# Wavelengths for observed objects — emitted or observed?

The WISE craft (Widefield Infrared Survey Explorer) surveys the sky in 4 wavelength bands; 3.4, 4.6, 12, and 22 $\mu$m. When it's observing an object with an estimated redshift (given by

$z = \frac{\lambda_{obs} - \lambda_{emit}}{\lambda_{emit}}$

from Wikipedia) of, say, 0.373 (the lowest redshift for one of the objects I'm studying), would the wavelength it's seen in be its observed wavelength? I'm interested in calculating the wavelength actually emitted by the object.

• Your data are observed fluxes (or magnitudes) given the effective wavelengths of the telescope as the observed wavelengths. Simply, rest-frame wavelength = observed wavelength / (1+z). Note that you might also need to do K correction if you simply transform the wavelength like this. Or, you might try to work around by other methods. – Kornpob Bhirombhakdi Aug 7 '18 at 13:40

If the redshift is $z$, then the wavelength of light you observe is at a wavelength that is $1+z$ times longer than the wavelength emitted in the frame of reference of the galaxy.

In this case $z=0.373$, so when you observe light centered on say the 3.4 micron band, then the light was emitted at a wavelength of 3.4/1.373 microns.

The WISE craft (Widefield Infrared Survey Explorer) surveys the sky in 4 wavelength bands; 3.4, 4.6, 12, and 22 $$\mu$$m.

They are only using 3.4 and 4.6 since the coolant ran out. Source: FAQ "The Near-Earth Object Wide-field Infrared Survey Explorer at IPAC".

When it's observing an object with an estimated redshift of, say, 0.373 (the lowest redshift for one of the objects I'm studying), would the wavelength it sees be in its observed wavelength?

Yes, as long as it's within the very wide bandwidth of the imager filters it will be observable at such a small redshift (as long as you don't need the 12 and 22 $$\mu$$m bands, see spectrum below).

Sources/Proof:

• "Optical identifications of high-redshift galaxy clusters from Planck Sunyaev-Zeldovich survey" (Jan 13 2018), by R. A. Burenin, I. F. Bikmaev, I. M. Khamitov, I. A. Zaznobin, G. A. Khorunzhev, M. V. Eselevich, V. L. Afanasyev, S. N. Dodonov, J. A. Rubiño-Martín, N. Aghanim, and R. A. Sunyaev, page 2:

"Clusters located at redshifts below z ≈ 0.6 can be identified using the data of SDSS survey (Rykoff et al., 2014), using additional data from WISE all-sky survey it is possible to identify galaxy clusters at higher redshifts, up to z ≈ 0.7 (Burenin, 2017). To identify clusters at even higher redshifts, deeper direct imaging data in red and near IR bands are required.".

• "An extension of the Planck galaxy cluster catalogue" (Mar 20 2017), by R. A. Burenin, page 3:

"For galaxy cluster observations, the 3.4 µm photometric band is most useful. In this band, distant galaxy clusters are well detected at redshifts up to z ≈ 1–2 (e.g., Burenin, 2015).".

Figure 5a - The QE-based (response per photon) relative system response (RSR) curves normalized to a peak value of unity, on a logarithmic scale.