How Did Mars Get Such A Thin Atmosphere? New Solar Irradiance Data Promises New Insights

Maven spacecraft collects data for solar irradiance applicable to Mars.

According to a new study by E.M. B. Thiemann et al (Journal of Geophysical Research: Space Physics) a new line of evidence has been found to ascertain the evolution of Mars' early atmosphere. We know it is remarkably thin now and assorted hypotheses have been offered over the years to account for this, ranging from erosion on account of the solar wind, to simple atmospheric outgassing owing to changing planetary conditions.

In respect of the latter, the standard theory for Martian loss of atmosphere had been based on the escape of atmospheric particles  due to reaching escape velocity from thermal effects. Calculations show, in fact, that if the mean molecular speed is as much as one-third of the planet's velocity of escape (or 1.7 km/sec for Mars) the planet will lose one half of its atmospheric gas in only a few weeks.

If the mean molecular speed is even one fifth of escape velocity (1.02 km/sec for Mars) the gas will disperse into space in a few hundred million  years. To hold a gas of sufficient atmospheric density to allow standing water-for billions of years - would necessitate a velocity of escape 6-8 times the mean molecular speed of the gas in question.  This is simply not the case for Mars, where one can easily work out the mean molecular speed of  oxygen, say from:

v =  Ö( (3 k T/m)

where k is Boltzmann's constant (1.38 x 10 ^-23   J/K), T is the absolute temperature applicable in degrees K, and m is the mass of a single gas  molecule.  Then compare it to Mars' escape velocity of ~ 5.1 km/sec, as well as to one -third values and one -fifth values of that velocity.

The new research is based on using data collected from NASA's Mars Atmosphere and Volatile Evolution (MAVEN) mission to calculate the solar irradiance at the planet.  This is the amount of EM power delivered by electromagnetic waves over a given area of the Martian atmosphere.   It can also be thought of as the output of light energy from the entire disk of the Sun, measured at Mars.

A fairly basic equation can in fact be used to get first estimates, and we can compare values for the Earth and Mars.  We use:

L = 4π R² (K)

for the Earth where K is the  solar irradiance (at Earth) we seek and  K' for Mars:

L = 4π R'² (K')

Here, L is he solar luminosity or power delivered, e.g.  L = = 3.9 x 10 ²⁶ W 

R = 1.5 x 10 ¹¹ m   or the Earth - Sun mean distance (semi-major axis)

R' = 2.4 x 10 ¹¹ m, or the Mars-Sun mean distance.

Then the estimated solar irradiance at Earth will be:

K   =   L  / 4π R²     =  ( 3.9 x 10 ²⁶ W )/  4π (1.5 x 10 ¹¹ m)² 

K  =   1360 Wm^-2

And for Mars: 

K'   =   L  / 4π R'²     =  ( 3.9 x 10 ²⁶ W )/  4π (2.4 x 10 ¹¹ m)² 

K  =   539  Wm^-2

As expected the value for Mars is significantly less given its mean distance is 1.6 times greater. Thus the effective luminous radiant sphere at its distance is much larger so the impacting radiation (the "irradiance") is more diffuse. 

Now the Thiemann team, working with data collected by the MAVEN is shedding new insights based on the measurement of solar extreme ultraviolet (EUV) radiation.  These wavelengths ranged from 6 nm to 120 nm, and we know solar EUV heats the upper atmosphere of both Mars and Earth.  The resulting interactions with existing atmospheric gases, e.g. CO2, have an impact on the composition of the planet's atmosphere.

MAVEN's  EUV monitor takes measurements every second that the Sun is in the instrument's field of view, or roughly 60 percent of the time.   Also of use by the team is a mathematical model (the Flare Irradiance Spectral Model- Mars)  or FISM-M, which uses the EUV measurements to calculate the spectral irradiance.  This is the solar irradiance received for a specific wavelength.

Why use a flare-referenced model? Because we already know large solar flares can propel radiance enhancements more than 50 times greater than normal, thereby affecting irradiance. Thus, a means to correct for these extraordinary energetic events needs to be factored in.

In the case of the FISM-M model, the algorithms used incorporate concurrent  solar EUV data  collected in Earth's upper atmosphere by NASA's Solar Dynamics Observatory .  That data from the SDO then helps to calibrate MAVEN data and enable calculation of the solar irradiance at Mars.  This is not only on a daily basis where no exceptional solar events may occur but also after the most explosive solar flares.

