Primordial black holes in the main lensing galaxy of FBQ 0951+2635

TL;DR

This paper uses 16 years of microlensing variability in the doubly imaged quasar FBQ 0951+2635 to probe PBH populations in its main lensing galaxy. By generating 90 physical scenarios that combine smoothly distributed matter, stars, and PBHs across a range of PBH masses and source sizes, and comparing observed difference light curves to a large ensemble of simulated light curves, the authors find no model that reproduces the full signal but identify scenarios that reasonably match the slow, long-term microlensing variability. The results suggest a predominance of SDM with only a small PBH fraction near the mean stellar mass, while Jupiter-mass PBHs could be constrained if the source size is small; larger PBHs (∼10 M⊙) can yield moderate consistency but require longer light curves to robustly constrain. The study underscores the value of long-duration, low-noise monitoring and independent source-size measurements for tightening PBH population constraints, and points to the potential role of PBHs along lines of sight in contributing to lensing signals.

Abstract

Although dark matter in galaxies may consist of elementary particles different from those that make up ordinary matter and that would be smoothly distributed (still undetected), the so-called primordial black holes (PBHs) formed soon after the initial Big Bang are also candidates to account for a certain fraction of mass in galaxies. In this paper, we focused on the main lensing galaxy ($z$ = 0.260) of the doubly imaged gravitationally lensed quasar FBQ 0951+2635 ($z$ = 1.246) for probing possible PBH populations. Assuming that the mass of the galaxy is due to smoothly distributed matter (SDM), stars, and PBHs, the 16-yr observed microlensing variability was compared in detail with simulated microlensing signals generated by 90 different physical scenarios. Among other details, the simulated signals were sampled as the observed one, and the observed variability in its entirety and over the long term were used separately for comparison. While none of the scenarios considered can reproduce the overall observed signal, the observed long-term variability favours a small mass fraction in PBHs with a mass of the order of the mean stellar mass. Furthermore, it is possible to obtain strong constraints on the galaxy mass fraction in Jupiter-mass PBHs, provided that a reverberation-based measurement of the source size is available and relatively small. To constrain the mass fraction in $\sim$10 $\rm{M_{\odot}}$ PBHs, light curves five times longer are probably required.

Figures (6)

• Figure 1: Observed difference light curves of FBQ 0951+2635 in the $r$ band. They are built from time delay values of 16 d (ODLC1) and 13.3 d (ODLC2). For each delay, the light curve of A is time shifted, and its shifted magnitudes around the dates in B are interpolated and subtracted from the magnitudes of B. The final step is to subtract the average magnitude difference. We also show two linear fits (green and red dashed lines) to the observed microlensing signals (altough they can barely be distinguished from each other in the plot).
• Figure 2: Examples of magnification maps for the first approach. First row from the top: standard scenario without PBHs and with 90% of mass in SDM. Second row: non-standard scenario with 50% of mass in SDM and 45% of mass in PBHs having $M_{\rm pbh} \sim$ 0.001 $\rm{M_{\odot}}$. Third row: non-standard scenario with 10% of mass in SDM and 81% of mass in PBHs having $M_{\rm pbh} \sim$ 0.1 $\rm{M_{\odot}}$. Fourth row: non-standard scenario with 50% of mass in SDM and 45% of mass in PBHs having $M_{\rm pbh} \sim$ 10 $\rm{M_{\odot}}$. In all scenarios, the quasar source has the intermediate size (see main text). The colour scale represents magnification values, with 2.66 and 0.56 being the macro-magnifications of A and B, respectively.
• Figure 3: Comparison between the ODLC in the first approach and SDLCs for all scenarios in Figure \ref{['fig:examaps']}. After generating 10$^5$ SDLCs from each pair of maps, we show the best-fit SDLC (minimum $RMS$; left panels) and 10 randomly chosen SDLCs that are characterised by $RMS <$ 2.60 (out of a total of $n$; right panels). Each row corresponds to the same row position in Figure \ref{['fig:examaps']}, so the results for the standard scenario without PBHs are depicted in the first row from the top ($RMS_{\rm min}$ = 1.67 and $n$ = 10 919) and those for the non-standard scenarios are shown in successive rows: 45% of mass in Jupiter-mass PBHs ($RMS_{\rm min}$ = 1.60 and $n$ = 1 536; second row), 81% of mass in $\sim$0.1 $\rm{M_{\odot}}$ PBHs ($RMS_{\rm min}$ = 1.68 and $n$ = 152; third row), and 45% of mass in $\sim$10 $\rm{M_{\odot}}$ PBHs ($RMS_{\rm min}$ = 1.69 and $n$ = 13 381; fourth row).
• Figure 4: Statistical properties of the $RMS$ distributions. For each approach in Table \ref{['tab:massol']}, we display the $\langle RMS \rangle$ and $\sigma_{RMS}$ values associated with 9 standard (circles) and 81 non-standard (triangles) physical scenarios. Three intervals of consistency probability are also highlighted with colours red, blue, and green (see main text).
• Figure 5: Consistency probability between the observed slow extrinsic variability and simulated microlensing signals in relevant physical scenarios. The open circles (standard scenarios) and dashed lines (non-standard scenarios) represent the results from the first approach, and the filled squares (standard scenarios) and solid lines (non-standard scenarios) indicate the results using the second approach. The x-axis represents the logarithm of the $M_{\rm pbh}/M_{\rm star}$ ratio and includes the three values used in the non-standard scenarios, i.e., $r_{\rm pbh}$ = $-$2.5, $-$0.5, and 1.5. We have arbitrarily put the results for the standard scenarios at $r_{\rm pbh}$ = $-$3.4 for a better visual comparison. The source size is highlighted with colours blue, green, and red (see main text).