CONVERTING NEAR EARTH OBJECTS MAGNITUDES INTO DIAMETERS
 
To convert the absolute magnitude distribution into a size distribution, we need to develop a model of the albedo distribution of Near Earth Objects.
This is relatively easy to do in the framework of our model. In fact our model establishes the fraction of NEOs supplied by each of our 5 NEO source regions (see methodology).  Hence, if we know the albedo distribution of the asteroids in/close to these sources, we can  deduce the albedo distribution of the NEO population.

 

 

The albedo distribution in the 5 main sources is obtained through a main belt asteroid model, calibrated on the color distribution observed by the Sloan Digital Sky Survey (Izevic et al., Astron. J. , 122, 2749, 2001):
 
 
fraction* with albedo 2 - 9% fraction* with albedo 9 - 11% fraction* with albedo 11 - 35% fraction* with albedo > 35%
population in nu6 source                        7 %                           5%                          74%                          14%
population in 3;1 source                       10%                          4%                          79%                            7%
population in IMC source                       21%                          6%                          63%                          10%
population in OB source                       47%                         11%                          39%                            3%
population in JFC source                     100%                           0%                            0%                             0%
*fraction computed for a population brighter than a given H

From this, we deduce the albedo distribution of the NEOs:
 
fraction* with albedo 2 - 9% fraction* with albedo 9 - 11% fraction* with albedo 11 - 35% fraction* with albedo > 35%
NEO population                        20%                          5%                           65%                          10%
*fraction computed for a population brighter than a given H

From this albedo distribution we estimate that the total number of NEOs with diameter D larger than 1 kilometre is  855 +/-110  which, compared to the total number of NEOs with H<18 (960 +/- 120), shows that the usually assumed conversion H=18 <=>D=1 km slightly overestimates the number of kilometre-size objects. The correct conversion should be H=17.85 +/- 0.03 <=> D=1km.
 
 
Comparison between the number of NEOs brighter than absolute magnitude H=18 and the number of NEOs larger than 1 kilometre in diameter, as a function of the orbital semi major axis. Because the dark NEOs come mainly from the outer main belt or are dormant cometary nuclei, their orbits typically have large semi major axis.  Therefore, the NEOs with D>1 km outnumber those with H<18 for a>2.5 AU, while the opposite is true for a<2.5 AU.

If we assume that most bodies with albedo smaller than 9% belong to the C taxonomic class, while the others belong to the S taxonomic class, we estimate that the C/S ratio in the NEO population should be ~0.25. This ratio is in agreement with the observed ratio (0.165 for H<20) once observational biases have been taken into account.

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