Are Red Dwarfs Home to Earth-Sized Water Worlds?

[|Glitch|]

Earth-sized planets covered in water may be abundant around red dwarfs, the most common type of star in the Universe.

Yann Alibert and Willy Benz at the University of Bern used computer simulations to predict the properties of planets that could form around red dwarfs and host liquid water. They found that the radius of the planets would be 0.5–1.5 times that of Earth, with most being around the same size as Earth. More than 90% of the simulated planets were at least 10% water by mass, suggesting that they were completely surrounded by deep oceans.

Source: Small stars host water worlds - Nature 539, 8 (November 3, 2016), doi:10.1038/539008d

It has always been my impression than spectral type M stars were notorious for being flare stars. As a result of their small radius and relatively low effective surface temperature, the Habitable Zone has to be relatively close to the surface of the star and small in size. As a result, it would seem to preclude exoplanets with a viable atmosphere in the Habitable Zone of such stars. However, I find that my initial impression may not have been correct.

A sample of 23,253 stars in Walkowicz et al. (2011), with effective temperature T_eff less than 5,150°K (which includes spectral type K and M main sequence stars) and a surface gravity log g > 4.2 was examined for flares over a time period of 33.5 days. Of those 23,253 stars, only 373 stars were identified as having obvious flares. Some stars had only one flare, while others showed as many as fifteen. The strongest events increased the brightness of the star by 7% to 8%. That is a population of only 1.6%. Granted, 33.5 days is not a very long period, but that is still not the percentage of flare stars I originally assumed would be associated with spectral type M stars.

Althougth, the Walkowicz et al. (2011) study does add a caveat that younger stars tend to be more active than older stars. What that means in the case of spectral type M main sequence stars, which could potentially live for trillions of years, I am not exactly sure. In a universe that is only ~13.78 billion years old, is there such a thing as an "old" spectral type M main sequence star?

Furthermore, Walkowicz et al. (2011) explains that observations made of solar flares from spectral type M main sequence stars tend to be 10 to 1,000 times as energetic as solar flares. For the 1.6% of flare stars this pertains to, that would seem to rule out any possibility of an exoplanet within the Habitable Zone from having an atmosphere, much less liquid water on its surface. However, that still leaves 98.4% of spectral type M main sequence stars that are not flare stars.

Since the above study, Alibert et al. (2016), used 0.1 M_☉, 1.004 R_☉, and 2,935°K T_eff for its initial conditions, I was able to estimate the "conservative" Habitable Zone, using Kopparapu et al.(2014), as being between 0.14 AU and 0.38 AU, with the frost-line/snow-line (160°K) at 0.79 AU. Interestingly, they found through their simulation that planets with low mass (specifically < 0.4 M_⊕) tend to be totally devoid of water.

Alibert et al. (2016) also assumes that the mean surface temperature of the simulated exoplanet is no colder than 273.16°K (0.01°C; 32.02°F) with a minimum atmospheric pressure of 611.657 pascals (6.11657 mbar; 0.00603659 atm; 0.088713417 psi) at "sea level."

Sources:
Formation and composition of planets around very low mass stars - arXiv 1610.03460
A terrestrial planet candidate in a temperate orbit around Proxima Centauri - Nature 536, 437-440 (August 25, 2016), doi:10.1038/nature19106 (arXiv free preprint)
White-light flares on cool stars in the Kepler Quarter 1 Data - The Astronomical Journal, Volume 141, Number 2, January 13, 2011 (free article)
Evolution of protoplanetary disks: constraints from DM Tauri and GM Aurigae - Astronomy & Astrophysics, Volume 442, Number 2 (November 1, 2005) (arXiv free preprint)
Flares on active M-type stars observed with XMM-Newton and Chandra - Thesis by Urmila Mitra Kraev, University College London [PDF]
Habitable Zones Around Main-Sequence Stars: Dependence on Planetary Mass - The Astrophysical Journal Letters, Volume 787, Number 2 , May 15, 2014 (free article)

 

[SerbianQuantum]

I would just like to thank you. I love reading about habitat zones, especially the ones in our relative proximity.

