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I've seen several papers that discuss the Lyman-Werner Background (LWB) when modeling star and galaxy formation in the early universe. One in particular (https://arxiv.org/abs/1803.04527) even varies the strength (?) of the LWB using the units $J_{21}$. I assume the subscript is referencing the 21cm band, as opposed to a more generic use of $J_{c}$. But I am equally confused as to what the flux in terms of J is referring to. I've found and read on Lyman-Werner photons but going from these photons to a variable "background" is where I'm having a disconnect.

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The Lyman-Werner background (LWB) is the part of the "meta-galactic" background radiation consisting of photons that are able to photo-dissociate molecular hydrogen ($H_\mathrm{2}$), but not ionize atomic hydrogen (HI). These photons are in ultraviolet, with energies ranging from $11.2\,\mathrm{eV}$ to $13.6\,\mathrm{eV}$, originating mainly from hot, massive stars.

Part of the reason this radiation field is interesting particularly in the early Universe is that a sufficiently high intensity will prevent gas from cooling. In order for gas to form stars, it cannot be too hot, since a hot gas cannot collapse to form structure. A gas with a high metallicity is able to cool through the many different atomic transitions in the metals, but in the early Universe, where stars haven't yet produced the metals, the most important coolant at these temperatures is $H_\mathrm{2}$.

It also has implications for the formation of supermassive black holes in the early Universe, since once you form a large amount of stars, the feedback from the massive stars (both through radiation pressure and heating of the interstellar medium) makes it difficult to have gas collapse directly into the supermassive black holes.

In simulations, you often have to assume a value of the LWB, since performing the "true" radiative transfer is computationally very expensive. Hence, these authors apparently have experimented with two different fields of $100\,J_\mathrm{21}$ and $1000\,J_\mathrm{21}$, respectively. Here, the term $J_\mathrm{21}$ doesn't have anything to do with $21\,\mathrm{cm}$ radiation (which is in the other end of the spectrum), but is simply the intensity in units of $10^{-21}\,\mathrm{erg}\,\mathrm{s}^{-1}\,\mathrm{cm}^{-2}\,\mathrm{Hz}^{-1}\,\mathrm{sr}^{-1}$.

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