Download 3.2 Spectra and Spectral Classification

3.2 Spectra and Spectral Classification
3.2.1 Temperature
Temperature is usually measured by comparing the radiation of a star with that of a blackbody.
Effective temperature Teff : T. of a blackbody with the same total flux density as the star
σ Teff4 = Φ
(Stefan-Boltzmann law)
where Φ = Φ(R) is the total (bolometric) flux density at the surface of the star.
At a distance r from the star, we measure the flux density Φ(r).
Φ(R)
r 2
As Φ~ r -2 , we have
=( )
Φ(r)
R
i.e.
Φ(R) = Φ(r)/δ2 where δ = R/r is the angular radius of the star
In order to estimate Teff , we have to measure
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the total flux density (at all wavelengths; difficult particularly in the UV)
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the angular radius of the stars (difficult; see later)
This is possible only for a small number of stars.
3.2 Spectra and Spectral Classification
With Teff , the luminosity can be expressed as
L = 4π R 2 Φ(R) = 4π R 2 σTeff4
Or for the absolute magnitude
M ~ log R + 4 log T eff
This relation provides an
interesting interpretation of
the colour-magnitude diagram
from Sect. 3.1.4:
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A constant B-V corresponds to
a constant T
Different M at the same B-V
must therefore reflect different
radii R (brighter stars must be
larger than fainter stars of the
same T)
Giants
MV
●
Supergiants
Mai
nS
equ
enc
e
White Dwarfs
B-V
3.2 Spectra and Spectral Classification
Other temperature definitions
Colour temperature T c :
T. of a blackbody that has the same colour index as the star.
As the colour index m1 - m 2 = -2.5 log[Φ(λ1)/Φ(λ 2)], the ratio of the flux densities at two
wavelengths have to be the same.
Φ(λ 1 )
Bλ1(Tc)
=
Φ(λ 2 )
Bλ2(Tc)
and therewith m 1 - m
2
= -2.5 log
Bλ1(Tc )
Bλ2(Tc )
hc
λ 5
= -2.5 log (λ1 ) +2.5
2
kTc
( 1λ1 - 1λ2 ) log e
for the Wien approximation for the optical part of the spectrum (provided that T is not too high).
m 1- m 2 = a + b
i.e. a simple relation between T and colour index
Tc
Wien temperature: T. from Wien's displacement law
Brightness temperature: T. of a blackbody with the same flux density at some wavelength
Kinetic temperature: related to the average speed of the gas particles
Ionization temperature: T. necessary for ionizing the gas
Remark: Since the stars are not exactly blackbodies, the values for the different temperatures are
not exactly the same.
3.2 Spectra and Spectral Classification
3.2.2 Spectroscopy of stars
(a) Low-resolution spectroscopy
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Simplest version: objective prism spectroscopy (slitless)
Advantages:
- easy to realize
- large number of spectra simultaneously
Disadvantages: - low spectral resolution
- spectra overlap
- strong influence of sky background
Detector
Main mirror
Objective prism spectrum exposure of the Hyades star cluster. The telescope was slightly moved
perpendicular to the dispersion direction in order to increaase the width of the spectrum.
3.2 Spectra and Spectral Classification
3.2.2 Spectroscopy of stars
(b) High-resolution spectroscopy
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Light from
telescope
Collimating
mirror
Entrance
slit
Slit spectrograph with diffraction grating
Spectral resolution A =λ/dλ depends on
- resolution of the grating (number of grooves)
- resolution of detector (pixel size)
- width of the entrance slit
… must be optimized
Diffraction
grating
Camera
mirror
Computer
High-resolution solar spectrum. The combination of high resolution and
wide wavelength coverage results in a linear spectrum that would be much
too wide to be registered on a single detector. Therefore the spectrum is
„folded“ so that different wavelength intervals are one upon the other.
