Notes & Considerations on Proposal for Astrosphere Catalog and Baseline Model for Comparison and Reference over Time
Jayson Abalos^{1}
^{1}Amateur, Wasilla, Alaska 99623
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Abstract
The proposition of a catalog for comparing diverse astropause and astrosphere modeling equations and methods is outlined and examined. Sound method is found possible, and good reason is found for the generation for such a catalog.
Introduction
Throughout the field of astrophysics, there lacks a consistency on estimating astropause and astrosphere distances (for brevity’s sake both will be referred to as astrosphere for the remainder of this paper). The equations for the estimates themselves differ, and even when the equations are sympathetic, the values assumed and applied differ. As an example, the solar system had been given a range of estimates from at least 74 AU to 150 AU until Voyager 1 reported 121.7 AU. With other systems, we are in absence of Voyager records and we cannot simply await similar probes for validation. Presently, there are many factors that cause these differences. A few examples to convey the concept of difference are: one equation working off of massloss rate and negating wind speed, another equation factoring in ISM cloud considerations differently, or another factoring in electromagnetic considerations where others do not. There is no simple solution to these problems as the current period of exploration will naturally generate dissimilar approaches and solutions. Further, there is currently no convenient means to find and compare multiple approaches against each other to attempt to discern definition and pattern. What could be created is a catalog which has a steady and predictable line which estimates could be compared against and kept on file. This would allow estimates to be made and plotted against a predicted model which does not suppose itself to be dependent upon real factors and variables within the equation, but instead works inversely from sample to produce an “ideal” model by which estimates can be lined up against. The reason for doing so would allow for estimates to be examined in long view against a trend and pattern with a known skeleton model from which they deviate, as opposed to now where estimates are aligned and compared against nothing and we have a lack of direction or focus as to the culmination of these estimates being generated.
Construction of Hunt Catalog Foundation
The Hunt catalog is comprised of the baseline, sample estimates, and profiles of those estimates defined by the differences between the estimates and the baseline. What follows are the components to assembling and then employing the Hunt line catalog for an example.
Brief Definition of “Hunt” Variable et al.
In this paper a variable is created for application as outlined. This value is given a name of “Hunt” variable, and al subsequently derived productions from the employment of the Hunt variable adopt the name “Hunt” (e.g. “Hunt line”). The Hunt variable is considered adjustable as this value is a result of the data’s average being applied as a value for approximation in equations outlined later. For clarity, the Hunt variable is given a symbol H. It is referred to as “Hunt” since it is employed to approximate a finding of an unknown radius given the related radius opposite of the one approximated. The Hunt variable implies a direct correlation between the two radii proportionately. The results of employing the Hunt variable are only considered an approximation because the Hunt variable is only a value from an average from the data collected so far and as such is not specific to a particular object’s constituency or definition. No application of the Hunt variable should ever be found to be applied in place of typical models and methods. The purpose and application of the Hunt variable are confined to the operations and functions defined within this paper.
Due to the limited quantity of verifiable star astrospheres, the initial Hunt baseline is built from atoms and a few stars. This was done because the atomic data is more readily available in high quantity and good record. Atoms divide the radius of their nucleus (standing in for the star) by the radius of their covalent bond (standing in for the astrosphere), while stars divide the radius of the star by the radius of the astrosphere. The average of the results comprise the Hunt variable. The current “Hunt library” is defined as:
(1)
H = “Hunt Variable”, = Radius of star, R_{AP} = Radius of astropause/sphere, R_{nuc} = Radius of nucleus, R_{cov} = Covalent bond radius.
Initial Data Results
The data was collected form literature and the percent of the energy core of the system (nucleus/star) determined from the boundary of the whole system (covalent bond/astrosphere) for each sample and the percent of all samples was averaged as per the Hunt definition in equation (1). The results were then tested against that average in a standard deviation and standard error to test meaningfulness of the determined average. The sample set for stars was 13. The sample set for atoms was 95. For this analysis, the total sample group was 108.
Table 1 shows the resulting combined average (~ 0.0039%). Table 2 shows each set (stars/atoms) separately to check how different the star set is from the atomic data. The difference between the two sets when separated is a factor of 1.07. This produced a confidence of proportionate relationship close enough to merit reliance upon atoms to measurably serve as the scaffolding for the core library in the absence of a larger verified star data set (which ideally should replace this starting library at a later date).
