RadioAstron Space VLBI Imaging of the Jet in M87. I. Detection of High Brightness Temperature at 22 GHz

M87 was observed by the RadioAstron mission at 22.236 GHz (λ = 1.3 cm; K band) from 2014 February 4, 16:00 to 2014 February 5, 12:53 UT, as a part of the Nearby AGN Key Science Program (experiment code raks03b; gs032; see, e.g., Bruni et al. 2020 for the description of the program). The ground array consisted of in total 21 telescopes. Their names, VLBI station code, antenna diameters, and SEFDs estimated from the station DPFU and system temperatures during the imaging observations are listed in Table 1. The ground stations observed the source and calibrators 1226 + 032 (3C 273) and PKS 1236 + 077 in both left- and right-handed circular polarizations (LCP and RCP, respectively), at an central observing frequency of 22.236 GHz with a total bandwidth of 32 MHz (total data bit rate of 256 Mbps with 2 bit sampling) using two intermediate frequency (IF) bands (thus 16 MHz per IF per polarization). The Space Radio Telescope (SRT) simultaneously observed M87 at both 5 and 22 GHz bands, with the same 64 MHz total bandwidth (total data bit rate of 128 Mbps with 1 bit sampling), using two IFs at each band and only in LCP. This setup resulted in the data bandwidth of 16 MHz per IF per polarization. We refer to E. V. Kravchenko et al. (2023, in preparation) for the reduction, analysis, and discussions of the 5 GHz band data. The maximum distance to the SRT was ∼11.5 Earth diameter (D_Earth), corresponding to the fringe spacing of ∼10.9Gλ at our observing frequency. The projected (u, v) coverage is shown in Figure 1. We note the highly elongated orbit of the spacecraft in the E–W direction, which gives higher resolution along the direction of the nearly E–W oriented jet in M87 87.

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The observed raw data were correlated at the Max-Planck-Institut für Radioastronomie using the DiFX correlator (Deller et al. 2011), adjusted for space VLBI in order to account for the special and general relativistic effects related to the orbiting antenna (Bruni et al. 2016). Before fully processing the post-correlation data set, we first examined the quality of ground-to-space baseline fringes using PIMA (Petrov et al. 2011), by making use of the baseline-based fringe algorithm, to inspect residuals of the fringe rates due to the acceleration of the orbiting antenna. We note that PIMA has unique advantages for calibrating the space baselines. Specifically, the program can accurately determine the space-antenna acceleration term and thus significantly constrain ranges of the residual fringe solutions in the subsequent calibration. For this reason, PIMA has been routinely used for post-correlation calibration of RadioAstron observations. Fringes were clearly detected at <1D_Earth baselines at PIMA signal-to-noise ratio (S/N) values of ∼8–72, while there was no clear initial fringe detection at longer (u, v) spacings. ²⁰ After this examination, the post-correlation data were loaded into the Astronomical Image Processing System (AIPS) software (Greisen 2003) in order to perform the full a priori calibrations and, more importantly, to improve the fringe detection for ground-space baselines, taking the advantage of the antenna-based global fringe-fitting algorithm, which can stack baselines after phase-calibrating the ground stations (see other literature for further details, e.g., Gómez et al. 2016; Thompson et al. 2017; Savolainen et al. 2021). We note that the subsequent AIPS calibration still made use of the PIMA results in the cross-comparison of the fringe solutions for robust fringe detections. In the following, we describe the details of the AIPS data calibration. To start with, we only calibrated the ground-based stations in order to obtain a ground-only image of M87 that can provide a source model for improved fringe fitting of the space baselines (see, e.g., Giovannini et al. 2018; Savolainen et al. 2021). In particular, the manual phase and delay offsets of each ground antenna were determined using high-S/N scans on the calibrators. Already at this early stage, we could not find any fringes to AT and MP. Accordingly, these stations were dropped out from further analysis. Then, a global fringe fitting was performed, using the AIPS FRING task, setting an S/N threshold of 4.5. Solutions were successfully found for most of the scans. The left panel of Figure 2 shows the fringe detection and the corresponding (u, v) coverage of the ground array. The a priori amplitude calibration was performed using the AIPS task APCAL, based on the aperture efficiencies and system temperature measurements. Bandpasses of ground stations were also calibrated using their autocorrelation power spectra.

