★ Sándor Demes

François Lique
email: francois.lique@univ-rennes1.fr

Alexandre Faure

Floris F S Van Der Tak

An accurate set of H 3 O + -H 2 collisional rate coefficients for non-LTE modelling of warm interstellar clouds

Keywords: molecular processes -molecular data -methods, laboratory, molecular -astrochemistry -ISM, moleculesradiative transfer

Hydronium (H 3 O + ) was first detected in 1986 in interstellar molecular clouds. It was reported in many galactic diffuse and dense regions, as well as in extragalactic sources. H 3 O + plays a major role both in interstellar oxygen and water chemistry. However, despite the large number of H 3 O + observations, its collisional excitation was investigated only partially. In the present work we study the state-to-state rotational de-excitation of ortho-and para-H 3 O + in collisions both with ortho-and para-H 2 . The cross sections are calculated within the close-coupling formalism using a highly accurate potential energy surface developed for this system. The rate coefficients are computed up to 300 K kinetic temperature. Transitions between the lowest 21 rotation-inversion states were studied for para-H 3 O + , and the lowest 11 states for ortho-H 3 O + , i.e. all levels with rotational energies below 430 K (∼ 300 cm -1 ) are considered (up to 𝑗 ⩽ 5). In order to estimate the impact of the new rate coefficients on the astrophysical models for H 3 O + , radiative transfer calculations were also carried out. We have examined how the new collisional data affect the line intensities with respect to older data previously used for the interpretation of observations. By analysing all detected transitions we find that our new, accurate rate coefficients have a significant impact (typically within a factor of 2) on radiation temperatures, allowing more accurate estimation of column densities and relative abundances of hydronium, especially in warm molecular clouds, paving the path towards better interpretation of interstellar water and oxygen chemistry.

INTRODUCTION

The presence of the hydronium cation (H 3 O + ) in various interstellar molecular clouds was reported by many observational research papers, including its prediction in a fundamental work by Herbst & Klemperer (1973) followed by the first nearly simultaneous observations in 1986 by Wootten et al. (1986) and Hollis et al. (1986), then the confirming detections in the 90s of the past century (Wootten et al. 1991;Phillips et al. 1992;Timmermann et al. 1996), and later in early 2000s by van der Tak et al. (2006van der Tak et al. ( , 2008)). In the 2010s there were several new observations of H 3 O + reported in different interstellar environments (Benz et al. 2010;Gerin et al. 2010;González-Alfonso et al. 2013;Lis et al. 2014;Indriolo et al. 2015;Benz et al. 2016;Ando et al. 2017), while the most recent studies were published by Martín et al. (2021) and Holdship et al. (2022). The existing observational detections of hydronium will be reviewed thoroughly in Section 2. Chemical models involving hydronium were also developed intensively, as one can see, for example, in the works of Sternberg & Dalgarno (1995); Goicoechea & Cernicharo (2001); Hollenbach et al. (2012); van Dishoeck et al. (2013); Faure et al. (2019), which all reported that it plays a key role in oxygen and water or D (van der Tak et al. 2009). In interstellar clouds, such splitting may be observed for the H 3 O + isotopologues H 17 3 O + and H 2 DO + . Its electron-impact excitation was studied also earlier (Faure & Tennyson 2003). The collisional excitation studies of hydronium are very limited however. The first, approximated collisional cross section were provided by Offer & van Hemert (1992), which has given a basis then for interpreting the observations of H 3 O + in both dense and diffuse interstellar clouds. However the authors did not report rate coefficients, so their data were scaled in combination with NH 3 collisional data of Danby et al. (1988). Later El Hanini et al. (2019) studied the rotational excitation of hydronium by helium atoms (as a template for H 2 ), but for a limited energy and temperature range (up to 50 K). Recently we have computed state-to-state collisional rate coefficients up to 100 K for the rotational excitation of both 𝑜𝑟𝑡ℎ𝑜and 𝑝𝑎𝑟𝑎-H 3 O + in collision with 𝑝𝑎𝑟𝑎-H 2 (Demes et al. 2021). A detailed discussion about the previous collisional excitation studies (Offer & van Hemert 1992;El Hanini et al. 2019) was already given in this work, including a comparative analysis of the cross sections and rate coefficients.

It is worth to emphasise again that, according to the authors of several observational studies (see, for example, the works by Wootten et al. (1991); van der Tak et al. (2008)) reliable and precise collisional rate coefficients are needed to correctly interpret the astrophysical observations of H 3 O + in ISM clouds. Without such data the molecular abundances could be only approximated, assuming local thermodynamic equilibrium (LTE), which is usually not a good approximation for typical interstellar conditions (Roueff & Lique 2013).

In the present work we provide a complete set of rotational excitation cross sections and thermal rate coefficients for the H 3 O + -H 2 collisional system, which are calculated based on an accurate 5-dimensional interaction potential (Demes et al. (2020), referred as Paper I hereinafter). The new collisional data presented here have several crucial improvements compared to Paper II: the calculations are extended to ortho-H 2 , and we compute accurate rate coefficients up to 300 K (over 100 K in Paper II). To demonstrate the impact of the new collisional data on radiative transfer calculations are provided as well and their results obtained with different sets of rate coefficients are compared.

The paper is organised as follows: In Section 2 the literature of the H 3 O + observations is reviewed in a chronological order. In Section 3 the details of the interaction potential as well as the scattering calculations are presented. The state-to-state collisional data for the rotational de-excitation of H 3 O + by H 2 are discussed in Section 4, where subsection 4.1 introduces the cross section and subsection 4.2 presents the thermal rate coefficients, respectively. In Section 5 we also report radiative transfer calculation results, while our concluding remarks are drawn in Section 6.

OBSERVATIONAL DETECTIONS OF H 3 O +

The first prediction of the presence of H 3 O + in dense molecular clouds of the Orion/KL and Sgr B2 regions (where the approximate hydrogen density is ∼ 10 6 cm -3 ) was given by Herbst & Klemperer (1973). More than a decade later Wootten et al. (1986) and Hollis et al. (1986) almost simultaneously reported the first detections. Both groups used the NRAO 12 m telescope and both measured the 307.2 GHz emission line in the OMC-1 and Sgr B2 sources. The confirming detection was reported soon by Wootten et al. (1991) in the same environments with the identification of the 3 + 2 → 2 - 2 transition of ortho-H 3 O + at 364 GHz (note that the rotational states of H 3 O + are denoted by 𝑗 𝜖 𝑘 , where 𝑗 is the total angular momentum, 𝑘 is its projection on the 𝐶 3 main rotational axis, and 𝜖 = ± is the inversion symmetry index, see Rist et al. (1993) for more details). In these first observations the authors reported kinetic temperatures above 70 K with an H 2 density of about 10 6 cm -3 and they also emphasise the importance of a non-local thermodynamic equilibrium (non-LTE) analysis, since the low excitation temperature of H 3 O + are poorly described in an LTE approach (which was the only available model for H 3 O + at that time due to the lack of collisional data). Later Phillips et al. (1992) reported a more clear detection of three -396, 364 and 307 GHz -submillimeter lines in more than 10 galactic sources, besides the spectroscopically confusing OMC-1 and Sgr B2 clouds, the G34.3+0.15 and W51 clouds as well as different highmass star formation regions, for example the W3 IRS 5 cloud. Most of them are exhibiting high-density (𝑛 H 2 ≈ 10 6 -10 7 cm -3 ) and high temperature (𝑇 kin ≳ 50 K) conditions. The authors found that the typical H 3 O + abundance is 10 -10 -10 -9 in these regions. The 4 - 3 → 3 + 3 far-infrared emission line of H 3 O + at 69.524 𝜇m (4312 GHz) was measured soon after by Timmermann et al. (1996) in the Orion BN-IRc2 region with NASA's Kuiper Airborne Observatory. The authors reported it as a possible H 3 O + detection, which might originate from very dense clumps. They also reported high hydrogen densities (≳ 5 × 10 8 cm -3 ) and temperatures (≳ 100 K) in this environment. For their model and analysis the authors used scaled, approximated collisional rate coefficients based on the work of Offer & van Hemert (1992), and they estimated the column densities of H 3 O + in the range from 9 × 10 13 cm -2 (under LTE conditions and 300 K) up to 7 × 10 16 cm -2 (under non-LTE conditions and 𝑇 = 100 K).

Ten years later van der Tak et al. ( 2006) detected strong emission in the H 3 O + 364 GHz and 307 GHz lines both in the M core and OH envelope of the Sgr B2 region with the APEX telescope. The authors reported column densities in the range between 3.7 × 10 15 and 1.36 × 10 16 cm -2 in the envelope and in the core, respectively and they found the hydronium abundance to be ∼ 3 × 10 -9 relative to H 2 and the H 3 O + /H 2 O ratio to be about 1/50 in this region. The physical conditions in the M core are 𝑇 = 200 K and 𝑛 H 2 = 10 7 cm -3 , while in the low-density OH envelope the temperature is about 60 K only and the H 2 density is 10 6 cm -3 . Later hydronium was detected in extragalactic environments as well by van der Tak et al. (2008). Observations with the JCMT targeted the well-known 364 GHz emission line of the 3 + 2 → 2 - 2 transition in the centers of M 82 and Arp 220, where the expected kinetic temperature is ∼ 100 K and the hydrogen density is at least 10 5 cm -3 . With an estimated 𝑝𝑎𝑟𝑎-H 3 O + column density of 0.7 -1.3 × 10 13 cm -2 for Arp 220 and 3.0-5.5×10 13 cm -2 for M 82, the authors found that the typical hydronium abundance is 2 -10 × 10 -9 relative to H 2 . For radiative transfer modelling of these environments both in the work of van der Tak et al. (2006) and van der Tak et al. (2008) the scaled collisional data were derived from Offer & van Hemert (1992) and Danby et al. (1988).

