<p>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 <a href="http://en.wikipedia.org/wiki/Color_index">colour index</a>. Blue stars have a low colour index ($B-V&lt;0$) 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.</p>

<p>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 <a href="https://docs.kde.org/stable/en/kdeedu/kstars/ai-colorandtemp.html">webpage</a>).</p>

<p>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 <a href="http://en.wikipedia.org/wiki/Stellar_classification">wikipedia page on stellar classification</a>.</p>

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

<p>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.</p>

<p>An example:</p>

<p>The following record is for the star Arcturus (α Boötis):</p>

<pre><code>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 
</code></pre>

<p>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 $T\approx 4000 \textrm{K}$ (<a href="https://docs.kde.org/stable/en/kdeedu/kstars/ai-colorandtemp.html">from figure 2 on this webpage</a>). The spectral type is K2IIIp, i.e. the spectral class is K2 and the luminosity class is III, a normal giant star.</p>

<p>An indication for the Radius can be found from the Hertzsprung-Russel Diagram in which radii are added (see <a href="http://astro.wsu.edu/worthey/astro/html/im-Galaxy/hr-radii.gif">Figure here</a>). 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 <a href="http://en.wikipedia.org/wiki/Absolute_magnitude">absolute magnitude ($M_V$):</a>
$$ M_V = m_V -5(\log{d}-1)$$
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 <a href="http://en.wikipedia.org/wiki/Magnitude_(astronomy)">luminosity</a> 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 <a href="http://astro.wsu.edu/worthey/astro/html/im-Galaxy/hr-radii.gif">Hertzsprung-Russel diagram</a> we get a radius for Arcturus of about $R \approx 10  \textrm{R}_{\textrm{sun}}$.</p>

CC BY-SA 3.0
2015-02-01T13:32:03.053Z
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 http://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?
MiscellaneousUser
CC BY-SA 3.0
2015-02-01T13:58:31.560Z
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)'.
Dieudonné
CC BY-SA 3.0
2015-02-01T20:15:41.960Z
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.
MiscellaneousUser
CC BY-SA 3.0
2015-02-02T08:15:55.093Z
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.)
Dieudonné
CC BY-SA 3.0
2015-02-02T08:22:57.653Z
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).
Dieudonné
CC BY-SA 3.0
2015-07-27T23:10:20.153Z
The formula $L=10^{M-M_{sun}}$ is not correct.  It has a sign error, and does not divide the magnitude difference by 2.5. The version in your answer is better but does not incorporate a (temperature dependent) bolometric correction. and so only works for stars  similar to the Sun (i.e. not Arcturus).
ProfRob
CC BY-SA 3.0
2015-02-01T00:35:10.553Z
2015-02-01T00:35:10.553Z
Dieudonné
<p>Using data from the Hipparcos Catalog download file, is there a way to determine the Visual or Apparent Magnitude from the data within?</p>

<p>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?</p>

CC BY-SA 3.0
2015-01-31T22:08:17.987Z
You should furnish some links with examples of your data.
Py-ser
<star>
Mass, Radius, Colour, Size, Type of a Star from the Hipparcos Catalog
MiscellaneousUser
# Mass, Radius, Colour, Size, Type of a Star from the Hipparcos Catalog

(Asked by: username_0 on 2015-01-31)

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?

**Tags:** star
> **Comments:**
> **username_1**: You should furnish some links with examples of your data.  

---

## 1 answers

### Answer by username_2 on 2015-02-01. Score: 6 | Accepted answer

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 $R \approx 10  \textrm{R}_{\textrm{sun}}$.

> **Comments:**
> **username_0**: 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 http://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?  
> **username_2**: 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)'.  
> **username_0**: 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.  
> **username_2**: 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.)  
> **username_2**: 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).  
> **username_3**: The formula $L=10^{M-M_{sun}}$ is not correct.  It has a sign error, and does not divide the magnitude difference by 2.5. The version in your answer is better but does not incorporate a (temperature dependent) bolometric correction. and so only works for stars  similar to the Sun (i.e. not Arcturus).  

---