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The ground-array-only data were exported outside AIPS for imaging of M87 in the Difmap software (Shepherd et al. 1994) using the CLEAN algorithm. By making iterative use of the CLEAN task and phase and amplitude self-calibrations, we obtained an image of the jet of M87 at an angular resolution of 0.19 × 0.30 mas (0.22 × 0.70 mas) at the beam major axis position angle of −1° (−7°) with uniform (natural) weighting.

This image was loaded back into AIPS and later used as a model for the global fringe fitting of the SRT with respect to the sensitive reference antennas EF and GB (see also other literature, e.g., Gómez et al. 2016; Giovannini et al. 2018; Savolainen et al. 2021, for the details of calibrating the SRT). Before fringe fitting the SRT, we applied additional global fringe fitting of only the ground stations with a short solution interval of 1 minute by AIPS FRING, using the ground-only M87 jet image as a model. This step was meant to self-calibrate rapid phase fluctuations due to the atmosphere and thus improve the coherence timescales for baselines to the SRT (i.e., over several minutes). Next, we performed manual phase-calibrations of the SRT by selecting scans on M87 at short (u, v) spacing (<1D_ED; near the perigee), successfully obtaining suitable delay solutions at both IFs.

After connecting the two IFs in phase, we began searching for fringe solutions scan-by-scan using AIPS FRING by combining the two IFs, starting from short to long baselines, with a progressively increasing fringe solution interval of 1–10 minutes. This implementation was necessary to take into account the acceleration of the SRT at short (u, v) spacings (e.g., <1D_Earth), which in turn introduces large phase and delay rate drifts and practically limits the coherence time. In addition, we took the advantage of the phased-calibrated ground array to stack ground baselines connecting the reference stations EF and GB to SRT, setting AIPS FRING dparm(1) = 3. To examine the quality of the fringe solutions and judge on the fringe detection, we particularly searched for smooth and continuous change of the delays and delay rates in time (also in the (u, v) distance) so that we can avoid selecting spurious peaks in the fringe search window. At the short <1D_Earth distances to the SRT, we successfully obtained continuously varying fringe solutions with the AIPS fringe peak S/N of >6 and consistently small residual delays and delay rates at both IFs. Here, "AIPS S/N" refers to the peak-to-noise ratio from the initial baseline-based signal search with simple fast Fourier transform (FFT), and the final, global fringe S/N after the least-square stage is higher (see, e.g., Schwab & Cotton 1983). The right panel of Figure 2 shows the space fringe detections at the <1D_Earth baselines. We also show the time evolution of the fringe solutions in Figure 3. The time-evolving rate and jumps over the scans indicate clear fringe residuals due to the acceleration of the spacecraft near the perigee. These fringe delays and rates, obtained from AIPS, were also consistent with values from the initial PIMA fringe search, providing further confidence on the source detection.

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At >1D_Earth, we first calibrated away a large delay offset of ∼1 μs for the SRT, which was already known from simultaneous RadioAstron 4.8 GHz observations of M87 (E. V. Kravchenko et al. 2023, in preparation). Then, we adopted the full length of each scan, ∼10 min, as the solution interval of AIPS FRING with an S/N threshold of 3, using narrow delay and rate windows. From this, we were able to find fringes to the SRT up to ∼2.8D_Earth baseline length (∼3 G λ) at an AIPS initial FFT S/N value of 3.4. The corresponding improvement of these detections for the final (u, v) coverage are highlighted in color in the right panel of Figure 2. The significance of this detection was rigorously tested in multiple ways, including inspection of how much the fringe solutions in two different IFs were consistent and quantitative analysis of the probability of false fringe detection using a dedicated Monte Carlo simulation. The latter was performed following Petrov et al. (2011) and Savolainen et al. (2021). More details of the Monte Carlo simulation are presented in Appendix A. After these tests, we were confident with the source detection at this (u, v) spacing, with the false fringe detection probability of <10⁻⁴. We also show in Figure 4 example closure phases of the fringe-detected scans. The upper panel shows closure phases in the small triangle whose values are centered nearly around ∼0° with some scatter, indicating a symmetric source structure. The zero closure phases can be due to the bright Gaussian-shaped VLBI core, which is symmetric. On the other hand, clear and nonzero closure phases in the large triangle (bottom panel) suggest the presence of a complex source structure within the beam of the ground array.

