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0001 <sect1 id="ai-magnitude">
0002 <sect1info>
0003 <author>
0004 <firstname>Girish</firstname> <surname>V</surname>
0005 </author>
0006 </sect1info>
0007 <title>Magnitude Scale</title>
0008 <indexterm><primary>Magnitude Scale</primary>
0009 <seealso>Flux</seealso>
0010 <seealso>Star Colors and Temperatures</seealso>
0011 </indexterm>
0012 <para>
0013 2500 years ago, the ancient Greek astronomer Hipparchus classified the
0014 brightnesses of visible stars in the sky on a scale from 1 to 6.  He
0015 called the very brightest stars in the sky <quote>first magnitude</quote>, and the
0016 very faintest stars he could see <quote>sixth magnitude</quote>.  Amazingly, two
0017 and a half millenia later, Hipparchus's classification scheme is still
0018 widely used by astronomers, although it has since been modernized and
0019 quantified.</para>
0020 <note><para>The magnitude scale runs backwards to what you
0021 might expect: brighter stars have <emphasis>smaller</emphasis>
0022 magnitudes than fainter stars).
0023 </para>
0024 </note>
0025 <para>
0026 The modern magnitude scale is a quantitative measurement of the
0027 <firstterm>flux</firstterm> of light coming from a star, with a
0028 logarithmic scaling:
0029 </para><para>
0030   m = m<subscript>0</subscript> - 2.5 log (F / F<subscript>0</subscript>)
0031 </para><para>
0032 If you do not understand the math, this just says that the magnitude
0033   of a given star (m) is different from that of some standard star (m<subscript>0</subscript>)
0034 by 2.5 times the logarithm of their flux ratio.  The 2.5 *log factor
0035 means that if the flux ratio is 100, the difference in magnitudes is 5
0036 mag.  So, a 6th magnitude star is 100 times fainter than a 1st magnitude
0037 star.  The reason Hipparchus's simple classification translates to a
0038 relatively complex function is that the human eye responds
0039 logarithmically to light.
0040 </para><para>
0041 There are several different magnitude scales in use, each of which serves
0042 a different purpose.  The most common is the apparent magnitude scale;
0043 this is just the measure of how bright stars (and other objects) look
0044 to the human eye.  The apparent magnitude scale defines the star Vega
0045 to have magnitude 0.0, and assigns magnitudes to all other objects using
0046 the above equation, and a measure of the flux ratio of each object to
0047 Vega.
0048 </para><para>
0049 It is difficult to understand stars using just the apparent magnitudes.
0050 Imagine two stars in the sky with the same apparent magnitude, so they
0051 appear to be equally bright.  You cannot know just by looking if the
0052 two have the same <emphasis>intrinsic</emphasis> brightness; it is
0053 possible that one star is intrinsically brighter, but further away.
0054 If we knew the distances to the stars (see the <link
0055 linkend="ai-parallax">parallax</link> article), we could account for
0056 their distances and assign <firstterm>Absolute magnitudes</firstterm>
0057 which would reflect their true, intrinsic brightness.  The absolute
0058 magnitude is defined as the apparent magnitude the star would have if
0059 observed from a distance of 10 parsecs (1 parsec is 3.26 light-years,
0060   or 3.1 x 10<superscript>18</superscript> cm).  The absolute magnitude (M) can be determined
0061 from the apparent magnitude (m) and the distance in parsecs (d)
0062 using the formula:
0063 </para><para>
0064 M = m + 5 - 5 * log(d)   (note that M=m when d=10).
0065 </para><para>
0066 The modern magnitude scale is no longer based on the
0067 human eye; it is based on photographic plates and photoelectric
0068 photometers.  With telescopes, we can see objects much fainter than
0069 Hipparchus could see with his unaided eyes, so the magnitude scale has
0070 been extended beyond 6th magnitude.  In fact, the Hubble Space Telescope
0071 can image stars nearly as faint as 30th magnitude, which is one
0072 <emphasis>trillion</emphasis> times fainter than Vega.
0073 </para><para>
0074 A final note: the magnitude is usually measured through a color filter
0075 of some kind, and these magnitudes are denoted by a subscript
0076 describing the filter (&ie;, m<subscript>V</subscript> is the magnitude through a <quote>visual</quote>
0077 filter, which is greenish; m<subscript>B</subscript> is the magnitude through a blue filter;
0078 m<subscript>pg</subscript> is the photographic plate magnitude, &etc;).
0079 </para>
0080 </sect1>