<figure><img src="image_30.png" /><figcaption>**Figure 27.** Comparison of the results from THEMIS imaging (top row), full-track geometric modeling (middle row), and snapshot modeling (bottom row) across different combinations of April 6 and 7 data sets. The first column shows results from fitting to the April 6 data, the second column shows results from fitting to the April 6 data after flagging baselines between Chile and LMT, the third column shows results from fitting to the April 7 data, and the fourth column shows results from fitting to the combined April 6 and 7 data. In all panels, we show an image corresponding to the posterior mean; for the THEMIS imaging results, each sample image has been shifted during averaging so as to maximize the normalized cross-correlation computed with respect to a reference sample. The full-track and snapshot modeling results show fits to the HOPS pipeline low-band data, while the imaging results show fits to the HOPS pipeline combined low- and high-band data. All of the images share a common brightness color scale; the absolute brightness scale is arbitrary because each image has been normalized to have unit total flux density, and a modest amount of saturation has been permitted in the brightest regions to enhance the visibility of low-brightness features.</figcaption></figure>

## Appendix C
### Single-day Fits

In this section we present the results from analyses carried out on the April 6 and April 7 data sets individually. Figures 28

and 29 show single-day images from each of the analysis pipelines (analogous to those shown in Figure 20), and Figure 30 shows the corresponding measurements of morphological properties (analogous to those shown in Figure 21).
<figure><img src="image_31.png" /><figcaption>**Figure 28.** Same as Figure 20, but showing results obtained from using only the April 6 data.</figcaption></figure>

<figure><img src="image_32.png" /><figcaption>**Figure 29.** Same as Figure 20, but showing results obtained from using only the April 7 data.</figcaption></figure>
<figure><img src="image_33.png" /><figcaption>**Figure 30.** Similar to Figure 21, but showing results obtained from fitting to the April 6 and 7 data sets separately. Each column from Figure 21 has now been split into a pair of columns showing April 6 results on the left and April 7 results on the right.</figcaption></figure>

## Appendix D
GRMHD Synthetic Data Set Generation

To calibrate measurements of the angular gravitational radius $\theta_g$ (see Section 4.4), we rely on the library of GRMHD simulations and associated GRRT synthetic movies produced and described in Paper V. In this appendix we provide an overview of our model selection and data generation procedures, which are conceptually similar to the calibration analysis carried out in M87\* Paper VI.

We select 90 simulations from the GRMHD library to be used for $\theta_g$ calibration and another 10 simulations to be used to validate this calibration. The 90 calibration data sets uniformly grid a range of GRMHD parameters: every combination of the two MAD and SANE accretion states, five black hole spin values of [-0.94, -0.5, 0, 0.5, 0.94], three inclinations of [10°, 50°, 90°], and three $R_{high}$ values of [10, 40, 160] are represented.161 The 10 validation data sets are split evenly between MAD and SANE, but the black hole spins are randomly selected from [-0.94, -0.5, 0, 0.5, 0.94], the inclinations are randomly selected from [30°, 70°, 110°, 130°,

150°], and the $R_{high}$ values are randomly selected from [10, 40, 160]. The resulting model images contain a large variety of possible image morphologies, along with self-consistent dynamics as governed by the equations of GRMHD and GRRT. The GRMHD parameters corresponding to each selected calibration and validation model are listed in Table 7, and some example average images are shown in Figure 31.

After selecting the GRMHD models and prior to generating synthetic data, we first modify their orientations and angular sizes from their default simulation values. We rotate each simulated movie by a position angle that is a uniformly chosen integer in the range [-180°, 180°]. Each of the simulations from Paper V was produced assuming a mass of $M = 4.14 \times 10^6 M_{\odot}$ and a distance of 8.127 kpc (Do et al. 2019; Gravity Collaboration et al. 2019), corresponding to an angular gravitational radius of $\theta_g = 5.03$ µas. To avoid biasing our calibration in favor of any one value of $\theta_g$, we modify the overall spatial scale of each simulated movie by a random factor that is uniformly drawn from the range [0.7, 1.3]. The input position angles and gravitational radii for each movie are listed in Table 7.

Once the GRMHD models are selected and their movies rotated and scaled, we generate synthetic data sets in the same manner as for the synthetic data sets used in Paper III. We use the eht-imaging software to first apply artificial scattering to the source structure per the scattering model from Johnson

<footnote n="161">161 $R_{high}$ is a parameter that sets the ratio of ion to electron temperatures in the simulated images; see M87\* Paper V, Paper V, and Mościbrodzka et al. (2016) for details. For the GRMHD calibration suite, we have not included models with $R_{high} = 1$ because these models tend to produce images with substantial extended emission that is large compared to the black hole shadow size; we note that the $R_{high} = 1$ models are also rejected by the model selection constraints applied in Paper V.</footnote>
<figure><img src="image_34.png" /><figcaption>**Figure 31.** Example average images from some of the GRMHD movies selected for synthetic data generation; each movie has been light-curve-normalized prior to averaging. The data set indices are labeled in the upper left corner of each panel, and the corresponding GRMHD parameters are listed in Table 7. All of the images share a common brightness color scale; the absolute brightness scale is arbitrary because each image has been normalized to have unit total flux density, and a modest amount of saturation has been permitted in the brightest regions to enhance the visibility of low-brightness features. We note that these average images tend to have much smoother structure than the individual frames of the movies that were averaged to produce them (see, e.g., Figure 26 for several example frames from one movie); the synthetic data sets themselves are produced from the movies and not from the average images.</figcaption></figure>

et al. (2018) and then sample the Fourier transform of each movie at a cadence and at (u,v) locations identical to those of the EHT observations of Sgr A*. The resulting visibilities are then corrupted with thermal noise and station-based gain and leakage effects at a level that is consistent with the Sgr A* data (Paper II). Eight synthetic data sets are generated for each GRMHD model, corresponding to the (u,v)-coverage on four observing nights—2017 April 5, 6, 7, and 10—and two frequency bands (see Section 2).

## Appendix E
Representative $\chi^2$ Values for Each Analysis Method

In this section we provide some example representative $\chi^2$ values and associated quantities for each of the analysis methods used in this paper. Specifically, we report values corresponding to the example fits shown in Figures 9, 15, and 17.

For any fitted data quantity $q$ with modeled counterpart $\hat{q}$ and associated measurement uncertainty $\sigma$, we determine the $\chi^2$ as

$$ \chi^2 = \sum_i^{N_{\text{data}}} \left( \frac{q_i - \hat{q}_i}{\sigma_i} \right)^2, \qquad (\text{E1}) $$

where the sum is understood to be taken over all $N_{\text{data}}$ fitted data points. We also define a reduced-$\chi^2$ value,

$$ \chi_{\text{red}}^2 = \frac{\chi^2}{N_{\text{dof}}}, \qquad (\text{E2}) $$

where $N_{\text{dof}}$ is the number of degrees of freedom remaining in the data after accounting for the free parameters in the model.

However, we note that despite their familiarity, the interpretation of either of these $\chi^2$ statistics is complicated by several aspects of the analyses presented in this paper.

The first complication is that the number of degrees of freedom is generically unknown, rendering $\chi^2_{\text{red}}$ difficult to define in practice. The use of informative priors and the presence of correlations among model parameters mean that $N_{\text{dof}}$ cannot be determined as simply the difference between $N_{\text{data}}$ and the number of free parameters in the model. For example, in the RML imaging methods (eht-imaging and SMILI), the number of effective image parameters is implicitly reduced—relative to the number that would be assumed by simply counting the total number of image pixels—by a large factor by the imposition of regularization terms (e.g., smoothness, sparseness) in the objective function (Paper III). Additionally, for all methods that fit to complex visibilities or visibility amplitudes, station gains are reconstructed as part of the fitting process; for those methods that simultaneously reconstruct high- and low-band data, the gains for the two bands are necessarily strongly correlated. Furthermore, strong priors are imposed by network calibration (Paper II; M87* Paper III), further reducing the number of effective model parameters and growing the effective number of degrees of freedom.

