Is feedback-free star formation possible?

It has been suggested that, if the free-fall time of star-forming clouds is shorter than the lifetime ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> Myr) of massive stars exploding as supernovae (SN), a large fraction of the cloud gas can be converted into stars during an allegedly `feedback-free’ phase. Here, we show that radiation pressure from Ly <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>α</mml:mi> </mml:math> photons produced in the pre-SN phase can instead erase feedback-free conditions, and severely limit the star formation efficiency (SFE). We find that, for a constant star formation rate, all clouds with gas surface density have <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>ϵ</mml:mi> <mml:mo>*</mml:mo> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:mn>0.08</mml:mn> </mml:mrow> </mml:math> . Higher SFE values can only be reached if Ly <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>α</mml:mi> </mml:math> -driven shells fragment and form stars. While advanced RHD simulations are required to establish the importance of this effect, adopting an optimistic guess, we find that the SFE increases with cloud surface density, rising from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>ϵ</mml:mi> <mml:mo>*</mml:mo> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.023</mml:mn> </mml:mrow> </mml:math> at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>37</mml:mn> <mml:mspace width="0.222em"/> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> <mml:mspace width="0.222em"/> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> <mml:msup> <mml:mi mathvariant="normal">c</mml:mi> <mml:mrow> <mml:mo mathvariant="normal">−</mml:mo> <mml:mn mathvariant="normal">2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>ϵ</mml:mi> <mml:mo>*</mml:mo> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.27</mml:mn> </mml:mrow> </mml:math> at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>1.7</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>5</mml:mn> </mml:msup> <mml:mspace width="0.222em"/> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> <mml:mspace width="0.222em"/> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> <mml:msup> <mml:mi mathvariant="normal">c</mml:mi> <mml:mrow> <mml:mo mathvariant="normal">−</mml:mo> <mml:mn mathvariant="normal">2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> </mml:math> . Given the optimistic assumptions adopted, these numbers should be regarded as upper limits. We conclude that Ly <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>α</mml:mi> </mml:math> radiation pressure strongly limits the SFE, even at solar metallicities, erasing the possibility that a feedback-free star formation mode with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>ϵ</mml:mi> <mml:mo>*</mml:mo> </mml:msub> <mml:mo>≳</mml:mo> <mml:mn>0.4</mml:mn> </mml:mrow> </mml:math> exists in the pre-SN phase. This conclusion remains valid even when other effects such as dust destruction of Ly <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>α</mml:mi> </mml:math> photons, presence of HII regions, velocity gradients, atomic recoil, and turbulence are considered.