﻿ 宇宙几何学初步应用—天体的光度和绝对星等等价不变性的证明 Primary Application of Cosmic Geometry—Proof of Equivalence and Invariant of Astronomical Object’s Luminosity and Absolute Magnitude

Astronomy and Astrophysics
Vol.06 No.03(2018), Article ID:26213,17 pages
10.12677/AAS.2018.63005

Primary Application of Cosmic Geometry

—Proof of Equivalence and Invariant of Astronomical Object’s Luminosity and Absolute Magnitude

Xun Huang*

Ningjiang Middle School, Xingning Guangdong

Received: Jul. 10th, 2018; accepted: Jul. 24th, 2018; published: Jul. 31st, 2018

ABSTRACT

Cosmic geometry is cosmic even gravity geometry derived by General Relativity. When redshift Z > 0.0041, one astronomical object lightness (flux density or apparent magnitude) is distance’s variable and its corresponding luminosity or absolute magnitude is the variable that doesn’t change as distance varies. Above is presented as theory in basic textbook, but without literature of mathematical derivation and validation for its universality. The following is the strict mathematical derivation and validation for its universality (Luminosity and absolute magnitude is equivalent and invariant). And universality of gravitational lens galaxy mass’s calculation is validated by using cosmic even gravity geometry and central gravity geometry. Validation above is based on basic data from observation of galaxy, which can prove the universality of cosmic geometry.

Keywords:New Gravitational Cosmic Metric, Gravity Geometry, Apparent Magnitude, Gravitational Lens, Luminosity

—天体的光度和绝对星等等价不变性的证明

1. 引言

2. 宇宙几何学简介

2.1. 宇宙几何学理论初步应用

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

$\Delta r={r}_{12}={r}_{21}={r}_{s}\sqrt{{\left(1-{\text{e}}^{-{Z}_{1}}\right)}^{2}+{\left(1-{\text{e}}^{-{Z}_{2}}\right)}^{2}-2\left(1-{\text{e}}^{-{Z}_{1}}\right)\left(1-{\text{e}}^{-{Z}_{2}}\right)\mathrm{cos}\theta }$ (2)

Full 306，(为方便略去坐标或名，仅用叙号)红移 ${Z}_{V1}=0.448182$，通量密度 ${F}_{u1}=0.067312$${F}_{g1}=1.106049$${r}_{2}$ ：Full 298，红移 ${Z}_{V2}=4.164000$，通量密度 ${F}_{u2}=0.115925$${F}_{g2}=1.325061$，通量密度单位是3.631 μJy。对应有效波长分别是λEu358.68 nm，λEg471.67 nm。列表1

$\vartheta =\text{arcos}\frac{1-{\left(1-{\text{e}}^{-{Z}_{1}}\right)}^{2}-{\left(1-{\text{e}}^{-{Z}_{2}}\right)}^{2}}{2\left(1-{\text{e}}^{-{Z}_{1}}\right)\left(1-{\text{e}}^{-{Z}_{2}}\right)}={81.94743859}^{\circ }$ (3)

${\lambda }_{n}={\lambda }_{E}{\text{e}}^{\left({Z}_{n}-{Z}_{E}\right)/2}$(4)

$m-M=5\mathrm{log}\left[2{r}_{s}\mathrm{sinh}\left(Z/2\right)\right]-5$(5)

$m=22.5-2.5\mathrm{log}\left({F}_{\lambda }/3.631\text{\hspace{0.17em}}\mu \text{Jy}\right)$(6)

$L=8\text{π}{r}_{s}^{2}{F}_{\lambda }\left(c/\lambda \right)\left(\mathrm{cosh}Z-1\right){\text{e}}^{Z/2}$(7)

Table 1. Two quasars’ redshift, flux and effective wavelength. Flux density’s unit is 3.631 μJy

${F}_{n\lambda }\left(\mathrm{cosh}{Z}_{n}-1\right){\text{e}}^{{Z}_{n}/2}/{\lambda }_{n}={F}_{E\lambda }\left(\mathrm{cosh}{Z}_{E}-1\right){\text{e}}^{{Z}_{E}/2}/{\lambda }_{E}$，即