Table 1: Summary of all data collected
Average of All Data Sample 
0.00003950 
Standard Deviation 
0.00001073 
Standard Error 
0.00000103 
Table 2: Summary of Stellar and Atomic Systems separated
Average of Only Star Data 
0.00004193 
Standard Deviation 
0.00001963 
Standard Error 
0.00000103 
Average of Only Atomic Data 
0.00003916 
Standard Deviation 
0.00000900 
Standard Error 
0.00000092 
The following figures elaborate upon the results of the sample average data. Figure 1 is a histogram of the sample data. Figure 2 is a plot of each stellar radii as well as atomic nuclear radii.
Figure 1: Histogram
Figure 2: Comparison of Star/Nuc. R to Astroshere/Cov. Bond r (factor)
Preliminary Functional Test
To test if the average obtained is sufficient to rely on for generating approximately an average sample representation, the average  as the Hunt variable  was applied in two ways for testing.
To test the ability to reflect the average of the sample in regards to astrosphere and covalent bond radius, equation (2) was used.
(2)
To test the ability to reflect the average of the sample in regards to the star and nucleus radius, equation (3) was used.
(3)
Where R_{eff} stands for effective radius of the system (i.e. astrosphere/covalent bond), and R_{nuc} stands for the radius of either the star or nucleus.
The results of the equations per sample were compared to the listed values from literature and the difference by factor was derived. All differences by factor were averaged. Table 3 and 4 summarize the resulting average of applying equations (2) & (3) for testing the Hunt variable.
Table 3: Summary of equation (2) test
Average 
1.00 
Standard Deviation 
0.27 
Standard Error 
0.03 
Table 4: Summary of equation (3) test
Average 
1.09 
Standard Deviation 
0.41 
Standard Error 
0.04 
The following Table 5 is a display of stars with astrosphere listing from literature and values from Hunt equation (2).
Table 5: Equation (2) test  Stars
Star ID 
Published Astrosphere (AU) 
(AU) 
Difference (factor) 
Kepler437 
290 
80.0 
0.2760 
Kepler32 
180 
62.4 
0.3466 
Kepler88 
140 
107.1 
0.7651 
Kepler445 
30 
24.7 
0.8240 
Kepler186 
59 
55.3 
0.9377 
Sun 
121.7 
117.7 
0.9672 
CW Leonis 
84000 
82398.9 
0.9809 
Kepler448 
170 
191.9 
1.1287 
HD 210839 
2062 
2483.7 
1.2045 
HD 182488 
84 
103.6 
1.2332 
HD 14412 
72 
90.6 
1.2589 
Kepler42 
11 
20.0 
1.8192 
Kepler20 
54 
111.1 
2.0578 




The following Table 6 is a display of nuclei from literature and values from equation (2).
It should be noted that serving to arrive at approximations for covalent bond radii is not the focus; the only focus here of the operation is to serve as the disclosure of a test.
