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Graphical illustration of the impact that the three possible choices for the computation of the relative velocity between PBH and surrounding matter have on the final luminosity of the system, for both the collisional (left) and photo-ionization (right) models. As term of reference, we compare the average radiation luminosity $\langle L_{\rm rad} \rangle$ to the Eddington luminosity~$L_\mathrm{edd}$.

Graphical illustration of the impact that the three possible choices for the computation of the relative velocity between PBH and surrounding matter have on the final luminosity of the system, for both the collisional (left) and photo-ionization (right) models. As term of reference, we compare the average radiation luminosity $\langle L_{\rm rad} \rangle$ to the Eddington luminosity~$L_\mathrm{edd}$.

Graphical illustration of the dependence of the emission efficiency $\epsilon$ on the geometry of the accretion (spherical on the left, disk on the right) as well as on the ionization mechanism (photoionization as solid lines, collisional ionization as dashed lines) for different choices of the PBH mass. In all cases we assume $f_{\rm PBH}=1$. The horizontal dashed-dotted lines represent the benchmark outflow efficiencies $\epsilon_{\rm non-th}$ discussed in section \ref{subsec: imp_lum}.

Graphical illustration of the dependence of the emission efficiency $\epsilon$ on the geometry of the accretion (spherical on the left, disk on the right) as well as on the ionization mechanism (photoionization as solid lines, collisional ionization as dashed lines) for different choices of the PBH mass. In all cases we assume $f_{\rm PBH}=1$. The horizontal dashed-dotted lines represent the benchmark outflow efficiencies $\epsilon_{\rm non-th}$ discussed in section \ref{subsec: imp_lum}.

Graphical illustration of the dependence of the emission efficiency $\epsilon$ on the geometry of the accretion (spherical on the left, disk on the right) as well as on the ionization mechanism (photoionization as solid lines, collisional ionization as dashed lines) for different choices of the PBH mass. In all cases we assume $f_{\rm PBH}=1$. The horizontal dashed-dotted lines represent the benchmark outflow efficiencies $\epsilon_{\rm non-th}$ discussed in section \ref{subsec: imp_lum}.

Graphical illustration of the dependence of the emission efficiency $\epsilon$ on the geometry of the accretion (spherical on the left, disk on the right) as well as on the ionization mechanism (photoionization as solid lines, collisional ionization as dashed lines) for different choices of the PBH mass. In all cases we assume $f_{\rm PBH}=1$. The horizontal dashed-dotted lines represent the benchmark outflow efficiencies $\epsilon_{\rm non-th}$ discussed in section \ref{subsec: imp_lum}.

Graphical representation of the impact of the outflow effects (MF and non-thermal emissions) on the total luminosity of the system as a function of the PBH mass. As in figure~\ref{fig: plot_eps}, both the spherical and disk accretion scenarios are shown (on the left and on the right, respectively) as well as the different possible ionization models (photo-ionization in solid and collisional ionization in dashed). In all cases we assume $f_{\rm PBH}=10^{-3}$, $\epsilon_{\rm non-th}=10^{-4}$ and we restrict ourselves only to the representative redshift $z=600$ (as justified in the text).

Graphical representation of the impact of the outflow effects (MF and non-thermal emissions) on the total luminosity of the system as a function of the PBH mass. As in figure~\ref{fig: plot_eps}, both the spherical and disk accretion scenarios are shown (on the left and on the right, respectively) as well as the different possible ionization models (photo-ionization in solid and collisional ionization in dashed). In all cases we assume $f_{\rm PBH}=10^{-3}$, $\epsilon_{\rm non-th}=10^{-4}$ and we restrict ourselves only to the representative redshift $z=600$ (as justified in the text).

Graphical representation of the impact of the outflow effects (MF and non-thermal emissions) on the total luminosity of the system as a function of the PBH mass. As in figure~\ref{fig: plot_eps}, both the spherical and disk accretion scenarios are shown (on the left and on the right, respectively) as well as the different possible ionization models (photo-ionization in solid and collisional ionization in dashed). In all cases we assume $f_{\rm PBH}=10^{-3}$, $\epsilon_{\rm non-th}=10^{-4}$ and we restrict ourselves only to the representative redshift $z=600$ (as justified in the text).

Graphical representation of the impact of the outflow effects (MF and non-thermal emissions) on the total luminosity of the system as a function of the PBH mass. As in figure~\ref{fig: plot_eps}, both the spherical and disk accretion scenarios are shown (on the left and on the right, respectively) as well as the different possible ionization models (photo-ionization in solid and collisional ionization in dashed). In all cases we assume $f_{\rm PBH}=10^{-3}$, $\epsilon_{\rm non-th}=10^{-4}$ and we restrict ourselves only to the representative redshift $z=600$ (as justified in the text).

