Strömgren Sphere analysis of an emission nebula

Joachim Köppen Kiel/Strasbourg/Illkirch April 2000

The Strömgren sphere Applet treats the observations of an emission line nebula as coming from the sphere of ionized gas around a star hot enough to keep the surrounding gas ionized by its output of photons with energies above 13.5 eV, the ionization energy of hydrogen.

I wrote this to allow a quick check on whether the observed data of a nebula are consistent with e.g. a certain distance or a certain luminosity of the central star.

It can be used to deduce the distance from the observed flux in the Hbeta recombination line, the angular diameter, and the density of the gas. One can also compute the angular diameter of such a nebula, for assumed distance, density, and flux. From any three observed or assumed values, one determines the fourth quantity by clicking the associated radio button.

The applet also computes the number of ionizing photons the star must radiate per sec in order to maintain the nebula. And, given a value for the star's temperature, the luminosity of the exciting star is computed.

The other buttons and text fields allow to change the assumed electron temperature, to switch to the intensity of the Halpha line (if it had been observed in place of Hbeta), to enter the extinction constant to take into account the interstellar extinction, to switch between the ionization bounded model (where there is enough gas around the star to absorb all photons) and the density bounded model (when the size of the nebula is determined by the finite mass of the gas available - note that in this case the luminosity of the central star will be an lower limit only!),

Radio Buttons :
here one enters the observed flux in logarithms of the line flux from the whole nebula in cgs units. If the aperture is smaller than the nebula, one has to extrapolate to the whole size
Angular Diameter
to be given in arc seconds
Electron Density
in particles per cubic cm
in kpc
Note: clicking the radio button (right) makes the corresponding quantity to be computed from the other three. If one hits the Enter-key after putting a new value in one of the fields, the computation is re-done with the current values
Other controls :
Extinction c(Hbeta)
the extinction constant for Hbeta, which is about 1.5 E(B-V). See the Extinction Curve Applet Hitting the Enter-key after changing the entry will cause recomputation.
Electron Temperature
Hitting the Enter-key after changing the entry will cause recomputation.
Volume filling factor
Hitting the Enter-key after changing the entry will cause recomputation.
button specifies for which line the flux is given
ionization/density bounded
button switches between these two models. Note that in density bounded nebulae the luminosity for the central star will only be a lower limit. There is no simple way to tell how many stellar photons are not absorbed by the nebula.

Ionizing Photons
is what the star emits per sec in order to keep the nebula ionized. It will be a lower limit for density bounded model
stellar Temperature
here we give our assumed value, for which the applet computes the luminosity of the star which would emit the required number of ionizing photons. Hitting the Enter-key after changing the entry will cause recomputation.
the stellar luminosity in units of the solar luminosity
the stellar radius in units of the solar radius

is shown in pc
expansion velocity
enter a value in km/s ...
expansion age
... and you'll get the age in years

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