在這論文中，我們收集了含有5707 個橢圓星系的目錄。這些星系來
自史隆數位巡天（Sloan Digital Sky Survey-SDSS,包含g’,r’,i’,z’波段），
並且在二微米巡天(Two Micron All-Sky Survey -2MASS,包含J,H,Ks 波段)
有光學對應體。我們也選擇出另外共有716 個大橢圓星系（在七個波段
中，其等效半徑(effective radius)皆大於6 角秒(arcsec)）的次樣本。
這兩個樣本皆符合基礎平面關係（fundamental plane-FP）。我們檢驗
了這兩份樣本分別在g’,r’,i’,z’, J, H, Ks，共七個波段中的基礎平面關係。
我們使用兩個質量模型（一為，金氏模型（King’s model）在牛頓動
力學下，另一為多方模型（polytropic model）在牛頓動力學修正（MOND）
下）計算出每一個星系的質量。星系中牛頓力學下的質量總是大於牛頓動
力學修正下的質量。我們也注意到質光比（mass to light ratio），跟質量有
些許的關係。假設質光比正比於質量的α次方，我們發現α在不同質量模
型、不同波段中有不同的數值。
星系的大小視觀測的波長而定。我們研究星系的大小-波長關係。 我
們把星系分成四類。（一）從可見光到近紅外為單一冪次法則，（二）等
效半徑在可見光跟近紅外有中斷，（三）最小值出現在可見光跟近紅外轉
換處，（四）不屬於上面三類。我們預期，星系大小在大星系樣本中比較
正確，並且發現在大星系樣本中，有62.3%屬於第一類、21.2%屬於第二
類、 10.5%屬於第三類，和6.0%屬於第四類。換句話說，超過80%的橢圓
星系擁有老年恆星多於年輕恆星的中心。

In this thesis, we collect a catalog of 5707 galaxies from SDSS(g’,r’,i’,z’) which have
counterpart in 2MASS(J,H,Ks). A subsample of 716 galaxies is selected for their larger
effective angular size (effective radius larger than 3 aresec in all 7 bands).
Both samples fit a fundamental plane (FP) as expected. We examine the FP for 7 bands
including g’,r’,i’,z’,J,H,Ks.
We work out the mass of each galaxy by two mass models (one is King’s model in
Newtonian dynamics, one is polytropic model in MONDian dynamics). The Newtonian
mass is always larger than MONDian mass. We note that the mass-to-light ratio depends
on mass weakly. Assuming M/L ∝ M , we find that is different in different dynamics,
in different band.
The size of each galaxy depends on observing wavelength. We study the size-wavelength
relation. We can classify the galaxies into four groups. (1) single power law from
optical to infrared, (2) a break in effective radius between optical and infrared, (3) a
minimum around the transition between optical and infrared, (4) cannot be classified
into the previous 3 classes. We expect that the size is more reliable in the larger galaxies
samples, and find that in this sample, 62.3% are class-1, 21.2% are class-2, 10.5% are
class-3, and 6.0% are class-4. In other world, there are more than 80 % ellipticals have
more concentrated older star population than younger one.

Bender, R., et al . 1992, ApJ, 399, 462
Bernardi, M., et. al . 2003a, AJ, 125, 1866
Bernardi, M., et. al. 2003b, AJ,125, 1882
Bessell, M. S. 1990, PASP, 102, 1181
Blantonn, M. R. & Roweis, S. 2007, ApJ, 133, 734
Cohen, M., Wheaton, W. A., & Megeath, S. T. 2003, AJ, 126, 1090
de Vaucouleurs, G. 1948, Annales d’Astrophysique, 11, 247
Djorgovski, S. & Davis, M. 1987, ApJ, 313, 59
Efstathiou, G., et. al. 2002, MNRAS, 330, L29
Gibbons, R. A., Fruchter, A. S., & Bothun, G. D. 2001, AJ, 121, 649
Hendry, M. A. & Simmons, J. F. L. 1995, Vistas in Astronomy, 39, 297
Jarrett, T. H., et. al . 2000, AJ, 119, 2498
Kelson, D. D., Illingworth, G. D., van Dokkum, P. G., & Franx, M. 2000, ApJ, 531, 184
King, I. R. 1966, AJ, 71, 64
Milgrom, M. 1983, ApJ, 270, 365
Pahre, M. A., de Carvalho, R. R., & Djorgovski, S. G. 1998, AJ, 116, 1606
Peacock, J. A. 1999, Cosmological Physics (Cosmological Physics, by John A. Peacock,
pp. 704. ISBN 052141072X. Cambridge, UK: Cambridge University Press, January 1999.)
Sanders, R. H. 2000, MNRAS, 313, 767
Scodeggio, M. 1997, PhD thesis, AA(CORNELL UNIVERSITY)
York, D. G., el. al . 2000, AJ, 120, 1579