What effect would liquid sulfur oceans, sulfur dioxide in the atmosphere have on visibility, sound propagation and other environmental information?

Question

EDIT: I eventually managed to find the absorption spectra of SO₂ online - it absorbs in the ultraviolet range only, not in the visible light range, so the only factor affecting light transmitting through the atmosphere will be the level of sulfur vapor humidity. Sections of the question have been struck out or added (in bold) to reflect this.

Question: I'm having trouble (after lots of googling and reading) finding information on the physical properties that the atmosphere and oceans would have - specifically, the penetration of light and transmittance of sound through the atmosphere and seas.

The only relevant information I found was from Freitas' famed Xenology book, which said of atmospheric sulfur vapor "At 1 atm pressure, blue light is cut to below human eye visibility in less than half a meter, and the red is gone in fifty meters. So if the partial pressures of [sulfur vapor] exceed perhaps 0.001-0.01 atm, no light of any color will be able to reach the surface of the planet from the outside"

I couldn't find anything for sulfur dioxide in the air (see edit at top) or liquid sulfur.

My specific questions are:

• What will the lighting conditions be like?

  • What would the effect of sulfur vapor humidity in the air be on visibility? Specifically, what partial pressure of vapour seems reasonable? (I can approximate from the quote above from Freitas)

  • How far will light penetrate through the sea?

  • How much light will reach the surface?

  • What wavelengths will penetrate the atmosphere? (presumably only the yellow color of the liquid sulfur's own color would penetrate through the sea itself for any appreciable distance)

• How far and how well will sound travel through the sea?

• How effective would detection of electric fields be in a sulfur sea? (E.g. for prey detection, as in sharks)

I don't need super accurate answers; ballpark figures in terms of comparisons to earth atmosphere and oceans would be fine - e.g. that light penetration at 1 meter depth in the sulfur sea would be equivalent to 1km in the earth's oceans.

The species of focus (which I expect I will have other questions about later) lives around the ocean surface - just below the surface in shallow waters, at the surface, and on coastal land areas, so I need this information to check that the creature's design - senses, communication methods etc - are ball-park plausible. E.g. I don't want to write about how they use echolocation or an electric sense to find prey if it turns out that they would only be effective at a range of millimeters.

I am aiming for a situation where enough light reaches the surface of the planet for photosynthesis to be reasonable (this doesn't have to be earth-like - more efficient pigments than chlorophyll are handwavable), and where light penetrates through the ocean at least far enough to make monochromatic vision useful for communication/close navigation. For sound, echolocation and vocal communication in the oceans (conversation style in a social animal, not cross-ocean whale song) would be nice but not a deal breaker. Shark-like electrosense is just a possibility I'm exploring - if it's feasible life would evolve a way to exploit it.

Background: The planet is (probably - see below) tidally-locked, with a bright-side surface temperature range of approximately 120°C to 170°C. At these temperature ranges, sulfur is liquid - light yellow and relatively thin up to about 157°C, and then dark red and viscous (but less dense) above that. Rivers and oceans will be mostly the yellow form, with dark red viscous patches floating on top at the hottest ocean areas, dark red viscous rivers and lakes on the hottest land masses, and interesting lava-lamp like effects over underwater hot vents or lava flows.

Due to wind currents blowing warm air to the dark side, and ocean currents circulating eastwards around the planet (due to coriolis forces), the dark side temperatures are not too far below (sulfur's) freezing point (113°C). There are thus large regions of solid sulfur 'ice,' but also regions where sulfur remains liquid.

The atmosphere contains sulfur dioxide, and some fluorine compounds (for biological reasons), and probably (but the precise details are not very important) carbon monoxide, carbon dioxide and nitrogen or other gases. The atmosphere will contain sulfur vapor also, due to the liquid sulfur oceans. The atmosphere does not need to be very dense - tidally locked planets can maintain fairly warm dark side temperatures with a relatively thin atmosphere and ocean circulation, and I can handwave it a bit with the very potent greenhouse capability of some fluorine compounds

The planet is host to carbon-based life where plants photosynthesize by absorbing SO₂, storing the O, and releasing S. Animals eat the oxygen-containing plant tissues, 'inhale' sulfur, and exhale SO₂. Proteins etc are fluorocarbon based, but this is a behind-the-scenes detail.