The W3 IRS 5 cloud was later studied by Benz et al. (2010), searching for the major hydrides in this region of the ISM. The authors detected several rotational transitions of H 3 O + in this high-mass star-forming region using HIFI on the Herschel Space Observatory. Emissions from the 4

+ 3 → 3 - 3 (1031.3 GHz), 4 - 2 → 3 + 2 (1069.8 GHz), 6 + 2 → 6 - 2 (1454.6 GHz) and 2 + 1 → 2 - 1 (1632.
1 GHz) 𝑜𝑟𝑡ℎ𝑜and 𝑝𝑎𝑟𝑎-H 3 O + transitions were measured. The authors found the column density is typically about 10 14 cm -2 , and the corresponding hydronium abundance is 4.2(±1)×10 -10 relative to atomic hydrogen. The gas density of the environment exceeds 10 7 cm -3 , and the rotational temperature is about 205 -285 K (the gas temperature can be even higher). In parallel a weak 984 GHz absorption line of H 3 O + was also detected with the HIFI/Herschel along the massive starforming region G10.6-0.4 (W31C) (Gerin et al. 2010). The authors derived the hydronium column density 𝑁(H 3 O + ) ∼ 4 × 10 13 cm -2 for the 𝑉 LSR velocity range of 7 -45 km s -1 . According to Gerin et al. (2010) in this diffuse cloud the hydrogen density is only about 10 2 -10 3 cm -3 and the temperature can be as low as 5 K.

González-Alfonso et al. ( 2013) also reported excited hydronium in the extragalactic NGC 4418 and Arp 220 regions based on Herschel/PACS observations. The column density of H 3 O + is found to be about (0.9 -2.7) × 10 16 cm -2 in Arp 220, and the observed pure inversion, metastable lines have a very high rotational temperature of ∼ 500 K. The authors characterise the source as a relatively low density (≳ 10 4 cm -3 ) interclump medium. They presented the detection of a series of lines of hydronium in the 70 -180 𝜇m spectral range, involving several states with 𝑗 = 2 -5 rotational quantum numbers and above. It is also shown by González-Alfonso et al. ( 2013) that the states with 𝐾 > 1 projection quantum numbers can be populated only through collisions or via molecular formation in high-lying levels. The authors still used scaled rate coefficients based on the data from Offer & van Hemert (1992) and Danby et al. (1988) for non-LTE modelling of the H 3 O + excitation. In the NGC 4418 source the work reports (5 -8) × 10 15 cm -2 column densities and 𝑇 gas ∼ 150 K for the transitions from lower 𝐾 ⩽ 5 as well as 𝑇 gas ∼ 500 K for the ones from higher rotational states . Just a year later Lis et al. (2014) presented the results of Herschel observations of the 6 - 6 → 6 + 6 and 9 - 9 → 9 + 9 inversion transitions of hot hydronium toward the diffuse Sagittarius B2(N) and W31C sources, with estimated column densities of 7 × 10 14 cm -2 and 1.2 × 10 13 cm -2 , respectively. The authors report rotational temperatures of about 500 K and 380 K, so the kinetic temperature can reach 400 -600 K. The next Herschel observation of H 3 O + was presented by Indriolo et al. (2015) for diffuse interstellar clouds along 20 Galactic sight lines toward bright submillimeter continuum sources. The authors measured the 1 - 1 → 1 + 1 (1655.8 GHz) transition in absorption and the 0 - 0 → 1 + 0 (984.7 GHz) line in emission and they derived column densities in the range from 3 × 10 14 up to 1.66 × 10 13 cm -2 depending on the source. The authors suggested a kinetic temperature of 100 K, which represents the average temperature in diffuse clouds, and they considered hydrogen densities as low as 35 cm -3 . Another observation by Herschel (Benz et al. 2016) reported the 4 + 3 → 3 - 3 (1031.3 GHz) emission line of 𝑜𝑟𝑡ℎ𝑜-H 3 O + in several young stellar objects. The authors considered a wide range of gas densities (10 4 -10 6 cm -3 ) and kinetic temperatures (from 10 K up to several hundreds of K).

Emission from the 3 + 2 → 2 - 2 line of H 3 O + (364 GHz) was detected again recently by Ando et al. (2017) in the starburst galaxy NGC 253, based on ALMA Band 7 observations. According to the authors, this is a dense (𝑛 H 2 ⩾ 10 6 cm -3 ) and hot environment with typical kinetic temperatures ⩾ 100 K. The latest observations of hydronium were reported by Holdship et al. (2022) within the ALMA Comprehensive High-Resolution Extragalactic Molecular Inventory. The research has targeted the central molecular zone of the extragalactic NGC 253 source, studying the impact of cosmic-ray ionization rates on the abundance ratio of H 3 O + and SO. The authors estimated the fractional abundance of hydronium to be about 5 × 10 -10 -10 -9 . They varied the gas density and temperature in a wide range, respectively from 10 4 to 10 7 cm -3 and from 50 up to 300 K. Their analysis was performed based on the well-studied 364 GHz (3 + 2 → 2 - 2 ) and 307 GHz (1 + 1 → 2 + 1 ) transitions of H 3 O + , leading to a conclusion that the H 2 density most likely vary between 0.4 -9.8 × 10 5 cm -3 depending on the source.

METHODS

In Paper II we described the relevant approach of the scattering calculations. Here we briefly summarise the most important points and provide the details for the new calculations that are presented in this paper.

Potential energy surface

The scattering calculations were performed using our recent 5D rigidrotor potential energy surface (Paper I) for the H 3 O + -H 2 interaction. This potential was calculated by the rigorously tested and very accurate CCSD(T)-F12 (explicitly correlated coupled-cluster theory with singles and doubles with perturbative corrections for triple excitations) ab initio theory with a moderate-size aug-cc-pVTZ (augmented correlation-consistent polarised valence-triple-𝜁) basis set. This combination of method + basis set ensures the necessary high quality of the PES with a reasonable computational cost.

The collisional system is defined in a Jacobi coordinate system using the molecular frame (body-fixed) representation. Consequently, the center of the coordinate system is set in the center of mass (c.o.m.) of the target H 3 O + cation. One spatial parameter (𝑅) defines the distance between the colliders, while four spherical angles describe the position and relative orientation of the H 2 projectile with respect to the origin of the coordinate system. The H 2 bond length was set at 𝑟 H-H = 1.44874 a 0 (Bubin & Adamowicz 2003), and for H 3 O + we used the experimental bond properties by Tang & Oka (1999):

𝑟 O-H = 1.8406 a 0 and 𝛼 H-O-H = 113.6 • .
The ab initio PES was fitted using a standard least square procedure, resulting in a set of 208 radial expansion functions for each 𝑅, with anisotropies up to 𝑙 1 = 16 and 𝑙 2 = 4. The root mean square (rms) residual was found to be lower than 1 cm -1 in the long-range of the potential and also in the well region (which is about 1887.2 cm -1 deep). The rms error on the expansion coefficients was also found to be smaller than 1 cm -1 in these regions of the PES. A cubic spline interpolation of the analytical coefficients was performed using for distances between 𝑅 = 4 -30 a 0 and it was smoothly connected then to standard extrapolations using the switch function proposed by Valiron et al. (2008). Since there is no experimental observables for the H 3 O + -H 2 system, we cannot assess the accuracy of our interaction potential. However, from similar PES calculations by Faure et al. (2016); Pirlot et al. (2021); Godard Palluet et al. (2022), where the accuracy of the potential was estimated based on a comparison with experimental dissociation and/or bound states energies, we expect that its overall accuracy is at the wavenumber level of accuracy and is always better than 10 per cents. For full details about the interaction potential and the analytical fit, see Paper I.

We used the following units throughout this paper (until otherwise noted): atomic units (a 0 ) for distances (1 a 0 = 1 bohr ≈ 5.29177×10 -9 cm), wavenumbers ( cm -1 ) for energies (1 cm -1 ≈ 1.4388 K).

Scattering calculations

We have calculated the state-to-state rotational de-excitation cross sections and thermal rate coefficients for the collision of ortho-and para-H 3 O + with para-H 2 in our previous work (Demes et al. 2021). This work is an extension of the previous one with several crucial improvements. First, we have studied all the possible nuclear spin isomers, so the calculations are extended to collisions with ortho-H 2 as well, which is the dominant collider in interstellar clouds with temperatures above 100 K. Second, we have significantly increased the interval of collision energies for the cross section calculations, which allowed us to compute accurate rate coefficients up to 300 K. These improved collisional data allows one to provide a precise non-LTE modelling for warm molecular clouds involving H 3 O + (see, for example, the observations by van der Tak et al. (2008) at several hundred Kelvins).

In current work we determined the cross sections by the full quantum (close-coupling, CC) approach using the HIBRIDON scattering code (Manolopoulos 1986;Alexander & Manolopoulos 1987). They were computed up to 1700 cm -1 total energies for H 3 O + collisions with o-H 2 and up to 1500 cm -1 total energies for collisions with p-H 2 . The o-H 3 O + spin species is characterised with 𝑘 = 3𝑛 quantum numbers (where 𝑛 are integer numbers), while all other 𝑘 quantum numbers refer to p-H 3 O + .

