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What is the timescale of start of nuclear fusion as T Tauri type star transforms into a Main Sequence star?

Wikipedia article on T Tauri type stars mentions:

Their central temperatures are too low for hydrogen fusion. Instead, they are powered by gravitational energy released as the stars contract, while moving towards the main sequence, which they reach after about 100 million years.

The mentioned 100 million years is the period of the star being in its stable (well, as stable as the turbulent T Tauri type stars get) state without nuclear fusion. Then, once the fusion starts, we get between 3 million and hundreds of billions years of main sequence, depending on mass of the resulting star.

What I'm interested is how long is the period of transition between the two - ignition of the nuclear reaction - time between "all energy produced by gravitational contraction" and "most of energy produced by nuclear fusion".

I imagine this period could be quite short, and the effect quite rapid and turbulent as the initial fusion increases local temperature (and as result pressure) drastically, leading to conditions conductive for fusion spreading rapidly over the volume which is already on brink of entering the fusion everywhere within the protostar, essentially a nuclear wildfire encompassing the gathered gas, a chain reaction starting.

Am I right in my guess this process is rather rapid? Was it ever observed? Or contrary, does the intensity of the fusion reaction rise gradually and slowly from zero over many millions years of star formation?

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I have mulled over this a couple of times (it's a really interesting question!), and hopefully come up with a somewhat enlightening answer. I haven't been able to find a good, modern reference for these details (perhaps I just suck at literature searches...) so there's a little mucking around in the history books

The total timescale of evolution onto the main sequence for a protostar in the T Tauri mass range ( < 3 solar masses) is on the order (of magnitude) of several tens of millions of years. The ignition of fusion is not precisely a "runaway" reaction: however it occurs relatively quickly and once it starts, gravitational contraction quickly ceases.

The evolution of a 1 solar mass protostar follows these basic steps. Things are a little different for different masses - too complicated to explain here but the references should provide ample further reading!

  1. A Jeans-unstable cloud of gas and dust begins to contract, exchanging gravitational potential energy for kinetic energy, and thus heat. The luminosity of the protostellar cloud increases as it collapses. It takes around 100,000 years for the initial period of rapid collapse to finish, at this point the cloud is very luminous (perhaps 20 solar luminosities and 8000K).

  2. Over the next 1 million years, the protostellar cloud slowly contracts and cools to around 4500K. The protostar then travels down the Hayashi track, contracting further but changing little in temperature - its luminosity continues to fall. This is the stage where T Tauri stars are at. Most T Tauri stars are younger than 3 million years old.

  3. The star then follows the Henyey track, where the luminosity begins to slowly increase again as a radiative zone develops in the star's core and it continues to slowly contract. This can take some tens of millions of years.

  4. Finally, the conditions in the core are extreme enough for fusion to begin. The timescale from all the energy being provided by gravitational contraction to all the energy being provided by fusion, is on the order of 1 million years. The star's luminosity (counter-intuitively) decreases again when this happens, as the energy from fusion doesn't quite offset that from gravitational contraction, which ceases when fusion begins.

Figure: the The Lg/L curve describes the amount of energy gained from gravitational contraction over the total luminosity of the star. The logarithmic time axis is in seconds (reproduced from Iben (1965), Figure 3).

References:

Interesting reading I came across for somewhat higher mass protostellar formation:

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