When we are scanning planets for signs of life, there are levels of priorities based on what attributes the planet has – some planets are more likely to harbor life, as far as we know, than others, and therefore the largest effort should be put into extracting information from these planets.
These parameters are mostly very obvious. We don't want one that is too hot or too cold, as life is an organic process and its molecules are destroyed by heat and inactivated by cold. We don't want one that is too big or too small, as the big ones have to be gas giants as they can hold onto their hydrogen, and the little ones can't hold onto any atmosphere at all. Earthlings think having a small atmosphere is a requirement for life, and it probably is a requirement for the origination of life. An advanced alien civilization might find living on an airless planet not very difficult.
There are two planetary parameters in play here. One is rotation rate and the other is axial tilt. If they are both zero, there is no seasonality. Every minute is the same, provided the ellipticity of the orbit is also small. Unless the atmosphere had some type of difficult-to-imagine instability, then the weather would be the same from one minute to the next and one year to the next as well. It would be possible to define sidereal months, but they would be inconsequential. Nothing would ever change. The assumptions in this extreme case include no moon of significant mass.
Rotation rate goes to zero from the effects of solar tidal forces on the planet. The moon has suffered this and so have other moons in our solar system. No planets have, but Mercury comes close, with a 3:2 phase locking. Venus also has a very low rotation rate. An alien planet with this situation would place life on the planet in a strange situation: nothing every changes about the environment.
This is a different type of fitness test than was present on Earth. There shouldn't be variation in the winds, which would be driven by constant convection forces. Things are about as constant as they can possibly be, and life on such a planet would evolve to a very stable arrangement as well. On a planet such as this, latitude certainly plays a role as it does on every planet, but here longitude is like a variation of latitude. A rotating planet averages over longitude, so that only latitude makes a difference, but on a non-rotator, walking around the equator is very similar to walking to the north pole. There are simply circles of constant illumination, dependent on the angle the sun makes. It keeps the same angle and same position in the sky perpetually. The substellar point would likely be the hottest, and once one passed to the dark side, everything would be cold, except for heating done by winds and the ground.
Winds would likely flow inward on the surface toward the substellar point, driven by the heating of the atmosphere there. That means the flow of air at upper altitudes would be away from the substellar point, and where it would descend is somewhat indeterminate. Likely, descent would be in the circular band near the perimeter where the star is just on the horizon, although it could be a bit inside this. The atmosphere would be too thin to support the toroidal flows that are seen on our solar system's larger planets.
With no tectonics going on, as this needs to be driven by rotation interacting with tidal forces, if there is water, it would be in a circular ring. If the planet were hot enough, no surface water would exist at the substellar point, but as one moved away, there would be a place where water could exist, and perhaps it would create a tremendous moat. On the other side of the moat might be ice, which could continue onto the dark side.
Evolution takes place in a locality, as a huge gene pool takes too long to modify genes by fitness testing. So, in each radial band, circumscribing the substellar point, there would be optimized life forms. Each life form must have some form of mobility, although it might be quite different than here on Earth. With a constant surface wind blowing away from the substellar point, wind-blown seeds would only move outward, and reseeding at the location where a plant was already rooted would not happen. Thus, heavy seeds, such as in a fruit, would be likely in all the various bands.
Evolution likes to migrate, however, so plants would likely have something like rhizomes to move inward toward the substellar point, up to the ring where there is no longer any rain. Animals have no such constraints and could move freely toward and away from the substellar point, as their capabilities to compete in adjacent bands developed.
The other two possibilities, bring closer in or farther out from the star, would provide different bull's eye patterns. Too far out and there would be ice everywhere, with only snow falling near the substellar point and nothing beyond a certain radius. Too far in and there would be no liquid water on the lighted side, and perhaps some chemotropes living in the dark but wet band just past the light boundary.
Whether or not life could originate on such a planet depends on how it originates. If the theory expounded in this blog, the organic oceans theory, where life only could originate in an early Earth-like setting, would rule out life originating on a phase-locked planet, unless some very unusual planetary movements had taken place. Maybe if there was a moon, but it eventually drifted so far out that it could detach from its planet, and then the planet became phase-locked, something might be possible. If some other theory is the correct one, such as the sea-vent concept, this planet would would be a loser, as without continents and oceans, there would be no sea vents. Perhaps life would find a completely unique way of originating on such a planet however, but out preoccupation with life here on Earth inhibits our realizing how it might happen.
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