Designing a Planetary System: Output

All planets, side view

While procrastinating and enjoying my weekend I decided to go berserk on a full scale system building spree. This is the second part of the planetary system building series. The first part can be found here. I have updated it and made some corrections.

If you decided to make planets of your own after all, I suggest reading these papers: A Hybrid Symplectic Integrator that Permits Close Encounters between Massive Bodies, J. E. Chambers, 1998; Making More Terrestrial Planets, J. E. Chambers, 2001; Building the terrestrial planets: Constrained accretion in the inner Solar System, Raymond et al. 2009.

Now, let’s get down to our business.

In the previous post I promised to make a sample system. Here it is; you can use the following data as you like since I don’t plan to use it anywhere in my stories, but give me credit (or at least drop a comment here).

I have based my system on existing stars; this binary star system age estimations range from 6 to 8 Gyr (we’ll start somewhere at the beginning of the main sequence). The distance between the primary and the secondary is shortened to as close as 55 AU (the original distance is 1061 AU).

The primary has little or no variability and only low emission from its chromosphere.

Some notes on stellar evolution

You can build a system the same way I did; you can also use stellar model grids (as mentioned in this post, or the ones here and here, for example); or you can use this awesome Stellar Evolution Simulator to calculate parameters of your star’s evolution. You can also plot your personal H-R diagram after the simulation run.

When stars are studied spectroscopically it is found that most stars are composed of around 70% hydrogen and 28% helium by mass, very similar to what we see in the Sun. The fraction of all other elements is small and varies considerably from 2 or 3 % by mass in Sun-like stars (population I) to 0.1 to 0.01 percent by mass in stars found in globular clusters (population II). The Sun has about 1.8% heavy elements by mass.

Among the Solar-type stars observed in the Galaxy, many appear to be metal-rich relative to the Sun. The case of planets hosts is particularly interesting in that respect since they present, on average, an overmetallicity [Fe/H] of 0.2 dex. This metallicity is probably original, from the protostellar nebula, but it could also have been increased by accretion of hydrogen-poor material during the early stage of planetary formation.

Once nuclear fusion of hydrogen becomes the dominant energy production process and the excess energy gained from gravitational contraction has been lost, the star lies along a standard main sequence curve on the HR diagram. Astronomers will sometimes refer to this stage as “zero age main sequence”, or ZAMS. The ZAMS curve can be calculated using computer models of stellar properties at the point when stars begin hydrogen fusion. From this point, the brightness and surface temperature of stars typically increase with age.

Pre-main sequence to ZAMS stellar evolution (masses 0.1 to 6 solar). Credit: The Formation of Stars. Steven W. Stahler and Francesco Palla, 2005
Pre-main sequence to ZAMS stellar evolution (masses 0.1 to 6 solar). Credit: The Formation of Stars. Steven W. Stahler and Francesco Palla, 2005

A star’s position on the ZAMS depends on both its mass and its initial helium abundance.

The mass fractions in H, He, and all elements heavier than He (“metals”) are labeled by the capitalized letters X, Y, and Z, respectively. They are related by: X + Y + Z = 1.

Often (Z/X) ratios are quoted, so
X = (1 + Y)/(1 + (Z/X))
Y = 1 – Z – Z/(Z/X)
Z = (1 – Y)/(1 + 1/(Z/X)).

Mazzitelli (1989) gives stellar evolution model with helium mass fraction depending on metallicity, in which helium content Y for stars is given by the empirical relation Y=0.243+(dY/dZ)*Z and where 0.243 is the primordial helium mass fraction. The reasonable value for dY/dZ is considered 2.0, though it is a very uncertain quantity and varies from object to object, e.g. the model with original solar values, Y = 0.267 and Z = 0.0188, would have a different dY/dZ value (note that X+Y+Z=1 must hold). An increase in Y decreases the main-sequence lifetime, and an increase in Z increases the main-sequence lifetime. The habitability for planetary systems is thus robust under changes in stellar model parameters (Jones et al. 2005).

HZs for a 0.9 solar mass star with the original values Y = 0.303, Z=0.0298 following the above-mentioned relation (black lines) and Y = 0.269 (solar value), Z = 0.0317 (increased metallicity) (grey lines). Credit: Jones et al, 2005.
HZs for a 0.9 solar mass star with the original values Y = 0.303, Z=0.0298 following the above-mentioned relation (black lines) and Y = 0.269 (solar value), Z = 0.0317 (increased metallicity) (grey lines). Credit: Jones et al, 2005.

Stars with higher initial helium abundances have higher luminosities and effective temperatures. This is predicted by homology; homologous stars are built with the assumption that star with mass M1 will just be a scaled version of a star with mass M0, because the physics which determines the structure of main sequence stars does not change rapidly with mass. Thus the higher mean molecular weight translates into lower core pressures. Helium rich stars therefore are more condensed, which mean they have higher core temperatures and larger nuclear reaction rates.

Changes in metallicity shift the location of the ZAMS; the metal-poor main sequence is blueward of the solar metallicity main sequence. This is primarily due to the reduced amount of bound-free absorption throughout the star (which only comes from metals). The smaller opacity of metal poor stars allows the energy to escape more easily, and thus increases the luminosity.

Typically the portion of heavy elements is measured in terms of the iron content of the stellar atmosphere, as iron is a common element and its absorption lines are relatively easy to measure. Because the molecular clouds where stars form are steadily enriched by heavier elements from supernovae explosions, a measurement of the chemical composition of a star can be used to infer its age.

