Obtaining accurate redshifts from mid-infrared ( MIR ) low-resolution ( R \sim 100 ) spectroscopy is challenging because the wavelength resolution is too low to detect narrow lines in most cases .
Yet , the number of degrees of freedom and diversity of spectral features are too high for regular spectral energy distribution ( SED ) fitting techniques to be convenient .
Here we present a new SED-fitting based routine for redshift determination that is optimised for MIR low-resolution spectroscopy .
Its flexible template scaling increases the sensitivity to slope changes and small scale features in the spectrum , while a new selection algorithm called Maximum Combined Pseudo-Likelihood ( MCPL ) provides increased accuracy and a lower number of outliers compared to the standard maximum-likelihood ( ML ) approach .
Unlike ML , MCPL searches for local ( instead of absolute ) maxima of a “ pseudo-likelihood ” ( PL ) function , and combines results obtained for all the templates in the library to weed out spurious redshift solutions .
The capabilities of MCPL are demonstrated by comparing its redshift estimates to those of regular ML and to the optical spectroscopic redshifts of a sample of 491 Spitzer /IRS spectra from extragalactic sources at 0 < z < 3.7 .
MCPL achieves a redshift accuracy \Delta ( z ) / ( 1 + z ) < 0.005 for 78 % of the galaxies in the sample compared to 68 % for ML .
The rate of outliers ( \Delta ( z ) / ( 1 + z ) > 0.02 ) is 14 % for MCPL and 22 % for ML . \chi ^ { 2 } values for ML solutions are found to correlate with the SNR of the spectra , but not with redshift accuracy .
By contrast , the peak value of the normalised combined PL ( \gamma ) is found to provide a good indication on the reliability of the MCPL solution for individual sources .
The accuracy and reliability of the redshifts depends strongly on the MIR SED .
Sources with significant polycyclic aromatic hydrocarbon emission obtain much better results compared to sources dominated by AGN continuum .
Nevertheless , for a given \gamma the frequency of accurate solutions and outliers is largely independent on their SED type .
This reliability indicator for MCPL solutions allows to select subsamples with highly reliable redshifts .
In particular , a \gamma > 0.15 threshold retains 79 % of the sources with \Delta ( z ) / ( 1 + z ) < 0.005 while reducing the outlier rate to 3.8 % .