Protostar Formation – Infographic

Infographic of the formation of protostars. Based on An Introduction to Modern Astrophysics by Carrol and Ostlie.

Infographic of the formation of protostars. Based on An Introduction to Modern Astrophysics by Carrol and Ostlie.

Took me a while to do that. I hope that you like what I did.

In some respects, I am not happy. I wanted to fit much, much more info. But I saw very soon that that was not going to be possible, at least in the way in which I originally conceived the infographic.

Adding more information without cluttering up too much would surely ask for a change in format. I tried to keep it as simple as possible.

In addition, my original idea was quite different from this. I had in mind something more hand made, more organic. However I also wanted to try Illustrator out, which gives a different feeling. At least in my hands.

Only one explanation is pertinent:

I used the greek letter Tau to represent optical depth, which is a measure of opacity (see also Stellar Atmospheres).

Other symbols are more obvious. L stands for luminosity, T is temperature, D is deuterium, H is hydrogen.

If you are looking at this, I’d truly appreciate your opinion about the infographic.


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Protostar formation – mindmap

Study mindmap for protostar formation - based on "An Instroduction to Modern Astrophysics" by Carrol and Ostlie

Study mindmap for protostar formation – based on “An Introduction to Modern Astrophysics” by Carrol and Ostlie

Edit: see the infographic HERE

Why this, actually?

Once upon a time, I had an astrophysics exam. I took this book and put myself to work. I read the relevant chapters carefully, and crafted summaries and mindmaps for each block of content. In the end, I overstudied (!), since the exam ended up being far, far easier than I expected.

The book is truly excellent in content quality and clarity. Still, it was a long and daunting journey, and perhaps I’d have stopped before the end if I didn’t have that exam. In the end, I can say it was worth it, because astrophysics is a truly exciting topic by itself.

Often one can get a fair glimpse of this grand topic, which you can typically get by watching a well done documentary (some episodes of the new series Cosmos were very remarkable). However, the details become invisible by this approach. With my posts, I’d like to help you to get closer to the details, without asking you to spend long hours reading the book by Carrol and Ostlie. Still, if you find the time and have the passion, I HIGHLY encourage you to read that book, which could be almost considered as the bible of astrophysics.

One way of conveying the information is via mindmaps like the one above (also take a look at Toni’s Mindmap book).

Another (obvious) way is the good old classic blogpost, like any one from IFLS.

A third way that  I find particularly attractive: the infographic. As a matter of fact, I am preparing an infographic about protostars formation, with content similar to the one above but much, much more detailed. You can find a bunch of science infrographics in pinterest (although I have more in mind the illustrations of awesome educational books that I had as a child).

Now a few things to say about the mindmap. In fact, you could only understand it by having previously permeated yourself with the topic. The mindmap’s goal is not to understand and learn, its goal is to connect and memorize information effectively.

The mindmap above is designed following a few key ideas:

  • Information is tiered in 3 levels, from general to specific
  • The upper tier is marked in blue and corresponds to the central topic
  • The mid tier (subtopics within the main central topic) is indicated by red.
  • The bottom tier (aspects of each subtopic) is indicated in green.
  • Arrows indicate chronological order.
  • Grey boxes show content which complements and expands the concept to which they are linked
  • Black lines around boxes are meant so that a greyscale version of the mindmap is still usable. Notice that blue has all sides in black, red the upper and bottom sides, and green only the bottom one, respectively blackened.

Let me repeat: the mindmap is not meant to stand alone since it is not understood without a previous knowledge in the area. Additional content will come and I’ll link to it here and in the “Astrophysics” section, in the index.

See you!

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Animated astronomy video

I just found this video in YouTube, created by the same people who makes PhD comics.

After watching it I had to share it in here. This is good stuff. Albeit not thorough, frenetically fast, deceptively messy, and beautifully executed. Really cute stuff.

Watch it now.

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Carolyn Porco: This is Saturn

I wanted to share this with you. A TED talk about the exploration of Saturn by Carolyn Porco.

I hope that you enjoy it!

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The Solar Neutrino Problem

The solar core emits neutrinos as a result of the nuclear reactions in the pp-chain.

The thing with neutrinos is, they have a very small cross-section, and therefore are very difficult to detect (they can go all the way through Earth without interacting with anything).

The Homestake experiment, Lead, South Dakota, had the collection and counting of neutrinos coming from the Sun as a purpose. It consisted on a tank with 100,000 gallons (~380,000 L) of C2Cl4.

Cl-37 can interact with neutrinos of sufficient energy to produce radioactive Ar-37, with a half-life of 35 days.


The counting rate of neutrinos was measured in solar neutrino units (SNU, 1 SNU = 1e-36 reactions per target atom per second). The standard solar model predicts a rate of 7.9 SNU, while the outcome of the experiment was 2.23 ± 0.26 SNU. This discrepancy is the solar neutrino problem (SNP).

The Super-Kamiokande: Consisted on a tank of 3,000 metric tons of water. Neutrinos are able to scatter electrons, and the Kamiokande detector is able to detect the Cherenkov radiation produced when this happens. Cherenkov radiation is produced when an electron travelling in a medium (e.g. in water) travels faster than the speed of light in that medium (which is not physically impossible, since the speed of light in any medium is always slower than in vacuum). This is somewhat analogous to breaking the sound barrier.

The Kamiokande experiment was the first able to experimentally verify that the neutrinos have a non-zero mass.

