Redshift: Spectroscopic and Photometric Techniques

Redshift:

By definition, redshift is the shift in an emission or absorption line with respect to the rest frame estimate of the same line. In this notation, "z" represents the redshift, subscript "o" represents the observed quantity and subscript "e" represents the rest frame quantity and lambda stands for wavelength.

The middle spectrum would be the spectrum seen in the laboratory when the source and observer are not moving with respect to each other.

The top spectrum suggests that the source and the earth are moving toward each other because the lines are shifted to the blue part of the spectrum.

The bottom spectrum suggests that the source and the earth are moving away from one another because the lines are shifted to the red part of the spectrum.

In practice, one needs to identify the emission (absorption) lines wavelength and compare it with rest frame  wavelength using the above formula. This is sometimes called spectroscopic redshift or just redshift for short.

Photometric Redshift:

What do we do when we don't have the spectrum?

Photometric redshifts rely on multiband photometry with broad to medium filters. The more filters the better, but 3-4 are recommended at minimum. Robust photometry is essential for robust photo-z, including identical apertures in all images and corrections for different PSFs.

Artificial Neural Networks technique

• ANNz learns the relation between photometry and redshift from an appropriate training set of galaxies for which the redshift is already known.

The ANNz package is demonstrated on the Sloan Digital Sky Survey Data Release 1, and for this particular data set the r.m.s. redshift error in the range 0 < z < 0.7 is σ_rms = 0.023.

How to use ANNz:

• Step 1 ) Using annz_net to create the Network architecture. We have 4 filters

Number of filters (minimum 1): 4
Number of hidden layers (minimum 1): 2 
Nodes in hidden layer 1: 10 
Nodes in hidden layer 2: 10 
Number of outputs (minimum 1): 1 

==This creates "arch.4.10.10.1.net" ==

recommended to use committee of several networks so we can create:

arch.4.10.10.1.net
arch.4.15.15.1.net
arch.4.20.20.1.net ...

• Step 2 ) Using the trained network above on a test data

annz_train arch.4:10:10:1.net sdss.ugri.train sdss.ugri.valid sdss1.wts -7252
annz_train arch.4:15:15:1.net sdss.ugri.train sdss.ugri.valid sdss2.wts -7252 ...

==This creates the "sdss1.wts" and "sdss2.wts" ==

• Step 3 ) Using annz_train to training the network using the SDSS train set and validation set provided by the code

annz_test data.ugri.test results.set sdss1.wts sdss2.wts 
==This creates the "results.set" ==
==Using committee of 2 networks, sdss1.wts and sdss2.wts== 

Where the file "data.ugri.test" includes 4 magnitudes ugri and then their errors respectively 

Further details of the ANNz method and package are given in:

• Firth, A.E., Lahav, O. & Somerville, R.S., 2003, MNRAS, 339, 1195

• Collister, A. A. & Lahav, O., 2004, PASP, 116, 345 (astro-ph/0311058)