New constraints on primordial black holes abundance from femtolensing of gamma-ray bursts

The abundance of primordial black holes is currently significantly constrained in a wide range of masses. The weakest limits are established for the small mass objects where the small intensity of the associated physical phenomenon provides a challenge for current experiments. We used gamma-ray bursts with known redshifts detected by the Fermi Gamma-ray Burst Monitor (GBM) to search for the femtolensing effects caused by compact objects. The lack of femtolensing detection in the GBM data provides new evidence that primordial black holes in the mass range ${10}^{17}–{10}^{20}\mathrm{g}$ do not constitute a major fraction of dark matter.

Figure 1

Simulated spectrum obtained with GRB 090424592. The spectrum was fitted with $\mathrm{\text{femtolensing}}+\mathrm{BAND}$ model. The fit has ${\chi }^2=79$ for 73 d.o.f. The fit parameters are: $A=0.32\pm 0.01\mathrm{ph}{\mathrm{s}}^{-1}{\mathrm{cm}}^{-2}{\mathrm{keV}}^{-1}$, $E_{\mathrm{peak}}=179\pm 3\mathrm{keV}$, $\alpha =-0.87\pm 0.02$, and $\beta =-3.9\pm 7.5$. The simulated femtolensing effect is caused by a lens at redshifts $z_L=0.256$ and a source at $z_S=0.544$. The simulated mass is $M=1\times {10}^{18}\mathrm{g}$ and the mass reconstructed from the fit is $1.01\times {10}^{18}\mathrm{g}$. The source is simulated at position $r_S=2$. The position reconstructed from the fit is $r_S=1.9$.

Figure 2

Simulated femtolensed spectrum fitted with the BAND model. The fit has ${\chi }^2=752$ for 75 d.o.f. The fit parameters are: $A=0.36\pm 0.01\mathrm{ph}{\mathrm{s}}^{-1}{\mathrm{cm}}^{-2}{\mathrm{keV}}^{-1}$, $E_{\mathrm{peak}}=174\pm 5\mathrm{keV}$, $\alpha =-0.8\pm 0.02$, and $\beta =-2.4\pm 0.1$. The smoothly broken power law (SBKN) model fit is almost indistinguishable from the broken power law (BKN) model fit.

Figure 3

The spectrum of GRB 090424592 using NaI detector n7, with the BAND and femtolensing fits superimposed. The parameters are $r_S=1$, 2, and lens mass $1\times {10}^{18}\mathrm{g}$. The models are convolved with the response matrix.

Figure 4

The spectrum of GRB 090424592 using NaI detector n7. The BAND and femtolensing fits are superimposed. The parameters are $r_S=3$, 4, and lens mass $1\times {10}^{18}\mathrm{g}$. The excess at 33 keV (K edge) is an instrumental effect seen on many bright bursts.

Figure 5

Minimum and maximum detectable $r_S/r_E$ as a function of lens mass for GRB 090424592.

Figure 6

Constraints on the fraction (or normalize density) of compact objects. The zones above the curves are excluded at the 95% confidence level.