# Mass, Radius, Colour, Size, Type of a Star from the Hipparcos Catalog

Using data from the Hipparcos Catalog download file, is there a way to determine the Visual or Apparent Magnitude from the data within?

Can I obtain the Mass, Radius, colour, temperature, type (dwarf, sun-like, hypergiant, etc) of the star from the catalog? Which column relates to which item i'm looking for? Any examples?

• You should furnish some links with examples of your data. Jan 31 '15 at 22:08

The apparent magnitude (in V ~ visual) is in column 42-46. Other magnitudes are BT magnitude (columns 218-223) and VT magnitude (columns 231-236). These are magnitudes recorded with different (colour) filters. The colour ($B-V$) can be found in columns 246-251, expressed in magnitudes. This is the difference between V (visual) magnitude and B (blue) magnitude also known as the colour index. Blue stars have a low colour index ($B-V<0$) as the star will be brighter in the blue (B) passband (filter), and will therefore have a low B magnitude, while red stars will have a higher $B-V$ colour index.

Mass, Radius, and Temperature are not in the catalogue. Mass can only be directly determined for multiple star systems and requires a lot of observations per multiple star. Radius is determined from stellar models. And Temperature can be determined from the spectrum of the star. A crude indication can be gotten from the colour index of the star. (see for instance this webpage).

Finally the type can be found in the star's spectral type. The spectral type is in columns 436-447. These spectral types are not always easy to read but they consist of a spectral class (e.g. O, or F type stars) and the luminosity class (and some other information). The luminosity class gives the type of class in roman numerals. Below is the list from the wikipedia page on stellar classification.

• 0 or Ia+ (hypergiants or extremely luminous supergiants). Example: Cygnus OB2#12 (B3-4Ia+)[12]
• Ia (luminous supergiants). Example: Eta Canis Majoris (B5Ia)[13]
• Iab (intermediate luminous supergiants). Example: Gamma Cygni (F8Iab)[14]
• Ib (less luminous supergiants). Example: Zeta Persei (B1Ib)[15]
• II bright giants. Example: Beta Leporis (G0II)[16]
• III normal giants. Example: Arcturus (K0III)[17]
• IV subgiants. Example: Gamma Cassiopeiae (B0.5IVpe)[18]
• V main-sequence stars (dwarfs), Example: Achernar (B6Vep)[15]
• sd (prefix) subdwarfs. Example: HD 149382 (sdB5)[19]
• D (prefix) white dwarfs.[nb 2] Example: van Maanen 2 (DZ8)[20]

The Sun's spectral type is G2V, which means that the spectral class is G2 and the luminosity class is V, which means that the Sun is a main-sequence star.

An example:

The following record is for the star Arcturus (α Boötis):

H|       69673|H|14 15 40.35|+19 11 14.2|-0.05|1|G|213.91811403|+19.18726997|*|  88.85|-1093.45|-1999.40|  0.92|  0.42|  0.74|  0.60|  0.52|-0.52| 0.16|-0.13|-0.07| 0.05|-0.01| 0.03|-0.12|-0.03|-0.31|  7| 2.01| 69673| 1.629|0.010| 0.286|0.009|*| 1.239|0.006|G|1.22|0.02|A|*| 0.1114|0.0020|0.015| 70|*| 0.09| 0.14|       |U|2| |14157+1911|H| 1| 2|C| |A|AB|198|  0.255|0.039| 3.33|0.31|S| | |124897|B+19 2777 |          |          |1.22|K2IIIp      |X


The apparent visual is(V) magnitude $-0.05$. The colour index is $B-V = 1.239$, which means that it is probably a red K type star with temperature $T\approx 4000 \textrm{K}$ (from figure 2 on this webpage). The spectral type is K2IIIp, i.e. the spectral class is K2 and the luminosity class is III, a normal giant star.

