- Suppose That A Star You Observe Towards The Highly Extincted Galac Tic Center Is Reddened More Than You Assume Because 1 (48.24 KiB) Viewed 40 times
b. Show that if the region between you and a star has optical depth τλ of 0.5 (if you are not familiar with this term, see Equation 1.21 of Sparke & Gallagher and text around that), that the star you’re observing will be 0.543 magnitudes fainter at that wavelength λ.
Suppose that a star you observe towards the highly extincted Galac- tic center is reddened more than you assume, because a small dust cloud is in the way between you and the star that you do not correct for. Because of this, the de-reddened magnitude that you assume for its apparent magni- tude is 0.05 magnitudes off. You do however know its absolute magnitude precisely and accurately as the star is a standard candle. What is the er- ror (in percentage) that you make in the distance you determine for this star? Show that if the region between you and a star has optical depth TX of 0.5 (if you are not familiar with this term, see Equation 1.21 of Sparke & Gallagher and text around that), that the star you're observing will be 0.543 magnitudes fainter at that wavelength A.