Young, gas-rich proto-planetary disks orbiting around solar-type young stars represent a crucial phase in disk evolution and planetary formation. Of particular relevance is to observationally track the evolution of the gas, which governs the overall evolution of the disk and is eventually dispersed. However, the bulk of the mass resides in the plane, which is so cold and dense that virtually all heavy-element-bearing molecules freeze out onto the dust grains and disappear from the gas phase. In this paper, we show that the ground-state ortho-H2D+ transition is the best, if not the only, tracer of the disk-plane gas. We report the theoretical models of the chemical structure of the plane of the disk, where the deuterated forms of , including H2D+, play a major role. We also compare the theoretical predictions with the observations obtained towards the disk of the young star DM Tau and show that the ionization rate is probably enhanced there, perhaps owing to the penetration of X-rays from the central object through the disk plane. We conclude by remarking that the ground-state ortho-H2D+ transition is such a powerful diagnostic that it may also reveal the matter in the dark halos of external galaxies, if it is hidden in cold, dense and small clouds, as several theories predict.
The Solar System formed from the so-called Solar Nebula, a disk-shaped structure of dust (small solid particles) and gas around the young Sun, approximately 4.6 Gyr ago. The material that made up this disk came to the system from the molecular cloud out of which the Solar System formed. Initially, it must have had a composition like that cloud, i.e. 100 times more gas than dust. At present, this ratio is completely different, with most planets (except Jupiter and Saturn) consisting largely of material that was initially solid dust and ice. Prior to the formation of the planets, dust and gas did get partially separated; solid particles settled to a thin layer in the disk and this is where planet formation started. Some of the gas was later accreted by the planets, while a lot of it was lost back to interstellar space. How this transition from the originally well-mixed disk to the chemically different planets occurred is a central question in astronomy.
The history of material processed into planets actually starts much earlier, with the collapse of a small quasi-spherical condensation inside a molecular cloud (the pre-stellar core and protostellar phases), and passes through the crucial phase in which the material is almost entirely distributed on the equatorial plane, in a proto-planetary disk. From observations we know that these disks are initially rich in gas, but eventually change into a disk entirely dominated by dust grains (the so-called debris disks), and probably a few unseen planets. This dramatic transition takes apparently about 10 Myr. Tracking the history of the proto-planetary disk gas in the first million years is therefore crucial to understanding the fate of the system, whether or not it will form planets, and what kind of planets are formed and where.
While we can readily see the dust grains in disks, the problem of probing the gas in the proto-planetary disks has proved to be a challenging task. The bulk of the gas is so cold (approx. 10 K) and dense (greater than or equal to 1×105 cm−3) that the usual tracer of molecular gas, CO, condenses out onto the grains and disappears from the gas phase. Along with CO, all heavy-element-bearing molecules freeze out onto the grains. The only species remaining in the gas phase are those composed of H and D atoms. However, the two major reservoirs of both elements, H2 and HD, respectively, can only probe warm (greater than or equal to 100 K) gas. The only species that can therefore be used to probe the cold gas of the proto-planetary disk are the trace species composed of H and D atoms. As in a good sudoku game, there are not many possibilities and the solution to the problem is rather unique. Only the H+ and molecular ions and the deuterated counterparts of the latter—H2D+, H and —remain in the gas phase. Of those species, only H2D+ and H have ground-state transitions observable from ground-based telescopes capable of probing cold gas, with H2D+ having the more easily observable transition. However, considering that deuterium is 1×105 times less abundant than hydrogen, at face value this does not seem to be a feasible way to detect the gas.
In this paper, we will show that, although difficult, this task is feasible after all, because the H2D+ and H abundances are hugely enhanced in the cold gas of proto-planetary disks. We will present the theoretical background and modelling of the chemistry leading to the enhancement of these trace molecules in proto-planetary disks (§3), after discussing the physical structure of a typical proto-planetary disk (§2). In §4, we will report the detection of H2D+ in the disk surrounding the solar-type protostar DM Tau, and we will discuss the implications of this detection in the light of the modelling of this source. Section 5 will conclude this paper, with a discussion of the far-reaching diagnostic power of H2D+ in probing the darkest regions of our Universe, even beyond our Galaxy.
