Space Forum / Space Science / April 2005

***{After a considerable amount of digging and a few e-mails, I have
managed to get a definitive answer concerning the bona fides of the
photo linked above (i.e., at
http://sciforums.com/attachment.php?attachmentid=3999). This comes from
a source close to the European Space Agency who for the time being shall
remain nameless: "This is a real picture, no specific image processing
was used."

Daytime temperatures on Mars are frequently well above freezing, and I
have seen reports of daytime summer temperatures upwards of 20 deg. C,
though that is apparently unusual and those temperatures would probably
not be reached at the bottom of a deep, dark canyon such as Valles
Marineris. Under those circumstances, temperatures of 5 or 10 deg C
might be attained, but the maxima attained under more favorable  
conditions would be very unlikely. Looking in an old edition of the
*Handbook of Chemistry and Physics*, I see that the vapor pressure of
pure distilled water at 5 deg C is 6.543 mmHg, and that the vapor
pressure at 10 deg C is 9.209 mmHg. Since water can only exist in liquid
form when its vapor pressure is less than atmospheric pressure, it
follows that atmospheric pressure in Valles Marineris must lie within or
above that range in order for pure, liquid water to exist there..

So, what is the atmospheric pressure at the bottom of Valles Marineris
at the point where the photo was taken?

Well, typical "surface" pressures on Mars, according to *The Facts on
File Dictionary of Astronomy* (pg. 268), are around 7 mb, which is
(7/1013)(760) = 5.25 mmHg, and so on the face of it liquid water should
not be able to exist there. However, at the location shown on the photo,
the bottom of Valles Marineris is about 5 km beneath the arbitrarily
chosen "surface" level. [See pg. 1, Adsorption water-driven processes on
Mars, D. Möhlmann, DLR-PF, Berlin, available at the ESA website.] Since
pressure increases as altitude decreases, the question is not whether
liquid water can exist at the artifically designated "surface" level on
Mars, but whether it can exist 5 km further down, under the higher
pressures that prevail at the bottom of Valles Marineris.

To try to answer that question, let's use the so called "barometric
pressure formula:"

P = P0e^(-Mg0z/RT)

In the above P0 is the pressure at the lower level, P is the pressure at
the upper level, e is the base of natural logarithms, M is the mass of 1
mole of atmosphere, g0 is the appropriate gravitational acceleration, z
is the vertical distance from the lower level to the upper level, R is
the molar gas constant, and T is the average absolute temperature in the
vertical column of atmosphere beginning at P0 and ending at the top of
the stratosphere (i.e., the bottom of the ionosphere).

Why the top of the stratosphere? Because the barometric formula only
calculates the effects of gravity on pressure. It is, in effect, a way
of determining the weight of a vertical column of atmosphere of unit
cross section at one level, based on knowledge of its weight at another
level and its average temperature. Since simple pooling of air molecules
under the influence of gravity ceases to be the dominant determinant of
pressure at the top of the stratosphere, the column of air to which the
barometric formula applies stops when the ionosphere is reached. That is
not to say that the air above the stratosphere, beginning with the
ionosphere, has no effect on pressures at lower levels. Rather it is to
say that the effects in question have very little to do with the
*weight* of the material, and a lot to do with such things as the solar
wind, solar  radiation, magnetic field lines, etc.--things which the
barometric formula does not take into account. During the day, in fact,
the presence of upper atmosphere material has the effect of reducing the
ground level pressure rather than increasing it, which is the exact
opposite of what we would  expect based on its weight. Thus to avoid
calculating a ground level pressure that is too high, I will ignore the
presence of that material.  

We want to determine the pressure at the lower level, so we will solve
the barometric formula for P0, which gives the following:

P0 = P/e ^(-Mg0z/RT)          (1

The various values on the right side are as follows:

(1) P = 7 mb, or 700 Pa.

(2) The value of e is 2.718....

(3) The Martian atmosphere is .95 CO2, .027 N2, .016 A, and .0015 O2, so
the mass of a mole of atmosphere is M = [.95(44) + .027(28) + .016(40) +
.0015(32)]/1000 = .04324 kg.

