Download Astronomy 252: Short Project 2 Stellar Spectra: Their Classification

Name:
Spring 2010
Astronomy 252: Short Project 2
Stellar Spectra: Their Classification and Interpretation
Due:
Friday, Jan 29, 2010 at 3pm
Introduction:
Classification lies at the foundation of nearly every science. We are all aware that biologists classify plants
and animals into subgroups called genus and species. Geologists also have an elaborate system of
classification for rocks and minerals. Scientists develop classification systems to understand patterns in and
relationships among objects in nature. Astronomers also engage in classification. Astronomers classify
planets into Terrestrial and Jovian; galaxies into spirals, ellipticals and irregulars; and stars according to the
appearance of their spectra. In this lab exercise, we will study the method that astronomers use to classify
stars; it is called the MK Spectral Classification system. MK stands for the initials of the founders of this
system, W.W. Morgan and P.C. Keenan. The exercise has three parts: (1) becoming familiar with the spectral
display program, (2) classifying a sample of stellar spectra, and (3) interpreting spectroscopic and photometric
measurements of a few stars and finding the sizes and luminosities of these stars.
Goals: 1. To learn the basic techniques and criteria used in stellar spectral classification.
2. To determine fundamental stellar properties using spectral information.
Background:
From the lectures you already know that stars come in a wide range of sizes and temperatures. The hottest
stars in the sky have temperatures in excess of 40,000 K, whereas the coolest stars that we can detect optically
have temperatures on the order of 2000 - 3000 K. As you might guess, the appearance of the spectrum of a
star is very strongly dependent on its temperature. For instance the very hottest stars (called the O-type stars)
show absorption lines due to ionized helium (He II), and doubly and even triply ionized carbon, oxygen and
silicon. On the other hand, the coolest stars (the M-type stars) show lines due to molecules in their spectra.
Morgan and Keenan (and their predecessors) based their spectral classification system on this dramatic
change in the appearance of the spectrum with temperature. They set up a spectral sequence starting with the
hottest stars, (type O), and running through intermediate classes (B, A, F, G, K) to the very coolest stars (type
M). Each class can be divided into subtypes (for instance, A0, A1, A2, …, A9). To make certain that every
astronomer around the world would be able to classify stars using their system, they set up a sequence of
standard stars that can be observed. For instance, Vega is the standard for A0, and the sun is the standard star
for type G2. Hence, to classify the spectrum of a star, an astronomer must first obtain spectra of all of the
standard types with his/her telescope. The unknown spectrum can then be classified by the simple process of
visually comparing the appearance of the spectrum with the standard spectra. Because standards have not
been defined for all of the subtypes, interpolation is sometimes necessary. For instance, if you find that a
spectrum lies in appearance about midway between the A0 and A5 standards, you would classify it as either
A2 or A3.
The MK classification system actually has two dimensions. We have already discussed the temperature
dimension, using spectral classes O through M. The other dimension is luminosity; the luminosity classes are
represented by Roman numerals and are as follows: dwarf (V), subgiant (IV), giant (III), bright giant (II),
supergiant (Ib), bright supergiant (Ia). Hence the full spectral type of a star requires both a temperature type
and a luminosity type. For example, the sun is classified as G2 V. Vega is A0 V, Rigel is B8 Ia, Betelgeuse
M2 Ia.
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In this exercise we will only be classifying in the temperature dimension and all of the stars we will be
considering will be dwarfs, but keep in mind that a full classification requires a luminosity class as well. It
turns out that luminosity classification is much more difficult than temperature classification.
1. Classification criteria:
We will first become acquainted with the change in the appearance of the spectra of stars over the range from
hot to cool. Log into the computer, using userid = .astro101.misc.stu.vu and the assigned password. Look
under Start: Physics Programs: Astrolab, then double click on “Spectra Classification” and you are ready to
begin.