2. The physical structure of proto-planetary disks
Young, gas-rich proto-planetary disks orbiting around young solar-type stars come with different sizes and masses. The typical disks observed with present millimetre and submillimetre telescopes have masses of about 0.01 M⊙ and radii around 400 AU. In this paper, we will focus on these types of disks.
The physical structure of young, gas-rich proto-planetary disks has been studied by several authors (D'Alessio et al. 1997; Dullemond et al. 2001; Dullemond & Dominik 2004; Gorti & Hollenbach 2004). For the calculations presented in this paper, we use a model of passively irradiated hydrostatic flaring circumstellar disks (Dullemond et al. 2001; Dullemond & Dominik 2004). This model computes the structure (i.e. the density and temperature distribution) in a self-consistent way. A low-mass star with a mass of M⋆ and a luminosity of L⋆ is located in the centre of the disk. Around the star we distribute Mdisk of material in a disk ranging from 0.1 AU to Rdisk, with a surface density power law Σ∝r−1 (in gr cm−2), implying that the disk mass per unit radius is constant, i.e. both inner and outer disks contain significant amounts of mass. The disk contains dust at a mass fraction fd/g, which we assume to be fully mixed with the gas. While in reality, there probably exists a distribution of grain sizes in the disk, we choose a single grain size for the present calculation. This allows us in a simple way to study the effects of grain size. The structure of the disk is then computed by iterating between a one-plus-one-dimensional continuum radiative transfer code that computes the dust temperature in the entire disk and a hydrostatic equilibrium code that computes the vertical density and pressure distribution, under the assumption that the gas and dust temperatures are equal. For the technical details of the modelling procedure, we refer to Dullemond et al. (2001). A typical temperature and density profile across the disk is shown in figure 1. The disk is flaring as can be seen from the upwards-curved temperature contours. We anticipate that heavy-element-bearing molecules will freeze out; therefore, deuterium fractionation will be significant at about 25 K (approximately the CO condensation temperature for the involved densities) and below. These conditions are only fulfilled in the outer disk, approximately outside of 20 AU. The low-temperature region becomes geometrically thick at large distances from the star. For example, at a distance of 300 AU, the 15 K contour reaches a height of 60 AU. Typical densities in this region are and above, up to in the innermost parts of the outer disk, near 100 AU.
3. The theory of deuteration in the plane of proto-planetary disks
The chemistry of a cold gas mostly composed of H and D is relatively simple, even in the presence of dust particles (Roberts et al. 2003; Walmsley et al. 2004; Ceccarelli & Dominik 2005). The starting point for the chemistry in such gas is the interaction of cosmic rays with molecular hydrogen, which results in its ionization. The successive reaction with H2 leads to . Similarly, reacts with HD to give H2D+. This is the start of deuterium enrichment chemistry whose overwhelming importance has recently been recognized. In fact, H2D+ reacts with all neutrals and, in this manner, transmits deuterium atoms to the molecules. For example, H2D+ reacts with CO to give DCO+ once in every three reactions. Therefore, the HCO+: DCO+ ratio directly depends on the H2D+: ratio. The same logical scheme applies also to the other species in the gas. In summary, H2D+ is the key species in molecular deuteration.
The major route to the formation of H2D+ is the destruction of by the reaction(3.1)
How much H2D+ is formed depends on the competition of this loss with respect to others. Another route of loss is the recombination with electrons. In the plane of proto-planetary disks, densities are larger than about 1×106 cm−3, and the gas is ionized mostly by cosmic rays, for X-rays and/or far ultraviolet (FUV) photons are readily absorbed in the disk atmosphere. In these conditions, it is easy to demonstrate that the ionization degree is low; consequently, the recombination is small when compared to reaction (3.1). Similar arguments apply to the recombination with grains, both charged and neutral. The latter will become positively charged, but then are very quickly re-neutralized by electrons. A second major loss of , in ‘standard’ molecular cloud gas, is the interaction of with neutrals, and particularly with CO—the second most abundant molecule after H2. However, in the plane of proto-planetary disks, all heavy-element-bearing molecules are frozen onto the grain mantles, so that the reaction with heavy-element-bearing molecules is inefficient too. Therefore, the amazingly simple conclusion is that, in the plane of proto-planetary disks, is destroyed only to form H2D+, which can become more abundant than itself.
