Fundamental Physics Opportunities with the Next-Generation Event Horizon Telescope

EHTC images of M87* (left) and \sgra~(right). The central solid blue circles show the largest possible diameter (in GR) of each BH's event horizon, i.e., the Schwarzschild value of $4~r_{\rm g}$, where $r_{\rm g}$ is the BH gravitational radius (see Sec.~\ref{sec:Light_ring}). The size of the event horizon in the observed image would appear slightly larger than the solid blue circles, due to gravitational lensing. Note that the event horizons fit within the central dark regions of both images (the central brightness depression). Pairs of dashed blue circles delineate the estimated diameter range of the bright ring from image domain analysis of M87* ($42~\pm~3 ~\mu$as) and \sgra~($51.8~\pm~2.3 ~\mu$as). These ranges are consistent with the prediction of the Schwarzschild BH shadow diameter ($2\sqrt{27}~r_{\rm g}$). The white circles in the lower right of both panels show the $20~\mu$as FWHM circular Gaussian beam (EHT 2017). See \cite{EventHorizonTelescope:2019dse} and \cite{EventHorizonTelescope:2022xnr} for further information. Figure reproduced from \cite{Younsi_review_in_prep}.

Vision for the ngEHT array. Current EHT sites are shown in white, candidate ngEHT Phase 1 sites are blue, and candidate ngEHT Phase~2 sites are green. In addition, yellow markers show four additional sites that are planned to come online over the next five years: the 37~m Haystack Telescope \citep[HAY;][]{Kauffmann_2023}, the 15~m Africa Millimetre Telescope \citep[AMT;][]{Backes_2016}, the Large Latin American Millimeter Array \citep[LLA;][]{Romero_2020}, and the Yonsei Radio Observatory of the Korea VLBI Network \citep[KVN-YS;][]{Asada_2017}. For additional details on the ngEHT array, see \citetalias{ngEHT_refarray}. Figure reproduced from \citetalias{ngEHT_KSG}.

Observing frequencies and imaging angular resolutions for current and next generation facilities. The EHT and ngEHT have significantly finer imaging resolution than any other telescope. The ngEHT will significantly expand the frequency coverage of the EHT and will provide access to larger angular scales. Figure reproduced from \citetalias{ngEHT_KSG}.

Left: near-critical null geodesics emanating from a flare (orange sphere) in an optically thin equatorial emission disk around a Kerr BH with $a_*=0.94$. The blue light ray has half-orbit number $n=1$, while the green ray has $n=2$. Right: image of the disk as would be seen by an infinite-resolution distant observer at an inclination of $17^\circ$. Strongly lensed light rays, which undergo multiple half-orbits, appear on the observer screen close to the ``critical curve'', displaying enhanced brightness, and compose the photon ring. Correlated images of the same spacetime event (e.g., the flare) appear at different angles and times along the ring (blue and green dots on the right image). Figure from \cite{Hadar:2020fda}.

Left: $n=0$ and $n=1$ images from a MAD GRMHD simulation viewed with parameters appropriate for M87* at 230 GHz. Right: visibility response along the $u$ and $v$ axes of the decomposed and full image. At the baseline lengths accessible to the ngEHT, the $n=0$ and $n=1$ image have comparable correlated flux density.

Polarized interferometric indication of the \sgra~photon ring. Left: a MAD GRMHD simulation of \sgra with $R_{\rm low}=1$, $R_{\rm high}=80$, and viewed at $30^\circ$, after corruption by interstellar scattering. Middle panels: divergence-free $B$-mode polarization defined relative to the image center, showing the sign flip between the direct and indirect image. Right panel: the phase of the polarimetric spiral quotient defined in \citet{Palumbo_2023} after averaging over 24 hours of the simulation movie at left, which reveals the presence of the photon ring $B$-mode reversal even without phase information constraining the image center. This detection mechanism is only possible with long-baseline 345 GHz detections which just barely reach the indirect image-dominated regime.

Geometric model fits containing two geometric ``m-rings'' with identical prior volume adapted from \citet{Tiede_2022_photon_rings}. The fits assume that the two rings, 0 and 1, have hierarchical widths. Increasing data quality and coverage eventually requires the presence of a sharp ring. Here $w_1$ specifies the mean and $1\sigma$ uncertainty on the thinner ring's thickness. Starting with the EHT 2022 array, all arrays have joint 230~GHz and 345~GHz coverage, the most crucial difference in capability of recovering sharp features.

