Notes & Considerations on Proposal for Astrosphere Catalog and Baseline Model for Comparison and Reference over Time

Notes & Considerations on Proposal for Astrosphere Catalog and Baseline Model for Comparison and Reference over Time

Jayson Abalos1

1Amateur, 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 mass-loss 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, RAP = Radius of astropause/sphere, Rnuc = Radius of nucleus, Rcov = 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.

https://www.authorea.com/users/108093/articles/136515/master/file/figures/histogram/histogram.png

Figure 1: Histogram

https://www.authorea.com/users/108093/articles/136515/master/file/figures/plotofallsamples/plotofallsamples.png

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 Reff stands for effective radius of the system (i.e. astrosphere/covalent bond), and Rnuc 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)

Kepler-437

290

80.0

0.2760

Kepler-32

180

62.4

0.3466

Kepler-88

140

107.1

0.7651

Kepler-445

30

24.7

0.8240

Kepler-186

59

55.3

0.9377

Sun

121.7

117.7

0.9672

CW Leonis

84000

82398.9

0.9809

Kepler-448

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

Kepler-42

11

20.0

1.8192

Kepler-20

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.

https://www.authorea.com/users/108093/articles/136515/master/file/figures/plothunttest1/plothunttest1.png

Figure 3: Equation 2 Test Plot

https://www.authorea.com/users/108093/articles/136515/master/file/figures/plothunttest2/plothunttest2.png

Figure 4: Equation 3 Test Plot

https://www.authorea.com/users/108093/articles/136515/master/file/figures/hunttest1targetsheet/hunttest1targetsheet.png

Figure 5: Equation 2 Test – Astrosphere (AU) & Cov. Bond values (pm) – CW Leonis not shown

https://www.authorea.com/users/108093/articles/136515/master/file/figures/hunttest1targetsheet-cwleonis/hunttest1targetsheet-cwleonis.png

Figure 6: Equation 2 Test – Astrosphere values of CW Leonis results

https://www.authorea.com/users/108093/articles/136515/master/file/figures/hunttest2targetsheet/hunttest2targetsheet.png

Figure 7: Equation 3 Test – Star radius values (Mag. of Sun) & Nuc. Radius values (fm) – CW Leonis Not Shown

https://www.authorea.com/users/108093/articles/136515/master/file/figures/hunttest2targetsheet-cwleonis/hunttest2targetsheet-cwleonis.png

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.

https://www.authorea.com/users/108093/articles/136515/master/file/figures/Hunt_Line_Raw/Hunt_Line_Raw.png

Figure 9: Hunt Line. Y-axis: Astrosphere (AU). X-axis: 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.

https://www.authorea.com/users/108093/articles/136515/master/file/figures/hunt_line_example/hunt_line_example.png

Figure 10: Hunt Line with Estimate Sets Example. Y-axis: Astrosphere (AU). X-axis: 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 five-part 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 two-tail T-Test between the estimate set and the Hunt line, and (5) the P value of an F-Test 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 two-tail T-Test and an F-Test 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

2.28E-01

1.64E-01

2

Frisch 1993

0.46

0.82

0.11

1.79E-14

1.13E-15

3

Yeghikyan 2013

1.43

2.99

0.83

7.60E-02

2.54E-03

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: T-Test between set and Hunt line P value, E: F-Test 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 T-Test 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 F-Test, 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.

https://www.authorea.com/users/108093/articles/136515/master/file/figures/Hunt_Profile/Hunt_Profile.png

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

Frisch, P. C. (1993). G-star astropauses - A test for interstellar pressure.

Genya, T., Ford, E., Sills, A., & al., e. (2013). Structure and Evolution of Nearby Stars with Planets II. Physical Properties of 1000 Cool Stars from the Spocs Catalog.

Johnson, M., Redfield, S., & Jensen, A. (2015). The Interstellar Medium in the Kepler Search Volume.

Repolust, T., Puls, J., & Herrero, A. (2004). Stellar and wind parameters of Galactic O-stars.

Sahai, R. (2010). The Astrosphere of the Asymptotic Giant Branch Star IRC+10216.

Santerne, A., Moutou, C., Tantaki, M., Bouchy, F., & al., e. (2013). SOPHIE velocimetry of Kepler transit candidates.

Webber, W., McDonald, F., Cummings, A., & al., e. (2012). At Voyager 1 Starting On about August 25, 2012 At a Distance Of 121.7 AU From the Sun, a Sudden Sustained Disappearance Of Anomalous Cosmic Rays and an Unusually Large Sudden Sustained Increase of Galactic Cosmic Ray H and He Nuclei and Electrons Occurred.

Weigelt, G., Balega, Y., Blocker, T., & al., e. (1998). 76 mas speckle–masking interferometry of IRC +10 216 with the SAO 6 m telescope: Evidence for a clumpy shell structure.

 

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