我們藉由Jeans equation和函式形式的質亮比研究早型星系的質量分佈，探討十四個從Hubble Legacy Archive(HLA)得到波長為555奈米的星系。我們使用power-law作為我們研究中的質亮比形式，並且考慮了三種不同異向性的情形。與之前研究不同的是，我們將質亮比的對數梯度定為一個自由的參數。在我們的研究中，有11個星系在使用power-law的質亮比時，得到最好的擬合結果。此外，在我們的結果中，有8個星系的質亮比的對數梯度為負值，這是過往文獻沒有的結果。負值的質亮比梯度顯示在早型星系中沒有明顯的暗物質光暈，進一步地更指出暗物質聚集在靠近星系內部的位置。除此之外，質量比的對數梯度與星體質量、暗物質質量和超大質量黑洞質量等皆有關聯。暗物質與星體質量、亮度和超大質量黑洞的質量顯示出線性關係。另外，從討論中我們得知較亮的星系，其質亮比的對數梯度較大，且其具有較多的暗物質質量和較重的超大質量黑洞。與之相反，較暗星系的質亮比的對數梯度較小，暗物質質量較少，超大質量黑洞的質量也較小，並且，其顯示出較不明顯的暗物質光暈。

Through Jeans equation and functional total Mass-to-Light ratio (M/L), we study the mass distribution in Early-Type Galaxies (ETGs). Fourteen galaxies from Hubble Legacy Archive (HLA) in F555W wavelength have been studied. We introduce a new probable form for M/L, i.e., power-law M/L and considered three kinds of anisotropic condition (Isotropic, Generally constant, Osipkov-Merritt model). Being different from literature (Napolitano et al. 2005; Alabi et al. 2016), we set logarithmic gradient of M/L as a free parameter. There are eleven galaxies have a best fit with power-law M/L in our work. Additionally, there is a new result from literature that 8 galaxies have negative value in the logarithmic gradient of M/L. The negative value in logarithmic gradient shows a non-significant dark halos in ETGs and further indicates the gathering of dark matter at small radii. Besides that, logarithmic gradient correlates with stellar mass, dark matter mass, and Supermassive black hole (SMBH) mass, etc. Dark matter content also shows the linear correlation with stellar mass, luminosity and Supermassive black hole (SMBH) mass. Additionally, we have the conclusion that brighter galaxies have larger value of logarithmic gradient, more dark matter mass, and more massive SMBH. On the contrary, fainter galaxies have smaller value of logarithmic gradient, less dark matter mass, less massive SMBH, and they show a relatively weak dark halo as well.

[1] Alabi, A. B., et al., 2016, MNRAS, 460, 3838
[2] Baes, M., van Hese, E., 2007, A&A, 471, 419
[3] Bessell, M. S., 2005, Annual Review of Astronomy & Astrophysics, 43, 293
[4] Binney, J., Mamon, G. A., 1982, MNRAS, 200, 361
[5] Bosma, A., van der Kruit, P. C., 1978, A&A, 79, 281
[6] Capaccioli, M., Napolitano, N. R., Arnaboldi, M., 2002, Sakharov Conference of Physics (Moskow, June 2002)
[7] Cappellari, M., et al., 2002, ApJ, 578, 787
[8] Cappellari, M., et al., 2006, MNRAS, 366, 1126
[9] Cappellari, M., et al., 2013, MNRAS, 432, 1862
[10] Carter, D, Jenkins, C. R., 2009, MNRAS, 263, 1049
[11] Carrasco, E. R., et al., 2006, AJ, 132, 1796
[12] Ciotti, L., 1991, A&A, 249, 99
[13] Coccato, L., et al., 2009, MNRAS, 394, 1249
[14] Conroy, C, Pieter, G. van Dokkum, 2012, ApJ, 760, 71
[15] Dehnen, W., 1993, MNRAS, 265, 250
[16] de Vaucouleurs, G., 1948, Annales d’Astrophysique, 11, 247
[17] de Vaucouleurs, G., 1953, MNRAS, 113, 134-161
[18] de Vaucouleurs, G., et al., 1991, Third Reference Catalogue of Bright Galaxies (Volume 1-3, XII, 2069 pp. 7 figs.. Springer-Verlag Berlin Heidelberg New York)