Detector
(CCD)
3.2 Spectra and Spectral Classification
3.2.2 Spectroscopy of stars
(c) Emission- and absorption spectra
Hot, dense source
(solid body, opt. dense gas)
continuum spectrum
(without lines)
Hot, optically thin gas
Continuum source plus
hot, optically thin gas
emission line spectrum
(no continuum)
absorption line spectrum
(with continuum)
3.2 Spectra and Spectral Classification
3.2.2 Spectroscopy of stars
(d) Components of stellar spectra
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Section of a CCD exposure of a spectrum
Continuum
Absorption lines from various chemical elements
(Emission lines in rare cases only)
Wavelength calibrated tracing of the spectrum
Equivalent width Wλ : measure of the strength
of a spectral line relative to the continuum
Φ
Wλ Φc = ∫ Φ(λ) dλ
[Å]
line
continuum
Φc
Def.: Equivalent width of an absorption line
= width of a rectangular and absolutely dark spectral
region with the hight of the local continuum and
the total flux equal to the total flux of the line
λ
0
Wλ
(Note that stellar absorption lines are usually not
completely dark, even in the line cores.)
3.2 Spectra and Spectral Classification
3.2.3 Spectral classification of stars
(e) Spectral sequence – early versions
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Photographic objective prism spectra
available at the end of 19th century
Different types of spectra with different
complexity
First classifications according the strengths
of the lines that occur in nearly all spectra
Later found that these are the lines of the
hydrogen atom (H)
3.2 Spectra and Spectral Classification
3.2.3 Spectral classification of stars
Partucularly simple spectrum for Vega
regular series of absorption lines
= Balmer series of the H atom
(Hα, Hβ, Hγ, ...)
Transition between two energy states of the H atom,
n1 and n 2 , corresponds to a photon wavelength λ with
1 = R (1 - 1 )
λ
n 12 n 22
R: Rydberg constant
(Balmer-Rydberg formula)
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Early classification set spectra of this type
= type A
Continued with B,C,D,E,... according to
decreasing strength of the Balmer lines
3.2 Spectra and Spectral Classification
(f) Spectral classification – Harvard Sequenz
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Edward C. Pickering
(1846-1919)
Annie J. Cannon
(1863-1941)
By World War I, photographic objective
prism spectra of more than 250 000 stars for
the Henry-Draper (HD) Catalogue
A. J. Cannon and her team provided classifications for 225 300 spectra in only 4 years
New classification scheme based on all prominent lines instead of Balmer lines only
→ ABC types re-ordered
Cannon realized that T is the principal
distinguishing feature
New system: O – B – A – F – G – K – M – L
(„Oh Be A Fine Girl Kiss Me“)
With fine structure of 10 subclasses:
A0,...,A9,B0,....,B9,...
Temperature sequence
Remark: type L was added only recently
Harvard Observatory College (1913): A. J. Cannon and her team of Ladies at
Harvard working for years on the classification of steller spectra. In 1897 Cannon
was hired by Pickering to classify the spectra of stars of the southern hemisphere.
Cannon and her team classified stars at an average rate of 5,000 spectra per
month, up to three per minute.
3.2 Spectra and Spectral Classification
(f) Spectral classification – Harvard Sequenz: example spectra
M4
F6
M7
M3
F9
O5
O7
G1
M0
G6
M4e
B3
B6
G9
M6
M2
A2
K4
A6
A8
K5
M5
K7
A9
4000
6000
Wavelength (Å)
8000
Hot stars (>10000K)
● continuum rising into
the blue and UV
● steady increase of H
Balmer lines
4000
6000
Wavelength (Å)
8000
F6-K5 (7000-4000K)
● Center of continuum
shifts to longer λ
● Balmer lines weaker
● Metallic lines
4000
6000
Wavelength (Å)
8000
Cool stars (<4000K)
● Center of continuum
shifts to longer λ
● Metallic lines
● Molecular bands
Credit: University of Oregon (Department of Physics), Silva & Cornell (1992), Astrophysical Journal
4000
6000
Wavelength (Å)
8000
Very cool stars
● Center of continuum
shifts to near IR
● Vera strong
molecular bands
3.2 Spectra and Spectral Classification
(f) Spectral classification – Harvard Sequenz: compact version
400 nm
He II (strong)
Hydrogen
650 nm
O
30 000 K
Helium
He I, H
20 000 K
B
Helium
H (very strong), CaII (weak)
Calcium
10 000 K
A
Calcium
H (strong), CaII, Fe (weak)
Iron
F
7 000 K
Iron
Oxygen
Magnesium
CaII, neutral metals (strong),
H (moderately), neutral metals
G
CaII, neutral metals (maximum)
K
4 000 K
Strong molecular bands (TiO)
M
3 000 K
6 000 K
Oxygen
Many molecules
Credit: 2005 Pearson Prentice Hall, Inc.
