Would exoplanets like those of Kepler-70 possess magnetic fields? The B-type subdwarf, Kepler-70  (aka KIC 5807616) is believed to have two planets orbiting it, at average distances 0.006 AU and 0.0076 AU (source). Due to their proximity to their parent star, they are almost certainly tidally locked to it (although I don't know if tidal forces between the planets themselves might counter this, since they apparently pass within a few hundred thousand miles of each other and have short orbital periods.)

Now, the "day side" of each of these planets would have surface temperatures exceeding that of the Sun! (i.e. > 6000 K.) If, indeed, they are tidally locked, we might also expect a significant temperature difference between the "night" and "day" sides. The planets are believed to be the rocky/iron cores of gas giants that were engulfed when their parent star expanded. If I have understood the paper by Nordhaus et al. correctly, the gas giants would have had to be significantly larger than Jupiter. Certainly, however, the Chthonian planets that they turned into are now hot enough for metal/rock to be evaporating on at least one side, and possibly both. It would seem unlikely that they would be mostly solid.

If this is correct, then:


We have two planets, each mostly liquid/gaseous, with significant temperature differences between different regions. So it looks to me as though there would be convection.
If the planets have significant metallic content, they would also be conductive.
They are certainly also rotating, at the speed required to keep one side continuously facing the star.


Am I correct, therefore, that they probably have magnetic fields generated by the dynamo effect? Or is there some factor, possibly related to the extraordinarily high temperatures involved (or my own lack of knowledge :-) ) that would imply otherwise?

Sources:


J. Nordhaus, D. S. Spiegel, L. Ibgui, J. Goodman, A. Burrows, Tides and tidal engulfment in post-main-sequence binaries: period gaps for planets and brown dwarfs around white dwarfs, Monthly Notices of the Royal Astronomical Society, Volume 408, Issue 1, October 2010, Pages 631–641, https://doi.org/10.1111/j.1365-2966.2010.17155.x
Charpinet S. et al. A compact system of small planets around a former red giant star. Nature vol. 480 (2011)
Bear, E., &amp; Soker, N. (2012). A tidally destructed massive planet as the progenitor of the two light planets around the SDB star KIC 05807616. The Astrophysical Journal Letters, 749(1), L14.
Although it's not proven, I've just read a research paper which provides evidence for the planets having magnetic fields. Assuming that they exist, of course.

The paper is "A tidally destructed massive planet as the progenitor of the two light planets around the SDB star KIC 05807616."

The authors state:


  Considering that the planets have suffered a recent strong tidal deformation with continuous strong tidal force from the central EHB star, and that they are heated by the central star radiation, they are expected to be hot and liquid, and possess a differential rotation. It is very probable that a strong dynamo is operating in each planet, leading to the required magnetic field.


Bear and Soker also calculate the expected time of evaporation for the closer of the two planets, resulting from the star's intense UV radiation. They arrive at a figure of $\approx 10,000,000$ years. However, Kepler-70 has been a B-subdwarf for 18.4 million years (source: Charpinet et al.) and its exoplanets would therefore be at least that old.

They state:


  the expression is highly uncertain, and we might overestimate the evaporation rate.


However, their calculations show that a planetary magnetic field about 10 times as strong as that of Earth is plausible, and would suffice to protect the exoplanet from evaporation. They find this more likely than uncertainty in the aforementioned calculation.


  Our preferred explanation for a low evaporation rate is the existence of a magnetic field ...  More likely we find the possibility that a planetary magnetic field, about 10 times as strong as that of Earth ... will substantially reduce the evaporation rate by holding the ionized gas.