Universal, self-similar structure in the autocorrelation function $\mathcal{C}(T,\Phi=\varphi-\varphi')$, Equation~\eqref{eq:photon ring correlator}, for polar observations of an equatorial disk surrounding a Kerr BH with $a_{*}=0.94$. The colored peaks arise from pairs of correlated photons with the same half-orbit numbers $n=n'$ (red), and different half-orbit numbers $\left|n-n'\right|=1$ (blue), $\left|n-n'\right|=2$ (green), and $\left|n-n'\right|=3$ (purple). The (identical) shapes of the correlation peaks are determined by source properties, while their locations and relative magnitudes are determined by the spacetime geometry. Here $\gamma_0$, $\delta_0$, and $\tau_0$ are photon ring critical exponents \citep{Johnson:2019ljv,Gralla:2019drh}. Figure from \cite{Hadar:2020fda}.

Left: predicted joint constraints on mass and spin from measurements of the primary and secondary images (i.e., the $n=0$ and $n=1$ photon rings) of the emission about a BH with mass $M = 6.5\times10^9~M_{\odot}$ and spin $a_{*} = 0.85$, appropriate for M87*. The two lines show the degenerate constraint when the emission is dominated by that at $2~r_{\rm g}$ (black) and $6~r_{\rm g}$ (orange). The combined $1\sigma$ regions are indicated in blue for diameter measurements of various precision, ranging from $\sigma_d/b=0.1\%$ to $0.4\%$. Right: estimates of the precision of mass (top) and spin (bottom) for different intrinsic BH spins, as a function of diameter measurement precision. The open points show the fiducial value in Equation~\ref{eq:diameter_precision}.

Time-averaged images of the direct ($n=0$) image and first lensed ($n=1$) image from MAD GRMHD simulations at various spins, rotated so that the approaching jet is oriented $288^\circ$ East of North \citep[adapted from][]{Palumbo_2022}. Ticks show the EVPA. Polarization spirals about the ring become more radial at higher spin magnitudes, reverse direction over radius in retrograde flows ($a_{*}<0$), and approximately reflect through the origin across sub-image index $n$. These images use the $R_{\rm high}$ electron heating prescription, each having $R_{\rm high}=80$, a reasonable value for both M87* and Sgr A* \citep{Mosci_2016, EventHorizonTelescope:2019pgp,Collaboration2019_V}. The simulations themselves were generated with \texttt{iharm3d} \citep{Gammie_HARM_2003} and ray traced with \texttt{ipole} \citep{IPOLE_2018}. See \citet{Wong_2022} for additional details on the ray tracing.

Fractional error in the mass of Sgr A* ($\Delta M/M$ with $\Delta M$ denoting 1-$\sigma$ error in M) vs. 1-$\sigma$ error in the dimensionless spin of Sgr A* ($\Delta a_*$) achieved from various observations. The dimensionless spin parameter is defined as $a_{*}=|\vec{S}|/M^2$~\citep{Kramer:2004hd}. Observation of the star S2 with GRAVITY places a constraint on $M$ with $\Delta M=1.3\times10^4\,M_{\odot}$~\citep{GRAVITY:2021xju}, shown by the horizontal range in blue. Implementing such bounds on mass, GW observations with LISA can achieve $\Delta a_*=0.013$~\citep{Tahura:2022ffs} (vertical range in green). The orange bar shows the precision of mass and spin measurements the future GRAVITY instrument can achieve ($\Delta M /M \simeq 0.05\%$ and $\Delta a_*=0.035$), given that S-stars are found closer to Sgr A*~\citep{Psaltis:2015uza, Zhang_2015}. Projected pulsar timing observations can obtain $\Delta a_{*}=0.024$ (horizontal range of the red line), while $\Delta M/M$ is of the order $10^{-6}$~\citep{Psaltis:2015uza}, which is much smaller than the scale of the above figure. The $\delta_d/b=0.2\%$ case in Figure~\ref{fig:photon_ring_spin_est} is reproduced here for comparison, as labeled by ``Light Ring''. Future pulsar timing and GRAVITY experiments have the potential to provide the most precise spin measurements.