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At even longer baseline lengths (>3D_Earth), we could not find any reliable fringe-fit solutions to the SRT, and thus concluded >3D_Earth scans were nondetections. We also tried to apply bandpass corrections for the SRT, but we did not obtain reasonable solutions, and those solutions did not improve the fringe detection rates in subsequent attempts to fringe-fit the data. Therefore, we did not correct for the bandpass of the SRT.

The fully calibrated data set was finally exported from AIPS for imaging with Difmap. First, we loaded the data set into Difmap and applied amplitude self-calibration loops to the ground-only array using the CLEAN model of the ground-only image, to prepare a final imaging-ready data set. The ground-only model was removed at this point, to take advantage of the higher angular resolution with the addition of the SRT. We then applied iterative CLEAN and phase-only self-calibrations, with the selfcal solution interval down to 1 min for the SRT (i.e., equivalent to that of AIPS FRING) and adopting the CLEAN windows of the ground-only model. The latter especially helped avoid oversubtraction of spurious CLEAN components in the counterjet region. In the course of imaging, we tested various combinations of parameters in Difmap, in particular the (u, v) weighting by choosing UVWEIGHT = (0, −1), (2, 0), (5, 0), (2, −1), and (5, −1) (the third and last so-called superuniform weighting; see Gómez et al. 2016; Giovannini et al. 2018; Savolainen et al. 2021). We found that the choice of (2, −1) provided the best compromise for the angular resolution, image sensitivity, and overall reliability of the resulting image against overfitting thermal noises and systematic sidelobes. We also attempted to self-calibrate the amplitudes of the SRT but only derived a single constant correction factor, in order to investigate the accuracy of the amplitude calibration of the SRT. The self-calibration resulted in ≲10% change in the amplitude of the SRT. This correction neither changed the image quality nor major features in the image significantly. Therefore, we did not apply further amplitude self-calibration solutions.

Before determining the final image, we examined the reliability of detailed features in the map by (i) imaging the real data set by different authors without their mutual interactions about the images, and (ii) creating and imaging a realistic synthetic data set, which adopted the same S/N ratio and (u, v) coverage as the real observation, and also adopted a known ground-truth source image. Details of the synthetic data generation and imaging tests are described in Appendix B. These tests provided confidence that the presence of the counterjet, well-resolved nucleus of the jet, and their overall structure are reliable. In the end, a final image was produced at an angular resolution of 0.15 × 0.47 mas with uvweight =(2, −1) at a beam position angle (PA) of −16°. For completeness information, we also report the beam sizes corresponding to the uniform and superuniform weightings from uvweight=(2,0), (5,0), and (5,-1), which are 0.10 × 0.32 mas at PA −202, 0.09 × 0.28 mas at PA −204, and 0.14 × 0.41 mas at PA −163, respectively.

For comprehensive multiwavelength analysis of the jet in M87, the source was also observed by the Very Long Baseline Array (VLBA) on 2014 February 5 at 08:09−12:46 UT, which was interleaved with RadioAstron scans (see Section 2.1). The VLBA observation was configured with the central observing frequency of 43.136 GHz with a total bandwidth of 64 MHz in two circular polarizations (LCP and RCP), split between two 16 MHz IFs. Standard procedures were similarly applied to fringe-fit the data and calibrate the amplitudes in AIPS, and to image the source structure in Difmap. For the imaging in Stokes I, the data were averaged over 30 s in time; see descriptions for the ground-array data in Section 2.1. A final image was obtained at an angular resolution of 0.15 × 0.37 mas with the beam position angle of −16.

In addition to the imaging experiment, M87 was regularly monitored by RadioAstron as part of the AGN survey program (see Kovalev et al. 2020). The survey observations were performed in the visibility tracking (nonimaging) mode with few ground stations participating in each experiment. If fringes to the space baselines are detected, comparing the correlated flux densities measured at ground-ground and ground-space baselines to a simple Gaussian source model can provide estimates for the angular size and brightness temperature of a source from such snapshot observation. The survey observations expand to much longer in the (u, v) space, up to ∼25 Gλ. Those observations were made during 2013–2016, and therefore it is not straightforward to directly combine those complex visibilities with the 22 GHz imaging data. In spite of the limitation, however, the survey data still provide significant constraints on the presence or absence of any small-scale structure in the jet of M87 in the time-averaged sense. Also, adding the survey data to the imaging observation can potentially boost the angular resolution of the final image (e.g., Gómez et al. 2022). Therefore, we also adopted those data sets to search for the most compact structure in M87 at 22 GHz. More details of those data, including the scheduling, observation, data reduction, and analysis can be found in Kovalev et al. (2020).

