Context :

Aims : Our aims are to quantify the far-infrared line emission from low-mass protostars and the contribution of different atomic and molecular species to the gas cooling budget , to determine the spatial extent of the emission and to investigate the underlying excitation conditions .
Analysis of the line cooling will help us to characterize the evolution of the relevant physical processes as the protostar ages .

Methods : Far-infrared Herschel-PACS spectra of 18 low-mass protostars of various luminosities and evolutionary stages are studied in the context of the WISH key program .

Results : Most of the protostars in our sample show strong atomic and molecular far-infrared emission .
Water is detected in 17 out of 18 objects ( except TMC1A ) , including 5 Class I sources .
CO transitions from J = 14 - 13 up to J = 49 - 48 are found and show two distinct temperature components on Boltzmann diagrams with rotational temperatures of \sim 350 K and \sim 700 K. H _ { 2 } O has typical excitation temperatures of \sim 150 K. Emission from both Class 0 and I sources is usually spatially extended along the outflow direction but with a pattern depending on the species and the transition .
In the extended sources , emission is stronger off source and extended over \geq 10,000 AU scales ; in the compact sample , more than half of the flux originates within 1000 AU of the protostar .
The H _ { 2 } O line fluxes correlate strongly with those of the high - J CO lines , both for the full array and for the central position , as well as with the bolometric luminosity and envelope mass .
They correlate less strongly with OH fluxes and not with [ O i ] fluxes .
In contrast , [ O i ] and OH often peak together at the central position .

Conclusions : The PACS data probe at least two physical components .
The H _ { 2 } O and CO emission likely arises in non-dissociative ( irradiated ) shocks along the outflow walls with a range of pre-shock densities .
Some OH is also associated with this component , likely resulting from H _ { 2 } O photodissociation .
UV-heated gas contributes only a minor fraction to the CO emission observed by PACS , based on the strong correlation between the shock-dominated CO 24-23 line and the CO 14-13 line .
[ O i ] and some of the OH emission probe dissociative shocks in the inner envelope .
The total far-infrared cooling is dominated by H _ { 2 } O and CO , with the fraction contributed by [ O i ] increasing for Class I sources .
Consistent with previous studies , the ratio of total far-infrared line emission over bolometric luminosity decreases with evolutionary state .