We computed all inelastic cross sections for the transitions between rotational levels with an internal energy of ⩽ 430 K (∼ 300 cm -1 ), including states up to 5 + 2 for p-H 3 O + and 5 + 3 for p-H 3 O + . For the full list of the rotational states involved for H 3 O + , see Table A1 in Appendix A. Both the rotational basis ( 𝑗 max ) and the maximum total angular momentum (𝐽 tot ) were selected depending on the nuclear spin symmetry and collision energy. Their particular values are set based on preliminary convergence test calculations with the following convergence-threshold criteria: maximum 1% mean deviation for 𝑗 max and 0.01% mean deviation for 𝐽 tot . As discussed in Paper II, in order to adequately describe the strong resonances in the cross sections, a very small step size (𝐸 step = 0.1 cm -1 ) was chosen at low collision energies, which was gradually increased then. The values of the 𝑗 max , 𝐽 tot and 𝐸 step parameters, which were used in the calculations for the particular total energy intervals from 𝐸 init to 𝐸 fin are listed in Tables B1 andB2 of Appendix B. The values of 𝑗 max here refer to the highest rotational states of the H 3 O + cation used in the CC calculations. For the H 2 projectile the two lowest rotational states were considered in the scattering calculations, i.e. 𝑗 H 2 = 0, 2 for p-H 2 and 𝑗 H 2 = 1, 3 for o-H 2 . The convergence test calculations have shown that the 𝑗 H 2 = 2 and 3 excited states of H 2 have a significant effect on the cross sections' magnitude, and should not be neglected in the CC calculations. For a few energies we performed scattering calculations with a larger H 2 rotational basis as well ( 𝑗 H 2 = 0 -5). We found that the impact from these additional hydrogen levels is usually not too large, they have a ∼ 5% effect on the magnitude of the cross sections in general, which decreases with increasing collision energy. The largest relative difference detected in the collisional data calculated with this extended basis compared to what was computed in the systematic CC calculations is ∼ 25%. Even the 𝑗 H 2 = 0 -3 basis is very large however, which makes the systematic quantum calculations extremely demanding computationally, especially in the case of the p-H 3 O + target molecule, which is characterised with two times more levels than o-H 3 O + if the same internal energy is considered. Thus, for example, for the p-H 3 O +o-H 2 collision in the high energy regime (⩾ 1450 cm -1 ) the number of coupled channels exceeded 8000, for which the computational cost to calculate the cross sections for a defined total energy reaches several thousands of CPUhours. According to our estimations, about 600.000 CPU-hours were spent in total for the calculation of all H 3 O + -H 2 cross sections.

The rate coefficients were computed up to 300 K kinetic temperatures following the well-known integration method over a Maxwell-Boltzmann distribution of relative velocities:

𝑘 i→f (𝑇) = 8 𝜋𝜇𝑘 3 B 𝑇 3 1 2 ∫ ∞ 0 𝜎 i→f 𝐸 c 𝑒 -𝐸c 𝑘 B 𝑇 𝑑𝐸 c , (1)
where 𝐸 c is the collision or kinetic energy, 𝜎 i→f is the energy-dependent cross section for the transition from a particular initial (i) to a final state (f), 𝜇 is the reduced mass of the collisional system and 𝑘 B is the Boltzmann constant in atomic units. By summing all possible error contributions (induced both in the PES and scattering calculations) we expect that the accuracy of the collisional rate coefficients is generally as low as a few per cents and always better than 25 -30%.

RESULTS AND DISCUSSION

In Paper II we have shown the behaviour of the H 3 O + -p-H 2 rotational de-excitation cross sections and thermal rate coefficients over a limited energy and temperature range. We have presented a comparison of our state-to-state collisional data with the most relevant theoretical works for the H 3 O + -He (El Hanini et al. 2019) and for the NH 3 -H 2 1 (Bouhafs et al. 2017) collisions. We examined several Δ 𝑗 and Δ𝑘 transitions in Paper II, showing that there is a significant difference between the cross sections we calculated and those of El Hanini et al. (2019) and Bouhafs et al. (2017) in the whole energy range considered (typically our cross sections are about an order of magnitude larger than those from the literature). Another important finding of Paper II is that there is no direct (linear) scaling between the compared quantities, so the new cross sections and rate coefficients have a significant importance, since they show a large improvement in quality in contrast with the previously published collisional data. Since such a comparative analysis with the available literature was provided and discussed in detail in our previous work, we are not repeating it here.

Rotational de-excitation cross sections

In Figs. 1 and2, the dependence of the H 3 O + rotational de-excitation cross sections is presented with respect to the collision (kinetic) energy in collisions with both 𝑝-H 2 (solid lines) and 𝑜-H 2 (dashed lines). In Fig. 1 we compare the cross sections for 𝑜-H 3 O + target species, while Fig. 2 shows the corresponding cross sections for 𝑝-H 3 O + for transitions with randomly selected Δ 𝑗 and Δ𝑘 parameters and changes in the inversion splitting index.

First, it is important to notice that the cross sections usually monotonically decrease with increasing collision energy (except for some particular transitions) following a typical Langevin-behaviour, as expected for ion-molecule collisions (see, for example, the work by Desrousseaux et al. (2019)). The few exceptions (see, for example, the 2 - 1 → 1 + 1 transition in Fig. 2) are most probably related to wide shape resonances, which are associated to quasi-bound states formed due to the multiple secondary wells along the potential energy surface (see Paper I for PES details). With increasing collision energy (outside the resonances) these cross sections are also expected to follow a Langevin-behaviour, at sufficiently high energies however they will probably rather flatten. Similar cross sections with wide shape resonances were reported earlier for other multi-well collisional systems, like SH --He (Bop et al. 2017), C 5 S -He (Khadri et al. 2020), or HF -He (Stoecklin et al. 2003). The cross sections are characterised by a very dense resonance structure for all transitions, especially at total energies below 800 -900 cm -1 . These Feshbach-type and shape (orbiting) resonances are typical for van 10 0 10 1 10 2 10 3 E kin (cm 1 ) 10 0 10 1 10 2 Cross section (Å 2 )

ortho-H 3 O + + para/ortho-H 2 0 0 1 + 0 3 3 1 + 0 3 + 0 2 0 3 + 0 3 + 3 6 + 6 1 + 0 6 + 6 3 + 0 5 + 3 1 + 0 Figure 1.
The variation of rotational de-excitation cross sections for some selected transitions of 𝑜-H 3 O + in collision with 𝑝-H 2 (solid lines) and 𝑜-H 2 (dashed lines) projectiles.

der Waals-type complexes with a large well depth. More rigorously, the Feshbach resonances appear due to the formation of bound states via short trapping of the projectile in the potential well, while the shape resonances are related to quasi-bound states which are formed due to tunneling via the centrifugal energy barrier (Costes & Naulin 2016). At higher energies the resonances are not as pronounced, so the energy step size was increased.

Our further important finding following the analysis of cross sections is that the data obtained for the 𝑝-H 2 and 𝑜-H 2 projectiles are very similar. This is an expected behaviour, and the same tendency was observed earlier for several other 'ion + molecular hydrogen' collision schemes, for example recently for NS + + H 2 (Bop et al. 2022) (Kłos & Lique 2011). According to Lara-Moreno et al. (2019) these similarities between the 𝑝-H 2 and 𝑜-H 2 cross sections could be attributed to the features of the short-range interaction of the colliders, which gives relevant contributions in the coupling matrix elements equally for 𝑝-H 2 and 𝑜-H 2 . Also, the long range part of the PES is weakly anisotropic with respect to the rotation of H 2 (see Paper I for details).

In accordance with the results of previous authors, the cross sections we computed with the ortho-H 2 projectile are somewhat larger compared to the para-H 2 data, but the differences usually do not exceed 10%. It is worth noticing that for some transitions we observe more pronounced differences (up to about 20 -30%) at higher energies (⩾ 400 cm -1 ), which is different from what was generally found for other ion + molecule collisions, where the main differences were present in the low-energy regime (see, for example, the works by Bop et al. (2022) and Denis-Alpizar et al. (2022)). This feature is most probably associated to the larger anisotropy of the PES with respect to H 2 rotation in the short range. The resonances are not so remarkable in the case of the 𝑜-H 2 collider (analogously as it was 10 0 10 1 10 2 10 3 E kin (cm 1 ) 10 0 10 1 10 2 Cross section (Å 2 )

para-H 3 O + + para/ortho-H 2 2 + 2 1 + 1 2 + 1 1 + 1 1 1 1 + 1 3 + 2 1 + 1 2 1 1 + 1 4 + 4 1 1 5 + 4 1 + 1 Figure 2.
The variation of rotational de-excitation cross sections for some selected transitions of 𝑝-H 3 O + in collision with 𝑝-H 2 (solid lines) and 𝑜-H 2 (dashed lines) projectiles found by other systems), but this feature is likely to be related to the high number of overlapping resonances due to the significantly higher number of channels and couplings compared to 𝑝-H 2 (remember, the rotational basis involves the 𝑗 H 2 = 0, 2 for 𝑝-H 2 and 𝑗 H 2 = 1, 3 states for 𝑜-H 2 ).

Rate coefficients

Once the state-to-state cross sections were calculated we computed the corresponding rate coefficients for the H 3 O + -H 2 collision (see subsection 3.2 for details). In Fig. 3 2011)). The magnitude of the rate coefficients with 𝑜-H 2 is somewhat higher for all transitions. These differences are almost constant above 100 K, and usually do not exceed 10% except for some particular transitions for which they can reach a maximum of 15 -20%.

It is worth noting also that there is no constant linear scaling (uniform temperature dependence) observed between the rate coefficients compared in Fig. 3 with respect to the change in kinetic temperature. If we examine for instance the 0 - 0 → 1 + 0 and 3 + 0 → 2 - 0 transitions, we can see some significant differences: for collision with 𝑜-H 2 the rate coefficients for the former decrease from 7.5 • 10 -9 down to 3.8 • 10 -9 cm 3 s -1 (i.e. by a factor of 2) between 15 and 300 K, while for the latter transition the rate coefficients are quasi constant in the whole temperature range. The rate coefficients exhibit a non-

para-H 3 O + + para/ortho-H 2 2 + 2 1 + 1 2 + 1 1 + 1 1 1 1 + 1 3 + 2 1 + 1 2 1 1 + 1 4 + 4 1 1 5 + 4 1 + 1 Figure 4.
Kinetic temperature dependence of the rate coefficients for the same rotational transitions as shown in Fig. 2 for 𝑝-H 3 O + collision with 𝑝-H 2 (solid lines) and 𝑜-H 2 (dashed lines) projectiles.

linear behaviour on the logarithmic scale dominantly only in the low-temperature regime, i.e. below 50 K. The close magnitude and similar temperature dependence of the state-to-state rate coefficients computed with 𝑝-H 2 ( 𝑗 = 0) and 𝑜-H 2 ( 𝑗 = 1) colliders imply a weak dependence of the collisional data on the rotational state of H 2 .

Based on this one can expect that the rate coefficients for H 3 O + are very similar in collision with a rotationally hot hydrogen projectile ( 𝑗 H 2 = 2, 3, ...)

