• Journal of The Korean Astronomical Society
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• v.49 no.5
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• pp.193-198
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• 2016

Early-type galaxies (ETGs) are supposed to follow the virial relation $M=k_e{\sigma}^2R_e/G$, with M being the mass, σ_* being the stellar velocity dispersion, R_e being the effective radius, G being Newton's constant, and k_e being the virial factor, a geometry factor of order unity. Applying this relation to (a) the ATLAS^3D sample of Cappellari et al. (2013) and (b) the sample of Saglia et al. (2016) gives ensemble-averaged factors 〈k_e〉 = 5.15 ± 0.09 and 〈k_e〉 = 4.01 ± 0.18, respectively, with the difference arising from different definitions of effective velocity dispersions. The two datasets reveal a statistically significant tilt of the empirical relation relative to the theoretical virial relation such that $M{\propto}({\sigma}^2_*R_e)^{0.92}$. This tilt disappears when replacing R_e with the semi-major axis of the projected half-light ellipse, a. All best-fit scaling relations show zero intrinsic scatter, implying that the mass plane of ETGs is fully determined by the virial relation. Whenever a comparison is possible, my results are consistent with, and confirm, the results by Cappellari et al. (2013). The difference between the relations using either a or R_e arises from a known lack of highly elliptical high-mass galaxies; this leads to a scaling (1 - ϵ ) ∝ M^0.12, with ϵ being the ellipticity and $R_e=a\sqrt[]{1-{\epsilon}}$. Accordingly, a, not R_e, is the correct proxy for the scale radius of ETGs. By geometry, this implies that early-type galaxies are axisymmetric and oblate in general, in agreement with published results from modeling based on kinematics and light distributions.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.29 no.4
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• pp.206-216
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• 2017

The temporal distribution of the turbulence kinetic energy (TKE) and the vertical component of Reynolds stresses ($-{\bar{u^{\prime}w^{\prime}}}$) was measured during one wave period under high wave energy conditions. The wave data were obtained at Hujeong Beach in the east coast of Korea at January 14~18 of 2017 when an extratropical cyclone was developed in the East Sea. Among the whole thousands of waves measured during the period, hundreds of regular waves that had with similar pattern were selected for the analysis in order to give three representing mean wave patterns using the ensemble average technique. The turbulence properties were then estimated based on the selected wave data. It is interesting to find out that $-{\bar{u^{\prime}w^{\prime}}}$ has one clear peak near the time of flow reversal while TKE has two peaks at the corresponding times of maximum cross-shore velocity magnitudes. The distinguished pattern of Reynolds stress indicates that vertical fluxes of such properties as suspended sediments may be enhanced at the time when the horizontal flow direction is reversed to disturb the flows, supporting the turbulence convection process proposed by Nielsen (1992). The characteristic patterns of turbulence properties are examined using the CADMAS-SURF Reynolds-Averaged Navier-Stokes (RANS) model. Although the model can reasonably simulate the distribution of TKE pattern, it fails to produce the $-{\bar{u^{\prime}w^{\prime}}}$ peak at the time of flow reversal, which indicates that the application of RANS model is limited in the prediction of some turbulence properties such as Reynolds stresses.