Role of the outflows in the impact on the free electron fraction of the accretion process (shown are the free electron fraction -- lower panels -- and its relative difference with respect to the $\Lambda$CDM prediction -- upper panels). From top to bottom we compare three representative choices of the PBH mass (same as in figure~\ref{fig: plot_eps}), while from left to right we compare the spherical and disk accretion scenarios (for the latter we assumed $\lambda=0.01$ and $\delta=0.1$). In the bottom panels the $\Lambda$CDM prediction is shown in black. The irregular shape of the collisional ionization curve in the top left panel is due to numerical noise.

Role of the outflows in the impact on the free electron fraction of the accretion process (shown are the free electron fraction -- lower panels -- and its relative difference with respect to the $\Lambda$CDM prediction -- upper panels). From top to bottom we compare three representative choices of the PBH mass (same as in figure~\ref{fig: plot_eps}), while from left to right we compare the spherical and disk accretion scenarios (for the latter we assumed $\lambda=0.01$ and $\delta=0.1$). In the bottom panels the $\Lambda$CDM prediction is shown in black. The irregular shape of the collisional ionization curve in the top left panel is due to numerical noise.

Role of the outflows in the impact on the free electron fraction of the accretion process (shown are the free electron fraction -- lower panels -- and its relative difference with respect to the $\Lambda$CDM prediction -- upper panels). From top to bottom we compare three representative choices of the PBH mass (same as in figure~\ref{fig: plot_eps}), while from left to right we compare the spherical and disk accretion scenarios (for the latter we assumed $\lambda=0.01$ and $\delta=0.1$). In the bottom panels the $\Lambda$CDM prediction is shown in black. The irregular shape of the collisional ionization curve in the top left panel is due to numerical noise.

Role of the outflows in the impact on the free electron fraction of the accretion process (shown are the free electron fraction -- lower panels -- and its relative difference with respect to the $\Lambda$CDM prediction -- upper panels). From top to bottom we compare three representative choices of the PBH mass (same as in figure~\ref{fig: plot_eps}), while from left to right we compare the spherical and disk accretion scenarios (for the latter we assumed $\lambda=0.01$ and $\delta=0.1$). In the bottom panels the $\Lambda$CDM prediction is shown in black. The irregular shape of the collisional ionization curve in the top left panel is due to numerical noise.

Role of the outflows in the impact on the free electron fraction of the accretion process (shown are the free electron fraction -- lower panels -- and its relative difference with respect to the $\Lambda$CDM prediction -- upper panels). From top to bottom we compare three representative choices of the PBH mass (same as in figure~\ref{fig: plot_eps}), while from left to right we compare the spherical and disk accretion scenarios (for the latter we assumed $\lambda=0.01$ and $\delta=0.1$). In the bottom panels the $\Lambda$CDM prediction is shown in black. The irregular shape of the collisional ionization curve in the top left panel is due to numerical noise.

Role of the outflows in the impact on the free electron fraction of the accretion process (shown are the free electron fraction -- lower panels -- and its relative difference with respect to the $\Lambda$CDM prediction -- upper panels). From top to bottom we compare three representative choices of the PBH mass (same as in figure~\ref{fig: plot_eps}), while from left to right we compare the spherical and disk accretion scenarios (for the latter we assumed $\lambda=0.01$ and $\delta=0.1$). In the bottom panels the $\Lambda$CDM prediction is shown in black. The irregular shape of the collisional ionization curve in the top left panel is due to numerical noise.

Role of the outflows in the impact on the free electron fraction of the accretion process (shown are the free electron fraction -- lower panels -- and its relative difference with respect to the $\Lambda$CDM prediction -- upper panels). From top to bottom we compare three representative choices of the PBH mass (same as in figure~\ref{fig: plot_eps}), while from left to right we compare the spherical and disk accretion scenarios (for the latter we assumed $\lambda=0.01$ and $\delta=0.1$). In the bottom panels the $\Lambda$CDM prediction is shown in black. The irregular shape of the collisional ionization curve in the top left panel is due to numerical noise.

Role of the outflows in the impact on the free electron fraction of the accretion process (shown are the free electron fraction -- lower panels -- and its relative difference with respect to the $\Lambda$CDM prediction -- upper panels). From top to bottom we compare three representative choices of the PBH mass (same as in figure~\ref{fig: plot_eps}), while from left to right we compare the spherical and disk accretion scenarios (for the latter we assumed $\lambda=0.01$ and $\delta=0.1$). In the bottom panels the $\Lambda$CDM prediction is shown in black. The irregular shape of the collisional ionization curve in the top left panel is due to numerical noise.

