching/pitching … bright + dark features …
Jupiter’s atmosphere absorbs some sunlight, reflects some
Solar absorption lines :
Ca II H & K
Earth
Radiation
J H K
M
L
trace gas
trace gas
trace gas
trace gas
What Is a Stellar Atmosphere?
• Basic Definition: The transition between the inside and the
outside of a star
• Characterized by two parameters
– Effective temperature – NOT a real temperature, but rather the
“temperature” needed in 4pR2sT4 to match the observed flux at a
given radius
– Surface gravity – log g (note that g is not a dimensionless number!)
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Log
Log
Log
Log
g
g
g
g
for
for
for
for
the Earth is 3.0 (103 cm/s2)
the Sun is 4.4 (2.7 x 104 cm/s2)
a white dwarf is 8
a supergiant is ~0
• Mostly CGS units…
복사전달
• 방출, 흡수 가스를 통과하는 복사에너지의 흐름
•  가스 구름이나 별에서 나오는 스펙트럼 예측
 관측과 비교하여 가스 구름이나 별의 화학조
성비, 온도, 밀도 추정
• 별의 경우 : 온도와 밀도는 깊이에 따른 함수 :
각 층에 총 복사 에너지 보존유지.
•  각 층마다의 총 프럭스 보존 (각 파장에 프럭
스는 변화하더라도), 즉 에너지 보존에 따른 프
럭스 일정(flux constancy)
• 항성대기모형 : 깊이에 따는 온도와 밀도 변화
• 성간분자운 : 일정 온도 가정도 가능.
Steady State
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Steady State :
general (exception : shock, solar flare)
statistical equilibrium
 excitation, ionization, dissociation
 each energy state of atoms and
molecules :
•  a large matrix and a set of
differential equations.
열역학적 평형 (Thermodynamic
Equilibrium : TE)
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복사장 : 프랑크 함수
속도 분포 : 막스웰 함수
에너지 준위에 따른 입자 비 : 볼즈만 함수
이온 상태에 따른 입자 비 : 사하 방정식
• 국부 열역학적 평형 (LTE) :
Basic Assumptions in Stellar Atmospheres
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Local Thermodynamic Equilibrium
– Ionization and excitation correctly described
by the Saha and Boltzman equations, and
photon distribution is black body
Hydrostatic Equilibrium
– No dynamically significant mass loss
– The photosphere is not undergoing large
scale accelerations comparable to surface
gravity
– No pulsations or large scale flows
Plane Parallel Atmosphere
– Only one spatial coordinate (depth)
– Departure from plane parallel much larger
than photon mean free path
– Fine structure is negligible (but see the Sun!)
Basic Physics – Ideal Gas Law
PV=nRT or P=NkT where N=r/m
Densities, pressures in
stellar atmospheres are
low, so the ideal gas law
generally applies.
P= pressure (dynes cm-2)
V = volume (cm3)
N = number of particles per unit volume
r = density (gm cm-3)
n = number of moles of gas (Avogadro’s # = 6.02x1023)
R = Rydberg constant (8.314 x 107 erg/mole/K)
T = temperature in Kelvin
k = Boltzman’s constant
1.38 x 10–16 erg K-1 (8.6x10-5 eV K-1)
m = mean molecular weight in AMU (1 AMU = 1.66 x 10-24 gm)
Don’t forget the electron pressure: Pe = NekT
Thermal Velocity
Distributions
• RMS velocity = (3kT/m)1/2
• Most probable velocity = (2kT/m)1/2
• Average velocity = (8kT/pm)1/2
• What are the RMS velocities of 7Li, 16O, 56Fe, and
137Ba in the solar photosphere (assume T=5000K).
• How would you expect the width of the Li resonance
line to compare to a Ba line?
Excitation – the Boltzman Equation
N n g n  Dc / kT

e
Nm gm
g is the statistical weight and Dc is the difference in
excitation potential. For calculating the population of a
level the equation is written as:
Nn
gn
qc n

10
N u (T )
u(T) is the partition function (see def in text). Partition
functions can be found in an appendix in the text.
Note here also the definition of q = 5040/T = (log e)/kT
with k in units of electron volts per degree (k= 8.6x10-5 eV K-1)
since c is normally given in electron volts.
Ionization – The Saha
Equation
The Saha equation describes the ionization of atoms (see the text for
the full equation).
(2pme ) 2 / 3 (kT )5 / 2 2u1 (T )  I / kT
N1
Pe 
e
3
N0
h
u0 (T )
Pe is the electron pressure and I is the ionization potential in ev.
Again, u0 and u1 are the partition functions for the ground and first
excited states. Note that the amount of ionization depends inversely
on the electron pressure – the more loose electrons there are, the less
ionization. For hand calculation purposes, a shortened form of the
equation can be written as follows
N1
 5040
u1
log
Pe 
I  2.5 log T  log  0.1762
N0
T
u0
Home work 1
• During the course of its evolution, the Sun will
pass from the main sequence to become a red
giant, and then a white dwarf.
• Estimate the radius of the Sun (in units of the
current solar radius) in both phases, assuming
log g = 1.0 when the Sun is a red giant, and log
g=8 when the Sun is a white dwarf.
• What assumptions are useful to simplify the
problem?
Home Work -2
• Using the ideal gas law, estimate the number density
of atoms in the Sun’s photosphere and in the Earth’s
atmosphere at sea level.
• For the Sun, assume P=105 dyne cm-2.
• For the Earth, assume P=106 dyne cm-2.
• How do the densities compare?
Home work -3
• At (approximately) what Teff is Fe 50%
ionized in a main sequence star? In a
supergiant?
• What is the dominant ionization state of
Li in a K giant at 4000K? In the Sun? In
an A star at 8000K?