Astronomical data convertion from Jy/pixel to MJy/sr?

For both conversions, you need a bit more information about the data.

1. How can we switch from Jy/pixel to MJy/sr? The Jy -> MJy part is just a factor of $10^{6}$ Jy/MJy. The pixel -> sr (steradian) part requires that you know the angular size of a pixel on the sky. For PACS it looks like the pixel size is different for different wavelengths; see Table 3.1. Once you know the pixel size in arcseconds, then the conversion is 206265 arcseconds / radian (or more precisely, 3600*180/pi). Square the size in radians to get the area in steradians. You also may be able to find the pixel size for your data by looking in the FITS header, if you have FITS images.

2. Is "Jy/beam" equivalent to "Jy/deg^2" or "Jy/sr"? No, but you can convert between the two. Both are flux per angular area on the sky. You need to know the angular area of the telescope beam (e.g. in square degrees, or steradians) and then you can convert between the two.

The README for the ATLAS survey says this about the conversion in their SPIRE maps:

"To convert the maps from Jy/beam to Jy/pixel, in order to carry out aperture photometry, the values in the maps should be divided by the ratio between the beam area and the pixel area in arcsec^2 (469/36, 831/64 and 1804/144 at 250, 350 and 500 microns respectively). The mean of the maps should also be subtracted. Users interested in the most accurate aperture photometry of extended sources should consider scaling the SPIRE fluxes using the K4 corrections for extended sources. They should also consider making an aperture correction."