The bright star Aldebaran in Taurus is a red giant with a parallax of 0.049’’, a

Question

The bright star Aldebaran in Taurus is a red giant with a parallax of 0.049’’, an apparent V magnitude of mV = 0.86, and an apparent B magnitude of mB=2.40. Use these numbers and Appendix G in your text to determine the following parameters (show calculations and/or explain your reasoning; don’t just copy values from the text)

a) its distance (in parsecs)
b) its absolute visual magnitude MV c) its bolometric magnitude
d) its luminosity (in ergs/s)
e) its radius (in solar radii)
f) its spectral type

Explanation / Answer

a.) We use the formula for parallax d = 1/p, where d is in parsec and p in arcsec, to find the distance to the star.

Since p = 0.049, we find d = 1/p = 1/0.049 = 20.4081 parsecs.

b.) We've the equation m M = 5 5 log d, where m is apparent magnitude & M is absolute magnitude

we've mV=0.86 & d = 20.4081 parsecs (from part(a))

Substituting these values in m M = 5 5 loge d,

We've 0.86-M =5 - 5loge(20.4081)

M= 5(3.016)-4.14 = 15.08 - 4.14= 10.94

Hence, absolute visual magnitude Mv=10.94

c.) We've the equation  mbol = Mbol + 5 log (d/10) where mbol is the apparent B magnitude & Mbol is the absolute one & d is in parsecs.

mbol = 2.4 (given)

Substituting the values in the equation,

2.4 = Mbol + 5 loge(20.4081/10)

Solving for Mbol, Mbol = -2

d.) Mbol = 4.8 2.5 log (L/Lo) , where star has a luminosity L & Lo is the solar luminosity

-2 = 4.8 - 2.5 ln (L/(4*1033) )

6.8=2.5 ln (L/(4*1033) )

Solving for L,

L= (4* 1033).e68/25 = (4* 1033)*15.18

L=60.72*1033 ergs/s

(e) Appendix G required

(f) Appendix G required

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