The second complication is that, with the exception of the snapshot modeling presented in Section 6 (Comrade and DPI), all models make use of an added uncertainty budget to account for source variability. For the THEMIS imaging and full-track modeling analyses, the parameters describing this excess variability noise are simultaneously fit alongside those describing the image structure. In both cases, the impact is to
<table><caption>**Table 8**
Representative $\chi^2$ Values and Ancillary Model Information</caption><thead><tr><th>Method</th><th>Day</th><th>Band</th><th>χ<sup>2</sup></th><th>N<sub>data</sub></th><th>N<sub>gains</sub><sup>a</sup></th><th>N<sub>params</sub><sup>a</sup></th></tr></thead><tbody><tr><td>eht-imaging imaging</td><td>Apr 7</td><td>HI+LO</td><td>4174.5</td><td>12082</td><td>6358</td><td>6400</td></tr><tr><td>SMILI imaging</td><td>Apr 7</td><td>HI+LO</td><td>2192.9</td><td>6806</td><td>3562</td><td>5625</td></tr><tr><td>DIFMAP imaging</td><td>Apr 7</td><td>HI+LO</td><td>4194.5</td><td>12082</td><td>6358</td><td>2262</td></tr><tr><td>THEMIS imaging</td><td>Apr 6+7</td><td>HI+LO</td><td>1444.5</td><td>2990</td><td>1323</td><td>58</td></tr><tr><td>THEMIS full-track modeling</td><td>Apr 6+7</td><td>LO</td><td>1237.0</td><td>1562</td><td>666</td><td>19</td></tr><tr><td>Comrade snapshot modeling</td><td>Apr 6+7</td><td>LO</td><td>1987.2</td><td>4977</td><td>1345</td><td>3328</td></tr><tr><td>DPI snapshot modeling</td><td>Apr 6+7</td><td>LO</td><td>1752.7</td><td>3176</td><td>...</td><td>1664</td></tr></tbody></table>

**Note.** The $\chi^2$ values, number of data points fit ($N_{data}$), number of station gain parameters ($N_{gains}$), and number of parameters describing the image structure ($N_{params}$) for representative example fits from each of the analysis methods used in this paper. For the eht-imaging and SMILI analyses, $N_{params}$ is equal to the number of pixels in the image Paper III; for the DIFMAP analyses, $N_{params}$ is determined by the number of CLEAN components, with each component contributing three parameters. For the THEMIS imaging and full-track modeling analyses, $N_{params}$ is equal to the number of model parameters used to specify the image structure (see Paper III and Section 7, respectively). For the Comrade and DPI snapshot modeling analyses, each of the $N_s$ snapshots contributes 13 and 8 parameters, respectively, to the total $N_{params}$ count (see Section 6). Note that because the DPI analysis fits only to closure quantities, it does not contain any station gain parameters.

a Note that the listed numbers of gains and model parameters are solely those necessary to forward-compute the model data values, i.e., these values characterize a property of the model specification. Importantly, due to model nonlinearity and strong correlations between parameters, these numbers are not generally suitable for determining $N_{dof}$ (see Appendix E).

drive the $\chi^2_{red}$ value toward unity, rendering the resulting $\chi^2_{red}$ value not particularly meaningful as a metric of fit quality.

Nevertheless, in Table 8 we present the $\chi^2$ values and relevant properties of the data sets and models used for representative examples from each analysis pathway. In lieu of a well-defined number of degrees of freedom, we consider two limits. An optimistic estimate is given by the procedure adopted in Paper III, in which $N_{dof} \approx N_{data}$, appropriate when the total number of effective model parameters is much less than the number of data points. In this limit, $\chi^2_{red}$ ranges from 0.35 to 0.79 for the fits listed in Table 8. A more pessimistic accounting is given by $N_{dof} \approx N_{data} - N_{gains} - N_{params}$. This quantity is negative for some analyses, a consequence of the strong correlations that limit the effective number of model parameters in practice (e.g., for RML imaging and for certain individual snapshot models). Among those analysis methods that do not exhibit this pathology in the $N_{dof}$, the pessimistic $\chi^2_{red}$ estimates range from 0.9 to 1.4.

## Appendix F
Snapshot Modeling Likelihood Functions

In this appendix we provide specific expressions for the likelihood functions used during the snapshot geometric modeling analyses described in Section 6. We assume the high signal-to-noise ratio limit for all data products, which is not strictly satisfied for the relatively short integration times (120 s) employed in the snapshot modeling analyses, but which has the benefit of reducing all likelihood functions to Gaussians.

### F.1. Visibility Amplitude Likelihood

For each snapshot and baseline, the visibility amplitudes are distributed according to a Rice distribution, which in the high signal-to-noise ratio limit becomes Gaussian (e.g., Wardle & Kronberg 1974; Broderick et al. 2020a). We can thus write the visibility amplitude likelihood function as

$$ \mathcal{L}_{|V|,sb} = \frac{1}{\sqrt{2\pi\sigma_{sb}^2}} \exp \left[ -\frac{(|\hat{V}_{sb}| - |g_i||g_j||\hat{V}_{sb})^2}{2\sigma_{sb}^2} \right], \quad (\text{F1}) $$

where b is a baseline index that runs over all station pairs {i, j} in snapshot s. Here $|\hat{V}_{sb}|$ is the model visibility amplitude and $|g_i|$ and $|g_j|$ are the individual station gain amplitudes (see Equation (2)). We use this Gaussian approximation to the Rice distribution for all of the snapshot geometric modeling analyses. For a snapshot s, the joint visibility amplitude likelihood across all baselines is then given by

$$ \mathcal{L}_{|V|,s} = \prod_{b} \mathcal{L}_{|V|,sb}, \quad (\text{F2}) $$

where the product is taken over all baselines b.

### F.2. Closure Phase Likelihood

The visibility phases in EHT data sets are heavily corrupted by atmospheric fluctuations (M87* Paper II; M87* Paper III), so all of our snapshot geometric modeling analyses work instead with closure phases $\psi$ (see Equation (3)). In the high signal-to-noise ratio limit, the variance in the closure phase on the triangle containing stations i, j, and k is given by

$$ \sigma_{\psi,ijk}^2 = \sigma_{\ln|V|,ij}^2 + \sigma_{\ln|V|,jk}^2 + \sigma_{\ln|V|,ki}^2, \quad (\text{F3}) $$

where

$$ \sigma_{\ln|V|,ij} = \frac{\sigma_{ij}}{|V_{ij}|} \quad (\text{F4}) $$

is the uncertainty in the log visibility amplitude in the same limit and $\sigma_{ij}$ is the uncertainty in $V_{ij}$. Hereafter we replace the triangle indices ijk with a single multi-index t for clarity. We approximate the closure phase likelihood for a single triangle t and snapshot s by a von Mises distribution,

$$ \mathcal{L}_{\psi, st} = \frac{1}{2\pi I_0(\sigma_{\psi,t}^{-2})} \exp \left[ \frac{\cos(\psi_t - \hat{\psi}_t)}{\sigma_{\psi,t}^2} \right], \quad (\text{F5}) $$

where $\hat{\psi}$ denotes a measured closure phase and $I_0(x)$ is a modified Bessel function of the first kind of order 0. In the high signal-to-noise ratio limit, the von Mises becomes a Gaussian distribution with mean $\hat{\psi}_t$ and standard deviation $\sigma_{\psi,t}$. Note that
up to a normalization $\ln \mathcal{L}_{\psi}$ is equal to the closure phase $\chi^2$ defined in Paper III.

Because a full set of closure phases is highly redundant (i.e., the set is not linearly independent; see Blackburn et al. 2020), we use eht-imaging (Chael et al. 2016, 2018) to construct a minimal nonredundant set within every snapshot. The minimal set of closure phases is constructed by selecting all triangles that contain the most sensitive station in the array (typically ALMA), which ensures that the resulting closure phases are minimally covariant. We ignore the remaining covariances and approximate the joint closure phase likelihood for a snapshot s as

$$ \mathcal{L}_{\psi,s} = \prod_t \mathcal{L}_{\psi, st}, \qquad (F6) $$

where the product is taken over all triangles $t$ in the minimal set.

### F.3. Log Closure Amplitude Likelihood

Some of our snapshot modeling fits use log closure amplitudes in place of visibility amplitudes. In the high signal-to-noise ratio limit, the variance in the log closure amplitude on the quadrangle containing stations i, j, k, and ℓ is given by

$$ \sigma_{\ln A, ijk\ell}^2 = \sigma_{\ln|V|, ij}^2 + \sigma_{\ln|V|, k\ell}^2 + \sigma_{\ln|V|, ik}^2 + \sigma_{\ln|V|, j\ell}^2. \qquad (F7) $$

Hereafter we replace the quadrangle indices $ijk\ell$ with a single multi-index $q$ for clarity. For a single log closure amplitude on quadrangle $q$, we thus have the Gaussian likelihood

$$ \mathcal{L}_{\ln A, sq} = \frac{1}{\sqrt{2\pi\sigma_{\ln A, sq}^2}} \exp \left[ - \frac{(\ln A_{sq} - \ln \hat{A}_{sq})^2}{2\sigma_{\ln A, sq}^2} \right], \qquad (F8) $$

in the same limit. We use eht-imaging to construct a minimal nonredundant set of log closure amplitudes within every snapshot, and for the joint likelihood over all of the linearly independent quadrangles within that snapshot we again ignore covariance and treat the data products as being statistically independent. The joint likelihood is then given by

$$ \mathcal{L}_{A,s} = \prod_q \mathcal{L}_{A,sq}, \qquad (F9) $$

where the product is taken over all quadrangles $q$ in the minimal set.

