Dynamical Modeling of Velocity Profiles: The Dark Halo around the Elliptical Galaxy NGC 2434
Dynamical Modeling of Velocity Profiles: The Dark Halo around the Elliptical Galaxy NGC 2434
复制标题
DOI：
10.1086/304733
复制
发表时间：
1997-02
期刊：
影响因子：
--
通讯作者：
H. Rix;T. Zeeuw;M. Carollo;N. Cretton;R. V. D. Marel
中科院分区：
文献类型：
--
作者：
H. Rix;T. Zeeuw;M. Carollo;N. Cretton;R. V. D. Marel
我们描述了一个强大的技术来模拟和解释恒星的视线速度分布的星系。它是基于史瓦西的方法来建立完全通用的动力学模型。一个代表性的轨道库计算在一个给定的潜力，并确定这些轨道的非负叠加，最适合一组给定的观测约束。我们实现的最重要的新功能是，我们计算和拟合全速度剖面形状，由高斯-厄米级数表示。这允许我们在拟合中约束轨道各向异性。我们还使用客观的χ2度量拟合质量，考虑到每个观测约束的误差。给定观测约束的χ2，该技术评估给定潜力中不同轨道组合以及具有不同潜力的模型的相对可能性。在我们的实现中，只有投影，可观测的量被包括在拟合中，孔径合并和看到卷积的数据被适当地考虑，并且可以通过正则化来加强相空间中的模型的平滑度。该方案适用于任何几何体。在这种方法的第一个应用程序中，我们专注于球形几何，轴对称建模中所描述的同伴论文Cretton等人。和货车德Marel等人。我们测试的计划从各向同性Hernquist模型绘制的伪数据，然后将其应用到椭圆星系周围的暗晕的问题。我们的模型径向扩展恒星运动学数据E0星系NGC 2434获得的E0星系NGC 2434的E0等。这个星系被选中，因为它可能是近圆的，在这种情况下，目前的球形建模是适用的。无论轨道各向异性如何，具有恒定质光比的模型显然被排除在外。为了研究与数据相匹配所需的暗物质数量，我们考虑了一系列宇宙学激发的“星星+晕”势。这些潜力是基于Navarro等人的CDM模拟，但也解释了重子物质的积累;它们由恒星质光比B和特征晕速度V200来指定。星星+晕模型提供了一个极好的数据拟合，其中λ *，B = 4.35 ± 0.35（B波段太阳单位）和V200 = 450 ± 100 km s-1。最佳拟合势的圆速度Vc在0.2到3个有效半径之间保持在约10%的范围内，并且与最佳拟合对数势非常相似，其Vc = 300 ± 15 km s-1。在NGC 2434中，有效半径内大约有一半的质量是暗的。相比之下，我们没有暗晕的模型估计的恒星数量的质光比是它的两倍。如果NGC 2434是一个非常扁平的系统，那么在没有进一步观测限制的情况下，限制引力势将变得更加困难。
We describe a powerful technique to model and interpret the stellar line-of-sight velocity profiles of galaxies. It is based on Schwarzschild's approach to build fully general dynamical models. A representative library of orbits is calculated in a given potential, and the non-negative superposition of these orbits is determined that best fits a given set of observational constraints. The most significant new feature of our implementation is that we calculate and fit the full velocity profile shapes, represented by a Gauss-Hermite series. This allows us to constrain the orbital anisotropy in the fit. We also use an objective χ2 measure for the quality of fit, taking into account the error on each observational constraint. Given χ2 from the observational constraints, the technique assesses the relative likelihood of different orbit combinations in a given potential, and of models with different potentials. In our implementation only projected, observable quantities are included in the fit, aperture binning and seeing convolution of the data are properly taken into account, and smoothness of the models in phase space can be enforced through regularization. This scheme is valid for any geometry. In a first application of this method, we focus here on spherical geometry; axisymmetric modeling is described in companion papers by Cretton et al. and van der Marel et al. We test the scheme on pseudo-data drawn from an isotropic Hernquist model and then apply it to the issue of dark halos around elliptical galaxies. We model radially extended stellar kinematical data for the E0 galaxy NGC 2434 obtained by Carollo et al. This galaxy was chosen because it may be nearly round, in which case the present spherical modeling is applicable. Models with constant mass-to-light ratio are clearly ruled out, regardless of the orbital anisotropy. To study the amount of dark matter needed to match the data, we considered a sequence of cosmologically motivated “star + halo” potentials. These potentials are based on the CDM simulations by Navarro et al., but also account for the accumulation of baryonic matter; they are specified by the stellar mass-to-light ratio ϒ*,B and the characteristic halo velocity, V200. The star + halo models provide an excellent fit to the data, with ϒ*,B = 4.35 ± 0.35 (in B-band solar units) and V200 = 450 ± 100 km s-1. The best-fitting potential has a circular velocity Vc that is constant to within ~10% between 0.2 and 3 effective radii and is very similar to the best-fitting logarithmic potential, which has Vc = 300 ± 15 km s-1. In NGC 2434 roughly half of the mass within an effective radius is dark. In comparison, our models without a dark halo estimate a mass-to-light ratio for the stellar population that is twice as large. If NGC 2434 is a significantly flattened system seen nearly face-on, it would be considerably more difficult to limit the gravitational potential without further observational constraints.