In this work, we identify the VLBI core as the most compact and brightest component at the base of the approaching jet, which is the location of the intensity peak. To characterize the basic properties of this region, we fitted an elliptical Gaussian to the region close to the peak of the intensity. Before doing so, we subtracted from the visibility CLEAN components outside ±0.3 mas and ±0.1 mas from the peak in R.A. and decl., to avoid fitting the extended jet emission by the core Gaussian model. We note that an elliptical Gaussian is more reliable than fitting several smaller circular Gaussians, when defining the overall size of the nucleus and estimating brightness temperature, since the latter can be strongly affected by the size estimate (e.g., Kovalev et al. 2005; Jorstad et al. 2017). For the actual fitting, we primarily use the modelfit procedure implemented in Difmap to fit the Gaussian to the long baseline visibilities. We note that statistical uncertainties of the fitted parameters can be, in principle, determined using the parameters and residuals of the fit (e.g., Fomalont 1999). However, the underlying systematic uncertainties can be significantly larger in our case, due to the highly elongated (u, v) coverage of the space VLBI observation. Therefore, we performed an independent fit of the elliptical Gaussian in the image domain, using the JMFIT task in AIPS (see, e.g., Hada et al. 2013, 2016). We note that the image plane method can also well describe the overall nuclear region, as long as the main interest is the overall size and flux density of a feature and not the fine-scale subnuclear structures that are often smaller than the nominal beam.

After having performed these fitting procedures and obtained the parameters, we took the average of the fitted parameters from the image and visibility and half of their differences as the values and associated uncertainties of the Gaussian modelfit parameters. This approach resulted in the following uncertainties for the fitted parameters: ∼10% (0.09 Jy) for the flux density, ∼11% (0.04 mas), and ∼8% (0.01 mas) for the sizes along the major and minor axes, respectively, and accordingly ∼18% for the brightness temperature (see Section 4). The ∼10% flux error is slightly larger than the usual flux uncertainties of ∼5% for the Gaussian modeling of well-separated jet components in typical centimeter-VLBI observations (e.g., Lister et al. 2009). On the other hand, the size uncertainties are of the order of ∼10% of the space VLBI beam size, which might still be slightly underestimated compared to ∼20% beam sizes that were suggested as characteristic size errors by other studies (see, e.g., Homan et al. 2002; Lister et al. 2009; Jorstad et al. 2017 and references therein). We note that adopting the larger 20% size error could increase the brightness temperature uncertainty by ∼30%; however, this is not large enough to affect the main findings of our observations (in Section 4) and discussions (in Section 5), and therefore we do not discuss it further.

Even though significant fringes are not found for the long >3D_Earth baselines, it is possible to estimate their flux upper limits and obtain further insights about the most compact structure in the source (e.g., Johnson et al. 2021). To this end, we analyzed more deeply the probability density distributions of fringes of all of the scans with the SRT to determine at what σ level the space baselines are not detected. For this analysis, we have primarily chosen PIMA because the software provides well-understood statistics for the fringe fitting in the low-S/N regime (see Petrov et al. 2011). We have also performed similar calculations with AIPS for cross-checks. The detailed procedures for the generation of the probability density distributions, their inspection, and cross-comparison between PIMA and AIPS results are discussed in Appendix A. By comparing the independent PIMA and AIPS fringe-fit results, we found consistent detections and nondetections, when a false fringe detection probability of 10⁻⁴ was chosen in PIMA (corresponding to PIMA and AIPS S/N threshold values of ∼6.1 and ∼3.3, respectively). Accordingly, we ran the PIMA fringe search for all of the scans and obtained the amplitude of each scan (A_calib) or its upper limit (A_upper), depending on their statistical significance with respect to the threshold false probability value 10⁻⁴. Specifically, the amplitude A_calib is obtained by A_calib = A_raw × SEFD_net where A_raw is the raw visibility amplitude (i.e., correlation coefficients), and ${\mathrm{SEFD}}_{\mathrm{net}}=\sqrt{{\mathrm{SEFD}}_{1}{\mathrm{SEFD}}_{2}}$ is the net system equivalent flux density that can be estimated from the antenna gains and system temperature information of two antennas 1 and 2 of each baseline. As for the nondetection cases, A_upper is obtained by ${A}_{\mathrm{upper}}={A}_{\mathrm{raw}}\times {\mathrm{SEFD}}_{\mathrm{net}}\times ({\rm{S}}/{{\rm{N}}}_{\det }/{\rm{S}}/{\rm{N}})$ where "S/N" is the S/N value from PIMA and ${\rm{S}}/{{\rm{N}}}_{\det }=6.1$ is the aforementioned detection threshold (i.e., A_upper = A_calib if S/N = 6.1 and A_upper > A_calib otherwise).