## Appendix G

### Snapshot Modeling Prior Distribution Consistency

In specifying the hypermodel for combining geometric modeling results from individual snapshots (see Section 6.3), we have selected a set of snapshot priors $\pi(\theta_s)$, an average model prior $\pi(\theta)$, and a hypermodel $\pi(\theta_s|\hat{\theta})$. A self-consistent set of hypermodel and snapshot priors should satisfy the relation

$$ \pi(\theta_s) = \int \pi(\theta_s|\mu, \sigma) \pi(\mu) \pi(\sigma) d\mu d\sigma. \qquad (G1) $$

However, because we have carried out the hierarchical modeling from Section 6 in two stages—i.e., first fitting the mG-ring model to individual snapshots, then combining the results from all snapshots—the priors on the model parameters

<figure><img src="image_35.png" /><figcaption>Figure 32. Illustration of the centralizing bias induced by specifying both the snapshot priors and hypermodel priors separately, using the diameter parameter as an example. The orange curve shows the diameter prior specified during mG-ring model fitting of an individual snapshot, and the blue curve shows the effective prior on this parameter after snapshots are combined via the procedure specified in Section 6.3.</figcaption></figure>

during each stage are selected for local convenience, and the relation in Equation (G1) does not strictly hold.

As a result, the final posteriors for each parameter behave as though the individual snapshot fits were carried out using effective priors that differ from the priors we actually imposed (see Table 1). Figure 32 illustrates how the original priors differ from the effective priors induced by the snapshot-combining procedure. The net result is a modest (≈20% maximum probability density deviation) bias for parameter values to fall toward the center of the original (flat) prior range and away from the edges of that range. Because the widths of the individual snapshot posteriors are typically much narrower than the full prior range (see, e.g., Figure 13), we expect the impact of this centralizing bias on our reported values to be negligible.

## Appendix H

### Snapshot Geometric Modeling Validation Tests

We cross-validate the results of each snapshot modeling software using a single snapshot of the low-band Sgr A* data from April 7 processed with the HOPS pipeline. The specific snapshot selected begins at 12.65 hr UTC, where the $(u,v)$-coverage of the observation is maximized (Farah et al. 2022). Given the differences in model specification and fitted data products between Comrade/eht-imaging and DPI, we run two separate cross-validation tests:

1. The first test compares the results between Comrade and eht-imaging when fitting an $m=3$ mG-ring model to visibility amplitudes (including gain amplitudes as model
<figure><img src="image_36.png" /><figcaption>**Figure 33.** Comparison of the 2D joint posterior distributions obtained from fitting an mG-ring model to a 120 s snapshot starting at 12.65 hr UT in the Sgr A* April 7 HOPS low-band data set. The left plot compares the results from Comrade (blue) and eht-imaging (orange), fitting to visibility amplitudes (including gains) and closure phases with an *m* = 3 mG-ring. The right triangle plot shows the results from Comrade (blue), eht-imaging (orange), and DPI (green), fitting to closure amplitudes and closure phases for an *m* = 2 mG-ring. In both cases we only show the results for the diameter, width, and fractional Gaussian component flux parameters. Since DPI fits the diameter of the blurred m-ring *d*′ (Equation (42)), the DPI diameter was debiased so that it corresponds to the infinitesimally thin m-ring diameter that is fit by eht-imaging and Comrade (see also M87* Paper VI*). The contours show 1σ, 2σ, and 3σ levels of the posterior distributions.</figcaption></figure>

parameters) and closure phases. We do not include DPI in this comparison because it cannot currently fit for station gain parameters.

2. The second test compares the results between Comrade, DPI, and eht-imaging when fitting an *m* = 2 mG-ring model to log closure amplitudes and closure phases.

Figure 33 shows the diameter, thickness, and fractional central flux posteriors obtained from performing the tests described above. The posteriors show generally good agreement across codes.

# Appendix I
## Analysis Specifics and Validation of Calibration Strategy

Our calibration strategy for determining the scaling factor $\alpha$ that relates measured ring diameters to intrinsic angular gravitational radii $\theta_g$ is described in Section 4.4. In this appendix, we summarize the elements of this strategy that are specific to the different analysis pathways described in Sections 5, 6, and 7. We also validate the calibration procedure by applying the calibrated $\alpha$ values to ring diameter measurements from 10 synthetic GRMHD data sets. For these data sets we know the underlying ground-truth $\theta_g$ values, and so we can use them to verify whether our measurement and calibration strategy is working as intended.

### 1.1. IDFE Specifics

To perform an IDFE-based $\theta_g$ calibration, top-set and posterior images are produced for each of the 90 synthetic GRMHD-based data sets described in Section 4.4 (see also

Appendix D). Each of these images is run through both REx and VIDA in the same manner as described in Section 5 for the Sgr A* data.

### 1.2. Snapshot Geometric Modeling Specifics

We carry out snapshot geometric modeling of the GRMHD calibration and validation data sets in the same manner as described in Section 6 for the Sgr A* data. For all synthetic data sets we use the same data preparation and snapshot timescale as for the fits to the Sgr A* data. We also retain the same model specification, fitting an *m* = 4 mG-ring for all Comrade analyses and an *m* = 2 mG-ring for all DPI analyses. The DPI analyses are carried out on the low-band data sets only, while the Comrade analyses are carried out on both low- and high-band data sets.

### 1.3. Full-track Geometric Modeling Specifics

We carry out full-track geometric modeling of the GRMHD calibration and validation data sets in the same manner as described in Section 7 for the Sgr A* data. For all synthetic data sets we use the same data preparation as for the fits to the Sgr A* data (see Section 7.1). In particular, we derive appropriately individualized priors on the noise model parameters by performing model-agnostic variability quantification (per Section 3.3) on multiday instantiations (corresponding to April 5, 6, 7, and 10; see Appendix D) of each of the synthetic data sets. We also retain the same geometric model specification, fitting an *m* = 4 mG-ring for all analyses.
<figure><img src="image_37.png" /><figcaption>**Figure 34.** Distributions of recovered $\theta_g$ values relative to the known input value, from the GRMHD validation exercise for each analysis pathway. For geometric modeling results the left- and right-hand distributions show the results from fitting to LO and HI bands, respectively. For the IDFE results, the left- and right-hand distributions show the results from using *REx* and *VIDA*, respectively. No metronization-based culling has been applied to the IDFE results.</figcaption></figure>
<figure><img src="image_38.png" /></figure>

<figure><img src="image_39.png" /><figcaption>**Figure 35.** Time-averaged images for GRMHD simulations that produce anomalously small (left) and typical (right) $\alpha$ calibrations for each geometric modeling and IDFE method used to estimate the mass of Sgr A*. Left: shown are the GMRHD simulations within the calibration set that result in the five smallest median $\alpha$ values (computed across the applicable posterior or top set). Above each collection of images, the number of calibration data sets that find $\alpha < 7.5$ is listed, in comparison to the total number of calibration experiments (HI/LO band, $REX$/VIDA ring radius measurements). Right: five GRMHD simulations randomly chosen from within the peak of the distribution of $\alpha$ values. Above each collection of images, the number of calibration data sets within one standard deviation of the mean $\alpha$ across the calibration set is listed. In each panel, the corresponding simulation index in Table 7 and the median $\alpha$ across the relevant posterior or top set are given in the upper left and right, respectively.</figcaption></figure>

## 1.4. Validation

For each of the analysis pathways, we validate the $\theta_g$ calibration using an additional 10 synthetic GRMHD-based data sets. Figure 34 shows the results of carrying out ring diameter measurements and subsequent $\theta_g$ conversions on these 10 validation suite data sets, for each of the IDFE, snapshot, and full-track analyses. All analysis pathways are able to successfully recover the correct value of $\theta_g$ to within their determined level of calibration uncertainty.

## 1.5. Origin and Nature of Calibration Outliers

The distributions of calibrated $\alpha$ values from each ring diameter measurement technique show heavy tails toward small $\alpha$, which manifest as heavy tails to large $\theta_g$ in Figure 34 (see also Figure 22). This behavior appears to be generic across all classes of geometric modeling and IDFE analyses used in

this paper, and it implies that some fraction of the calibration data sets are reconstructed to have systematically smaller rings than would be predicted from the known values of $\theta_g$ in each of the input ground-truth simulations.

