1 Introduction

The south part of the NGC 1333 reflection nebulae, in the Perseus cloud, is an active star forming region, containing many infrared sources associated with molecular flows and numerous Herbig-Haro objects. IRAS 4 was first identified by Jennings et al. (1987), and further observations (Sandell et al. 1991) revealed IRAS 4 it was a binary system resolved into two components, named IRAS 4A and IRAS 4B, and separated by 31 $\hbox{$^{\prime\prime}$ }$. Interferometric observations (Lay et al. 1995; Looney et al. 2000) have shown further multiplicity of the two sources. IRAS 4A is itself a binary system with a separation of 10 $^{\prime\prime}$, and there is some evidences that IRAS 4B could also be a multiple system, with a separation of 0.5 $^{\prime\prime}$.

The distance of the NGC 1333 cloud is much debated. Herbig & Jones (1983) found a distance of 350 pc for the Perseus OB2 association (a more recent estimate based on the Hipparcos data gives $318\pm 27$; de Zeeuw et al. 1999), but extinction observations towards NGC1333 itself (Cernis 1990) suggest that it may be as close as 220 pc. Assuming a distance of 350 pc, Sandell et al. (1991) measured a system total luminosity of 28  ${L}_{\odot}$ (11  ${L}_{\odot}$ at 220 pc) equally shared between IRAS 4A and B. They derived an envelope mass of 9 and 4  ${M}_{\odot }$ respectively (3.5 and 1.5  ${M}_{\odot }$ at 220 pc). This relatively large mass, together with the low bolometric luminosity suggest that both sources are deeply embedded and probably very young. They have been classified as Class 0 sources (Andre et al. 1993). IRAS 4A and B are both associated with molecular outflows, detected in CO, CS (Blake et al. 1995) and SiO (Lefloch et al. 1998) millimeter transitions. The outflow originating from IRAS 4A is very highly collimated, whereas that originating from IRAS 4B is rather compact and unresolved in single dish observations (Knee & Sandell 2000). The dynamical ages of both outflows are a few thousands years.

In the past years, many observational studies have been focused on the continuum emission of IRAS 4. Recent works include maps of the region obtained with IRAM at 1.3 mm (Lefloch et al. 1998) and with SCUBA at 450 and 850 $\mu$m (Sandell & Knee 2001). An accurate modeling of the continuum emission has been very recently carried out by Jørgensen et al. (hereafter JSD02, 2002), who reconstructed the dust temperature and density profiles across the two envelopes.

The molecular line emission is probably a better and certainly a complementary tool to probe the dynamical, chemical and physical structure of the envelopes of IRAS 4. The last decade has seen flourishing several studies of molecular line profiles (e.g. Gregersen et al. 1997; Evans 1999) and line spectra (Blake et al. 1995), all having in common the goal of reconstructing the physical structure of the protostellar envelopes. Specifically, Blake et al. (1995) carried out a multifrequency study of several molecules in IRAS 4, including H₂CO and CH₃OH. Their two major results regarding the structure of the IRAS 4 envelopes are: 1) a large depletion, around a factor 10-20, of CO and all molecules in the envelope, and 2) the presence of a region with an increased abundance of CS, SiO and CH₃OH, that the authors attribute to mantles desorption caused by grain-grain collisions induced by the outflows originating from the two protostars. More recently interferometric observations by Di Francesco et al. (2001, see also, Choi et al. 1999) detected an inverse P-cygni profile of the H₂CO 3_2,1-2_1,1 line on a 2''scale towards both IRAS 4A and B, providing the least ambiguous evidence of infall motion towards a protostar ever. From a simple two-layer modeling, they derived an accretion rate of $1.1 \times 10^{-4}$ and $3.7 \times 10^{-5}$  ${M}_{\odot }$ $~{\rm yr}^{-1}$, an inner mass of 0.7 and 0.2  ${M}_{\odot }$, and an age of 6500 and 6200 yr (assuming constant accretion rate) for IRAS 4A and IRAS 4B respectively.

