Astrophysics Problem - Effects of cloud on flux density

[Physics Dad]

Hi,

I am attempting the following question:

1. Homework Statement
If the extinction in the infrared K-band (filter central wavelength = 2.13 micrometres) is 10 times less than it is in the optical V-band (filter central wavelength = 550 nanometres), what affect would a cloud of Av = 3 have on the flux density observed in V and K if the stars intrinsic V-band apparent magnitude is 12?

Homework Equations

(i) m₁-m₂=-2.5log(F₁/F₂)
(ii) m_vobs-m_vo=A_v
(iii) F_λ=F/Δλ
(iv) E(K-V)=(K_obs-V_obs)-(K_o-V_o)
(v) E(K-V)=A_k-A_v

A_v=3
m_vo=12

The Attempt at a Solution

OK,

So I know that to start things off, A_k is 10 times less than A_v so A_k=0.1*A_v=0.3. Using this, I can calculate the value of E(K-V) using the known value of A_v and equation (v) to get E(K-V)=-2.7.

I can get the ratio of fluxes from the V-band quite easily, knowing I have the intrinsic apparent magnitude (m_vo), I can rearrange equation (ii) to see that the observed apparent magnitude in the V band (m_vobs) is 15 (12+3).

From here I can simply plug into equation (i) and rearrange for the flux ratio (F_vobs/F_vo) = 0.063

I can also use equation (iv) and the calculated value of E(K-V) to rearrange for m_kobs-m_ko to get this value to = 0.3.

Again, from here I can calculate the ratio of fluxes in the K-band using equation (i) again to find that (F_kobs/F_ko)=0.759.

First of all, I am assuming that this is the right approach and if it is then I am stuck as to what to do next.

Is this as simple as then looking at the ratio of fluxes and multiplying by ΔF_λ?

Am I right in assuming that ΔF_λ is simply 2.13μm-0.55μm=1.58μm?

Any pointers gratefully received!

 

[anathema]

Hello,

Your approach seems to be correct so far. To calculate the flux density in each band, you can use equation (iii) and multiply by the appropriate Δλ for each band. So for the V-band, you would multiply by 550 nm and for the K-band, you would multiply by 2.13 μm. This will give you the flux density in units of J/m^2/μm.

To convert this to a more common unit, such as J/m^2/Hz, you can use the following conversion:
Fν = Fλ * c / λ^2
Where Fν is the flux density in J/m^2/Hz, Fλ is the flux density in J/m^2/μm, c is the speed of light in m/s, and λ is the central wavelength in meters.

Hope this helps! Let me know if you have any other questions.