In their paper the research team presented solar irradiance measurements calculated using FISM-M between October 2015 and November 2016. These measurements varied due to fluctuations in solar EUV radiation caused by solar flares, the rotation of the Sun, Mars’s elliptical orbit around the Sun, and the progression of the Sun’s 11-year cycle.

The EUV monitor is just one of an array of instruments and sensors that MAVEN uses to study Mars’s upper atmosphere as it seeks clues to the atmospheric history of the Red Planet. The information presented by Thiemann’s team will help inform future research with FISM-M, as well as improvements to the model itself. 

Solar and space physicists definitely look forward to further corroborating results of this work, as well as extending them further - perhaps with the aid of new mathematical models. Solving each clue, say using solar and related spectral irradiance puts us on a more confident path to knowing how Mars' atmosphere evolved - and why it is so very tenuous now.


Interested readers can find an overview of the paper here:

http://onlinelibrary.wiley.com/doi/10.1002/2016JA022677/full

Get A Look At Our Sun In A Time-Lapse Movie: Celebrating the Solar Dynamics Observatory

It's past time to celebrate the Solar Dynamics Observatory which saw it's five year anniversary on Feb. 11th. Over 200 million images have been taken (at the rate of just over 1 per second) and actually compiled into a compressed time lapse movie which you can view here:

https://www.youtube.com/watch?v=GSVv40M2aks


Pay attention especially to the magnificent loops of plasma: the coronal loops which are structured such as shown in the detailed diagram below, and occur in solar active regions,


And also the bursting loops associated with solar prominences, which are some of the most energetic and stupendous sights visible on the Sun.

One such giant prominence which exploded some years ago is shown in the image below:



















The physical basis for these prominences has been known for some time and can best be explained by reference to the diagram shown below:


This shows the motion - tied to the plasma flow - relative to the local magnetic or B-field.  The key point to note is that the flow's cutting action on the field line triggers a change in the magnetic flux and an induced current.  The only way for the plasma to avoid the unrealistic situation we call "infinite conductivity" is for it to be constrained to follow the B-field lines rather than to cross them. This is what is meant by "field freezing" and if you look carefully at the SDO movie you will spot a number of instances where this occurs!

'The Most Complete Observational Evidence for Solar Magnetic Reconnection To Date'

The plasma flow represents the motion relative to the existing (B)-field(say in a local solar field), and its "cutting" action on the field line leads to a change in magnetic flux and induced current.  The only way to avoid this unrealistic situation is for the plasma to be constrained to follow B-field lines rather than cross them. This is what is meant by field freezing.

The region of a large Solar flare, Note the magnetic field lines which follow the solar plasma - this is at about the level of the solar chromosphere.

Magnetic reconnection - the topic of this post- requires solar plasma to temporarily deviate from the infinitely conducting condition displayed in the very top image.  In this situation, when opposite polarity magnetic regions get pushed together, the changing magnetic flux generates a sheet of electric current (called a 'current sheet') that flows perpendicular to the plane of the page. Let this current be strong enough and the plasma's ability to conduct electricity is impeded- which allows the electric field in the plasma to build up and the magnetic field lines to reconnect, generating heat via joule dissipation. The newly connected field lines are then able to lower their energy by snapping back from the reconnection region, converting the magnetic energy into bulk kinetic energy and heat - what we observe in solar flares.



Image of solar corona taken at 211Å by the Atmospheric Imaging Assembly of the Solar Dynamics Observatory (SDO). Note carefully the lines - which are magnetic field lines - which have actual reality in the solar corona and are not merely artificial constructs.

      Three years ago NASA launched the Solar Dynamics Observatory, with great expectations. Much was expected on account of the Atmospheric Imaging Assembly (AIA)  equipped with the capability of obtaining images of the Sun with greater speed and resolution than ever before.

 

 

     Now that expectation has more than paid off, with the first detailed observation yet of magnetic reconnection in a solar flare. As one solar researcher, Eric Priest, has put it (Physics Today, September, p. 12): "This is exactly the type of event many of us have been waiting for, for years". 

