| Software | Version |
|---|
| Python | 2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)] |
| IPython | 2.3.1 |
| OS | Linux 3.13.0 45 generic x86_64 with debian jessie sid |
| numpy | 1.9.1 |
| matplotlib | 1.4.2 |
| pandas | 0.15.2 |
| Tue Feb 24 20:53:45 2015 CET |
"
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"\\begin{tabular}{|l|l|}\\hline\n",
"{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
"Python & 2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)] \\\\ \\hline\n",
"IPython & 2.3.1 \\\\ \\hline\n",
"OS & Linux 3.13.0 45 generic x86\\_64 with debian jessie sid \\\\ \\hline\n",
"numpy & 1.9.1 \\\\ \\hline\n",
"matplotlib & 1.4.2 \\\\ \\hline\n",
"pandas & 0.15.2 \\\\ \\hline\n",
"\\hline \\multicolumn{2}{|l|}{Tue Feb 24 20:53:45 2015 CET} \\\\ \\hline\n",
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"Software versions\n",
"Python 2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\n",
"IPython 2.3.1\n",
"OS Linux 3.13.0 45 generic x86_64 with debian jessie sid\n",
"numpy 1.9.1\n",
"matplotlib 1.4.2\n",
"pandas 0.15.2\n",
"Tue Feb 24 20:53:45 2015 CET"
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"source": [
"An interesting educational activity about the H-R diagrams is [The Hertzsprung-Russell Diagram](http://skyserver.sdss.org/dr12/en/proj/advanced/hr/hrhome.aspx) in the Sloan Digital Sky Survey III (SDSS III)."
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Some theory"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some relevant facts in the development of a Hertsprung-Russel diagram (H-R diagram in short) are:\n",
"\n",
"* On the one hand there is a relationship between the absolute magnitude of a star and its luminosity, which has been described in this post: [The color of celestial objects: part I](http://balbuceosastropy.blogspot.com.es/2013/11/the-color-of-celestial-objects-part-i.html)\n",
"\n",
"* There is also a relationship between the spectral class of the star (O B A F G K M), its surface temperature and its color index (eg. B-V). This relationship between color index and temperature can also be seen in the previous post. Regarding the relationship between spectral classes and surface temperatures, you can read my post [The color of celestial objects: part II](http://balbuceosastropy.blogspot.com.es/2013/11/the-color-of-celestial-objects-part-ii.html)\n",
"\n",
"* The purpose of the H-R diagram is to show the relationship between both groups of magnitudes. The \"classic\" H-R diagram shows the spectral class of the stars (or the corresponding color index B-V) on the horizontal axis and the absolute magnitudes on the vertical axis.\n",
"\n",
"* The position of a star in the H-R diagram tells us something about its characteristics. Thus for example if a star has a spectral class indicating a \"cold\" surface temperature (for example classes K or M), but its absolute magnitude / luminosity is high, this indicates that the star has a large surface, whereby the big radiative surface \"compensates\" the low intensity of the radiation due to its low temperature. Ie it would be a \"giant\" star or \"supergiant\". As the color indices corresponding to cold temperatures tend to red, we would speak for instance of \"red giants\"."
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"The HIPPARCOS catalog"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The biggest difficulty to build an H-R diagram is to determine the luminosity or absolute magnitude of the stars, as this involves knowing their distances. In this sense, the catalog of celestial objects SDSS I've been using so far in previous posts is not the most suitable because its main purpose is the photometry of extragalactic objects, providing little information of stars in our galaxy, and certainly lacking accurate information on the distance that separates us from them.\n",
"\n",
"For this reason, the catalog of stars that we will use is [HIPPARCOS](http://en.wikipedia.org/wiki/Hipparcos), given that the priomordial objective of this mission was precisely to make accurate measurements of about 120000 stars. Furthermore, the information in this catalog includes the spectral class of the vast majority of these objects, so it is the most suitable source that we can use to make an H-R diagram.\n",
"\n",
"A description of the fields in the catalog can be downloaded in pdf format at the following page: [Hipparcos Overview](http://www.rssd.esa.int/index.php?project=HIPPARCOS&page=Overview). In particular, for this post, we are interested in the following fields:\n",
"\n",
"* H1 Identifier (HIP)\n",
"* H5 V Johnson magnitude (Vmag)\n",
"* H11 Trigonometric parallax, expressed in units of milliarcsec (Plx)\n",
"* H37 Colour index (B-V)\n",
"* H76 Spectral type (SpType)\n",
"\n",
"The absolute magnitudes can be calculated from the values of V. For this you can use the relationship between the absolute magnitude $M$, the apparent magnitude $m$ and the parallax $p$ parallax in arcseconds. See for example the wikipedia article [Absolute magnitude](http://en.wikipedia.org/wiki/Absolute_magnitude):\n",
"\n",
"$$ M = m + 5 (1 + \\log_{10} p )$$\n",
"\n",
"If parallax is expressed in milliarcseconds (Plx), and taking as apparent magnitude the value $V$ in the catalog, we obtain:\n",
"\n",
"$$ M = Vmag + 5 (1 + \\log_{10} \\frac{Plx}{1000}) $$\n",
"\n",
"That once simplified gives:\n",
"\n",
"$$ M = Vmag + 5 * log_{10} \\frac{Plx}{100} $$\n",
"\n",
"To download the catalog you must access the [VizieR Search Page](http://vizier.u-strasbg.fr/viz-bin/VizieR-3?-source=I/239/hip_main) for the catalog I/239 from the Strasbourg astronomical Data Center (CDS). Select only the fields listed above: HIP, Vmag, Plx, BV, SpType. In the left pane, under \"Preferences\" select \"unlimited\" and \"; -Separated Values\" Press the \"Submit\" button and download the file, which I called *I_239_selection.tsv* and occupies only 3.8 MB. Opening it with a text editor is found that it is a text file with a header of a few lines explanatory of the contents, followed by 118322 entries with the five selected fields separated by the ; character. At the end of the file there is also a blank line we should skip when reading the file.\n",
"\n",
"Now I will read the file creating a Pandas DataFrame:"
]
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"cell_type": "code",
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"input": [
"filename = '../Hipparcos/I_239_selection.tsv'\n",
"df = pd.read_table(filename, skiprows=44, sep=';', header=None, index_col=0,\n",
" names = ['HIP', 'Vmag', 'Plx', 'B-V', 'SpType'],\n",
" skipfooter=1, engine='python')"
],
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{
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"input": [
"df.head()"
],
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"outputs": [
{
"html": [
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