(4) Mars "surface" gravity is .37735849056603776 times that of Earth, so
g0 = 3.698 m/sec^2.

(5) The altitude difference is z = 5000 meters.

(6) The molar gas constant is R = 8.314 J/kg.

(7) To come up with a value for T, the average absolute temperature
below the ionosphere, requires a bit of work.

To begin, note that measurements by NASA's Mars Global Surveyor put the
top of the Martian stratosphere at about 93,000 meters. [See
http://agena.bu.edu/mars.htm.] That, therefore, will be the altitude of
the top of the column of atmosphere with which we are concerned. And the
altitude of the bottom of the column, for present purposes, will be 0
meters.

What we want is the average absolute temperature in that column of
atmosphere. To get it, we cannot simply take the middle altitude and
look up the temperature at that altitude, because the masses within the
column are not distributed evenly. The temperature of a mole of gas is T
= pv/R, and there are more moles per unit volume at the bottom of a
column of atmosphere than at the top, because the atmosphere gets
progressively thinner at higher altitudes. The average temperature, in
short, comes at the altitude of average density. Thus we will calculate
the average density, and then plug that value into the NASA Martian
Atmosphere Calculator (see
http://www.lerc.nasa.gov/WWW/K-12/airplane/atmosi.html) to determine the
temperature at that altitude. That will be the value of T that we seek.

According to the hydrostatic pressure formula, p = hdg. We will re-write
it as:

d = p/gh

d  is the average density of the atmosphere in a column of unit cross
section stretching from the "surface" to the ionosphere.

p is the pressure at the bottom of the column--i.e., the surface  
pressure of 700 Pa.

h in this case is the distance from ground level to the ionosphere:
93,000 meters.

g is the gravitational acceleration on Mars, which is 3.698 m/sec^2.

The average density in the Martian atmosphere is therefore

d = p/gh = (700)/(3.698)(93000))

= .00203 kg/m^3, or .002, rounded.

Turning to the NASA calculator mentioned above and selecting "Mars" and
"metric units", we find that the density of the Martian atmosphere is
0.002 at an altitude of 20,433 meters, and that the temperature at that
altitude is -73 deg C. That, therefore, is the average temperature of
the portion of the Martian atmosphere which lies below the ionosphere.
The average absolute temperature in that region is therefore 273 - 73 =
200 K.

The estimated pressure at the bottom of Valles Marineris is therefore

P0 = 700/(2.718)^-(.04324)(3.698)(5000)/(8.314)(200), or

P0 = 1132.18 Pa, which is 11.3218 mb or 8.4942 mmHg.

Looking back at my vapor pressure tables for pure water, I find that
they are less than 8.4942 mmHg for temperatures up to 8.8 deg C. That
means pure water can exist in liquid form up to 8.8 deg C or 47.8 deg F,
at the location shown in the photo.

But, of course, any water flowing into the bottom of Valles Marineris
will without a doubt be mineral laden water from underground
hydrothermal sources. The salinity will be high, and as dissolved
minerals accumulate in water, its vapor pressure declines. Moreover, it
is a simple, linear relationship known as Raolt's law--to wit: the vapor
pressure of a solvent containing dissolved minerals is directly
proportional to the mole fraction of the solute in the solution, where
"mole fraction" is simply the number of moles of the substance (water,
in this case) divided by the total number of moles in the solution. Thus
if V0 is the vapor pressure of pure water at a given temperature, f is
the mole fraction of water in the solution, and V is the vapor pressure
of the solution, then according to Raolt's law, V = fV0.

Sea water, for example, contains 35 gm of dissolved salts for every kg
of water, with the salts being mostly NaCl. Let's simplify slightly and
assume the 35 gms are entirely NaCl. In that case, since the molecular
weight of NaCl is 58, the solution contains 35/58 = .6 mol, and, since
there are 1000 gms of H2O, which is 55.6 moles, it follows that the mole
fraction of H2O in sea water is 55.6/(55.6 + .6) = .989, and so for sea
water V = (.989)V0 as per the Raolt's law formula.