The left half of Figure 35 shows average images from the input GRMHD calibration suite simulations corresponding to the five smallest $\alpha$ values recovered by each analysis pathway. The number of simulations for which the reconstructed ring corresponds to a “small” value of $\alpha$ depends on the analysis method; for instance, the fraction of reconstructions having median $\alpha < 7.5$ ranges from ~4% for snapshot geometric modeling with Comrade up to ~14% for imaging with SMILI. We can see in Figure 35 that many of these small-$\alpha$ simulations have structures that are not obviously ring-like. Common morphologies in the small-$\alpha$ simulations include images dominated by compact regions of bright emission (typical of highly edge-on systems), or images containing
prominent diffuse emission extending well outside the shadow region of interest. Such structures cannot necessarily be well measured by, e.g., the mG-ring model or IDFE techniques aimed at extracting signatures of a ring-like emission morphology, and attempts to apply these techniques to such data sets can yield results that are difficult to interpret. However, we note that not all of the small-α simulations exhibit such morphological difficulties; some of the poor reconstructions are obtained from simulations with readily apparent ring-like structures, indicating that other difficulties (e.g., strong variability) may be playing a more important role in these cases.

The right half of Figure 35 shows average images from the input GRMHD calibration suite simulations corresponding to five “typical” α values recovered by each analysis pathway; each of these images has been randomly selected from the set whose reconstructed α falls within one standard deviation of the mean. In contrast to the small-α simulations, these images more commonly exhibit ring-like morphologies of the sort that we would expect to be amenable to mG-ring modeling or ring extraction techniques. Furthermore, for most analysis methods a large fraction (~75%) of the data sets are contained within one standard deviation of the mean; the fact that this fraction is larger than the ~68% that we would expect for a Gaussian distribution is another manifestation of the heavy tails in the α distributions, and it indicates that the majority of reconstructions are narrowly peaked around the mean (see also Figure 34). However, even among the well-reconstructed images we still find a small number of less obvious ring structures, including some that are dominated by compact emission regions like many of the small-α simulations. Again, the presence of such simulations indicates that the ground-truth emission morphology is not the sole driver of whether or not the underlying ring structure can be successfully reconstructed.

The ring measurement analysis techniques developed in this paper are designed to be appropriate for application to the EHT Sgr A* data. When applying these techniques to a suite of GRMHD simulations containing very diverse image morphologies, we find that a fraction of the reconstructed rings have unreliable diameter measurements. These poor reconstructions contribute to the uncertainty in our α calibration, where they manifest as heavy tails in our calibrated α distribution. The corresponding large uncertainty in α is a consequence of the fact that many of the images in the calibration suite do not resemble Sgr A*, and thus analysis techniques designed for the latter do not necessarily function well when applied to the former. A calibration suite that was more directly tailored to match the properties of the EHT Sgr A* observations may result in smaller α calibration uncertainties and a correspondingly tighter constraint on θg.

## ORCID iDs

Kazunori Akiyama https://orcid.org/0000-0002-9475-4254

Antxon Alberdi https://orcid.org/0000-0002-9371-1033

Juan Carlos Algaba https://orcid.org/0000-0001-6993-1696

Richard Anantua https://orcid.org/0000-0003-3457-7660

Keiichi Asada https://orcid.org/0000-0001-6988-8763

Rebecca Azulay https://orcid.org/0000-0002-2200-5393

Uwe Bach https://orcid.org/0000-0002-7722-8412

Anne-Kathrin Baczko https://orcid.org/0000-0003-3090-3975

Mislav Baloković https://orcid.org/0000-0003-0476-6647

John Barrett https://orcid.org/0000-0002-9290-0764

Michi Bauböck https://orcid.org/0000-0002-5518-2812

Bradford A. Benson https://orcid.org/0000-0002-5108-6823

Lindy Blackburn https://orcid.org/0000-0002-9030-642X

Raymond Blundell https://orcid.org/0000-0002-5929-5857

Katherine L. Bouman https://orcid.org/0000-0003-0077-4367

Geoffrey C. Bower https://orcid.org/0000-0003-4056-9982

Hope Boyce https://orcid.org/0000-0002-6530-5783

Christiaan D. Brinkerink https://orcid.org/0000-0002-2322-0749

Roger Brissenden https://orcid.org/0000-0002-2556-0894

Silke Britzen https://orcid.org/0000-0001-9240-6734

Avery E. Broderick https://orcid.org/0000-0002-3351-760X

Dominique Broguiere https://orcid.org/0000-0001-9151-6683

Thomas Bronzwaer https://orcid.org/0000-0003-1151-3971

Sandra Bustamante https://orcid.org/0000-0001-6169-1894

Do-Young Byun https://orcid.org/0000-0003-1157-4109

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Dirk Heumann https://orcid.org/0000-0002-7671-0047

Luis C. Ho (何子山) https://orcid.org/0000-0001-6947-5846

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Chih-Wei L. Huang https://orcid.org/0000-0001-5641-3953

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C. M. Violette Impellizzeri https://orcid.org/0000-0002-3443-2472

Makoto Inoue https://orcid.org/0000-0001-5037-3989

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David J. James https://orcid.org/0000-0001-5160-4486

Buell T. Jannuzi https://orcid.org/0000-0002-1578-6582

Michael Janssen https://orcid.org/0000-0001-8685-6544

Britton Jeter https://orcid.org/0000-0003-2847-1712

Wu Jiang (江悟) https://orcid.org/0000-0001-7369-3539

Alejandra Jiménez-Rosales https://orcid.org/0000-0002-2662-3754

Michael D. Johnson https://orcid.org/0000-0002-4120-3029

Svetlana Jorstad https://orcid.org/0000-0001-6158-1708

Abhishek V. Joshi https://orcid.org/0000-0002-2514-5965

Taehyun Jung https://orcid.org/0000-0001-7003-8643

Mansour Karami https://orcid.org/0000-0001-7387-9333

Ramesh Karuppusamy https://orcid.org/0000-0002-5307-2919

Tomohisa Kawashima https://orcid.org/0000-0001-8527-0496

Garrett K. Keating https://orcid.org/0000-0002-3490-146X

Mark Kettenis https://orcid.org/0000-0002-6156-5617

Dong-Jin Kim https://orcid.org/0000-0002-7038-2118

Jae-Young Kim https://orcid.org/0000-0001-8229-7183

Jongsoo Kim https://orcid.org/0000-0002-1229-0426

Junhan Kim https://orcid.org/0000-0002-4274-9373

Motoki Kino https://orcid.org/0000-0002-2709-7338

Jun Yi Koay https://orcid.org/0000-0002-7029-6658

Prashant Kocherlakota https://orcid.org/0000-0001-7386-7439

Patrick M. Koch https://orcid.org/0000-0003-2777-5861

Shoko Koyama https://orcid.org/0000-0002-3723-3372

Carsten Kramer https://orcid.org/0000-0002-4908-4925

Michael Kramer https://orcid.org/0000-0002-4175-2271

Thomas P. Krichbaum https://orcid.org/0000-0002-4892-9586

Cheng-Yu Kuo https://orcid.org/0000-0001-6211-5581

Noemi La Bella https://orcid.org/0000-0002-8116-9427

Tod R. Lauer https://orcid.org/0000-0003-3234-7247

Daeyoung Lee https://orcid.org/0000-0002-3350-5588

Sang-Sung Lee https://orcid.org/0000-0002-6269-594X

Po Kin Leung https://orcid.org/0000-0002-8802-8256

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Zhiyuan Li (李志远) https://orcid.org/0000-0003-0355-6437

Rocco Lico https://orcid.org/0000-0001-7361-2460

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Kuo Liu https://orcid.org/0000-0002-2953-7376

Elisabetta Liuzzo https://orcid.org/0000-0003-0995-5201

Wen-Ping Lo https://orcid.org/0000-0003-1869-2503

Andrei P. Lobanov https://orcid.org/0000-0003-1622-1484

Laurent Loinard https://orcid.org/0000-0002-5635-3345

Colin J. Lonsdale https://orcid.org/0000-0003-4062-4654

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Nicola Marchili https://orcid.org/0000-0002-5523-7588

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Daniel P. Marrone https://orcid.org/0000-0002-2367-1080

Alan P. Marscher https://orcid.org/0000-0001-7396-3332

Iván Martí-Vidal https://orcid.org/0000-0003-3708-9611

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Lynn D. Matthews https://orcid.org/0000-0002-3728-8082

Lia Medeiros https://orcid.org/0000-0003-2342-6728

Karl M. Menten https://orcid.org/0000-0001-6459-0669

Daniel Michalik https://orcid.org/0000-0002-7618-6556

Izumi Mizuno https://orcid.org/0000-0002-7210-6264

Yosuke Mizuno https://orcid.org/0000-0002-8131-6730

James M. Moran https://orcid.org/0000-0002-3882-4414

Kotaro Moriyama https://orcid.org/0000-0003-1364-3761

Monika Moscibrodzka https://orcid.org/0000-0002-4661-6332

Cornelia Müller https://orcid.org/0000-0002-2739-2994

Alejandro Mus https://orcid.org/0000-0003-0329-6874

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Andrew Nadolski https://orcid.org/0000-0001-9479-9957

Hiroshi Nagai https://orcid.org/0000-0003-0292-3645

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Michael A. Nowak https://orcid.org/0000-0001-6923-1315
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Héctor Olivares https://orcid.org/0000-0001-6833-7580

