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Astron. Astrophys. 341, 304-311 (1999)

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4. O2 Production by particle irradiation in pre-cometary grains

Is there a major difference between the particle irradiation of the Saturn's icy satellites and that of pre-cometary grains? The former are in an environment where the particle flux is large because of Saturn's magnetosphere and the latter may be efficiently protected from the protostar's wind by the dense protoplanetary nebula. We are asking whether the premise by Noll et al. is correct: the integrated particle flux (fluence) received by pre-cometary grains in a protoplanetary nebula may not be sufficient to produce an significant amount of O2 - O3. We will make a quantitative estimate of the oxygen production.

4.1. Production of O2 by proton irradiation of H2O ice

The chemistry induced by high energy particle irradiation of solids has been studied by different groups (e.g. Roessler, 1991). Specifically, the irradiation of H2O ice by protons leads to an erosion and production of O2. The former is attested by the decrease in the strength of the IR bands of H2O in an irradiated ice film and the latter by the outgasing of O2 from the films (Rocard et al., 1986; Bénit, 1987; Bénit et al., 1987, 1991).

The yield of O2 molecules per incident proton in ice, of prime importance for our purpose, is at most half the H2O molecule destruction rate, Y. Measurements of Y have been made by the authors named above. They have found that the yield per unit length, [FORMULA], varies approximately as the square of the particle energy loss, [FORMULA], and [FORMULA] molecules/proton.

The energy loss of protons in H2O ice has been studied (Biersach & Ziegler, 1996) and is shown in Fig. 1. The corresponding function, [FORMULA], is shown in Fig. 2. The range (mean free path) of protons in ice and the integrated quantum yield, [FORMULA], of ice erosion are shown in Figs. 3 and 4 respectively. It is remarkable that, for high energy cosmic rays, a large number of H2O molecules can be destroyed by a single proton, e.g. 120 molecules per 1 MeV proton. This phenomenon has been (incorrectly) called "giant sputtering" of ice.

[FIGURE] Fig. 1. Energy loss of protons in H2O ice ([FORMULA]) versus proton energy (from code SRIM-96 by Biersack & Ziegler, 1996)

[FIGURE] Fig. 2. Differential quantum yield of H2O erosion by protons in water ice, expressed in number of eroded molecules per proton per unit length, versus the proton energy. It is calculated by assuming its proportionality to the square of the proton energy loss per unit length in the material and scaled on experimental points (Rocard et al., 1986: Bénit, 1987 and Bénit el al., 1987, 1991)

[FIGURE] Fig. 3. Range or projected mean free path of protons in H2O ice ([FORMULA]) versus proton energy from code SRIM-96 by Biesack and Ziegler (1996)

[FIGURE] Fig. 4. Quantum yield of H2O erosion by protons in a semi infinite water ice medium calculated with same assumptions as for Fig. 2. The large number of extracted H2O molecules per high energy proton is (incorrectly) called "giant sputtering"

If the proton irradiation of the grains in protoplanetary disks can be estimated, an upper limit of O2 production in icy pre-cometary grains can be calculated and an upper limit of the [FORMULA] mixing ratio in comets will result.

4.2. Expected proton flux in protoplanetary disks

Our present understanding of planetary and cometary formation in protoplanetary disks is based on the sedimentation and growth of dust grains, the formation of planetesimals, which are comets when located further out than the ice boundary, and their accretion into telluric planets or giant planet cores. During these processes, the major source of high energy particles is the protostar and its surroundings.

- Irradiation duration
The volume production of O2 can be important only when the precometary grains are small because its occurs in their outer layers, at least for the moderate energy particles, the most abundant ones. Typical exposure time before growing to 1 cm is [FORMULA] yr (Weidenschilling & Cuzzi, 1993).

- Disk structure
We use the standard "minimum mass" protoplanetary disk model (Beckwith et al., 1990; Cuzzi et al., 1993 ; Shu et al., 1997). In this model, the temperature T, surface density [FORMULA], disk thickness [FORMULA], and volume density [FORMULA] vary with reduced distance [FORMULA] AU to a Sun-like star as:


with cut off radii: [FORMULA] and [FORMULA] . The mass of the disk is [FORMULA].