Look first at the sequence of standard spectra on the right-hand side of the screen. Notice that these spectra
(shown in black and white although this part of the spectrum is actually blue-violet in color) are absorptionline spectra. That is, the bright continuum is crossed by a number of dark "absorption lines." These dark
lines are due to absorption of the light by atoms and ions in various excited states in the atmosphere of the
star. On the left-hand side of the screen you can see three enlarged spectra. The top and bottom spectra are
the first two spectra in the standard star sequence displayed on the right-hand side of the screen. You can
scroll through the entire standard spectral sequence by pressing on the  and ↓ arrow keys. ↑ takes you to
higher temperatures and ↓ to lower temperatures. Don't press the arrow keys too rapidly; it can take a few
seconds for the spectra to scroll. Above the top spectrum on the left-hand side, you will see a scale that
identifies some of the more prominent and useful absorption lines in the spectrum. This scale will change as
you scroll towards lower temperatures. As you learned in class, there are certain spectral features used to
classify the different spectral types of stars.
Now use this scale and the sequence of spectra on the right side of the screen to now answer questions 1-5
below.
Spectral Classification Questions
Q1. The hydrogen lines of the Balmer sequence are marked on the top scale with an "H". At what spectral
type do these hydrogen lines reach maximum strength?
Q2. The Helium I (neutral helium) lines are marked on the top scale with "HeI". At what spectral type do
these neutral helium lines reach maximum strength?
Q3. (a) At what spectral type does the G-band (due to the molecule CH) first make its appearance?
(b) What happens to the G-band as you go toward cooler temperatures?
Q4. (a) The Ca II "K-line", marked on the upper scale as "Ca k" appears first at what spectral type?
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As you can see, it grows rapidly in strength towards cooler temperatures, and soon becomes equal in
strength to the adjacent line that is a blend of a hydrogen line and another line due to ionized calcium
called the Ca II "H-line.”
(b) At what spectral type does the K-line become equal in strength to the H-line?
Q5. Notice the wavelength scale at the bottom of the screen. Estimate by eye the wavelengths of the three
visible hydrogen lines (these are, in order of increasing wavelength, Hε, Hδ and Hγ) and the G-band.
2. Classifying the spectrum:
Now that you have become acquainted with the spectral sequence, we can begin to classify our "program"
stars. The beautiful thing about spectral classification is that one does not really need to know anything about
stellar astrophysics to classify a spectrum. Think of spectral classification as simply an exercise in pattern
matching. What you want to do is to "bracket" the unknown spectrum between two spectra in the standard
spectral sequence. For instance, if you find that your unknown falls between the A0 and A5 standards, but is
closer to A5, you will probably classify it as A4. It may happen that the program spectrum looks identical to
one of the standards, in which case it will have the same spectral type as the standard. When you are
comparing the unknown spectrum with the standards, look at the whole spectrum. The lines identified on the
top scale, however, are the ones that are most sensitive to temperature. Once you have classified the first
program spectrum, use the "+" key to go on to the next. Use the ↑ and ↓ keys to change the standard stars on
either side of the program spectrum. The "-" key can be used to backup through the program spectra. In
Table 1, record the spectral type of the program spectrum and some notes to explain why you arrived at that
particular spectral type. Warning! A few of the program spectra are "peculiar stars" in that they do not fit
very well into the spectral sequence. Try to describe these peculiar spectra in terms of the standard spectra as
best as you can.
Key:
↑
+
Esc
change to hotter standard spectra
change to next program spectrum
to exit
↓
—
change to cooler standard spectra
change to previous program spectrum
Most of the spectra used in this exercise were obtained by Dr. Chris Corbally, S.J. of the Vatican Observatory
on the 90" Steward Observatory telescope on Kitt Peak, near Tucson, Arizona. A few of the spectra are
"synthetic spectra," calculated with a complex computer program written by Dr. Richard Gray (Appalachian
State University) as part of his research.
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TABLE 1: CLASSIFICATION OF THE PROGRAM STARS
Name
Spectral Type
48 Cet
A1
Comments
K-line slightly stronger than A0
ω1 Sco
15 Mon
HD 23585
HR 2328
S10
S24
S27
S14
HR 8086 *
Ceres
HR 1279
22 Sco
ρ Aur
α Dra
HD 27808
HD 9878
α PsA *
HD 46149
HR 6806
BD 364864
HR 5544
HD 23156
78 Uma *
T25
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3. Determining stellar properties:
Several stars in our sample have had their parallaxes measured. Table 2 contains three of these nearby stars.