My Primary is more enriched in heavy elements than the Sun, with almost two times solar abundance of iron; it is therefore classified as a rare “super metal-rich” (SMR) star. This abundance of metal makes estimating the star’s age and mass difficult, as evolutionary models are less well defined for such stars.

If you’re into stellar astrophysics, you might want to try and write your own code to simulate stellar structures and evolution. References: Stellar structure model, Stellar Modeling, The ATON 3.1 stellar evolutionary code and the ATON 3.1 stellar evolutionary code, a version for asteroseismology.

The model

Data Box 1 – Original stellar data

Star A, yellow dwarf, the primary
Spectral class: G8V
Mass: 0.95 solar masses
Radius: 1.152 solar radii
Luminosity (bolometric): 0.63 solar
Temperature: 5373 K
Apparent magnitude: 5.95
Absolute magnitude: 5.46
U−B color index : 0.65
B−V color index: 0.86
Metallicity: [Fe/H] = 0.31 (that makes Z = 0.038, greater than solar)

Star B, red dwarf, the companion
Spectral class: M3.5-4V
Mass: 0.13 solar masses
Radius: 0.30 solar radii
Luminosity (bolometric): 0.0076 solar
Temperature: 3134 K (calculated)
Apparent magnitude: 13.15
Absolute magnitude: 12.66
U−B color index : 1.66
B−V color index: 1.21

Presumably the region this system formed in was dense and metal-rich. So I decided to go with six planets (and don’t forget the extra star). Three of them are terrestrials and the rest are gas and ice giants. Now, before you start arguing about various possible issues with this configuration, the plausibility of such system will be discussed in the upcoming Extension post, dedicated to binary and multiple star systems.

Data Box 2 – Planetary system data

Open/download all as text file.
Download archived files of the run and of the star evolution tracks.

The lifetime of the primary on the main sequence is about at least 11.37 Gyr (the greatest estimate was 14.6 Gyr). The companion star will have a very long life, at least twice that of the primary. So there is plenty of time to live.

A brief calculation gave me current water & UV habitable zones for the primary between 0.8753 AU and 1.3574 AU, and the frost line at 2.436 AU. I have modeled probable evolution of the main star with Stellar Evolution Simulator and here is how the habzone might evolve.

Continuous HZ of star A
Continuous HZ of star A

Planet E might (or eventually will) be habitable; I have no information on its atmosphere and leave it to your imagination. Even if it is truly ‘earthlike’, it will still be nothing like we know.

Planet F is the local “Jupiter”. It’s HUGE and it rotates faster than our Jupiter does. It probably has similar atmosphere, but with even more spectacular bands and local “giant spots”.

This is the chart of the system at the end of the final integration run.

Full system, front & side views:

Full system, head on view
Full system, head on view
All planets, side view
All planets, side view

All planets, front & side views:

Planet system, head-on view
Planet system, head-on view
All planets, side view
All planets, side view

Four inner planets, front & side views:

4 inner planets, head-on view
4 inner planets, head-on view
4 inner planets, side view
4 inner planets, side view

Terrestrial group, front & side views:

Terrestrials, head-on view
Terrestrials, head-on view
Terrestrials, side view
Terrestrials, side view

All ephemerids can serve as a good basis for you fictional calendar later. If you are a Celestia user, then you can easily make all these numbers into visually pretty 3D.

Noname system dynamics and stability

I did 100 000 year integration run to see if the system is stable at least that long. With the time step of 8 days for moderate accuracy it takes around 1 hour to do this on my spare machine (its CPU ticks at 789 MHz). One tenth of a million years is too little to see what’s really happening in this system and how it will evolve. Its components barely started to adjust to their would-be regular paths. Some of the orbits that might survive for 1-20 Myrs would very probably not survive for 1 Gyr.

Here is a bunch of plots of orbital parameters from the final run (see initial data for it in Box 2).

Semimajor axes from full to detailed view:

Semimajor Axes, 0 - 100 000 years
Semimajor Axes, 0 – 100 000 years
Semimajor Axes, 0 - 10 000 years
Semimajor Axes, 0 – 10 000 years
Semimajor Axes closeup, 0 - 3000 years
Semimajor Axes closeup, 0 – 3000 years
Semimajor Axes, Inner planets C, D and E. 0 — 3000 years
Semimajor Axes, Inner planets C, D and E. 0 — 3000 years

Inclinations of all major objects in the system:

Inclination i
Inclination i

Eccentricities of all system components:

Eccentricity of planet C, 0 - 100000 years
Eccentricity of planet C, 0 – 100000 years
Eccentricity of planet D, 0 - 100000 years
Eccentricity of planet D, 0 – 100000 years
Eccentricity of planet E, 0 - 100000 years
Eccentricity of planet E, 0 – 100000 years
Eccentricity of planet F, 0 - 100000 years
Eccentricity of planet F, 0 – 100000 years
Eccentricity of planet G, 0 - 100000 years
Eccentricity of planet G, 0 – 100000 years
Eccentricity of planet H, 0 - 100000 years
Eccentricity of planet H, 0 – 100000 years
Eccentricity of companion B, 0 - 100000 years
Eccentricity of companion B, 0 – 100000 years

At first I have used inclination of 25 degrees, eccentricity of 0.055 and two different distances for star B. This had some strong effects on the planet C (closest to the primary): with companion B at a distance of 920 AU planet C was ejected into space somewhere at 54 000 years of integration; with companion B at a distance of 220 planet C became tilted at 100 degrees by the end of integration. The rest of the system remained relatively unaffected; e.g. the would-be habitable planet E didn’t have any scary shifts in eccentricity or obliquity (yet). Planetary rotation rates must be taken into account as well: they are less than 20 hours and this may give planetary axes additional stability. I didn’t include any moons into the system.