What limits the amount of H2D+ is, again, at what rate it is destroyed with respect to its rate of formation. The first important destruction reaction is the inverse of reaction (3.1), which is endothermic by about 220 K. Therefore, in the cold gas of the proto-planetary disk plane, this reaction is inefficient. Other routes of H2D+ loss are recombination and reactions with neutral molecules, but the same arguments valid for also apply to H2D+, so that these routes may not be the most important ones. It turns out that, depending on the density and therefore the location in the disk, the most important H2D+ destruction route is the formation of H, via the reaction of H2D+ with HD, following the same path as reaction (3.1). Similarly, H can mostly be destroyed by the reaction with HD to form , which is the end of the chain.
Accurate modelling of the chemical composition of the plane of proto-planetary disks has been carried out by Ceccarelli & Dominik (2005). The typical chemical structure for a 0.01 M⊙ disk orbiting around a 1 L⊙ young star is shown in figure 2. H2D+ is a major species in a large region of the outer disk, as expected. But the most surprising result is that is the most abundant molecular ion in the outer zones of the disk. It is unfortunate that this prediction will be extremely difficult to prove, for has only vibrational transitions in the near-infrared, at ca 5.4 μm (Ramanlal & Tennyson 2004). The only possibility is to observe the line in absorption against the 5 μm continuum. However, the is abundant only in the outer mid-plane of the disk, so that to detect the transitions in absorption, one should see through an edge-on disk. This is in contradiction with detecting the 5 μm continuum, because the 5 μm photons are absorbed by the cold dust in the outer mid-plane disk.
4. H2D+ in the proto-planetary disks of DM Tau
The ground-state transition of ortho-H2D+ at 372 GHz has been detected in the disk orbiting around the young star DM Tau (Ceccarelli et al. 2004). The measured signal, 76 mK km s−1, corresponds to an ortho-H2D+ column density in the disk equal to 4×1012 cm−2. In order to derive the total H2D+ and compare it with the model predictions reported in §3, one needs to know the ortho-to-para-H2D+ ratio. Unfortunately, the ground-state transition of the para-H2D+ lies at 1370 GHz, and is not observable from ground-based telescopes. Therefore, one has to entirely rely on theory to estimate the ortho-to-para-H2D+ ratio. Based on modelling as a function of temperature and density, the ortho-to-para ratio is approximately 0.3 for the conditions valid in the disk plane (Flower et al. 2004, 2006). However, one has to keep in mind that there is a considerable uncertainty, easily a factor of 3, associated with this value. Neglecting this uncertainty, we obtain that the measured H2D+ column density amounts to about 2×1013 cm−2.
Figure 3 shows the theoretical curves of assorted column densities, averaged for a face-on disk, a geometry similar to observing the top or bottom of a CD. The curves were obtained considering the detailed physical structure of the DM Tau disk (Ceccarelli et al. 2005). Note that the physical structure, namely the density and temperature profiles, has been derived by interpreting the spectral energy distribution of DM Tau via a sophisticated two-dimensional radiative transfer code coupled with the hydrostatic equilibrium equations (see §2).
