利用星系旋转曲线及行星近日点异常进动对弦理论中规范场限制的研究
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摘要
在本工作中我们主要讨论一个由弦理论启发而来、可用于天文和宇宙学的(唯像)模型。在该模型中物质通过与弦理论中的规范场耦合而受到额外的一个作用力,该作用力在一些宇宙学或者天文学现象及观察结果中可能会有所表现。我们首先从弦理论出发简单介绍该模型,然后将其应用于多个宇宙学或天文学现象的解释,涉及到的问题和现象包括星系旋转曲线问题以及太阳系中某些行星近日点的异常进动现象。
在星系旋转曲线问题方面,我们选取了总共二十二个星系的旋转曲线数据,利用该弦理论模型对这些曲线进行了拟合。作为比较,我们还利用一个简单的暗物质模型对同一组数据进行了拟合。根据拟合结果,该弦理论模型与该暗物质模型在这一数据源上显示出了相近的拟合能力。弦理论中的规范场强度是作为该弦理论模型中一个拟合参数的,根据这二十二个星系曲线数据的拟合,其在该组星系中的强度覆盖大约两个数量级。通过量纲分析我们还可以从该弦理论模型得出一个关于规范场强度,星系(大小)尺度以及星系总亮度之间的方程。我们利用这二十二个星系的数据以及弦理论模型对其拟合所得的结果对该方程进行了验证。
我们尝试利用该模型来解释最近发现的太阳系中某些行星近日点的异常进动现象。在此之前,我们首先进行了关于行星在受到微扰情况下近日点进动的理论分析,成功解决了以下两种情形下的一般进动问题：一、微扰为类磁场力；二、微扰为一般的幂次中心力。对第二种情形,我们还得到了一个判断该微扰导致正向进动还是反向进动的简单规则。我们随后将该模型应用于最近观察到的太阳系中某些行星近日点的异常进动,假设是该模型中的额外(类磁)力造成了此异常进动,利用之前得到的关于进动的理论工具,我们计算了在太阳系中几个行星所处位置上的规范场强度。根据场强度在各处的大小情况,我们接着对强度分布进行了一个带预设强度形式的拟合,该预设形式中太阳系中的场为两个分量的叠加：其一为太阳所产生的类偶极矩场,其二为银河系中其他物质所产生的常数背景场。作为比较,我们还利用了银河系旋转曲线来估计了银河系中的场强度,所得的强度与进动所得的处在类似的数量级上。
We discuss a cosmological model in which the string gauge field couples to matter and leads to an extra force which would have various effect on cosmological observations. We first introduce the model from considerations in string theory. Several tests on the model are then performed using astronomical observations including galaxy rotation curves and perihelion precession in the solar system.
For a set of 22 galaxies, we fitted their rotation curves with both the string model and a particular dark matter model. The two models showed similar fitting power for this set of curves. The string field strengths in these galaxies, which is a parameter adjusted to fit these curves, are found to lie in a range spanning about 2 orders of magnitude. By dimensional analysis, we derived from the string model a relation between field strength, galaxy size and luminosity which is then verified with data of the 22 galaxies.
The model is also used to explain anomalous perihelion precession of planets in the solar system. We solved precession motions for perturbations of 1) a magnetic-like force and 2) a general power law central force. For the latter case, a simple rule judging pro- or retrograde precession is derived. We then attributed the anomalous precession to the magnetic-like force due to string field and calculated field strengths in various locations in the solar system. The field distribution looks like a dipole field centered at the Sun. This feature is further explored using a field profile consisting of one part generated by the Sun and another background due to other matter in the Milky Way. As a compare with the result from precession, we also estimated the field strength in the Milky way by rotation curve, which turns out to be on a similar order of magnitude.