The “calm belt” is located between 0.4 and 5 AU as seen from orbital dynamics of planets D, E, and F. Planet F is the third massive body in the system after the primary and its companion. Planet C is strongly perturbed by star A; planets G and H are perturbed by both stars. If the system was real, the planets on G and H orbits may have never been formed.

Currently the system is widely chaotic; accidents might happen in the future. Planet C is probably the first candidate to fly away. Or maybe not.

What to watch for

1. Eccentricity (coupled with the distance from the primary)

Why? The orbital eccentricity of a habitable world might generally increase under the influence of other system bodies and might rise to the point where the planet is carried outside the HZ for a significant fraction of its orbital period. Whether a planet could be habitable in such a case depends on the response time of the atmosphere-ocean system; Williams & Pollard (2002) conclude that a planet like the Earth probably could.

2. Close encounters

The system bodies might perturb the orbit of the planet to the point it will be kicked out of the habitable orbital course or completely out of the system for good. Or even sent on a collision course with something not quite small (like a star or another planet; heck, even the moon will be enough). I don’t know what is worse in this case: being molten or frozen to death. In case of simply being kicked out of the system survival might still be possible with the help of technology, though.

3. Obliquity (axial tilt)

This is the most interesting part, since altogether with orbital parameters it governs insolation and climate of the planet. I will discuss this in detail in the appropriate post later on.

Here are the obliquities of planets in the noname system. The axial tilt of the earthlike world experiences quite large but not too severe variations (yet).

Obliquities:

Obliquities, 0 - 100 000 years
Obliquities, 0 – 100 000 years
Obliquity of planet E, 0 - 100 000 years
Obliquity of planet E, 0 – 100 000 years

Other experiments

Here is also an interesting simulation of the scenario when a planet inserted between the orbits of Mars and Jupiter. Multiple simulations were run, varying the eccentricity, orbital semi-major axis and mass of the inserted planet, and the resulting data analyzed with the help of visual data plots.

Designing a Planetary System: Input

This month’s post is long and quite complex. So I will split it in two parts: Input & Output. I also decided to write an Extension post to the series, where I will discuss binary and multiple star systems, and things related.

Designing an extremely realistic planet (along with the whole system) is not a simple task, so if you have no interest in it, I suggest you don’t read math & tech parts of this article (I will mark them as such). We’ll be doing some math here and there. Also, advanced level of computer knowledge is required. If you don’t know what a command line is, skip those parts and enjoy the rest. And last but not least, this task will require a few days of your time (mostly computer time though). So, if you have something to do, like mow grass on the football field, now is a perfect opportunity. With all this said I’m moving onto the main thing.

Countless planetary systems exist throughout the vastness of space. Some of them are small, consisting only of one planet per star; some of them are big, like our Solar System with 8 planets and lots of other stuff orbiting around the Sun. In fact, all planetary systems discovered up until now consist of smaller number of planets than the Solar System, with 2 to 4 planets being most common.

Before designing your own system it might be a good idea to look through descriptions of those systems. There are numerous catalogues with data. For example:

List of known exoplanets

The Extrasolar Planets Encyclopaedia

The NASA Star and Exoplanet Database

Exoplanet Transit Database

Extrasolar Planet Table on Astropical.net

For more planet stuff you can also read the Systemic blog, which is written by Greg Laughlin, Professor of Astronomy and Astrophysics at the University of California, Santa Cruz. Systemic reports recent developments in the field of extrasolar planets, with a particular focus on observational and theoretical astronomical research work supported by the NASA Astrobiology Institute, and by the Foundational Questions Institute (FQXi).

Now, there are two ways of getting your system up: top-to-bottom or bottom-to-top methods.

The top-to-bottom method suggests using some of the accretion algorithms to generate your system – you’ll get all stuff automatically, nothing to invent there. And I’m not talking about “planetary system generators” found on the web (e.g. StarGen), they don’t produce realistic systems. They tend to produce systems “similar to our own”; the truth is planetary systems don’t follow this “similarity” plan. A truly alien world will be something else, as you can see from worlds discovered up to date. Personally, at some point I’ve been using AstroSynthesis (v.3.0 will be released somewhere after September 30th). It does cool things, try it. I recommend it to those who don’t want to go deep into calculations.

State-of-the-art planetary accretion simulations typically use N-body integrations, but these are too computationally expensive and time consuming. So we’ll skip that part and get to the time when all planets are already in their respectful places. Trust your intuition; it’s better than some generator.

The bottom-to-top method implies you first imagine your main planet and do all the necessary calculations for its parameters (I will talk about those in detail below). The rest of the system is rather sketchy: all you decide is where to put other planets (semimajor axes) and how many there will be in total (you can also add some of their details as well, e.g. mass, density and orbital elements). This decision should be based on your star of choice and its parameters.

Planetary parameters

I assume you have already decided on mass, density and calculated radius. If not, check the previous post here.

Another two parameters required for our computations are axial tilt and rotation rate. The tilt can be anything you want from 0 to 180°. Note that object with tilt below 90° has a retrograde rotation, like Venus does. Also, planets usually move on their orbits in counterclockwise direction, with clockwise direction being retrograde orbital motion.

There are three cases of planetary rotation around its axis: normal (counterclockwise), retrograde and tidally locked (synchronous rotation or orbital resonance, e.g. Mercury’s 3:2 spin-orbit resonance).

When planets are born, they have their primordial spins. During their lifetimes planetary spins are affected by solar tides and tides inflicted by another bodies of the system. Planets and moons slow down, spin up (like Mars and Saturn did), or become tidally locked if too close to a star or any other massive body (e.g. Mercury, the Moon). Earth’s initial spin rate was about 6.5 hours comparing to modern 24 hour day.

