Hungaria - 2010 MA151 and 2017 BD92

 Backward simulation with Mercury6 (integrator BS, output every 100 days)

2005 UW252 and 2008 SO356

 Backward simulation based on nominal orbital parameters (Mercury6 simulator, BS integrator, output every 100 days):

2015 HB287 and 434936

Peter VanWylen noticed that these two asteroids stay very close to each other in the sky for many decades. He wondered whether they have  a common (recent) origin or it is a coincidence.

I run a Mercury6 simulation (output every 1 days) based on nominal parameters, while this is not a proof I think that the idea of a common origin should not be disregarded.

405222 (2003 RV20) and 2010 TH35

 Interesting couple, common origin?

2022 QV223 and 2012 SZ58

 Potentially interesting couple (common orgin?)

Gaia - SSO Reflectance Spectra

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 1034

The 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.

Every row has a flag that  indicates the expected quality of the measurement (0 - Good quality - 1 potential poor quality - 2 quality appears compromised).

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 ¹​denomination, 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:

1. cluster 1: wavelenghts 374 nm, 506 nm, 418 nm, 462 ... so let's say less than 506nm
2. cluster 2: wavelengths 1034 nm, 946 nm, 990 nm ... so let's say above 946 nm
3. cluster 3: other wavelengths, the two most similar columns (alsmost identical, wavelength 682 nm and 726 nm )

Following a comment from David Tholen, I tried to do a PCA analysis.

We have the reflectance values measured in 15 wavelengths.
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 1.00000

The two most important components PC1 and PC2 explain 74% of the observed variations.
The rotation matrix is:

PC1 PC2

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

The best way to see how the spectrum of the 15 wavelengths are related to PC1 and PC2  is to make a biplot graph:

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.

Thus, it is difficult to find an easy rule.

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 

(294003) 2007 TN89 versus 2020 OJ94

This is a potentially interesting couple (future studies may confirm if these two asteroids separated from a common body or not).

Clones Generation

I generated 100 clones for each asteroid trying to achieve the same orbital parameters distribution as the real asteroids (data from JPL - Small-Body Database Lookup)

2007 TN89

	Clones			Target
	mean	sd		mean	sd
q	2.68037919449023	1.02422758252756e-07		2.68037919030732	1.0278e-07
e	0.0332834075416157	3.72583687170622e-08		0.0332834084098655	3.723e-08
i	4.87064454567147	4.91926754962451e-06		4.87064467562245	4.9051e-06
peri	119.704478491351	9.26537293487407e-05		119.70447923946	9.1341e-05
node	165.541938400386	5.00609236406486e-05		165.541939646563	4.9617e-05
tp	2460623.98663213	0.000350292088224234		2460623.98664169	0.00035377

2020 OJ94

	Clones			Target
	mean	sd		mean	sd
q	2.68031516329671	5.80931724850316e-07		2.68031508062098	5.8247e-07
e	0.0332987005798029	2.12854522457715e-07		0.0332987315205281	2.1173e-07
i	4.8708823913187	1.03347748674252e-05		4.87088223032125	1.0457e-05
peri	119.702555842119	0.000210522154416148		119.70257257331	0.00021113
node	165.541174514102	0.000118615308715787		165.541191321507	0.00011803
tp	2460627.54541522	0.000804795345716826		2460627.54557597	0.00080474

Simulation

The backward simulationwas done with Mercury 6 software taking into account all planets + Ceres + Pallas + Vesta:

)O+_06 Integration parameters  (WARNING: Do not delete this line!!)

) Lines beginning with `)' are ignored.

)---------------------------------------------------------------------

) Important integration parameters:

)---------------------------------------------------------------------

 algorithm (MVS, BS, BS2, RADAU, HYBRID etc) = BS

 start time (days)= 2460125.5

 stop time (days) = -1d8

 output interval (days) = 100

 timestep (days) = 0.05

 accuracy parameter=1.d-12

Results

After the simulation finished, I compared all the 100x100=10^4 clone couples to determine the behaviour of the "best" couples sorting them by minimum relative velocity.

The top 10 couples behaved like this (relative distance in km, relative velocity in m/s):

           Year relative_Distance relative_Velocity

 1:  -79283.756          3578.058             0.008

 2: -167296.514         10004.868             0.008

 3: -144257.301          7417.041             0.009

 4: -101207.820          4225.343             0.009

 5:  -95159.236          4890.873             0.015

 6: -133453.520          5479.847             0.017

 7: -143202.385          4896.550             0.017

 8: -111727.954          6362.393             0.020

 9: -101200.975          5827.283             0.020

10: -225280.730         11845.825             0.020

The best couple (row 1) is this one: