Transcript Lecture3

II-3. Stellar Spectra and Temperature (Main Ref.: Lecture
notes; FK Ch. 5, Sec. 17-4, 17-5)
Lec 3
II-3a. Electromagnetic (em) Radiation - Review (Main Ref.: Lecture notes;
FK Ch. 5)
II-3a (i)
range.
(See FK 5-2)
Fig. II-8:
Range
II-3a (ii) Blackbody Radiation (See FK 5-3)
Fig.II-9: Continuum
Blackbody radiation
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II-3a (iii) Spectrum (See FK 5-2,
5-5, 5-6, 5-7, 5-8)
Fig. II- 10a: Rainbow
Angstroms Å
Å = 1010 m = 0.1 nm.
1 nm = 109 m
Fig.II-10b: Spectrum-continuum and
absorption lines
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Fig. II-11: Mechanism of Line Absorption and Emission –I (see FK Sec. 5-7, 5-8)
Bohr Atom

Fig. II-11a
e-

e-
nucleus
FK Figure 5-24
Fig. II-11b
H
 = photon
e- = electron
E = energy spacing
E
between electron
levels
(See class notes for
detailed explanation.)
Fig. II-11c: Energy Diagram
FK Figure 25
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Nature of Light: (see FK 5-2, 5-5)
Light : both wave (e.m. wave) and particle (photon) with
 = c / ,
Eqn(10a)
where  = frequency and  = wavelength of the em wave, c is velocity of light, and h is Planck’s
constant., with h = 6.625 x 10-34 Js, c = 3.0 x 108 m/s,  in cycles/sec = Hertz (Hz)
.
Planck’s Law:
E = h  = h c / ,
Eqn(10b)
where E is photon energy, h is Planck’s constant.
Line Spectra - Summary: (see FK 5-6 to 5-8)
Absorption line, produced when photon is absorbed by electron in a cool gas in a lower
energy level and it goes to a higher level., i.e., when an electron is excited, with
E = E = h  = h c / ,
Eqn(10c)
where E = energy interval between two bound states of electron.
Emission line, emitted when electron in a hot gas in a higher level loses energy and4
goes to a low`er level, with Eqn(10c).
Ionization: when a bound electron absorbs photon energy and escapes from the
atom  Atom is ionized and becomes an ion! It happens when
E = h  = h c /  > ,
Eqn(10d)
Excitation: when a bound electron absorbs photon energy and jumps from a
lower to higher (both bound) energy level, with Eqn(10c).
Ionization energy: . {e.g., H atom  = 13.6 ev}.
Excitation energy: E. {e.g., H atom E [n=1 (ground state) to
n = 2(1st excited state)] = 10.2 ev}.
Units (mks):
Energy = E = Joule (J)
Flux = F = L / area = energy / area-sec = W/s = J/m2s
ev = electron volt for energy E: 1ev = 1.602 x 10-19 J
Note: keV used for X-rays (1 keV = 103 ev)
MeV used for -rays (1 MeV = 10 6 ev)
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Spectral Analysis (See FK 5-6)
Fig. II-12a: Mechanism of Line Absorption and Emission - II ( see FK Fig. 5 -17)
Fig. II-12b: Dark hydrogen absorption lines
continuous visual spectrum Balmer series
– in
Fig. II-12c: Spectrograph
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Fig. II-13: Emission Lines of elements
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Fig. II-14:Absorption Spectrum of the Sun
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Each chemical element produces its own unique
set of spectral lines
Fig. II-15: The Sun’s continuum and absorption line spectrum
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• II-3b. Color and Temperature (Main Ref.: Lecture notes;
FK Sec.17-4)
• Color: A star’s color depends on its surface temperature
See class notes for explanation.
FK
Fig. II-16: Color (= FK Fig. 17-7)
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Photometry and Color Ratios
Color Ratio:
Measure brightness b, take brightness ratio
bB / bU; bV / bB  gives color
•Photometry measures the
apparent brightness of a
star
•The color ratios of a star
are the ratios of brightness
values obtained through
different standard filters,
such as the U, B, and V filters
•These ratios are a measure
of the star’s surface
temperature and color
Fig. II-17 UV Photometry
Fig. II-18:temperature vs color ratio
Fig. II-17:U, B,and V Filters
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U for UV (ultraviolet); B for Blue, V for Visual (near
yellow).
Study Fig. II-18
and Table II-2 (=
FK Table 17-1)
for temperature
and color ratio
of different stars.
Fig. II-18: Temperature, Color, and Color
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Ratio (= FK Fig. 17-9)
Table II-2: Color and temperature of selected stars
Color Index: CI = B – V (not in FK, see class notes!)
(Note: B = mB; V = mv)
CI = B – V = mB – mV = 2.5 log ( bV / bB )
mU – mB = 2.5 log ( bB / bU )
See class notes for derivation.
Eqn(11a)
Eqn(11b)
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EX 15a:
Red, cool star  bV / bB > 1;
CI = B – V > 0
Note: Lower T, cooler star, e.g., red star 
positive CI, and color ratio large > 1
Example: Betelgeuse: Red ;T = 3500 K; bV / bB = 5.55 - large!; CI = 1.86 > 0
EX 15b:
Blue, hot star  bV / bB < 1; CI = B – V < 0
Note: Higher T, hotter star, e.g., blue star 
negative CI, and color ratio small and < 1.
Example: Bellatrix: Blue; T = 21500 K; bV / bB = 0.81< 1; CI = – 0.23 < 1
EX 15c:
Yellow-white, medium temperature star 
bV / bB > but close to 1; CI = B – V close to 0.
Note: Medium T star, e.g., yellow star 
small CI, and color ratio close to 1.
Example: Sun: Yellow-white star; T = 5800 K; bV / bB = 1.87 > 1
but close to 1, CI =0.68, positive but small.
See class notes for the details.
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How to find `Peak Wavelength’ m?  By
Wien’s Law: (see FK 5-4)
m = 0.0029 / T (K),
(in meter)
Eqn(12)
m = `peak ’ where maximum
intensity I comes – shorter
T
for higher temperature T
(see Fig. II-19, 20 and
I
Fig. II-9, Lec 3, p.1)
I = intensity (= brightness)
m

Fig. II-19: Spectrum
METHOD: Measure b in B and V, find color ratio (or color index CI)
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 gives color; e.g., Table II-2 gives Temperature!
Wien’s law and the Stefan-Boltzmann law are useful
tools for analyzing glowing objects like stars
Fig. II-20: Blackbody Spectrum
•A blackbody is a
hypothetical object that is a
perfect absorber of
electromagnetic radiation at
all wavelengths
•Stars closely approximate
the behavior of blackbodies,
as do other hot, dense
objects
•The intensities of radiation
emitted at various
wavelengths by a blackbody
at a given temperature are
shown by a blackbody curve
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Fig. II-21: Sun’s Spectrum
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EX 16:
Star A: Wavelength peaks at 700 nm.
What is the temperature?
Ans: T = 4143 K (see class notes.)
EX 17:
Betelgeuse, Red star from EX 15a.
What is the peak wavelengh?
Ans: m = 828 nm (see class notes.)
************************************************************************
Note: 1 nm = 10–9 m.
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• II-3c. Stellar Spectra (Main Ref.: Lecture notes; FK Ch.
5, Sec.17-5)
• Spectral Class: O
B
Blue
A
F
G
K
M
Red
• Further classification: 0 to 9 subclasses in each class.
e.g., F0, F1, F2, ………….F9, etc.
e.g., Sun is G2 star.
• IDEA: Classify stars by spectrum
/color/temperature.
As the class proceeds from O… through… A, F, G,…to
K, M, temperature goes from high to low, color changes
from blue to red, and prominent spectral lines change.
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Prominent spectral lines of different classes (types):
Fig. II-22: Line strength vs temperature/spectral class (=FK Fig. 17-12)
See class notes for detailed explanation.
***********************************************************
The spectral class and type of a star are directly related to its surface
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temperature: O stars are the hottest and M stars are the coolest
WHY? Needs Atomic Physics, See Fig. II-11, p.3 and Fig. II-12, p.6 of
Lec. 3, and class notes for detailed explanation.
Note: In order to produce line by excitation,
E = E (= h = h c /  ) ~ k T
Eqn(13)
where E (= h = h c / ) = photon energy
Summary:
•
He lines strongest at high T, very hot star, because electrons in He most tightly bound
and hence binding energy is large, meaning E is very large (see Eqn(13)).
•
H lines strongest in the next hot stars because electrons in H is tightly bound next to
He.
•
H lines weak in hottest stars because T is so high in the hottest stars that
kT ~ h  > , which means electrons gain enough energy from photon to escape the
atom – ionization, i.e., E (= h) > , so no lines!
•
Metal lines (e.g., Fe, Ca) appear in moderate T stars because E of metals is smaller 21
(electrons more loosely bound).
• Lines of ions (= ionized element – meaning some electrons
missing) (e.g., He II, Ca II, Fe II) found in hotter stars than lines
from atoms (= neutral = not ionized) of the same element (e.g.,
He I, Ca I, Fe I) because electrons in ions of the same element
more tightly bound, since they have less electrons, and hence
have larger E.
• Molecular lines (e.g. TiO) strongest in cool stars because E is
smallest for their (molecular rotation and vibration) energy
levels.
• Note: He I means all of 2 electrons are bound, meaning He atom; He II
means singly ionized He, meaning one of 2 electrons is missing; similarly for
Ca I (i.e., Ca atom), Ca II (= Ca ion with 1 electron missing), etc.
• Study class notes for further details.
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• See FK for spectral classes of brown dwarfs, L and T – not covered in class.
Table II-3: Properties of spectral class
•Unlike true stars, brown dwarfs are too small to sustain
thermonuclear fusion
•Most brown dwarfs are in even cooler spectral classes called L
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and T
Fig. II-23
•The number of protons in an atom’s nucleus is the atomic number for
that particular element
•The same element may have different numbers of neutrons in its
nucleus. These slightly different kinds of elements are called isotopes
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class
G2of different classes of main sequence stars
Spectra
He lines
H
Fig. II-24: The spectra of real stars
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