#### 期刊菜单

Galaxy’s Approximate Luminosity Probability and Linear Statistic Analysis of Luminosity Graph

Abstract: Electromagnetic band complies with smooth function, when galaxy’s luminosity is at Z > 0.0041. Approximate luminosity exists in Z-logL graph. Approximate luminosity verifies that when galaxy’s luminosity is fixed value, calculating fixed luminosity has nothing to do with distance (or redshift). When some fixed luminosity is over certain distance that can’t be observed, even university’s extremely weak gravitational effect is one of the conditions that make dark matter exist. Only with logLλ1-logLλ2 graph, we can’t learn the compactness or dispersion of point set on the diagonal line. But it can be learned by linear statistics. Galaxy’s electromagnetic wave has very weak gravitational effect during long-distanced transmission. When the wavelength shortens by exp(Z/2), luminosity must increase by exp(Z/2). Analysis of galaxy’s approximate luminosity and linear relation of logLλ1-logLλ2 is more accurate than the analysis and validation of two data’s above. It replenishes the examples of galaxy group mainly based on galaxy great wall network.

1. 前言

2. 基础方程的列出

$\nu S\left(chZ-1\right)={\nu }_{n}{S}_{n}\left(ch{Z}_{n}-1\right)$ .(1)

${S}_{n}=\frac{\nu S\left(chZ-1\right)}{{\nu }_{n}\left(ch{Z}_{n}-1\right)}$ . (2)

${Z}_{n}=arch\left[\frac{\nu S\left(chZ-1\right)}{{\nu }_{n}{S}_{n}}+1\right]$ . (3)

$r=200\left(1-{\text{e}}^{-Z}\right)$ ，单位：亿光年。 (4)

$t=200Z$ ，单位：亿年。 (5)

${L}_{\mu m}=4\text{π}{d}_{L}^{2}\left(c/{\lambda }_{\mu m}\right)\left({10}^{-32}{S}_{\mu m}\right)$ ，其中 ${d}_{L}^{2}=2{r}_{s}^{2}\left(chZ-1\right)$(6)

${L}_{\lambda }=4\text{π}{S}_{\lambda }\left(或{F}_{\lambda }\right)\left(c/\lambda \right){d}_{L}^{2}$${L}_{\nu }=4\text{π}\nu {S}_{\nu }\left(或{F}_{\nu }\right){d}_{L}^{2}$ (6a)

$\mathrm{log}\left({L}_{3.6}/{L}_{sun}\right)=9.29186+\text{log}\left[{S}_{3.6}\left(\mathrm{cosh}Z-1\right)\right]$ . (7)

$\mathrm{log}\left({L}_{4.5}/{L}_{sun}\right)=9.19495+\mathrm{log}\left[{S}_{4.5}\left(\mathrm{cosh}Z-1\right)\right]$ . (8)

$\mathrm{log}\left({L}_{g}/{L}_{sun}\right)=10.73443+0.4\left(22.5-g\right)+\mathrm{log}\left(\mathrm{cosh}Z-1\right)$ .(9)

$\mathrm{log}\left({L}_{r}/{L}_{sun}\right)=10.6182+0.4\left(22.5-r\right)+\mathrm{log}\left(\mathrm{cosh}Z-1\right)$ . (10)

$\Delta k=2.5\mathrm{log}\left[{\text{e}}^{Z}/\left(1+Z\right)\right]$ . (11)

${m}_{k}=m+2.5\mathrm{log}\left[{\text{e}}^{Z}/\left(1+Z\right)\right]$ . (12)

3. 星系表中红外通量密度及红移近似等红外光度计算分析

Table 1 . Pick fixed value Full 142 in galaxy tableII/326/zcatrev. When flux density S3.6 = 346.29, Z = 0.762, log(L3.6) = 11.3151 or L3.6 = 2.1662 × 1011Lsun, When S4.5 = 221.61, log(L4.5) = 11.0243.When Magnitude gmag = 21.98, rmag = 20.52. log(Lg) = 10.4262, log(Lr) = 10.8940. When k is revised to gmag = 22.19, rmag = 20.72, log(Lgn) = 10.3422, log(Lrn) = 10.8140. When the galaxy is 10.6654 billion light year away from the earth, it needs 152.4 light years to transmit the luminosity, 22 values

Table 2 .Basing on the first column in Table II/326/zcatrev, according to Equation (2), to find 24 corresponding values S3.6n and Zn of S3.6 = 24.70 and Z = 0.914

Figure 1. Theoretically draw redshift-infrared 3.6 μm luminosity graph

Table 3. Luminosity’s average log L ¯ of Table 1, overall variance σ2L, standard variance σL

Table 4. Luminosity’s average log L ¯ of Table 2, overall variance σ2L, standard variance σL

$\nu S\left(chZ-1\right){\text{e}}^{Z/2}={\nu }_{n}{S}_{n}\left(ch{Z}_{n}-1\right){\text{e}}^{{Z}_{n}/2}$ ,(13)

${S}_{n}=\frac{\mu S\left(chZ-1\right){\text{e}}^{Z/2}}{{\nu }_{n}\left(ch{Z}_{n}-1\right){\text{e}}^{{Z}_{n}/2}}$ , (14)

${L}_{\mu m}=4\text{π}{d}_{L}^{2}\left[c/\left({\lambda }_{\mu m}{\text{e}}^{-Z/2}\right)\right]\left({10}^{-32}{S}_{\mu m}\right)$ . (15)

$\mathrm{log}\left({L}_{3.6}/{L}_{sun}\right)=9.29186+\mathrm{log}\left[{S}_{3.6}\left(chZ-1\right){\text{e}}^{Z/2}\right]$ . (16)