"Probably tidally locked:" the idea of tidal locking was initially just a way to create areas which would have low humidity (since sulfur vapor strongly absorbs light) yet were near/over oceans: (relatively) steady dry winds blowing over land from the dark side to the light side. I do quite like the idea but am not averse to changing it if it doesn't actually give me the situation I want.

This is my first question after a long period of lurking. Apologies if I've gotten the format wrong in any way (too many questions etc) - if I have, let me know and I'll edit

Answer 1

How far and how well will sound travel through the sea?

First, we need to figure out exactly what the sea is made out of. You've indicated that it's sulfur, but what kind of sulfur? Lopes & Williams (2005) is an excellent review article on Io that has a section discussing this. They identify different colored sections of Io with different sulfur compounds and allotropes:

• Red: $\text{S}_3$ and $\text{S}_4$, from the breakdown of more complicated sulfur molecules or from condensation of gases containing $\text{S}_2$.
• Yellow: $\text{S}_8$, cyclo-octasulfur.
• Green: Sulfur compounds with contamination by miscellaneous silicates.
• White-grey: $\text{SO}_2$ from crystallization after being deposited by volcanic plumes.
• Black: Silicate-rich areas near hotspots.

We therefore go to octasulfur, $\text{S}_8$, for our oceans. However, classic cyclo-octasulfur is a solid, and melts at around 115°C. The form of octasulfur we need is $\lambda$-sulfur, which is only slightly different (although it is liquid at the temperatures you need; it is generally not a solid form of sulfur).

The speed of sound in a liquid, $c_s$, is easy to determine: $$c_s=\sqrt{\frac{K}{\rho}}$$ where $K$ is the bulk modulus of the liquid and $\rho$ is the density. I was not able to find good measurements of the bulk modulus of $\text{S}_8$ at any temperature, but I did find a study that found the speed of sound at different temperatures, Kozhevnikov et al. (2004). Figure 6 shows some of their results:

They don't present any best-fit curves, but it appears that the results are linear in temperature, with one line valid through 80°C to 160°C and another for 160°C to 200°C. These measurements appear to be for $\text{S}_8$ (presumably $\lambda$-sulfur) and should therefore be perfect for your seas. There is not enough data about sound absorption to determine exactly how it behaves over a wide range of temperatures.

For comparison, the speed of sound in water is approximately 1,500 meters per second, a bit higher than the roughly 1300 meters per second in an $\text{S}_8$ ocean. However, the above results assume that the oceans are extremely pure; as I mentioned above, contamination is extremely likely, and therefore we can't assume that they will be perfectly pure.

How far will light penetrate through the sea?

Let's assume that the Beer-Lambert law is applicable here - which I assume it is. The law states that the intensity, $I$, of light is an exponentially-decaying function of depth: $$I(l)=I_0e^{-l/L}$$ where $I_0=I(0)$ and $L$ is the attenuation length, which determines how quickly the intensity drops off. The attenuation length is the reciprocal of the absorption coefficient, $\alpha$. I found a passing reference which states in its abstract that

The optical absorption coefficient alpha of liquid sulphur has been measured in a wide absorption range from 5.5*10^-2 to 2*10⁵ cm^-1 at temperatures from 130 to 450 degrees C.

I don't know if the relationship is linear or not (or if this is a form of octasulfur), but it appears to change by seven orders of magnitude within a range of about 300°C. In SI units, this is $5.5\times10^{-4}$ to $2\times10^3\text{ m}^{-1}$. Let's say that the relationship is linear. We then should have a slope of about 3°C/m^-1. Therefore, at 170°C, we should find $\alpha\sim120$, and so $$I(l)=I_0e^{-120l}$$ The above struck-out part is incorrect, as per Tharaib's answer. The coefficient's behavior is distinctly nonlinear with respect to temperature.

How effective would detection of electric fields be in a sulfur sea? (E.g. for prey detection, as in sharks)

Seawater is a decent electrical conductor, because it has free ions; these mean that free electrons can quite easily carry electric currents, and so it is easier for electric fields to permeate the water. For sulfur, things are substantially more complicated. Elemental Sulfur and Sulfur-Rich Compounds I states (page 106) that

under ambient conditions elemental sulfur is one of the best electrical insulators known.

In general, however, sulfur's conductivity rises with temperature, and we are indeed dealing with somewhat high temperatures. Synthetic Methods of Organometallic and Inorganic Chemistry, Volume 4, 1997 confirms that $\alpha$-sulfur is an excellent insulator. However, it, too, states that at high temperatures, sulfur's electrical conductivity (as well as other properties) change suddenly.