Exclusion regions in the BH spin-mass diagram obtained from the superradiant instability of Kerr BHs against massive bosonic fields for the two most unstable modes. The top, middle, and bottom panels refer to scalar, vector and tensor fields, respectively. For each mass of the field (reported in units of eV), the separatrix corresponds to an instability time scale equal to the Salpeter time $\tau_{\rm Salpeter} \approx 4.5\times 10^7 {\rm\, yr\,}$, i.e., inside each colored region the instability timescale would be shorter than $\tau_{\rm Salpeter}$. For illustration we consider bosons with masses ranging from $10^{-21}\,$eV to $10^{-17}\,$eV. For the massive tensor case we only show two masses to minimize clutter in the figure. The gray lines and error bars denote the measured mass of Sgr A*~\citep{GRAVITY:2021xju} and M87*~\citep{EventHorizonTelescope:2019dse}.

Exclusion regions for the two most unstable modes as a function of the spin of Sgr A* and M87* when fixing Sgr A*'s mass to $M \simeq 4\times 10^{6}M_{\odot}$~\citep{GRAVITY:2021xju} and M87*'s mass to $M \simeq 6.5\times 10^{9}M_{\odot}$~\citep{EventHorizonTelescope:2019dse}. As in Figure~\ref{fig:BHspin}, the separatrices correspond to an instability time scale equal to the Salpeter time $\tau_{\rm Salpeter} \simeq 4.5\times 10^7 ~{\rm yr}$.

{Left panel:} the evolution of the mass of the boson cloud $M_B$ (top) and of the dimensionless BH spin parameter $a_{\scriptscriptstyle *}$ (bottom), as a function of time in years for (initial) $\alpha = 0.2$ and for different choices of the bosonic nature: scalar field (red), vector field (blue), tensor field (green), with the set of quantum numbers as given in the text. The initial mass of the boson cloud is $M_B = 10^{-1}\,M_\odot$ (solid line) and $M_B = 10^{-6}\,M_\odot$ (dashed line). We assume an initial BH mass $M = 4.3\times 10^6\,M_\odot$ and initial spin $a_{*} = 0.99$. {Right panel:} evolution of shadow contours (gray lines) during different stages of superradiance for a vector with initial $\alpha = 0.2$ and a BH viewed at different inclination angles. The background depicts the intensity map with an initial value of $a_{\scriptscriptstyle *} = 0.99$. The coordinate origin is taken to be the BH location and the axes are specified in units of the initial gravitational radius.

{Left panel:} the evolution of the mass of the boson cloud $M_B$ (top) and of the dimensionless BH spin parameter $a_{\scriptscriptstyle *}$ (bottom), as a function of time in years for (initial) $\alpha = 0.2$ and for different choices of the bosonic nature: scalar field (red), vector field (blue), tensor field (green), with the set of quantum numbers as given in the text. The initial mass of the boson cloud is $M_B = 10^{-1}\,M_\odot$ (solid line) and $M_B = 10^{-6}\,M_\odot$ (dashed line). We assume an initial BH mass $M = 4.3\times 10^6\,M_\odot$ and initial spin $a_{*} = 0.99$. {Right panel:} evolution of shadow contours (gray lines) during different stages of superradiance for a vector with initial $\alpha = 0.2$ and a BH viewed at different inclination angles. The background depicts the intensity map with an initial value of $a_{\scriptscriptstyle *} = 0.99$. The coordinate origin is taken to be the BH location and the axes are specified in units of the initial gravitational radius.

Left panel: examples of deviations from the Kerr background photon geodesics as a function of the affine parameter, $\lambda$, generated by bosonic clouds with $\alpha = 0.2$. The initial values are $\lambda_{\rm 0} = 0,\, r_{\rm 0} = 10^3\, r_{\rm g}$, $i=17^\circ$, and $a_* = 0.94$. The gray vertical line shows the time at which the unperturbed orbit $x_{(0)}^\mu$ crosses the BH equatorial plane for the first time. Right panel: prospects for constraints on the total mass of a vector cloud using photon ring autocorrelations. We show both the ground state $(S,l,m)=(-1,1,1)$ with $\alpha<0.5$ and a higher mode $(S,l,m)=(-1,2,2)$. The constraint bands range from a conservative criterium based on ngEHT's spatial resolution $\sim 10~\mu$as to an optimistic criterium based on the intrinsic azimuthal correlation length of the accretion flow $\ell_\phi \approx 4.3^\circ$. Constraints from a joint observation of motion of stars and EHT ring size measurements~\citep{Sengo:2022jif} are shown in red, and theoretical bounds on the maximum superradiant extraction for $M_B/M$~\citep{Herdeiro:2021znw} are shown in green.