For all three (3) stars in Table 2, determine the properties discussed below, and list them in the appropriate
columns in Table 2. Show your work, at least one example for each calculation step.
a. Determine their distances (in pc).
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d = p"
1
b. Given their apparent visual magnitudes V, calculate their absolute visual magnitudes MV.
V - MV = 5 log (d) - 5.0
or: MV = V - 5 log (d) + 5.0
2
3
c. Using the bolometric corrections for these objects as listed in Table A (values in parentheses were obtained
through interpolation), calculate their absolute bolometric magnitudes Mbol.
Mbol = MV + BC
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d. Given that for the sun Mbol(Sun)=+4.72, calculate the luminosity of each star in terms of the solar
luminosity.
" L %
Mbol (*) ! Mbol (Sun) = !2.5log $ * '
# LSun &
! L $
log # * & = '0.4[M bol(*) ' Mbol (Sun)]
" LSun %
5
6
L*
= 10 !0.4 [M bol (*) ! Mbol (Sun)]
LSun
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e. Determine the surface temperature of each star based upon its spectral type. Use Table A
to find the relationship between spectral type and temperature.
f. Assuming the above temperature to equal the effective temperature and the star to radiate like a black body,
calculate its radius in terms of the solar radius. (For the sun, T=5800 K)
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L* = 4!R* "T*
2
4
L* !# R* $& !# T* $&
=
LSun " RSun % " TSun %
8
4
! L $! T $
R*
= # * & # Sun &
RSun
" LSun % " T* %
5
9
4
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g. We just calculated the radius of these three stars. (a) Do these numbers seem reasonable compared to the
Sun? (b) What relationship do you find between the physical properties of these three stars – T, L, R?
Table 2: Observed and Calculated Properties of Three Stars
Star
V (Mag)
p (")
HR 8086
6.03
0.285
α PsA
1.16
0.130
78 UMa
4.93
0.040
Star
BC (Mag)
Spectral Type
Mbol (Mag)
L (LSun)
HR 8086
α PsA
78 UMa
Show your work below for at least one case.
Honor code:
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d (pc)
T (K)
Mv (Mag)
R (RSun)
Table A. Temperature and Bolometric Correction
for Stars of Different Spectral Types
Teff (K)
BC
Teff (K)
BC
B5
16,000
-1.39
F8
(6,280)
(-0.05)
B6
(14,880)
(-1.19)
F9
(6,140)
(-0.06)
B7
(13,760)
(-0.99)
G0
6,000
-0.06
B8
(12,640)
(-0.80)
G1
(5,900)
(-0.07)
B9
(11,520)
(-0.60)
G2
(5,800)
(-0.08)
A0
10,400
-0.40
G3
(5,700)
(-0.08)
A1
(9,960)
(-0.35)
G4
(5,600)
(-0.09)
A2
(9,520)
(-0.30)
G5
5,500
-0.10
A3
(9,080)
(-0.25)
G6
(5,420)
(-0.12)
A4
(8,640)
(-0.20)
G7
(5,340)
(-0.14)
A5
8,200
-0.15
G8
(5,260)
(-0.15)
A6
(8,000)
(-0.14)
G9
(5,180)
(-0.17)
A7
(7,800)
(-0.12)
K0
5,100
-0.19
A8
(7,600)
(-0.11)
K1
(4,940)
(-0.29)
A9
(7,400)
(-0.09)
K2
(4,780)
(-0.40)
F0
7,200
-0.08
K3
(4,620)
(-0.50)
F1
(7,100)
(-0.07)
K4
(4,460)
(-0.61)
F2
(7,000)
(-0.06)
K5
4,300
-0.71
F3
(6,900)
(-0.06)
K6
(4,080)
(-0.81)
F4
(6,800)
(-0.05)
K7
(3,860)
(-0.91)
F5
6,700
-0.04
K8
(3,640)
(-1.00)
F6
(6,560)
(-0.04)
K9
(3,420)
(-1.10)
F7
(6,420)
(-0.05)
M0
3,200
-1.20
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