An analysis of star formation with Herschel in the Hi-GAL survey. I. The science demonstration phase fields

Aims. The Herschel survey of the Galactic plane (Hi-GAL) provides a unique opportunity to study star formation over large areas of the sky and different environments in the Milky Way. We use the best-studied Hi-GAL fields to date, two 2°·2° tiles centered on (ℓ, b) = (30°, 0°) and (ℓ, b) = (59°, 0°), to study the star formation activity in these regions of the sky using a large sample of well-selected young stellar objects (YSOs). Methods. We used the science demonstration phase Hi-GAL fields, where a tremendous effort has been made to identify the newly formed stars and to derive their properties as accurately as possible, e.g. distance, bolometric luminosity, envelope mass, and stage of evolution. We estimated the star formation rate (SFR) for these fields using the number of candidate YSOs and their average time scale to reach the zero age main sequence, and compared it with the rate estimated using their integrated luminosity at 70 μm, combined with an extragalactic star formation indicator. Results. We measure an SFR of (9.5 ± 4.3) × 10^(-4) M_⊙/yr and (1.6 ± 0.7) × 10^(-4) M_⊙/yr with the source counting method, in ℓ = 30° and ℓ = 59°, respectively. Results with the 70 μm estimator are (2.4 ± 0.4) × 10^(-4) M_⊙/yr and (2.6 ± 1.1) × 10^(-6) M_⊙/yr. Since the 70 μm indicator is derived from averaging extragalactic star forming complexes, we extrapolated of these values to the whole Milky Way and obtain SFR_(MW) = (0.71 ± 0.13) M_⊙/yr from l = 30° and SFR_(MW) = (0.10 ± 0.04) M_⊙/yr from ℓ = 59°. The estimates in ℓ = 30° agree with the most recent results for Galactic star formation activity. Conclusions. The source-counting method gives results that are only valid for the particular region under consideration. In contrast, the construction of the IR indicator leads to results that can be extrapolated to the whole Galaxy. In particular, when it is applied to the ℓ = 30° field, it provides an SFR that is consistent with previous estimates, indicating that the characteristics of this field are very likely close to those of the star formation-dominated galaxies used for its derivation. Since the sky coverage is limited, this analysis will improve when the full Hi-GAL survey is available. It will cover the whole Galactic plane, sampling almost the totality of Galactic star forming complexes. By means of the candidate YSO-counting method, it will then be possible to calibrate an SFR Galactic indicator and to test the validity of the extragalactic estimators