# General IR astronomy units

Wavelengths in infrared astronomy are commonly expressed in microns = micrometers = µm (or um if you don't have a µ).

• 5000 Å =500 nm =0.5 µm =Visible light
• ~0.9 to 5 µm =Near-infrared (~smoke particles)
• 5 µm to ~30 µm = Mid-infrared (~hair)
• 30 µm to ~350 µm = Far-infrared (~salt grain)

Brightnesses or fluxes are most likely to be given in Janskys (Jy) or mJy (milli Jy) or µJy (micro Jy). 1 Jansky = $10^{-26}$ Watts/m^2/Hz.

Jy can be converted to magnitudes which have historically been relatively rarely used in the mid- or far-infrared.

Because the unit is named for Karl Jansky, the plural of the unit is really Janskys, not Janskies.

# Fluxes and flux densities

Astronomically, it can be important to understand the difference between luminosity, flux, and flux density.

Colloquially, flux means the rate of something through something else, such as water through a pipe, or traffic on a highway. In physics and astronomy, it means basically the same thing, but it has a very specific meaning.

Flux is a measurement of energy per unit area per unit time. Using a traffic analogy, this would be the number of cars per lane per second that pass under a bridge on a highway (or grams of water through the cross-sectional area of a pipe per second). In measuring energy from celestial objects, the units of flux are Joules per second per meter squared if you like mks (meters-kilograms-seconds) units, or ergs per second per centimeter squared if you like cgs (centimeters-grams-seconds) units.

Luminosity is a measurement of energy per unit of time, such as Joules per second if you like mks units, or ergs per second if you like cgs units. This would be, in our traffic analogy, the total number of cars on the highway passing under the bridge per second. (The flux of cars is the luminosity per lane.)

Flux density is a measurement essentially of energy per unit area per unit time "per photon". In our traffic analogy, this would be the number of RED cars per lane per second that pass under the bridge on the highway. In this analogy, the "per photon" is seen in the red cars. In astronomy, the "per photon" manifests itself as a "per Hz" (unit of frequency) or "per cm" (unit of wavelength). A Jansky is proportional to Watts/m^2/Hz. Recall that Watts are energy per second. So this is energy per second per square meter per Hertz.

Now, just to further confuse things, the units of Spitzer and some Herschel mosaics are not just Janskys, but Janskys per area! To make the numbers easier, they are in MJy/sr, but they could also be in uJy/square arcsecond. Read on for more, including definitions and scale factors!

For completeness, we note here that magnitudes are proportional to the log of the ratio of two fluxes. Most magnitudes with which you are most likely familiar are tied to the magnitude of Vega, so a magnitude of 0 means that the object has the same flux as Vega.

Magnitudes has a different wiki page.

# Units of Spitzer and Herschel Images

Optical data with which you are familiar may be in counts or photons, or possibly (like Hubble data) calibrated to be energies. That, combined with the exposure time of the image, gives you flux units. Spitzer data (and some Herschel data) come in flux (density) per unit (pixel) area instead, MegaJanskys per steradian (MJy/sr). 1 MJy = $10^{6}$ Jy, and a sr is a solid angle.

If you've done photometry before, and expect to do it exactly the same way again here, it won't work, because this matters.

1 square arcsec is $2.3504\times 10^{-11}$ sr. (1 degree = 60 arcmin = 3600 arcsec, and a sphere subtends 4pi steradians.

If you want to convert the image from MJy/sr to uJy/square arcsec, multiply the image by 23.5045. The units of this number are (uJy/arcsec)/(MJy/sr).

If you want to take a Spitzer or Herschel image and use your previous routines on it, the most efficient way to do this is probably to take the image in MJy/sr and multiply out the "per sr" part of it so that it is instead in MJy/px. The subtlety in this step is that each Spitzer (or Herschel) detector has different pixel sizes, and the mosaics that we create have different sizes yet again from the original images. You can make mosaics with whatever size pixels you want, so if you get Spitzer(or Herschel) mosaics from more than one astronomer, or more than one Spitzer(or Herschel) wavelength, chances are excellent that the pixels will be slightly different sizes (and for Herschel, maybe slightly different units). The information on the pixel sizes are in the FITS header of each image.

To figure out the pixel size, look in the FITS header of the mosaics for keywords corresponding to pixel size -- they are often "CDELT1" and "CDELT2", but may be "PXSCAL1" and "PXSCAL2" or something else. These keywords are set to be the scale of the rows and columns in degrees per pixel. Using the values of these keywords, and the conversions above, you can figure out the number of square degrees per pixel, the number of square arcsec per pixel, and finally the number of steradians per pixel. Multiply the whole image in MJy/sr by the number of sr/px to get MJy/px.