${F}_{n\lambda }=\frac{{\lambda }_{n}{F}_{E\lambda }\left(\mathrm{cosh}{Z}_{E}-1\right){\text{e}}^{\left({Z}_{E}-{Z}_{n}\right)/2}}{{\lambda }_{E}\left(\mathrm{cosh}{Z}_{n}-1\right)}$ (8)

$\begin{array}{c}{M}_{\lambda }=27.5-2.5\mathrm{log}\left[{F}_{\lambda }/3.631\text{\hspace{0.17em}}\mu \text{Jy}{\left(2{r}_{s}\mathrm{sinh}Z/2\right)}^{2}\right]\\ =27.5-2.5\mathrm{log}\left[2\left({F}_{\lambda }/3.631\text{\hspace{0.17em}}\mu \text{Jy}\right){r}_{s}^{2}\left(\mathrm{cosh}Z-1\right)\right]\end{array}$(9 )

$\begin{array}{c}{M}_{\lambda }=27.5-2.5\mathrm{log}\left({F}_{\lambda }/3.631\text{\hspace{0.17em}}\mu \text{Jy}\right)-5\mathrm{log}\left[2{r}_{s}\mathrm{sinh}\left(Z/2\right)\right]\\ =27.5-2.5\mathrm{log}\left\{{F}_{\lambda }/3.631\text{\hspace{0.17em}}\mu \text{Jy}{\left[2{r}_{s}\mathrm{sinh}\left(Z/2\right)\right]}^{2}\right\}\\ =27.5+2.5\mathrm{log}\left[4\text{π}\left(c/\lambda \right)×3.631\right]+2.5\mathrm{log}{\text{e}}^{Z/2}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}-2.5\mathrm{log}\left[8\text{π}{r}_{s}^{2}\left(c/\lambda \right){F}_{\lambda }\left(\mathrm{cosh}Z-1\right){\text{e}}^{Z/2}\right]\\ ={M}_{\lambda 0}-2.5\mathrm{log}L\end{array}$ (10)

${M}_{\lambda 0}=27.5+2.5\mathrm{log}\left[4\text{π}\left(c/\lambda \right)×3.631\right]+2.5\mathrm{log}{\text{e}}^{Z/2}$(11)

${M}_{\lambda }={M}_{\lambda 0}+\alpha -2.5\mathrm{log}{L}_{\lambda }$(12)

$\alpha ={M}_{\lambda }+2.5\mathrm{log}{L}_{\lambda }-{M}_{\lambda 0}={M}_{\lambda }+2.5\mathrm{log}{L}_{\lambda }-{M}_{\lambda 0}$(12a)

${d}_{bL}={10}^{\left[\left(m-M+5\right)/5\right]}\text{pc}$ (13)

${d}_{L}=2{r}_{s}\mathrm{sinh}\left(Z/2\right)=1.22624×{10}^{10}\mathrm{sinh}\left(Z/2\right)\left(\text{pc}\right)$ (14)

${d}_{L}=2×1.892×{10}^{26}\mathrm{sinh}\left(Z/2\right)\text{\hspace{0.17em}}\left(\text{m}\right)$ (14a)

${Z}_{12}=-\mathrm{ln}\left(1-\Delta r/{r}_{s}\right)=1.08226182$(15)

${F}_{\lambda 76.82}=\frac{76.82×0.067312\left(\mathrm{cosh}0.448182-1\right){\text{e}}^{\left(0.448182-1.0822\right)/2}}{358.68\left(\mathrm{cosh}1.0822-1\right)}=0.00166238005$ (16)

$\begin{array}{c}\mathrm{log}{L}_{\lambda 76.82}=\mathrm{log}\left[8\text{π}{\left(1.892×{10}^{26}\right)}^{2}\left(c/76.82×{10}^{-9}\right)×1.662×{10}^{-3}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}×3.631×{10}^{-32}\left(\mathrm{cosh}1.0822-1\right){\text{e}}^{1.0822/2}\right]\\ =35.37077221\text{\hspace{0.17em}}\text{W}\end{array}$(17)

${M}_{\lambda 76.82}=27.5-2.5\mathrm{log}\left\{1.662×{10}^{-3}{\left[2×6.1312×{10}^{9}\mathrm{sinh}\left(1.0822/2\right)\right]}^{2}\right\}=-14.76617537$(16)

