There and Back Again: winter break

Titan’s predicted internal structure (Tobie et al., 2015)

  •  Eccentricity of Titan constrains amount of tidal energy dissipated since formation
    • no reason to beleive Titan was hit by major impact in recent years, which might have increased the value
    • a world with a liquid layer should have dissipated  its eccentricity, and theoretically models predict a liquid water layer if there is enough ammonia
    • They use an evolution model of  Titan’s orbit and interior  to study the effect of a liquid water layer that would freeze over time would have on eccentricity
  • Coupled model
    • Titans early structure: likely poorly differentiated, with a mixed ice rock core and a silicate mantle and an outter H2O layer. Core differentiation occurs ~1Ga after forming. Start at ~1Ga.
    • Tidal heating in core negligable, so mostly radiogenic
    • However, tides of saturn must have slowed down rotation even within the first 1 Gatidal-diss
    • With water ice shell, subocean liquid can become well mixed given a high enough rayleigh number
    • crystallization determined based on heat fluxes at surface and core (i.e. radiogenic)
  • Results (1Ga years after formation to now)
    • fr
      • If I understand correctly, these are the thicknesses of the current liquid layer and the amount of global ammonia needed to explain current eccentricity?
      • similarly, the needed initial e for current e seen at given NH3 concentration?
    • For lowest viscosity values and lowest ammonia
      fractions (domain A), higher initial eccentricity values are required,

      • because the ice Ih shell becomes convective and highly dissipative some time during Titan’s evolution. The later convection in the outer ice Ih layer starts, the smaller the required initial eccentricity is.
    • For the highest viscosity values and/or highest ammonia fractions (domain B), convection never initiates.
      • The ice Ih layer remains diffusive and low dissipative up to present time. Initial eccentricities lower than 0.1 can explain the current state.
    • for low viscosity and no ammonia, Titan would always have been solid. If it existed early on, it still exist, likely with significant amoungs of ammonia
    • Titan is in resonance with Hyperion, which complicates the relationship making it difficult to ascertain the initial eccentricity, but it limits it at probably .1-.2
  • Conclusion
    • most realistic model, e_0 <.2, predicts ice layer with liquid ocean of an ammonia fraction dependent on the viscosity could have been as thin as ~25 km (actually ~100km or less, Mitri et al., 2014)

Research Update


I’m still at a point of no progress. I emailed Zibi a while back and am still waiting for a response. Unfortunately, I’m still struggling to grasp a basic understanding of Fortran–the underlying program used by Tekton. I’m trying to understand some basic functions, so I’m going to walk through what they do (for future reference) and to help me figure out how to move forward.

  1. Any and all commands must start with ‘gfortran ‘ to use the fortran program
  2. I should get an output file ‘a.out’ using gfortran, instead I get an error
    1. Undefined symbols for architecture x86_64: “_main”, referenced from: implicit entry/start for main executable ld: symbol(s) not found for architecture x86_64 collect2: error: ld returned 1 exit status
    2.  This is according to getting started with Gfortran
    3. I tried another command Catherine provided and it gave the output of ‘a.o’, which is good
      • gfortran -c tecin.f
  3. Unfortunately the next command she gave (I think) doesn’t work
    1. gfortran tecin.o -o tecin.exe
      • I get the same error as read above. This makes me think this is just a mistake in the code format (like above).Maybe this is peforming the same thing as the other command and is facing the same problem, like a missing variable (see 1.3 below)
    2. the gfortran wiki I reference above suggests doing the following, but I get the same error
      • gfortran tecin.f -o tecin.exe
  4. The logical next step will be to google that error and inquire about in a gfortran forum. I’ll update later.

same day update

  1. I used tecin.f because there was a folder outside the source folder labeled tecin.zibi; I tried repeating the same steps for tekton.f, which also exists in the source file folder, but got a new error
    1. [leonis:Tekton_distribution/Tekton 2.3/fesource 2.3] jjosh_h% gfortran -c tekton.f
      tekton.f:1:13:c include ‘f3dlib.f’brary!nt flag on the desired library andestion*.ls.rrcetor
      Error: Invalid form of PROGRAM statement at (1)
    2. I take this to mean tecin.f is the right file and will move forward with it.
    3. I think the error in the original code is with a need to label or call to some variable ‘main’ and am working on identifying what that is.