Since this analysis can be extended to any data set from RadioAstron observations of M87, we have also incorporated more interferometric 22 GHz flux density measurements of M87 from the RadioAstron AGN survey observations. Applying the same analysis by PIMA yielded the corresponding flux upper limits on baseline lengths of up to ∼25 Gλ.

We additionally note on the uncertainties of A_upper. We consider the S/N of each data point to be estimated as accurately as possible, based on the dedicated Monte Carlo simulations. Thus, the dominating error can originate from limitations in our knowledge of the station gain and system temperature information. Inferring their uncertainties from previous RadioAstron experiments (e.g., Gómez et al. 2016; Giovannini et al. 2018; Bruni et al. 2020), we consider the overall accuracy of the flux upper limit to be accurate on the order of ∼10%–20% at this radio frequency. However, further systematic uncertainties can arise due to, for example, antenna pointing errors, which can rather significantly change the value of A_upper. While the antenna pointing errors can be largely corrected by the amplitude self-calibration in imaging observations, it is difficult to do so for the single-baseline AGN survey. We further note that those systematic effects tend to reduce the correlated amplitudes. Accordingly, we expect that the long space baseline A_upper values can be uncertain and larger by factors of ∼2 than what we estimated, if a conservative systematic pointing offset of half the beam is adopted.

In Figure 5 we show the fully calibrated visibilities of M87 observed by RadioAstron at 22 GHz. Fringes are clearly detected for both ground and space baselines at <1 Gλ. Fringes for the space baselines up to ≲3 Gλ are also detected, although at significantly decreased S/N. We refer to Table 2 where the probabilities of false fringe detection for specific AIPS S/N values are estimated according to our simulation. The large flux density of ∼2 Jy at the shortest (u, v) spacing decreases to ∼250 mJy at ∼2.2–3.0 Gλ, indicating significantly resolved structure of the nucleus.

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In Figure 6, we also show the corresponding images of M87 at various angular resolutions. The main parameters of those images, including the observing epoch, participating stations, observing frequency, total flux density, the image peak flux density as well as the image rms level, and achieved angular resolutions for specific visibility weighting, are listed in Table 3. The naturally weighted ground-only image consists of the bright compact core, extended jet, which slightly bends to the north at ∼2 mas core distance, and a weak counterjet. However, the limited angular resolution of the ground-only array, especially in the N–S direction, does not yet allow for a clear view toward detailed structure of the jet at ≲1 mas, such as limb-brightening. With the addition of RadioAstron, the jet becomes more clearly resolved both in the E–W and N–S directions. Applying slight overresolution (comparable to the superuniform weighting beam), the image reveals further edge-brightened jet and counterjet on ∼0.3 mas distances from the core. This morphology resembles the "X-shaped" inner jet structure (e.g., Kovalev et al. 2007; Walker et al. 2018; see Figure 22 and 23 of Walker et al. 2018) where both approaching and receding jets are edge-brightened, and thus supports the idea that the central engine of M87 is located close to the VLBI core.

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Table 3. Details of the Images Shown in Section 4 (Figures 6 and 10)

Epoch	Array	ν	Stot	Peak	σ	Beam
(YYYY-MM-DD)	(GHz)	(Jy)	(Jy beam−1)	(mJy beam−1)	(mas × mas, deg)	uvweight
2014-02-04	SRT+BD+EF+GB+HH+KZ+SV+	22.236	2.19	0.52	1.0	0.47 × 0.15, −157	(2,−1)
	TR+YS+ZC+VLBA(10)			0.29	1.0	0.20 × 0.10, 00	(2,0) a
2014-02-05	VLBA(10)	43.136	0.99	0.48	1.7	0.37 × 0.14, −161	(2,0)

Notes. From left, each column shows (1) the mean observing epoch in year-month-date format, (2) the observing array, (3) the central observing frequency, (4) the total VLBI flux density, (5) the image peak intensity, (6) the image rms noise, (7) the beam size, and (8) the Difmap uvweight parameter.