In Fig. 4 the rate coefficients for the 𝑝𝑎𝑟𝑎-H 3 O + collision with both 𝑝𝑎𝑟𝑎-H 2 and 𝑜𝑟𝑡ℎ𝑜-H 2 nuclear spin isomers are compared again up to 300 K for the same rotational transitions which are presented in Fig. 2. The overall behaviour and the variation of the rate coefficients with temperature are very similar to what was found in the case of the 𝑜𝑟𝑡ℎ𝑜-H 3 O + nuclear spin species. The rate coefficients computed with 𝑝-H 2 and 𝑜-H 2 colliders are similar, the differences between them is similar to those discussed in the paragraph above.

We have compared our rate coefficients with the corresponding data from the LAMDA data base (Schöier et al. (2005), see also van der Tak et al. ( 2020)). Currently these latter are used for astrophysical modelling of hydronium in interstellar clouds, but the data are rather limited: only a single set of rate coefficients are provided for H 3 O + for 100 K kinetic temperature, and only with 𝑝𝑎𝑟𝑎-H 2 collider. Another important limitation is that the data base involves collisional and spectroscopic data for states with 𝐾 ⩽ 3 only, missing some important states which can be populated ∼ 100 K. The collisional rate coefficients in the current LAMDA datafile were estimated from scaled radiative rates, following the scaling procedure described by van der Tak et al. (2020). For the non-radiative (dipole-forbidden) transitions, NH 3 collisional data of Danby et al. (1988) were adopted, because NH 3 is isoelectronic with H 3 O + and the two species are very similar in molecular mass. This places the H 3 O + LAMDA datafile in the category "rough scalings / similar species", which has an estimated uncertainty of a factor of 10, according to van der Tak et al. (2020). In contrast to this, we are providing exact rate coefficients for all nuclear spin species (including 𝑜𝑟𝑡ℎ𝑜-H 2 ) for a wide range of 𝑇 kin from 10 up to 300 K.

Due to the mentioned limitations of the reference data, in Fig. 5 we present ratios of the state-to-state rate coefficients with respect to the corresponding data from LAMDA at 100 K, for both 𝑜-H 3 O + and 𝑝-H 3 O + . As one can see, the ratios show a large scatter: no linear scaling trends can be observed between our collisional rate coefficients and those from the LAMDA data base. The calculated ratios imply significant differences between the compared sets of rate coefficients, with typical differences of up to a factor of 2 in both directions. Due to the rough scaling, some of the rate coefficients in the LAMDA data base are likely to be overestimated at values of 10 -10 cm 3 s -1 , while on the opposite side, some lower-magnitude collisional data were likely underestimated (in particular the series of rate coefficients at 10 -11 cm 3 s -1 ). Therefore it is not surprising that our quantum-level calculations show differences even up to a factor of 10 with the roughly scaled data.

Compared to the large variations with respect to the LAMDA values, no significant differences can be found in Fig. 5 between our data computed with 𝑜/𝑝-H 2 colliders. Some slight tendencies could be observed however. For instance, the large-magnitude rate coefficients from LAMDA systematically overestimate our collisional data. For the low-magnitude transitions (with values below about 2 × 10 -10 cm 3 s -1 ) we find an opposite trend however: the LAMDA data are significantly lower than ours. This means that the collisional data, which were used for astrophysical modelling before, overestimated the de-excitation probability of the dominant transition channels, while the contributions from weaker channels were underestimated. All these could lead to large uncertainties in previous modellings, and the improved set of rate coefficients we present here will have a significant impact on the abundance and excitation modelling of hydronium, especially in warm dense molecular clouds in the ISM. for these high temperatures due to the new, previously missing collisional data for o-H 2 , which becomes the dominant collider above 100 K. The 𝑜𝑟𝑡ℎ𝑜-to-𝑝𝑎𝑟𝑎 ratio of H 2 at different temperatures was considered based on an LTE-distribution, as implemented in the RADEX software: 0.23/0.77 at 50 K, 0.62/0.38 at 100 K, 0.75/0.25 at 200 and 300 K. However, due to the similarities between the 𝑜/𝑝-H 2 collisional data we do not expect significant impact on the modelling with respect to the variation of the 𝑜𝑟𝑡ℎ𝑜-to-𝑝𝑎𝑟𝑎 ratio.

RADIATIVE TRANSFER MODELLING OF HYDRONIUM IN WARM INTERSTELLAR CLOUDS

The aim of the radiative transfer modellings performed in present work is to demonstrate the impact of our new rate coefficients on the inferred column densities, and not to re-analyse and re-interpret the previous observations. For this purpose we compare the radiation (brightness) temperatures computed by using two different sets of collisional rate coefficients (similar modelings were performed in Paper II). For the first (reference) set we adopted the available rate coefficients for H 3 O + from the LAMDA data base (Schöier et al. 2005), which are available only for at 100 K and were derived from scaled NH 3 + p-H 2 ( 𝑗 = 0) collisional data of Danby et al. (1988), considering also the cross sections reported by Offer & van Hemert (1992). As the second set we have used our new rate coefficients, which cover a much larger temperature range (10 -300 K) and all possible nuclear species, including o-H 2 . The rotational energies along with the frequencies and Einstein 𝐴-coefficients of the modelled radiative transition were taken from the JPL data base (Pickett et al. (2010), Species Tag: 19004, version 3, compiled by Yu & Drouin, Jan. 2010). For more details about the states involved in the calculations, see Table. 1 in Paper II.

As shown in Section 2, H 3 O + was detected in several environments, which possess very different physical conditions. For example, in diffuse molecular clouds H 2 -densities from 35 up to 10 3 cm -3 were reported, while for dense clouds the hydrogen densities can be as high as 10 8 cm -3 , but are typically around 10 6 cm -3 . For column densities the observations report several values in a broad range from 0.7 × 10 13 up to 7 × 10 16 cm -2 . The typical temperatures of the environments, where hydronium was detected, are ⩾ 100 K, but some authors reported higher temperatures as well (∼ 200, ∼ 240, ∼ 380 and even ∼ 500 K). In diffuse ISM sources H 3 O + lines are usually detected in absorption (Gerin et al. 2010;Lis et al. 2014;Indriolo et al. 2015). It is worth mentioning however that emission from the 0 - 0 → 1 + 0 (984.7 GHz) line is also reported by Indriolo et al. (2015), which confirms the necessity of collisional rate coefficients even for low-density clouds. For this reason we decided to calculate the radiation temperatures for all observed transitions H 3 O + under specific constrained physical conditions, which were carefully selected based on the reported observations. In particular, 50, 100, 200 and 300 K kinetic temperatures were considered to cover the majority of the observations, but not going beyond the upper limit of our rate coefficients. We separately modelled diffuse and dense cloud conditions with hydrogen densities of 10 3 and 10 6 cm -3 , respectively. For column densities we have decided to sample strictly optically thin regions with 1 × 10 13 cm -2 as well as optically thick clouds with 1 × 10 16 cm -2 , which nearly cover the lower and upper boundaries of the reported observations. For the modellings in the optically thin region the opacity 𝜏 ≪ 1, while under optically thick conditions 𝜏 ≃ 1 -1000 except for some particular transitions at low H 2 -density (10 3 cm -3 ). The background temperature and the line width parameters were kept fixed in the calculations at 𝑇 bg = 2.7 K and Δ𝑉 = 1.0 km/s, respectively.

To demonstrate the reliability of our modellings, in Paper II we have calculated the radiation temperatures at 𝑇 kin = 50 and 100 K for the 1 - 1 → 2 + 1 , 3 + 2 → 2 - 2 and 3 + 0 → 2 - 0 transitions, which showed a good quantitative agreement with the results of Phillips et al. (1992). In this paper however, we compare the relative ratio of radiation temperatures for the observed radiative transitions of both ortho-and para-H 3 O + calculated for diffuse (Fig. 6.(a)) and dense (Fig. 6.(b)) molecular cloud conditions. The 𝑇 curr.work R radiation temperatures are computed from our new set of rate coefficients, while the 𝑇 LAMDA * R set is calculated based on the corresponding collisional data from the LAMDA data base (Schöier et al. 2005). The solid colour bars correspond to radiative transfer calculations in the optically thin environment (𝑁 = 10 13 cm -2 ), while the hatch-filled colour bars show the same ratios at large column densities (𝑁 = 10 16 cm -2 ).

As one can see in Fig. 6, there are very significant differences between the radiation temperatures calculated with the two set of rate coefficients. A ratio close to unity is observed only for very few transitions, under specific physical conditions. Also, no coherence patterns were found for the data presented, and the 𝑇 R ratios depend very strongly both on the kinetic temperature, on the H 3 O + column and H 2 volume densities as well as on the particular rotational transition. There are some slight trends towards temperature dependence only, since the ratios are usually decreasing as 𝑇 kin increases. It is not a strict rule however and several deviations from this are observed, most notably for larger column densities (i.e. for 10 16 cm -2 ). Moreover, since this tendency is mostly valid for the 𝑇 R ratios much below 1 as well, we can observe the highest relative deviations at higher 𝑇 kin . In particular, the radiation temperature ratio can be as low as ∼ 0.02 for the 4 - 0 → 3 + 0 transition at 4232 GHz in Fig. 6.(b), which means that the 𝑇 R calculated for this line with our new set of rate coefficients is more than a factor of 50 smaller than that is calculated from the LAMDA data. On the other hand, for the very close 4 - 1 → 3 + 1 para-H 3 O + transition at 4241 GHz an opposite tendency is observed: at 50 and 100 K differences up to more than a factor of 7 are found in the other direction. For most transitions the 𝑇 R ratios vary between 0.5 and 2. Larger than a factor of 3 differences are found for the 4 - 1 → 3 + 1 and 4 - 2 → 3 + 2 transitions most notably, as well as for some other transitions at 300 K (see the 307 and 396 GHz lines at 10 3 cm -3 and the 2981 and 4232 GHz lines at 10 6 cm -3 gas density). The observed large variation of the ratios are not only associated with the differences in the magnitude of the corre- ) molecular cloud conditions. The 𝑇 curr.work R data is computed from our new set of rate coefficients, while the 𝑇 LAMDA * R set is calculated based on the corresponding collisional data from the LAMDA data base (Schöier et al. 2005). The colour bars correspond for radiative transfer calculations in the optically thin environments (𝑁 = 10 13 cm -2 ), while the hatch-filled bars show the same quantities, but for optically thick regions (𝑁 = 10 16 cm -2 ).

