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"The colour-magnitude diagramme\n",
"\n",
"One important tool in astrophysics is the Hertzsprung–Russell (HR) diagramme, in which we plot the luminosity of a star as a function of its surface (or \"effective\") temperature. In practice, we use a logarithm-logarithm plot, as the ranges covered are rather large (10 orders of magnitudes in luminosity, 2 in temperature). Such diagrammes have proved very useful, as it was seen that the majority of stars (including the Sun) follow a line called the \"main sequence\", while others will occupy different regions in the diagramme, corresponding to giant stars, horizontal-branch stars or white dwarfs, for example.\n",
"\n",
"In principle, we do not know necessarily the temperature (which is obtained mostly with spectroscopy) nor the total luminosity (as we would need to observe it at all wavelength) of a star and so a different diagramme, the colour-magnitude diagramme (CMD), is used as a proxy. \n",
"\n",
"In astronomy, for historical reasons, we use magnitude in a different way as in other part of physics. Indeed, the Greek astronomer Hipparchus of Nicaea devised a numerical scale to describe the brightness of stars as seen with the unaided eye: the brightest star in the sky was assigned an apparent magnitude of 1, and the dimmest star visible assigned a value of 6. The difference between them corresponds roughly to a factor of 100 in brightness. Thus, as 5 magnitudes correspond to a factor 100, the magnitude is given as -2.5 times the logarithm of the brightness in a given wavelength range. Because of the minus sign, a star is brighter the smaller (or more negative) its magnitude is, as devised by Hipparchus.\n",
"\n",
"We also use two kinds of magnitude - the apparent (or observed) magnitude as described above and the absolute one. The apparent one tells us how we perceive the star as seen from Earth. However, a star can be close or far, and thus its intrinsic luminosity may be very different. This is taken into account into the absolute magnitude, which takes the distance into account. The later is thus a good proxy for the total luminosity of the star. Thus, the brightest star in the night sky, Sirius, has an observed magnitude of -1.46 because it is so close to us, but an absolute magnitude of 1.4. By comparison, one of the intrinsically brightest stars in our Galaxy, Eta Carinae, has an absolute magnitude of -8.6 (it is thus intrinsically 10,000 times brighter than Sirius), but an apparent magnitude of 4.3 (so it seems to us , as it is much farther away.\n",
"\n",
"The apparent magnitude of a given band, for example in the visible, is given by \n",
"V = -2.5 log FV + CV,\n",
"where CV is a constant and FV is the observed flux of the star in this band.\n",
"To determine the absolute magnitude, we need to take into account the distance, as well as the fact that the flux of the star is dimmed by all the matter and dust that lies between the star and us (the \"extinction\"). By definition, an object's absolute magnitude is defined to be equal to the apparent magnitude that the object would have if it were viewed from a distance of exactly 10 parsecs (32.6 light-years), without extinction. \n",
"MV = -2.5 log (FV * d102) + CV + AV, \n",
"where d10 is the distance of the star, in units of 10 parsecs, d10= d / 10 pc, with d expressed in parsec, and AV is the extinction.\n",
"\n",
"Thus,\n",
"MV = -2.5 log FV - 5 log d10 + CV + AV = V - 5 (log d - 1.) + AV = V + 5 - 5 log d + AV. \n",
"As the distance is often expressed in kilo-parsecs (kpc), i.e. 1000 pc, this is then rewritten\n",
"MV = V - 10 - 5 log d* + AV.\n",
"Using the parallax, varpi, in milli-arcseconds, instead, we have\n",
"MV = V - 10 + 5 log varpi + AV, as varpi = 1./d*.\n",
"Instead of looking into the V band, we can also look in any other band, and the same relation exists.\n",
"\n",
"One can use such absolute magnitude as a proxy for the total luminosity of a star. What about the temperature? We know that stars of different temperatures have different colours: the hotter stars are bluer, while the Sun with a surface temperature of about 5,800 K is yellow, and cooler stars are red. Such a colour can also be seen as the difference between the magnitude obtained in two different bands, a blue and a red one. Thus, if a star is bluer, its magnitude in the blue band will be smaller than in the red band, and the difference between the two magnitudes will be negative. The opposite is true for a red star. \n",
"\n",
"The Gaia satellite provides photometric observations in three bands: the G band, which is very wide, and in the blue (Bp) and in the red (Rp). One can thus create a colour-magnitude diagramme using Bp-Rp as the colour and an absolute magnitude based on the magnitude in G.\n",
"One needs to also correct these magnitudes for the extinction. This is done with:\n",
"A_G = 0.86117 * Av\n",
"A_Bp = 1.06126 * Av\n",
"A_Rp = 0.64753 * Av\n",
"\n",
"Let us for example look at the CMD for the open cluster Messier 7. As this is a cluster, it is defined by a single age and chemical composition and is thus representing a single population."
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\n",
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