Abstract

It is well established that a precursor star to our sun went supernova producing the heavier elements we find in our solar system. In a series of short papers an update as to when this may have happened has resulted in an estimate of 5.3 Gyr ago. One of the techniques used to estimate this time involves two isotopes of Rubidium. Using the ratio of Rb-85 to Rb-87 it is possible to estimate the mass of the precursor star to our sun that went supernova. As outlined in this short paper the mass estimate for the precursor star is (13.8 + 0.4 / – 0.5) solar masses.

The Time back to Supernova

In a series of three recent short papers an update has been provided to the estimate when a precursor star to our sun went supernova producing the heavier elements we find in our solar system.

The three estimates were arrived at using different techniques and are of the order of 5.3 Gyr (refer to Table 1):

Technique	Time Estimate (Gyr)
Rb-85 to Rb-87 [1]	(5.34 + 0.50 / – 0.50)
U-238 to U-235 [2]	(5.35 + 0.31 / – 0.31)
Th-232 to U-238 [3]	(5.35 + 0.01 / – 0.02)

Table 1: Time Estimates (Gyr) and the Technique

It seems significant that a similar time estimate of 5.35 Gyr is arrived at using several separate techniques.

The Lower and Upper Bounds to the Mass of Stars which go Supernova

Modeling of stellar life evolution and stellar lifetimes appears to set a lower and upper limit to the mass of stars that may go super nova:

In this short paper we shall use these bounds to our advantage.

Using the isotopes Rb-85 and Rb-87 as Benchmarks

A careful assay of the ratio of Rb-85 to Rb-87 in terrestrial and celestial materials found in our solar system finds a ratio of

Isotope	Abundance
Rubidium-85	72.17 %
Rubidium -87	27.83

Table 2: Present Abundance of Rubidium -85 and Rubidium-87

This means then that the measured ratio of Rb-85 to Rb-87 is

A simple model of the production of the two isotopes of Rb-85 to Rb-87 in a large supernova sets a simplistic value of 2.50 [4]

We will use these two ratios of Rb-85 to Rb-87 as an upper and lower bound to estimate the mass of a precursor star to our sun that went supernova producing the heavier elements we find in our solar system

Empirical Data Relating to Existing Stars

The following empirical data affords us with a linear model for the relationship between the stellar precursor mass and the Rb-85 to Rb-87 ratio:

Star Mass (Solar Masses)	Ratio of Rb-85 to Rb-87
5.0	1.58
6.5	1.79
9	2.07
15.5	2.72

Table 3: Star Mass and the Rb-85 to Rb-87 ratio

For the masses less than 8.0 solar mass refer to Table 3 in van Raal et al. [5]. Please note in van Raal the stated ratios are that of Rb-87 to Rb-85 (the inverse of to the ratio we are using in this paper).

For masses greater than 8.0 solar masses but less than 16 refer to the highest ratio values in Table 4 and Table 5 in Walker et al [6] Outliers have been excluded. The ratio for our top measure of 15.5 solar masses is stated as 2.72 (while the paper states it > 2.72). The mass estimate is not sensitive to minor changes to the top measure.

The largest value for the Rubidium ratio in the references papers are used for each mass in our Table 3.

Graphing these data points and finding a linear fit we find:

Fig. 1: Measured Rubidium Ratio as a Function of Star Mass

Analysis

An upper and lower bound to the mass estimate of the precursor star to our sun can be set by the Rubidium ratio measures found in reference [1] of 2.5 < R < 2.593.

For R = 2.5 we find that

For R = 2.593 we find that

This provides for an estimate to the mass of the precursor star to our sun of

This simple linear model provides for the following mass estimate

(13.8 + 0.4 / – 0.5) Solar Masses

Discussion

The Rubidium technique is made possible because at high stellar masses the r-process begins to dominant over the s-process when it comes to isotopes greater than A= 56.

There is obviously a need for refinement to the Rubidium astrophysical measurements and the need for additional data points to further refine this model.

As more data points become available it is predicted that the linear fit will change to a flatter curve and a precursor star mass uncomfortably close to 14.5 solar masses. Need we be reminded that above 15.5 solar masses is when remnants become black holes.

A precursor star mass of 13.8 solar masses begs the question how many stellar siblings does our sun have? The Rubidium ratio may perhaps be used for paternity purposes. This will be the subject of a subsequent paper.

A linear fit, as well as the upper bound of 14.5 solar masses, does help us to set a triangle ( 2.5 < R < 2.63) and ( 12.8 < mass < 14.5) solar masses inside of which may be found a better estimate to the precursor mass in subsequent analysis.

Conclusion

Using the Rb-85 to Rb-87 ratio as a benchmark we have a mass estimate of

(13.8 + 0.4 / – 0.5) Solar Masses

for the precursor star to our sun that went supernova.

Acknowledgements

I would like to acknowledge the kind and thoughtful assistance afforded me in the research leading up to the writing of this paper by Dr. Paul Hickson for providing me suggestions and useful reference material and to Mr. Bill Chang for his research assistance on the techniques used to estimate the time back to the supernova using the two isotopes of Rubidium

I would also like to acknowledge the encouragement afforded me by kind words from Dr. Jim Peebles of Princeton University regarding the techniques used to estimate the time back to the supernova using the two isotopes of Rubidium. “ … this looks reasonable.”

References

[1] Bruskiewich, P, Using two Isotopes of Rubidium to Estimate When a Supernova Created the Solar System’s Heavy Elements, July, 2019, available through Researchgate and at archive.org

[2] Bruskiewich, P., Revised Time Estimate to Supernovae of the Precursor Star to our Sun, Nov. 2019, available through Researchgate and at archive.org

[3] Bruskiewich, P., Revisiting the Th-232 to U-238 Ratio to Estimate the Time to Supernova of the Precursor Star to our Sun, Nov. 2019, available through Researchgate and at archive.org

[4] Refer to reference discussion and conclusions outlined in reference [1].

[5] van Raal, et al, Rubidium, zirconium, and lithium production in intermediate-mass asymptotic giant branch stars, arXiv:1202.2620v!, 13 Feb, 2012

[6] Walker, K., et al, Rubidium in the Interstellar Medium, Astro. J. 706: 614 – 622, 2009 Nov. 2009,