The figure shows the dependence of the computed average DM Tau disk column density of H2D+, as well as the other deuterated forms of plus the electrons, on the two major parameters of the employed model: the dust-to-gas ratio and the cosmic ionization rate. As discussed in §1, the dust-to-gas ratio is a major parameter in the theory of disk evolution and planet formation, and it varies across the disk and with time. One major reason to observe H2D+ in disks is indeed the possibility to study this important parameter observationally. The dependence of the H2D+ column density on the dust-to-gas ratio is not a simple one. For low dust-to-gas ratios, the H2D+ column density increases with decreasing dust-to-gas ratio, whereas for large ratios it decreases. However, in the parameter space in between, from dust-to-gas-ratios between about 0.001 and 0.1, it does not vary much. This effect is due to the different regimes of dominant positive charge carriers, whether the deuterated forms of or H+ (in which case grain recombination dominates the charge balance).
The value of the cosmic ray ionization rate is still strongly debated in the literature, and it is not clear whether it increases or decreases in dense gas, and even less known is its value in proto-planetary disks (van der Tak et al. 2000). For example, any ionization from X-rays penetrating the disk plane would end up as an increased ionization rate. Since the cosmic ray ionization rate regulates the overall ionization in the disk, the H2D+ column density directly depends on it. It is easy to demonstrate that, in a first approximation, the H2D+ column density varies with the square root of the cosmic ray ionization rate.
The comparison of the H2D+ column density measured in the disk of DM Tau with the theoretical predictions yields a tight constraint on the ionization rate, which has to be within 3×10−17 and 3×10−16 s−1. There is therefore evidence that the ionization rate is increased in the plane of the disk of DM Tau when compared to the value derived in protostars and/or molecular clouds. It is possible that this is because X-rays penetrate into the plane of the DM Tau. Unfortunately, the dust-to-gas ratio cannot be efficiently constrained by these observations, owing to the specific structure of the DM Tau disk, to which the H2D+ column density is not very sensitive.
5. Concluding remarks
There are regions in the Galaxy so cold and dense that the standard molecule to probe the molecular gas, CO, freezes out onto the grain surfaces and disappears from the gas phase. This effect occurs, for example, in the centre of pre-stellar cores (Vastel et al. 2006) and in the mid-plane of young proto-planetary disks orbiting solar-type young stars. In the last few years, it has been found that the gas in these regions can be probed by the ground-state transition of ortho-H2D+ at 372 GHz. In pre-stellar cores, H2D+ observations open the possibility of revealing the first movements of the collapse that will eventually lead to the formation of a sun and its planetary system (van der Tak et al. 2005). In young, gas-rich proto-planetary disks, observations of H2D+ permit probing the gas in the mid-plane, where the bulk of the matter resides, and estimating the overall ionization rate and, in principle, the dust-to-gas ratio (Ceccarelli et al. 2004; Ceccarelli & Dominik 2005).
On a totally different galactic scale, it has long been suggested that a substantial amount of matter is hidden in cold (up to 10 K), dense (greater than or equal to 1×105 cm−3) and small (up to 1000 AU) clouds, called cloudlets (Pfenniger et al. 1994; de Paolis et al. 1995; Gerhard & Silk 1996). The cloudlets are thought to be distributed in large halos, the so-called dark-matter halos above and below galactic planes, as revealed by galactic rotational curves (Rubin et al. 1962). The physical conditions in these cloudlets are very similar to the gas in the centres of pre-stellar cores and in the planes of proto-planetary disks; all heavy-element-bearing species, if at all present, are doomed to freeze out onto the dust grains. Indeed, the situation is probably more extreme than that in the pre-stellar cores and/or proto-planetary disks, for the matter is, in addition, almost primordial and therefore not or only weakly enriched in heavy elements. This paucity causes a very small abundance of dust grains, which makes these cloudlets particularly difficult to observe. Indeed, it is exactly this difficulty that makes them dark and therefore candidates for the dark-halo constituents. The recent studies showing the diagnostic power of the ground-state transition of ortho-H2D+ also open new possibilities in this field. In principle, the 372 GHz line can probe the existence of the cloudlets in the galactic halos. Dedicated modelling of the emission of this line from the cloudlets confirms that the ground-state transition of ortho-H2D+ can reveal the long-searched presence of cloudlets, if they exist (Ceccarelli & Dominik 2006).