That, of course, means there is very little reduction in vapor pressure
when sea water is substituted for pure water. In fact, that only takes
us up to 8.9 deg C, where the vapor pressure drops to V = (.989)(8.551)
= 8.457 mmHg, which is just slightly less than the atmospheric  pressure
of 8.49 mmHg. Thus if the water pouring into Valles Marineris were like
sea water on Earth, then it would remain liquid at temperatures up to
8.9 deg C, or 48 deg F.

However, sea water on Earth is not saturated with NaCl. In fact, 358 gms
of NaCl can be dissolved in 1 kg of water at 10 deg C (and more at
higher temperatures). That would be 358/58 = 6.17 moles.  The 1000 gm of
H2O is 51 moles. Hence  the mole fraction of water would be f =
55.6/(55.6 + 6.17) = .9. Result: V = (.9)V0. And that, based on another
look at the vapor pressure tables, is enough to permit liquid water to
exist up to 10.2 deg C, or about 50 deg F.

Other solutes, or multiple solutes, can take us even higher. Most
effective are salts with a low molecular weight and a high solubility,
so that the mole fraction of the solute jumps up, thereby reducing the
mole fraction of the solvent (water). Looking in my handbook again, I
see that the solubility (by interpolation) of LiCl at 12 deg C is 733 gm
in 1000 gm of H2O. Molecular weight of LiCl is 42, so that's 17.45
moles. The 1000 gm of H2O is 55.6 moles. Therefore the mole fraction of
water is 55.6/(55.6 + 17.45) = .761. Hence at 12 deg C we find that V =
(.761)(10.52) = 8.01 mmHg. And that works: with P = 8.49 mmHg and V =
8.0 mmHg, the water will remain liquid at 12 deg C, or 53.6 deg F.

Getting from 10 to 12 deg C by means of lithium chloride sounds like a
stretch, of course, but it could happen. It seems likely that the water
flowing into Valles Marineris is icemelt caused by heat emanating from
the magma chambers of the nearby Tharsis volcanos, and if the ultimate
source of the water is Mars' long since frozen ancient seas, it might
very well contain lots of dissolved salts, including LiCl. On Earth, for
example, it is estimated that there are 230 billion tons of lithium
chloride in sea water, but only 14 million tons on land. [See
http://202.221.217.59/print/news/nn04-2004/nn20040418a9.htm.] Moreover,
there is a process that would automatically raise all solutes to
saturation, given sufficient time. (See explanation further down.)

Anyway, regardless of how far above 10 deg C water can remain liquid in
Valles Marineris, it is a sure thing that pools of liquid water are a
real possibility there. Given the photo referenced earlier, showing the
fog and the apparent pools of blue water, it is my guess that Valles
Marineris was carved by underground icemelt flowing into the bottom of
the canyon, with the source of heat being the magma chamber under the
nearby Tharsis volcanos. I would suggest that geothermal heating from
magma near Valles Marineris melts buried ice from an ancient Martian
sea, and that liquid water then flows out into the bottom of the canyon.
Based on the above calcs, such water could remain liquid at least to 10
deg C and, arguably, to 12 deg C. Since solar heating would seldom push
the summer temperature above 10 deg C, and since water flows entering
the canyon from vents at the bottom would cool quickly by evaporation to
temperatures at which they would remain liquid, it follows that if
steady inflows of geothermally heated water are available at the bottom
of the canyon, pools of liquid water will exist there.

Interestingly, there is a photo of a portion of Reull Vallis, one of the
canyons feeding into Valles Marineris from the north, which appears to
show a lake of liquid water more than 100 km in length, and averaging 15
or 20 km in width. See
http://www.esa.int/export/SPECIALS/Mars_Express/SEMAZ625WVD_1.html to
view this photo.

If you see nothing but bare rocks, then I suggest that you note the
following facts:

(1) If there is no wind or other source of disturbance, the surface of
water is as flat as a sheet of glass.

(2) If there are no suspended particulates, water is perfectly
transparent.