 

       On paper- or in theoretical plasma physics classes - magnetic field lines are treated as theoretical constructs with no reality in and of themselves. But in the Sun's corona, they have  physical reality, as seen in the last image taken with the SDO's AIA.  Plasma in the corona is an excellent conductor or electricity because the ratio of kinetic energy density to magnetic energy density is less than one, in fact much less than one. In such a circumstance, the magnetic fields are said to be "force free" and the condition applies such that:  J x B = 0

 
     Here J is the current density and B denotes the magnetic field intensity.  This condition means that the magnetic field lines cannot move perpendicularly to the underlying solar plasma - which case is depicted in the top most graphic.  In that case, for a non-force free situation one would have:  grad p = J X B

      where grad p denotes the pressure gradient.  As opposed to this, in the corona, the magnetic field lines are entrained with the plasma and move in the same sense. As the Sun rotates and its plasma convects, the field lines will be affected dynamically by the rotation (think of Coriolis forces as on Earth) and become contorted into an ever more series of complicated loops whose topology (under ideal plasma conditions, i.e. J x B = 0) cannot change. But in force free conditions they can - as described in the text for the second image.

 

        Before going on to the comprehensive SDO discovery - observation, let's be clear what the AIA's limits and capabilities are: It basically uses four telescopes to obtain images of then in ten channels - 7 in the extreme ultra violet (EUV) ranging in wavelength from 94   to  335   -  two in the ultraviolet (UV) and one in the visible spectrum. It can collect one image of the Sun every 12 seconds with a spatial resolution of 0.6 arc seconds (for comparison, the full Moon's diameter is about a half degree or 1800 arcsecs.). It is also possible to collect images even more rapidly by restricting the field of view - say to just part of the Sun, maybe to observe a flare in real time - such as the second image shows.

 

        In the case of the solar flare of interest, and the subject here - Yang Su (University of Graz, Austria) and an international team of collaborators reported the most comprehensive observations of field reconnection ever for a flare that occurred on Aug. 17, 2011, and just after 4h 00m Universal time. While many flares have erupted in the 3 years since SDO's launch none have shown the explicit features of reconnection as well as the 8/17/11 flare. This also meant it didn't saturate the sensitive AIA detectors and obscure the flare region as other events have.

 

      Movies obtained of the entire flare - at the full 12 sec resolution - are even more impressive. The film shows hot solar plasma pinned to the magnetic loops flowing away from the reconnection region. One of the images extracted from the movie is shown here (credit Physics Today:)

 

 

       One problem the researchers need to reckon with is reconciling the inherent 3D nature of the Aug. 17, 2011  flare  and the typical 2D models of magnetic reconnection. What we need therefore is a proper three dimensional model of reconnection as it would apply to the solar corona's events

 

 

     TO see other events occurring the same date;

 

http://www.youtube.com/watch?v=SSmH2H1ajGE

 

 

 

Solar Oblateness May Be Constant Over Time

As with all rotating celestial bodies - planets included - the Sun is "oblate", meaning that it "bulges" at the waist, i.e. solar equator. The measure of this bulge is then the ratio of the equatorial diameter's excess (i.e. over the polar dia. or (a- b)) to the polar diameter (b) itself. Or:

Obl = (a - b)/ a

Solar oblateness came to the fore some decades ago when it was invoked to challenge the standard Einsteinian General Relativity. This was as part of the Jordan- Brans- Dicke theory of gravity proposed by Robert Dicke of Princeton and Carl Brans - my former mathematical physics prof at Loyola University ca. 1966.(See, e.g. http://chn.loyno.edu/physics/bio/carl-h-brans)

What Brans and Dicke hoped to find, to validate their theory, was a departure from spherical symmetry large enough that it had the potential to affect Mercury's orbit. This quantity, dubbed 'eta' by Einstein, referred to the advance of the perihelion in seconds of arc, over a century. It is instructive to first revisit this and show how Einstein obtained his value of 43 seconds of arc per century.

Thus: eta = [24 (π)^3* a^2]/ T^2 *c^2*(1 - e^2)


where 'eta' is the advance of perihelion in seconds of arc, T is the period of revolution in seconds, c the velocity of light in cm/s and e the eccentricity of the orbit. From a Table of distances, Mercury's semi-major axis = 0.387 AU or:  a = (1.5 x 10^13 cm) (0.387) = 5.8 x 10^12 cm

The period, T (in seconds) is just the length of Mercury's year (in days = 87.96, again from a Table) multiplied by the seconds-length of an Earth day, or 86,400 s:

T = 7.6 x 10^6 s

The eccentricity, e from a similar Table is e = 0.205.