Table 2. Use value of Table 1 to calculate two quasars’ luminosity, absolute magnitude and constant α observed on the earth

Table 3. Below is observed wavelength of the two effective wavelength of Table 1 on two quasars

Table 4. Below are observed fluxes of the two fluxes of Table 1 on two quasars. Unit is 3.631 μJy

$L=8\text{π}{r}_{s}^{2}{F}_{\lambda }\left(c/\lambda \right)\left(\mathrm{cosh}Z-1\right)$(7a)

${F}_{n\lambda }=\frac{{\lambda }_{n}{F}_{E\lambda }\left(\mathrm{cosh}{Z}_{E}-1\right)}{{\lambda }_{E}\left(\mathrm{cosh}{Z}_{n}-1\right)}$(8a)

${M}_{\lambda }={M}_{\lambda 0}+\alpha +-2.5\mathrm{log}{L}_{\lambda }$(12b)

$\alpha ={M}_{\lambda }+2.5\mathrm{log}\left({L}_{\lambda }\right)-{M}_{\lambda 0}={M}_{\lambda }+2.5\mathrm{log}{L}_{\lambda }-{M}_{\lambda 0}$(12c)

Table 5. When θ = 17 .6324576 ∘ , luminosity and absolute magnitude of u and g wavelength observed on r 1 and r 2

Table 6. When θ = 72.7365032 ∘ , luminosity, absolute magnitude and constant ɑ of u and g wavelength observed on r 1 and r 2

Table 7. When redshift ZE = 2.634562, the observed wavelength changed, and it’s not the value of the last column in Table 1, but the wavelength calculated in Equation (4)

Table 8. Comparison of corresponding value in Table 2. Luminosity is smaller than the corresponding one in Table 2. Absolute magnitude is equal to the one. Constant α = 2.446878250 ± 7 × 10 − 9 is close to the one

2.2. 宇宙几何学理论验证应用

Table 9. n is luminosity and absolute magnitude calculated by ten fluxes F of 10 quasars

Table 10. The average value of 10 luminosities and absolute magnitudes and variance σ in Table 9

Table 11. n is luminosity and absolute magnitude calculated by ten redshifts and fluxes F of 12 quasars

Table 12. The average value of 10 luminosities and absolute magnitudes and variance σ in Table 11

3. 超新星和VizieR星系、类星体表统一规范分析

Table 13. The comparison of original and new luminosity distance of six supernovas. The third column m-M(mag) is the calculated value in original figure Photometry for. The fourth is calculated value of Equation (13), according to the second and third column. The fifth (b) is the original value and the last column (c) is value calculated by Equation (14) according to the second column

VizieR http://vizier.u-strasbg.fr/viz-bin/VizieR-3?-source=VII/250/2dfgrs (1998-2003)。

VizieR http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=VII/275 (2016)这2个表的视星等、绝对星等、光度距离很多错误值不可用了。

VizieR http://vizier.u-strasbg.fr/viz-bin/VizieR-3?-source=J/PASJ/63/S379/modswide (2011)这个表的视星等、绝对星等、光度很多错误值不可用了，只能用通量密度和红移。

VizieR http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=J/ApJ/684/136 (2008)这2个表纯通量密度和红移，据此用上文所导出的方程很适用。

VizieR http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=II/284 (2007)表中i波长的通量密度计算的视星等不匹配。

VizieR http://vizier.u-strasbg.fr/viz-bin/VizieR-3?-source=VII/270/dr10q (2014)表中u g r i z波长的通量密度计算的视星等错误值多，不能全部引用。

VizieR http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=VII/279 (2017)表中u g r i z波长的通量密度计算的视星等错误值多，不能全部引用。

VizieR http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=J/A%2BA/590/A31 (2016)有4个表(2个星系集群)的10个波长(B V…IRAC2)的视星等很多错误值不可用了，只能用通量密度和红移据此用上面所导出的方程很适用。不能全部引用。

Table 14. Rmag in the table is not in accordance with other tables. nRmag is calculated by Equation (6). Rλeff642.78 nm, logLR is calculated by Equation (7a). ɑ is calculated by Equation (12c) and ɑ = 2.44687 ± 0.00002