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Tomoaki Oyama https://orcid.org/0000-0003-4046-2923

Daniel C. M. Palumbo https://orcid.org/0000-0002-7179-3816

Georgios Filippos Paraschos https://orcid.org/0000-0001-6757-3098

Jongho Park https://orcid.org/0000-0001-6558-9053

Harriet Parsons https://orcid.org/0000-0002-6327-3423

Nimesh Patel https://orcid.org/0000-0002-6021-9421

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Dominic W. Pesce https://orcid.org/0000-0002-5278-9221

Richard Plambeck https://orcid.org/0000-0001-6765-9609

Oliver Porth https://orcid.org/0000-0002-4584-2557

Felix M. Pötzl https://orcid.org/0000-0002-6579-8311

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Freek Roelofs https://orcid.org/0000-0001-5461-3687

Alan Rogers https://orcid.org/0000-0003-1941-7458

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Cristina Romero-Cañizales https://orcid.org/0000-0001-6301-9073

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Alan L. Roy https://orcid.org/0000-0002-1931-0135

Ignacio Ruiz https://orcid.org/0000-0002-0965-5463

Chet Ruszczyk https://orcid.org/0000-0001-7278-9707

Kazi L. J. Rygl https://orcid.org/0000-0003-4146-9043

Salvador Sánchez https://orcid.org/0000-0002-8042-5951

David Sánchez-Argüelles https://orcid.org/0000-0002-7344-9920

Miguel Sánchez-Portal https://orcid.org/0000-0003-0981-9664

Mahito Sasada https://orcid.org/0000-0001-5946-9960

Kaushik Satapathy https://orcid.org/0000-0003-0433-3585

Tuomas Savolainen https://orcid.org/0000-0001-6214-1085

Jonathan Schonfeld https://orcid.org/0000-0002-8909-2401

Karl-Friedrich Schuster https://orcid.org/0000-0003-2890-9454

Lijing Shao https://orcid.org/0000-0002-1334-8853

Zhiqiang Shen (沈志强) https://orcid.org/0000-0003-3540-8746

Des Small https://orcid.org/0000-0003-3723-5404

Bong Won Sohn https://orcid.org/0000-0002-4148-8378

Jason SooHoo https://orcid.org/0000-0003-1938-0720

Kamal Souccar https://orcid.org/0000-0001-7915-5272

He Sun (孙赫) https://orcid.org/0000-0003-1526-6787

Fumie Tazaki https://orcid.org/0000-0003-0236-0600

Alexandra J. Tetarenko https://orcid.org/0000-0003-3906-4354

Paul Tiede https://orcid.org/0000-0003-3826-5648

Remo P. J. Tilanus https://orcid.org/0000-0002-6514-553X

Michael Titus https://orcid.org/0000-0001-9001-3275

Pablo Torne https://orcid.org/0000-0001-8700-6058

Efthalia Traianou https://orcid.org/0000-0002-1209-6500

Sascha Trippe https://orcid.org/0000-0003-0465-1559

Matthew Turk https://orcid.org/0000-0002-5294-0198

Ilse van Bemmel https://orcid.org/0000-0001-5473-2950

Huib Jan van Langevelde https://orcid.org/0000-0002-0230-5946

Daniel R. van Rossum https://orcid.org/0000-0001-7772-6131

Jesse Vos https://orcid.org/0000-0003-3349-7394

Jan Wagner https://orcid.org/0000-0003-1105-6109

Derek Ward-Thompson https://orcid.org/0000-0003-1140-2761

John Wardle https://orcid.org/0000-0002-8960-2942

Jonathan Weintroub https://orcid.org/0000-0002-4603-5204

Norbert Wex https://orcid.org/0000-0003-4058-2837

Robert Wharton https://orcid.org/0000-0002-7416-5209

Maciek Wielgus https://orcid.org/0000-0002-8635-4242

Kaj Wiik https://orcid.org/0000-0002-0862-3398

Gunther Witzel https://orcid.org/0000-0003-2618-797X

Michael F. Wondrak https://orcid.org/0000-0002-6894-1072

George N. Wong https://orcid.org/0000-0001-6952-2147

Qingwen Wu (吴庆文) https://orcid.org/0000-0003-4773-4987

Paul Yamaguchi https://orcid.org/0000-0002-6017-8199

Doosoo Yoon https://orcid.org/0000-0001-8694-8166

André Young https://orcid.org/0000-0003-0000-2682

Ken Young https://orcid.org/0000-0002-3666-4920

Ziri Younsi https://orcid.org/0000-0001-9283-1191

Feng Yuan (袁峰) https://orcid.org/0000-0003-3564-6437

Ye-Fei Yuan (袁业飞) https://orcid.org/0000-0002-7330-4756

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Guang-Yao Zhao https://orcid.org/0000-0002-4417-1659

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The EHT Collaboration et al.,

