Investigating the residuals in the $M_\bullet-M_*$ relation using the SIMBA cosmological simulation

Abstract

We study the scaling relation between the black hole and stellar mass ($M_\bullet-M_*$), diagnosing the residual $Δ\log(M_\bullet/M_\odot)$ ($Δ$) in this relation to understand the coevolution of the galaxy and black hole (BH) in the cosmological hydrodynamic simulation SIMBA. We showed that SIMBA can reproduce the observed $M_\bullet-M_*$ relation well with little difference between central and satellite galaxies. By using the median value to determine the residuals, we found that the residual is correlated with galaxy cold gas content, star formation rate, colour and black hole accretion properties. Both torque and Bondi models implemented in SIMBA, contribute to this residual, with torque accretion playing a major role at high redshift and low-mass galaxies, while Bondi (also BH merge) takes over at low redshift and massive galaxies. By dividing the sample into two populations: $Δ>0$ and $Δ<0$, we compared their evolution paths following the main progenitors. With evolution tracking, we proposed a simple picture for the BH-galaxy coevolution: Early-formed galaxies seeded black holes earlier, with stellar mass increasing rapidly to quickly reach the point of triggering `jet mode' feedback. This process reduced the cold gas content and stopped the growth of $M_*$, effectively quenching galaxies. Meanwhile, during the initial phase of torque accretion growth, the BH mass is comparable between galaxies formed early and those formed later. However, those galaxies that formed earlier appear to attain a marginally greater BH mass when shifting to Bondi accretion, aligning with the galaxy transition time. As the early-formed galaxies reach this point earlier -- leaving a longer time for them to have Bondi accretion as well as merging, their residuals become positive, i.e., having more massive BHs at $z=0$ compared to these late-formed galaxies at the same $M_*$. This picture is further supported by the strong positive correlation between the residuals and the galaxy age, which we are proposing as a verification with observation data on this story suggested by SIMBA.

Figures (8)

• Figure 1: The $M_{\bullet} - M_*$ scaling relation for central and satellite galaxies, which are shown with red and cyan dots, respectively. The best-fit power-law relations for central (red line) and satellite galaxies (blue line) are compared to the observational results from Kormendy2013 (KH2013, black dashed line), and the best-fit parameters are indicated in the lower-right legend. This plot highlights the very small discrepancy between central and satellite galaxies, as well as the observational relation.
• Figure 2: The $M_{\bullet} - M_*$ scaling relation for galaxies at $z=0$, $z=1$, $z=2$ and $z=3$ from left to right panels, colour coded by the $\rm log SFR$. The median $M_{\bullet}$ value in each $M_*$ bin is shown as black dots, with the black lines being the best-fit relation of these median values, which will be used as the median $M_{\bullet} - M_*$ scaling relation for calculating residuals. The best-fit parameters are presented in the bottom legend. Clearly, galaxies with lower SFR at a given $M_*$ tend to host more massive BHs.
• Figure 3: The correlations between residuals and galaxy properties. From top to bottom, we show galaxy SFR, Hi mass ($M_\ion{H}{i}$), $\rm H_2$ mass ($M_{\rm H_2}$), and metallicity (Z), respectively, colour coded by their stellar mass ($\log M_*$). From left to right, we show these relations at $z=0$, $z=1$, $z=2$ and $z=3$, respectively. The correlation coefficient values between these relations are shown at the bottom of each panel.
• Figure 4: The correlation between residual and galaxy colour $g-r$ at $z=0$, colour coded by $\log M_*$. The correlation coefficient between colour and the residual is shown at the bottom.
• Figure 5: The correlations between the residual and BH properties. From top to bottom, we show BH mass attributed to torque accretion ($M_{\rm Torque}$), the torque accretion rate ($\dot M_{\rm Torque}$), the BH mass attributed to Bondi accretion ($M_{\rm Bondi}$), Bondi accretion rate ($\dot M_{\rm Bondi}$) and Eddington ratio ($f_{\rm edd}$), respectively, colour coded by $\log M_*$. The red dashed lines in the bottom row indicate $f_{\rm edd} = 0.2$, when the 'jet mode' feedback is about to start. In the panels for $\dot M_{\rm Torque}$, $\dot M_{\rm Bondi}$, and $f_{\rm edd}$, we represent BHs with zero accretion rate as $10^{-7}$. From left to right, we show these relations at $z=0$, $z=1$, $z=2$, and $z=3$, respectively. The correlation coefficients between these relations are shown at the bottom of each panel.