Left panel: examples of deviations from the Kerr background photon geodesics as a function of the affine parameter, $\lambda$, generated by bosonic clouds with $\alpha = 0.2$. The initial values are $\lambda_{\rm 0} = 0,\, r_{\rm 0} = 10^3\, r_{\rm g}$, $i=17^\circ$, and $a_* = 0.94$. The gray vertical line shows the time at which the unperturbed orbit $x_{(0)}^\mu$ crosses the BH equatorial plane for the first time. Right panel: prospects for constraints on the total mass of a vector cloud using photon ring autocorrelations. We show both the ground state $(S,l,m)=(-1,1,1)$ with $\alpha<0.5$ and a higher mode $(S,l,m)=(-1,2,2)$. The constraint bands range from a conservative criterium based on ngEHT's spatial resolution $\sim 10~\mu$as to an optimistic criterium based on the intrinsic azimuthal correlation length of the accretion flow $\ell_\phi \approx 4.3^\circ$. Constraints from a joint observation of motion of stars and EHT ring size measurements~\citep{Sengo:2022jif} are shown in red, and theoretical bounds on the maximum superradiant extraction for $M_B/M$~\citep{Herdeiro:2021znw} are shown in green.

{Left panel:} illustration of a covariant radiative transfer simulation (\texttt{ipole}) of the polarised emission from a Kerr BH surrounded by an axion cloud. Different colors on the EVPA quivers, which range from red through to purple, represent the time variation of the EVPA in the presence of the axion-photon coupling. White quivers are the EVPAs when the axion field is absent. The intensity scale is normalized so that the brightest pixel is unity. {Right panel:} the upper limit on the axion-photon coupling \citep{Chen:2021lvo}, characterized by $c \equiv 2 \pi g_{a \gamma}\,f_a$, derived from the EHT polarimetric observations of SMBH M87$^\star$ \citep{EventHorizonTelescope:2021bee} and prospect for ngEHT \citep{Chen:2022oad}. The bounds from other astrophysical observations assuming $f_a = 10^{15}~$GeV are shown for comparison.

{Left panel:} illustration of a covariant radiative transfer simulation (\texttt{ipole}) of the polarised emission from a Kerr BH surrounded by an axion cloud. Different colors on the EVPA quivers, which range from red through to purple, represent the time variation of the EVPA in the presence of the axion-photon coupling. White quivers are the EVPAs when the axion field is absent. The intensity scale is normalized so that the brightest pixel is unity. {Right panel:} the upper limit on the axion-photon coupling \citep{Chen:2021lvo}, characterized by $c \equiv 2 \pi g_{a \gamma}\,f_a$, derived from the EHT polarimetric observations of SMBH M87$^\star$ \citep{EventHorizonTelescope:2021bee} and prospect for ngEHT \citep{Chen:2022oad}. The bounds from other astrophysical observations assuming $f_a = 10^{15}~$GeV are shown for comparison.

Images of spacetimes where specular reflection takes place, but with partial absorption ($\Gamma=0.5$) and an intrinsic brightness ($\eta=10^{-2}$) included. We take an inclination $i=0^{\circ}$, $\epsilon=10^{-3}$, without filter (top row) and a Gaussian filter with the EHT angular resolution of $20\ \mu\mbox{as}$ (bottom row). We see that these values of $\eta$ change appreciably the structure of the central depression in brightness.

Results of applying a Gaussian filter with an angular resolution of $5\ \mu\mbox{as}$ for $\epsilon=10^{-3}$, $\Gamma=0.5$, $\eta=10^{-3}$, $i=0^{\circ}$ (top row) and $i=85^{\circ}$ (bottom row). The optimistic value of angular resolution of $5\ \mu\mbox{as}$ can pick up the innermost structure of the simulated image. However, higher inclination angles make it more difficult to discern the features associated with the existence of a surface.