Kazunori Akiyama¹,²,³ ID, Antxon Alberdi⁴ ID, Walter Alef⁵, Juan Carlos Algaba⁶ ID, Richard Anantua³,⁷,⁸ ID, Keiichi Asada⁹ ID, Rebecca Azulay¹⁰,¹¹,⁵ ID, Uwe Bach⁵ ID, Anne-Kathrin Baczko⁵ ID, David Ball¹², Mislav Balokovic¹³ ID, John Barrett¹ ID, Michi Bauböck¹⁴ ID, Bradford A. Benson¹⁵,¹⁶ ID, Dan Bintley¹⁷,¹⁸ ID, Lindy Blackburn³,⁷ ID, Raymond Blundell⁷ ID, Katherine L. Bouman¹⁹ ID, Geoffrey C. Bower²⁰,²¹ ID, Hope Boyce²²,²³ ID, Michael Bremer²⁴ ID, Christiaan D. Brinkerink²⁵ ID, Roger Brissenden³,⁷ ID, Silke Britzen⁵ ID, Avery E. Broderick²⁶,²⁷,²⁸ ID, Dominique Broguiere²⁴ ID, Thomas Bronzwaer²⁵ ID, Sandra Bustamante²⁹ ID, Do-Young Byun³⁰,³¹ ID, John E. Carlstrom³²,¹⁶,³³,³⁴ ID, Chiara Ceccobello³⁵ ID, Andrew Chael³⁶,³⁷ ID, Chi-kwan Chan¹²,³⁸,³⁹ ID, Koushik Chatterjee³,⁷ ID, Shami Chatterjee⁴⁰ ID, Ming-Tang Chen²⁰ ID, Yongjun Chen (陈永军)⁴¹,⁴² ID, Xiaopeng Cheng³⁰ ID, Ilje Cho⁴ ID, Pierre Christian⁴³ ID, Nicholas S. Conroy⁴⁴,⁷ ID, John E. Conway³⁵ ID, James M. Cordes⁴⁰ ID, Thomas M. Crawford¹⁶,³² ID, Geoffrey B. Crew¹ ID, Alejandro Cruz-Osorio⁴⁵ ID, Yuzhu Cui (崔玉竹)⁴⁶,⁴⁷,⁴⁸ ID, Jordy Davelaar⁴⁹,⁵⁰,⁵² ID, Mariafelicia De Laurentis⁵¹,⁴⁵,⁵² ID, Roger Deane⁵³,⁵⁴,⁵⁵ ID, Jessica Dempsey¹⁷,¹⁸,⁵⁶ ID,
Gregory Desvignes<fnref n="5" />,<fnref n="5" />,<fnref n="7" /> ID, Jason Dexter⁵⁸ ID, Vedant Dhruv<fnref n="14" /> ID, Sheperd S. Doeleman<fnref n="3" />,<fnref n="7" /> ID, Sean Dougal<fnref n="12" /> ID,
Sergio A. Dzib²⁴,<fnref n="5" /> ID, Ralph P. Eatough⁵⁹,<fnref n="5" /> ID, Razieh Emami<fnref n="7" /> ID, Heino Falcke²⁵ ID, Joseph Farah⁶⁰,⁶¹ ID, Vincent L. Fish<fnref n="1" /> ID,
Ed Fomalont⁶² ID, H. Alyson Ford<fnref n="12" /> ID, Raquel Fraga-Encinas²⁵ ID, William T. Freeman⁶³,⁶⁴ ID, Per Friberg¹⁷,¹⁸ ID,
Christian M. Fromm⁶⁵,⁴⁵,<fnref n="5" /> ID, Antonio Fuentes<fnref n="4" /> ID, Peter Galison<fnref n="3" />,<fnref n="6" />,⁶⁶,⁶⁷ ID, Charles F. Gammie<fnref n="14" />,⁴⁴,⁶⁸ ID, Roberto García²⁴ ID,
Olivier Gentaz²⁴ ID, Boris Georgiev²⁷,²⁸,²⁶ ID, Ciriaco Goddi⁶⁹,⁷⁰ ID, Roman Gold⁷¹,⁴⁵ ID, Arturo I. Gómez-Ruiz⁷²,⁷³ ID,
José L. Gómez<fnref n="4" /> ID, Minfeng Gu (顾敏峰)⁴¹,⁷⁴ ID, Mark Gurwell<fnref n="7" /> ID, Kazuhiro Hada⁴⁷,⁴⁸ ID, Daryl Haggard²²,²³ ID, Kari Haworth<fnref n="7" />,
Michael H. Hecht<fnref n="1" /> ID, Ronald Hesper⁷⁵ ID, Dirk Heumann<fnref n="12" /> ID, Luis C. Ho (何子山)⁷⁶,⁷⁷ ID, Paul Ho<fnref n="9" />,¹⁸ ID,
Mareki Honma⁴⁷,⁴⁸,⁷⁸ ID, Chih-Wei L. Huang<fnref n="9" /> ID, Lei Huang (黄磊)⁴¹,⁷⁴ ID, David H. Hughes⁷² ID, Shiro Ikeda<fnref n="2" />,⁷⁹,⁸⁰,⁸¹ ID,
C. M. Violette Impellizzeri⁸²,⁶² ID, Makoto Inoue<fnref n="9" /> ID, Sara Issaoun<fnref n="7" />,³⁷ ID, David J. James⁸³ ID, Buell T. Jannuzi<fnref n="12" /> ID,
Michael Janssen<fnref n="5" /> ID, Britton Jeter<fnref n="9" /> ID, Wu Jiang (江悟)⁴¹ ID, Alejandra Jiménez-Rosales²⁵ ID, Michael D. Johnson<fnref n="3" />,<fnref n="7" /> ID,
Svetlana Jorstad⁸⁴ ID, Abhishek V. Joshi<fnref n="14" /> ID, Taehyun Jung³⁰,³¹ ID, Mansour Karami²⁶,²⁷ ID, Ramesh Karuppusamy<fnref n="5" /> ID,
Tomohisa Kawashima⁸⁵ ID, Garrett K. Keating<fnref n="7" /> ID, Mark Kettenis⁸⁶ ID, Dong-Jin Kim<fnref n="5" /> ID, Jae-Young Kim⁸⁷,³⁰,<fnref n="5" /> ID,
Jongsoo Kim³⁰ ID, Junhan Kim<fnref n="12" />,¹⁹ ID, Motoki Kino<fnref n="2" />,⁸⁸ ID, Jun Yi Koay<fnref n="9" /> ID, Prashant Kocherlakota⁴⁵ ID, Yutaro Kofuji⁴⁷,⁷⁸ ID,
Patrick M. Koch<fnref n="9" /> ID, Shoko Koyama⁸⁹,<fnref n="9" /> ID, Carsten Kramer²⁴ ID, Michael Kramer<fnref n="5" /> ID, Thomas P. Krichbaum<fnref n="5" /> ID,
Cheng-Yu Kuo⁹⁰,<fnref n="9" /> ID, Noemi La Bella²⁵ ID, Tod R. Lauer⁹¹ ID, Daeyoung Lee<fnref n="14" /> ID, Sang-Sung Lee³⁰ ID, Po Kin Leung⁹² ID,
Aviad Levis¹⁹ ID, Zhiyuan Li (李志远)⁹³,⁹⁴ ID, Rocco Lico<fnref n="4" />,⁹⁵ ID, Greg Lindahl<fnref n="7" /> ID, Michael Lindqvist³⁵ ID, Mikhail Lisakov<fnref n="5" /> ID,
Jun Liu (刘俊)<fnref n="5" /> ID, Kuo Liu<fnref n="5" /> ID, Elisabetta Liuzzo⁹⁶ ID, Wen-Ping Lo<fnref n="9" />,⁹⁷ ID, Andrei P. Lobanov<fnref n="5" /> ID, Laurent Loinard⁹⁸,⁹⁹ ID,
Colin J. Lonsdale<fnref n="1" /> ID, Ru-Sen Lu (路如森)⁴¹,⁴²,<fnref n="5" /> ID, Jirong Mao (毛基荣)¹⁰⁰,¹⁰¹,¹⁰² ID, Nicola Marchili⁹⁶,<fnref n="5" /> ID,
Sera Markoff¹⁰³,¹⁰⁴ ID, Daniel P. Marrone<fnref n="12" /> ID, Alan P. Marscher⁸⁴ ID, Iván Martí-Vidal<fnref n="10" />,<fnref n="11" /> ID, Satoki Matsushita<fnref n="9" /> ID,
Lynn D. Matthews<fnref n="1" /> ID, Lia Medeiros¹⁰⁵,¹⁰⁶,<fnref n="12" /> ID, Karl M. Menten<fnref n="5" /> ID, Daniel Michalik¹⁰⁷,¹⁶ ID, Izumi Mizuno¹⁷,¹⁸ ID,
Yosuke Mizuno⁴⁶,¹⁰⁸,⁴⁵ ID, James M. Moran<fnref n="3" />,<fnref n="7" /> ID, Kotaro Moriyama⁴⁵,<fnref n="1" />,⁴⁷ ID, Monika Moscibrodzka²⁵ ID, Cornelia Müller<fnref n="5" />,²⁵ ID,
Alejandro Mus<fnref n="10" />,<fnref n="11" /> ID, Gibwa Musoke¹⁰³,²⁵ ID, Ioannis Myserlis¹⁰⁹ ID, Andrew Nadolski⁴⁴ ID, Hiroshi Nagai<fnref n="2" />,⁴⁸ ID,
Neil M. Nagar¹¹⁰ ID, Masanori Nakamura¹¹¹,<fnref n="9" /> ID, Ramesh Narayan<fnref n="3" />,<fnref n="7" /> ID, Gopal Narayanan²⁹ ID, Iniyan Natarajan⁵³,¹¹² ID,
Antonios Nathanail⁴⁵,¹¹³ ID, Santiago Navarro Fuentes¹⁰⁹ ID, Joey Neilsen¹¹⁴ ID, Roberto Neri²⁴ ID, Chunchong Ni²⁷,²⁸,²⁶ ID,
Aristeidis Noutsos<fnref n="5" /> ID, Michael A. Nowak¹¹⁵ ID, Junghwan Oh¹¹⁶ ID, Hiroki Okino⁴⁷,⁷⁸ ID, Héctor Olivares²⁵ ID,
Gisela N. Ortiz-León⁹⁹,<fnref n="5" /> ID, Tomoaki Oyama⁴⁷ ID, Daniel C. M. Palumbo<fnref n="3" />,<fnref n="7" /> ID, Georgios Filippos Paraschos<fnref n="5" /> ID, Jongho Park<fnref n="9" />,¹¹⁷ ID,
Harriet Parsons¹⁷,¹⁸ ID, Nimesh Patel<fnref n="7" /> ID, Ue-Li Pen<fnref n="9" />,²⁶,¹¹⁸,¹¹⁹,¹²⁰ ID, Dominic W. Pesce<fnref n="7" />,<fnref n="3" /> ID, Vincent Piétu²⁴ ID,
Richard Plambeck¹²¹ ID, Aleksandar PopStefanija²⁹ ID, Oliver Porth¹⁰³,⁴⁵ ID, Felix M. Pötzl¹²²,<fnref n="5" /> ID, Ben Prather<fnref n="14" /> ID,
Jorge A. Preciado-López²⁶ ID, Hung-Yi Pu¹²³,¹²⁴,<fnref n="9" /> ID, Venkatessh Ramakrishnan¹¹⁰,¹²⁵,¹²⁶ ID, Ramprasad Rao<fnref n="7" /> ID,
Mark G. Rawlings¹²⁷,¹⁷,¹⁸ ID, Alexander W. Raymond<fnref n="3" />,<fnref n="7" /> ID, Luciano Rezzolla⁴⁵,¹²⁸,¹²⁹ ID, Angelo Ricarte<fnref n="7" />,<fnref n="3" /> ID,
Bart Ripperda¹³⁰,⁵⁰ ID, Greek Roelofs<fnref n="7" />,<fnref n="3" />,²⁵ ID, Alan Rogers<fnref n="1" /> ID, Eduardo Ros<fnref n="5" /> ID, Cristina Romero-Cañizales<fnref n="9" /> ID,
Arash Roshanineshat<fnref n="12" /> ID, Helge Rottmann<fnref n="5" /> ID, Alan L. Roy<fnref n="5" /> ID, Ignacio Ruiz¹⁰⁹ ID, Chet Ruszczyk<fnref n="1" /> ID, Kazi L. J. Rygl⁹⁶ ID,
Salvador Sánchez¹⁰⁹ ID, David Sánchez-Argüelles⁷²,⁷³ ID, Miguel Sánchez-Portal¹⁰⁹ ID, Mahito Sasada¹³¹,⁴⁷,¹³² ID,
Kaushik Satapathy<fnref n="12" /> ID, Tuomas Savolainen¹³³,¹²⁶,<fnref n="5" /> ID, F. Peter Schloerb²⁹ ID, Jonathan Schonfeld<fnref n="7" /> ID, Karl-Friedrich Schuster²⁴ ID,
Lijing Shao⁷⁷,<fnref n="5" /> ID, Zhiqiang Shen (沈志强)⁴¹,⁴² ID, Des Small⁸⁶ ID, Bong Won Sohn¹⁷,¹⁸,³⁰,³¹,¹³⁴ ID, Jason SooHoo<fnref n="1" /> ID,
Kamal Souccar²⁹ ID, He Sun (孙赫)¹⁹ ID, Fumie Tazaki⁴⁷ ID, Alexandra J. Tetarenko¹³⁵,³⁷ ID, Paul Tiede<fnref n="7" />,<fnref n="3" /> ID,
Remo P. J. Tilanus<fnref n="12" />,²⁵,⁸²,¹³⁶ ID, Michael Titus<fnref n="1" /> ID, Pablo Torne¹⁰⁹,<fnref n="5" /> ID, Efthalia Traianou<fnref n="4" />,<fnref n="5" /> ID, Tyler Trent<fnref n="12" /> ID, Sascha Trippe¹³⁷ ID,
Matthew Turk⁴⁴ ID, Ilse van Bemmel⁸⁶ ID, Huib Jan van Langevelde⁸⁶,⁸²,¹³⁸ ID, Daniel R. van Rossum²⁵ ID, Jesse Vos²⁵ ID,
Jan Wagner<fnref n="5" /> ID, Derek Ward-Thompson¹³⁹ ID, John Wardle¹⁴⁰ ID, Jonathan Weintroub<fnref n="3" />,<fnref n="7" /> ID, Norbert Wex<fnref n="5" /> ID, Robert Wharton<fnref n="5" /> ID,
Maciek Wielgus<fnref n="5" /> ID, Kaj Wiik¹⁴¹ ID, Gunther Witzel<fnref n="5" /> ID, Michael F. Wondrak²⁵,¹⁴² ID, George N. Wong¹⁰⁶,¹⁴³ ID, Qingwen Wu
(吴庆文)¹⁴⁴ ID, Paul Yamaguchi<fnref n="7" /> ID, Doosoo Yoon¹⁰³ ID, André Young²⁵ ID, Ken Young<fnref n="7" /> ID, Ziri Younsi¹⁴⁵,⁴⁵ ID, Feng Yuan
(袁峰)⁴¹,⁷⁴,¹⁴⁶ ID, Ye-Fei Yuan (袁业飞)¹⁷,¹⁸,¹⁴⁷ ID, J. Anton Zensus<fnref n="5" /> ID, Shuo Zhang¹⁴⁸ ID, Guang-Yao Zhao<fnref n="4" /> ID, Shan-Shan Zhao
(赵杉杉)⁴¹ ID, and Dominic O. Chang<fnref n="3" />,<fnref n="7" />

