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It is found that the natural frequencies of sandwich panels decrease as the gradient changes of the DG foam cores increase under the condition of that the core masses keep constant.
In order to understand how the measured masses and radii of such planets can inform their structures and compositions, we construct models both for solid layered planets and for planets with solid cores and gaseous envelopes, exploring a range of core masses, H2–He envelope masses, and associated envelope entropies.
With the intent of generating (3 M_{odot }) and (4 M_{odot }) Helium-star progenitors, we begin with a (12.9 M_{odot }) and (16.0 M_{odot }) zero-age models with metallicity (Z = 0.02),4 which are predicted by SSE to end with the required helium core masses.
Initially it is a slow process, increasing the core masses up to in a few million years.
For even larger core masses, the core temperature becomes high enough to allow photodisintegration and the core collapses completely into a black hole.
For core masses of, the collapse halts and the star remains intact, but core collapse will occur again when a larger core has formed.
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This is the tightest constraint to date on the core mass of a hot Jupiter.
The most likely value isMcore,b=11M⊕, which is similar to the core mass theoretically required for runaway gas accretion.
The prestellar core mass function (CMF) is consistent with lognormal form, resembling the stellar system initial mass function, as has been reported previously.
If the core mass exceeds three solar masses, the core collapse is too great to produce a neutron star; the imploding star is compressed into an even smaller and denser body namely, a black hole.
We explore the effect of surface temperature and core mass fraction on the scaling laws for these planets.
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