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Star Magnitude Distance

Spectroscopic Parallaxis the method of using the Hertzsprung - Russell (H-R) diagramand the distance modulus formulato determine the approximate distanceof the star. This technique can be applied to lots of stars, however the value determined for absolute magnitude from the H-R diagram can carry a large percentage error. Therefore you can use this method only to know the approximate distance not the exactly one.

This method involves several steps to find out the distance to the star.

Using the photometryto measure the apparent magnitude (m) of the star. Photometryis the measurement of the brightness of a source of light or other radiation.

Using spectroscopyto determine the spectral class and the luminosity class of the star.

Using B and V filtersto determine the blue apparent magnitude (B). Therefore we can determine the star's colour index from the equation which is CI = B – V.

Using the H-R diagramto read off the absolute magnitude (M) from the vertical line's scale. Horizontal axis for the appropriate spectral class and if we know its luminosity class then we can constrain its position along this line more accurate.

Now we know the M and m, so we can use the distance modulus formulato find the distance to the star.

Distance modulus formula; m- M= 5 log(d/10)

Note; distance is in a parsecs.

Using the H-R diagramto find distances to the stars is one of the important methods in the Spectroscopic Parallax.

Luminosity classes (Ia) through (V) have been added to as a function of spectral type to the H-R diagram. From the spectrum of a star, astronomers can determine both the spectral type (OBAFGKM) and luminosity class (Ia-V). Therefore the absolute magnitude of the star can be read off from the vertical scale on the diagram. A comparison of the absolute brightness of the stars that measured apparent brightness will give you the distance to the star.

Measuring colourof the stars has been changing through the human life. There are lots of varieties of colour of the stars, this variation is not obvious through your eyes. Eg. Aldebaran found in the constellation of Taurus, this is a red giant. However before it was known as a subtle pink when studied with unaided eyes, because of that the human eyes are most sensitive to the colour of yellow-green portion in the visible spectrum. This way of magnitude determined is called visual magnitude.

Later, the measurement of star magnitudes changed to photographically, and referred to as the photographic magnitudes. However in this measurement has another problem was that photographic film is most sensitive to the blue end of the visible spectrum which is inconsistent with visual magnitudes.

These days, the magnitudes of the stars measured by using the photometers. These devices are very sensitive and accurate, but also they are sensitive enough to get much wider range of wavelength such as UV and infra-red which the human eyes can't detect and insensitive.

In the photometer, the sensitive of determine the stars' colour depends on which standard coloured filter to put in front of it. There are three different colour magnitudes can be measured from the each stars.

These filtersis the yellow-green (V) for visual magnitudes, the blue (B) for photographic magnitudes, and the ultraviolet (U) for extra sensitivity in the photometer. This is become to known as the UBV system.

These filtersare also used to measure the apparent magnitudeof the stars. As I mentioned before that Betelgeuse will appear brightest through the V filter and V magnitude will be lower than its B or U magnitudes. Today, ranges of filters used in astronomical photometry include ultraviolet, blue, yellow-green, red, infrared filters. Comparison of each filter's magnitude is useful, but because these colour magnitudes are numbers. Therefore the comparisons are made numerically and this leads to the purpose of the colour index.

Colour indexmeans that difference between the photographic magnitude (B) and the visual magnitude (V).

Formula: Colour index = B – V

Eg. Betelgeuse will appear brightest through V filter than a B, so that means its V magnitude is lower than its B magnitude as you know. As a result, the expression B – V will result in a small positive number. There is a table of showing the collection of this.

Relationshipbetween the colour index and temperature is not equal every time such as colour index of – 0.6 to zero covers a range of 4000K, but the colour index of + 0.6 to + 2.0 covers about 4000K.

The concept of magnitudeis used to indicate the brightness of a star. Apparent magnitude (m)shows the how bright the star appears to an observer on the Earth, therefore it's directly measured from Earth. This number depends with the distance of the star from the observer that means the further the observer is from a star, the fainter the star appears and increase its magnitude number. This is because of the brightness of a star varies inversely with the square of the distance from the star which is known as the inverse square law.

Another type of magnitude is that absolute magnitude (M)expresses the brightness of the stars would have to an observer at a fixed distance of 10 parsecsfrom the star. This number doesn't change because of the fixed distance from the star. This shows by the comparison with reference stars of the same spectral class and of known distance. Eg. If a star is further away than 10 pc, its apparent magnitude (m) is larger than its absolute magnitude (M). If it was closer then the m is smaller than M.

If both m and Mare known, then we can use their difference by using the distance modulus m – M to calculate the distance to the star using the distance modulus equation:

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