sponding rate coefficients, but also to the larger temperature range covered, larger number of rotational states involved as well as to the presence of collisional data with ortho-H 2 collider presented in this work (although the impact is limited to ∼ 20%). These conclusions are supported also by the fact that large differences are found also for radiation temperatures, which are calculated close to local thermodynamic equilibrium conditions (with 𝑛(H 2 ) = 10 6 cm -3 ), where the state-to-state collisional rate coefficients usually have less influence on the results of radiative transfer modellings. About the rotational states involved it is important to mention that we have considered 21 para-and 11 ortho-H 3 O + levels, including states with 𝐾 ⩽ 6 quantum numbers, while the LAMDA data base provides rate coefficients for 14 and 9 levels of them, respectively, with 𝐾 ⩽ 3 only. In addition to the higher rotational states (i.e. those with 𝐽 = 5), the LAMDA set of rate coefficients also excludes some of the lower states (see Table A1 in Appendix A for details), which can be populated already at moderate temperatures (from about 100 K). Due to this, some of the rotational levels could be overpopulated in radiative transfer modelling, which can lead to additional significant differences when using the LAMDA rate coefficients or those from this work. To estimate the magnitude of these differences, we have also computed the 𝑇 R ratios with an equivalent set of rotational states, thus involving our present rate coefficients only for those levels, which are present in the LAMDA data base, and neglecting all others in the radiative transfer model. We found that the ratios of the radiation temperatures still significantly deviate from unity, which confirms that the largest impact is related to the differences in magnitude of the rate coefficients. The other, non-negligible, contribution is due to the missing levels and transitions. It is also important to notice that population inversion can be observed for several transitions of hydronium under non-LTE conditions, and the new collisional data have a significant impact of their characteristics even at lower kinetic temperatures, as we demonstrated earlier in Paper II for some low-frequency transitions at 50 and 100 K (see subsection 3.3 therein).

In general, Fig. 6.(a) and (b) show that the variation of the 𝑇 curr.work R /𝑇 LAMDA * R relative ratios are large and not clearly correlated to any physical properties. The ratios are changing notably from transition to transition and there are no unambiguous patterns of their dependence on the particular upper or lower rotational states. There is no correlation found neither with respect to molecular, neither column densities. The only systematic behaviour found is the slight kinetic temperature dependence, which is also not valid for all transitions and at any density conditions. Based on these findings we conclude that the new rate coefficients proposed in present work have a significant impact on astrophysical modellings, more particularly on the determination of column densities. This can lead consequently to more precise interpretation of H 3 O + observations in various dense and diffuse interstellar environments by deriving more accurate hydronium abundances, which can be remarkably different from those reported previously for this species.

CONCLUSIONS

We have presented in this work state-to-state rotational de-excitation cross sections and thermal rate coefficients for the collision of hydronium (H 3 O + ) with molecular hydrogen. For theoretical calculations the best available and most accurate close-coupling scattering theory has been used based on our state-of-the-art five-dimensional rigid-rotor potential energy surface (Paper I). All nuclear spin configurations (ortho/para) are considered for both colliding partners, so the collisions with ortho-H 2 were studied as well, which is the most abundant collider in interstellar clouds with temperatures above 100 K.

As it is expected to be valid for all ion + molecule collisional systems, most of the cross sections monotonically decrease as the collision energy is increasing, following a typical Langevin-behaviour. They exhibit a very dense resonance behaviour, especially below 800 -900 cm -1 kinetic energies, which are associated with the formation of bound and quasi-bound states in the potential well. We have also found that there are no significant differences between the collisional data computed with ortho-and para-H 2 colliders. Due to this one can expect that H 3 O + collisional data are similar for collisions with rotationally hot hydrogen ( 𝑗 H 2 = 2, 3, ...). We have observed also a relatively weak temperature dependence in the case of the rate coefficients.

Having a full set of collisional data for all rotational levels of hydronium below 420 K (292 cm -1 ), we have presented a comparison for all particular rotational transitions individually with the available rate coefficients from the LAMDA data base (Schöier et al. 2005), which were used earlier by many authors for the interpretation of H 3 O + observations in interstellar clouds. Significant differences are found between the two data sets, typically up to a factor of 2, but occasionally up to a factor of 10. The tendencies we observed in this analysis indicate that the collisional data, which were used earlier for astrophysical modelling, overestimate the de-excitation probability of the dominant channels, while the weaker channels are underestimated.

In order to estimate the impact of the new rate coefficients on the astrophysical models, we have performed radiative transfer modelling of H 3 O + based on the the LVG approximation by the RADEX non-LTE code. We compare the radiation temperatures computed by using two sets of rate coefficients: first, the available data for H 3 O + from the LAMDA data base (Schöier et al. 2005) and, second, the new collisional rate coefficients presented in this work. We observed very significant differences between the 𝑇 R calculated with the two set of rates, once we compared their relative ratios. For most of the lines the ratios of the calculated radiation temperatures are far from unity, typically within factors of 2 in either direction, which is similar to what was found for the rate coefficients. The ratios also depend very strongly on the kinetic temperature, column and hydrogen densities as well as on the particular transitions, so they do not correlate with the physical conditions. It is important to notice that these large variations of the ratios are not only associated with the differences between the stateto-state rate coefficients, but also with the larger temperature range covered, the larger number of rotational levels involved as well as to the additional collisional data for ortho-H 2 .

Based on the results of the analysis in the present work we conclude that the new, accurate (within 10 -20%) rate coefficients without doubt have a significant impact on the radiative transfer modelling of astronomical environments, including dense and diffuse molecular clouds. Consequently, the new collisional data allow a more adequate interpretation of hydronium observations in interstellar clouds, leading to more accurate estimations for column densities and relative abundances of hydronium, especially in warmer molecular clouds of the ISM at 𝑇 ⩾ 100 K. This ensures a more robust indirect way to estimate the rate of O 2 and H 2 O production in interstellar regions.

Table B1. The converged values of rotational basis size ( 𝑗 max ) and maximum total angular momentum (𝐽 tot ) parameters for the particular total energy intervals (from 𝐸 init to 𝐸 fin ) for the o/p-H 3 O +p-H 2 collision. The step size for the energies (𝐸 step ) in these intervals are also listed.

ortho-H

Figure 3 .

 3 Figure3. Kinetic temperature dependence of the rate coefficients for the same rotational transitions as shown in Fig.1for 𝑜-H 3 O + collision with 𝑝-H 2 (solid lines) and 𝑜-H 2 (dashed lines) projectiles.

Figure 6 .

 6 Figure6. The relative ratio of radiation temperatures at 50, 100, 200 and 300 K kinetic temperatures for the majority of the observed radiative H 3 O + transitions calculated for diffuse (panel (a), 𝑛(H 2 ) = 10 3 cm -3 ) and dense (panel (b), 𝑛(H 2 ) = 10 6 cm -3 ) molecular cloud conditions. The 𝑇curr.work

  , HCS + + H 2 (Denis-Alpizar et al. 2022), HCO + and DCO + + H 2 (Denis-Alpizar et al. 2020), CF + + H 2 (Desrousseaux et al. 2019) and also for collisions of negative ions like C 3 N -+ H 2 (Lara-Moreno et al. 2019) or CN -+ H 2

  the rate coefficients for the 𝑜-H 3 O +collision with both 𝑝-H 2 and 𝑜-H 2 colliders are compared for the same rotational transitions which are presented in Fig.1. In the whole kinetic temperature interval from 10 to 300 K the temperature dependence is relatively weak, which is in accordance with the Langevin capture model. Analogously as in the case of the cross sections, the rate coefficients calculated for 𝑝-H 2 and 𝑜-H 2 are very similar both in their behaviour and magnitudes, in agreement with previous findings in the literature (see, for example,Bop et al.

	(2022); Denis-Alpizar et al. (2022); Desrousseaux et al. (2019); Kłos
	& Lique (

  Radiative transfer modelling was performed to study the excitation of H 3 O + in astrophysical media based on the new set of rate co-Ratios of our recent state-to-state thermal rate coefficients for all nuclear spin configurations of the H 3 O + + H 2 collision with respect to the corresponding data listed in the LAMDA data base(Schöier et al. 2005) at 100 K kinetic temperature. The reference collisional data LAMDA data base are only available for 𝑝-H 2 collider.

	10 9	para-H3O + + para-H2 para-H3O + + ortho-H2 ortho-H3O + + para-H2 ortho-H3O + + ortho-H2	y=2*x y=x/2 y=x
	/s)
	10 10 curr. work (cm 3
	k
	10 11 10 11	10 10 k LAMDA (cm 3 /s)	T kin = 100 K	10 9
	Figure 5.

efficients with ortho-and para-H 2 colliders. The calculations were performed using the latest version of the RADEX non-LTE radiative transfer computer program (van der

Tak et al. 2007

) based on the large velocity gradient (LVG) approximation. The new set of rate coefficients allows one to explore a significantly larger range of kinetic temperatures (up to 𝑇 = 300 K) compared to our previous work (Paper II) and also supports more reliable radiative transfer modelling

Table B2 .