Math Box 1 – Initial rotation of a planet

Approximate initial planetary spin can be estimated from its mass.

First, you calculate initial angular velocity using Dole’s equation (output is in rad/s). M is the mass of the planet; k is the moment of inertia ratio (I/MR^2), a value of 0.33 is taken for a terrestrial planet (you can look at planet moments of inertia in these fact sheets); r is planet’s radius, and j is 1.46E-20 m²/s²kg.

ω = [(2*j*M) / (k*r^2)] ^ 0.5

Then, initial rotation rate in seconds is calculated as t = (2*PI)/ω

To get it in hours th = t/3600

Studies suggest that primordial spins are randomly determined by a few giant impacts during accretion, e.g. Agnor et al. (1999). So primordial spin might be whatever you want (the boundary is the velocity at which the planet will fall apart).

Math Box 2 – Planetary rotation at a certain age

Now, from this point onward things start to slow down, because a tidal deceleration torque from the primary is applied. (On some occasions things might actually spin up.)

>> dω/dt = (dωe/dt)*(ke/kp)*(rp/re)*(me/mp)*((Mstar/Msol)^2)*((Rsol/Rstar)^6)

Here (dωe/dt) = (-1.3E-6 /10^9) rad s-1/yrs; k is as mentioned above for terrestrials; m is a planetary mass; index letter e stands for Earth and p for planet.

You can estimate planetary angular velocity at any age of the system. In the following formula system age is in seconds. The new angular velocity then becomes

ωnew = Initial angular velocity ω + (system age (s) * tidal deceleration torque dω/dt)

Rotation rate in seconds is calculated >> t = (2*PI)/ωnew

In hours >> th = t/3600

Thus you can determine how your planet day becomes longer. However, the primary isn’t the only one influencing rotation rate of a planet. There’s also atmospheric drag, and a small influence of the system’s bodies. (Some of the formulas above are taken from Fogg, 1992.)

Note: If you have a moon or two, things get more complicated. You’ll have to take them into account as well.

Note 2: I suggest you calculate rotation rate this way instead of integrating the whole system for considerable amount of time; that could take days on an average machine, especially if precision and long timespan (more than 100×10^8 to X × 10^9 years) are chosen.

Angular velocity also gives us a clue to planetary flattening and difference between polar and equatorial radii.

Math Box 3 – Planet flattening (dynamical ellipticity) and radii

The radius you determined from mass and density is the mean radius, R. If not, the time is now:

R=0.5*[(mass/density)*(6/PI)]^(1/3)

or, if given mass and log g, through relation
Mstar/Msun=((Rstar/Rsun)^2)*10^(loggstar-loggsun).

Ellipticity e = SQRT(f*(2-f)) is related to flattening, which can then be expressed as f = 1-SQRT(1-e^2) or f = (1/SQRT(1-e^2))-1; or, if you have only radii, flattening becomes f=(Re-Rp)/R.

Flattening f is also calculated as f* = (5/4)*(((ω^2)*(R^3))/(M*G)); ω – from calculations above (math box 1 & 2); R – mean radius; M – planetary mass; G = 6.67259E-11. Equatorial radius thus becomes Re = R*(1+(f/3)), and polar Rp = R*(1-((2*f)/3)). The difference between radii is expressed as Re-Rp, or simply as mean R*f.

*Note: We’ll get somewhat overestimated degree of rotational flattening of the planet because the formula takes planet’s interior as incompressible fluid of uniform density. In reality terrestrial planet’s core is much denser than its crust. Or, in case of gaseous planets, an overestimate will rise from the fact that they have a mass distribution which is strongly concentrated at their cores.

Now, when we have our rotation rates, we can move onto the next step.

Orbits and orbital elements

The traditional orbital elements are the Keplerian elements. They describe the orbit of the body in space.

Keplerian elements can be obtained from and converted to orbital state vectors (x-y-z coordinates for position and velocity) by manual transformations or with computer software. For our integration Keplerian elements should be enough. If you want something else, the body-centered, inertial rectangular components of the radius vector can be determined from the classical orbital elements (see math box 4).

Math Box 4 – Orbital State Vectors

The mean longitude λ = M + ω + Ω where M is the mean anomaly, ω is the argument of perigee, Ωis the longitude of the ascending node.

The true anomaly ν is found from the expression ν=λ-Ω-ω

The body-centered, inertial rectangular components of the radius vector can be determined from the classical orbital elements as follows:

Position formulas
Position formulas
Velocity formulas
Velocity formulas

Here a is the semimajor axis, e is the eccentricity, i is the inclination; in these equations p is called the semiparameter of the orbit and is calculated from p=a*(1-e^2). η is the gravitational constant of the primary or central body.

Math Box 5 – The spin angular momentum*

*this will be necessary for the main integration part to calculate obliquities and spin rates. If you won’t do integration, skip this part.

SAM is a vector, it has 3 components. It is calculated as H = H * Ĥ

H = 0.4 * M * (R^2) * v

Here, R is planet’s equatorial radius, M is planetary mass, and v is a spin rate (angular velocity).

The initial coordinates of unit vector Ĥ in the reference frame are:

X = sin ψ * sin ε
Y = cos ψ * sin ε
Z = cos ε

Where ψ is precession in longitude and ε is axial tilt of a planet.

The precession in longitude ψ is defined by ψ = L – Ω, where Ω is the longitude of the ascending node, and L is the inclination of ecliptic. The angle between the planet’s equato­rial plane and inclination of ecliptic is the obliquity ε.

