Double Star Discovery: TYC 724-273-1

On 20 Oct 2021 UT, I observed the star TYC 724-273-1 in the constellation Orion being covered up by the asteroid 444 Gyptis. The star disappeared at 5:31:53.856 UT and reappeared at 5:32:10.506, a duration of 16.65 seconds.

The published apparent visual magnitude of this star is 11.5 and the published apparent visual magnitude of 444 Gyptis at the time of the event is 12.5.

The combined magnitude (mc) of star + asteroid just before (and after) the occultation event is given by

m_{c}=m_{o}-2.5\log_{10}\left (10^{0.4(m_{o}-m_{*})}+1  \right )

where mo is the magnitude of the asteroid
     and m* is the magnitude of the star

This gives us a combined magnitude of 11.14 just before the occultation.

While the asteroid is covering up the star, you should only see the asteroid, so the magnitude should decrease from 11.14 to 12.5, a magnitude drop of 1.36 magnitudes.

Much to my surprise, I observed a magnitude drop of only 0.54.

Is it possible that 444 Gyptis only covered up one component of a previously undiscovered double star? That idea is bolstered by the fact that the event occurred 14.8 seconds earlier than predicted, a full 3.7σ early.

Entertaining the double-star idea, our task is to determine the magnitudes of the two blended stars and which one got covered up. Let us call the magnitudes of the two components m*1 and m*2, with m*1 being the component that got covered. We already know that m*1 + m*2 must equal m* = 11.5. We also know that the observed magnitude drop of the m*1 plus the unobserved magnitude drop that the m*2 star would have had must equal the expected magnitude drop of 1.36. This gives us enough information to calculate m*1 and m*2 individually.

m_{*1} = -\log_{10}\left (10^{-\left (m_{c}+\Delta m_{obs}  \right )/2.5}-10^{-0.4m_{o}}  \right )/0.4

m_{*2} = -\log_{10}\left (10^{-\left (m_{*}/2.5\right )}-10^{-0.4m_{*1}}  \right )/0.4

where mo is the magnitude of the asteroid
     and m* is the magnitude of the star
     and mc is the magnitude of the star + asteroid
     and m*1 is the magnitude of the occulted star component
     and m*2 is the magnitude of the unocculted star component
     and Δmobs is the observed magnitude drop

This gives us a magnitude of 12.36 for the occulted component and 12.15 for the unocculted component. Thus we can see that I observed the fainter component of the double star being occulted by asteroid 444 Gyptis.

Finally, we can do an extra check to make sure that the magnitudes of the two star components plus the asteroid equals the combined magnitude of 11.14 we expected right before the occultation occurred.

m_{c}=-2.5\log_{10}\left (10^{-0.4m_{*1}}+10^{-0.4m_{*2}}+10^{-0.4m_{o}}  \right )

Here’s a little SAS program I wrote to do the calculations.

data magdrop;
   format mstar mastr mcomb pdelm odelm mstr1 mstr2 mtot 5.2;
   mstar = 11.5;
   mastr = 12.5;
   odelm = 0.54;
   x = 0.4*(mastr - mstar);
   mcomb = mastr - 2.5*log10(10**x + 1);
   pdelm = mastr - mcomb;
   mstr1 = log10(10**((mcomb+odelm)/-2.5) - 10**(-0.4*mastr))/-0.4;
   mstr2 = log10(10**(mstar/-2.5) - 10**(-0.4*mstr1))/-0.4;
   mtot = -2.5*log10(10**(-0.4*mstr1)+10**(-0.4*mstr2)+10**(-0.4*mastr));
   file print;
   put 'Published Magnitude of Occulted Star = ' mstar;
   put 'Magnitude of Asteroid = ' mastr;
   put 'Combined Magnitude Right Before Occultation = ' mcomb;
   put 'Predicted Magnitude Drop = ' pdelm;
   put 'Observed Magnitude Drop = ' odelm;
   put 'Magnitude of Star Component Occulted = ' mstr1;
   put 'Magnitude of Star Component Not Occulted = ' mstr2;
   put 'Total Magnitude of Both Star Components + Asteroid = ' mtot;
run;

Published Magnitude of Occulted Star = 11.50                                                      
Magnitude of Asteroid = 12.50                                                                     
Combined Magnitude Right Before Occultation = 11.14                                               
Predicted Magnitude Drop = 1.36                                                                   
Observed Magnitude Drop = 0.54                                                                    
Magnitude of Star Component Occulted = 12.36                                                      
Magnitude of Star Component Not Occulted = 12.15                                                  
Total Magnitude of Both Star Components + Asteroid = 11.14