 B2 3 O +para-H 2 collision para-H 3 O +para-H 2 collisionThe converged values of rotational basis size ( 𝑗 max ) and maximum total angular momentum (𝐽 tot ) parameters for the particular total energy intervals (from 𝐸 init to 𝐸 fin ) for the o/p-H 3 O +o-H 2 collision. The step size for the energies (𝐸 step ) in these intervals are also listed.ortho-H3 O +ortho-H 2 collision para-H 3 O +ortho-H 2 collision

	𝐸 init [cm -1 ] 55.4 100 150 175 200 225 250 350 375 400 425 700 725 750 775 810 910 960 1000 1050 [cm -1 ] 175.0 200.0 225.0 250.0 275.0 300.0 320.5 325.0 375.0 500.0 522.5 525.0 550.0 600.0 650.0 675.0 700 800 850 900 1000 1130 1180 990 𝐸 init 𝐸 fin 𝐸 step 𝑗 max 𝐽 tot 𝐸 init 𝐸 fin [ cm -1 ] [ cm -1 ] [cm -1 ] [ cm -1 ] 99.9 0.1 9 23 47.1 74.9 149.9 0.1 9 30 75 99.9 174.5 0.5 9 34 100 124.9 199.5 0.5 9 35 125 149.9 224.5 0.5 10 42 150 174.5 249.5 0.5 10 43 175 199.5 349.5 0.5 10 50 200 224 374.5 0.5 10 51 225 249 399.5 0.5 10 55 250 274 424.5 0.5 10 56 275 299 449.5 0.5 575 620 720 5 13 84 625 695 745 5 13 85 700 745 770 5 13 87 750 800 800 5 13 93 810 820 900 10 13 94 830 870 950 10 13 95 880 920 980 20 13 95 930 940 -50 13 98 950 970 -50 13 106 980 𝐸 fin 𝐸 step 𝑗 max 𝐽 tot 𝐸 init 𝐸 fin [ cm -1 ] [ cm -1 ] [cm -1 ] [ cm -1 ] 199.9 0.1 16 26 165.9 174.9 224.9 0.1 16 27 175.0 199.9 249.9 0.1 17 31 200.0 249.9 274.9 0.1 17 35 250.0 274.9 299.9 0.1 16 42 275.0 299.9 320.0 0.2 16 46 300.0 319.8 324.5 0.5 16 46 320.5 349.5 374.8 0.5 16 67 350.0 500.0 499.5 0.5 18 67 502.5 547.5 520.0 1 18 67 550.0 597.5 -2.5 18 67 600.0 647.5 547.5 2.5 16 67 650.0 697.5 597.9 2.5 16 69 705 820 647.5 2.5 16 71 825 870 674.5 2.5 16 72 875 920 697.5 2.5 16 73 925 945 795 5 16 74 950 995 845 5 16 75 1000 1090 895 5 15 78 1100 1120 995 5 15 88 1130 1140 1120 10 14 88 1150 1200 1170 10 14 89 1220 1260 1240 10 13 91 1280 1320 1250 1270 10 13 101 1340 -	𝐸 step [ cm -1 ] 0.1 0.1 0.1 0.1 0.5 0.5 1 1 1 1 5 5 5 5 10 10 10 10 10 𝐸 step [ cm -1 ] 0.1 0.1 0.1 0.1 0.1 0.2 0.5 0.5 2.5 2.5 2.5 2.5 5 5 5 5 5 10 10 10 10 20 20 20	𝑗 max 17 17 17 17 17 17 17 17 17 17 17 16 16 16 16 16 15 15 15 𝑗 max 16 16 16 16 16 16 16 16 16 17 17 17 16 16 16 14 14 14 14 13 13 13 13	𝐽 tot 18 22 26 30 34 38 39 43 44 48 60 62 63 65 66 68 70 71 71 𝐽 tot 22 29 36 38 45 52 56 60 60 64 68 75 75 77 80 80 87 89 90 91 96 96 103

MNRAS 000,1-11 (2022)

Our motivation for the comparison with ammonia collisional data is related to their isoelectronic nature and structural similarities, and NH 3 was assumed to be a template for collisions with H 3 O + for a long time.MNRAS 000,1-11 (2022)

This paper has been typeset from a T E X/L A T E X file prepared by the author.MNRAS 000,1-11 (2022)

ACKNOWLEDGEMENTS

We acknowledge financial support from the European Research Council (Consolidator Grant COLLEXISM, Grant Agreement No. 811363) and the Programme National "Physique et Chimie du Milieu Interstellaire" (PCMI) of CNRS/INSU with INC/INP cofunded by CEA and CNES. We wish to acknowledge the support from the CEA/GENCI for awarding us access to the TGCC/IRENE supercomputer within the A0110413001 project and also the KIFÜ for awarding us access to HPC resources based in Hungary. S.D. acknowledges the support from COST Action CA18212 -Molecular Dynamics in the GAS phase (MD-GAS), supported by COST (European Cooperation in Science and Technology). F.L. acknowledges the Institut Universitaire de France.

The authors dedicate this paper to the memory of Tom Phillips, a pioneer of submillimeter observations in general and astronomical H 3 O + spectroscopy in particular, who passed away on August 6, 2022, at the age of 85.

DATA AVAILABILITY

The data that support the findings of this study are available within the article and its supplementary material at MNRAS online.

The molecular data files in RADEX-format, which were used in the radiative transfer calculations, and which include the particular state-to-state rate coefficients for ortho/para-H 3 O + collisions with ortho/para-H 2 up to 300 K are provided as supplementary material. The data files containing the energy-dependent de-excitation cross sections are also provided as supplementary material.

The data underlying this article will be made publicly available also through the EMAA https://emaa.osug.fr/, LAMDA https: //home.strw.leidenuniv.nl/~moldata/ and BASECOL https: //basecol.vamdc.eu/ data bases.

APPENDIX A: A NOTE ON THE ROTATIONAL LEVELS OF H 3 O + CONSIDERED IN THE SCATTERING CALCULATION

The complete set of the rotational states 𝑗 𝜖 𝑘 considered in this work both for ortho-and para-H 3 O + are provided in Table A1 ( 𝑗 is the total angular momentum of the H 3 O + cation, 𝑘 is its projection on the 𝐶 3 rotational axis, and 𝜖 = ± is an inversion symmetry index). Ortho-H 3 O + is characterised with 𝑘 = 3𝑛 quantum numbers (where 𝑛 = 0, 1, 2, . . . ), while all other 𝑘 quantum numbers (e.g. 𝑘 = 1, 2, 4, 5, . . . ) refer to para-H 3 O + . For ortho-H 2 and para-H 2 the two lowest even rotational states were taken into account in the scattering calculations, i.e. 𝑗 H 2 = 0, 2 and 𝑗 H 2 = 1, 3, respectively.

Table A1. List of the rotational energy levels (in cm -1 and K) for ortho-and para-H 3 O + , which were considered in collisional studies of the present work. The corresponding energies are taken from JPL data base (Pickett et al. (2010), Species Tag: 19004, version 3, compiled by Yu & Drouin, Jan. 2010). The state labels with star (*) symbol indicate those H 3 O + levels, which are missing in the LAMDA data base (Schöier et al. 2005).

para-H

APPENDIX B: A NOTE ON THE CONVERGED VALUES OF THE BASIS SET SIZE AND TOTAL ANGULAR MOMENTA IN SCATTERING CALCULATIONS

The values of the 𝑗 max , 𝐽 tot and 𝐸 step parameters are discussed here for all total energy intervals ranging from 𝐸 init to 𝐸 fin . These particular parameters are used in inputs for our close coupling scattering calculations and their values were selected following systematic convergence test calculations with a maximum of 1% mean deviation threshold criteria for 𝑗 max and 0.01% for 𝐽 tot , respectively. Table B1 shows the corresponding parameters for 𝑜𝑟𝑡ℎ𝑜-H 3 O + and 𝑝𝑎𝑟𝑎-H 3 O + collision with 𝑝𝑎𝑟𝑎-H 2 , while Table B2 provides those of for collision with 𝑜𝑟𝑡ℎ𝑜-H 2 projectile. Due to the higher ground rotational level of 𝑜𝑟𝑡ℎ𝑜-H 2 , the maximum total energy considered for collision with this species is consequently higher.


Denis Berthier
email: denis.berthier@int-evry.fr

Artificial Agents and their Ontological Status

Keywords: Epistemology, intentionality, Artificial Intelligence, virtual, interoperability

Can an artificial agent "really" think? can it be "really" intelligent ? can it "really" have beliefs, goals, intentionality? Such questions have been plaguing AI since its inception. The solution we propose is to assert that an "artificial agent" is a virtual agent -and that all the cognitive or mentalistic attributes we may be tempted to grant it are also virtual. Whereas the first qualifier is purely descriptive, the second one is about the ontological status of such things as appear to us as agents. Our solution relies on: 1°) eliciting a precise core meaning for the word "virtual", a meaning that differs radically from the one used by philosophers (Bergson, Deleuze,…) but that has always been implicit in specialized contexts ("virtual image", "virtual world") and that should now be given its full ontological generality; 2°) relating the virtual to a broadened notion of interoperability, which justifies our assertion on technical and psychological instead of philosophical grounds. We relate this interpretation of AI to strong AI, to weak AI and to Dennett's intentional stance. We stress its implications for the cognitive sciences project of "naturalizing" intentionality. Finally, we mention some consequences in the information systems domain, relative to the acceptance of agent concepts for the modelling of organizations and their business processes.

I. INTRODUCTION TO THE PROBLEM AND TO THE PROPOSED SOLUTION

A question has been plaguing for decades all debates about Artificial Intelligence (AI), sometimes in so heated and inconclusive ways that it seems nearly everybody is sick with them and nothing new is to be expected. Can an "artificial agent" be "really" intelligent? can it "really" think? can it "really" have knowledge, beliefs, goals, intentions, emotions and so on? can it "really" have intentionality (in the full phenomenological, Husserlian sense), i.e. can it "really" refer to things in the world out there and to things in our heads? can it "really" communicate with us, share knowledge with us, collaborate with us -and what does all this mean? Disregarding all the hype about AI and all the frustration it generated, the main dilemma initially raised by such questions is not only still present; it gets stronger than ever as AI goes deeper and deeper into the simulation of complex human behaviours: -on the one hand, two very strong and complementary arguments, one technical and one psychological, plead in favor of an agent oriented vision : a) in order to design some complex software systems, it is very helpful (or even necessary) to consider them as agents and to use some related formal mentalistic concepts 1 ; b) moreover, in the proper context (i.e. in the operation framework it has been designed for), such an "artificial agent" is spontaneously perceived as having the aforementionned mentalistic attributes 2 ; as a consequence one cannot be satisfied by just blaming AI (as is often the case) for a lack of precaution in its vocabulary; -on the other hand, for philosophical, religious or common sense reasons, very few people are willing to "really" grant mentalistic attributes to a machine, however sophisticated it may be.