 

[|Glitch|]

Because I had my initial perception of red dwarf stars and the viability of their habitable zones altered by the study I posted above, I did some further research into the subject matter in order to get better insight.

The “conservative” liquid water Habitable Zone (LW-HZ) around red dwarf main sequence stars is extremely close (< 0.5 AU) due to the very low effective surface temperature of the star. As a result, any exoplanet within 0.5 M_⊕ to 4.162 M_⊕ will most likely be tidally locked. Due to this tidal locking, the magnetosphere of the exoplanet will be diminished, allowing Coronal Mass Ejections (CMEs) and the strong solar winds to slowly erode the atmosphere of the exoplanet. An exoplanet without an atmosphere cannot support liquid water on its surface.

Larger exoplanets (> 4.162 M_⊕) would have a stronger magnetosphere, even though they may also be tidally locked, and therefore may be able to retain some of its atmosphere. However, exoplanets greater than 1.599 R_⊕ may not be terrestrial/rocky.

While the Alibert et al. (2016) paper above does take into account the irradiation of the star in some of their simulations, they do not take into consideration tidal locking and the diminished effect it has on the magnetosphere of Earth-like exoplanets within the LW-HZ, or the erosive effect the CMEs and strong solar winds have on the exoplanet's atmosphere.

We do not take into account tidal interactions with the star, as they are only important for very close-in planets (see Bolmont et al., 2012).

Source: Small stars host water worlds - Nature 539, 8 (November 3, 2016), doi:10.1038/539008d (arXiv free preprint)

Interestingly, I came across a couple of articles recently in Astrobiology that suggests that CMEs may be an important factor for life on terrestrial/rocky exoplanets within the LW-HZ. They do take into consideration tidal locking and the weakening effect this has on the exoplanet's magnetosphere.

High XUV radiation of an active dwarf star (more than about 50 XUV_Sun) results in considerable expansion of the upper atmosphere of an Earth-like exoplanet orbiting it. An unmagnetized exoplanet or an exoplanet that has a weak intrinsic magnetic moment and is exposed to high XUV fluxes and CME impacts with the maximum estimated plasma density during a 1-Gyr period is in a real danger of being stripped of its whole atmosphere even if it orbits its parent M star within an HZ at 0.2 AU.

Source: Coronal Mass Ejection (CME) Activity of Low Mass M Stars as An Important Factor for the Habitability of Terrestrial Exoplanets. II. CME-Induced Ion Pick Up of Earth-like Exoplanets in Close-In Habitable Zones - Astrobiology, Volume 16, Number 10, October 2016, Online ISSN: 1557-8070 (free article)

However, the study goes on to conclude that if there is a sufficiently strong enough magnetosphere to prevent complete atmospheric erosion, and high concentrations of CO₂ in the atmosphere, an Earth-like (0.5 M_⊕ to 4.162 M_⊕) exoplanet in the LW-HZ of a red dwarf main sequence star may be able to support life.

One other consideration needs to be factored into the climate of Earth-like exoplanets within the LW-HZ of red dwarf main sequence stars: Assuming the exoplanet is able to retain at least 6.11657 mbar of atmospheric pressure and a temperature of 273.16°K at the surface of the exoplanet, a tidally-locked exoplanet may find the vast majority of its liquid water trapped in ice-sheets on the dark side of the exoplanet, while the daylight side is a vast desert. The "Water-Trapped Worlds" article listed below provides some interesting possibilities to consider.