Your both precession angle ψ and obliquity ε should be in radians.

**You can calculate your precession rate as well. Note that precession formulas use semimajor axis (a) and eccentricity (e). You can start integration at the beginning of the system age (if you have time and patience) to get all things neatly; or you can skip to the necessary age and use the “invented” data as initial point. Whatever works for you.

The final step is to multiply each component of Ĥ by the quantity H.

Hx = H * X
Hy = H * Y
Hz = H * Z

Integration will require these quantities in AU^2/day, so take mass as Mass/Mass of the star, R of a planet as R/149597870.7, and angular velocity in radians/day.

TECH TOOLBOX: Environment and Integrator

Note: Numerous programs exist to perform integrations of n-body systems. If you want to learn more, google something like “n-body integrator”.

Currently I’m using Mercury, a hybrid symplectic integrator for orbital dynamics developed by John Chambers. A corrected version of the main file can be downloaded here.

Mercury is written in Fortran77 in a slightly non-standard code and before you can use it, you have to compile it. So, first of all, you need a compiler. I used GNU gfortran for this purpose. Depending on your operating system there are some options:

Installing GCC (any OS) or

Installing Cygwin with compiler packs (Windows)

Assuming you installed all necessary things, we now can move onto our main goal – Mercury package.

The package has the manual, the file called mercury6.man and can be opened with any text editor of your choice. Read it CAREFULLY and follow all the instructions.

If using gfortran, compile the drivers typing lines
gfortran -o mercury6 mercury6_2.for
gfortran -o element6 element6.for
gfortran -o close6 close6.for

To run what you have compiled, just type
./mercury6

and hit enter.

Pretty simple.

If you have questions regarding installation and usage, feel free to ask. But please note that I’m running all this under Windows XP and might not know about any issues with other operating systems.

So far I had no issues with any software mentioned here.

Integration of orbits

When integrating the equations of motion in classical or relativistic celestial mechanics, one has to know the values of the parameters, in particular the masses and the initial conditions (orbital parameters or state vectors). I won’t be going into the n-body problem details here. If you are interested I suggest reading some good literature on the subject, e.g. Gravitational N-body Simulations: Tools and Algorithms by Sverre J. Aarseth (a cheap copy can be found on abebooks.com or on any of their international sites).

So far all necessary info on required parameters is in the Mercury manual.

Useful Julian date converter can be found here.

Planetary system stability

Are planetary systems stable? Probably. You can’t tell just by looking at them; the invisible force out there guides all the interactions between the bodies. That’s why scientists perform numerical integrations of planetary orbits.

#For the next part I’ll do a small sample system integration.

From Stars to Planets: The Loners

Brown dwarf glows feebly in the dark depths of space. Artwork by David Aguilar, Harvard-Smithsonian CFA

The word planet means “wanderer”; the Greeks called them planētēs aster, “wandering stars”. Indeed planets travel on their orbits, wandering around their stars for millions and billions of years. Stars move along their paths in galaxies, wandering, until the end of their time. Some objects, however, do not follow this familiar pattern. These objects include planets, brown dwarfs, stars, and even black holes, bringing up the most challenging setting for a science fiction story.

Shadowy neighbors

Our Galaxy alone is full of unusual stuff. Objects known as brown dwarfs were only a theoretical concept until they were first discovered in 1995. It is now argued that there might be as many brown dwarfs as there are stars, and our closest neighbor might turn out to be an ultracool brown dwarf rather than Proxima Centauri.

Brown dwarf glows feebly in the dark depths of space. Artwork by David Aguilar, Harvard-Smithsonian CFA
Brown dwarf glows feebly in the dark depths of space. Artwork by David Aguilar, Harvard-Smithsonian CFA

These objects fall somewhere between the smallest stars and the largest planets on the heavenly spectrum, and have masses that range between twice the mass of Jupiter and the lower mass limit for nuclear reactions (0.08 solar masses). They are thought to form the same way low-mass stars do – from a collapsing cloud of gas and dust. However, as the cloud collapses, it does not form an object which is dense enough at its core to trigger and maintain hydrogen-burning nuclear fusion reactions. Their spectral characteristics are different to those of very cool stars, showing an absorption line of the short-lived element lithium. Furthermore, they have fully convective surfaces and interiors, with no chemical differentiation by depth. In young brown dwarfs, when combined with rapid rotation, their turbulent interior motion can lead to a tangled magnetic field that can heat their upper atmospheres, or coronas, to a few million degrees Celsius. Even if not fusion powered, these mysterious objects are also known to have flares.

The nuclear fusion is what fuels a star and causes it to shine, but brown dwarfs are very cool and dim compared to stars. The coolest brown dwarf yet discovered is about as hot as boiling water, with a temperature of less than 100 degrees Celsius (~ 370 K).

Update September 7th 2013: A new study shows that some brown dwarf stars may be as cool as room temperature.

Dwarf comparison: from stars to planets
Dwarf comparison: from stars to planets

The trouble with brown dwarfs is that they are hard to find. An isolated (not in a multiple system) brown dwarf is typically visible only at ages < 1 Gyr because of the rapidly fading luminosity. The lighter brown dwarfs are more sensitive to this effect. Young brown dwarfs are visible at relatively large distances but evolve rapidly, making it difficult to catch them when they are in their earliest stages of formation. Old brown dwarfs will only be visible if they are nearby. So we have more chance of discovering brown dwarfs that have just recently formed.

Dumping more mass on a brown dwarf doesn’t make it bigger, it just makes it denser. A 70-Jupiter-mass and 20-Jupiter-mass brown dwarf are both about the size of Jupiter.

