[Professor Mega-Mind (OP)]

    Egomen , start yer go-carts !
 Lately , certain esteemed "Astronomy Domine" researchers have been claiming that the the Trappist1 worlds are wrapped in
extremely thick water shells . My response is "Don't you believe it!" .  Developmentally , red-dwarf systems are close cousins to Jovian systems . Their dimensions , planetary mass-ratios , orbital characteristics , etc. , are all basically Jovian , writ heavy .  The immediate implication is that the compositions are ( were ) Jovian  also .  Formed with massive volatile shells , most of their original complement has been lost to red-dwarf radiation-stripping .  Those further out lost less , but still only retain a fraction of their original volume .  These planets now have low-densities not because of an excess of water , but because of a dearth of metals .  Both Mars and Luna are close by analogs of this type of rocky world . 
 Giant telescopic arrays may be able to image exoplanet surfaces , but only spectroscopy  will show how much leached-out salt is in the oceans .  Combined with age , this could indicate total oceanic volume , and thus oceanic depth.  Partial, and full , glaciation could greatly obscure such measurements . 
Alright , I let off some steam! P.M
 

[chiralSPO]

I don't see how analogy to the Jovian system supports your arguments here...

Io (one of Jupiter's moons, for others reading this, who don't know) has the greatest density of any of the moons in our solar system, supposedly because of its high abundance of iron. Also, Europa (another of Jupiter's moons) has a thick water shell.
https://en.wikipedia.org/wiki/Io_(moon)
https://en.wikipedia.org/wiki/Europa_(moon)

Granted, this is by no means proof (or even evidence) of water shells on the Trappist1 worlds, but these two facts do appear to challenge your line of reasoning, unless I have misunderstood your meaning...
edit: repair some URLs...

[Professor Mega-Mind (OP)]

'Ello , argu-mahn !
Take a gander at the relative core masses of those moons .  Then , separately guage their heavy metals content .  Now , how many Callistos would it take to provide Io with it's full complement of iron .  I put it to you that Io was once huge, with a much lower density . Billions  of years of spewing have removed much of it's lighter elements , in a quite uneven  manner , leaving a disproportionate complement of the heavier elements .  The further out moons were made smaller and less dense , plus they lost less of their initial materials to space . The kicker is that Jupiter would have drawn in a significant amount of the formation disc's metals , whereas the hotter Trappist1 would have kept them at distance . 
Okay , stellar distillation it is !  P.M.

[chiralSPO]

Interesting. I hadn't thought about that explanation for the composition of Io, but it fits with what I know. Thank you for sharing

That said, I'm still not entirely sure that this helps refute the idea of water worlds around Trappist1...

(NOTE: I am not an expert in astronomy, astrophysics, etc. but I am interested in it, and I am a chemist)

[Professor Mega-Mind (OP)]

To:ChiralSPO
 If you thought THAT was gnarly , dig this !  : 
 Most of these rocky worlds start out with a significant water complement .  Each one then has a unique chemical & physical developmental history .  The result is a mad panoply of extreme worlds .  These range from tide-locked "Crematoria" class planets , to ice-capped "Barsoom" planets , to "Interstellar" planets with Denali-waves , and serious overloads of chlorine , etc.  . 
 The most surprising class of rocks is the "Mercury" class .  Normally tide-locked, airless, and sometimes thousands of degrees on the front-side , these offer rich mining , and comfortable underground living on the back-side .  They even have enough water & lighter elements frozen in their dark-side craters ! 
 As you can see , it's crazy-rich out there .  The trick is us getting our act together here .  Sending peopsicles hurtling across the cosmos is about here , the question is , can we handle the power ?....................................P.M.

[Professor Mega-Mind (OP)]

    Addendum to Trappist1 issue .
A comparison of the density of the Trappist1 planets yields a Mars-like density for T.1b , & a moon-like density for T.1d !  The explanation for T.1b lies in the proto-planetary disk .  As the innermost planet was forming , the proto-star's powerful  magnetic field leached much of the accretion disk's metal content out , and into the star . In addition ,weak radiation pressure from the .dwarf allowed much of the heaviest disk material to actually accrete all of the way onto the star's surface .
T.1d's low density has a different cause .  Early in the formation process there were two medium-density planets drawn into a race- track formation .  Eventually they had a glancing collision . The result was an oversized Moon-like body , and a very  Earth-like body .  Tidal forces ensured that T.1d assumed an independent orbit around Trap.1 while T.1e took up orbit directly outside of it .  This exchange displaced much of the smaller impactor's core material into the larger impactor , witness the much greater mass & density of T.1e .
Anyhoo , anomaly explained !...P.M.
Note - It is even more plausible that Trappist1 C experienced the  collision , and that the lighter moon-like body was forced into a higher orbit , while the Earth-like body settled into a lower orbit .

[Professor Mega-Mind (OP)]

..................Appearances
What is the typical appearance of a warm , close-in , red-dwarf star , Earth-sized planet ?  Such are inevitably tide-locked .  A glaciated night-side is the norm , as is an arid day side .  Differences in the planetary parameters  (equilibrium temp. , gravity , magnetic field strength , etc.) determine the amount of volatile stripping the planet experiences .  This variation  gives rise to a plethora of planetary  surface types .  More water left means larger glaciers , more rain , and larger seas . Less atmosphere  means less rain , and less green-house effect . Hotter temp.s mean  less glaciation , more rain , larger seas , more cloud cover .  The variations are numerous , and include atmospheric super-rotation  induced , planetary slow-rotation .  This would likely be much slower than that of Venus , the close-in planets having much larger tidal-bulges and interactions with their parent stars .  They also tend to have thinner atmospheres , suffused with "fossil" oxygen, from disassociated H2O . 
These "warm" worlds must be differentiated from the "hot" worlds , with Venus-class atmospheres , and the "cold" worlds , with heavy volatile-laden atmospheres/seas .  There are , of course , many water/ice worlds also .  These benefit from conditions more amenable to the retention of H20 .  More gravity , stronger magnetic field , less stellar irradiance , less stellar-wind , more cometary impact & replenishment , greater planetary mass , and numerous other factors , can affect planetary water/ice content , distribution , and form .  As with Venus , these can change profoundly as the planet ages , and evolves .
Okay , close-in planets have a potential !
D.H.
Note-Trappist1f appears to be a "Warm-world" .  Being water-laden , it has likely undergone significant hydrospheric/geo-chemical processing+alteration by now .  Atmospheric-stripping , particularly of H2. , would have eliminated most of the early + powerful greenhouse-effect .  The end-result will have been a much colder planet , shrouded in ice , possibly having some open ocean directly under the "sun" .
Note # 2 - The fundamental source of the slight torque upon close-in planets is stellar radiation .The photons+particles  emitted by the stars have a small amount of angular momentum (rotational energy) .  When they impact the planetary  surfaces , they push them side-ways slightly .  Over time , a balance between torque , and crustal friction , is achieved .  The faster the star rotates , the faster the planet does , also .