We report on the star formation histories and extinction in the central kpc region of a sample of starburst galaxies that have similar far infrared ( FIR ) , 10 \mu m and K-band luminosities as those of the archetype starburst M 82 .
Our study is based on new optical spectra and previously published K-band photometric data , both sampling the same area around the nucleus .
Model starburst spectra were synthesized as a combination of stellar populations of distinct ages formed over the Hubble time , and were fitted to the observed optical spectra and K-band flux .
The model is able to reproduce simultaneously the equivalent widths of emission and absorption lines , the continuum fluxes between 3500–7000 Å , the K-band and the FIR flux .
We require a minimum of 3 populations — ( 1 ) a young population of age \leq 8 Myr , with its corresponding nebular emission , ( 2 ) an intermediate-age population ( age < 500 Myr ) , and ( 3 ) an old population that forms part of the underlying disk or/and bulge population .
The birthrate parameter , which is defined as the ratio of the current star formation rate to the average past rate , is found to be in the range 1 to 12 .
The contribution of the old population to the K-band luminosity depends on the birthrate parameter and remains above 60 % in the majority of the sample galaxies .
Even in the blue band , the intermediate age and old populations contribute more than 40 % of the total flux in all the cases .
A relatively high contribution from the old stars to the K-band nuclear flux is also apparent from the strength of the 4000 Å break and the Ca ii K line .
The extinction of the old population is found to be around half of that of the young population .
The contribution to the continuum from the relatively old stars has the effect of diluting the emission equivalent widths below the values expected for young bursts .
The mean dilution factors are found to be 5 and 3 for the H \alpha and H \beta lines respectively .