From up close, a young brown dwarf would look like a low-mass star, but an old brown dwarf would look more like Jupiter.

Brown dwarfs aren’t brown, they would look red to the naked eye.

Brown dwarfs radiate most of their energy in infrared light.

Some brown dwarfs spin so fast that they complete one rotation in less than an hour.

Brown dwarfs have hydrogen cores.

The average density of a brown dwarf is about 70 grams per cubic centimeter, which is 5 times the density at the center of the Earth.

Robert Naeye, Astronomy magazine, August 1999, p. 36-42

Brown dwarfs have also been discovered embedded in large clouds of gas and dust. Accretion discs were detected around some of these failed stars, even around those as small as 10 Jupiter masses. Astronomers discovered that some disks contain dust particles that have crystallized and are sticking together in what may be the early phases of planet assembling. A relatively large and many small grains of mineral called olivine was found; another sign of dust gathering up into planets is the flattening of brown dwarfs’ disks. But such systems will be tiny compared to our own Solar System.

Brown dwarfs emit faint visible light, but are cool enough to retain a somewhat Jupiter-consistent atmosphere. For example, Gliese 229B, discovered in 1995. Its luminosity is about one tenth of the faintest star and its spectrum has large amounts of methane and water vapor. Methane could not exist if the surface temperature were above 1200K. Astronomers consider its temperature to be about 950K (compared to Jupiter’s 130K), its mass to be between 0.02 and 0.05 of solar, and the age of the binary system to be between 2 and 4 billion years. It has a smoggy haze layer deep in its atmosphere, essentially making it, much fainter in visible light than it would otherwise be. It is possible that ultraviolet light from its companion star changes its atmospheric properties from those of an isolated brown dwarf. Theory now also suggests that young brown dwarfs are hot enough (with temperatures as high as 2000 Kelvin) to have clouds of iron and silicates. These clouds “rain out” as the brown dwarf cools and becomes dimmer. But this raining out causes a temporary brightening as obscuring clouds are cleared from the atmosphere. Considering the age and the temperature of Gliese 229b, its atmosphere should be clear of clouds, leaving it a featureless ball glowing a dull red, like a coal, from internal heat. Any moons that might had formed too close to the brown dwarf would have been torn apart by tidal forces long ago. Surviving moons, if they exist, may be heated enough by tidal forces for methane or nitrogen geysers to form.

This paper describes a collection of evolutionary models for brown dwarfs and very-low-mass stars for different atmospheric metallicities, with and without clouds.

Children of the Demon Planet. The massive Brown Dwarf with its array of moons, by Christian Thrower*
Children of the Demon Planet. The massive Brown Dwarf with its array of moons, by Christian Thrower*

*You should check out his website, Christian’s paintings are awesome!

Brown dwarfs are members of a group known as substellar objects. This group also includes planetary mass objects, or planemos, ranging from satellite planets and belt planets to rogue planets, to sub-brown dwarfs.

All planets are planetary mass objects by definition; their mass is expected to be greater than of minor objects (e.g. meteoroids, asteroids or minor planets) but smaller than that of brown dwarfs or stars, yet a planetary mass object (PMO) is a celestial object, which do not conform to typical expectations for a planet.

Free floating planets not orbiting a star may be rogue planets ejected from their systems (during system formation, death or some instability within its lifetime), or objects that have formed through cloud-collapse rather than accretion. Isolated PMOs with masses lower than the 13-Jupiter-mass definition of a brown dwarf, which were not ejected, but have always been free-floating and are thought to have formed in a similar way to stars, are called sub-brown dwarfs.

A rogue planet (also known as an interstellar planet, or orphan planet) is a planetary-mass object that has been ejected from its system and is no longer gravitationally bound to any star, brown dwarf or other such object, and that therefore orbits the galaxy directly. Recently, some astronomers have estimated that there may be twice as many Jupiter-sized rogue planets as there are stars. Is it getting crowded here?

If interstellar space is full of substellar objects, they might become our stepping stones for robotic (or even manned) missions in the (very) distant future. It would mean interstellar space could be reached through an “island-hopping” strategy. Even if there won’t be much of planetary systems, the resources could still be used by probes (or humans, to live in ships or whatever space habitats there might be developed).

Planets and substellar objects aside, there are even more bizarre things happening out there.

Stellar hamburgers

Blue stragglers are main sequence stars in open or globular clusters that are more luminous and bluer than stars at the main sequence turn-off point for the cluster. With masses two to three times that of the rest of the main sequence cluster stars, blue stragglers seem to be exceptions to the rule of positioning all cluster stars on a clearly defined curve set by the age of the cluster, with the positions of individual stars on that curve determined solely by their initial mass.

The explanation for this might lie in collisions and mass transfer between binary stars of the cluster. The merger of two stars would create a single more massive star, potentially with a mass larger than that of stars at the main sequence turn-off point. These blue stagglers are common residents of the galaxies. However, some blue stagglers have even more dramatic emergence.

Studies have already shown that our Galaxy is able to “eject” stars once in about every 100,000 years. And the one responsible for such deeds is none other than the black hole at the center of the Galaxy.

The tragic case of the star HE 0437-5439. Credit: NASA, ESA, E. Feild (STScI)
The tragic case of the star HE 0437-5439. Credit: NASA, ESA, E. Feild (STScI)

The incredible fate of HE 0437-539 summarized in 5 steps. 1: a triple-star system was drawn to the black hole in the center of our Galaxy. 2: one of the three stars was grabbed by the black hole and the two others ejected. 3: the duo broke away from our Galaxy. 4: on aging, the two stars merged. 5: the merger gave rise to a blue straggler which continues to move away from our Galaxy. Alone… Well, maybe not.

