This page further illustrates the use of the Three Phase ISM tool. It assumes that you already has some familiarity with the tool. If you do not, you should first try out the beginner tutorial.
The particular problem addressed in this tutorial is that of the concentration of 129I in the interstellar medium and its three phases. In 1960, Reynolds discovered excesses of 129Xe, which indicated that its parent 129I was alive in the early solar system. From the abundance ratio for 129I / 127I inferred from Reynold's measurements, it quickly became clear that the early solar system had too little 129I compared to expectations for the average ISM. This suggested that there was an interval of roughly 108 years between the end of nucleosynthesis and the formation of the first solar system solids.
An alternative scenario is that proposed by Clayton in his three-phase mixing model that is the motivation for this tool. We illustrate the idea in this tutorial.
Species 1
Open the Three Phase ISM tool by clicking on the 'Launch Three Phase ISM Tool' button located on the main tool page. In the Species 1 panel, enter the appropriate data for 129I, that is, chemical symbol I, mass number 129, and half life 1.6e7 years.
Species 2
In the Species 2 panel, enter the appropriate data for the second species, 127I. Here the chemical symbol is I, the mass number is 127, and the half life is Stable since 127I is not radioactive.
Chemical Evolution
In the Chemical Evolution panel, enter the appropriate values for the age of the Galactic disk in years, the timescale Delta for infall of metal-poor gas to build up the disk, and k, the integer describing the family of infall functions. In this example, enter the default values of a Galactic disk age of 1010 years, a Delta of 2.0x108 years, and an infall parameter k of 3.
Production Ratio
Both 127I and 129Xe are predominantly produced in the r-process of nucleosynthesis. Furthermore, all r-process 129Xe derives from parent 129I. The production ratio for 129I/127I may thus be inferred from the solar system's abundance of 129Xe, which is 1.28 (on the scale Si = 106), and of 127I, which is 0.9 (on the scale Si = 106). This results in a 129I/127I production ratio of 1.28/0.9=1.42. Enter 1.42 as the production ratio in the Production Ratio panel.
Masses of Phases
Enter each of the three phase masses. Be sure to use the same mass unit for each phase. In this example, choose the default values, which are 30% of the mass of the interstellar medium in phase 1, 30% in phase 2, and 40% in phase 3.
Mixtime Values
In the last panel, enter in the mixing times between phases 1 and 2 (Time 1) and 2 and 3 (Time 2). In the present case, choose 107 years for both mixing times.
Calculate Results
After you have entered the mixing times between the phases, click on Calculate Results. This is the result of the calculation, that is, the window that opens when you click Calculate Results.
Interpret Your Results
If you have not already done so, click on the result link above. The pop-up window gives your results. For our input, the average ISM abundance ratio for 129I/127I is 0.012767255. This is two orders of magnitude greater than the early solar system ratio 10-4 inferred from meteorites. As discussed above, this suggested to many that the solar cloud was isolated from the rest of the ISM for 10-8 years before the meteorites formed. Such a decay interval would allow the 129I to decay to 1.3% of its original abundance and thus give a 129I/127I ratio of 2 x 10-4, which is much closer to the meteoritic value.
In the three phase ISM model, we should compare the abundance ratio of 129I/127I in the meteorites to that in the cold molecular clouds (phase 1). For the mix times we have chosen, the ratio in phase 1 is lower than the average ISM and closer to the meteoritic value. Nevertheless, mix times of 107 years are too short to decrease the 129I down to the meteoritic value.
At this point, it is worth noting the relative concentrations of the 127I in the three phases. In each case, we see that the mass fraction relative to the average ISM mass fraction is 0.99999997. First, the number differs from unity because of numerical inaccuracies in the calculation in the eighth decimal place. This is the limit of numerical accuracy for single precision calculations. The second point of note is that the numbers are all the same. This is because 127I is stable and we are using a steady-state approximation to apportion the abundances among the three phases.
Let us now try to match the meteoritic values better. Change both mix times to 108. Leave all other input the same. Here are the changed results. With the larger mixing times, it takes longer for 129I, which is injected into the hot ISM (phase 3), to work its way into phase 1. This drops the phase 1 abundance ratio to 0.00085084782, which is closer to the meteoritic value although still high. Such a result suggests even longer mix times. Mix times of 3 x 108 get the ratio close to the meteoritic value. These are rather long (and perhaps unrealistic) mixing times. It may still be that the last r-process events that contributed to the solar cloud were sufficiently separated in time or space from the birth of the Sun to account for the low ratio.
As a final note, we comment on the fact that the phase 1 abundance ratio in the calculation with mix times of 108 is only a factor 33 down from the phase 3 ratio. One might expect a much smaller value since 129I is decaying as it moves from phase 3 to phase 2 and then to phase 1. Indeed, naively one would compute that a total mix time of 2 x 108 years from phase 3 to phase 1 would make the phase 1 abundance ratio roughly 6000 times smaller than the phase 3 value. The crucial feature of the model, however, is that mass is moving both into and out of each phase. Thus, for example, 129I-rich material mixes from phase 3 into phase 2, thereby enriching phase 2 in 129I. On the other hand, relatively 129I-poor material mixes from phase 2 into phase 3 and dilutes the 129I in phase 3. The same is true for the mixing between phases 2 and 1. In this way, the relation between the abundance ratio in phases 3 and 1 is not that from a simple exponential decay law.