I currently cannot get you exact values for $\lambda$-sulfur's electrical conductivity, but it appears that it would be much harder for organisms to sense electric fields in a liquid sulfur ocean.

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Answer in progress!

Answer 2

According the site rules, answering your own questions is encouraged to provide a useful resource to the community, so here goes (I hope someone finds this useful....).

After my initial edit when I found that SO₂ absorbs in the UV only, I continued to do more reading, and think I have found reasonablely satisfactory answers to 3 out of my 4 questions, which were:

1. What would the effect of sulfur vapor humidity in the air be on visibility? Specifically, what partial pressure of vapour seems reasonable? (I can approximate from the quote above from Freitas)
2. How far will light penetrate through the sea?
3. How far and how well will sound travel through the sea?
4. How effective would detection of electric fields be in a sulfur sea? (E.g. for prey detection, as in sharks)

I'm still not sure how to address the humidity question - I might have to just guess since so many variables could affect it.

My answers so far are:

2. How far will light penetrate through the sea? 
 In his answer, HDE 226868 found values for the optical absorption coefficient in liquid sulphur (thank you very much!) - a range of 5.5 x 10^-4 m^-1 at 130°C to 2 x 10⁵ m^-1 at 450°C. However the variation in absorption coefficient over this range will not be linear as he assumed - liquid sulfur is light yellow up to 157°C where it becomes dark red, and then at 225°C it becomes black. Clearly the variation in absorption will experience large jumps at the transitions between the three forms. The maximum absorption of 2 x 10⁵ m^-1 at 450°C corresponds to the black form; the lower bound of 5.5 x 10^-4 m^-1 at 130°C is just below the middle of the temperature range of the light yellow form (113°C - 157°C).

In my question I specified a temperature range of 120°C to 170°C for the planet, with most oceans and rivers in the yellow form, so it's reasonable to take the 130°C figure as a rough guide - 0.00055 m^-1 .

For comparison with water, absorption coefficients range from: 0.0044 m^-1 at 418 nm (violet) 0.02 m^-1 - 500 nm (green) 0.2 m^-1 600 nm (orange) 0.6 m^-1 700 nm (red) 3 m^-1 740 nm (red)

The absorption coefficient at 130°C is an order of magnitude smaller than the absorption coefficient of the least absorbed wavelength of light (violet). However, liquid sulfur's color clearly demonstrates that a narrower range of frequencies get through (i.e. we can assume that absorption coefficients for other frequencies are much higher than they are for water), so perhaps overall illumination would not be as bright as the lower absorption coefficient would suggest. It seems reasonable to assume that yellow light will penetrate a sulfur sea less deeply and illuminate less brightly than is the case for sunlight in seas on earth, but not so much less that vision and photosynthesis in surface dwelling species would be unreasonable (the photic zone would just be shallower). This does not take into account stronger 'sun'light from the planet's star - I can handwave that a little to reduce the differences further.

Overall, I consider a reasonable answer to my question to be that the seas will be yellow and darker than our seas, but not so much so that it should make vision or an oceanic ecosystem drastically less viable than on earth."

3. How far and how well will sound travel through the sea?

Thanks again to HDE 226868, for the information about the speed of sound!

According to the majority of sources I found while google-trawling, absorption losses are minimal compared to the inverse-square law losses. At low frequencies especially, losses due to viscosity are pretty low.

I consider it reasonable that sound will travel reasonably well and not that much differently to in earth's oceans, and so echolocation and sound communication would be reasonable.


4. How effective would detection of electric fields be in a sulfur sea? (E.g. for prey detection, as in sharks)

I hadn't noticed at first, but the aforementioned Freitas book actually contains a value for the relative permittivity of liquid sulfur - 3.48. Water has a typical relative permittivity of 81.1, which means that an electric field at a given distance from a charge would be 24 times stronger in liquid sulfur than in water (since electric field strength is inversely proportional to permittivity). This is not what I was expecting and I am a little concerned I have had a small attack of cerebral flatulence while working this out, but it seems to be correct.

It would seem that detecting electric fields would be a very viable option for animals living in the darker bottoms of a yellow sulfur sea

If anything is obviously wrong with these answers, please point it out!