Theoretical HDO emission from low-mass protostellar envelopes

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172 B. Parise et al.: Models of HDO emissionii)These molecules are not observed in the cold gas withlarge abundances measured in the inner regions of theenvelopes surrounding solar-type protostars. Indeed,they are direct and indirect products of the grain mantleevaporation, so that they are linked to the pre-collapsephase.Deuterated molecules observed with extremely large abundances,which can only be formed during the cold, denseand CO depleted phase of the pre-collapse (Roberts &Millar 2000; Roberts et al. 2003). Notable examples areformaldehyde (Ceccarelli et al. 1998), methanol (Pariseet al. 2002, 2004), hydrogenated sulfide (Vastel et al. 2003)and ammonia (Lis et al. 2002; van der Tak et al. 2002).HDO belongs to the second class of molecules, signs of thepast pre-collapse phase. The above-mentioned moleculesshow extremely large deuteration ratios in low mass starformingregions: singly deuterated molecules are morethan 10% of their H-counterparts, whereas doubly andtriply deuterated molecules can respectively be as highas 10% and ∼1%. On the contrary, HDO is only a relativelysmall fraction of H 2 O, about 3% at best (Parise et al. 2005),andnoD 2 O has been detected so far, at relatively low upperlimits to our knowledge (Cernicharo, private communication).The above relative small values agree with thenon-detection of solid HDO in protostars (e.g. Dartoiset al. 2003; Parise et al. 2003). Thus, there is evidencethat water deuteration follows a different route with respectto the other molecules. In addition, the study of theavailable observations in IRAS 16293–2422 suggests thatthe deuteration ratio is not the same in the inner and outerenvelope: 3% and ≤0.2% in the inner and outer enveloperespectively (Parise et al. 2005). Thus, in order to better understandthis difference, one needs to be able to disentanglewhere the different emissions come from. The presentstudy aims at giving a theoretical tool for the estimate ofthe HDO abundance in protostellar envelopes, in the innerand outer regions, and, possibly, the evaporation temperature,and, consequently, at indicating the best observationsto obtain this information. Specifically, given that thesatellite HSO will be launched in 2007, particular care willbe devoted to discussing whether observations with instrumentson this satellite will be required to derive the HDOabundance and evaporation temperature in low mass protostellarenvelopes, compared to observations that can beobtained with ground based telescopes.The paper is organized as follows: we describe the adoptedmodel and code in Sect. 2, we present the HDO molecule aswell as the instruments available to observe its rotational spectrumin Sect. 3. We describe the general characteristics of thepredicted spectrum in Sect. 4 and give the results in Sect. 5for a relatively high (30 L ⊙ )andlow(5L ⊙ ) luminosity case.Section 6 contains a discussion about the best lines to observeto derive the HDO abundance in the inner and outer envelope,as well as the HDO ice evaporation temperature. We also discussthe interest of carrying out space-based versus groundbasedHDO observations to constrain these parameters.2. The model descriptionThe model used to compute the HDO emission in collapsingenvelopes has been adapted from the original model developedby CHT96 to predict the OI, CO and H 2 O line emission,and successively modified to compute the H 2 CO line emission(Ceccarelli et al. 2003). Here we describe the basic assumptionsof the model.The envelope density structure and dynamics are assumedto follow the “inside-out” collapse picture (Shu 1977), for aspherical initial isothermal sphere undergoing collapse. In theouter envelope, not yet affected by the collapse, the molecularhydrogen number density distribution n H2 (r) is given by:n H2 (r) =a 22πµm H G r−2( ) 2= 2.8 × 10 8 ar −20.35 km s −1 100 AU cm−3 (1)where a is the sound speed, m H is the hydrogen mass, µ is themean molecular mass in amu units, equal to 2.8, r 100 AU is thedistance from the center in 100 AU units, and G is the gravitationalconstant. In the inner collapsing regions the density isdescribed by the free-fall solution:n H2 (r) =(1 Ṁ 2 ) 12r− 3 24πµm H 2GM ⋆(2)= 1.2 × 10⎛⎜⎝7 Ṁ−52 ⎞ 12⎟⎠M ⋆ r100 3 AUcm −3 . (3)The free fall velocity is given:( ) 12GM⋆2v(r) =r( ) 1M⋆1 2= 4.2 km s −1 ,r 100 AU(4)where Ṁ is the mass accretion rate, related to the sound speedby( ) 3Ṁ = 0.975 a3G = a10−50.35 km s −1 M ⊙ yr −1 . (5)Ṁ −5 is Ṁ in units of 10 −5 M ⊙ yr −1 ,andM ⋆1 is the mass of thecentral object M ⋆ in units of 1 M ⊙ . The gravitational energyof the collapsed mass is released radiatively as material fallsonto the core radius R ⋆ , so that the luminosity of the centralobject is:L ⋆ = GM ⋆ṀR ⋆= 22( )M⋆M ⊙Ṁ −5 R −112 L ⊙ (6)where R 12 = R ⋆ /10 12 cm.The spherical symmetry is conserved throughout the collapsein this model. In this sense, the model gives accurate resultsonly for that part of the envelope in which spherical symmetryis a good approximation, i.e. probably for radii largerthan a few tens of AUs (Ceccarelli et al. 2000a). At smallerscales large deviations from the spherical symmetry are expectedbecause of the presence of a circumstellar disk.The gas temperature is computed self-consistently byequating the cooling and heating mechanisms at each point