Substituting all these values into the given equation yields: eta = 5.036 x 10^-7 radian

However, this is not in seconds of arc but radian measure. To get the equivalent seconds of arc (or arcsec) we use the fact that 1 rad (radian) = 57.3 deg and one degree has 3600 seconds. Thus, 1 radian = 2.063 x 10^5 arcsec

So, the associated arcsec for eta will be 5.036 x 10^-7 rad) x (2.063 x 10^5 arcsec/ rad) =0.104 arcsec

We are still not finished because the quantity is defined per CENTURY

At this point, you need to recall the PERIOD of Mercury is 0.24085 YRS.

So, the number of arcsec of perihelion advance per Earth years is:

0.104 arcsec/ 0.24085 years = 0.431

and over 100 years:

eta = 100 yr x (0.431 arcsec/ yr) ~ 43.1 arcsec, compared to the value of 42.98 "/century predicted by Einstein.

Interrelated with the above is the fact that an oblateness gives the Sun what is called a "quadrupole moment" which we designate J2. The dimensionless parameter J2 is defined (cf. 'Gravitation and Spacetime' by Hans C., Ohanian and Remo Ruffini, W.W. Norton, p.18):

J2 = Q^33/  2M R^2

where M is the mass of the Sun, R is its radius, and Q^kl = Q^33 is the mass quadrupole tensor (op. cit., p. 17).  To assess a baseline perspective, if the Sun were rotating totally uniformly oblateness effects minimal) then J2 would be roughly 1 x 10^-7. In this case, the corresponding contribution to the advance of Mercury's perihelion would be a few hundredths of an arcscond per century, or in other words, within the observed value of the uncertainty for 'eta'.

Interestingly, Brans and Dicke (1961), originally proposed a 'scalar-tensor' theory of gravitation which avoided conflict with the Einstein GR prediction. In their field the scalar field replaced the gravitational constant and becomes instead a function of space and time, so oe gets a variable value for G - the Newtonian gravitational constant. Effectively, on is looking at a quantity G'/G where G' denotes the first time derivative, or dG/dt/

Meanwhile, in 1967, Dicke and Goldenburg obtained an unexpectedly large J2 ~ 2.4 x 10^-5 which would show significant deviation from the Einstein eta. It would also have required that the solar interior rotate at a much faster rate than the surface.Such a large quadripole moment would have led to an additional 3 arcsecs per century over Einstein's value. Thus, leading to eta ~ 46"/ century. This large value has never been confirmed, and indeed, Dicke et al (1985) using a solar vibration method found J2 = 1.7 x 10^-7.

Quite obviously, what the preceding showed is that better methods of measuring oblateness (and hence the quadripole moment J2) were needed, which exceeded optical methods, including digital photocells, and also oscillatory -vibration methods. Such an advance on observational quality became feasible in 2010 with the launch of NASA's Solar Dynamics Observatory (SDO). This Observatory was able to measure with record precision the shape of the solar limb (the solar disk's edge) and in addition ascertain variations in the limb over a solar cycle.

The results forthcoming were simply amazing, i.e. that the Sun's equatorial radius exceeded its poalr radius by 7.2  + 0.5 milliarcseconds, and with NO evidence of departure from constancy. Given the Sun's diameter of 1.4 miilion kilometers subtends a half degree in the sky (1800" roughly) then the difference between its equatorial and polar radii would amount to barely 5 km. In other words, it's almost perfectly spherical. Most remarkably, the 5 km difference is small even when compared to the turbulence on the solar surface

Further refinement - especially useful over solar cycles - was obntained by incorporating best -fit quadrupole (C2) and hexadecapole (C4) coefficients. The to 4th order the difference between equatorial and polar radii is given by:

D = -3C2/ 2  - 5C4/8

Amazingly, within the range of observational uncertainties, both C2 and C4 have been consistent with constancy over two years. Moreover, C4 is effectively zero (contributes very little to solar oblateness) so:

D = -3C2/ 2

Further analysis using Legendre polynomial multipole data discloses a marginal hint of correlation between C4 and the sunspot cycle - which may or may not assume importance for future sunspot -flare forecasts. This association, for the time being, is theorized to be "a result of magnetic stresses localized at mid-latitudes or in near surface flows". (Physics Today, Oct., p. 14).

Of course, we must not be too hasty in drawing firm conclusions about constancy of oblateness from just two years of observation. But thus far, it looks pretty good.