In this paper we concentrate on the far infrared (FIR) line spectrum, and in particular the water line spectrum observed with the Long Wavelength Spectrometer (Clegg et al. 1996, herein after LWS) on board ISO (Kessler et al. 1996) in the direction of IRAS 4. The goal of this study is to check whether the observed water line emission can be attributed to the thermal emission of the envelopes surrounding the IRAS 4 protobinary system. Water lines have in fact been predicted to be a major coolant of the gas in the collapsing envelopes of low-mass protostars (Ceccarelli et al. 1996, hereafter CHT96; Doty & Neufeld 1997). Given the relatively large range of level energies (from $\sim$100 to $\sim$500 K) and spontaneous emission coefficients (from 10^-2 to $\sim$1 s^-1) of the water transitions observed by ISO-LWS, the observed lines can in particular probe the innermost regions of the envelope. This makes the analysis of the ISO-LWS water lines a precious and almost unique tool (when considering the water abundance across the envelope). The reverse of the coin is that assessing the actual origin of the water emission is somewhat difficult and still debated, as the spectral and spatial resolutions of ISO-LWS are relatively poor to disentangle the various components falling into the beam. For example, strong molecular line emission is often associated with the outflows emanating from young protostars (e.g. Bachiller & Perez Gutierrez 1997). As already mentioned, the line emission from CO, CS and other molecules are certainly contaminated by the outflowing gas in IRAS 4. Nonetheless, low lying lines seem to be more affected than high lying lines in first instance, and different molecules suffer differently from this "contamination'', as proved by the Di Francesco et al. (2001) observations. Although water has been predicted to be very abundant in shocked gas, the published ISO observations show that the water emission is usually stronger towards the central sources and weaker, if detected at all, in the direction of the peaks of the outflows powered by low mass protostars (see Ceccarelli et al. 2000a, for a review). When water lines are detected in clear-cut shocked regions, the water abundance seems to be lower than that predicted by the models, like in the case of HH54 (Liseau et al. 1996) or HH7-11 (Molinari et al. 1999; Molinari et al. 2000), or in the outflows of IRAS 4 (see next section). Finally, SWAS observations seem to support the evidence that the water abundance in the shocked regions is a few times 10^-6 (Neufeld et al. 2000). These facts, together with the apparent correlation between the observed water emission and the 1.3 mm continuum, and the lack of correlation with SiO emission in low mass protostars (Ceccarelli et al. 1999) play in favor of a relatively low contamination of the ISO-LWS observed water emission by the outflow and encourage us to explore in detail this hypothesis for the IRAS 4.

In the specific case of IRAS 4, the Submillimiter Wavelengths Astronomical Satellite (SWAS; Melnick et al. 2000) observed the ground o-H₂O line at 557 GHz (Neufeld et al. 2000; Bergin et al. 2002). Given its relatively large linewidth ($\sim$18 km s^-1) the 557 GHz line is certainly dominated by the outflow emission. Nonetheless, this does not imply that the ISO FIR water lines also originate in the outflow, and this for two reasons. First, the beamwidth ($\sim$4') of the SWAS observations, being about 3 times that of ISO-LWS, encompasses the entire outflow, whereas the ISO observations do not encompass the two emission peaks of the outflow (see also 3.1), but only the envelope. Second, the 557 GHz transition, being the water ground transition, is more easily excited than the FIR water lines, and therefore the latter probably probe different regions. In fact, Bergin et al. (2002) find that most of the 557 GHz line must originate in a component colder, hence different, by that probed by the FIR water lines, even under the assumption that they probe the outflow. To summarize, decicing whether the observed FIR water emission in IRAS 4 originates in the outflow or in the envelope remains an open question, based on the available present observations. In this article we explore in detail the latter hypothesis and submit it to the scrutiny of an accurate modeling, trying hence to answer to the question on a theoretical basis. At this scope we used the CHT96 model, already successfully applied to the solar type protostar IRAS 16293-2422 which allowed to explain more than two dozen observed ISO-LWS water lines and ground-based millimeter SiO and H₂CO lines (Ceccarelli et al. 2000a; Ceccarelli et al. 2000b). One of the major results of that work is the prediction of the existence of a hot core like region in the innermost part of the envelope of IRAS 16293-2422, in which the dust temperature exceeds the evaporation temperature of interstellar ice ($\simeq$100 K). These studies have been confirmed by the recent analysis by Schöier et al. (2002) of several other molecular transitions. Such hot cores are well studied around massive protostars where - driven by reactions among the evaporated ice molecules in the warm gas - their chemical composition differs substantially from that of quiescent clouds (Walmsley 1989; Charnley et al. 1992). Hot cores around low mass protostars may actually have a different chemical composition (Ceccarelli et al. 2000b). This molecular complexity may be of prime interest on account of a possible link to the chemical history of the solar nebula and hence the molecular inventory available to the forming Earth and other solar system planets and satellites.

In order to understand the physical and chemical processes that take place during the first stages of star formation, it would be necessary to undertake a work similar to that the one done on IRAS 16293-2422 on a larger sample of protostars. In this paper we present a study of the structure of the envelope of NGC 1333-IRAS 4, obtained using ISO-LWS observations of the H₂O far-infrared lines. A preliminary analysis of the same set of data has already been presented in Ceccarelli et al. (1999) and Caux et al. (1999a). Here we revisit the data using a new calibration and compare the observations with the CHT96 model predictions, testing a large range of model parameters. This study is part of a large project aimed to model the water emission in several low mass protostars. The water observations are complemented with formaldehyde and methanol ground based observations, to have a complete budget of the most abundant molecules in the innermost regions of the protostellar envelopes (Maret et al. in preparation). Finally, the structure obtained by the analysis of these observations will be compared with that independently obtained by continuum observations by JSD02.

The outline of the article is the following. In Sect. 2 we present the data, in Sect. 3 we describe the modeling of the observed lines and in Sect. 4 we discuss the physical and chemical structure of the envelope, namely the density and temperature profiles, as well as the abundances of the major species across the envelope. Besides, the central mass of the protostar and its accretion rate can also be constrained by these observations and modeling, yielding an alternative method to measure these two key parameters. In Sect. 4 we compare the results of the present study with previous studies of IRAS 4. Finally, we discuss the similarities and differences between IRAS 4 and IRAS 16293-2422, and highlight the importance of complementary ground-based, higher spatial and spectral resolution observations to understand the physical and chemical processes taking place in the innermost regions of low-mass envelopes.