VizieR http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=VII/274 (2015)

4. 引力透镜新应用

${\beta }_{E}^{2}=\frac{4GM{D}_{sL}}{{c}^{2}{D}_{Es}{D}_{EL}}$ (9.1.5)

$M=\frac{{c}^{2}{\beta }_{E}^{2}{r}_{s}{\text{e}}^{-{Z}_{L}}\left(1-{\text{e}}^{-{Z}_{L}}\right)\left(1-{\text{e}}^{-{Z}_{s}}\right)}{4×{206264.8}^{2}G\left({\text{e}}^{-{Z}_{L}}-{\text{e}}^{-{Z}_{s}}\right){M}_{\Theta }}$ (18)

M为透镜星系质量，宇宙视界上面给出取m为单位。M是太阳质量1.998 × 1030 kg。

•QSO 0957 + 561：两个像分离角为6.1，故 ${\beta }_{E}=3.05\text{'}\text{'}$，以下同法， ${Z}_{L}=0.36$${Z}_{s}=1.41$，代入方程(18)计算出透镜星系质量 $M\cong 2.450×{10}^{12}{M}_{\odot }$，和银河系质量相当。

•B 0218 + 357：两个像分离角为0.335， ${Z}_{L}=0.68$${Z}_{s}=0.96$，同法计算(以下计算同法)出透镜星系质量 $M\cong 2.621×{10}^{10}{M}_{\odot }$

•PKS 1830-211：两个像分离角为1.0， ${Z}_{L}=0.89$${Z}_{s}=2.507$，计算出透镜星系质量 $M\cong 1.265×{10}^{11}{M}_{\odot }$

•SDSS J1000 + 0221： [6] 两个像分离角为0.35， ${Z}_{L}=1.53$${Z}_{s}=3.417$，计算出透镜星系质量 $M\cong 2.050×{10}^{10}{M}_{\odot }$。原文 [2] 计算值是6×1010M，透镜星系质量同数量级。

•SDSS J2222 + 2745： [7] 两个像分离角为15.1， ${Z}_{L}=0.49$${Z}_{s}=2.82$，计算出透镜星系质量 $M\cong 1.724×{10}^{13}{M}_{\odot }$

•SDSS J1029 + 2623： [8] 两个像分离角为0.1， ${Z}_{L}=0.60$${Z}_{s}=2.197$，计算出透镜星系质量 $M\cong 9.421×{10}^{8}{M}_{\odot }$。原文 [8] 计算值约是109M。透镜星系质量同数量级。

•SDSS J1029 + 2623：[9]当透镜星系为集群时 ${\beta }_{E}=\text{15}.\text{25}0\text{5}$ , ${Z}_{L}=0.584$ , ${Z}_{s}=2.197$，计算出透镜星系群质量 $M\cong 8.558×{10}^{13}{M}_{\odot }$。原文 [9] 计算值约是 $1.55×{10}^{14}{h}^{-1}{M}_{\odot }$

•SDSS J1000 + 0221： [6] 两个像分离角为0.35， ${Z}_{L}=1.53$${Z}_{s}=3.417$，计算出透镜星系质量 $M\cong 2.050×{10}^{10}{M}_{\odot }$。原文 [6] 计算值约是6~7.6×1010M。透镜星系质量同数量级。

•J1004 + 4112： [10] 两个像分离角为14.6时， ${Z}_{L}=0.68$${Z}_{s}=1.734$，计算出透镜星系质量 $M\cong 2.490×{10}^{13}{M}_{\odot }$

•SDSS J1029 + 2623： [11] ${Z}_{L}=0.58$${Z}_{s}=2.197$，图像有A，B，C，BC挨近，在G1 G2大致取为中心O，量出AO，BO，CO角径分别为19.57，18.91，19.17。用方程(1)计算出透镜星系质量３个值19.21，取平均值为 $M\cong 1.350×{10}^{14}{M}_{\odot }$

•B1608 + 656： [12] ${Z}_{L}=0.6304$${Z}_{s}=1.394$，图像有A，B，C，过这3个类星体像有光弧近圆，量出弧平均角半径的角秒为爱因斯坦角半径3.765，计算出透镜星系质量 $M\cong 6.994×{10}^{12}{M}_{\odot }$