The explanation for the SNP is that, since neutrinos have non-zero mass, they can transform between different types or flavors. Thus, there are 3 types of neutrinos:

  • Electron neutrinosνe
  • Muon neutrinos, νµ
  • Tau neutrinosντ

The transformation between one flavor and the others (called neutrino oscillation) takes place when neutrinos interact with electrons. The experiments only detected the electron neutrinos, explaining why a smaller number of neutrinos than that predicted by the models was detected.

EDIT: The transformation between flavors seems to be of a more complex nature than simply “interact with electrons”, which I don’t fully understand. To get some clue, read the paragraph under the “Theory” heading in this wikipedia article.

Neutrino oscillation was evidenced by the Sudbury Neutrino Observatory.

See the text under the heading “Resolution” in the wikipedia article. The explanation is quite neat.

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Solar Model

The Sun, a typical main-sequence star of spectral class G2, with a surface of composition X = 0.73 (mass fraction of hydrogen) and Z = 0.02 (mass fraction of metals). Current estimated age: 4.52e9 years.

The standard solar model applies physical stellar modelling to describe the Sun (see Stellar Modelling).

  • The center of the Sun is rich in He-4 (product of pp-chain), and poor in hydrogen (low X, high Y).
  • The surface of the Sun is rich in hydrogen and poor in He-4. This is due to diffusive settling of heavier elements toward the center.
  • Since the birth of the Sun, its radius has increased by 10%, and its luminosity has increased by 40%.
  • The Sun’s primary energy source is the pp-chain.
  • 90% of the Sun’s mass is located within one half of its radius.
  • The luminosity suddenly increases at around 10% of the solar radius, which means that at this point the energy production is maximum. Two factors to take into account for this:
    (1) The energy production is higher as the mass within one shell increases, this is naturally happening as we get further away from the center.
    (2) The concentration of fuel available to generate energy (hydrogen) decreases as we move further away from the center.
    These two factors cause a maximum in the derivative of the Sun’s interior luminosity (dL/dr) at 10% of the solar radius (i.e. maximum of energy production).
  • At 71% of the solar radius, the energy transport regime changes from radiative transport (r < 0.71R) to convective transport (r > 0.71R).
Dependency of composition and luminosity on solar radius.

Dependency of composition and luminosity on solar radius.

Helioseismology = study of the oscillations of the Sun.

The Sun oscillates with roughly ten million vibration modes, typically with a very low amplitude (surface velocity of < 10cm/s, and luminosity variation  dL/L ~ 1e-6). Two kinds of modes identified.

  • p-modes, or five-minute oscillations, with periods between 3 and 8 minutes.
  • g-modes, with longer periods of about 160 minutes.

More about helioseismology.

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Stellar Modelling

Stellar Models require:

  • The fundamental stellar structure equations (FSSE)
  • The constitutive relations (CR): “equations of state” describing the physical properties of the matter of the star.


If the structure of the star is changing, the influence of gravitational energy must be included. This introduces a time dependence not present in the static (time-independent) case.



Also, if acceleration is non zero, the acceleration term must be added to the pressure differential (first equation in FSSE):


The CR represent P, κ, and ϵ as a function of ρ, T, and composition.


Boundary Conditions: specify physical constraints to our equations.

  • Interior mass Mr and interior luminosity Lr vanish in the center of the star (r=0).
  • Another set of boundary conditions are required at a r=R* somewhere at the surface of the star. The simplest conditions are assuming that the temperature T, the pressure P and the density ρ vanish at r=R*. Strictly speaking, these conditions are never obtained in reality, so more sophisticated conditions may be needed.

How is it all used? The volume of the star is imagined to be constructed of spherically symmetric shells of width Δr. These shells separate the volume of the star into discrete Δr increments (…, ri-2, ri-1, ri, ri+1, ri+2, …, thus i is a “label” for one given shell), and the different properties are calculated via numerical integration for each r, using the Stellar Structure Equations, and the Constitutive Relations.

This numerical integration can be done starting from one boundary (either r=0 or r=R*) or somewhere in the middle point of one star radius, and integrate in both directions (i.e. toward the center and toward the surface). By doing this, for each value of i we can find the respective Pi, Mi, Li, and Ti.

In the end, the values obtained should match with the defined boundary conditions in both ends with a desired accuracy. Usually, it requires several iterations, which means that if the properties at the boundaries do not match the desired values, we must change the initial conditions and repeat the numerical integration.

In sum:

  1. Decide a starting point, and a set initial conditions (guess).
  2. Perform numerical integration toward both boundaries (center and surface).
  3. Check accuracy of solution. If the solution is not accurate enough, return to step 1. Otherwise, you’re done.


Vogt-Russell Theorem: take as a general rule, more than a rigorous law.

The mass and composition of a star uniquely determine its radius, luminosity, and internal structure, as well as its subsequent evolution.

Changes of properties in Main sequence stars…

  • Larger M mean larger central P and T.
  • In low-M stars, the pp-chain dominates.
  • In high-M stars, the CNO cycle dominates.
  • Star lifetimes decrease with decreasing L.
  • Stars of the main sequence have masses which range between:
    – M < 0.08 M (no nuclear reactions taking place).
    – M > 90 M (energy pulsation mechanism and unstable stars).
  • A M change of 3 orders of magnitude corresponds to:
    – A L change of 9 orders of magnitude (i.e. a damn huge change)
    – Only moderate T change (factor of 20, 2,700K — 53,000K).
  • A lower T involves a higher opacity (κ), i.e. low T favors convection domination.

Source (modified)

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