There will be only one…

The similar situation seems to be with another objects galaxies might like to dispose of. They indeed are very violent creatures, and during their “mating rituals” they probably can even rip out hearts.

This artist's conception shows a rogue black hole that has been kicked out from the center of two merging galaxies. The black hole is surrounded by a cluster of stars that were ripped from the galaxies. Credit: STScI
This artist’s conception shows a rogue black hole that has been kicked out from the center of two merging galaxies. The black hole is surrounded by a cluster of stars that were ripped from the galaxies. Credit: STScI

In such hypercompact stellar systems the supermassive black hole keeps the stars moving in very tight orbits about the center of the cluster, where it resides. These objects are believed to be fairly common. In theory, hundreds of massive black holes left over from the age of galaxy formation could be lurking in the nearby universe, because they are expected to be gravitationally bound to the galaxy cluster that had produced them. So the best place for finding such objects would be regions of space dense with thousands of galaxies that have been merging for a long time, since black hole mergers within these galaxies may have resulted in violent kicks.

Update: April 2013

New computer simulations predict as many as 2000 black holes living on the outskirts of the Milky Way. Some might have been stripped bare, while others may carry a few clusters of stars and dark matter.

From Stars to Planets: Objects in Space and Habitability Potential

Planetary system development (artist’s impression)

Only about 4% of the total mass of the Universe is made of atoms or ions, and thus represented by chemical elements. Hydrogen is the most abundant element, making up 75% of normal matter by mass and over 90% by number of atoms. It is found in great quantities in stars and gas giant planets, as well as in the interstellar medium.

Most of the mass of the Universe, however, is not in the form of chemical-element type matter. It is postulated to occur as forms of mass such as dark matter and dark energy.

The first stars that formed after the Big Bang, provided the Universe with the first elements heavier than helium (‘metals’), which were incorporated into low-mass stars that have survived to the present. For example, eight stars in the oldest globular cluster in our Galaxy, NGC 6522, were found to have surface abundances consistent with the gas from which they formed being enriched by massive stars during the early phases of the seeding of heavy elements.

Recent study suggests that the very first star might have been born much earlier than previously thought, when the Universe was only 30 million years old. Interesting question about the earliest stars is, were these monsters blue-violet and luminous or dark and glowing infrared? Could the early Universe possibly have had both types? In a place that had not yet witnessed chemical and magnetic stellar feedback, the formation of the first stars is a well-defined problem for theorists.

Of 118 known only 94 elements occur naturally. Most of the elements heavier than helium are synthesized in stars when lighter nuclei fuse to make heavier nuclei. The process is known as nucleosynthesis. The rest is produced in supernovae and other violent cosmic events. The material in our sun (and solar system) has been cycled through at least several stars.

Stellar Cycle. Image credit: Seth Stein
Stellar Cycle. Image credit: Seth Stein

The more rounds of star birth and death there have been, the larger the ratio of carbon to oxygen. Towards the center of our Galaxy, in the regions of more evolved stellar population, you’d expect to find more carbon worlds than silicate planets like Earth. Similarly, over time, the gas clouds across the whole galaxy are getting progressively more carbon-rich, and in a few billion years, most of new planets might turn out to be carbon worlds.

As the Universe ages, one might ask, is there a possibility of appearance of yet unknown elements with changes in stellar populations? Well, no. In our present-day Universe naturally occurring exotic Unobtanium is unlikely. Even if technology is involved, the existing periodic table plus some antimatter (anti-hydrogen anyone?) is all we get. Perhaps, in another universe with slightly different laws of physics, allowing such metamorphosis? Who knows?

Elemental abundances in the Universe drop off exponentially with increasing atomic number (Z) up to Z ~ 60; thereafter remain almost constant. Even-Z elements are more abundant than their odd-Z neighbors. Li, Be & B show marked depletion relative to both higher and lower-Z elements.

Element abundance curve and production processes
Element abundance curve and production processes

Abundance may be variously measured by the mass-fraction (the same as weight fraction), or mole-fraction (fraction of atoms by numerical count, or sometimes fraction of molecules in gases), or by volume-fraction. Measurement by volume-fraction is a common abundance measure in mixed gases such as planetary atmospheres.

Assuming that life can only evolve on the basis of carbon compounds, there are several extremely important elements, required for life.

Important elements for life
Important elements for life

By mass, human cells consist of 65–90% water and 99% of the mass of the human body is made up of the six elements, which are oxygen (65%), carbon (18%), hydrogen (10%), nitrogen (3%), calcium (1.5%), and phosphorus (1.2%). Needless to say, life is built from the most abundant stuff, available at the spot. However, note that Earth is silicon-rich and carbon-poor, e.g. has more silicon (27.69%, second after oxygen by mass) than carbon (only 0.094%) in its crust, and life still had chosen carbon as its base; that’s probably universal.

Also, hydrogen may be the most abundant element in the Universe, but oxygen has an importance that is disproportionate to its abundance, since it plays a critical role in so many fundamental planetary system processes. The very nature of the terrestrial planets in our own Solar System would be much different had the oxygen/carbon ratio in the early solar nebula been somewhat lower than it was, because elements such as calcium, iron and titanium would have been locked up during condensation as carbides, sulfides and nitrides and even (in the case of silicon) partly as metals rather than silicates and oxides.

Playing chess on the periodic table

Extrasolar planets often differ tremendously from the worlds in our solar system. Rather than assume planets around other stars are scaled-up or scaled-down versions of the planets in the Solar System, it is necessary to consider all types of planets that might be possible, given what is known about the composition of protoplanetary discs.