Shu et al. (1997) have proposed a model for the production of high-energy particles by the star-disk system (Fig. 5). For our purpose, the crucial point is that there is no major trajectory impinging on the disk at distances where the pre-cometary grains are located ([FORMULA] for [FORMULA]). This implies that the grains are not subject to particle irradiation because the direct irradiation in the disk plane is null. This model has been able to explain independent and unexpected observations in the Solar System, e.g. evidence of flash heating of the chondrules in chondritic meteorites and their containing short-life radioactive elements such as [FORMULA] and [FORMULA].

[FIGURE] Fig. 5. Scheme of the model of a protostar and its disk by Shu et al. (1997). The matter flows follow the magnetic field lines. The inner part of the disk, the X-region, starts at 12 [FORMULA] = 5.5 10 -2 AU for a solar mass protostar. Note that no high energy particle impinges on the disk (courtesy of Shu et al., 1997)

However, it cannot be excluded completely that, in special conditions, some magnetic field lines skim over the surface, with few of them penetrating into the disk. Below, we estimate an upper limit for O2 synthesis by this hypothetical irradiation.

- High energy protons flux produced by protostars
The spectrum of protons emitted by protostars can be estimated (Shu et al., 1997) using the X ray emission of these objects in dark clouds as observed by the satellite ASCA (Koyama et al., 1996), [FORMULA] erg [FORMULA] for 0.4 to 12 keV X rays, and the Sun as a model for the proton to X ray luminosity ratio, [FORMULA] (Kahler, 1992 ; Haisch et al., 1995). Approximating the proton differential spectrum by that of the Sun (Van Hollebeke et al., 1975), we have:


where [FORMULA] MeV

- Proton spectrum after shielding by the disk
This spectrum can be numerically computed from the energy loss curve (Fig. 1) and the initial spectrum [FORMULA]. The energy loss, in a material with specific mass [FORMULA], depends upon its electron density and can be approximated, for [FORMULA], as:


where [FORMULA] and [FORMULA] for most material but hydrogen [FORMULA]). As a result, a particle with energy [FORMULA] will cross a hydrogen column density [FORMULA] and exit with an energy [FORMULA]


if this quantity is positive, or will be absorbed if it is negative.
If incoming protons have a spectrum [FORMULA], the exiting spectrum, [FORMULA], is,


[FORMULA] and [FORMULA] being related by (5).

As anticipated, the flux coming in a straight line from the star to the icy region of the disk is completely negligible, even if there were no magnetic field. The H column density calculated from (1) and an inner radius of the disk [FORMULA] (T = 1 000 K), is [FORMULA] or one ton per [FORMULA] !   Even protons with [FORMULA] GeV would be absorbed (Eq. (5)).

- Casual irradiation of pre-cometary grains
If some magnetic field lines were to penetrate into the disk what would be the irradiation of grains?

As grains condense towards the disk plane, they are protected from above and below by a layer of hydrogen gas. At the distance of Neptune's orbit, Eqs. (2) give a disk thickness corresponding to a column density [FORMULA]. We consider that all the grains are protected by a 3 g cm -2 layer of hydrogen as a minimum. Only impinging protons with a small pitch angle and initial energy [FORMULA] can go through such a layer. We accept that [FORMULA] of the protostellar flux at that distance can penetrate into the disk with a small pitch angle although there is no evidence of such a process in the present models of preplanetary disks. Their spectra result from (3) and (6).


For a given grain, considered as a sphere with radius a, we assume that particles with energy [FORMULA] less than [FORMULA], the energy corresponding to a mean path of protons in ice of [FORMULA], are stopped in the grains and the maximum production of O2 per incident proton is half the quantum yield of H2O erosion or [FORMULA]. For more energetic particles that traverse grains, we approximate the maximum production of O2 as half the product of the differential quantum yield by the grain diameter, [FORMULA]. An upper limit of that casual production of O2 is obtained by multiplying this yield by the impinging proton flux, [FORMULA], the exposure duration, [FORMULA], and summing over [FORMULA]:


The [FORMULA] mixing ratio, x, is obtained by divi-ding [FORMULA] by the number of H2O molecules in the grain, [FORMULA]. Using the preceding data, one finds:

[FORMULA] for grains smaller than 10 µm,

[FORMULA] and [FORMULA] for icy bodies with radius 1 cm and 1m, respectively.

We conclude that even with overestimating assumptions, the production of O2 by high energy protons from the protostar in cometary grains is minute within the framework of present models of protostellar disks and winds.

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Online publication: November 26, 1998