Unit Conversion - Flux Densities

[deedsy]

Homework Statement

I need to convert from a fv in units of Jy to fλ in units of erg s^-1 cm ^-2 A^-1

fv = 1.0254e-2 Jy

Homework Equations

fv dv = fλ dλ
fλ = fv dv/dλ
and because v = c/λ...

fλ = fv*c / λ^2

Also 1 Jy = 10^-23 erg cm^-2 s^-1 Hz ^-1

The Attempt at a Solution

fλ = [(1.0254e-2 Jy)(10^-23 erg cm^-2 s^-1 Hz ^-1) (3e10 cm/s)(1A/10^-8 cm)] / [1 A^2]

*note: A = angstrom units

my final answer was fλ = 3.0762e-7 erg s^-1 cm^-2 A^-1

But I checked my answer on an online converter and it was wrong, but I don't know why because all my units canceled out correctly.

 

[phyzguy]

You have done the conversion as though your given fv was measured at a wavelength of 1A. I doubt this is the case. When you put in the c/λ^2 factor, you need to do it at the wavelength (frequency) of the measurement. Was this given?

 

[deedsy]

You have done the conversion as though your given fv was measured at a wavelength of 1A. I doubt this is the case. When you put in the c/λ^2 factor, you need to do it at the wavelength (frequency) of the measurement. Was this given?

The first part of the question had us convert a magnitude (12) into fv given a zero point for the magnitude system (fv=647 Jy). So I used m-m0 = -2.5 (f/f0) to solve for f where m0 = 0 and f0 = 647 Jy and m =12. This gave a value of fv = 1.0254e-2 Jy. Then we just have to convert that value into fλ

Here's the question as it appears on the assignment:
Given that the zeropoint of the magnitude system is fv=647 Jy. Find the flux density of a 12th magnitude star in Janskeys (which is in fv) and then convert it to fλ (in units of ergs^-1cm^-2A^-1)(ignore any minus signs in the conversion).That's all the information I have.

 

[phyzguy]

Well, I may be wrong, but I think you have to assume some wavelength to do the conversion. If they are visible magnitudes, I would use the center of the V band, which is at 0.55 μm.