Synthetic horizontal branch morphology for different metallicities and ages under tidally enhanced stellar wind

It is believed that, except for metallicity, some other parameters are needed to explain the horizontal branch (HB) morphology of globular clusters (GCs). Furthermore, these parameters are considered to be correlated with the mass loss of the red giant branch (RGB) stars. In our previous work, we proposed that tidally enhanced stellar wind during binary evolution may affect the HB morphology by enhancing the mass loss of the red giant primary. As a further study, we now investigate the effects of metallicity and age on HB morphology by considering tidally enhanced stellar winds during binary evolution. We incorporated the tidally enhanced-stellar-wind model into Eggleton's stellar evolution code to study the binary evolution. To study the effects of metallicity and age on our final results, we conducted two sets of model calculations: (i) for a fixed age, we used three metallicities, namely Z=0.0001, 0.001, and 0.02. (ii) For a fixed metallicity, Z=0.001, we used five ages in our model calculations: 14, 13, 12, 10, and 7 Gyr. We found that HB morphology of GCs becomes bluer with decreasing metallicity, and old GCs present bluer HB morphology than young ones. These results are consistent with previous work. Although the envelope-mass distributions of zero-age HB stars produced by tidally enhanced stellar wind are similar for different metallicities, the synthetic HB under tidally enhanced stellar wind for Z=0.02 presented a distinct gap between red and blue HB. However, this feature was not seen clearly in the synthetic HB for Z=0.001 and 0.0001. We also found that higher binary fractions may make HB morphology become bluer, and we discussed the results with recent observations.Comment: 16 pages, 6 figures, 3 tables, accepted for publication in Astronomy & Astrophysic

On 2D Viscoelasticity with Small Strain

An exact two-dimensional rotation-strain model describing the motion of Hookean incompressible viscoelastic materials is constructed by the polar decomposition of the deformation tensor. The global existence of classical solutions is proved under the smallness assumptions only on the size of initial strain tensor. The proof of global existence utilizes the weak dissipative mechanism of motion, which is revealed by passing the partial dissipation to the whole system.Comment: Different contributions of strain and rotation of the deformation are studied for viscoelastic fluids of Oldroyd-B type in 2

A blowup criterion for ideal viscoelastic flow

We establish an analog of the Beale-Kato-Majda criterion for singularities of smooth solutions of the system of PDE arising in the Oldroyd model for ideal viscoelastic flow