在星系旋转曲线问题方面,我们选取了总共二十二个星系的旋转曲线数据,利用该弦理论模型对这些曲线进行了拟合。作为比较,我们还利用一个简单的暗物质模型对同一组数据进行了拟合。根据拟合结果,该弦理论模型与该暗物质模型在这一数据源上显示出了相近的拟合能力。弦理论中的规范场强度是作为该弦理论模型中一个拟合参数的,根据这二十二个星系曲线数据的拟合,其在该组星系中的强度覆盖大约两个数量级。通过量纲分析我们还可以从该弦理论模型得出一个关于规范场强度,星系(大小)尺度以及星系总亮度之间的方程。我们利用这二十二个星系的数据以及弦理论模型对其拟合所得的结果对该方程进行了验证。
我们尝试利用该模型来解释最近发现的太阳系中某些行星近日点的异常进动现象。在此之前,我们首先进行了关于行星在受到微扰情况下近日点进动的理论分析,成功解决了以下两种情形下的一般进动问题：一、微扰为类磁场力；二、微扰为一般的幂次中心力。对第二种情形,我们还得到了一个判断该微扰导致正向进动还是反向进动的简单规则。我们随后将该模型应用于最近观察到的太阳系中某些行星近日点的异常进动,假设是该模型中的额外(类磁)力造成了此异常进动,利用之前得到的关于进动的理论工具,我们计算了在太阳系中几个行星所处位置上的规范场强度。根据场强度在各处的大小情况,我们接着对强度分布进行了一个带预设强度形式的拟合,该预设形式中太阳系中的场为两个分量的叠加：其一为太阳所产生的类偶极矩场,其二为银河系中其他物质所产生的常数背景场。作为比较,我们还利用了银河系旋转曲线来估计了银河系中的场强度,所得的强度与进动所得的处在类似的数量级上。
We discuss a cosmological model in which the string gauge field couples to matter and leads to an extra force which would have various effect on cosmological observations. We first introduce the model from considerations in string theory. Several tests on the model are then performed using astronomical observations including galaxy rotation curves and perihelion precession in the solar system.
For a set of 22 galaxies, we fitted their rotation curves with both the string model and a particular dark matter model. The two models showed similar fitting power for this set of curves. The string field strengths in these galaxies, which is a parameter adjusted to fit these curves, are found to lie in a range spanning about 2 orders of magnitude. By dimensional analysis, we derived from the string model a relation between field strength, galaxy size and luminosity which is then verified with data of the 22 galaxies.
The model is also used to explain anomalous perihelion precession of planets in the solar system. We solved precession motions for perturbations of 1) a magnetic-like force and 2) a general power law central force. For the latter case, a simple rule judging pro- or retrograde precession is derived. We then attributed the anomalous precession to the magnetic-like force due to string field and calculated field strengths in various locations in the solar system. The field distribution looks like a dipole field centered at the Sun. This feature is further explored using a field profile consisting of one part generated by the Sun and another background due to other matter in the Milky Way. As a compare with the result from precession, we also estimated the field strength in the Milky way by rotation curve, which turns out to be on a similar order of magnitude.
引文
[1]Horizon web interface. http://ssd.jpl.nasa.gov/?horizons
[2]Nasa/ipac extragalactic database. http://nedwww.ipac.caltech.edu
[3]H. W. Babcock. The topology of the sun's magnetic field and the 22-year cycle. Astrophysical Journal,133,1961.
[4]E Battaner and E Florido. The rotation curve of spiral galaxies and its cosmological implica-tions. Fund. Cosmo Phys.,21,2000.
[5]Yeuk-Kwan E. Cheung, Laurent Freidel, and Konstantin Savvidy. Strings in gravimagnetic fields. JHEP,0402:054,2004.
[6]Yeuk-Kwan E. Cheung, Konstantin Savvidy, and Hsien-Chung Kao. Galaxy rotation curves from string theory. Feb 2007.
[7]Yeuk-Kwan E Cheung and Feng Xu. Fitting the galaxy rotation curves:Strings versus nfw profile. Oct 2008.
[8]E.N.Parker. Cosmic-ray modulation by solar wind. Physical Review,110,1958.
[9]Herbert Goldstein, Charles P. Poole, and John L. Safko. Classical Mechanics,3rd Edition. Addison Wesley,2002.
[10]M. B. Green, J. H. Schwarz, and E. Witten. Superstring theory. Volume 1-Introduction.1987.
[11]Φyvind Grφn and Harald H. Soleng. Experimental limits to the density of dark matter in the solar system.1995.
[12]Mareki Honma and Yoshiaki Sofue. Rotation curve of the galaxy. Publ. Astron. Soc. Japan, 49,1997.
[13]Lorenzo Iorio. The Astronomical Journal 137 3615,2009.
[14]P. Meyer, E. N. Parker, and J. A. Simpson. Solar cosmic rays of february,1956 and their propagation through interplanetary space. Physical Review,104,1956.
