So I have a table of data for the following stars: Vega, $$\alpha$$ Crv, $$\beta$$ CVn and $$\epsilon$$ Eri. I have been given their parallax, luminosity, $$m_{B}$$ magnitude and the $$m_{V}$$ magnitude. Now I'm asked to first calculate the distance $$d$$ of all the stars aswell as the absolute bolometric magnitude $$(M_{bol})$$ of the stars. Now I used the basic parallax formula for the distances: $$d=\frac{1 AU}{\tan{\theta}}$$ with $$\theta$$ the parallax in milli-arcsec. Now as for the absolute bolometric magnitude, I first wanted to use the distance modulus to calculate the absolute magnitude, but since I don't have the bolometric magnitude this isn't possible I think, so I used the formula that uses the luminosity given by: $$M_{bol}=M_{bol,\odot}+2.5\log\frac{L_{\odot}}{L}$$ I think I found the right values, but now there is a second question where they ask to compare the apparent magnitude in the V-band of the four stars with the observed apparent magnitudes of stars with the same B-V index in the Pleiades cluster, where they've given a figure of the HR-diagram of the Pleiades. Then they ask to calculate the distance to the Pleiades based on the mean apparent visual magnitudes. So as I said the first question I think I have, so the distance and absolute bolometric magnitude, but I don't know how we can find a distance for the Pleiades based on all that.

• Also the HR-diagram of the Pleiades, the y-axis is $m_{V}$ and the x-axis is the $B-V$ index Aug 20 at 11:33

i.e. If we take two stars of the same spectral type and assume that they have the same absolute magnitude $$M$$: $$m_1 - M = 5\log d_1 - 5$$ $$m_2 - M = 5\log d_2 -5$$ subtracting one from the other: $$m_1 - m_2 = 5(\log d_1 - \log d_2)\ .$$
Since you know the apparent magnitude and distance to your calibration stars ($$m_1$$, $$d_1$$), then you can work out the distance of stars in the Pleiades that have apparent magnitude $$m_2$$ and the same spectral type. If you have many stars to compare or a a range of apparent magnitudes in the Pleiades at the same colour (remember that some of these may be binaries) then you will need to do some averaging.
• I've found the difference between the apparent magnitudes of the stars respectively: $0, 0.34, 0.61$ and $0.88$. Now if I took a look at the HR-diagram the same $B-V$ index corresponds with respectively apparent magnitudes on the main sequence between: $6-8, 8-9, 9-11$ and $10-12$ with here and there some stars that also have that $B-V$ index but lie way above or beneath the main sequence. But okay I kind of understand what you are saying, but in order to find the distance to the Pleiades with the distance modulus I also need to find the absolute magnitude of the Pleiades, or is that incorrect Aug 20 at 12:03