In a previous post I did map close bow shocks. Bow shocks can form either if the star moves against the interstellar dust (runaway star) or if the interstellar dust moves against the star (like in the Orion Nebula).
Most of the close bow shocks I did map do not agree with proper motion and bow shock.
Additionally the bow shocks from the Lower Centaurus Crux Subgroup do point into almost the same direction and none of them agree in proper motion and bow shock arc. My wild guess is that Supernovas and massive stars in the Loop I Bubble do produce a strong current of interstellar gas and dust and that the Lower Centaurus Crux Subgroup bow shocks are located in a tunnel connected to the Loop I Bubble.
The only bow shocks that agree with proper motion and bow shock arc are Zeta Ophiuchi, Delta Scorpii and Epsilon Persei.
My next step was to find a Mass-Distance-bowshockSize correlation. In other words: How does the size of the bow shock change with the mass of the star?
For this I did measure the size of the bow shock as a radius in arcminutes from the driving star. But the bow shocks often show multiple rings. This is why I did measure the smallest and the largest ring.
Beta Crucis (left/WISE) that shows two rings and Epsilon Persei (right/WISE) that shows only one ring. For both it is required to measure the smallest and largest ring or minimum and maximum.
After the measurement I did calculate the ring sizes in parsec:
So I get the formula rpc=(0.0185*M-0.0801)±0.03 and because rpc=dpc*tan(r°) you can calculate the distance if you know the mass of the star and the size of the largest ring:
rpc is the larger radius in parsec, r° is the larger radius in degree, M is the mass of the star in solar masses and dpc is the distance in parsec.
You can also calculate the mass of the driving star, if you know the distance of the driving star and the size of the largest ring. Or you can calculate the size of the largest ring, if you know the mass of the driving star and the distance.
For other bow shocks you can also find largest and smallest rings in more distant bow shocks. The current bow shock catalog with 709 bow shocks do show the angular seperation between central source and bow shock. In some cases, like Beta Crucis, this is closer to the smallest ring. In other cases, like bow shock no.263, this is closer to the largest ring.