Gaia DR3 has a table named SSO Reflectance spectrum containing the reflectance spectra for 60518 asteroids.
As explained in the documentation, the table contains the mean BP/RP reflectance spectra of asteroids computed as the ratio between the asteroid flux and an averaged solar analogue flux. In each row, the reflectance spectrum of a given asteroid is given at a given wavelength. Entries for all asteroids are concatenated into a single table.
The reflectance spectrum is sampled at the following wavelengths (nanometers):
374 418 462 506 550 594 638 682 726 770 814 858 902 946 990 1034The reflectance value for the wavelength 550 nm is always equal to 1 as a consequence of a normalization performed by design as part of the Gaia processing.
Occasionaly, the measurement for one or more of the above wavelength is missing. In order to simplify, I took into account only asteroids with complete measurements and also having flag = 0
I ended up with a table containing data for 9926 asteroids, the top rows are shown here:
number_mp denomin…¹ 374_n…² 418_n…³ 462_n…⁴ 506_n…⁵ 550_n…⁶ 594_n…⁷ 638_n…⁸ 682_n…⁹ 726_n…˟ 770_n…˟ 814_n…˟ 858_n…˟ 902_n…˟ 946_n…˟ 990_n…˟ 1034_…˟
<int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 18 melpomene 0.709 0.765 0.853 0.933 1 1.04 1.06 1.11 1.16 1.17 1.14 1.11 1.14 1.11 1.16 1.18
2 38 leda 0.739 0.825 0.924 0.970 1 0.999 0.979 0.981 0.986 1.00 1.02 1.04 1.05 1.06 1.08 1.12
3 58 concordia 0.809 0.871 0.936 0.979 1 0.996 0.970 0.969 0.976 0.980 1.00 1.01 1.03 1.05 1.08 1.15# … with abbreviated variable names ¹denomination, ²`374_nm`, ³`418_nm`, ⁴`462_nm`, ⁵`506_nm`, ⁶`550_nm`, ⁷`594_nm`, ⁸`638_nm`, ⁹`682_nm`,
# ˟`726_nm`, ˟`770_nm`, ˟`814_nm`, ˟`858_nm`, ˟`902_nm`, ˟`946_nm`, ˟`990_nm`, ˟`1034_nm`Every row contains the spectrum for a given asteroid, the reflectance values have been allocated in the appropriate column (i.e., the reflectance value measured at 374 nm is in column name 374_nm etc. etc.).
Based on the table, I generated the following boxplot to show the overall distribution of the reflectance values at different wavelengths:
There seems to be a lot of "dispersion" at greater wavelength, specially at 1034 nm - not clear if this is a consequence of data acquisition or if there is another reason.
Let's see which asteroid has the minimum//maximum reflectance for any given wavelength:
Min Reflectance Max Reflectance
374_nm "MUTOJUNKYU" "2001 FZ25"
418_nm "TERUHIME" "2001 EM24"
462_nm "TERUHIME" "SHERMAN"
506_nm "1997 YQ5" "1986 TD"
594_nm "1999 AD6" "2001 AA24"
638_nm "BHATTACHARYYA" "2001 AA24"
682_nm "COURBET" "1998 AR"
726_nm "BRAGA-RIBAS" "CLAVIUS"
770_nm "BHATTACHARYYA" "1999 RM166"
814_nm "1997 VP2" "BREWER"
858_nm "2000 EG87" "JUSTITIA"
902_nm "LINMICHAELS" "JUSTITIA"
946_nm "LINMICHAELS" "JUSTITIA"
990_nm "1999 XU188" "1990 QF9"
1034_nm "2001 EM24" "NABOKOV" Thus, it seems that asteroid "2001 EM24" has at the same time maximum reflectance at 418 nm (blue region) and minimum reflectance at 1034 nm (infrared region).
This fact suggests a question: is there any correlation between the reflectance in different regions of the spectrum?
In order to answer this question, I tried to plot the heatmap showing the correlation between the reflectance at various vavelengths:
Looking specifically at the correlation between 418 nm and 1034 nm, it appears that the correlation is almost null so it is not obvious for 2001 EM24 to have those characteristics.
