where m and r are the mass and radius of the exoplanet of x composition (iron or water), respectively. The constants are m₁ = 5.80, r₁ = 2.52, k = [-0.209490, 0.0804, 0.394] for pure iron, r_i, and m₁ = 5.52, r₁ = 4.43, k = [-0.209396, 0.0807, 0.375] for pure water, r_o. Also note that this equation is only valid for masses below ~20 Earth masses (Seager et al., 2007). The HZC is defined as:

where exoplanets with HZC values between -1 and +1 have a habitable composition with an iron-rock-water mix. Values below -1 correspond to unlikely high dense iron bodies (i.e. a core from a dead gas giant). Those above +1 correspond to gassy bodies like Uranus, Neptune, Jupiter, and Saturn. HZC values closer to zero are generally better candidates for a habitable bulk composition (Figure 2).

Figure 1. Radius vs mass for those confirmed exoplanets with both values (red dots). The dotted curves show the mass-radius relationships for pure water planets (blue), silicates (green), and iron planets (red). Rocky planets fall between the water and iron boundaries. Venus, Earth, and Mars are shown for comparison (black dots).

Figure 2. This is essentially the same information shown in figure 1 but instead of radius in the vertical axis is the HZC, as a measure of composition. HZC values between -1 to +1 corresponds to planets with a potential habitable bulk composition. None of the shown exoplanets here (red dots) are in the stellar habitable zone. Six have the right bulk composition of a habitable exoplanet but not at the right orbital position to sustain a liquid surface water, a different issue. It is much easier to visualize and compare the relative composition of exoplanets in HZC units.

    The HZC complements the Habitable Zone Distance (HZD) as a habitability metric to quickly identify and assess potential habitable exoplanets. Those with the right orbital distance from the star (HZD between -1 and +1) and the right bulk composition (HZC between -1 and +1) are habitable candidates (Figure 3). Another metrics, the Habitable Zone Atmosphere (HZA), evaluates the presence of an atmosphere suitable for life.

Figure 3. This figure shows how some confirmed exoplanets, with known both mass and radius, rank as to position in their stellar habitable zone (HZD) and composition suitable for life (HZC). Only those falling in the darker green region (-1 < HZD <+1 and -1 < HZC < +1) are considered potentially habitable. The middle vertical red line corresponds to the uncertainty of Kepler-22 b in this plot. It has a HZD = -0.5, similar to Earth, but without its mass there is no constrains in its composition or habitability. Solar System terrestrial planets are shown for comparison. Note that this conservative analysis fails to exclude Venus or Mars from the potential habitable planets. Other metrics are used to recognize or exclude these objects.