Table 6: Equation (3) test  Atoms
Atom 
Published Cov. Bond r (AU) 
(AU) 
Difference (factor) 
Li 
128 
60.70 
0.4742 
K 
203 
108.00 
0.5320 
Na 
166 
90.48 
0.5451 
Ca 
176 
108.89 
0.6187 
Rb 
220 
139.62 
0.6346 
Mg 
141 
92.17 
0.6537 
Cs 
244 
162.39 
0.6655 
Sc 
170 
113.14 
0.6656 
Be 
96 
66.22 
0.6898 
Ti 
160 
115.55 
0.7222 
Sr 
195 
141.33 
0.7248 
Fr 
260 
192.97 
0.7422 
Y 
190 
142.02 
0.7475 
Ba 
215 
164.17 
0.7636 
V 
153 
117.96 
0.7710 
Al 
121 
95.44 
0.7888 
La 
207 
164.79 
0.7961 
Ce 
204 
165.27 
0.8102 
Pr 
203 
165.58 
0.8157 
Zr 
175 
143.24 
0.8185 
Nd 
201 
166.88 
0.8302 
B 
84 
70.36 
0.8376 
Pm 
199 
167.14 
0.8399 
Cr 
139 
118.77 
0.8544 
Sm 
198 
169.20 
0.8546 
Eu 
198 
169.80 
0.8576 
Mn 
139 
120.96 
0.8703 
Si 
111 
96.72 
0.8714 
Gd 
196 
171.75 
0.8763 
Ra 
221 
193.83 
0.8771 
Nb 
164 
144.12 
0.8788 
Tb 
194 
172.36 
0.8884 
Ac 
215 
194.12 
0.9029 
Dy 
192 
173.64 
0.9044 
Ho 
192 
174.50 
0.9089 
Fe 
132 
121.69 
0.9219 
Tm 
190 
175.90 
0.9258 
Er 
189 
175.32 
0.9276 
P 
107 
99.93 
0.9339 
Mo 
154 
145.67 
0.9459 
Yb 
187 
177.32 
0.9482 
Th 
206 
195.53 
0.9492 
C 
76 
72.87 
0.9588 
Cu 
132 
126.98 
0.9620 
S 
105 
101.09 
0.9628 
Pa 
200 
195.25 
0.9763 
Co 
126 
123.83 
0.9828 
Ni 
124 
123.66 
0.9973 
Tc 
147 
147.16 
1.0011 
U 
196 
197.20 
1.0061 
Ru 
146 
148.22 
1.0152 
Hf 
175 
179.16 
1.0238 
Cl 
102 
104.53 
1.0248 
Ar 
106 
108.78 
1.0262 
H 
31 
31.90 
1.0292 
Np 
190 
196.93 
1.0365 
Ag 
145 
151.47 
1.0446 
Rh 
142 
149.11 
1.0501 
Zn 
122 
128.20 
1.0508 
Ta 
170 
179.98 
1.0587 
Pu 
187 
198.85 
1.0634 
Cd 
144 
153.57 
1.0665 
W 
169 
180.94 
1.0706 
Ga 
122 
130.97 
1.0735 
N 
71 
76.70 
1.0803 
Pd 
139 
150.79 
1.0848 
In 
142 
154.66 
1.0891 
Am 
180 
198.58 
1.1032 
Ge 
120 
132.75 
1.1062 
Sn 
139 
156.39 
1.1251 
As 
119 
134.14 
1.1273 
Sb 
139 
157.71 
1.1346 
Se 
120 
136.52 
1.1377 
Br 
120 
137.05 
1.1421 
I 
139 
159.91 
1.1504 
Xe 
140 
161.73 
1.1552 
Te 
138 
160.20 
1.1608 
Cm 
169 
199.67 
1.1815 
Re 
151 
181.70 
1.2033 
Kr 
116 
139.80 
1.2052 
O 
66 
80.18 
1.2148 
At 
150 
189.13 
1.2609 
Os 
144 
183.00 
1.2709 
Bi 
148 
188.83 
1.2759 
Rn 
150 
192.68 
1.2845 
Pb 
146 
188.29 
1.2897 
Ti 
145 
187.43 
1.2927 
Ir 
141 
183.64 
1.3024 
Po 
140 
188.83 
1.3488 
Pt 
136 
184.55 
1.3570 
Au 
136 
185.14 
1.3613 
Hg 
132 
186.27 
1.4111 
F 
57 
84.91 
1.4896 
Ne 
58 
86.63 
1.4936 
He 
28 
50.52 
1.8044 
The following figures elaborate on the Hunt equation test results. Figure 3 shows a plot of Table 3’s summary in full detail per sample. Figure 4 shows a plot of Table 4’s summary in full detail per sample. These two plot graphs show the resulting differences by factor of the approximations of equations (2) & (3) from the values from literature. Figures 5 and 6 show raw value plots of astrosphere and covalent bond radii generated by employing the Hunt variable equation (2). Figure 7 and 8 show raw value plots of star and nucleus radii generated by employing the Hunt variable equation (3). Figures 5 through 8 show values from literature as plotted black circles, and results of the approximation Hunt equations (2) & (3) as plotted red X’s.