<footnote n="1">¹ Massachusetts Institute of Technology Haystack Observatory, 99 Millstone Road, Westford, MA 01886, USA; D'Ward-Thompson@uclan.ac.uk</footnote>

<footnote n="2">² National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan</footnote>

<footnote n="3">³ Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA</footnote>

<footnote n="4">⁴ Instituto de Astrofísica de Andalucía-CSIC, Glorieta de la Astronomía s/n, E-18008 Granada, Spain</footnote>

<footnote n="5">⁵ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn, Germany</footnote>

<footnote n="6">⁶ Department of Physics, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, Malaysia</footnote>

<footnote n="7">⁷ Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA</footnote>

<footnote n="8">⁸ Department of Physics & Astronomy, The University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249, USA</footnote>

<footnote n="9">⁹ Institute of Astronomy and Astrophysics, Academia Sinica, 11F of Astronomy-Mathematics Building, AS/NTU No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan,
R.O.C.</footnote>

<footnote n="10">¹⁰ Departament d'Astronomia i Astrofísica, Universitat de València, C. Dr. Moliner 50, E-46100 Burjassot, València, Spain</footnote>

<footnote n="11">¹¹ Observatori Astronòmic, Universitat de València, C. Catedrático José Beltrán 2, E-46980 Paterna, València, Spain</footnote>

<footnote n="12">¹² Steward Observatory and Department of Astronomy, University of Arizona, 933 N. Cherry Ave., Tucson, AZ 85721, USA</footnote>

<footnote n="13">¹³ Yale Center for Astronomy & Astrophysics, Yale University, 52 Hillhouse Avenue, New Haven, CT 06511, USA</footnote>

<footnote n="14">¹⁴ Department of Physics, University of Illinois, 1110 West Green Street, Urbana, IL 61801, USA</footnote>

<footnote n="15">¹⁵ Fermi National Accelerator Laboratory, MS209, P.O. Box 500, Batavia, IL 60510, USA</footnote>
¹⁶ Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA

¹⁷ East Asian Observatory, 660 N. A'ohoku Place, Hilo, HI 96720, USA

¹⁸ James Clerk Maxwell Telescope (JCMT), 660 N. A'ohoku Place, Hilo, HI 96720, USA

¹⁹ California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, USA

²⁰ Institute of Astronomy and Astrophysics, Academia Sinica, 645 N. A'ohoku Place, Hilo, HI 96720, USA

²¹ Department of Physics and Astronomy, University of Hawaii at Manoa, 2505 Correa Road, Honolulu, HI 96822, USA

²² Department of Physics, McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada

²³ McGill Space Institute, McGill University, 3550 rue University, Montréal, QC H3A 2A7, Canada

²⁴ Institut de Radioastrophysique Millimétrique (IRAM), 300 rue de la Piscine, F-38406 Saint Martin d'Hères, France

²⁵ Department of Astrophysics, Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radboud University, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands

²⁶ Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo, ON N2L 2Y5, Canada

²⁷ Department of Physics and Astronomy, University of Waterloo, 200 University Avenue W, Waterloo, ON N2L 3G1, Canada

²⁸ Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, ON N2L 3G1, Canada

²⁹ Department of Astronomy, University of Massachusetts, Amherst, MA 01003, USA

³⁰ Korea Astronomy and Space Science Institute, Daedok-daero 776, Yuseong-gu, Daejeon 34055, Republic Of Korea

³¹ University of Science and Technology, Gajeong-ro 217, Yuseong-gu, Daejeon 34113, Republic Of Korea

³² Kavli Institute for Cosmological Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA

³³ Department of Physics, University of Chicago, 5720 South Ellis Avenue, Chicago, IL 60637, USA

³⁴ Enrico Fermi Institute, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA

³⁵ Department of Space, Earth and Environment, Chalmers University of Technology, Onsala Space Observatory, SE-43992 Onsala, Sweden

³⁶ Princeton Center for Theoretical Science, Jadwin Hall, Princeton University, Princeton, NJ 08544, USA

³⁷ NASA Hubble Fellowship Program, Einstein Fellow

³⁸ Data Science Institute, University of Arizona, 1230 N. Cherry Ave., Tucson, AZ 85721, USA

³⁹ Program in Applied Mathematics, University of Arizona, 617 N. Santa Rita, Tucson, AZ 85721

⁴⁰ Cornell Center for Astrophysics and Planetary Science, Cornell University, Ithaca, NY 14853, USA

⁴¹ Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, People's Republic of China

⁴² Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, Nanjing 210008, People's Republic of China

⁴³ Physics Department, Fairfield University, 1073 North Benson Road, Fairfield, CT 06824, USA

⁴⁴ Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 West Green Street, Urbana, IL 61801, USA

⁴⁵ Institut für Theoretische Physik, Goethe-Universität Frankfurt, Max-von-Laue-Straße 1, D-60438 Frankfurt am Main, Germany

⁴⁶ Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shengrong Road 520, Shanghai, 201210, People's Republic of China

⁴⁷ Mizusawa VLBI Observatory, National Astronomical Observatory of Japan, 2-12 Hoshigaoka, Mizusawa, Oshu, Iwate 023-0861, Japan

⁴⁸ Department of Astronomical Science, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

⁴⁹ Department of Astronomy and Columbia Astrophysics Laboratory, Columbia University, 550 W. 120th Street, New York, NY 10027, USA

⁵⁰ Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA

⁵¹ Dipartimento di Fisica "E. Pancini," Università di Napoli "Federico II," Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli, Italy

⁵² INFN Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli, Italy

⁵³ Wits Centre for Astrophysics, University of the Witwatersrand, 1 Jan Smuts Avenue, Braamfontein, Johannesburg 2050, South Africa

⁵⁴ Department of Physics, University of Pretoria, Hatfield, Pretoria 0028, South Africa

⁵⁵ Centre for Radio Astronomy Techniques and Technologies, Department of Physics and Electronics, Rhodes University, Makhanda 6140, South Africa