  1. I don’t think ‘main’ is a missing variable in the tecin.f code.
    1. I suppose it might be something another program its calling, so I need to look into it and try and figure out what other subcodes it involves
    2. I’m also going to have to keep looking into the error


  1. I found the same error online. I will work to try and implement the solution.
    1. When you compile the file, the compiler invokes the linker which tries to generate an executable. But it cannot because you didn’t provide a function named main which is the function that will be executed when your program is launched.Either you don’t want to run the linker because you want to compile several files separately then combine then. In that case, use the -c flag to tell the compiler to skip the link stage.Or either you want to execute the compiled file. Then you need to implement the function main.


I’ve been in contact with Zibi and she’s provided me with more info on how to move forward. I was focusing too much on one file. the tecin.o file is one of all the source files needed to compile the program it seems.


Then there is a series of codes that can be compiled to plot it. I’m still having issues converting a couple of the source codes, but I’m waiting on help to figure out what the issue is. Then I can try and run them all together. Hopefully, once done, it will be as simple as tweaking the numbers (somehow) to begin testing different parameters.

What I study at Western, and why.

Overwhelmed by Stress:
the Role of Viscous Relaxation on Titan’s Craters

J. E. Hedgepeth(1,2) (, C. D. Neish(1), E. P. Turtle(3)
(1)Western University, (2)Georgia Institute of Technology, (3)John Hopkins University

“The Earth is a very small stage in a vast cosmic arena.” – Carl Sagan. There are billions and billions of other worlds that we could study. The most recent estimate puts the universe at ~2000 Billion Galaxies with each galaxy having ~200 Billion stars with each star probably having at least one or two worlds. There is so much to be learned, and while it may not seem important to our everyday lives, each of these worlds can help us better understand Earth, ourselves, and our place in the cosmos. That is why I, and so many others, study planetary science. 


My focus is on Titan, Saturn’s largest moon with a diameter only slightly larger than the width of the United States. It has a thick atmosphere made of nitrogen and methane. Beneath it lies a thick water ice crust.

titan-riversOn it we find lakes of liquid methane that cycle through the atmosphere creating a complex system of exogenic processes, like the fluvial erosion that creates the drainage channels seen here.

They work to alter the morphology of the surface. Researchers have demonstrated that these play a prominent role in the resurfacing of Titan. However, there are other processes to consider.

These being endogenic processes—things that happen internally—like tectonics or viscous relaxation. I am modeling the effect of viscous relaxation, which happens internally, to ensure that its accurately accounted for. Viscous relaxation is the slow creep of ice to a more stable configuration.giphy

Imagine a glacier, stationary to the naked eye, but creeps slowly over longer periods of time. This doesn’t happen on Earth because the rocky crust is too strong, but even on Titan, the surface temperature is so low that its only happening on the order of 10s to 1000s of millions of years. So its understandable why scientists may assume it has a negligible effect. But it isn’t enough to assume; it has to be demonstrated quantitatively. That is what I am going to do.

I’ll do this numerically, using a finite element model, like the one used by Melosh and Raefsky to model the deformation of a slab under subduction. We’ll create a mesh like the one seen here, but modeled for a crater topography, like what is seen here from Thomas and Squyres 1988. Each point or node in the mesh allows us to track the changes of the topography on a finite scale.

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We have a good understanding on the process of viscous relaxation. Other worlds like Gaynemde, Callisto and Europa work as test cases for how craters relax without an atmosphere to degrade the surface more quickly as seen on Titan’s craters.

Craters on Titan, from Neish et al. 2013
Craters on Ganymede (top left), Callisto (top right), and Europa (bottom) from Schenk 2002

It’s important model this process for Titan to ensure that viscous relaxation is accounted for when modeling Exogenic processes. This will better constrain the thermal, mechanical, and compositional properties of Titan’s surface and interior. Thus improving our understanding of Titan’s volatile history that is known to have changed significantly in the last eon alone (e.g. Nixon et al., 2012; Neish et al., 2014)