3.2 Spectra
Excurs:
and Ionized
SpectralHelium
Classification
Exercise:
The ionizing energy of the Helium atom is 24 eV. Therefore, the
photoionization of He requires a radiation field where the typical
photon energy is E = 24 eV. The temperature should be estimated.
E = hν = hc/λ = 24 eV
λ = 64 nm
Wien's law:
T W = 0.0029 K m / 64 nm = 45 000 K
Note on the terminology:
He I = neutral helium
He II = singly ionized helium
3.2 Spectra and Spectral Classification
(f) Spectral classification – Harvard Sequenz: summary
Main properties
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The spectral sequence is a
sequence of decreasing
effective tempereture
The strength of the
characteristic spectral lines
varies systematically along
sequence
Relative width of
absorption lines
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50
effective temperature [1000 K]
25
10
8
6
5
spectral type
Note on the terminology:
He I = neutral helium
He II = singly ionized helium
3.2 Spectra and Spectral Classification
(d) Luminosity classes (MK system)
Are there any differences between the spectra of main sequence stars and those of giants?
(see Sect. 3.2.1)
Observation:
compared to giants, dwarf stars have
1. broader Balmer lines
2. stronger lines of neutral metals
(i.e. weaker lines of ionized metals)
Theoretical explanation:
● Line strength depends not only on T, but
also on the pressure P
● Giants (extended atmospheres) have lower
P at the same T as dwarfs
Consequence of the higher pressure in the atmospheres of dwarfs:
1. Electric field of ions in the neighbourhood of an H atoms shift the energy levels (Stark effect)
→ line broadening
2. Higher density → higher probability for recombinations → lines of neutral metals stronger
3.2 Spectra and Spectral Classification
(d) Luminosity classes (MK system)
Ia
Iab, Ib
II
III
IV
V
VI
D (*)
Bright supergiants
Supergiants
Bright giants
Giants
Subgiants
Main sequense stars (dwarfs)
Subdwarfs
White dwarfs
(*) DA, DB, DC
Complete spectral classification: luminosity class plus spectral type
(two-dimensonal spectral classification)
e.g. G2V for the Sun, A0V for Vega, ...
3.2 Spectra and Spectral Classification
3.2.4 Hertzsprung-Russell
Diagram (HRD)
Diagram showing the relationship between
(a) absolute magnitude or luminosity
and
(b) spectral type or effective temperature
(sometimes also color index)
That means there exist different forms of
this diagram, usually
● log L versus spectral type
● log L versus log T
● M versus B-V
Right: HRD for 23 000 stars for which
accurate distances (relative error <10%)
are known (mostly from the HIPPARCOS
satellite).
3.2 Spectra and Spectral Classification
3.2.4 Hertzsprung-Russell
Diagram (HRD)
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The HRD displays the relationship
between fundamantal properties of the
stars (→ key diagram for stellar structure
and evolution)
Stars tend to fall only in certain regions of
the HRD:
- main sequence (most prominent)
- giants and supergiants
- white dwarfs
Right: Schematic HRD showing the
densely populated areas as well as many of
the well known stars. Diagonal lines
correspond to the L-R-T based on the
Stefan-Boltzmann law (Sect. 3.2.1)
3.2 Spectra and Spectral Classification
HRD of the nearby stars
HRD for the brightest stars
HRD of the stars within about 5 pc of the
Sun. The diagonal lines correspond to
constant stellar radius.
100 brightest stars in the sky. This HRD is
biased in favor of the most luminous stars
—which appear toward the upper left.
3.2 Spectra and Spectral Classification
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Usually ~10 2 stars
Loosely bound
Concentrated toward
Galactic plane
Globular star cluster
Apparent magnitude V
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Apparent magnitude V
Open star cluster
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B-V
HRD
● „Long“ MS (towards blue stars)
● MS turnoff point at small B-V
● In general, only very few giants
B-V
Usually ~105 stars
Compact clusters
Not concentrated
to Galactic plane
HRD
● „Short“ MS (no blue MS stars)
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MS turnoff point redder (larger B-V)
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Many giants, complex structure:
SGB: sub-giant branch
RGB: red giant branch
AGB: asymptotic giant branch
HB: horizontal branch
BS: blue stragglers
P-AGB: post asymptotic giant branch