Sources:
UV habitable zones around M stars - Icarus, Volume 192, Issue 2, December 15, 2007, Pages 582–587 (arXiv free preprint)
Water-Trapped Worlds - The Astrophysical Journal, Volume 774, Number 1, August 16, 2013 (free article)
Magnetospheric Structure and Atmospheric Joule Heating of Habitable Planets Orbiting M-dwarf Stars - The Astrophysical Journal, Volume 790, Number 1, July 3, 2014 (free article)
Coronal Mass Ejection (CME) Activity of Low Mass M Stars as An Important Factor for the Habitability of Terrestrial Exoplanets. I. CME Impact on Expected Magnetospheres of Earth-like Exoplanets in Close-In Habitable Zones - Astrobiology, Volume 16, Number 10, October 2016, Online ISSN: 1557-8070 (free article)
Coronal Mass Ejection (CME) Activity of Low Mass M Stars as An Important Factor for the Habitability of Terrestrial Exoplanets. II. CME-Induced Ion Pick Up of Earth-like Exoplanets in Close-In Habitable Zones - Astrobiology, Volume 16, Number 10, October 2016, Online ISSN: 1557-8070 (free article)
Most 1.6 Earth-Radius Planets are not Rocky - The Astrophysical Journal, Volume 801, Number 1, March 2, 2015 (free article)
Red Dwarf Planets Face Hostile Space Weather Within Habitable Zone - Astrobiology Magazine, June 11, 2014

 

[Bandersnatch]

Nice summary, Glitch.

however, exoplanets greater than 1.5 M⊕ may not be terrestrial/rocky.

I'm pretty sure this is incorrect, unless you meant radius rather than mass - but even then I'd like to see where it's coming from.

 

[|Glitch|]

Nice summary, Glitch.I'm pretty sure this is incorrect, unless you meant radius rather than mass - but even then I'd like to see where it's coming from.

Yes, I meant radius, not mass. My mistake. I have corrected it. Thanks for pointing it out.

Source: Most 1.6 Earth-Radius Planets are not Rocky - The Astrophysical Journal, Volume 801, Number 1, March 2, 2015 (free article)

 

[Bandersnatch]

You should perhaps reconsider other instances you've used mass there too - the range 0.5-1.5 M⊕ for a likely water-hosting exoplanet does not follow now, since you can easily get over 5 Earth masses on the far end of the rocky planet range.

 

[|Glitch|]

You should perhaps reconsider other instances you've used mass there too - the range 0.5-1.5 M⊕ for a likely water-hosting exoplanet does not follow now, since you can easily get over 5 Earth masses on the far end of the rocky planet range.

I used the 0.5_⊕ because Alibert et al. (2016) concluded that low-mass exoplanets (< 0.4 M_⊕) could not support liquid water. As to the high end, according to Weiss et al. (2014) (see equation #3), you can only get a mass of 4.162 M_⊕ if you limit the radius to 1.599 R_⊕.

 

[Bandersnatch]

(see equation #3)

That's their statistical fit to data - it has a large scatter (see the rms error). Just look at the table of observables they used.

 

[|Glitch|]

That's their statistical fit to data - it has a large scatter (see the rms error). Just look at the table of observables they used.

Granted, they use a very limited set of observable planets to formulate their equation, but is there anything better? At least it uses real-world examples as opposed to pure speculation.

 

[Bandersnatch]

The point is, it's a statistical analysis rather than a physical model. It's erroneous to use it to make categorical statements about how much mass a planet 'can' have per given radius. All you can say, is that in a large sample the trend is to fit that model.
E.g., if you'll find in the sample two planets with the same radius, but with widely differing masses (due to density differences), the equation would be (roughly speaking) fitted to draw a line going through the average of those values. It would be silly to then claim that a planet of that radius can only have that average value as its mass.

 

[colinjohnstoe]

This is a very interesting topic, and Glitch has done a great job summarising some of the main question. I work on these topics in my own research so I am always interested in getting into any discussion on it. I have some comments about what has been written so far.

The “conservative” liquid water Habitable Zone (LW-HZ) around red dwarf main sequence stars is extremely close (< 0.5 AU) due to the very low effective surface temperature of the star.