^a Approximately 63% superresolution in the N–S direction applied.

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The shape of the core is also highly resolved with the slight overresolution (Figure 6 bottom), and its appearance is significantly elongated in the N–S direction, larger than the adopted beam size, with the brighter spot in the south. Although such a structure was not seen in previous VLBI images of M87 at 22 GHz, we consider that this structure is real. Specifically at this observing frequency, the angular resolution in the N–S direction of the new RadioAstron image is roughly ∼0.45 mas for the (2, −1) weighting. This is significantly smaller than that of the previous VLBA observations (see Hada et al. 2013), which is ∼0.6 mas. Also, we have parameterized the overall structure of the resolved nucleus by fitting an elliptical Gaussian model as described in Section 3.1 both in the Fourier and image domains, finding comparable values of the Gaussian parameters. These numbers are summarized in Table 4. Compared to the previous VLBI core size measurements for M87 at 23 GHz (see, e.g., Table 1 in Hada et al. 2013), the new FWHM sizes reported here—∼0.13 mas and ∼0.36 mas along the minor and major axes, respectively—are generally consistent with the previous measurements, except for the more highly resolved size in the E–W direction. The N–S elongation of the core of ∼0.36 mas is also comparable to the angular resolution of the RadioAstron observation with uniform weighting. This further supports that the overall elongation and complicated substructure of the nucleus are resolved and real.

Table 4. Parameters of the Core

Method	${S}_{\mathrm{core}}$	${\psi }_{\min }$	ψmaj	${\mathrm{PA}}_{\mathrm{core}}$	TB
(1)	(2)	(3)	(4)	(5)	(6)
	(Jy)	(mas)	(mas)	(deg)	(1010 K)
Difmap	0.74	0.12	0.32	−3.38
JMFIT	0.91	0.13	0.40	−3.60
Nominal	0.83 ± 0.09	0.13 ± 0.01	0.36 ± 0.04	−(3.49 ± 0.11)	4.4 ± 0.8

Note. (1) Methods used for the Gaussian model-fitting of the core. Difmap and JMFIT, respectively, indicate fitting methods working in the visibility and image domains, respectively. The nominal values and their uncertainties are obtained by averaging and half the difference of the two independent estimates. (2) Flux density of the model-fitted core, (3) and (4) lengths of the minor and major axes of the Gaussian, respectively. (5) Position angle of the major axis as measured from north to east, and (6) apparent brightness temperature of the core.

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We also calculate the apparent brightness temperature, T_B, of the core in the observer's frame using the core parameters in Table 4, by

$$\begin{eqnarray}&&{T}_{{\rm{B}}}=1.22\times {10}^{12}\displaystyle \frac{{S}_{\mathrm{core}}}{{\nu }_{\mathrm{core}}^{2}{\psi }_{\mathrm{maj}}{\psi }_{\min }}(1+z)\end{eqnarray} \tag{ 1 }$$

(Kim et al. 2018b) where ${S}_{\mathrm{core}}$ is the core flux density in janskys, ${\nu }_{\mathrm{core}}$ is the observing frequency in GHz, ${\psi }_{\min ,\mathrm{maj}}$ are, respectively, the Gaussian FWHM component sizes along the minor and major axes in milliarcseconds, and z = 0.00436 is the redshift of M87 (Smith et al. 2000). Using Equation (1) and parameters in Table 4, we obtain T_B = (4.4 ± 0.8) × 10¹⁰ K. This value is slightly lower than those from 15 GHz VLBI observations of M87 (e.g., Kovalev et al. 2005) and higher than those from measurements at ≳86 GHz (e.g., Hada et al. 2016; Kim et al. 2018b; Event Horizon Telescope Collaboration et al. 2019), following the general trend of decreasing T_B of the VLBI core of various AGNs at high radio frequencies (e.g., Lee et al. 2008; Kim et al. 2018b; Nair et al. 2019; Cheng et al. 2020).

