Pittard and colleagues investigated the numerical resolution requirements to inflate a stellar wind bubble in surrounding medium. They found that the radius of wind injection region (rinj) must be below a maximum value of radius of injection (rinj,max), in order for a bubble to be produced, but must be significantly below this value if the bubble is to be modelled correctly. Their study recently appeared in Arxiv.
Massive stars lose a significant fraction of their mass in the form of stellar wind, which expands into the surrounding medium. As it expands, the stellar wind collides with the gas in the interstellar medium (ISM), creating a low density hot interiors bubble, expanding over time. This wind-blown bubble provide significant momentum boost, which is key to having strong stellar wind feedback. But, in order to correctly determine the momentum boost, one requires certain numerical resolution in simulations which has not always been achieved yet.
Thus, Pittard and colleagues examined the requirements of the numerical resolution to blow stellar wind bubbles in a uniform medium. From simulations, they have determined a maximum radius for the wind injection region, above which a bubble will not usually grow and applied this to all 3 wind injection mechanisms: momentum and energy overwrite (method meo), momentum and energy injection (method mei) and thermal energy injection (method ei).
“We know that we will miss some of the momentum boost that the bubble provides if we do not satisfy 𝑡 << 𝑡eq, and we want to explore how this loss varies with 𝜒 function. To do so we run simulations with a fixed (non-expanding) grid.”— they said.
They found that, if 𝜒 = 𝑟inj / 𝑟inj,max < 1 is only marginally satisfied, the resulting bubble will be only marginally overpressured and unable to generate the large momentum boost that it should.
They added that, in order for the bubble momentum to match analytical predictions, a very high resolution is required in order to capture early growth of the bubble accurately. To ensure this, they suggested that the flow time of the wind out to the edge of the injection region, should be significantly less than the time at which the free-flowing wind and bubble momenta are equal (𝑡eq). This requires that, 𝑟inj << 𝑡eq/𝑣w, where, rinj is the radius of injection, vw is terminal speed of the wind and teq is equivalent flowtime of wind in seconds.
“If radius of injection (rinj) is appropriately chosen, the two-shocks that initially develop when using method meo should both move outwards. This ensures that no mass, momentum, or energy is lost from the simulation. All 3 injection methods yield the same bubble properties and the “correct” momentum for such small values of 𝑟inj.”— they said.
Finally, they investigated the radial momentum of the bubble, as a function of 𝜒, for the 3 wind launch models (as shown in Table 1). They showed that, as 𝜒 is increased, the bubble loses more and more momentum, due to the absence of the high initial pressures that actual bubbles have. When 0.1 < 𝜒 ≤ 1.0 the momentum and energy (mei) wind injection method outperforms the other methods.
However, if 𝜒 = 0.1, they found that 20-25% of the bubble momentum is still missed. To be within 10% of the correct momentum requires 𝜒 ≲ 0.02, in which case all wind injection methods perform similarly without the need for such additional restrictions.
“We highlighted that the injection region of the stellar wind must be adequately resolved. Because our calculations are one dimensional, restrict cooling at unresolved interfaces, and do not include thermal conduction or explicit mixing of hot and cold phases, the cooling of the hot gas inside the bubble is minimised, and the momentum of the bubble is maximised. Future studies are required to determine the actual impact of these restrictions and processes.”— they concluded.
Reference: J. M. Pittard, C. J. Wareing, M. M. Kupilas, “Thar she blows! How to inflate a wind-blown bubble”, Arxiv, pp. 1-9, 2021.
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