Another factor is the smaller radii of low mass stars, which means that they have smaller surface areas. Both that and the lower effective surface temperatures means that the stars are less luminous and therefore a planet must be closer into get the same flux of light from the star. What is interesting though, is that the lower effective temperature actually means that in order for the planet to have an appropriate surface temperature for water, it needs less light than it would if it orbited a G star like the Sun. The difference is in the spectrum and the fact that photons with different energies heat the surface a different amount. The details, I do not know, but this is a result of the climate modelling done in studies like Kopparapu et al.(2014) cited above. Concisely put, a planet orbiting a cooler star gets more surface heating per unit input energy than it would orbiting a hotter star.

However, the study goes on to conclude that if there is a sufficiently strong enough magnetosphere to prevent complete atmospheric erosion, and high concentrations of CO2 in the atmosphere, an Earth-like (0.5 M⊕ to 4.162 M⊕) exoplanet in the LW-HZ of a red dwarf main sequence star may be able to support life.

It is very interesting, but it is all still very speculative. There is an idea floating around right now that very active (magnetically) stars produce winds that are dominated by coronal mass ejections. This is based primarily on observations of a correlation between flares and CMEs on the Sun, and observations of high flare rates, and very strong flares, on very active stars. No CMEs have ever actually been observed coming from any of these stars. In the habitable zones of M stars, we would expect these CMEs to be very dense and therefore influence the atmospheres of planets. However, how they will influence the atmospheres is still very difficult to say. I think we need to develop a better theoretical understanding of atmospheric loss mechanisms.

Anyway, I want to write some more on this, but I have got to go back to work. Maybe later.

 

[|Glitch|]

It is very interesting, but it is all still very speculative. There is an idea floating around right now that very active (magnetically) stars produce winds that are dominated by coronal mass ejections. This is based primarily on observations of a correlation between flares and CMEs on the Sun, and observations of high flare rates, and very strong flares, on very active stars. No CMEs have ever actually been observed coming from any of these stars. In the habitable zones of M stars, we would expect these CMEs to be very dense and therefore influence the atmospheres of planets. However, how they will influence the atmospheres is still very difficult to say. I think we need to develop a better theoretical understanding of atmospheric loss mechanisms.

Anyway, I want to write some more on this, but I have got to go back to work. Maybe later.

I tried to keep speculation to a minimum. The second astrobiological study, Lammer et al. (2016), is where I derived the conclusion you cited:

A high CO₂ atmospheric mixing ratio results in enhanced IR cooling and inhibited expansion of an atmosphere, and, therefore, it leads to reduced non-thermal atmospheric erosion due to CMEs. However, if an Earth-like exoplanet has no substantial magnetic moment, its atmosphere may have no chance to survive CME-induced erosion under high XUV radiation exposure of an active M star even if its atmosphere has a high CO₂ mixing ratio. On the other hand, if an Earth-like exoplanet can generate a strong enough intrinsic magnetic moment and has a high CO₂ mixing ratio, its atmosphere may survive CME-induced erosion if XUV fluxes are less than about 50–70 times than that of the present Sun.

As I mentioned at the very beginning of the thread, this is not the conclusion I would have arrived at initially. However, having read the sources I posted above, I have come to a completely different understanding. An exoplanet within the LW-HZ of a red dwarf main sequence star that is able to retain its atmosphere has a much greater chance of supporting life, as opposed to an exoplanet that has its atmosphere eroded away.

 

[colinjohnstoe]

I tried to keep speculation to a minimum. The second astrobiological study, Lammer et al. (2016), is where I derived the conclusion you cited:

Yes, you of course came to the correct conclusions based on the paper. What I meant is the arguments in the paper that CMEs can cause a significant amount of atmospheric mass loss are quite speculative. The reason is that it is unclear that these strong continuous streams of CMEs even exist since they have never been observed coming from any star except the Sun and have not been predicted from physical models. The idea comes simply from analogies with the solar flare-CME correlation.