•HE0435-1223： [13] ${Z}_{L}=0.4541$${Z}_{s}=1.689$，图像有A，B，C，D。4个类星体像光弧近圆，量出近圆平均角半径的角秒为爱因斯坦角半径1.25，计算出透镜星系质量 $M\cong 4.913×{10}^{11}{M}_{\odot }$

•SDSS J2222 + 2745： [14] 透镜星系 ${Z}_{L}=0.49$${Z}_{s}=2.82$，类星体像光弧近圆，量出近圆平均角半径的角秒为爱因斯坦角半径7.34，计算出透镜星系质量 $M\cong 1.630×{10}^{13}{M}_{\odot }$。原文 [14] 计算值约是 $1.12×{10}^{13}{M}_{\odot }$

•CS82+VICS82 [15] 透镜星系 ${Z}_{L}=0.4541$，星系 ${Z}_{s}=1.689$，环半径3，计算出透镜星系质量 $M\cong 2.830×{10}^{12}{M}_{\odot }$

•HE1104-1805 [16] 两个像分离角为3.15时， ${Z}_{L}=0.729$${Z}_{s}=2.319$，计算出透镜星系质量 $M\cong 1.090×{10}^{12}{M}_{\odot }$

${\beta }_{E}$ 近1'时，透镜星系不能为单个，或为星系集群( $M\le {10}^{13~14}{M}_{\odot }$ )；当 ${\beta }_{E}$ 超过1'时，透镜星系集群，可能是星系长城局域( $M>{10}^{14}{M}_{\odot }$ ) [2] [3] 。计算时与 ${Z}_{L}$${Z}_{s}$ 密切相关。

5. 小结与讨论

1) 以上计算分析符合星系观测数据实际基础，应该是必知的基础，在红移Z > 0.0041定义域内，以上方程都是红移的光滑函数，且是普适。2) 方程(4)至(12a)在具体观测例子分析导出光度与绝对星等等价性，很精确，文献中找不到这么精准的理论分析。3) 反复思考分析§1-4，并对§4的不同作者公布的星系表计算(篇幅限制，不能在此列大表，读者可以在VizieR表中下载验证以上方程)，常量ɑ随光度与绝对星等的精确个数变化，从表2表8表9表11表14的常量ɑ变化规律。4) §4倒数2段中找出各文献的4个不同视星等方程，经计算比较，因视星等变了值，绝对星等和常量ɑ变了值，方程(4)至(12a)仍正确，不再在此讨论，有兴趣者据VizieR表计算分析。5) 方程(4)至(12a)具体观测例子精准的理论分析，可以和天体力学理论，热力学与统计物理学，电动力学，量子力学一样媲美精准。现在天文学界需共同讨论规范统一亮度，光度与绝对星等方程，那么宇宙天体物理学可以与本科理论物理学一样严谨精准。6) 引力透镜方程(18)受到观测数据制约，引力透镜星系质量精确度较差。7) Einstein引力场方程导出的新引力宇宙度规，在分析星系观测数据的距离(绝对距离，相对距离，光度距离，角径距离和光锥距离 [3] )，角径，亮度，光度，引力透镜，引力延时 [17] [18] ，其结论与文献同类结论相近似，有的超过或优于文献结论，请参阅以上结论对比文献。8) 从理论分析天体运动历史可知，理论分析星系观测数据必似Newton《自然哲学的数学原理》，Newton仅用万有引力定律理论分析行星运动，不用其他理论。只用新引力宇宙度规分析星系观测数据完全能自然展开。巨量的星系观测数据理论分析完全可行(γ爆，x射线和射电光度分析，以上方程完全适用，另文讨论)。9) Einstein在他的《相对论的意义》中指出：物理定律在宇宙中任何地方都是普适(或同权)的，以上分析进一步验证他这句定律，请人们用标准宇宙学验证他这句定律！？

Primary Application of Cosmic Geometry—Proof of Equivalence and Invariant of Astronomical Object’s Luminosity and Absolute Magnitude[J]. 天文与天体物理, 2018, 06(03): 58-74. https://doi.org/10.12677/AAS.2018.63005

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19. NOTES

*退休教师。