This page describes the calculations to convert the sunrise outputs to magnitudes or count rates. Note: remember that Sunrise comes with no warranty, and that includes this page. Before using these calculations in your paper, you'd better double check them yourself.

Image units

The Sunrise output images have units of surface brightness. They are generally SI units, which means the units are "W/m/m^2/sr". The first /m comes from the fact that the units are luminosity per wavelength, the /m^2 means it's an energy flux per square meter at the observer, and the /sr means that it is luminosity per steradian. Ie, it's a surface brightness.

The advantage of making the images have units of surface brightness is that it is a distance-independent quantity. So, while the images are made by cameras at a certain distance (set by the cameradistance parameter), the surface brightness is valid for all distances, up to cosmological ones. There is one catch, and that is the cosmological redshift dimming. If you set the redshift parameter when running broadband, this will be taken care of in the images of the filters you have defined. This entails dimming the values by a factor of (1+z)^-5 and shifting the wavelength scale appropriately.

(As an aside, you might want to argue that cosmological surface brightness dimming goes as another power of 1+z. The powers are different whether you are talking about bolometric, nu, or lambda energy units. You'll have to work hard to convince me that it's anything but 5 for the lambda units used in Sunrise.)

To mimic some observation with a particular instrument, you'll need to convert the surface brightness to count rates, which depend on the total flux hitting the pixels. For this, you need first to calculate the solid angle subtended by the pixels when the object is put at the correct redshift. The pixels correspond to a certain physical scale, which you can get from the WCS in the images. To get the solid angle, you then calculate Omega_pix = A_pix/d_A^2, where d_A is the angular diameter distance to the redshift of the object, and A_pix is the physical area of the pixels in the image. By multiplying the pixel values by Omega_pix, you get the flux the object would give on a detector.

What remains is then to change the pixel scale from linear units to angular units. This should be straightforward, again using the angular diameter distance. Once you know the angular scale of the pixels, you can now rebin (while keeping the pixel valuel constant) to the pixel scale of your instrument and calculate a count rate. (Note that to convert the lambda units to nu units, for example if you need to calculate Jy or AB magnitudes, the simplest thing to do is to multiply by the value L_lambda_to_L_nu keyword for the chosen filter (this is in the FILTERS HDU, see BroadbandConfigAndOutputFileFormat).

Integrated absolute AB magnitudes

The broadband FITS files contain absolute AB magnitudes for each filter. The calculation is done in broadband.cc by the integrated_magnitudes function, but it is good to understand what it's doing, especially if you want to convert from the SEDs on your own rather than take magnitudes from the FITS file.

The zero-point for the AB system is 3.63e-20 ergs s^-1 cm^-2 Hz^-1 = 3.63e3 Jy = 3.63e-23 W m^-2 Hz^-1 (the last being Sunrise units). Thus to calculate absolute AB magnitude for a given L_nu (in Sunrise units, W Hz^-1) one uses:

AB = -2.5 log10 [ (L_nu / 4 pi (10 pc)^2 ) / 3.63e-23 W m^-2 Hz^-1 ]

In Sunrise L_nu is in units of W Hz^-1. So, all that's left is to make the units consistent above by adding a factor of (1 pc / 3.09e16 m)^2 inside the brackets. Since 2.5 log10 [ 4 pi (3.09e17)^2 ] = 90.19, we have

AB = -2.5 log10 [ L_nu / 3.63e-23 W Hz^-1 ] + 90.19

--> AB = -2.5 log10 L_nu + 34.09

when L_nu is in Sunrise units (W Hz^-1).