Role of the outflows in the impact on the free electron fraction of the accretion process (shown are the free electron fraction -- lower panels -- and its relative difference with respect to the $\Lambda$CDM prediction -- upper panels). From top to bottom we compare three representative choices of the PBH mass (same as in figure~\ref{fig: plot_eps}), while from left to right we compare the spherical and disk accretion scenarios (for the latter we assumed $\lambda=0.01$ and $\delta=0.1$). In the bottom panels the $\Lambda$CDM prediction is shown in black. The irregular shape of the collisional ionization curve in the top left panel is due to numerical noise.

Role of the outflows in the impact on the free electron fraction of the accretion process (shown are the free electron fraction -- lower panels -- and its relative difference with respect to the $\Lambda$CDM prediction -- upper panels). From top to bottom we compare three representative choices of the PBH mass (same as in figure~\ref{fig: plot_eps}), while from left to right we compare the spherical and disk accretion scenarios (for the latter we assumed $\lambda=0.01$ and $\delta=0.1$). In the bottom panels the $\Lambda$CDM prediction is shown in black. The irregular shape of the collisional ionization curve in the top left panel is due to numerical noise.

Role of the outflows in the impact on the free electron fraction of the accretion process (shown are the free electron fraction -- lower panels -- and its relative difference with respect to the $\Lambda$CDM prediction -- upper panels). From top to bottom we compare three representative choices of the PBH mass (same as in figure~\ref{fig: plot_eps}), while from left to right we compare the spherical and disk accretion scenarios (for the latter we assumed $\lambda=0.01$ and $\delta=0.1$). In the bottom panels the $\Lambda$CDM prediction is shown in black. The irregular shape of the collisional ionization curve in the top left panel is due to numerical noise.

Role of the outflows in the impact on the free electron fraction of the accretion process (shown are the free electron fraction -- lower panels -- and its relative difference with respect to the $\Lambda$CDM prediction -- upper panels). From top to bottom we compare three representative choices of the PBH mass (same as in figure~\ref{fig: plot_eps}), while from left to right we compare the spherical and disk accretion scenarios (for the latter we assumed $\lambda=0.01$ and $\delta=0.1$). In the bottom panels the $\Lambda$CDM prediction is shown in black. The irregular shape of the collisional ionization curve in the top left panel is due to numerical noise.

CMB temperature (upper panels) and polarization (lower panels) power spectra for $M_{\rm PBH}=10^2$~$M_\odot$ and $f_{\rm PBH}=10^{-3}$. As in figure~\ref{fig: xe_Cl_1}, the spherical and disk accretion scenarios are shown in the left and right panels, respectively, while solid and dashed lines represent the photo- and collisional ionization cases.

CMB temperature (upper panels) and polarization (lower panels) power spectra for $M_{\rm PBH}=10^2$~$M_\odot$ and $f_{\rm PBH}=10^{-3}$. As in figure~\ref{fig: xe_Cl_1}, the spherical and disk accretion scenarios are shown in the left and right panels, respectively, while solid and dashed lines represent the photo- and collisional ionization cases.

CMB temperature (upper panels) and polarization (lower panels) power spectra for $M_{\rm PBH}=10^2$~$M_\odot$ and $f_{\rm PBH}=10^{-3}$. As in figure~\ref{fig: xe_Cl_1}, the spherical and disk accretion scenarios are shown in the left and right panels, respectively, while solid and dashed lines represent the photo- and collisional ionization cases.

CMB temperature (upper panels) and polarization (lower panels) power spectra for $M_{\rm PBH}=10^2$~$M_\odot$ and $f_{\rm PBH}=10^{-3}$. As in figure~\ref{fig: xe_Cl_1}, the spherical and disk accretion scenarios are shown in the left and right panels, respectively, while solid and dashed lines represent the photo- and collisional ionization cases.

CMB temperature (upper panels) and polarization (lower panels) power spectra for $M_{\rm PBH}=10^2$~$M_\odot$ and $f_{\rm PBH}=10^{-3}$. As in figure~\ref{fig: xe_Cl_1}, the spherical and disk accretion scenarios are shown in the left and right panels, respectively, while solid and dashed lines represent the photo- and collisional ionization cases.

CMB temperature (upper panels) and polarization (lower panels) power spectra for $M_{\rm PBH}=10^2$~$M_\odot$ and $f_{\rm PBH}=10^{-3}$. As in figure~\ref{fig: xe_Cl_1}, the spherical and disk accretion scenarios are shown in the left and right panels, respectively, while solid and dashed lines represent the photo- and collisional ionization cases.

CMB temperature (upper panels) and polarization (lower panels) power spectra for $M_{\rm PBH}=10^2$~$M_\odot$ and $f_{\rm PBH}=10^{-3}$. As in figure~\ref{fig: xe_Cl_1}, the spherical and disk accretion scenarios are shown in the left and right panels, respectively, while solid and dashed lines represent the photo- and collisional ionization cases.

CMB temperature (upper panels) and polarization (lower panels) power spectra for $M_{\rm PBH}=10^2$~$M_\odot$ and $f_{\rm PBH}=10^{-3}$. As in figure~\ref{fig: xe_Cl_1}, the spherical and disk accretion scenarios are shown in the left and right panels, respectively, while solid and dashed lines represent the photo- and collisional ionization cases.

Impact of outflows on the CMB constraints on the fractional PBH abundance for the two main types of accretion geometry (spherical on the left and disk on the right) and ionization models (photo-ionization in solid and collisional ionization in dashed) assuming a MMD. The blue contours represent the scenarios without outflows and update the bounds first derived in \cite{AliHaimoud2017Cosmic} (left) and \cite{Poulin2017CMB} (right), while the magenta, red and organge lines assume MF with $f_{\rm LS}=0.1$ and non-thermal emissions with $\epsilon_{\rm non-th}=10^{-6,-4,-2}$, respectively.

Impact of outflows on the CMB constraints on the fractional PBH abundance for the two main types of accretion geometry (spherical on the left and disk on the right) and ionization models (photo-ionization in solid and collisional ionization in dashed) assuming a MMD. The blue contours represent the scenarios without outflows and update the bounds first derived in \cite{AliHaimoud2017Cosmic} (left) and \cite{Poulin2017CMB} (right), while the magenta, red and organge lines assume MF with $f_{\rm LS}=0.1$ and non-thermal emissions with $\epsilon_{\rm non-th}=10^{-6,-4,-2}$, respectively.

Impact of outflows on the CMB constraints on the fractional PBH abundance for the two main types of accretion geometry (spherical on the left and disk on the right) and ionization models (photo-ionization in solid and collisional ionization in dashed) assuming a MMD. The blue contours represent the scenarios without outflows and update the bounds first derived in \cite{AliHaimoud2017Cosmic} (left) and \cite{Poulin2017CMB} (right), while the magenta, red and organge lines assume MF with $f_{\rm LS}=0.1$ and non-thermal emissions with $\epsilon_{\rm non-th}=10^{-6,-4,-2}$, respectively.

Impact of outflows on the CMB constraints on the fractional PBH abundance for the two main types of accretion geometry (spherical on the left and disk on the right) and ionization models (photo-ionization in solid and collisional ionization in dashed) assuming a MMD. The blue contours represent the scenarios without outflows and update the bounds first derived in \cite{AliHaimoud2017Cosmic} (left) and \cite{Poulin2017CMB} (right), while the magenta, red and organge lines assume MF with $f_{\rm LS}=0.1$ and non-thermal emissions with $\epsilon_{\rm non-th}=10^{-6,-4,-2}$, respectively.

Same as in figure~\ref{fig: bounds}, but for a lognormal EMD. The figure shows the collisional and photoionization regimes for the spherical accretion case (left and center panels, respectively) and the disk accretion model (right panels). We report here all the cases in absence of MF and non-thermal emission (top panels), and with those effects included (middle and bottom panels) for different non-thermal efficiencies. The grey shaded area represents the region of parameter space that cannot be described appropriately by the theoretical model employed in this work.

Same as in figure~\ref{fig: bounds}, but for a lognormal EMD. The figure shows the collisional and photoionization regimes for the spherical accretion case (left and center panels, respectively) and the disk accretion model (right panels). We report here all the cases in absence of MF and non-thermal emission (top panels), and with those effects included (middle and bottom panels) for different non-thermal efficiencies. The grey shaded area represents the region of parameter space that cannot be described appropriately by the theoretical model employed in this work.

Uncertainty bands of both geometries and ionization models with (orange) and without (blue) the inclusion of outflows. The corresponding filled regions of parameter space represent the region where the true constraint lies.

Uncertainty bands of both geometries and ionization models with (orange) and without (blue) the inclusion of outflows. The corresponding filled regions of parameter space represent the region where the true constraint lies.