We compare the simulated high-resolution image (far-left panel) of a horizonless spacetime (generated by overspinning a regular BH to $a_*=1.01$) and its reconstructions using the ehtim toolkit~\citep{Chael:2018oym}, as seen by: (i) the 2017 EHT array (middle-left panel), (ii) the 2022 EHT array (middle-right panel), (iii) a multifrequency observation at 230 GHz and 345 GHz of a potential ngEHT array with ten additional telescopes (far-right panel). We also show (for the three reconstructed images) contour lines at $0.035$~Jy, $0.05$~Jy, and $0.065$~Jy (whenever they exist) to visualize the structure of the central brightness depression. See also~\citet{Eichhorn:2022fcl}.

Ray-traced images from GRMHD simulations of accretion onto a Kerr BH (left) and a boson star (right) with the mass and distance of Sgr A*. Despite the different size, these simulations show that under some circumstances, a horizonless, surfaces ECO can mimic the morphology of a BH image by a combination of GRMHD and lensing effects. Figures taken from \citet{Olivares:2018abq}.

Ray-traced images from GRMHD simulations of accretion onto a Kerr BH (left) and a boson star (right) with the mass and distance of Sgr A*. Despite the different size, these simulations show that under some circumstances, a horizonless, surfaces ECO can mimic the morphology of a BH image by a combination of GRMHD and lensing effects. Figures taken from \citet{Olivares:2018abq}.

Ray-traced images of a Schwarzshild BH (left) and a Proca star (right) surrounded by thin accretion disks terminating at the location predicted by the spacetime properties. The lower panels are blurred by a Gaussian kernel, highlighting the possible degeneracy when observing at a single frequency without resolving the thin photon ring. Figure reproduced with permission from~\cite{Herdeiro:2021lwl}.

We show the inner shadow (inner shaded region) and the first lensing band (outer shaded band) of deviations from a Kerr BH with spin $a_{*}=0.9$ viewed at near-face-on inclination of $17^{\circ}$. In each panel, we compare the Kerr case (blue-shading and the same throughout all panels) to spacetimes with varying KRZ parameters~\citep{2016PhRvD..93f4015K} (orange-shading) $\delta\omega_{00}$ and $\delta a_{00}$. The parameter $\delta\omega_{00}$ relates to deviations of the asymptotic spin parameter. The parameter $\delta a_{00}$ relates to deviations in the first parameterized post-Newtonian coefficients. See also \citep{Cardenas:2022}.

We show the inner shadow (inner shaded region) and the first lensing band (outer shaded band) of deviations from a Kerr BH with spin $a_{*}=0.9$ viewed at near-face-on inclination of $17^{\circ}$. In each panel, we compare the Kerr case (blue-shading and the same throughout all panels) to spacetimes with varying KRZ parameters~\citep{2016PhRvD..93f4015K} (orange-shading) $\delta\omega_{00}$ and $\delta a_{00}$. The parameter $\delta\omega_{00}$ relates to deviations of the asymptotic spin parameter. The parameter $\delta a_{00}$ relates to deviations in the first parameterized post-Newtonian coefficients. See also \citep{Cardenas:2022}.

Left: example GRMHD snapshot image of \m87 for a MAD accretion model onto a BH with mass $M=6.2\times10^9\,M_\odot$ and spin $a_{*}=0.9375$ \citep{2021ApJ...918....6C}. Center left: the same GRMHD snapshot image, convolved with a Butterworth filter with a cutoff frequency of $1/10\,\mu$as. Center right: reconstruction of the simulation model from synthetic data generated on EHT2017 baselines. Right: reconstruction of the simulation model from synthetic data generated from a concept ngEHT array. The top row shows images in a linear color scale and the bottom row shows the same images in gamma scale. In all images, the white curve shows the boundary of the inner shadow, while the cyan curve shows the boundary of the shadow. The BH spin vector points to the left (East).

Simulation and reconstruction brightness cross sections along the East-West axis. The yellow curve shows the 1D brightness profile of the \m87 GRMHD simulation snapshot in Figure~\ref{fig:Inner_Shadow_Reconstructions}. The dashed green curve shows the 1D brightness profile from the same simulation after convolution with a Gaussian with a FWHM of $5~\mu$as. The solid blue line shows the median brightness profile extracted from the \texttt{Comrade} ngEHT reconstructions. The band shows the 99\% posterior credible interval for the 1D brightness profile. The gray band along the bottom shows the region interior to the BH shadow, and the black band shows the inner shadow region.

