January 30th, 2018, 03:52 PM  #1 
Senior Member Joined: Sep 2012 Posts: 201 Thanks: 1  Finding Distance of star cluster
Can someone please advise me whether I have gone wrong on this question as I feel I have? Question Vega is a star of spectral type A0V at a distance of 7.76pc and has by definition $\displaystyle m_V =m B =0.0\space mag$. Observations of a star cluster show that all stars in the cluster with a spectral type A0V have an apparent magnitude of $\displaystyle m_V =15 \space mag$ and a colour index of $\displaystyle BV=1.39 \space mag$. Assuming an interstellar reddening law of $\displaystyle A V /E(BV)=3.2$ calculate the distance of this star cluster. Equation I used to solve mM=5log(d/10) \space [1] E(BV)=(BV)(BV)_0 \space [2] m_v=M_v+5log(d)5+A_v \space [3] My solution Step 1: To calculate the intrinsic brightness which is $\displaystyle (BV)_0$ so I used vega to do so. I did this because according to wiki intrinsic brightness is a measure of absolute magnitude. So my reasoning is that if as the cluster and vega are in the same spectral band then they would share the same absolute magnitudes. $\displaystyle 0M_v=5\log(7.76/10)=0.55$ Step 2: Substituting this in to my equation 2 as follows i.e. colour excess equation. $\displaystyle E(BV)=1.390.55=0.84$ Step 3: Rearrange the equation $\displaystyle A V /E(BV)=3.2$ to calculate the extinction value $\displaystyle A_v$ $\displaystyle A_v=(3.2)(0.84)=2.69$ Step 4: Using equation [3] the modified distance modulus and rearranging to make d the subject, I make d the following: $\displaystyle 10^{\frac{m_v M_v+5A_v}{5}}=d$ $\displaystyle 10^{\frac{15 0.55+52.69}{5}}=2249pc$ Have I made a wrong calculation or is my assumption in the first step completely wrong, or have I complete misunderstood the question? Any advice would be much appreciated; thanks in advance. Last edited by skipjack; January 30th, 2018 at 04:25 PM. 

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cluster, distance, finding, star 
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