Exoplanetary Mass Function

Figure 6.5 shows a mass histogram representing all exoplanets as well as solid lines showing sub-samples of short, intermediate and long period exoplanets. All indicate a rise in the number of exoplanets per unit mass towards lower masses despite the selection bias toward finding heavier exoplanets. This overall distribution is similar to the mass function based on subsamples of the long-period and intermediate-period exoplanets. Also over-plotted on this graph for comparison is a dotted line for dN/dM x M-1 1 (following Butler et al. 2006). The sensitivity of the radial velocity planets below 1 Mjup sin i is limited (see Fig. 6.3 caption) and so the turnover that both mass functions exhibit below 1 MJUP sin i is expected. Authors making corrections for incompleteness find steeper relationships, e.g., dN/dM x M-16 Lineweaver, Grether & Hidas (2003). Cumming et al. (quoted in Butler et al. 2006) finds dN/dM x M-11 for M <0.6 MJUP sin i and dN/dM x M-19 for M>0.6 MJUP sin i. However, until an approach such as that in Cumming et al. (2003), including a full treatment of eccentricity which incorporates a knowledge of detection sensitivities for a single sample, is made such results

Fig. 6.5. The plot shows various representations for the number of exoplanets per unit mass. By the dotted lines it may depicit the apparently different mass functions prevalant for close-orbiting planets and others. The two solid lines which approximately follow the shape of the histogram are smoothed sub-samples of exoplanets with intermediate (0.241.52) and large (1.6-11.4) values of au. The dashed line among them is the power law for the number of exoplanets scaling as dN/dM x M-1'1. To the left of the plot is a steeper solid line which is a smoothed version of the small (0.0177-0.238) au sample as well as a dotted line showing dN/dM x Ma tantalising indication that the close-orbiting exoplanet mass function may be steeper.

Fig. 6.5. The plot shows various representations for the number of exoplanets per unit mass. By the dotted lines it may depicit the apparently different mass functions prevalant for close-orbiting planets and others. The two solid lines which approximately follow the shape of the histogram are smoothed sub-samples of exoplanets with intermediate (0.241.52) and large (1.6-11.4) values of au. The dashed line among them is the power law for the number of exoplanets scaling as dN/dM x M-1'1. To the left of the plot is a steeper solid line which is a smoothed version of the small (0.0177-0.238) au sample as well as a dotted line showing dN/dM x Ma tantalising indication that the close-orbiting exoplanet mass function may be steeper.

are problematic. Nonetheless, it is noteworthy that the short-period mass function appears to have a somewhat different form. In Fig. 6.5 it is plotted with a thicker line and is overplotted with a normalised curve for dN/dM « M-3.

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