Modified Variable Drake Equation

[badgerchap]

I would like to explore a new version of the famous Drake equation. Below I have formulated a rough starting point, with an explanation of why I have chosen particular values. The intention would be that, with discussion and a whole lot of tweaking, modification and probable complete rewriting, we might, as a collective, stumble upon a more accurate interpretation of Frank Drake's vision. Not optimistic or owt!

Please give honest thoughts, as I am only too aware of my own shortcomings and the more heads go into it the better. Enjoy!

Nmax = ns fp fc fl fs (ag/tc)

where:

Nmax = Maximum number of communicative civilizations in existence today

ns = Number of stars in the galaxy today

fp = fraction of those stars likely to support planets

fc = fraction of those which have the capability to support life

fl = fraction of those which do support life

fs = fraction of lifeforms which survive and develop the capability to transmit complex communications

ag = age of the galaxy

tc = time taken for a lifeform upon a planet to develop the technological capability to transmit complex communications

Nmax = (3 x 10^11)(0.49)(0.25 x 0.5)(2.5 x 10^-8) (1.3 x 10^10/4.5 x 10^9)

which produces a conservative value of 1327 civilizations currently capable of transmitting complex communications currently in existence within our galaxy.

An explanation of the values used:

ns – The number of stars in the galaxy today is taken as 300 billion, as taken from Wikipedia. Whilst a variation in this number may cause a change in the final result, most estimates agree in that this number is correct in its order of magnitude. Hence any number within this range can be considered acceptable.

fp – This is one of the most uncertain values within the equation, and I have therefore tried to maintain a conservative figure. To obtain this, I have excluded all O, B and A type stars, which make up around 0.19% of all the stars in the galaxy. For F, G and K stars, I have taken as read that they can support habitable planets, as the Sun, being a G type star, lies within this range and close to all of the stars within it, with regard to mass and luminosity. F, G and K type stars make up roughly 23% of the stars in the galaxy. As for the remaining stars, or at least 76%, we assume that they are M type dwarfs. Current theory is divided on whether or not dwarf type stars are habitable. Many sources are of the opinion that tidal locking and flares could make habitability impossible. However, according to a paper published in Astrobiology (“A reappraisal of the Habitability of Planets around M type dwarf stars” Jill C Tarter et al. DOI 10.1089/ast.2006.0124), it seems that there may indeed be the possibility of habitable planets in these systems. F,G,K and M stars make up 98% of all stars and so after taking the uncertainty into account, it seems fair to me that a value of half of this (a fraction of 0.49) should be used for the sake of this calculation.

fc – Fraction of planets in a system capable of supporting life. We have only our own solar system at which to look for evidence in this. A conservative figure would be 1 in 8 (i.e. just the Earth) and an optimistic one might be 3 in 8 (Earth, Mars, Venus) and so I have taken the midpoint – 2 in 8 or 0.25.

fl Fraction of these which do indeed support life – again we must look at our own solar system. Having said that 2 planets are capable of supporting life and that 1 indeed does, this figure must be 0.5.

fs – Fraction of lifeforms which survive and develop the capability to transmit complex communications. Again, we can only take the Earth as evidence for this. I have taken an educated guess (after looking at Number of species on Earth tagged at 8.7 million : Nature News, rounding up and multiplying by 2 to give the total number of species ever to have existed on Earth) at the total and taking as read that only 1 of these (us) has ever been able to develop complex communications.

ag – Age of the galaxy is taken to mean, more specifically, the maximum age of a star in the Milky Way. According to Wikipedia, the age of the oldest star in the galaxy is 13.2 billion years, so this figure has been used.

tc – Time taken for a a lifeform upon a planet to develop the technological capability to transmit complex communications. As this is a conservative equation, we must use evidence from the only lifeform known to have done this, ourselves. Since the formation of our star, it has taken roughly 4.5 x 109 years for us to accomplish this.

Now I know there will be plenty of problems with this, viscous disagreements and all kinds of different opinions on this. I hope so anyway

Please discuss and let me know what you think, and hopefully it can be drastically improved!

[ronin]

fc = fraction of those which have the capability to support life: The value used is I suspect high. We tend to assume simply right temperature and with water. This I would guess is too simple.

We have a liquid metal core that supports a magnetic field, this magnetic field shields us from the majority of high energy particals thrown off of the sun. Another planet would have to have this as well.

ag – Age of the galaxy: To form carbon the first generation stars have to have existed and gone nova. So the age of the galaxy could be misleading. To get the higher elements that life needs would not have existed until these nova and then the recondensation of the resultant material. So how about age of secondary stars, say half the age of the galaxy ? Recall reading that we are a third generation star.

Possibly another factor to throw in is the fraction of stars that would support life. A cool red star may not produce enough energy for high order life, one of the Orion belt stars would fry life.

Can we dismiss all binary stars?

Can we dismiss all stars at the galactic core?

Can we dismiss variable stars.

If we could dismiss those then that would reduce the number of stars by a significant amount.

How about the number of stars = the number that match our sun in type? Not what are in the Galaxy, large reduction there. Think we are G type and Wiki say 7.6% of main sequence are G type. So stars that could allow life is about 1/15.

I would say that the Drake equation needs possible updating with more recent data and possibly the inclusion of additional factors. Lets be honest it was a first guess made in 1961, most of astronomy has changed significantly since then.

[badgerchap]

Agree about the age of the galaxy, definitely. Might have to come up with a fraction of stars from each gen.

As for fraction of stars than can support habitable planets, I've only excluded O,B and A's. Opinion seems to be pretty divided about the suitability of F,K and M. Have totalled these classes and halved, for pessimism, but obviously this needs refinement.

As for fc, attempting to strike a balance between life as we know it and life as we dont. Could you suggest a more personably favourable fraction?

Agree also about variables, binaries etc. I guess (and guess is the operative word) that some cases may be favourable to life while others may not (i.e. orbital periods, degree & type of variability etc.). This fraction by itself could be tied to a long and complex equation of its own.

I suppose the difficulty with the original equation (and more so for this one!) is that, as you say, it was kinda just thrown hastily together. I'm quite sure Drake never envisaged the level of scrutiny it would receive!

[carldr]

In my opinion, at least one more variable needs to be added - The number of years that radio transmissions are made by a civilisation. For us, now we're moving away from analogue technologies, the number is something like 120 years.

But even that's not really the whole story. Apart from one exception, we've never deliberately beamed transmissions into space, and it's debatable that any civilisation listening for us will have equipment sensitive enough to hear us.

With our current technology, it's estimated our radio broadcasts would only be detectable from 0.3 light years away. So assuming the civilisations were even distributed throughout the galaxy, they would need equipment several orders of magnitudes more sensitive.

Civilisations might deliberately decide to avoid broadcasting radio into space for the fear of being found - it's not guaranteed another civilisation will be friendly.

This doesn't alter the number of civilisations out there of course, but it reduces the number we're likely to find. It's certain that advanced civilisation is rare enough that it can be assumed that if a civilisation doesn't want to be found, it won't be. So perhaps we need another variable indicating the number of civilisations who want to be found.

Also, what about a variable to indicate how long a civilisation exists for? If an extinction event happens before we are able to populate other planets, or if we end up destroying ourselves, we might only be around for a relatively short period of time. So what are the chances that another civilisation finds us during that time period, assuming they have similar issues?

C.

[badgerchap]

In my opinion, at least one more variable needs to be added - The number of years that radio transmissions are made by a civilisation. For us, now we're moving away from analogue technologies, the number is something like 120 years.

.....

With our current technology, it's estimated our radio broadcasts would only be detectable from 0.3 light years away. So assuming the civilisations were even distributed throughout the galaxy, they would need equipment several orders of magnitudes more sensitive.

.....

Also, what about a variable to indicate how long a civilisation exists for? If an extinction event happens before we are able to populate other planets, or if we end up destroying ourselves, we might only be around for a relatively short period of time. So what are the chances that another civilisation finds us during that time period, assuming they have similar issues?

C.

I think this raises the question "What should such an equation attempt to achieve?" Are we looking for the number of civilizations with whim we might communicate, or are we merely trying to ascertain the number of advanced civilizations in the galaxy? A good point carldr.

As for the 'lifetime' of the civilization, this was a tricky part of the original equation. We have very little evidence (alright no evidence!) to suggest how long an advanced civ. might survive. I suppose the only decent thing to do is assume that once a civilization develops advanced technology that it will survive for x years, and then divide the final number of civs by (age of the universe divided by x). Whatever x might be!

[carldr]

I have to admit, I got a little confused to what the equation was trying to achieve while writing my post!

Drake's original equation was trying to find the number of civilisations in our galaxy with which communication might be possible, so considering whether we can detect them (or them us) is valid I think. If a civilisation doesn't want to be found, or isn't actively looking for other civilisations, or even they do find us but choose to not show themselves, I think they fall outside of "communication might be possible" on the basis that such civilisations are so rare that you won't find them by chance, and so you can't communicate with them.

I think that's subtly different to your Nmax of course, which implies they would be counted. So perhaps a couple of those variables aren't valid for your updated equation, but as you say, it raises the question of whether they should be.

I suppose it's more useful to try and estimate the number of civilisations, and from there we can calculate how likely it is we'll come across one, either by chance or by design, as it would allow us to determine a distance for how close the nearest civilisations ought to be.

The milky way is about 39 million million cubic light years in volume. There could be millions of civilisations in our galaxy, and still the chances of us detecting any of them is minute given our current technology. This naturally overlaps with the Fermi Paradox, of course.

[badgerchap]

The milky way is about 39 million million cubic light years in volume. There could be millions of civilisations in our galaxy, and still the chances of us detecting any of them is minute given our current technology. This naturally overlaps with the Fermi Paradox, of course.

