早期型星系之尺度關係 (scaling relations) 可用來連接星系的各種性質，其中又以基本面 (fundamental plane) 為最早的一個應用實例，它藉由有效半徑Re、速度瀰散σ和平均表面亮度三者的關聯性，來估算星系的距離 (Dressler 1987; Djorgovski and Davis 1987)。後續的相關研究也經常地應用這種尺度關係技術，找出早期型星系各種性質間的關聯性。本論文，是以能量的觀點建構一個均功基本面 (virial Fundamental Plane, vFP), 它以質量密度 (ρ ~ M/V) 和均功能量密度 (VED ~ M2/ReV) 兩個變數去建立與其他早期型星系性質之間的關聯性，如質量M，光度L, Re, σ 和年齡Age。本研究使用兩組樣本 --- 核心樣本和延伸樣本：核心樣本包括258個早期型星系 (z < 0.011), 採自ATLAS3D觀測計劃 (Cappellari et al. 2011, 2013b); 延伸樣本包括3,128個早期型星系 (0.01< z < 0.1), 選自SDSS Data Release 4 中有較精準星系形態資訊的14,034個星系 (Nair and Abraham 2010)。

本研究結果顯示：可與ρ -VED vFP構建出性質面的早期型星系性質包括σRe, σRe/8, Vcirc, L, E/L和Age。並且，由vFP建構的MDM面,可用來估計早期型星系在一個Re範圍內的暗物質質量，而這估算出來的暗物質質量可將 Mstar和 Mtotal 數據點由隨機散佈的形態轉變成平面的分佈形態。本研究於分析計算星系體積V時，已將星系橢圓度ε考量進去，並獲得關係式 Mstar ~ Mtotal(1−ε)0.5 和 MDM ~ Re Mtotal0.5 (1−ε)0.75。同時，研究所得數據揭示：質量愈大的早期型星系具有較小的質量密度，這表示，若早期型星系藉由多次星系合併而演化，且其最後總質量為各合併星系質量之和，則其總體積卻大於原各合併星系個別體積之和。另一方面，由獲得結果得知質光比和星系演化年齡有著Mstar ⁄L ~ Age 1/(0.93~0.96) 和Mtotal ⁄L ~ Age 1/(1.00~1.02) 的關係。
關鍵詞: 早期型星系 (ETGs), 基本面 (FP), 均功基本面 (vFP), 均功能量密度(VED), 星系性質, 性質面

Scaling relations of early-type galaxies (ETGs) connect galaxy properties. The ETG fundamental plane is one of the earliest examples that correlates effective radius Re with velocity dispersion σ. and surface brightness and is applied to estimate distance (Dressler 1987; Djorgovski and Davis 1987). Follow-up studies frequently utilize this scaling technique to find correlations among different properties of ETGs. In this study, based on the energy point of view, we construct our virial Fundamental Plane (vFP) with two variables of total mass density (ρ ~ M/V) and Virial Energy Density (VED ~ M2/ReV) to correlate properties of early-type galaxies, such as mass M, luminosity L, Re, σ and Age. Two sets of sample, core sample and extended sample, are included. The core sample includes 258 ETGs (z < 0.011), which are adopted from the ATLAS3D project (Cappellari et al. 2011, 2013b). The extended sample includes 3,128 ETGs (0.01< z < 0.1), which are selected from 14,034 galaxies (Nair and Abraham 2010), a subset of SDSS Data Release 4 (DR4).

The results show that the properties of ETGs can be well constrained by the ρ -VED vFP, which could construct surfaces of σRe, σRe/8, Vcirc, L, E/L and Age. The vFP can define the MDM –surface, which offers a good solution to estimate the DM masses within one Re of ETGs. Simultaneously, the obtained DM masses could transform the distribution of Mstar –surface and the Mtotal –surface from a random type to a flat type with small thicknesses. We also note that both the stellar mass and dark matter mass are significantly correlated with ETG ellipticity ε, if it is not ignored in the galaxy volume estimate. The connections are Mstar ~ Mtotal(1−ε)0.5 and MDM ~ Re Mtotal0.5 (1−ε)0.75. Our results also reveal that the more massive ETGs are, the lower their mass density, which means if an ETG grows via multiple -merging evolution and keeps the original masses of the mergers, its volume becomes larger than the sum of the individual volumes of the mergers. On the other hand, the mass-to-light ratio and the stellar-to-dynamical mass ratio also evolve during the lifetime of ETGs, as our obtained correlations suggest Mstar ⁄L ~ Age (1/0.93~0.96) and Mtotal ⁄L ~ Age (1/1.00~1.02).
Keywords: ETGs, fundamental plane (FP), vFP, VED, galaxy properties, property surface

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