Planets can have a wide range of sizes and masses but planets made of the same material will have the same density regardless of their size and mass. For example, a huge, massive planet can have the same density as a small, low-mass planet if they are made of the same material. No matter what material a planet is made of, the mass/diameter relationship follows a similar pattern. All solids compress in a similar way because of the structure. If you squeeze a rock, nothing much happens until you reach some critical pressure, then it breaks. The same goes for planets, but their operating pressure is composition-dependent.

In 2007 a team of scientists have created models for 14 different types of solid planets that might exist in our Galaxy. The 14 types have various compositions, and the team calculated how large each planet would be for a given mass. Some are pure water ice, carbon, iron, silicate, carbon monoxide, and silicon carbide; others are mixtures of these various compounds.

Comparison of sizes of planets with different compositions. Credit: Marc Kuchner/NASA GSFC
Comparison of sizes of planets with different compositions. Credit: Marc Kuchner/NASA GSFC

Planets fall into different classes, with our solar System being represented only by two of them – rocky terrestrials and gas giants. But rocky planets almost as big as Uranus seem far more common in the Universe than suspected. These Super-Earths, now an officially defined planet class, have masses in the range from Earth to Uranus, exactly the range that is missing from our Solar System.

Terrestrial planets have overall densities around 4-5 g/cm^3 with silicate rocks on the surface. Silicate rock has a density ~ 3 g/cm^3 and iron has a density ~ 8 g/cm^3. Ocean planets will probably be somewhere between 2 and 4 g/cm^3 (depending on interior materials), and gaseous planets are thought to be holding at ~ 0.6 – 2 g/cm^3 (check out Saturn, which is less dense than water!) but there were some surprises as well. In 2006 a planet with extremely low density was discovered. This extrasolar planet, TrES-4b is 70% larger but actually less massive than Jupiter. With the large size, and lower mass, the planet has a low density of only 0.22 grams per cubic centimeter, and is probably composed of hydrogen and helium. And this isn’t the sole case. Currently there is a whole group of such diffuse “puffy” planets. These gas giants with a large radius and very low density sometimes are called “hot Saturns”, due to their similar density to Saturn.

Terrestrial planet’s bulk density can be approximated as rho_planet = rho_earth*(Mplanet/Mearth)^0.2, where Mplanet and Mearth are body masses and rho_earth is the mean density of Earth. The uncompressed density of such planet would be earthlike, and so will the composition. More massive objects have stronger gravities. As a result, more massive objects get more compressed than less massive objects. This compression means that the bulk density of the object will be greater. Uncompressed density is free of mass dependence.

Now summing up all things previously said, composition along with planetary mass plays a vital role for habitability potential, allowing or restricting such things as atmosphere, magnetic field and plate tectonics to create ocean basins, with volcanism driving carbonate-silicate cycle, and, eventually, life.

Size of a habitable planet

Very small terrestrial planets (around or less than 0.3 Earth masses) are less likely to retain the substantial atmospheres (because of low gravity) and ongoing tectonic activity probably required to support life. By “ongoing” I mean several billions of years. The same is with the upper mass limits. Very large terrestrial planets (perhaps, larger than 2 Earth masses) might have some problems with becoming geologically dead faster than life might evolve there, or being hyperactive, reshaping their surface quite fast. I will talk about plate tectonics (and maps!) in details somewhere in the following posts, so I’m not going to focus on that here.

Then, there is another issue with the size. In 2010, model simulations of rocky super-Earths between 2 and 10 Earth-masses showed that high pressures could keep their cores solid instead of molten, which would prevent a magnetic field from forming to protect developing surface life from stellar radiation. Other scientists argue that the interiors of super-Earth may still get hot enough to melt their iron cores despite the pressure due to other factors not yet considered by the model simulation.

Magnetic shielding

Planets in HZs are exposed to stellar winds; the closer to the star, the denser the wind. Without a magnetic field generated by a rotating molten metallic core, the atmosphere of such a planet would also face progressive erosion by the stellar wind of its host star. The planet, even if rotating slowly (as in tidally locked), can have strong magnetic shielding given the suitable mass, size, chemical composition and effective convection in its interiors. This was very well shown in the model by Barnes et al, 2010.

Magnetic moment strength. The values are lower limits to the expected magnetic moment strengths. Image credit: Barnes et al. 2010
Magnetic moment strength. The values are lower limits to the expected magnetic moment strengths. Image credit: Barnes et al. 2010

The image represents magnetic moment model estimates for planets up to 12 Earth masses, a pure iron core, and perovskite/ferropericlase mantle compositions. The color scale on the right corresponds to magnetic moment values between 0 and 80 times that of the Earth. The region below the colored squares corresponds to planets made out of core materials denser than iron, while the region above corresponds to planets with radii too large, and therefore too low density, to have a core capable of generating a magnetic field.

However, note that planets under extreme conditions (i.e. highly inhomogeneous heating or very strong stellar winds), will have their magnetic fields affected.

All this corresponds pretty well with the previous model.

Mass/Diameter/Composition Relation. Credit: Marc Kuchner/NASA GSFC
Mass/Diameter/Composition Relation. Credit: Marc Kuchner/NASA GSFC

Consider now a habitable ocean planet. In order to protect the ocean from evaporating you need an atmosphere. A magnetic field is necessary to prevent the atmosphere from eventually being stripped away by stellar wind. Also, a planet too close to its star or a giant planet (in case of a satellite) can be a subject to serious tidal heating. So give a thought about planet’s interiors and how they work.