(3) The intrinsic color of water is blue, a fact that is revealed
progressively, as the water becomes deeper and deeper. [See
http://webexhibits.org/causesofcolor/5B.html.]

(4) The sky is not blue on Mars, so there is no opportunity for
reflection to make shallow water appear to be blue, as often happens  on
Earth. Thus if water on Mars shows blue, it will be deep water only.

With those facts in mind, I suggest that you download the hi-res tiff
version of the above referenced photo and study it carefully. If you do,
you will note that a distinct water line is visible most of the way
around the lake, and that as the water gets deeper and deeper, its blue
coloration is progressively revealed.

I say that's a lake--a huge one, as a matter of fact.

Here is how such a lake would come into being:

(1) An upwelling of hot water from a deep geothermal source would spread
out on the bottom of the canyon.

(2) Atmospheric pressure at the bottom of the canyon would be roughly  
8.49 mmHg and, if the air temperature were above roughly 10 to 12 deg C,
vaporization by boiling would promote rapid cooling of the water and
would increase its salinity.

(3) Over the eons, the salinity of the remaining water would be
progressively increased, each time the atmospheric temperature rose high
enough to cause a repetition of (2), above.

(4) Eventually, the salinity of the water, due to the buildup of
multiple solutes, would be so high that boiling would seldom occur.

Conclusion: the photo of the fog shows an episode where the air
temperature rose high enough to promote boiling; and the photo of the
lake in Reull Vallis shows the normal case, where the air temperature is
*not* high enough to promote boiling.

Interestingly, a continuation of such boiling episodes for millions or  
billions of years would result in total saturation of the water, and
continued "salting out" of minerals onto the bottom. The result would be
a buildup of immense mineral deposits in the locations where the
repeated boiling episodes were occurring. The area beneath and around
the lake at Reull Vallis, for that reason, may very well contain some of
the richest surface mineral deposits in the Solar System.

There probably aren't any fish in the lake, however. :-)  

--Mitchell Jones}***  

Thanks for your extraordinary message, one of the best ones
I have seen in this newsgroup for years.

NASA is brain dead.
We must somehow work around it.

ES

I have to raise a couple of points which haven't been taken into account yet.
At least I haven't noticed them - I have to admit that I didn't read through
all the stuff you wrote, Mitchell. The messages were loooong. :)

Anyway: The sensitivity of the different HRSC color channels varies. You might
notice that if you look at the raw images (available somewhere in the ESA web
chaos*) from which the 'color' images are derived from. You get the appr.
wavelength curves from the HRSC portion of ESA SP-1240, available at
h€ttp://sci.esa.int/science-e/www/object/index.cfm?fobjectid=34885
But still, this doesn't give you the correlation between the color channels.
I should be aware of any such c€orrelatios, since I am working in the HRSC
Science team, and to my knowledge no accuate correlations have been achieved.

In other words, the colors in the images have not been retouched as such, but
the "blue" you see in the imges is just _bluer_ than the rest. I bet there is
considerable stretching in the histograms of the original images for PR
purposes, i.e. to _emphasize_ the features seen in the image. Thus, the fog in
Valles Marineris is, yes, bluer and brighter than the ground. And yes, the
Reull Vallis center is brighter in blue channel and darker in red and green
channels. But no, it is NOT as blue in real life as shown in the PR image, and
no, I can not see any kind of lake in the close-up images. You have to
remember that the original HRSC images (which I am looking at as I write this)
are up to 20 meters/pixel in that region, and even better resolution MOC
narrow angle images* go up to 2 m/pixel. And there is no indication of a
liquid surface in those images. There are indications of formations carved or
otherwise created by liquid flowing matter, however.

* If you want the web addresses for these, I'll give you them. Don't have time
to search the idiotically arranged web sites now... :)

Jarmo

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Jarmo Korteniemi       * http://www.student.oulu.fi/~jkorteni *

Planetology group, Astronomy, University of Oulu, Finland

s-posti / email: jarmo DOT#1 korteniemi AT oulu DOT#2 fi
puhelin / phone: +358 (45) 6362264
huone / room:    TÄ215 (klo 12-20, ajoittain aiemminkin)
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