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January 30th, 2018, 02:52 PM   #1
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Finding Distance of star cluster

Can someone please advise me whether I have gone wrong on this question as I feel I have?

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 $\displaystyle B-V=1.39 \space mag$. Assuming an interstellar reddening law of $\displaystyle A V /E(B-V)=3.2$ calculate the distance of this star cluster.

Equation I used to solve

m-M=5log(d/10) \space [1]

E(B-V)=(B-V)-(B-V)_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 $\displaystyle (B-V)_0$ 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.

$\displaystyle 0-M_v=5\log(7.76/10)=0.55$

Step 2: Substituting this in to my equation 2 as follows i.e. colour excess equation.

$\displaystyle E(B-V)=1.39-0.55=0.84$

Step 3: Rearrange the equation $\displaystyle A V /E(B-V)=3.2$ 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:

$\displaystyle 10^{\frac{m_v -M_v+5-A_v}{5}}=d$

$\displaystyle 10^{\frac{15 -0.55+5-2.69}{5}}=2249pc$

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 03:25 PM.
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