In summary, the last decade has seen the detection of , a key molecule for understanding chemistry in the interstellar medium. In the last 3 years or so, it has been realized that its singly deuterated form, H2D+, has a huge diagnostic power. The observational studies of this molecular ion are still difficult with the available instrumentation. At present, we only have a handful of pre-stellar cores observed in the ortho-H2D+ ground-state transition, and only one proto-planetary disk. But the new generation of telescopes (Atacama Pathfinder Experiment) and interferometers (Submillimetre Array and Atacama Large Millimetre Array) will make these studies much easier and routine in the near future. Finally, H2D+, a small and strange molecular ion, whose abundance and importance has long been overlooked, may even be the tool to reveal a substantial component of our Universe.
S. C. O. Glover (Astrophysikalisches Institut Postdam, Germany). Do you assume steady-state chemical abundances, and if so, how quickly is steady state reached? Is the time short enough that you don't need to worry about dynamical effects such as turbulent mixing?
C. Ceccarelli. Indeed, in our model of Ceccarelli & Dominik (2005), we assume steady-state chemical abundances. The time-scale for turbulent mixing in the outer disk (greater than or equal to 100 AU) is greater than about 200 years, whereas the time-scale for H2D+ formation from reaction (3.1) is around 500 years in the disk mid-plane. However, since the steady-state H2D+ abundance can be perturbed by the presence of the CO in the gas phase from the disk upper layers rather than from a variation of the abundance, the chemical time-scale is rather determined by the time needed for CO to re-condense onto the grain mantles. We do treat the freeze out of CO in a time-dependent manner, even though the time-scale of CO condensation in the disk plane at 100 AU is about 10 years, which justifies the steady-state approximation in a large part of the outer disk.
D. C. Schram (Eindhoven University of Teche, The Netherlands). Are the dust particles charged? And if so, does it influence surface chemistry?
C. Ceccarelli. Dust particles will be highly charged in the disk surface where UV photons lead to photoelectric ejection of electrons. However, in the disk mid-plane, the only charging processes are collisions with electrons and positive ions, both low in abundance. These processes generally lead to grains charged negatively by no more than a single elementary charge. The collision cross-section for negatively charged grains and neutral grains with positively charged ions are comparable, so the influence on surface chemistry as well as on recombination of positive ions on grains is minor.
S. Schlemmer (University of Cologne, Cologne, Germany). Is there an easy explanation that N(H2D+) is maximum for a given ionization rate at a dust-to-gas ratio of 1 : 100?
C. Ceccarelli. This is only an apparent maximum in a cut through a multidimensional parameter space.
M. Larsson (Stockolm University, Sweden). Is it possible that the cosmic ray ionization rate is lower across the proto-planetary disk as compared with a dark cloud?
C. Ceccarelli. Cosmic rays are believed to be absorbed at column densities larger than about 100 g cm−2. In principle, therefore, it is possible that the cosmic ray ionization rate is lower in some disk locations. In these regions, called dead zones in the literature, the magneto-rotational instability does not occur and they may be inactive in terms of viscous transport of angular momentum and mass. In the inner disk regions (few astronomical units), the surface densities can be high enough for cosmic rays to be excluded, but in the outer disk regions the surface densities are much too low. Low-energy cosmic rays may also be trapped by magnetic fields, leading to locally enhanced cosmic ray fluxes. Finally, low-energy cosmic rays can be excluded from a disk by the bubble blown by a stellar wind/outflow. In this case, the radiation intensity in a disk may be lower than that in a dark cloud. Note, however, that young stars are X-ray sources and thus produce their own ionizing flux. For all these reasons, measuring the ionization degree across the disk plane is extremely important for disk evolution theories (Semenov et al. 2004; Ceccarelli & Dominik 2005).
We are very grateful to Eric Herbst for his helpful comments and remarks on this manuscript.
One contribution of 26 to a Discussion Meeting Issue ‘Physics, chemistry and astronomy of ’.
- © 2006 The Royal Society