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Formulae

Converting Between F and F

One Jansky (Jy) is defined as 10^-26Wm^-2Hz^-1, so it is a unit of measurement of the spectral flux density, F.

For F in Jy, use the following formula:

F= F/²,

where is the wavelength in microns (µm), and is a constant chosen from Table 12.1 and depending on the units of F. (This is simply derived, using the fact that d/d= c/².)

Table 12.1: Constants for Converting F and F

F measured in

Wm^-2µm^-1

3x10^-12

Wcm^-2µm^-1

3x10^-16

erg sec^-1 cm^-2 µm^-1

3x10^-9

erg sec^-1 cm^-2 Å^-1

3x10^-13

F measured in
Wm^-2µm^-1	3x10^-12
Wcm^-2µm^-1	3x10^-16
erg sec^-1 cm^-2 µm^-1	3x10^-9
erg sec^-1 cm^-2 Å^-1	3x10^-13

Remember that 1W=10⁷erg sec^-1, and 1µm=10⁴Å.

Conversion Between Fluxes and Magnitudes

The spectral flux density F can be calculated from its magnitude as

F= 10^-m/2.5F_o

where m is the magnitude and F_o the zero-point flux for the given photometric band. We list the central wavelengths and zero-point fluxes for the more commonly encountered photometric bands below in Table 12.2. The CIT system was originally based on Beckwith et al (1976, Ap.J., 208, 390); the UKIRT system is in fact based on the original CIT system, but with adjustments made largely owing to different filter bandpasses. It should be noted that for a given photometric band there will be small differences in the effective wavelength and zero-point flux from one observatory to another, and for astronomical objects with radically different colors, so these figures can only be treated as approximate.

Table 12.2: Effective Wavelengths and Zero-points for Photometric Bands

Band

[µm]

Fo[Jy]

(CIT)

Fo[Jy]

(UKIRT)

V

0.56

3540

3540

R

0.70

2870

-

I

0.90

2250

-

J

1.25

1670

1600

H

1.65

980

1020

K

2.2

620

657

L

3.4

280

290

L'

3.74

-

252

M

4.8

150

163

N

10.1

37

39.8

Q

20.0

10

10.4

Band	[µm]	Fo[Jy] (CIT)	Fo[Jy] (UKIRT)
V	0.56	3540	3540
R	0.70	2870	-
I	0.90	2250	-
J	1.25	1670	1600
H	1.65	980	1020
K	2.2	620	657
L	3.4	280	290
L'	3.74	-	252
M	4.8	150	163
N	10.1	37	39.8
Q	20.0	10	10.4

Conversion Between Surface Brightness Units

Surface brightnesses are generally measured in Janskys arcsec^-2, MJy steradian^-1 or magnitudes arcsec^-2. If you have a surface brightness S in MJy steradian^-1, then you can use:

S[Jy arcsec^-2] = S[MJy ster^-1] x 0.084616.

If you have S in magnitudes arcsec^-2, you can simply use the formula and zero-points as given in the previous section for point sources.

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stevens@stsci.edu

Formulae

Converting Between F and F

Table 12.1: Constants for Converting F and F F measured in Wm-2µm-1 3x10-12 Wcm-2µm-1 3x10-16 erg sec-1 cm-2 µm-1 3x10-9 erg sec-1 cm-2 Å-1 3x10-13

F measured in

Conversion Between Fluxes and Magnitudes

Table 12.2: Effective Wavelengths and Zero-points for Photometric Bands Band [µm] Fo[Jy] (CIT) Fo[Jy] (UKIRT) V 0.56 3540 3540 R 0.70 2870 - I 0.90 2250 - J 1.25 1670 1600 H 1.65 980 1020 K 2.2 620 657 L 3.4 280 290 L' 3.74 - 252 M 4.8 150 163 N 10.1 37 39.8 Q 20.0 10 10.4

Band

[µm]

Fo[Jy]

(CIT)

Fo[Jy]

(UKIRT)

Conversion Between Surface Brightness Units

Table 12.1: Constants for Converting F and F

F measured in

Wm^-2µm^-1

3x10^-12

Wcm^-2µm^-1

3x10^-16

erg sec^-1 cm^-2 µm^-1

3x10^-9

erg sec^-1 cm^-2 Å^-1

3x10^-13