All About Astronomy

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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.

Fig 1. Spectrum

Fig 2. 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.
Fig. 3 & 4. Continuous, emission and absorption spectrum (respectively)

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.)

Fig 6. Star’s spectrum from different classes

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.

Fig 7. Star with different luminosity class in a H-R diagram

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).

Fig 8. Star’s motion

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.

Fig 9. Star’s proper motion

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 )

Fig 10. Red shift and blue shift

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
  3. Google images

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

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Photometry is a branch field of astrophysics which learned the quantity, quality, and the direction of the electromagnetic radiation from the sky’s objects. “Photo” in photometry which means “visual light” was used because the observation was used to limited in visual light.

Photometry was based on our knowledge about radiation law. We hypothesize that the astronomical objects have characteristics of a hypothetical black body.

The characteristics of the black body are:

  1. when thermal equilibrium is achieved, the object’s temperature is a function of how many energy it absorbs per second
  2. a black body doesn’t emit radiation in all wavelength in same intensity (some emits more radiation in blue region wavelength, and the way around. The wavelength which it emits most will determine its color).

The wavelength its emits most (λmaks) by a black body which temperature is T Kelvin is :

λmaks = 0,2898/ T …………………….. (eq. 1)

(λmaks expressed in cm and T in Kelvin)

The equation 1 is called Wien’s rule.

An example of implementing the Wien’s rule :

wien
(Warning : be clear that λmaks doesn’t mean the maximum wavelength but it means the wavelength that a body emits in the biggest intensity)

The total energy per time emitted by a black body per its surface area is called emitted energy flux. The value of the emitted energy flux from a black body with a surface temperatur T Kelvin is :

F = σT4 …………………….. (eq. 2)

(σ : Stefan-Boltzman constant: 5,67 x 10^-8 Watt/m2K4)

The total energy per unit time (= Power) that’s emitted by a black body with the surface temperature T Kelvin and surface area A is known as Luminosity. Its value (L) can be calculated by equation below:

L = A σT4 …………………….. (eq. 3)

For stars, we can assume it’s a perfect sphere. So, its surface area (A) is 4πR2 ; with R express star’s radius. So, a star’s luminosity (L) is equal to :

L = 4πR2 σT4 …………………….. (eq. 4)

he black body emits its radiation to all direction. We can assume the radiation pass through a sphere surface with a radius d in same energy flux (E).

E = L/(4πd2) …………………….. (eq. 5)

This amount of flux is received by an observer from a distance d from the black body. So, this flux is usually called received energy flux or brightness. (Warning : differ between E and F).

The equation above is often termed as the inverse square law for brightness (E) because this equation shows that brightness is inversely proportional to the square of its distance (d). So, the farther the distance, the less bright it is.

Review Questions:

  1. From an observation result, we know that an area of 1 cm2 in Earth’s outer atmosphere received Sun’s energy with intensity of 1,37 x 106 erg/cm2/s. If we know that the distance between Sun and Earth is 150 million kilometres, determine the Sun’s luminosity.
  2. Calculate the intensity of Sun’s radiation received by Saturn’s surface if we know that the distance between Saturn and Sun is 9,5 Astronomical Units (use the information from number 1)?
  3. The luminosity of a star is 100 times larger than Sun is, but the temperature of the star is only half of Sun’s temperature. Calculate the radius of the star expressed in Sun’s radius unit?
  4. Define the term Luminosity and Brightness using your own words
  5. Calculate the wavelength of maximum intensity radiation of a star which temperature is 10.000 Kelvin.
(source : Dr. Djoni N. Dawanas)
(translated from : belajar Astronomy).

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