# What is the average time between a nebula formation and a neutron star?

I have a star project, and I couldn't find anything on the amount of time it takes from nebula to neutron star.

How long does it take, from a nebula, to form a neutron star?

• Do you mean a star-forming nebula, so the star will need to go through its full evolution first, or the supernova remnant associated with the creation of the neutron star? – Ken G Dec 25 '16 at 3:52
• @KenG A star-forming nebula, full evolution. – bleh Dec 25 '16 at 3:54
• So most of the time is the main-sequence lifetime, which depends on the mass of the star. A few million years, perhaps ten, is typical. – Ken G Dec 25 '16 at 4:31

Short answer: It depends on the progenitor mass, but somewhere between 5 million and 30 million years.

I presume you are talking about the sum of the star formation timescale and the time it takes for the star to evolve through the various phases of its life and then explode as a supernova.

As LaserYeti has pointed out, the formation timescale is extremely short compared to the rest of a massive star's life. In fact, for the massive stars that will eventually yield supernovae, there really isn't a pre-main sequence phase at all.

The lifetime of the star then almost entirely depends on its mass, and to a lesser extent on its rotation and metallicity. The types of star that produce supernovae and neutron stars are probably in the range 9 to 40 solar-masses. Less massive progenitors produce white dwarfs, more massive progenitors probably produce black holes and there may not even be a supernova. Stars at 9 solar masses are about 30 times more commonly born than 40 solar-metallicity stars. To find their lifetimes we must appeal to theoretical models.

Schaller et al. (1992) provide a well-respected set of "vanilla" calculations for non-rotating, solar-metallicity stars. Their table 45, summing up the H-burning and He-burning stages (subsequent evolution happens comparatively instantaneously), suggests the evolutionary lifetimes range from about 30 million years for 9 solar-mass star, to as short as 5 million years for a 40 solar-mass star. These would be the numbers I would use, though rapid rotation can increase these lifetimes by perhaps 30%. Metallicity is a smaller effect.

Approximately greater than or equal to $2\times10^7$ years.

This approximate number comes from Stellar Structure and Evolution by Dina Prialnik

The contraction from nebula phase takes about $10^5$ years, and the red giant envelope dispersion takes about another $10^5$ years. Neither of which impact the timescale due to the two orders of magnitude longer MS lifetime.