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81 lines
3.8 KiB
81 lines
3.8 KiB
<sect1 id="ai-magnitude">
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<sect1info>
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<author>
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<firstname>Girish</firstname> <surname>V</surname>
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</author>
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</sect1info>
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<title>Magnitude Scale</title>
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<indexterm><primary>Magnitude Scale</primary>
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<seealso>Flux</seealso>
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<seealso>Star Colors and Temperatures</seealso>
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</indexterm>
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<para>
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2500 years ago, the ancient Greek astronomer Hipparchus classified the
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brightnesses of visible stars in the sky on a scale from 1 to 6. He
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called the very brightest stars in the sky <quote>first magnitude</quote>, and the
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very faintest stars he could see <quote>sixth magnitude</quote>. Amazingly, two
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and a half millenia later, Hipparchus's classification scheme is still
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widely used by astronomers, although it has since been modernized and
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quantified.</para>
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<note><para>The magnitude scale runs backwards to what you
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might expect: brighter stars have <emphasis>smaller</emphasis>
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magnitudes than fainter stars.
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</para>
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</note>
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<para>
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The modern magnitude scale is a quantitative measurement of the
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<firstterm>flux</firstterm> of light coming from a star, with a
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logarithmic scaling:
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</para><para>
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m = m_0 - 2.5 log (F / F_0)
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</para><para>
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If you do not understand the math, this just says that the magnitude
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of a given star (m) is different from that of some standard star (m_0)
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by 2.5 times the logarithm of their flux ratio. The 2.5 *log factor
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means that if the flux ratio is 100, the difference in magnitudes is 5
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mag. So, a 6th magnitude star is 100 times fainter than a 1st magnitude
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star. The reason Hipparchus's simple classification translates to a
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relatively complex function is that the human eye responds
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logarithmically to light.
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</para><para>
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There are several different magnitude scales in use, each of which serves
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a different purpose. The most common is the apparent magnitude scale;
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this is just the measure of how bright stars (and other objects) look
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to the human eye. The apparent magnitude scale defines the star Vega
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to have magnitude 0.0, and assigns magnitudes to all other objects using
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the above equation, and a measure of the flux ratio of each object to
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Vega.
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</para><para>
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It is difficult to understand stars using just the apparent magnitudes.
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Imagine two stars in the sky with the same apparent magnitude, so they
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appear to be equally bright. You cannot know just by looking if the
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two have the same <emphasis>intrinsic</emphasis> brightness; it is
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possible that one star is intrinsically brighter, but further away.
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If we knew the distances to the stars (see the <link
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linkend="ai-parallax">parallax</link> article), we could account for
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their distances and assign <firstterm>Absolute magnitudes</firstterm>
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which would reflect their true, intrinsic brightness. The absolute
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magnitude is defined as the apparent magnitude the star would have if
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observed from a distance of 10 parsecs (1 parsec is 3.26 light-years,
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or 3.1 x 10^18 cm). The absolute magnitude (M) can be determined
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from the apparent magnitude (m) and the distance in parsecs (d)
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using the formula:
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</para><para>
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M = m + 5 - 5 * log(d) (note that M=m when d=10).
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</para><para>
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The modern magnitude scale is no longer based on the
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human eye; it is based on photographic plates and photoelectric
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photometers. With telescopes, we can see objects much fainter than
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Hipparchus could see with his unaided eyes, so the magnitude scale has
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been extended beyond 6th magnitude. In fact, the Hubble Space Telescope
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can image stars nearly as faint as 30th magnitude, which is one
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<emphasis>trillion</emphasis> times fainter than Vega.
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</para><para>
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A final note: the magnitude is usually measured through a color filter
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of some kind, and these magnitudes are denoted by a subscript
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describing the filter (&ie;, m_V is the magnitude through a <quote>visual</quote>
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filter, which is greenish; m_B is the magnitude through a blue filter;
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m_pg is the photographic plate magnitude, &etc;).
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</para>
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</sect1>
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