a protostar has a high enough of what to become a star

A protostar becomes a star when it reaches a high enough temperature and density in its core to sustain nuclear fusion. The main factor that determines whether a protostar can achieve this high temperature and density is its mass.

To understand this in more detail, let's go through the process step by step:

1. Protostar Formation: A protostar forms from a massive cloud of gas and dust called a molecular cloud. Gravity causes the cloud to collapse inward, forming a dense core.

2. Gravitational Contraction: As the protostar continues to contract under its own gravity, its core becomes denser and hotter. The energy generated from this contraction increases its temperature and pressure.

3. Nuclear Fusion: Once the temperature and pressure at the core of the protostar reach a critical point, nuclear fusion begins. Fusion is the process where hydrogen atoms combine to form helium, releasing an enormous amount of energy.

4. Ignition: At this stage, the protostar has become a star. The energy released from nuclear fusion counteracts the force of gravity, maintaining the star's stability and preventing further collapse.

To specifically address your question, the protostar needs to achieve a high enough core temperature (about 15 million degrees Celsius) and density for nuclear fusion to occur. This can typically be achieved with a mass of at least 0.08 times the mass of our Sun, known as the "stellar mass limit." Below this threshold, the protostar would not have enough gravitational pressure to initiate fusion and would instead become a brown dwarf or sub-stellar object.

In summary, it is the high temperature and density in the core of a protostar, achieved through gravitational contraction, that allows it to become a star.