Question

In a certain part of the North America Nebula, the amount of interstellar extinction in the visual wavelength band is 1.1 magnitudes. The thickness of the nebula is estimated to be 20 pc and it is located 700 pc from Earth. Suppose that a B spectral class main-sequence star is observed in the direction of the nebula and that the absolute visual magnitude of the star is known to be M(V) = -1.1 from spectroscopic data. Neglect any other sources of extinction between the observer and the nebula. Show all your work, assumptions, equations, and units.1. Find the apparent visual magnitude of the star if it is lying just in front of the nebula.2. Find the apparent visual magnitude of the star if it is lying just behind the nebula.

Answer 1

Step-by-step explanation:

The apparent magnitude of a star is related to the distance modulus as follows

`m_(\lambda)= M_(\lambda)+5log_(10)d-5+A_(\lambda)`

`m_(\lambda)= \text {absolute visual magnitude}`

d = distance in parsec

`A_(\lambda)=\text {interstellar extinction}`

Substitute

absolute visual magnitude = -1.1

distance =700pc

interstellar extinction = 0

to determine the apparent visual magnitude of the star lying in front of nebula

`m_(\lambda)= M_(\lambda)+5log_(10)d-5+A_(\lambda)`

`=-1.1+5\log_(10)(700)-5+0\\\\=8.12`

Thus, the apparent visual magnitude of the star lying in front of nebula is 8.12

b) Substitute

absolute visual magnitude = -1.1

distance =700pc

interstellar extinction = 1.1

to determine the apparent visual magnitude of the star lying behind nebula

`m_(\lambda)= M_(\lambda)+5log_(10)d-5+A_(\lambda)`

`=-1.1+5\log_(10)(700)-5+1-1\\\\=9.22`

the apparent visual magnitude of the star lying behind nebula is 9.22

c)

without taking extinction i.e 0, the distance of the star lying just behind nebula is calculated as follows

`m_(\lambda)= M_(\lambda)+5log_(10)d-5`

`d=10^{(m_\lambda-M_(\lambda_5)/5)`

`d=10^((9.22+1.1+5)/5)\\\\=158.79pc`

Thus, without taking extinction , the distance of the star lying just behind nebula is 158.79pc

Compare the distance of nebula measured from earth with consideration of extinction to the distance of nebula without consideration of extinction

`(d_e)/(d) =(700pc)/(1158.8pc)`

= 60.4%

thus, the percentage error in determining the distance if the interstellar extinction neglected is 60.4%