The K corrections for galaxies of different morphological types are necessary to interpret the magnitude-redshift relation, the luminosity function of galaxies and for most of the spectrophotometric studies of distant objects.
The K correction is defined as the corrective term that needs to be applied to the observed magnitude in a certain band due to the effect of redshift. It does not take into account the effects of galactic evolution; when this cannot be neglected, it is necessary to apply a further correction, the evolutionary one (EC), that can be computed by using spectrophotometric models. Considering the fact that present observations reach high redshifts and progressively fainter magnitudes, establishing the connection between distant and local galaxies requires more and more often the knowledge of the galactic evolution and the use of both the corrections.
A number of authors have previously published tables of K corrections
(Hubble 1936; Humason et al. 1956; Oke & Sandage 1968;
Schild & Oke 1971; Whitford 1971; Oke 1971; Wells 1972;
Pence 1976; Ellis et al. 1977; Code & Welch 1979;
Coleman et al. 1980;
Frei & Gunn 1994). In most of the cases these works are limited
for one
or more of the following aspects: the number of photometric bands,
the number of galactic types, the maximum redshift considered.
Many of the papers mentioned above only deal with ellipticals, that are
considered the best standard candles at high redshifts.
The biggest efforts to supply an extended set of K corrections have
been made from Pence (1976) and Coleman et al. (1980).
Pence computed the K corrections for the 
filters of the
Johnson system and the R Sandage's filter for the following
morphological types; E/S0, Sab, Sbc, Scd, Im with a maximum redshift of
2.18.
Coleman et al. (1980) found K corrections in the 
bands for the bulges
of M 31 and M 81 and for Sbc, Scd, Im with a 
.
Frei & Gunn (1994) have used the energy distribution of Coleman et al.
to compute the K corrections at z=0.1, 0.2, 0.4, 0.6
of E, Sbc, Scd and Im for five photometric systems (Johnson UBV,
Gullixson et al. 
, Thuan and Gunn gri , 
and Cousins RI).
These studies make use of an empirical method: with a software programme, the observed spectral energy distribution of a given morphological type (averaged over a number of objects) is redshifted. The K corrections are then computed from these mean curves and using the filter transmission functions; in this case there is no need to assume a given cosmological model. With this method it is obviously not possible to compute the evolutionary corrections, for which the most direct computing method is making use of a model of spectrophotometric evolution.
Another advantage of using models instead of observations is that,
in order to cover a wide range of redshift,
the latter often requires the connection of observations in
various spectral regions,
most of the times obtained with different instrumentation;
such a connection requires a great accuracy, introduces an
uncertainty and moreover the necessary observations are not always
available.
On the basis of models, Bruzual (1983) calculated the total
corrections (
) and the total magnitudes (including K, EC and
luminosity distance) for the Johnson's 
bands and the
Koo-Kron F band. Bruzual's model did not include the
most advanced stellar evolutionary phases, that dominate the integrated flux
in the ultraviolet (Post-AGB)
and the infrared (AGB) region. From their spectrophotometric model,
Guiderdoni & Rocca-Volmerange (1988)
computed the predicted apparent magnitudes and colours of distant galaxies
for the Johnson 
filters, Koo-Kron 
,
gr from Thuan and Gunn and some broad-band filters from the Faint Object
Camera and the Wide Field Camera of the Hubble Space Telescope, taking into
account also the nebular emission and the internal extinction.
Buzzoni (1995) presented total corrections (
) computed from
an evolutionary synthesis model for an elliptical in the Johnson's 
bands and Gunn gri until a redshift of 1 for different
cosmological parameters.
In this paper both the K and the evolutionary corrections are given
for a set of photometric bands including infrared ones
(
). They are computed from an evolutionary synthesis model and
an attempt has been made to cover a wide range of morphological types
for sufficiently small intervals of redshift up to z=3.