# Astrophysics Problem - Effects of cloud on flux density

In summary, the conversation discusses how to calculate the flux density observed in the V and K bands when a cloud with Av=3 is present and the intrinsic apparent magnitude of the star is 12. The approach involves using equations (i), (ii), (iii), (iv), and (v) to calculate the flux ratio and then converting it to a more common unit using the formula Fν = Fλ * c / λ^2. The conversation also mentions using the appropriate Δλ for each band (550 nm for V-band and 2.13 μm for K-band) in equation (iii) to calculate the flux density.
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) 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?

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.

## 1. How does cloud cover affect the flux density of celestial objects?

Cloud cover can significantly impact the flux density of celestial objects by absorbing, reflecting, and scattering incoming electromagnetic radiation. This leads to a decrease in the amount of radiation that reaches Earth's surface, resulting in a decrease in flux density measurements.

## 2. What types of clouds have the greatest effect on flux density?

Thick, low-lying clouds such as stratus and cumulus clouds have the greatest impact on flux density. These types of clouds are dense and have high water content, making them effective at absorbing and reflecting incoming radiation.

## 3. Can cloud cover also affect the quality of flux density measurements?

Yes, cloud cover can significantly impact the quality of flux density measurements. Due to the absorption and scattering of radiation, the measurements may be distorted or obscured, leading to inaccurate or unreliable results.

## 4. Is there a way to correct for the effects of cloud cover on flux density?

Yes, there are various correction methods that can be used to account for the effects of cloud cover on flux density measurements. These include using atmospheric models, taking measurements at different wavelengths, and using calibration techniques.

## 5. How do scientists account for cloud cover when studying celestial objects?

Scientists use a combination of methods to account for the effects of cloud cover when studying celestial objects. These include using data from satellites, ground-based telescopes, and atmospheric models to correct for the effects of cloud cover on flux density measurements.

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