An indication for the Radius can be found from the Hertzsprung-Russel Diagram in which radii are added (see Figure here). The luminosity of Arcturus can be calculated as follows: $$d = \frac{1}{\varpi}$$ where $d$ is in parsec and $\varpi$ is the parallax in arsceconds. The parallax is in columns 80-86 and is $\varpi = 88.85mas = 0.08885^{\prime\prime}$ for Arcturus. The distance is, therefore, $d=11.25\textrm{pc}$. You can then calculate the absolute magnitude ($M_V$): $$M_V = m_V -5(\log{d}-1)$$ where $m_V$ is the apparent visual (V) magnitude. The absolute magnitude of Arcturus is: $M_V=-0.05 - 5(\log{11.25}-1)=-0.31$. The luminosity is then given by: $$M-M_{\textrm{sun}} = -2.5\log{\left( \frac{L}{L_{\textrm{sun}}}\right)}$$ where the absolute magnitude of the Sun is $M_{\textrm{sun}} = 4.83$ and $L$ is the luminosity of Arcturus. This gives: $$\log{\left( \frac{L}{L_{\textrm{sun}}}\right)} = 2.056$$ $$L = 114 \textrm{L}_{\textrm{sun}}$$ From the Hertzsprung-Russel diagram we get a radius for Arcturus of about $R \approx 10 \textrm{R}_{\textrm{sun}}$.

• Managed to follow everything up to the last two equations, I don't understand L (I presume LSun is the Sun value of L). I also don't understand -2.5Log(L/Lsun) , is that -2.5*Log() ? How do I turn R~10R into something that a non-astronomer could understand, i.e. multiple(10x the radius of the sun). did find skyserver.sdss.org/dr5/en/proj/advanced/hr/radius1.asp where they explain how they calculated the radius of Sirius but the last formula on the page, I couldn't understand, how would i convert that into computer code? Feb 1 '15 at 13:32
• First: Yes $-2.5\log(L/L_{\textrm{sun}})$ is $-2.5\times \log()$. As to converting this into computer code, I'm not sure what you do not understand. Maybe the conversion from $M-M_{\textrm{sun}} = \log{\frac{L}{L_{\textrm{sun}}}}$? This would become $\frac{L}{L_{\textrm{sun}}} = 10^{M-M_{\textrm{sun}}}$ so if you have a value for $M-M_{\textrm{sun}}$, say $2.056$, then you can calculate the luminosity (in solar luminosities) with 'pow(10,2.056)'. Feb 1 '15 at 13:58
• I don't know how you would calculate L from Hipparcos catalogue, what columns would I use from the data. Is there a formula which I can generate the values from? As for Arcturus temperature, how did you arrive at 4000k, when I used the wiki page, i calculated the temperature as being 3600-5200 which it is but how did you narrow it down to 4000, knowledge or is it possible from Hipparcos? I need a formula because i want to calculate alot of star data so don't want to keep looking at the graph to work out the temp. Feb 1 '15 at 20:15
• To calculate $L$ you will need the apparent (V) magnitude $m_V$ and the parallax to calculate first the distance (first equation above, and don't forget that Hipparcos gives the parallax in MILLIarcseconds) and then the absolute magnitude $M$ (second equation above). Together with the absolute magnitude of the Sun ($M_{\textrm{sun}}$ = 4.83) you can calculate the Luminosity with $L = 10^{M-M_{\textrm{sun}}}$. This is expressed in Solar Luminosities, i.e. the Sun will have a luminosity of $L=1.0 L_{\textrm{sun}}$. (The SI unit is Watt = Joule per second.) Feb 2 '15 at 8:15
• The value for the temperature $4000\textrm{K}$ was read from a graph so it is very imprecise. There are some empirical relations that transform colour index to temperature but they depend on the type of star. They can be found in the scientific literature and they will often involve transforming the colour index used in Hipparcos to other passbands (such as those used by SDSS). Feb 2 '15 at 8:22