 

[|Glitch|]

Yes, you of course came to the correct conclusions based on the paper. What I meant is the arguments in the paper that CMEs can cause a significant amount of atmospheric mass loss are quite speculative. The reason is that it is unclear that these strong continuous streams of CMEs even exist since they have never been observed coming from any star except the Sun and have not been predicted from physical models. The idea comes simply from analogies with the solar flare-CME correlation.

Actually, CMEs/solar flares have been observed on Proxima Centauri. We have known Proxima Centauri was a flare star since 1951. They have also observed that Proxima Centauri has a solar cycle every 7 years, where sun spot activity covers as much as 20% of the star's surface. A paper was released on this subject just last week.

Sources:
Solar-Like M-Class X-ray Flares on Proxima Centauri Observed by the ASCA Satellite - American Association for the Advancement of Science, Volume 268, Issue 5215, pp. 1327-1329, June 2, 1995
Optical, UV, and X-Ray Evidence for a 7-Year Stellar Cycle in Proxima Centauri - Monthly Notices of the Royal Astronomical Society, November, 11, 2016 (arXiv free preprint)

 

[colinjohnstoe]

Sure, many flares have been observed on many stars, but CMEs (i.e. the actual ejected material) have not been detected. There have been some attempts, and some hints for CMEs, but nothing concrete.

 

[|Glitch|]

Sure, many flares have been observed on many stars, but CMEs (i.e. the actual ejected material) have not been detected. There have been some attempts, and some hints for CMEs, but nothing concrete.

Isn't the mechanism that creates solar fares the same mechanism that produces CMEs - a strong magnetic field? Therefore, if a star produces strong solar flares, is it not almost certain that the same star will also produce CMEs? I understand that there has been no direct observations of CMEs on other stars, but the inference that they exist is extremely strong on stars that produce strong solar flares. To dismiss them as pure speculation merely because they have not been directly observed would defy reason.

 

[colinjohnstoe]

The mechanisms are quite poorly understood and the link between flares are CMEs are also quite poorly understood. Both are a result of the magnetic field, and more specifically, both are a likely to be a result of energy release from magnetic reconnection. However, a flare on the Sun is not necessarily followed by the release of a CME, and a CME is not necessarily preceded by a flare. For a good study on this, check out Aarnio et al. (2011). They analyse 6700 CMEs and 12,000 flares on the Sun and find only about 800 that are correlated. This is partly due to difficulties in correlating flares and CMEs; as far as I understand, the observatories that detect CMEs have to block out not just the Sun, but also a large region around the Sun, so they only see CMEs after they have already traveled quite far and it is quite difficult to trace them back to their sources. Interestingly, I heard (but don't have a reference at the moment) that the largest flares on the Sun are always followed by a CME.

Based on some of the correlations that can be seen in Aarnio et al. (2011), e.g. Fig 15, it is natural to assume that there are more CMEs and larger CMEs coming from active stars. I doubt many people would doubt this, but the magnitude of this increase is very unclear. One theoretical reason to think that there might not be is that active stars have very strong magnetic fields. Specifically, they have magnetic fields that have strong dipole components, meaning that the CMEs, once released from the surface, might have not be able to escape the corona through the strong magnetic field. I know some people are working on this now, but it is unclear. There have also been attempts to observe CMEs that have been unsuccessful (e.g. Leitzinger et al. 2014). Another difficulty is just how much of the energy produced in the star can be used for CMEs. Drake et al. (2013) found that when they took simple solar scaling laws, like those in Aarnio et al. (2011), and applied them to active stars, they got CMEs that were removing something like 10% of the available energy from the star. The energy was going into lifting the material away from the star's gravity and the kinetic energy that the CMEs had after reaching escape velocity. This huge number is quite unrealistic.