Left: the ratio of the mean radius of the lensed horizon $\bar{r}_{\rm h}$ to the mean radius of the critical curve $\bar{r}_{\rm c}$. In the low-inclination case, $\bar{r}_{\rm h}/\bar{r}_{\rm c}$ shrinks from $\approx\!55$\% at zero spin to $\approx\!45$\% at maximal spin. Right: simultaneous constraints on the BH mass-to-distance ratio $M/D$ and spin $a_{*}$ enabled by measuring the mean radius of the lensed horizon (blue, $\bar{r}_{\rm h}$) and critical curve (red $\bar{r}_{\rm c}$), when the inclination is fixed to $17^\circ$, as is appropriate for \m87 \citep{Mertens2016,CraigWalker:2018vam}. Without fixing the mass, multiple values of $a_{*}$ provide the same result for the size of each feature, but combining a measurement of both features breaks this degeneracy. The shaded regions show regions corresponding to $0.1$, $0.5$, and $1\,\mu$as errors on the radius measurement. The input mass scale and spin are $M/D=3.78\,\mu$as and $a_{*}=0.94$.

Multi-ring structures for specific circular deviations of Kerr spacetime ($b_{01}=5$ in the KRZ parameterization~\citep{Konoplya:2016jvv}) at fixed spin parameter of $a_{*}=0.9\,M$ and viewed at the inclination of M87*. From left to right we show (i) the $n=1$ lensing band (for Kerr spacetime in blue-dashed and with deviation in green-continuous), cf.~\cite{Cardenas:2022}; (ii) the resulting image in this spacetime assuming a specific disk model, cf.~\cite{Eichhorn:2022fcl}; (iii) the same image but blurred with a Gaussian kernel with $\sigma_\text{blur}=5\,\mu\text{as}$; and (iv) with $\sigma_\text{blur}=10\,\mu\text{as}$. (For the translation of $r_g=M$ to the overall image scale in $\mu\text{as}$, we determine the maximum diameter of the convex hull of all image pixels with at least half of the average intensity per pixel.)

As in Figure~\ref{fig:LB_multiring_KRZ} but for a non-spinning ($a_{*}=0$) regular BH with exponential falloff in the mass function as in~\citep{Simpson:2019mud}. The deviation is chosen near-critical such that if it is further increased, the regular spacetime would transition from a BH to a horizonless object.

GRMHD simulations of SMBHBs. Top: simulation viewed in in the equatorial plane for a binary with mass ratio 1:4, colored by logarithm (base 10) of plasma rest mass density (left) and normalized bremsstrahlung emissivity ($j_{\rm brem}$, right). A spiral shock is produced by the smaller mass secondary, increasing $j_{\rm brem}$. Bottom: the structure of the jet (colored by magnetization of the plasma) for three cases with different mass ratios: (a) 1:1 with zero spin, (b) 1:4 with zero spin, and (c) 1:4 with spin $a_{*}=0.7$ for both BHs. The jets form a ``braid'' structure for the 1:1 case, while the other cases show a more disordered structure \citep{olivares_binary_inprep}.

GRMHD simulations of SMBHBs. Top: simulation viewed in in the equatorial plane for a binary with mass ratio 1:4, colored by logarithm (base 10) of plasma rest mass density (left) and normalized bremsstrahlung emissivity ($j_{\rm brem}$, right). A spiral shock is produced by the smaller mass secondary, increasing $j_{\rm brem}$. Bottom: the structure of the jet (colored by magnetization of the plasma) for three cases with different mass ratios: (a) 1:1 with zero spin, (b) 1:4 with zero spin, and (c) 1:4 with spin $a_{*}=0.7$ for both BHs. The jets form a ``braid'' structure for the 1:1 case, while the other cases show a more disordered structure \citep{olivares_binary_inprep}.

Proxy for synchrotron emissivity at 230 GHz \citep[equation (18) of][]{EventHorizonTelescope:2019pcy} for a GRMHD simulation of accretion onto a binary with mass ratio 1:4 and aligned spins with $a_{*}=0.7$, viewed in the equatorial plane ({\it left}) and meridional plane ({\it right}). It is possible to observe emission from the spiral shock, and contrary to the Bremsstrahlung case (c.f., Figure \ref{fig:SMBBH_sim}), the primary appears brighter than the secondary \citep{olivares_binary_inprep}.