⁵⁶ ASTRON, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands

⁵⁷ LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Jules Janssen, F-92195 Meudon, France

⁵⁸ JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309, USA

⁵⁹ National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing 100101, People's Republic of China

⁶⁰ Las Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, CA 93117-5575, USA

⁶¹ Department of Physics, University of California, Santa Barbara, CA 93106-9530, USA

⁶² National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA

⁶³ Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 32-D476, 77 Massachusetts Ave., Cambridge, MA 02142, USA

⁶⁴ Google Research, 355 Main St., Cambridge, MA 02142, USA

⁶⁵ Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Emil-Fischer-Str. 31, D-97074 Würzburg, Germany

⁶⁶ Department of History of Science, Harvard University, Cambridge, MA 02138, USA

⁶⁷ Department of Physics, Harvard University, Cambridge, MA 02138, USA

⁶⁸ NCSA, University of Illinois, 1205 W. Clark St., Urbana, IL 61801, USA

⁶⁹ Dipartimento di Fisica, Università degli Studi di Cagliari, SP Monserrato-Sestu km 0.7, I-09042 Monserrato, Italy

⁷⁰ INAF—Osservatorio Astronomico di Cagliari, Via della Scienza 5, I-09047, Selargius, CA, Italy

⁷¹ CP3-Origins, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark

⁷² Instituto Nacional de Astrofísica, Óptica y Electrónica. Apartado Postal 51 y 216, 72000. Puebla Pue., México

⁷³ Consejo Nacional de Ciencia y Tecnología, Av. Insurgentes Sur 1582, 03940, Ciudad de México, México

⁷⁴ Key Laboratory for Research in Galaxies and Cosmology, Chinese Academy of Sciences, Shanghai 200030, People's Republic of China

⁷⁵ NOVA Sub-mm Instrumentation Group, Kapteyn Astronomical Institute, University of Groningen, Landleven 12, 9747 AD Groningen, The Netherlands

⁷⁶ Department of Astronomy, School of Physics, Peking University, Beijing 100871, People's Republic of China

⁷⁷ Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, People's Republic of China

⁷⁸ Department of Astronomy, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

⁷⁹ The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo, 190-8562, Japan

⁸⁰ Department of Statistical Science, The Graduate University for Advanced Studies (SOKENDAI), 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan

⁸¹ Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan

⁸² Leiden Observatory, Leiden University, Postbus 2300, 9513 RA Leiden, The Netherlands

⁸³ ASTRAVEO LLC, PO Box 1668, Gloucester, MA 01931

⁸⁴ Institute for Astrophysical Research, Boston University, 725 Commonwealth Ave., Boston, MA 02215, USA

⁸⁵ Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8582, Japan

⁸⁶ Joint Institute for VLBI ERIC (JIVE), Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands

⁸⁷ Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 702-701, Republic Of Korea

⁸⁸ Kogakuin University of Technology & Engineering, Academic Support Center, 2665-1 Nakano, Hachioji, Tokyo 192-0015, Japan
⁸⁹ Niigata University, 8050 Ikarashi-nino-cho, Nishi-ku, Niigata 950-2181, Japan

⁹⁰ Physics Department, National Sun Yat-Sen University, No. 70, Lien-Hai Road, Kaosiung City 80424, Taiwan, R.O.C.

⁹¹ National Optical Astronomy Observatory, 950 N. Cherry Ave., Tucson, AZ 85719, USA

⁹² Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

⁹³ School of Astronomy and Space Science, Nanjing University, Nanjing 210023, People's Republic of China

⁹⁴ Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University, Nanjing 210023, People's Republic of China

⁹⁵ INAF-Istituto di Radioastronomia, Via P. Gobetti 101, I-40129 Bologna, Italy

⁹⁶ INAF-Istituto di Radioastronomia & Italian ALMA Regional Centre, Via P. Gobetti 101, I-40129 Bologna, Italy

⁹⁷ Department of Physics, National Taiwan University, No.1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan, R.O.C.

⁹⁸ Instituto de Radioastronomia y Astrofísica, Universidad Nacional Autónoma de México, Morelia 58089, México

⁹⁹ Instituto de Astronomía, Universidad Nacional Autónoma de México (UNAM), Apdo Postal 70-264, Ciudad de México, México

¹⁰⁰ Yunnan Observatories, Chinese Academy of Sciences, 650011 Kunming, Yunnan Province, People's Republic of China

¹⁰¹ Center for Astronomical Mega-Science, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, 100012, People's Republic of China

¹⁰² Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, 650011 Kunming, People's Republic of China

¹⁰³ Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands

¹⁰⁴ Gravitation and Astroparticle Physics Amsterdam (GRAPPA) Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands

¹⁰⁵ NSF Astronomy and Astrophysics Postdoctoral Fellow

¹⁰⁶ School of Natural Sciences, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, USA

¹⁰⁷ Science Support Office, Directorate of Science, European Space Research and Technology Centre (ESA/ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands

¹⁰⁸ School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, People's Republic of China

¹⁰⁹ Institut de Radioastronomie Millimétrique (IRAM), Avenida Divina Pastora 7, Local 20, E-18012, Granada, Spain

¹¹⁰ Astronomy Department, Universidad de Concepción, Casilla 160-C, Concepción, Chile

¹¹¹ National Institute of Technology, Hachinohe College, 16-1 Uwanotai, Tamonoki, Hachinohe City, Aomori 039-1192, Japan

¹¹² South African Radio Astronomy Observatory, Observatory 7925, Cape Town, South Africa

¹¹³ Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, GR 15783 Zografos, Greece

¹¹⁴ Department of Physics, Villanova University, 800 Lancaster Avenue, Villanova, PA 19085, USA

¹¹⁵ Physics Department, Washington University CB 1105, St. Louis, MO 63130, USA

¹¹⁶ Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul, Republic of Korea

¹¹⁷ EACOA Fellow

¹¹⁸ Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada

¹¹⁹ Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada

¹²⁰ Canadian Institute for Advanced Research, 180 Dundas St. W., Toronto, ON M5G 1Z8, Canada

¹²¹ Radio Astronomy Laboratory, University of California, Berkeley, CA 94720, USA

¹²² Department of Physics, University College Cork, Kane Building, College Road, Cork T12 K8AF, Ireland

¹²³ Department of Physics, National Taiwan Normal University, No. 88, Sec. 4, Tingzhou Rd., Taipei 116, Taiwan, R.O.C.

¹²⁴ Center of Astronomy and Gravitation, National Taiwan Normal University, No. 88, Sec. 4, Tingzhou Road, Taipei 116, Taiwan, R.O.C.

¹²⁵ Finnish Centre for Astronomy with ESO, FI-20014 University of Turku, Finland

¹²⁶ Aalto University Metsähovi Radio Observatory, Metsähovintie 114, FI-02540 Kylmälä, Finland

¹²⁷ Gemini Observatory/NSF NOIRLab, 670 N. A'ohokū Place, Hilo, HI 96720, USA

¹²⁸ Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, 60438 Frankfurt, Germany

¹²⁹ School of Mathematics, Trinity College, Dublin 2, Ireland

¹³⁰ Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA

¹³¹ Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan

¹³² Hiroshima Astrophysical Science Center, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan

¹³³ Aalto University Department of Electronics and Nanoengineering, PL 15500, FI-00076 Aalto, Finland

¹³⁴ Department of Astronomy, Yonsei University, Yonsei-ro 50, Seodaemun-gu, 03722 Seoul, Republic of Korea

¹³⁵ Department of Physics and Astronomy, Texas Tech University, Lubbock, TX 79409-1051, USA

¹³⁶ Netherlands Organisation for Scientific Research (NWO), Postbus 93138, 2509 AC Den Haag, The Netherlands

¹³⁷ Department of Physics and Astronomy, Seoul National University, Gwanak-gu, Seoul 08826, Republic of Korea

¹³⁸ University of New Mexico, Department of Physics and Astronomy, Albuquerque, NM 87131, USA

¹³⁹ Jeremiah Horrocks Institute, University of Central Lancashire, Preston PR1 2HE, UK

¹⁴⁰ Physics Department, Brandeis University, 415 South Street, Waltham, MA 02453, USA

¹⁴¹ Tuorla Observatory, Department of Physics and Astronomy, University of Turku, Finland

¹⁴² Radboud Excellence Fellow of Radboud University, Nijmegen, The Netherlands

¹⁴³ Princeton Gravity Initiative, Princeton University, Princeton, NJ 08544, USA

¹⁴⁴ School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, People's Republic of China

¹⁴⁵ Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking, Surrey, RH5 6NT, UK

¹⁴⁶ School of Astronomy and Space Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing 100049, People's Republic of China

¹⁴⁷ Astronomy Department, University of Science and Technology of China, Hefei 230026, People's Republic of China

¹⁴⁸ Bard College, 30 Campus Road, Annandale-on-Hudson, NY 12504, USA