Hunting primordial black hole dark matter in the Lyman-$$\alpha $$ forest

Abstract A very pressing question in contemporary physics is the identity of Dark Matter (DM). Primordial Black Holes (PBHs) are one of the most well-motivated DM candidates. Light PBHs have been constrained by either the non-detection of their Hawking radiation itself, or by the non-observation of any measurable effects of this radiation on astrophysical and cosmological observables. We constrain the PBH contribution to the DM density by non-detection of their Hawking radiation’s effect on the intergalactic medium (IGM) temperature evolution. We use the latest deductions of IGM temperature from Lyman- $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> forest observations. We put constraints on the fraction of DM as PBHs with masses $$5 \times 10^{15}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>5</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>15</mml:mn> </mml:msup> </mml:mrow> </mml:math> g– $$10^{17}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>17</mml:mn> </mml:msup> </mml:math> g, separately for spinning and non-spinning BHs. We derive constraints by dealing with the heating effects of the astrophysical reionization sources on the IGM in two ways. In one way, we completely neglect this heating due to astrophysical sources, thus giving us weaker constraints, but completely robust to the reionization history of the universe. In the second way, we utilise some modelling of the ionization and temperature history, and use it to derive more stringent constraints. We find that for non-spinning PBHs of mass $$10^{16}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>16</mml:mn> </mml:msup> </mml:math> g, the current measurements can constrain the PBH-density to be $$\lesssim $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>≲</mml:mo> </mml:math> 0.1% of the total DM. We find that these constraints are competitive, and hence provide a new observable to probe the nature of PBH DM. The systematics affecting Lyman- $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> forest measurements are different from other constraining observations, and thus this is a complementary probe.