The solution we propose is to assert that an artificial agent is a virtual agent -and that all its cognitive or mentalistic attributes are also virtual. Here, the two qualifiers have completely different bearings: whereas the first one is purely definitional or descriptive, the second one is about its ontological status (where we understand "ontology" as being devoid of any form of essentialism). Moreover, if we decompose the expression, the adjective "artificial" means "produced by a technical activity", but the word "agent" does not suppose any specific definition of agenthood. So that our assertion should be understood with the broadest scope: as soon as, in its limited operation context, a software component appears to us as if it was an agent (whatever our notion of agenthood may be, whatever the implementation techniques it relies on may be) and it ceases to do so outside this context, then it is a virtual agent; the same applies to any of the mentalistic attributes we may grant it.

Our solution amounts to replacing a yes-or-no question by a question relating to ontological modalities in general. Admittedly, it is a nonsensical or a quasi void assertion and it is therefore a delusory solution, if one relies either on the standard meanings of the qualifier "virtual" (as they are recorded in the dictionnaries or as the word is used by most philosophers), or on its vague or nearly undefined meaning (as it is currently used on every occasion). Saying the agent is virtual may even not be completely new in this bare form 3 . However, what follows is new.

In the subsequent three sections, our assertion is first explained at three different levels of understanding: based on analogies, based on a new core definition of "virtual", based on the notion of interoperability. Then consequences are drawn regarding other interpretations of AI (strong AI, weak AI, Dennett's intentional stance) and the cognitive sciences project of naturalizing intentionality. The last section draws a consequence for information systems.

II. LEVEL ONE: ANALOGIES

1 As to the practical scope of this remark, let us remind that, giving its full meaning to [START_REF] Newell | The Knowledge Level[END_REF], sophisticated methodologies have been developed and are widely used in order to facilitate software development in terms of agents, such as Gaïa [START_REF] Wooldridge | The Gaia Methodology for Agent-Oriented Analysis and Design[END_REF] and KADS [START_REF] Schreiber | KADS: A Principled Approach to Knowledge-Based System Development[END_REF] or its multiagents version MAS-Common KADS [START_REF] Iglesias | Analysis and Design of Multiagent Systems Using MAS-Common KADS[END_REF].

2 "Every human being is so much predisposed by naïve psychology to conceive his actions and those of other people as the result of their goals, intentions, desires and beliefs that the least non human behaviour is irresistibly understood as that of an agent equipped with an intention or a goal" (Jacob, 2004, p. 13 -translation and italics are ours). 3 For instance, the FIPA (Foundation for Intelligent Physical Systems, the international association for the normalization of multi-agent systems) specifies in its norms that an agent has a virtual knowledge base; in this context, the word "virtual" may be understood with the meaning we have elicited, but FIPA has not noticed that such elicitation was necessary. We are not aware of any explicit claim about artificial agents as being virtual in any precise sense.

The example of a reflection in a mirror (which is technically a virtual image) is prototypical of the meaning we want to associate with "virtual". More generally, the following table (some terms of which will be explained later) lists the analogies we want to establish between the idea of an agent being virtual and the way this word is used in association with three other different phenomena. For each phenomenon, we display a short explanation and the framework defining its condition of possibility. There are four major points these analogies intend to stress. First, a virtual image or a virtual sound or a virtual world is not a real image or a real sound or a real world, but it is in all cases plainly actual -as opposed to potential. The only restriction is that there are conditions for my effective perception of it (to see a reflection in a mirror, I must be in the proper light cone and look in the proper direction), but it is a fact that the satisfaction of these restrictions is extrinsic to the situation itself, and therefore not of a kind such that one could find anything potential in this situation. Given a situation A of an object in front of a mirror, my entering a situation where I perceive the reflection is an event that doesn't change anything about the mirror, the object or its reflection -neither in the way the event of a dam breaking could change the state of the water it held (and the flood status of the valley below it), nor in the way the event of a measure on a photon could change (i.e., in this case, determine) its polarization state. This event, which is undoubtedly relative to situation A, could be called possible or contingent on it, but, being totally external to situation A itself, it cannot be called potential (nor latent); nor can anything in situation A itself.

Second, in all of these examples, the notion of a "context of validity" or "operation framework" is inseparable from our notion of the virtual. Concerning an artificial agent, this must be related to the fact that it appears to us as an agent only in the proper communication situation; we are aware of no artificial system that had no severe limitations on its operating context -hype notwithstanding. Of course, there is much research effort to alleviate such limitations, but enlarged context does not mean unlimited context.

Third, in any of these examples, there is nothing subjective or imaginary (in the sense "folle du logis" often associated to the word "imagination").

Fourth, one could object that there is no predefined absolute reality and that anything could therefore be said virtual. But this would be absurd in all the previous examples, a virtual "object" being defined in opposition to its real counterpart. And there is no virtual world without a real aparatus in a real world to support it. We cannot say for certain what "real" means, but anyway virtual can be defined only in opposition to it.

III. LEVEL TWO: ELICITING A NEW CORE MEANING FOR "VIRTUAL" 4

Considering etymology and the previous first three examples taken from science and technology, one can elicit a new core meaning for "virtual": that which is not real but displays the full qualities of the real, in a plainly actual -i.e. not potential -way. Contrary to the current meaning, this definition distinguishes clearly the virtual from the potential and it allows to understand why the virtual can have real effects.

The current standard meaning of "virtual" 5 , inherited from medieval Scolastics (and from the invention it made of the pseudo Latin virtualis), entails "not in actual fact" and can therefore hardly be distinguished from "potential"; the word, with this meaning, has been used intensively by the French philosopher Bergson (in Bergson 1896/1970, but also in many other of his works); a kind of a theory of the virtual as a process was developed by another French philosopher, Gilles Deleuze, in "Difference and Repetition" (1968), claiming to formalize Bergson's notion (a claim that may certainly be debated); more recently, Gilles-Gaston [START_REF] Granger | Le probable, le possible et le virtuel[END_REF] still adopts a similar meaning. Another current meaning of this word in colloquial usage is "nearly" or "quasi" or even "pseudo"; we consider it as mainly rhetorical, following a fashion associated with the information technologies boom. 6 But both of these meanings are in total contradiction with the intended meaning in our previous examples, in expressions such as "virtual image" (in geometrical optics) or "virtual sound" (in the music or movies industries) or "virtual world" (in the "virtual reality" domain -VR). Although these expressions are recorded in dictionnaries, they have not yet been related to any general core meaning for virtual (and therefore they have no compelling philosophical implications).

On the basis of etymology, virtual is "what has the virtue of"; and virtue (from the latin virtus, itself derived from vir -man, hero) means quality with underlying strength. Therefore, following [START_REF] Berthier | Méditations sur le réel et le virtuel[END_REF](Berthier , 2005a(Berthier , 2005c)), we define "virtual" as "that which is not real but displays the full qualities of the real, in a plainly actual -i.e. not potential -way". It is then easy to check that the above examples satisfy this definition.

There is a major consequence: something virtual can have actual effects -for instance, one can cure agoraphoby by walking in the "open air" in a virtual world. Even if the world we are in at some moment is virtual, all the mental experiences and feelings we live in it are still fully real. In ours analogies, this can be compared to the fact that the ligth rays "issued from" a virtual image are real. Any definition of the virtual that does not distinguish it clearly from the potential makes it logically very difficult (even impossible) to explain this fact: how could something that is potential and remains unchanged have actual effects? This would logically amount to ask how the water in a dam, which has the potential to flood the valley below, could flood it without changing its own situation.

Let us now consider our assertion that an artificial agent is a virtual agent. This is the place to notice that, at a first level, it rested on a vague analogy: the artificial system appears 4 Our work on the virtual was inspired by Wittgenstein's claim that "philosophy aims at the logical clarification of thoughts" (in his "Tractacus") and by its complementary idea that, in order to dispel our confusions, we should inquire how our "language games" are used (in his "Philosophical Investigations" §115): "A 'picture' held us captive. And we could not get outside it, for it lay in our language and language seemed to repeat it to us inexorably." Here, the "picture" was the idea that a simple yes-or-no answer was needed to questions raised about AI (intelligent or not? …). 5 Trésor de la Langue Française, Encyclopaedia Universalis, Wordnet… 6 One should also mention a regional meaning, in the information technologies domain: "digital" -which seems to us unnecessarily restrictive.

to us as if it was an agent, in the way a virtual image or a virtual sound appears to us as if it was real; but there are contexts were these appearances vanish; therefore let us call them virtual. What the present definition of the virtual provides is a second level of understanding of the assertion, i.e.: a) a meaning more precise than this mere analogy, because it involves instead a general ontological modality, defined from a general phenomenological standpoint; and b) a first phenomenological justification based on this meaning: it is a virtual agent because one can observe that, in its operation framework, it displays the full qualities of an agent.

IV. LEVEL THREE: JUSTIFYING OUR ASSERTION ON THE BASIS OF INTEROPERABILITY

The next step provides a stronger justification for our assertion by explaining why the artificial agent appears to us as an agent -much as explaining (in terms of light rays) why a virtual appears to us as a real image justifies calling it a virtual image. This is done by introducing a broadened notion of interoperabilty (which generalizes the technical meanings of this word in the information technologies domain) and eliciting its duality with our definition of the virtual.

This supposes an approach of AI that relies on its effective practices and results [START_REF] Berthier | Le savoir et l'ordinateur[END_REF][START_REF] Berthier | Méditations sur le réel et le virtuel[END_REF]) instead of on general claims of realizations to come "in the near future" 7 . And the effective results -the innumerable products that have reached industrial and commercial stage -are specialized agents that are designed according to precise methodologies to solve pre-specified types of problems in pre-specified operation frameworks (a fundamental notion, separating AI from science fiction 8 ).