[15]CW Misner, KS Thorne, and JA Wheeler. Gravitation. W. H. Freeman,1973.
[16]Chiara R. Nappi and Edward Witten. Wess-zumino-witten model based on a nonsemisimple group. Phys. Rev. Lett.,71(23):3751-3753, Dec 1993.
[17]E. N. Parker. dynamics of the interplanetary gas and magnetic fields. Astrophysical Journal, 128,1958.
[18]M.S. Roberts. Astronomical Journal,74,1969.
[19]J. H. Shirley and R. W. Fairbridge. Encyclopedia of Planetary Sciences. September 1997.
[20]Y. Sofue, Y. Tutui, M. Honma, A. Tomita, T. Takamiya, J. Koda, and Y. Takeda. Central rotation curves of spiral galaxies.1999.
[21]R. B. Tully and J. R. Fisher. A new method of determining distances to galaxies. J. R. Astronomy and Astrophysics, vol.54, no.3, pages 661-673, Feb 1977.
[22]Steven Weinberg. Gravitation and cosmology:principles and applications of the general theory of relativity. Wiley,1972.
[23]Feng Xu. Perihelion precession from power law central force and magnetic-like force. Phys. Rev. D,83(8):084008, Apr 2011.
[2]Nasa/ipac extragalactic database. http://nedwww.ipac.caltech.edu
[3]H. W. Babcock. The topology of the sun's magnetic field and the 22-year cycle. Astrophysical Journal,133,1961.
[4]E Battaner and E Florido. The rotation curve of spiral galaxies and its cosmological implica-tions. Fund. Cosmo Phys.,21,2000.
[5]Yeuk-Kwan E. Cheung, Laurent Freidel, and Konstantin Savvidy. Strings in gravimagnetic fields. JHEP,0402:054,2004.
[6]Yeuk-Kwan E. Cheung, Konstantin Savvidy, and Hsien-Chung Kao. Galaxy rotation curves from string theory. Feb 2007.
[7]Yeuk-Kwan E Cheung and Feng Xu. Fitting the galaxy rotation curves:Strings versus nfw profile. Oct 2008.
[8]E.N.Parker. Cosmic-ray modulation by solar wind. Physical Review,110,1958.
[9]Herbert Goldstein, Charles P. Poole, and John L. Safko. Classical Mechanics,3rd Edition. Addison Wesley,2002.
[10]M. B. Green, J. H. Schwarz, and E. Witten. Superstring theory. Volume 1-Introduction.1987.
[11]Φyvind Grφn and Harald H. Soleng. Experimental limits to the density of dark matter in the solar system.1995.
[12]Mareki Honma and Yoshiaki Sofue. Rotation curve of the galaxy. Publ. Astron. Soc. Japan, 49,1997.
[13]Lorenzo Iorio. The Astronomical Journal 137 3615,2009.
[14]P. Meyer, E. N. Parker, and J. A. Simpson. Solar cosmic rays of february,1956 and their propagation through interplanetary space. Physical Review,104,1956.
[15]CW Misner, KS Thorne, and JA Wheeler. Gravitation. W. H. Freeman,1973.
[16]Chiara R. Nappi and Edward Witten. Wess-zumino-witten model based on a nonsemisimple group. Phys. Rev. Lett.,71(23):3751-3753, Dec 1993.
[17]E. N. Parker. dynamics of the interplanetary gas and magnetic fields. Astrophysical Journal, 128,1958.
[18]M.S. Roberts. Astronomical Journal,74,1969.
[19]J. H. Shirley and R. W. Fairbridge. Encyclopedia of Planetary Sciences. September 1997.
[20]Y. Sofue, Y. Tutui, M. Honma, A. Tomita, T. Takamiya, J. Koda, and Y. Takeda. Central rotation curves of spiral galaxies.1999.
[21]R. B. Tully and J. R. Fisher. A new method of determining distances to galaxies. J. R. Astronomy and Astrophysics, vol.54, no.3, pages 661-673, Feb 1977.
[22]Steven Weinberg. Gravitation and cosmology:principles and applications of the general theory of relativity. Wiley,1972.
[23]Feng Xu. Perihelion precession from power law central force and magnetic-like force. Phys. Rev. D,83(8):084008, Apr 2011.