The point is, we don't know that CMEs are in fact a danger for planetary habitability for M stars because for all we know, the planets don't get hit by CMEs very often. This can be true, even if they are getting hit more often than the Earth is.
Sources:
Aarnio et al. (2011) "Solar Flares and Coronal Mass Ejections: A Statistically Determined Flare Flux - CME Mass Correlation" (http://adsabs.harvard.edu/abs/2011SoPh..268..195A)

Drake et a. (2013) "Implications of Mass and Energy Loss due to Coronal Mass Ejections on Magnetically Active Stars" (http://adsabs.harvard.edu/abs/2013ApJ...764..170D)

Leitzinger et al. (2014) "A search for flares and mass ejections on young late-type stars in the open cluster Blanco-1" (http://adsabs.harvard.edu/abs/2014MNRAS.443..898L)

 

[rootone]

We haven't seen evidence of CMEs at stars other than the Sun, and probably Proxima.
However there is no reason to assume the Sun (and Proxima) are very unusual, so it's likely that CMEs are a common feature of stars.
Not having observed them at other stars is more likely a limitation of our presently available instruments.

 

[colinjohnstoe]

Sure, but what I wrote is not that the existence of CMEs from other stars is speculative. The point is that the existence of strong CME dominated winds from other stars is speculative. Our solar wind is very far from being dominated by CMEs but there is speculation that more active stars shoot off so many CMEs that the wind is basically just one continuous stream of them.

 

[|Glitch|]

The mechanisms are quite poorly understood and the link between flares are CMEs are also quite poorly understood. Both are a result of the magnetic field, and more specifically, both are a likely to be a result of energy release from magnetic reconnection. However, a flare on the Sun is not necessarily followed by the release of a CME, and a CME is not necessarily preceded by a flare. For a good study on this, check out Aarnio et al. (2011). They analyse 6700 CMEs and 12,000 flares on the Sun and find only about 800 that are correlated. This is partly due to difficulties in correlating flares and CMEs; as far as I understand, the observatories that detect CMEs have to block out not just the Sun, but also a large region around the Sun, so they only see CMEs after they have already traveled quite far and it is quite difficult to trace them back to their sources. Interestingly, I heard (but don't have a reference at the moment) that the largest flares on the Sun are always followed by a CME.

Based on some of the correlations that can be seen in Aarnio et al. (2011), e.g. Fig 15, it is natural to assume that there are more CMEs and larger CMEs coming from active stars. I doubt many people would doubt this, but the magnitude of this increase is very unclear. One theoretical reason to think that there might not be is that active stars have very strong magnetic fields. Specifically, they have magnetic fields that have strong dipole components, meaning that the CMEs, once released from the surface, might have not be able to escape the corona through the strong magnetic field. I know some people are working on this now, but it is unclear. There have also been attempts to observe CMEs that have been unsuccessful (e.g. Leitzinger et al. 2014). Another difficulty is just how much of the energy produced in the star can be used for CMEs. Drake et al. (2013) found that when they took simple solar scaling laws, like those in Aarnio et al. (2011), and applied them to active stars, they got CMEs that were removing something like 10% of the available energy from the star. The energy was going into lifting the material away from the star's gravity and the kinetic energy that the CMEs had after reaching escape velocity. This huge number is quite unrealistic.

The point is, we don't know that CMEs are in fact a danger for planetary habitability for M stars because for all we know, the planets don't get hit by CMEs very often. This can be true, even if they are getting hit more often than the Earth is.
Sources:
Aarnio et al. (2011) "Solar Flares and Coronal Mass Ejections: A Statistically Determined Flare Flux - CME Mass Correlation" (http://adsabs.harvard.edu/abs/2011SoPh..268..195A)

Drake et a. (2013) "Implications of Mass and Energy Loss due to Coronal Mass Ejections on Magnetically Active Stars" (http://adsabs.harvard.edu/abs/2013ApJ...764..170D)

