Calculate the following quantities for Sterope, which has a spectral classificat

Question

Calculate the following quantities for Sterope, which has a spectral classification of B8 (and is one of the stars in Pleiades). Temperature T = Luminosity L = Mass M = Radius R = Volume V = Density = Calculate the following quantities for Sterope, which has a spectral classification of B8 (and is one of the stars in Pleiades). Temperature T = Luminosity L = Mass M = Radius R = Volume V = Density = Calculate the following quantities for Sterope, which has a spectral classification of B8 (and is one of the stars in Pleiades). Temperature T = Luminosity L = Mass M = Radius R = Volume V = Density =

Explanation / Answer

There are six physical quantities, which are used to define a star:

1) Temperature T

2) Luminosity L

3) Mass M

4) Radius R

5) Volume V

6) Density

1) Surface (Photospheric) Temperature and The photospheric temperature (T) is measured in terms of K. This can be calculated by direct observation from Earth. The photosphere of a star emits a continuous spectrum observable from the Earth. By dispersing the spectrum and graphing its Planck curve, the temperature can be determined by using Wien's Law,
which states that TWien = 2.898 x 10 –3 Km/ max where the maximum wavelength is
measured in meters.

Another method used to determine the temperature of a star is by interpreting its spectral signature. Astronomers have correlated the spectral lines seen with the degree of ionization present in the star’s photosphere. Since temperature determines the degree of ionization, once the spectral class of a star is identified, it is possible to use a table like the one below, to determine a star’s temperature. Remember the spectral sequence is O, B, A, F, G, K, M, with the O stars being the hottest. Each letter category is in turn divided into 10 sub-categories, ranging from zero to nine. A star with the classification B9 is therefore slightly cooler than B8, but hotter than A0.

2) The luminosity is the energy emitted by the star's photosphere each second and over all wavelengths of the electromagnetic spectrum. If the distance to the star is known, the luminosity can be calculated. Here are the steps by which that calculation is done:
The parallax angle of the star is measured.
The distance (d) is calculated.
The apparent visual magnitude (m) is measured.
The distance (d) is used to find the distance modulus, M - m, where M is the absolute visual magnitude.
The apparent visual magnitude (m) and distance modulus (M - m) are used to calculate the absolute visual magnitude (M), since M - m = 5 – 5logd.

The luminosity (L) is calculated from the absolute visual magnitude (M), using the equation, L = 85.51 x 10-0.4M where L is measured in solar units. This means if the value of L works out to be 5, the star is 5 times more luminous than the Sun. Unfortunately stars that are further than 150-200 pc are too far away for their parallax to be measured.

The luminosity for these stars has to be estimated using other
techniques. The luminosity of a hydrogen-burning, Main Sequence star can be estimated using the H-R Diagram (i.e., luminosity-temperature plot) which does not require knowing the distance. As a matter of fact once the luminosity is estimated from the H-R Diagram, the distance can then be estimated using the six steps from above (in reverse order). Estimating the distance of a star in this manner is called spectroscopic parallax.

3)The mass of a star is a measure of how many and what types of atoms it contains. Astronomers first measured the mass of stars in binary systems (i.e., systems that contain two stars gravitationally bound to each other). Approximately 50% of the stars are members of binary systems.

For nearby systems with a measured parallax and known distance, Newton's Law of Gravity and Kepler's Third Law of Planetary Motion can be used to calculate the total mass of the stars in these systems. Further observations of the two stars as they orbit about each other can be used to calculate each of the two masses. Of course not all stars are in binary systems, and not all binary systems have a measurable parallax. When astronomers compared the masses and luminosities of hydrogen-burning, Main Sequence stars, they discovered that the luminosity could be used to accurately estimate the mass. Today astronomers call this the MassLuminosity Relationship, again only valid for Main Sequence stars.

4) Radius & amp; Volume The luminosity represented the total energy output of the star per second. This is related to the star’s temperature as we noted above. But it is also related to the size of the star. A larger star will naturally have a higher energy output than a smaller one at the same temperature. Since stars are assumed to be spherical, it is possible to relate the luminosity L and temperature T of a star to its radius R, through the equation,

R = [L]1/2 / T2

In the equation above, the luminosity and temperature must be expressed in solar units. This means if you determine the real temperature of the star to be 8000 K, its value is (8000/5800) = 1.38 times that of the Sun. The number 1.38 rather than 8000 will be used in the equation above.

The volume compared to that of the Sun, i.e. the star’s relative volume will be V = R3. Density. Once the mass and volume of an object are known, its density demoted by can be determined, since density = mass/volume. Since the mass and volume of the star was determined relative to the Sun, the use of this equation provides the relative density, i.e. the density of the star in comparison to the Sun. Lifetime and chemical composition
The Sun is a hydrogen-burning, Main Sequence star. Its chemical composition is believed to be representative of the composition of other Main Sequence stars:

Element
Hydrogen
Helium
Others

The more mass it has, the longer it can remain “alive.” But how fast it burns its fuel, will also play a role. If its luminosity is high, it will be using up large amounts of its fuel very fast. In that case, it will not last very long, like a “gas-guzzling” automobile. The star’s life is thus inversely related to its luminosity and directly related to its mass. To calculate the star’s time on the Main Sequence, use = Mass / L , where Mass = stellar mass and L = stellar luminosity. Once again, since Mass and L are in solar units, the star’s lifetime will also be in comparison to the Sun.

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