Yes indeed, and therein lies the problem with SETI so far. I am excited about the possibility of targeting specific systems now that Kepler's on board. Exciting times!

[Photosbykev]

I think I'll stick with my quotation in my signature

[Capricorn]

Cannot recall on which programme it was said but I do remember one professor saying that it would take until this present stage of the Universe/Galaxy for life to develop sufficently for intelligence.

Possibly because of the heavy element formation required.

I notice that it is never considered that we may not be the only star+planet system for life to develop, but we may be the first. Some system would have to be. If we are then there possibly isn't anyone/thing to detect yet.

If the next most advanced system were say 1 million years behind us - which is a short time in stellar and evolutionary terms, then we are not going to detect anything for quite a time.

The Drake equation seems to assume that civilisations have been appearing since the start of the universe, which owing to the available elements is incorrect.

[badgerchap]

I notice that it is never considered that we may not be the only star+planet system for life to develop, but we may be the first. Some system would have to be. If we are then there possibly isn't anyone/thing to detect yet.

A very Anthropocentric view! But yes, it is certainly a concern. I suppose this brings in an element of chance, so in all fairness the only mathematically sound way of dealing with this would be to perform the calculation and then calculate the chances of being first?

[badgerchap]

Hahaha this has the potential to throw a cat among the pigeons....!

Microlensing Study Says Every Star in the Milky Way has Planets

[phat tony]

hi, love this thread. we are assuming that any other civilized life out there has the same requirements as us but the fact is that even here on earth we have so many life forms with totally different needs to survive. under the ice in the antarctic some creatures thrive and are larger and healthier than anywhere else in the world. who is to say that on the opposite side of the galaxy there is not a race of prawns with better motor skills then us who live on a a planet that we would see as uninhabitable. i do like your thinking but feel we could never get a real figure. as you said with more minds working we may get closer but as our own history has proving we can make mistakes in calculating things like ages.

[Dave Dubya]

It's a somewhat exciting time for the Drake Equation. We've gone from using one data point and a lot of varied estimations, to potentially having some clarity of the variables in the near future.

The milky way is about 39 million million cubic light years in volume. There could be millions of civilisations in our galaxy, and still the chances of us detecting any of them is minute given our current technology. This naturally overlaps with the Fermi Paradox, of course.

Indeed. But, if SETI weren't running the chances of detection would be zero.

And the methods and processes developed by SETI have found various other applications - so it's not been a waste of resources, even if it does prove fruitless for ET detections.

[johnb]

Why not be a little more prescriptive and have our version of the equation predict the number of civilisations that are similar to ourselves ?

fp = fraction of those stars likely to support planets

fc = fraction of those which have the capability to support life

if we did that I assume we can come up with sensible numbers for the above to plug in ?

John B

[RogerTheDodger]

I prefer this version...

[Capricorn]

F0 and F1 are not applicable. You could pay for a TV broadcast that covers more people but does not increase the chance of it being correct.

Av is the same: Telling the world on a blog does not make it any more true.

Dt should be (1-9/10) = 1/10. If 9/10 of the true bits are removed that leaves just 1/10 chance that what remains is true.

The Flake Equation was not made up by anyone with an idea of mathematics.

[Capricorn]

Suspect that most stars have planets around them in some form, why should ours be different. So finding that most stars have planets is not a great surprise.

The fraction of planets that can support life is I suspect very low.

What do we call life? Slime is life and was around the earth for quite some time.

Fractions that survive and develop complex communications. Two things there, survive - dinosaurs did that quite successfully. Develop complex communications harder to say, using us as an example, the only one we have, 5 Billion years. That is the approximate age of the sun and earth and is therefore how long it has taken to get this far.

One other factor is the composition of the dust cloud that the life supporting system came from. Without the appropriate amounts of elements it may be impossible for life to develop to the extent we see on this lump of rock. Not much carbon and there is not much life, similar for oxygen.

I suspect that the drake equation requires a significant update.

[RogerTheDodger]

Wow, who had a sense of humour failure today?

[philthy]

The real answer to the Drake equation is 43.

It has as much chance of being correct as any other guestimate you're going to get from it.

[UHF]

Sure its not 42

Sent from a planet somewhere in the vicinity of betelgeuse.

[philthy]

Yes 42 after they build that bypass.

[RogerTheDodger]

The Flake Equation was not made up by anyone with an idea of mathematics.

Oh yeah, he has a degree in Physics, and has worked at NASA.

[Dave Dubya]

Oh yeah, he has a degree in Physics, and has worked at NASA.

Yeah, Randall Monroe knows nothing about mathematics...

[Shibby]

To throw a bit of a spanner in the works... If you judge it by the way communication technology is progressing on our planet, everything is moving away from radio communication towards cable/fibre optic. It may be the case that civilisations that develop radio communication only make use of it for a few hundred years. This doesn't change the result of the equation per se, but does significantly reduce the chances of SETI detecting a signal. Boo