Setting up a star

The first step in creating a fictional exoplanet is to specify the star around which it orbits, since it is the star's energy output and spectrum that will determine thermal conditions on the planet, and it is the star's gravity that will determine its orbit.

Stellar parameters

If one sees stars as a dynamical entities, they are fiendishly complex in their functioning, evolving different mechanisms like radiative and convective heat transport to bring energy from their active energy-producing inner core to the surface, they have a complex and twisting magnetic field, show flares, protuberances and other ejection events --- and during their life cycle go through different phases, possibly ending spectacular in a supernova.

If one is however interested in a star as energy source for a planet and gravitational center of a solar system, then matters become much more simple. Chiefly, under these conditions we are interested in only few parameters:

Stellar mass: This is possibly the most relevant parameter for the star. It measures the amount of material the star consists of, which in turn directly determines how strongly spacetime in its vicinity is curved, i.e. how strong the gravitational binding of the rest of the star system is. However, more massive stars have - due to the high mass - also higher pressure in their core. This in turn means higher temperatures, higher nuclear fusion rates, yet higher temperatures and more energy output. As a rule, the more passive stars are therefore also the hotter stars. Conveniently, the stellar mass is measured in units of the solar mass.

Luminosity: The total energy output of a star is called its luminosity. Primarily, the energy is radiated away as a broad spectral distribution of electromagnetic radiation. Usually, luminosity is also measured in units of solar luminosity, so one can directly see how the energy output of a star differs from the sun.

Surface temperature: The surface temperature of a star is generally much less than its core temperature. However, it determines how the star appears, how much visible light is emitted vs. how much UV or IR radiation. Low surface temperatures make a star visibly red, high temperatures blue. The common unit to express surface temperatures is Kelvin.

Radius: While the mass describes how much material the star is made of, the radius indicates how that is distributed. There are very small and compact stars with extremely high densities, just as there are very large stars with extremely low density. Through simple geometry, the radius also determines how large the radiating surface of the star is. Usually stellar radii are given in kilometers or solar radii.

The parameters are however not independent. Generally one can, from the surface temperature, compute via the Stefan-Boltzmann law, how much energy a unit surface radiates. With the known radius, the total surface of the star can be computed, and combining the two results the luminosity can be obtained. Thus one cannot choose luminosity, radius and surface temperature independently.

For so-called 'main sequence stars' (the bulk of stars), there are more constraints - here there is a well-defined relationship between mass and luminosity ranging from 0.43 to 55 solar masses which allows to compute the luminosity directly from the mass. There is also an approximate relationship between mass and surface temperature.

For more exotic stars such as white dwarves or red supergiants, the relation between mass and luminosity is generally different, but also here the parameters are not independent.

One therefore needs to take care that the defined star is physically possible.

Entering main sequence stars

Most 'interesting' stars for exoplanets are main sequence stars (planetary systems around the remnants of main sequence stars exist, even around neutron stars, but presumably have lost all their atmosphere and water when ths star left the main sequence, so they are unlikely to harbour life).

In this case, the star can be specified with the keywords mass and T_surf, and optional a name can be added. A configuration file for our Sun would be as follows:


name Sun
mass 1
T_surf 5778.0

The mass is given in units of solar masses, and the surface temperature is 5778 K. The code automatically uses the mass-luminosity relationship to determine the luminosity, from there determines the radius via the surface size and emissivity and then uses the radius to compute the density.

Creating this file as sun.cfg and running from the commandline as ./world sun.cfg yields the console output

Mass [m_sun]: 1
Surface T [K]: 5778
Luminosity [L_sun]: 1
Radius [Mkm]: 0.69591
Mean density [g/cm^3]: 1.4086
Spectral fraction IR 0.511453
Spectral fraction vis 0.368739
Spectral fraction UV 0.119808

which prints out the parameters which have been computed (not very surprisingly, we find that the Sun has one unit solar luminosity). In addition, we can see what fraction of the stellar spectrum is in the infrared, the visible and the UV light, for instance the Sun has about 11.9% of its energy in the UV.

If we'd like to simulate an F-spectral class star, we can find the information that it has a mass range between 1.04 and 1.4 solar masses and surface temperatures from 6000 to 7000 K, so e.g. using

name F-class
mass 1.4
T_surf 7500.0

results in
Mass [m_sun]: 1.4
Surface T [K]: 7500
Luminosity [L_sun]: 3.8416
Radius [Mkm]: 0.809546
Mean density [g/cm^3]: 1.25271
Spectral fraction IR 0.337047
Spectral fraction vis 0.393602
Spectral fraction UV 0.269351

which is a star with significantly more UV radiation.

Entering exotic stars

Stars off the main sequence can also be specified, but there is no consistency check done, i.e. it is possible to define physically completely impossible stars (with main sequence stars, it is possible to err on the temperature side, however energy conservation is never violated). Data for such stars then needs to come from a database. For instance this is Sirius B, a white dwarf:

name SiriusB
mass 0.98
T_surf 25200
luminosity 0.0295
radius 0.0168

Here, luminosity and radius need to be given as well, both in units of solar luminosity and radius. Running the example will reveal the extremely high UV fraction of such hot stars.

Plotting spectra

Using the Planck radiation formula, the bulk spectrum of the star (without line features of course) can be computed. This needs the plot keyword, as well as a couple of other keywords which specify what variables are to be plotted on x and y axis (var_x and var_y), what the limits for the x-axis are (xmin and xmax) how many points should be plotted and, optionally, to what file the result should be written. Add the following section to an example configuration:

var_x lambda
var_y solar_spectrum
xmin 1e-7
xmax 3e-6
npoints 1000

file sun.dat
here we request the energy radiated into a wavelength band per square meter of emission surface as a function of wavelength lambda. The finished file needs an external software (such as gnuplot) to visualize, you should see something like this:

Spectral distribution of the Sun

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