B. Parise et al.: Models of HDO emission 173of the envelope. Details of these calculations can be found inCHT96. The cooling depends on the abundance of the atomicoxygen, CO and H 2 O, namely the main gas coolants across theenvelope. Hence their abundances are hidden parameters of themodel. The resulting gas temperature tracks the dust temperaturevery closely across the envelope, except where the icymantles evaporate. Because of the injection of large quantitiesof water in the gas phase and the consequent enhancement ofthe gas cooling, the gas and dust (thermally) decouple in a relativelysmall region after the icy mantles evaporation (see alsofor example Maret et al. 2002).Ceccarelli et al. (2000a) and Maret et al. (2002) demonstratedthat the gas temperature differs by no more than 10%from the dust temperature, and this occurs in a relatively smallregion just next to where the ices sublimate. There is some uncertaintyabout the water and oxygen abundances in protostars,as derivations of the H 2 O abundance has been obtained in twosources only, IRAS 16293 and NGC 1333–IRAS4 (Ceccarelliet al. 2000a; Maret et al. 2002). However, these uncertainties donot much affect the gas temperature derivation, as in the outerenvelope the gas is cooled mostly by CO 1 , and in the inner envelopeit is cooled by the sublimated water. At the same time, inthe inner region the heating of the gas is dominated by the collisionalde-excitation of the water molecules, photopumped bythe photons emitted by the innermost warm dust (CHT96), sothat the coupling between the dust and gas is always ensured.As a result, the HDO computed line intensity is insensitive tothese uncertainties.The original CHT96 model is time-dependent, but the authorsdemonstrated that the physical structure and water chemistrycan be computed at each time independently of the previoushistory, once the luminosity and the mass of the protostarare known. The reason for this is that in the outer cold envelopethe abundance of the water is practically constant with time,whereas in the inner warm envelope the water abundance is setby the ice evaporation, except in the very inner regions wherethe temperature exceeds 250 K. Since the sizes of the evaporationregion are set by the temperature and the density profile,for practical applications to real sources one needs to inputthem only. The velocity field is also needed to compute the lineintensity, and this can be derived as well from observations.For the standard case described in Sect. 4, we consideredthe case of IRAS 16293, whose velocity, density and temperatureprofiles have been derived by several authors from actualobservations. The computations shown in Figs. 2–7 adopted theprofile derived in Ceccarelli et al. (2000a). We also studied thecase of a low luminosity source, and we used the velocity, densityand temperature profiles derived for the source L1448 mmby Maret et al. (2004).We approximate the HDO abundance profile with a stepfunction. In the outer envelope the HDO abundance, x cold ,is relatively low and similar to that observed in molecularclouds. In the innermost regions of the envelope, wherethe dust reaches the evaporation temperature T evap , the HDO1 The CO lines are optically thick and, therefore, the cooling functiondoes not depend on the CO abundance unless it decreases by afactor of 100 with respect to the standard value.Fig. 1. First energy levels for the HDO molecule.abundance, x warm , jumps to larger values. These last three parameters– x cold , x warm and T evap – are the three free parametersof the present modeling, and they will be varied to study theirinfluence on the HDO line emission.Low-mass protostars exhibit energetic molecular outflows,where the gas can be very hot (up to 2000 K, as testified by theH 2 rovibrational emission observed in several outflows). Thisgas could in principle contribute to the HDO line emission, sothat it is important to evaluate whether the outflow emission canbe comparable to or even larger than the HDO emission fromthe envelope. From a theoretical point of view, since moleculardeuteration decreases exponentially with increasing gastemperature, the HDO abundance is expected to be very lowin the warm gas of molecular outflows (see also Bergin et al.1999). To support these theoretical expectations, observationsof outflows on several low-mass protostars have revealed noHDO emission, at a level at least 10 times fainter than towardsthe protostar (IRAS 16293, Parise et al. 2005; NGC 1333–IRAS2 and IRAS4A, Caux et al. in prep.). We therefore decidedto consider in the present study only the envelope contributionto the HDO emission.All the line fluxes are computed for a source at a distanceof 160 pc. The model computes the level population of the first34 levels of the HDO. The molecular data are from the JPL catalogue(http://spec.jpl.nasa.gov/home.html), and thecollisional coefficients are from Green (1989), for He-HDOcollisions between 50 and 500 K, scaled for collision with H 2 .Note that all abundances are reported here with respect to H 2 .3. The HDO rotational line spectrum3.1. The energy levelsHDO is a planar assymetric top molecule. Its dipole liesalong its a and b axies, with dipole moments µ a = 0.657 andµ b = 1.732 Debye (Clough et al. 1973). The allowed transitionsare thus a-type and b-type transitions:∆K a = 0and∆K c = ±1or∆K a = ±1 and∆K c = ±1.
Page 1: A&A 441, 171-179 (2005)DOI: 10.1051
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Theoretical HDO emission from low-mass protostellar envelopes

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