Figure 3: Equation 2 Test Plot
Figure 4: Equation 3 Test Plot
Figure 5: Equation 2 Test – Astrosphere (AU) & Cov. Bond values (pm) – CW Leonis not shown
Figure 6: Equation 2 Test – Astrosphere values of CW Leonis results
Figure 7: Equation 3 Test – Star radius values (Mag. of Sun) & Nuc. Radius values (fm) – CW Leonis Not Shown
Figure 8: Equation 3 Test – Star radius for CW Leonis results
Review of Exploration
The results of the tests showed that the average relation between a given star or nucleus of an atom and its astrosphere or covalent bond would typically be that the star or nucleus’ radius would account for ~0.0039% + 0.0010 of the total system size (when counting the “system” as that which is from the astrosphere to star, or from the covalent bond radius to the nucleus). When the stars were separated from the atomic data, the average became ~0.0041% + 0.0019 for the stars. The concept of sampling both stars and atoms to approximate a scaffolding from which to employ as the foundation to build upon appears statistically sufficient at this point; employing the atoms as a crutch to balance estimates upon a known measure of proportion for a system which has an energy core freely in space and a consequent system. The sampled average does indeed inversely produce approximations sympathetic to values from literature within acceptable ranges of deviation for the purposes at hand.
Disclaimer
It needs to be mentioned that the sampling of atoms and stars in this manner is purely functional in application only for this paper’s purpose as described and does not extend to supporting any claims regarding the relationships between atoms and stars in any manner. It also needs to be reminded that this data is the kind belonging to sample averages and does not claim to model an aspect of physical nature itself.
Assembling the “Hunt Line”
We can now build a line which has any given possible star radius and derive from that an average astrosphere radius if all systems were reflective of the ideal system (i.e. the sampled average). It should be remembered that all systems are not in reality reflective of the ideal. The purpose of accepting such an axiom is purely for the production of the measurement baseline for the catalog alone. This line is referred to as the “Hunt line”. The means for building the Hunt line is a sequential application of equation (2) along a scale. This operation and method produces a straight line at angle () correlated in increase between any given star radius magnitude and the radius of the astrosphere. The results create a plot line which looks like that in the following Figure 9.
Figure 9: Hunt Line. Yaxis: Astrosphere (AU). Xaxis: Radial Magnitude of Sun
It should be noted that the Hunt line is not considered to be an authoritative reference by which to make corrections to estimates. It is only a reference line for generating profiles and catalog.
Plotting Against the Hunt Line
We can now place estimates made by researchers along the Hunt line for the purposes of examining the overall trend of a given set by its deviation from the steady Hunt line. The following Figure 10 is an example in concept of what the visual appearance of the Hunt Line employment would look like. Discussion of the value of the Hunt Line will follow in the Hunt Profile section.
Figure 10: Hunt Line with Estimate Sets Example. Yaxis: Astrosphere (AU). Xaxis: Radial Magnitude of Sun
The Hunt Profile
From plotting against the Hunt line we can now create a cataloged profile for any given estimate set by its deviation from the Hunt line. The Hunt profile is a fivepart profile that is unlikely to be exactly alike between two different sets. The five attributes are (1) the mean of the difference by factor of the astrosphere values of the set from the Hunt line, (2) the maximum difference by factor of the astrosphere values of the set from the Hunt line, (3) the minimum difference by factor of the astrosphere values of the set from the Hunt line, (4) the P value of a twotail TTest between the estimate set and the Hunt line, and (5) the P value of an FTest between the estimate set and the Hunt line.
Creating a Hunt Profile
The first step in creating the Hunt profile is to assemble the astrosphere estimates and their related star radii, and to place the Hunt line approximations for the same astrospheres along side of the estimates. Then we divide the set’s astrosphere estimates from the Hunt line approximations to derive the difference by factor. We then find the mean of that difference by factor. We then note the maximum difference and the minimum difference in the set. Next we perform a standard twotail TTest and an FTest between the set and the Hunt line approximations. The T and F tests are ran on the raw values and not on the difference by factor. An example of what such a profile looks like is the following Table 7.