In this conception, AI can be understood as aiming at developing semiotico-cognitive interoperability between Man and the computer (and VR as aiming at developing sensorimotor interoperability -so that both together aim at developing interoperability in the two major modalities of ordinary human experience). Moreover, the virtual is the fundamental ontological modality necessary for the natural description of phenomena or situations that can be explained in a more analytical, or more scientific, way in terms of interoperability -in the same way as virtual images are the phenomenological description of what could otherwise be described in terms of light rays and the laws of reflection and refraction. As a result, it is on a technical and psychological rather than philosophical basis that we can state the agent and its mentalistic attributes are virtual.

"Cognitive" interoperability (with quotation marks) between artificial agents is a purely technical notion; although it was not formulated in such terms, one can consider that "cognitive" interoperability was already the aim of the famous 1990 KSE (Knowledge Sharing Effort) project. To underline its roots in classical computer science, let us define it briefly, in a bottom up way, as the top of an ascending scale of abstraction levels: 7 An example of such hype is Lenat's announcement of e-Cyc and its capacity for automatic knowledge acquisition from the Web (Austin Chronicle, Dec. 19, 1999). Under the title "Cyc Invades Cyberspace", he writes: "When e-Cyc becomes fully operational in early January, a thermonuclear explosion in the amount of information being pumped into Cyc's knowledge base is expected, with the result of Cyc becoming exponentially smarter and smarter". More than six years later, has anybody seen this invasion or this explosion? (This is not to deny the usefulness of CYC for practical purposes). 8 One might object that this is a very restrictive conception of AI. But we have not yet seen any AI product that could be considered as displaying "general intelligence" independent of any restriction on its operating context (even learning always occurs in predefined conditions). The notion of an operation framework seems to be essential to AI.

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-the lower levels of physical compatibility between computers and network equipments; -the level(s) of network protocols and data exchange; -the clasical level of data and programs interoperability: databases interoperability (with the two aspects of syntactic normalization -SQL -and "semantic integration" of databases schemas) and objects interoperability (through norms such as CORBA or Java RMI); -the level of "cognitive" interoperability between artificial agents (through conformance to KSE or to the more recent FIPA specifications -which includes: normalized means for translating between knowledge representation languages, for referring to ontologies and for communicating by standardized messages).

The next step, semiotico-cognitive interoperability (without quotation marks) between Man and artificial agents, is a non obvious extension of the previous ones; it involves some form of communication between man and the machine, preferentially close to natural language; it may display different degrees. It means that, in its pre-defined semioticocognitive operation framework, the artificial agent appears to behave in the same way as a human agent would in the same situation and, in particular, that (to a predefined extent) some meanings seem to be shared between the user and the agent. Due to the restriction on the operation framework, this does not imply a positive answer to another sulfurous question: has the Turing test been passed? This means no more and no less than the agent has been designed properly, relative to its intended goals and operation framework as an agent. Semiotico-cognitive interoperability should therefore not be construed as a general a priori property of an AI system but as a regulating goal of AI systems development.

Interoperability is the technical notion that enables us to get rid of the identification paradigm (in which man and the machine are confused in some vicious circle) and invites us to think our relationship to the computer and to virtual agents rather than thinking ourselves as computers -as has long been the case in some AI or cognitive science circles [START_REF] Berthier | Penser notre relation à la Machine, plutôt que nous penser comme des Machines[END_REF].

V. WEAKER THAN WEAK AI, STRONGER THAN DENNETT'S "INTENTIONAL STANCE"

Differences with classical interpretations of AI can be stated: while strong AI is simply defused, our conception appears to be weaker than weak AI (or functionnalism) but stronger than Dennett's intentional stance.

According to our view of AI, strong AI is simply defused. Once a new ontological modality has been defined and it is shown appropriate to qualify the artificial agents of AI and their mentalistic attributes, asking if these are "real" is essentially pointless: would anyone care to ask if a virtual image is real? That would be like trying to lit a fire with a virtual image. The scope of this remark should not be underestimated, considering that, disguised in new clothes, strong AI ideas are still lurking behind many undue interpretations or overstatements of some cognitive sciences results (for instance in relationship with the ideas of symbol grounding or embodiement).

But our conception is also weaker than weak AI or functionnalism 9 : instead of considering all observable behaviours of an artificial agent (observable by any objective external means), we are only interested in such behaviours as are observable by a human subject in a situation of interoperability with the agent, in its predefined operation framework. This includes two complementary restrictions: one on the artificial agent and its limited operation framework; the other on the observer, which must be human and in the appropriate situation. In the same way as you can perceive a reflection in a mirror only if you are at the proper place, you can perceive intentionality (or intelligence or any mentalistic attribute) in an artificial agent only if you interoperate with it in the proper operation framework. And you don't mind if a fly does not perceive it.

Morever, in both situations, it is a fact that you have no choice: even if you know that what you are seeing is just a reflection, you cannot avoid seeing it; even if you know that what you are interacting with is just a software component, you cannot avoid understanding its behaviour in terms of folk psychology: beliefs, goals, intentions and so on; this is in full accordance with the way we have defined the virtual. This distinguishes us from Dennett's intentional stance [START_REF] Dennett | The intentional stance[END_REF]). Dennett's vocabulary (words in italics afterwards) may suggest that we have a choice: the intentional stance is the strategy that consists in interpreting the agent's behaviour as if it was a rational agent whose actions are determined by beliefs and desires. This is undoubtedly very relevant from the point of view of system developement (which is not the one we are talking about here), but it is much too weak to describe the unsophisticated user's natural attitude.

VI. NATURALIZING INTENTIONALITY

Another consequence of our redefinition of the general modality of the virtual has been elicited in (Berthier, 2005c). It raises a new challenge for the cognitive sciences project of naturalizing intentionality10 . Since we have shown that real and virtual intentionality must be distinguished, any "natural" explanation of intentionality should be able to make a distinction between these two modalities. But this means not only that it should explain intentionality on the basis of (biological, phylogenetical…) specificities of mankind, but also that it should do so in a way that cannot be applied to artifacts simulating these specificities. As a result, it is very difficult to imagine how general approaches, like Thom and Petitot's morphodynamics, could do the job. But it is no less difficult to imagine how approaches based on Varela's general idea of the embodiement of the mind could work by simply producing specialized levels of detail for this embodiement.

VII. INFORMATION SYSTEMS AND BUSINESS PROCESSES MODELLING

Practical consequences are not limited to AI. Consider the information systems (IS) domain. IS are a main factor of economic competition and they are tracking us in almost every part of our social lives. They have been rapidly changing in nature in the last decade: whereas they were traditionally considered as supports for the operational activities of an organization and they were essentially procedural, they now tend to be considered as supports for new kinds of activities (project management, decision making, innovation processes) that are highly interactive and very difficult to model in a procedural paradigm. Moreover, integrative IS (IS that can federate different organizations or different processes in one organization, through some kind of interoperability) and flexible or adaptive IS (IS that can adapt "easily" to the changing business processes in a rapidly evolving world) are becoming main themes for research.

Considering agents and associated concepts seems to be inescapable in the highly interactive and evolving IS of the future. At the technical level, multi agent systems have naturally been considered by many researchers as a possible answer to the above problems [START_REF] Kishore | Enterprise integration using the agent paradigm : foundations of multi-agent-based integrative business information systems[END_REF][START_REF] Wagner | The Agent-Object-Relationship Metamodel : towards a unified view of state and behavior[END_REF]. But the same conclusion can be reached if we approach IS in terms that are meaningful for the organization it is designed to operate in and that allow one to make a link with its strategic orientations (Berthier & al., 2005).

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In fact, numerous differences can appear between an IS such as it was initially specified and designed and its final software implementation; moreover, after its introduction in an organization, numerous factors may have changed: in the organization, in its human actors, in its environment, in the development or maintenance team or in the system itself. So that, finally, the rationality that had initially led to the design of the IS can have become globally opaque to anybody in the organization. As a consequence, there is a risk that the IS tends to: a) locally, constrain every human actor by the interoperability modes it impones on him; b) globally carry a kind of autonomized rationality, becoming a kind of agent whose implicit micro-decisions elude every possible control -even if one does not want to consider it as such. With some exaggeration, it appears as if there was an army of ghost agents that secretely maintained alive past forgotten decisions of the designers. Explicitly introducing agents in the design would make all this more explicit and easier to change.

Nevertheless, and this is an instance of the dilemma we started with, the business world displays some blocking. The notion of an agent inevitably evokes a variety of other highly mentalistic notions linked to the characteristics of agenthood. Most practionners of IS are not likely to unconditionally admit introducing concepts such as an artificial agent, its goals and intentions, nor are they ready to hear about "social conventions" that would tie together such agents and real human agents. Stating clearly from the beginning that all such concepts are meant as virtual could make things much easier. Of course, we do not mean that this would solve the IS problems we started with. There remains a lot of work to be done; for instance: what ethic rules and legal regulations should apply to agent based IS? But having clarified the ontological status of the artificial agents should help tackling such questions.

VI. CONCLUSION

In order to solve the persistent dilemna of AI about the mentalistic attributes of artificial agents, this paper has introduced a new core meaning for the word "virtual", a meaning that distinguishes it clearly from "potential" -in opposition to all philosohical traditions but in accordance with many technical as yet isolated examples. As long as a software component appears to us as displaying some mentalistic attributes (intelligence, goal oriented behaviour, intentionality,…) in some operation framework, but can be denied these attributes in other contexts, then these attributes cannot be real; they have to be said virtual; and the agent itself must be said virtual. The new perspective on AI this definition allows has been related to its classical interpretations. Some practical consequences have been pointed out.

There are many conceptions of functionnalism(Pacherie,1993), but this is pointless here.

Here, we can consider any of the variants of this project (for a review of these variants, see[START_REF] Pacherie | Naturaliser l'intentionnalité[END_REF].