Leitzinger et al. (2014) "A search for flares and mass ejections on young late-type stars in the open cluster Blanco-1" (http://adsabs.harvard.edu/abs/2014MNRAS.443..898L)

That is not the conclusion that Aarnio et al., (2011) reaches. While it is true that solar flares do not necessarily correlate to a CME, all CMEs in their study directly correlate to preceding solar flare activity. The intensity of these solar flares can be used to determine the amount of material, and in most cases the velocity, of the CME. Aarnio et al., (2011) went further to draw a linear correlation between CME mass size and solar flare flux, with log(CME mass) = (18.5 ± 0.57) + (0.68 ± 0.10) × log(flare flux) describing the minimum CME mass, and log(CME mass) = (16.6 ± 1.30) + (0.33 ± 0.26) × log(flare flux) describing the maximum CME mass.

This also corresponds to Su et al., (2007), which concludes in part:

We have found that both measures show that for events with larger magnetic field strength, the corresponding peak flare flux tends to be larger and the corresponding CME speed tends to be faster. This result is consistent with previous theoretical studies by Lin (2002, 2004) and Reeves & Forbes (2005), who found that the cases with higher background fields correspond to fast CMEs and strong flares, whereas lower fields correspond to slow CMEs and weak flares.

This is further collaborated in conclusions drawn by Guo et al., (2007):

With a sample of 86 flare-CMEs initiating in 55 active regions near the central meridian, we studied the properties of the longitudinal magnetic field of flare-CME productive active regions and their statistic correlations with CME speed. Four measures, tilt angle (Tilt), total flux (F_t), length of the strong-field and strong-gradient on the main neutral line (Lsg) and effective distance (d_E), are used to quantify the magnetic properties. The main results are as follows:

1. For CMEs initiating in active regions, fast CMEs tend to initiate in active regions with large F_t or large d_E.
2. In flare-associated CMEs initiating in active regions, faster CMEs tend to be accompanied by more intense flares.
3. The parameters d_E, Lsg and F_t correlate well with one another, especially F_t and Lsg.
4. The occurrence of 11 slow CMEs and 1 fast CME in β type regions with Lsg far below the threshold reminds us of some exceptions to be considered when the Lsg with the threshold is used to predict CME productivity of active regions.

There as never been an observed CME that was not first preceded by solar flare activity. Therefore, while we cannot say with certainty that CMEs are produced on other stars with known solar flares because there has never been any direct observation of such events, we can infer that in the presence of transequatorial magnetic loops and strong solar flare activity CMEs are a distinct possibility. Solar flares may produce large amounts of X-rays that could cause a whole different sort of problems for life on exoplanets, or even sterilize the exoplanet, but they are not going to erode the atmosphere of the exoplanet. In order to erode the atmosphere of an exoplanet there needs to be strong solar winds and CMEs actually impacting the exoplanet's atmosphere by overcoming the magnetosphere of the exoplanet.

CMEs from red dwarf main sequence stars could erode, and even completely deplete, the atmosphere of exoplanets within the LW-HZ that exhibit a weak magnetosphere over the long term (1+ billion years). The close proximity of such exoplanets make the likelihood of being struck by CMEs even greater, even if those CMEs are infrequent. A tidally-locked exoplanet would also have a weaker magnetic field than a rotating exoplanet of comparable mass, and therefore more susceptible to atmospheric erosion.

Sources:
Solar Flares and Coronal Mass Ejections: A Statistically Determined Flare Flux-CME Mass Correlation - Solar Physics, Volume 268, Issue 1, pp 195–212, January 2011 (arXiv free preprint)
What Determines the Intensity of Solar Flare/CME Events? - The Astrophysical Journal, Volume 665, Number 2, August 20, 2007 (free article)
Magnetic properties of flare-CME productive active regions and CME speed - Astronomy & Astrophysics, Volume 462, Number 3, February 11, 2007 (free article)
The association of transequatorial loops in the solar corona with coronal mass ejection onset - Astronomy & Astrophysics, Volume 400, Number 2, March 3, 2003 (free article)

 

[colinjohnstoe]

all CMEs in their study directly correlate to preceding solar flare activity.

