Astrophysics Problem - Effects of cloud on flux density

  • #1
Hi,

I am attempting the following question:

1. Homework Statement

If the extinction in the infra-red 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) mvobs-mvo=Av
(iii) Fλ=F/Δλ
(iv) E(K-V)=(Kobs-Vobs)-(Ko-Vo)
(v) E(K-V)=Ak-Av

Av=3
mvo=12

The Attempt at a Solution


OK,

So I know that to start things off, Ak is 10 times less than Av so Ak=0.1*Av=0.3. Using this, I can calculate the value of E(K-V) using the known value of Av 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 (mvo), I can rearrange equation (ii) to see that the observed apparent magnitude in the V band (mvobs) is 15 (12+3).

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

I can also use equation (iv) and the calculated value of E(K-V) to rearrange for mkobs-mko 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 (Fkobs/Fko)=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 ΔFλ?

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

Any pointers gratefully received!
 

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