Stellar-mass black holes on the millimetre fundamental plane of black hole accretion

TL;DR

The paper extends the millimetre fundamental plane of black hole accretion to stellar-mass black holes by combining new 230 GHz ACA observations with archival mm and X-ray data for five X-ray binaries. Both ADAF-like accretion flows and compact jet models are shown to plausibly reproduce the observed correlations across mass scales, though model parameters calibrated for supermassive black holes introduce mass-dependent uncertainties. The XRBs largely lie on the same $M_{\rm BH}$--$L_{\nu,\mathrm{mm}}$ and mmFP relations as SMBHs, with state-dependent deviations suggesting the plane applies to hard/quiescent states. The work strengthens the case for universal accretion physics across mass scales while highlighting the need for simultaneous, well-constrained observations and refined plasma-physics modeling, potentially including hybrid jet-ADAF scenarios.

Abstract

Recent work revealed the existence of a galaxy "millimetre fundamental plane of black hole accretion", a tight correlation between nuclear $1$mm luminosity, intrinsic $2$ - $10$keV X-ray luminosity and supermassive black hole mass, originally discovered for nearby low- and high-luminosity active galactic nuclei. Here we use mm and X-ray data of $5$ X-ray binaries (XRBs) to demonstrate that these stellar-mass black holes also lie on the mm fundamental plane, as they do at radio wavelengths. One source for which we have multi-epoch observations shows evidence of deviations from the plane after a state change, suggesting that the plane only applies to XRBs in the hard state, as is true again at radio wavelengths. We show that both advection-dominated accretion flows and compact jet models predict the existence of the plane across the entire range of black hole masses, although these models vary in their ability to accurately predict the XRB black hole masses.

Figures (4)

• Figure 1: Correlation between $M_{\rm BH}$ and $L_{\rm \nu,mm}$ (left panel) and edge-on view of the $M_{\rm BH}$ -- $L_{\rm X,2-10}$ -- $L_{\rm \nu,mm}$ correlation (right panel), as Figure 1 of Ruffa24. The four stellar-mass black holes with archival data are plotted as red circles where the objects without 230GHz archival observations are shown as open circles. Green circles (or left-pointing triangles for upper limits) represents $L_{\rm \nu,mm}$ measured using our newly-acquired ACA data. The black filled circle is the ACA observation of GX 339-4. Where possible, a black line connects the original archival data points to the updated ones. Filled blue circles are for SMBH masses estimated dynamically, open blue circles for those estimated using the $M_{\rm BH}$ -- $\sigma_\star$ relation of Vandenbosch16. Error bars are plotted for all data points but some are smaller than the symbol used. The best-fitting power-law relations are overlaid as black solid lines, the observed scatters around those relations as black dashed lines. The red solid and dashed lines in the left panel show the best-fitting $M_{\rm BH}$ -- $L_{\rm \nu,mm}$ power-law relation and scatter of Ruffa24 when including only SMBHs. The correlation coefficients $\rho$ and $p$-values of the Spearman rank analyses are reported in the top-left corner of each panel.
• Figure 2: Correlation between $L_{\rm \nu,mm}$ and $L_{\rm X,2-10}$ for both SMBHs (blue data points) and stellar-mass BHs (green and red data points). The black grid illustrates the area covered by the ADAF model solutions as a function of $M_{\rm BH}$ and Eddington ratio $L/L_{\rm Edd}$ (see Section \ref{['sec:adaf_models']} for details). We only include data points with mm luminosities derived from the ACA data, with the exception of GX 339-4 (due to its substantial flux variability) where we use the archival data. We not include the archival data for XTE J1118+480 as it does not have archival 230GHz observations.
• Figure 3: Same as the right panel of Figure \ref{['fig:FP_SM_Fit']}, but with the grey shaded region representing the projection of the ADAF model grid onto the mmFP. We use the same sample as in Figure \ref{['fig:FP_SM_grid']}.
• Figure 4: Correlation between $L_{\rm \nu,mm}$ and $L_{\rm X,2-10}$ for both SMBHs (blue data points) and stellar-mass BHs (green and red data points). The black and green grids illustrate the areas covered by the compact jet model solutions as a function of $M_{\rm BH}$ ($10^{1}-10^{10}\,{\rm M_\odot}$) and jet power ($10^{-5.5}-10^{-1.5}{\rm L_{Edd}}$) for jet inclinations of $2.5^{\circ}$ and $90^{\circ}$, respectively. Solutions with intermediate inclinations lie between these two extremes (see Section \ref{['sec:compact_jet']} for details). We use the same sample as in Figure \ref{['fig:FP_SM_grid']}.