$\mathrm{log}\left({L}_{4.5}/{L}_{sun}\right)=9.19495+\mathrm{log}\left[{S}_{4.5}\left(chZ-1\right){\text{e}}^{Z/2}\right]$ . (17)

$\mathrm{log}\left({L}_{g}/{L}_{sun}\right)=10.73443+0.4\left(22.5-g\right)+\mathrm{log}\left[\left(chZ-1\right){\text{e}}^{Z/2}\right]$ . (18)

$\mathrm{log}\left({L}_{r}/{L}_{sun}\right)=10.6182+0.4\left(22.5-r\right)+\mathrm{log}\left[\left(chZ-1\right){\text{e}}^{Z/2}\right]$ . (19)

Table 5.30 data is based on 142*, the others are sought according to Equation (14). And then to calculate the luminosity of each wave band

Table 6.41 data is based on 42*, the others are sought according to Equation(14). Luminosity increases by exp(Z/2). And then to calculate the luminosity of each wave band

Table 7. Luminosity’s average log L ¯ of Table 5, overall variance σ2L, standard variance σL

Table 8. Luminosity’s average log L ¯ of Table 6, overall variance σ2L, standard variance σL

4. 星系红外光度logLλ1-logLλ2线性分析

4.1. 星系红外光度线性分析

$\mathrm{log}\left({L}_{5.8}/{L}_{sun}\right)=9.08473+\mathrm{log}\left[{S}_{5.8}\left(chZ-1\right)\right]$ (20)

$\mathrm{log}\left({L}_{8}/{L}_{sun}\right)=8.94507+\mathrm{log}\left[{S}_{8}\left(chZ-1\right)\right]$ (21)

$\mathrm{log}\left({L}_{24}/{L}_{sun}\right)=8.46795+\mathrm{log}\left[{S}_{24}\left(chZ-1\right)\right]$ (22)

$\mathrm{log}\left({L}_{5.8}/{L}_{sun}\right)=9.08473+\mathrm{log}\left[{S}_{5.8}\left(chZ-1\right){\text{e}}^{Z/2}\right]$ . (23)

$\mathrm{log}\left({L}_{8。0}/{L}_{sun}\right)=8.94507+\mathrm{log}\left[{S}_{8。0}\left(chZ-1\right){\text{e}}^{Z/2}\right]$ . (24)

$\mathrm{log}\left({L}_{24}/{L}_{sun}\right)=8.46795+\mathrm{log}\left[{S}_{24}\left(chZ-1\right){\text{e}}^{Z/2}\right]$ (25)

$\mathrm{log}\left({L}_{IR}\right)=1.37\left(±0.04\right)×\left(\mathrm{log}{{L}^{\prime }}_{CO}\right)-1.74\left(±0.40\right)$ , $\mathrm{log}\left({L}_{IR}\right)=1.13×\left(\mathrm{log}{{L}^{\prime }}_{CO}\right)+0.53$ .

Table 9. Linear statistic log L λ 2 = a ⋅ log L λ 1 + b , confidence level r, n ≤ 72

Table 10. Linear statistic log ( L λ 2 ) = a ⋅ log ( L λ 1 ) + b , confidence level r, n ≤ 72 . Each infrared luminosity increases by exp(Z/2)

4.2. 星系可见光度与红外光度线性分析及平均光度方差分布近似正态分布

Table 11. Table of linear luminosity and average luminosity of same wavelength. log L λ = a ⋅ log L R + b . r is confidence level. n is quantity of sample, which is same with each other in the same column

Table 12. It’s the statistic of variance σ L ¯ of each galaxy’s average luminosity and they approximately appear to be normal distribution

5. 星系长城局域补充

(简写为A)及后发座Coma Cluster。

$\Delta r={r}_{s}\left({\text{e}}^{-{Z}_{1}}-{\text{e}}^{-{Z}_{2}}\right)$ (26)

$D=\frac{{r}_{s}\theta {\text{e}}^{-Z/2}\left(1-{\text{e}}^{-Z}\right)}{206264.8}$ (27)

(2) http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=J/A%2BA/490/923表13中A1413、AM546-324和A85红移间距文献中可能不很准确，视纵向间距小于60 Mpc，文献中作者们对红移间距测量不很重视，没有上述分析内容。表13中的第3列红移间距有些值原文献中以cz = v表出，现统一用红移表出。充分验证了Z > 0.01的星系集群非团，应该是星系长城局域或星系纤维柱为主要特征。

Table 13. 15 Abell Cluster and the first, second, third, fifth column is the data of original literature in the bracket. The fourth and sixth column is calculated value of Equation (1) and (6) in Literature [1] (of Equation (26) and (27)). (P.S: the bracket in the first and sixth column is references)

6. 小结与讨论

Figure A1. The left is graph of flux density S250μm infrared luminosity-redshift, the right is graph of common infrared luminosity-redshift. Only graph of Z < 1 can be drawn according to the two diagrams and infrared luminosity diagram of all redshifts can’t be drawn, which is one of the most serious problems in standard cosmology. The two graphs can be extended to 10 times of redshift

Figure A2. The left is graph of $\left({L}_{IR}-{L}_{250\mu \text{m}}\right)$ and the right is graph of $\left({L}_{IR}-{L}_{100\mu \text{m}}\right)$ . Only graph of Z < 0.5 can be drawn according to the two graphs and Graph $\left(L-L\right)$ of all redshifts can’t be drawn. Point coordinates should gather closely on both sides of the diagonal. Especially in the left graph, point coordinates gather far away from the diagonal, which is one of the most serious problems in standard cosmology as well. The two graphs can be extended to 10 times of redshift. L-L graph’s compactness or dispersion can be analyzed by linear statistic

NOTES

*退休。

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