# The Basic of Star’s Spectroscopy

Posted on: January 10, 2009

Spectroscopy is a branch study in astronomy that focus on astronomical objects’ spectrum. From the spectrum, we can get informations, such as its temperatures, chemical compositions, movement speed, etc. That’s why spectroscopy can be considered as one of the fundamental field in astronomy. The spectrum of a star (or any other astronomical object) is acquired by using an instrument called spectrograph.

One of the fundamental law in spectroscopy is Kirchoff Law (1859) which stated that:

1. If a liquid or high pressure gas is ignited, they will emit energy in all wavelength which will produce a continuous spectrum.
2. If a low temperature gas is ignited, it will only emit energy in certain range wavelength and produce spectrum which have a dark background and some bright lines. That kind of spectrum is called the emission spectrum. The wavelength of each bright lines are the precise indicator of what gas that produce them. So, the same gas will produce bright lines in certain exact wavelength.
3. If a white light (which is a equal mixture of all colors) is passed through a cool low temperature gas, the gas will absorb energy at certain wavelength. The result spectrum will be continuous spectrum as the background with some dark lines in certain exact wavelength. The dark lines called absorption lines and that kind of spectrum is called the absorption spectrum. The wavelength of each dark lines are the precise indicator of what gas that produce them. So, the same gas will produce dark lines in certain exact wavelength.

Balmer Series
Switzerland scientist, Balmer, state a series equation to predict the wavelength of the absorption lines of hydrogen gas. The equation is widely known as Balmer series equation. with : λ: the wavelength of the absorption lines [cm]
RH : Rydberg constant (= 109678 ) Fig. 5 : Emission spectrum of hydrogen that exhibit the first four emission lines in Balmer’s series

Planck’s Quantum Law

Planck postulates that light is radiated in the form of small discrete package called quantum. This theory is the foundation of the birth of a new field in physics called quantum physics.

Planck state that energy of each photon

Eo = h. f = hc//λ

h : Planck’s constant (h = 6,63 x 10^-34 J.s)
f : frequency of the photon [Hz]
c = speed of light (= 3.10^5 km/s)
λ = photon’s wavelength

Star’s spectrum
Star’s spectrum pattern is wide in variety. In 1863, an astronomer called Angelo Secchi classified star’s spectrum in 4 groups based on the similarities of its’ absorption lines.

Miss A. Maury from Harvard Observatory establish another way to classify star’s spectrum and it was revised by Miss Annie J. Cannon. Miss Cannon’s classification is the most widely adopted today. Table 1 : Resume of the classification of star’s spectrum (to remember it use the donkey bridge : Oh Be A Fine Girl (or Guy), Kiss Me). (you can click the figure to get bigger and clearer version of the table above; .

Sub-classification of star’s spectrum
Star’s spectrum classification O, B, A, F, G, K, M is divided again to several sub-classes :
B0, B1, B2, B3, . . . . . . . . ., B9
A0, A1, A2, A3, . . . . . . . . ., A9
F0, F1, F2, F3, . . . . . . . . . ., F9

Bigger number represent lower temperature! The use of this sub-class is to narrow the specification’s range and become more precise.
(for further information, check this site.)

M-K Classification (Star’s Luminosity Class)

Stars with same certain spectrum’s class is found to have different luminosities. In 1913, Adam dan Kohlscutter from Mount Wilson Observatory showed that the width of spectrum’s lines can be used to estimate star’s luminosity.
Based on these facts. in 1943 Morgan and Keenan from Yerkes Observatory divided stars to several luminosity class as shown in the table below.

 Class1a Very bright super giant star Class 1b Less bright super giant star Class II Bright giant star Class III Giant star Class IV Sub-giant star Class V Main sequence star
Table 2. Morgan Keenan’s Luminosity Class

Morgan Keenan’s Luminosity Class (M-K class) is sketched in a Hertzprung-Russell diagram (H-R diagram) below.

Now, star’s classifications use the combination of spectrum class and luminosity class. For example : A G2 V star is a main sequence star that belongs to spectrum class G2

Star’s motion
Contrary to widely beliefs that star isn’t moving in space, star DO move in space. However, the movement of stars is hard to track. Beause of its immense distance, the movement of star only produce extremely small apparent movement in sky. We have to wait several years (or decades!) to track star’s movement in sky. Warning : the star’s movement that is discussed above is not the apparent daily motion of the star !

The star’s angular motion of a star is called proper motion (μ). Proper motion is usually measured in arc-second per year. Star with biggest proper motion is Barnard Star with μ = 10”,25 per year (In 180 years, this star will (only) move in extent as full Moon’s disk).

Relationship between tangential velocity (Vt) and the proper motion (μ):

Vt = 4,74 μ d

with :

Vt = tangential speed of the star [km/s]

μ = proper motion of the star [“/ year]

d = star’s distance [parsec]

the above equation also can be stated as :

Vt = 4,74 μ/p

with p is the parallax of the star (in arc second).

The proper motion is measured by two quantities: the position angle and the proper motion itself. The first quantity indicates the direction of the proper motion on the celestial sphere (with 0 degrees meaning the motion due north, 90 degrees due east, and so on), and the second quantity gives the motion’s magnitude, in seconds of arc per year.

The equations used to find the quantity of star’s proper motion are :

μα cos δ = μ sin θ
μδ = μ cos θ

with :
μα = proper motion in right ascension
μδ = proper motion in declination
μα and μδ is measurable –> μ and θ can be determined.

Beside proper motion, information about star’s motion can be obtained from its radial motion, which is the component of star’s motion that lies parallel to our line of sight.
Radial velocity (Vr) can be measured by its spectrum lines that shift (Doppler shift). For star which radial velocity (Vr) is significant compared to the speed of light: For Vr being much smaller compared to the speed of light (c), the equation can be simplified to:

Δλ/λo = Vr/c

with :
Δλ = the difference between static wavelength (λo) and observed wavelength (λ). [Å or nm]
λo = static wavelength. [Å or nm]
Vr = radial velocity [km/s]
c = speed of light (300.000 km/s )

Now, we are able to calculate Vt and Vr as discussed above and we will be able to calculate star’s true motion (linear motion):

V2 = (Vt)2 + (Vr)2

Reference:

1. “Astrofisika I” lecture notes, by Dr. Djoni N. Dawanas
2. Wikipedia

For other pages that discuss this material, you are advised to visit these sites:
1. Spectroscopy
2. Astronomynotes.com

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