This isn't true. They considered 6733 CMEs and found only a small fraction of them to be associated with flares. They discuss at several points in the paper the differences between CMEs associated with flares and those that are not. Have a look at the first sentence of the second paragraph of their Section 4.1.

"Of the 6 733 CMEs we perform the correlation with, 737 unique CMEs are found to be associated with flares; put another way, we find 11% of CMEs to be flare-associated"

Of course, this small number is most likely an underestimate given how hard it is to associate CMEs and flares. Also check out the review paper Webb & Howard (2011) in Living Reviews in Solar Physics. Early in Section 3.2, they write

"There is no one-to-one relationship between CMEs and flares. Many CMEs are associated with solar flares but many are not, just as most flares are not associated with mass ejection"

They go on to explain that there is a fundamental link between flares and CMEs, so the two phenomena are certainly linked.

Solar flares may produce large amounts of X-rays that could cause a whole different sort of problems for life on exoplanets, or even sterilize the exoplanet, but they are not going to erode the atmosphere of the exoplanet.

I don't know about stellar flares in general, but X-ray emission, and even more importantly Extreme Ultraviolet emission, from active stars will erode the atmosphere. This is possible because this radiation is absorbed in the upper atmospheres of planets, creating thermospheres and causing their atmospheres to expand. If enough of this energy is absorbed, the atmosphere can flow away hydrodynamically. Tian et al. (2008) showed this for models of the Earth's atmosphere. It depends of course very much on what the atmosphere is made of, because as you wrote earlier in this thread, things like CO2 can protect the atmospheres by cooling them.

Tian et al. (2008) "Hydrodynamic planetary thermosphere model: 1. Response of the Earth's thermosphere to extreme solar EUV conditions and the significance of adiabatic cooling" (http://adsabs.harvard.edu/abs/2008JGRE..113.5008T)

Webb & Howard (2011) "Coronal Mass Ejections: Observations" (http://solarphysics.livingreviews.org/Articles/lrsp-2012-3/)

 

[colinjohnstoe]

By the way, the reason I mentioned X-rays from active stars in relation to flares is that there are some reasons to think that the X-rays coming from very active stars are simply the super-position of many flares.

 

[Buzz Bloom]

The point is, it's a statistical analysis rather than a physical model. It's erroneous to use it to make categorical statements about how much mass a planet 'can' have per given radius. All you can say, is that in a large sample the trend is to fit that model.
E.g., if you'll find in the sample two planets with the same radius, but with widely differing masses (due to density differences), the equation would be (roughly speaking) fitted to draw a line going through the average of those values. It would be silly to then claim that a planet of that radius can only have that average value as its mass.

Hi @Bandersnatch:
.
I confess that I am confused what you mean by "categorical statements". I am guessing you mean a statement without error ranges, but I am not sure I have this right.

In a typical mathematical model based on a scatter diagram of two (or more) variables, one ( or more) assumed to be dependent on one assumed independent variable, one expects some kind of least-mean-squared fit - that is, a curve showing the average values of the model. The basis of the fit may be linear, or some polynomial, or some other mathematical form based on the particular physical model of the theory. However, an additional two curves is also typically shown, one above and one below the average curve. The two curves define an error range corresponding to some confidence limit. With the defined error range, one can reasonable say something like: For a given radius, it is 95% likely that a planet's mass with be between the corresponding upper and lower curve values.

Without such error ranges, the middle curve is not very useful. Is the the point you intended?

Regards,
Buzz

 

[Bandersnatch]

Without such error ranges, the middle curve is not very useful. Is the the point you intended?

Hi Buzz, thanks. That's what I meant. Notice what Glitch used the fit for - he attempted to name the maximum mass for a planet of a given radius based on that curve of average values.