At first glance, it seems that the correlation between the reflectance at adjacent wavelengths is positive but looking better there are three macro areas:
- wavelengths less than 506 nm: moderate positive correlation (orange-red) with reflectance of wavelengths less than 506 nm
- wavelengths greater than 594 nm: moderate positive correlation (orange-red) with reflectance of wavelengths greater than 594 nm
- wavelengths greater than 594 nm : moderate negative correlation (lightblue-blue) with reflecteance of wavelengths less than 506 nm
However, the last area has a notable exception: Looking at wavelength 1034 nm, the correlation with adjacent wavelength tends to decrease smoothly, going from medium values like 0.68 at 990 nm down to -0.11 at 462 nm but then very strangely it increases to 0.24 at 374 nm.
Another way to look at the heatmap is to sort the rows and columns to show those that have more similiarities:
Two/three macro clusters have been proposed by the heatmap clustering algorithm:
- cluster 1: wavelenghts 374 nm, 506 nm, 418 nm, 462 ... so let's say less than 506nm
- cluster 2: wavelengths 1034 nm, 946 nm, 990 nm ... so let's say above 946 nm
- cluster 3: other wavelengths, the two most similar columns (alsmost identical, wavelength 682 nm and 726 nm )
I am not sure If I did the PC analysis correctly, I used an R function called prcomp (with options: scale=TRUE, center=TRUE ), and I got 15 PCs:
Importance of components:
PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11 PC12 PC13 PC14 PC15
Standard deviation 2.8929 1.6682 1.06353 0.9675 0.67070 0.57156 0.48552 0.44024 0.38308 0.34102 0.29515 0.27139 0.23949 0.22285 0.21092
Proportion of Variance 0.5579 0.1855 0.07541 0.0624 0.02999 0.02178 0.01572 0.01292 0.00978 0.00775 0.00581 0.00491 0.00382 0.00331 0.00297
Cumulative Proportion 0.5579 0.7434 0.81884 0.8812 0.91123 0.93301 0.94872 0.96165 0.97143 0.97918 0.98499 0.98990 0.99372 0.99703 1.00000The two most important components PC1 and PC2 explain 74% of the observed variations.
The rotation matrix is:
374_nm 0.091 -0.210
418_nm 0.244 -0.311
462_nm 0.253 -0.283
506_nm 0.200 -0.249
594_nm -0.246 0.106
638_nm -0.283 0.134
682_nm -0.311 0.124
726_nm -0.320 0.127
770_nm -0.327 0.094
814_nm -0.334 -0.027
858_nm -0.307 -0.209
902_nm -0.256 -0.338
946_nm -0.222 -0.404
990_nm -0.202 -0.435
1034_nm -0.143 -0.369
I would like to add every asteroid to the biplot (PC1,PC2 values) giving it color blue when it has more reflectance in the ultraviolet-blue region and color red when it has more reflectance in the infrared region.
Considering the available wavelengths measured by Gaia, let's say that the boundary is 726 nm .
Let me make an example for a specific asteroid so I can check my understanding.
Let's look at asteroid tangshan:
374_nm 418_nm 462_nm 506_nm 550_nm 594_nm 638_nm 682_nm 726_nm 770_nm 814_nm 858_nm 902_nm 946_nm 990_nm 1034_nm
1.178925 0.9620726 0.927563 0.9703729 1 0.9914462 0.963688 0.9828192 0.9620575 1.012652 0.96741 0.9921364 1.02211 1.009736 1.021114 1.077629 Let's define a numeric rule for assigning the color.
My first naive approach would be to look for the maximum reflectance value: in this case, as the maximum reflectance value is found for wavelength 374 nm, the color would be blue.
A second approach would be to calculate the mean reflectance value for spectra below 726 nm and compare it with the mean reflectance value for spectra above 726 nm: the first mean is 0.993216
while the second mean is 1.004193 and so in this case the color woud be red.
If you apply rule 1, you get the following numbers and related biplot diagram:
Rule 1
blue red
733 9193 
If you apply rule 2, you get the following numbers and biplot (apparently blue and red asteroids are better separated)
Rule 2
blue red
245 9681 
No comments:
Post a Comment
Note: Only a member of this blog may post a comment.