[19] Ferrarese, L., 2002, ApJ, 578, 90
[20] Ferrarese, L. et al., 2006, ApJS, 164, 334
[21] Fisher, D., Illingworth, G., Marijn, F., 1995, ApJ, 438, 539
[22] Fruchter, A. S., Hook, R. N., 2001, Publications of the Astronomical Society of the Pacific, 114, 144
71
[23] Gebhardt, K., et al., 2000, ApJ, 539, L13
[24] Graham, A. W., et al., 2003, ApJ, 125, 2951
[25] Graham, A. W., Scott, N., 2013, ApJ, 764, 151
[26] Gultekin, K., et al., 2009, ApJ, 695, 1577
[27] Halliday, C., et al., 2001, MNRAS, 326, 473
[28] Ha ̈ring, N., Rix, H. W., 2004, ApJ, 604, L89
[29] Hernquist, L., 1990, ApJ, 356, 359
[30] Holtzman, J. A., et al., 1995, Publications of the Astronomical Society of the Pacific, 107, 1065
[31] Hubble, E., 1930, ApJ, 71, 231
[32] Ja↵e, W., 1983, MNRAS, 202, 995
[33] Jedrzejewski, R. I., 1987, MNRAS, 226, 747
[34] Jedrzejewski, R. I., Schechter, P. L., 1989, AJ, 98, 147
[35] Krist, J., 1995, ASPC, 77, 349
[36] Lauberts, A., Valentijn, E. A, 1989, Garching bei Munchen: European Southern Observatory
[37] Lauer, T. R., 1985, ApJS, 57, 473
[38] Lauer, T. R., 1999, Publications of the Astronomical Society of the Pacific, 111, 227
[39] Lauer, T. R., et al., 2005, ApJ, 129, 2138
[40] Loubser, S. I., et al., 2008, MNRAS, 391, 1009
[41] Lucy, L. B., 1974, AJ, 79, 745
[42] McConnell, N. J., et al., 2011, ApJ, 728, 100
[43] McConnell, N. J., Ma, C. P., 2013, ApJ, 764, 184
[44] McConnell, N. J. et al., 2013, ApJL, 768, L21
[45] Merritt, D., 1985, AJ, 90, 1027
[46] Merritt, D., 1985, MNRAS, 214, 25P
[47] Napolitano, N. R. et al., 2004, IAU Symposium, 220
[48] Napolitano, N. R. et al., 2005, MNRAS, 357, 691
[49] Osipkov, L. P., 1979, Pisma v Astronomicheskii Zhurnal, 5, 77
72
[50] Plummer, H. C., 1911, MNRAS, 71, 460
[51] Postman, M, Lauer, T. R., 1995, ApJ, 440, 28
[52] Pu, S. B., et al., 2010, A&A, 516, A4
[53] Richardson, W. H., 1972, J. Opt. Soc. Am., 62, 55
[54] Romanowsky, A. J. et al., 2003, Science, 301, 1696
[55] Saglia, R. P., et al., 1993, ApJ, 403, 567
[56] Samurovi ́c, S, Danziger, I. J., 2005, MNRAS, 363, 769
[57] Sargent, W. L. W., et al., 1978, ApJ, 221, 731
[58] Savorgnan, G. A. D., Graham, A. W., 2016, ApJS, 222, 10
[59] Sloan Digital Sky Survey Team, 2007, Sloan Digital Sky Survey Data Release 6
[60] S ́ersic, J. L., 1963, AAA, 6, 41
[61] S ́ersic, J. L., 1968, Atlas de galaxias australes, Cordoba, Argentina: Observatorio Astronomico
[62] Shen, J., Gebhardt, K., 2010 ApJ, 711, 484
[63] Simien, F., Prugniel, Ph., 1997, A&A, 126, 15
[64] Simien, F., Prugniel, Ph., 2002, A&A, 384, 371
[65] Toloba, E., et al., 2011, A&A, 526, A114
[66] Tortora, C., et al., 2011, MNRAS, 418, 1557
[67] van der Marel, R. P., 1994, MNRAS, 270, 271
[68] Watkins, L. L., et al., 2010, MNRAS, 406, 264
[69] Whitmore, B., 1995, Photometry with the WFPC2, Proceedings of a Workshop held at the Space Telescope Science Institute, in Baltimore, Maryland, May 15- 17, 1995.
[70] WFPC2 Instrument Handbook, Version 10.0 (Baltimore: STScI)
[71] Zwicky, F., 1937, ApJ, 86, 271