Table 7: Example Hunt Profiles
Set Number 
Estimate Author 
A 
B 
C 
D 
E 
1 
Johnson et al 2015 
1.48 
3.62 
0.49 
2.28E01 
1.64E01 
2 
Frisch 1993 
0.46 
0.82 
0.11 
1.79E14 
1.13E15 
3 
Yeghikyan 2013 
1.43 
2.99 
0.83 
7.60E02 
2.54E03 
A: mean difference from Hunt line by factor, B: Max difference from Hunt line by factor, C: Minimum difference from Hunt line by factor, D: TTest between set and Hunt line P value, E: FTest between set and Hunt line value.
Interpreting the Profile
To interpret the meaning of the profile, we understand that the closer to 1 the mean is, the closer to having the same mean as the Hunt line the set is. The more positive the P value beyond 0.05 the TTest is, the more the given set has a correlation between star radius and astrosphere radius. This means the stronger that correlation is, the more it is that it can be said that the given set has a condition which produces a larger astrosphere based in some relation upon the size of the star’s radius. The further the P value is below 0.05, the less of a correlation is found to exist in the set. The more positive the P value is beyond 0.05 of the FTest, the more the given set shares a similar variance as the Hunt line contains between different astrosphere sizes. Because of this, it becomes simple to see information about sets from a simple plot of these attributes. For example, if we take the three sets which were plotted against the Hunt line previously and put them into a Hunt profile plot, we see the following Figure 11.
Figure 11: Hunt Profiles Plot
In the Hunt line and Hunt profile figures, the data should also include the equation used by the set as well as the assumed values influencing the equation (if any), as well as basic attributes of the given star.
For example, the equations of the 3 example sets of estimates are:
Johnson et al 2015
(4)
Frisch 1993
(5)
Yeghikyan 2013
(6)
Note: The equation from Yeghikyan 2013 is one of the two equations employed in Yeghikyan’s estimates. Yeghikyan supplied two possible estimates by employing two separate equations. Here in this paper, only one of Yeghikyan’s equations are used. Both would be documented in an actual Hunt catalog and treated as two separate estimate sets.
These would be included as part of the estimate set definitions, as opposed to requiring researches to go hunt down he estimate equation that were used.
Generation of the Hunt Catalog
The Hunt catalog could be an online catalog which researchers could access and input their respective data, along with a copy of their publication and contact information for questions from the data analysts. The data would be analyzed by an analyst of submitted data and properly appropriated into the Hunt catalog. The Hunt catalog would be capable of being scaled by the user, as well as permitting the user to search the catalog for various parameters including authors, star id’s/names, constellations, distances from Earth, sizes of stars, classes of stars, sizes of astrosphere, various other data attributes (e.g ISM, wind speed, etc…), and by similarity of Hunt profile or similarity of the model’s equation.
Conclusion
The validity of a means for creating a catalog for
astropause and astrosphere estimates and methods has been explored. It has been
found that the means to pursue such a catalog are available and functionally
viable. More importantly, it was also shown to be particularly useful. With
such a catalog, we could quickly identify that Johnson et. al. 2015 and
Yeghikyan 2013 show a shared relationship with each other more than either
share with Frisch 1993. It is quickly evident, too, that Frisch 1993 contains a
very flat range of estimates which changes distance of astropause very little
regardless of their star magnitude. Meanwhile, both Johnson et. al. 2015 and
Yeghikyan 2013 show a greater range of diversity in astropause/sphere ranges
across a range of star magnitudes, with some correlation existing between
magnitude and astropause/sphere distances in scale. These kinds of
peculiarities could be examined in detail by researchers and analysts to
determine what in each of the estimate models cause shares attributes and what
cause deviating attributes. Once even a dozen such set have been cataloged, the
arrangement of comparisons for examination are voluminous. Every set added
expands the analytical power of the catalog even further.
The only remaining consideration is a matter of logistics to achieving the
catalog’s construction and maintenance, but that is a consideration beyond the
scope of this specific paper.
Special Thanks
The following are highlighted and thanked for their assistance in discourse, guidance, and thought.
· Dr. Robert Oldershaw of Amherst College
· Dr. Sten F. Odenwald of National Institute of Aerospace
· Appreciation is also extended to those academics whose abundant modesty prohibited their mention by name. Though you may think your contributions were not worth mention, their impact was fundamental.
References
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Reviews
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