In addition, we also directly estimate lower limits on the brightness temperature of the source, following Lobanov (2015) whose method uses only the correlated flux densities with fewer assumptions on the detailed model geometry, and thus suitable for experiments with sparse (u, v) coverage. We compute the minimum (${T}_{\min }$) and limiting (${T}_{\mathrm{lim}}$) brightness temperature, which provides a range of actual brightness temperature (see Lobanov 2015 for details). The results are shown in Figure 7, together with the estimate of T_B from Equation (1). As shown, the values of ${T}_{{\rm{B}},\min }$ agree well with the geometric modelfit result at ∼1 Gλ, while significantly larger ${T}_{{\rm{B}},\min }$ values appear at ≳2 Gλ (mean value $\lt {T}_{{\rm{B}},\min }\gt \sim {10}^{12}\,{\rm{K}}$ at 2–3 Gλ). This is likely related to the compact substructure in the VLBI core, which is suggested by Figure 6 (bottom panel).

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We also calculate the diameter and opening angles of the limb-brightened inner jet and counterjet as follows. First, we take the peak of the image as the center and circularly slice the jet side of the slightly overresolved image (Figure 6, bottom) at varying radial distances from the center. For each circular slice, we determine the positions of two local intensity maxima, to extract the ridge lines of the bright limbs. The linear distance between the two local maxima at a specific radial core distance, z, is then used as the full width of the jet, W, and the apparent opening angle of the jet, ϕ_app, is calculated by ${\phi }_{\mathrm{app}}=2\times \arctan (W/(2z))$ (e.g., Pushkarev et al. 2017; Kim et al. 2018a). The same procedure was applied to the counterjet side. For both jet and counterjet sides, the above calculations worked best at 0.2 mas ≲ z ≲ 0.5 mas. At z ≲ 0.2 mas, the bright core significantly contaminated the jet flux. At z ≳ 0.5 mas, the complicated jet structure and limited array sensitivity made it difficult to identify the edges of the limb-brightened jet. Therefore, we focused only on the reliable measurements, which were made at z ∼ 0.32 − 0.46 mas. At this core distance, we obtain W_j = 0.44 ± 0.10 mas (W_cj = 0.57 ± 0.10 mas) and ϕ_{app, j} = 48° ± 11° (ϕ_{app, cj} = 55° ± 10°), where the subscripts "j" and "cj" denote the jet and counterjet, respectively. Here, the uncertainties for the width, σ_W , are taken as 20% size of the interferometric beam in the N–S direction, and the angle uncertainties, σ_ϕ , are obtained by propagating the errors on σ_W .

The jet-to-counterjet brightness ratio (BR) is also estimated, using again the slightly overresolved image. Since our single epoch observation does not provide the jet kinematics, we rely on the integrated flux densities of the jet and counterjet over certain extended regions, instead of trying to identify pairs of jet and counterjet components. By integrating the jet and counterjet emission from 0.20–0.45 mas core distance along the jet at the position angle of −72° from north to east, we find BR ∼ 10 ± 3. Here we adopt a characteristic systematic uncertainty σ_BR = 3, which represents variation of the value of BR upon slight change in the shift of the integration region by, for example, ∼0.05 mas. This BR value falls in the range of those from previous observations (see, e.g., Kovalev et al. 2007; Ly et al. 2007; Hada et al. 2016; Kim et al. 2018b; Walker et al. 2018), however with some discrepancies, notably with Hada et al. (2016), who also observed the object in 2014 February. This is further discussed in Section 5.

In addition to the images, we also show results of the further analysis of the ground-space fringe detections and the flux density upper limits, including data from both the imaging and AGN survey observations (Section 2.3). The combined (u, v) coverage is shown in Figure 8. There is no clear fringe detection above the PIMA S/N threshold of 6.1 at ∼3–25 Gλ baseline lengths. Accordingly, we have only calculated the flux density upper limits. All of the detailed information including observing epoch, experiment code, two-letter code for the ground station, solution interval, values of S/N of actual data and detection threshold, length and position angle of the baseline, and derived flux upper limits are summarized in Table 5 in Appendix B. Figure 9 also shows summaries of the flux densities and the upper limits by combining both the imaging and survey observations. At the short (u, v) distances of ∼(0.2–0.8) Gλ, flux densities derived from the full AIPS data reduction and Difmap imaging with self-calibration agree well with the independent flux estimates from the PIMA analyzes (middle panel of Figure 9). This provides confidence that the choice of the PIMA S/N threshold and a priori amplitude calibration of the SRT are valid. Keeping this in mind, we note that the PIMA analysis indicates significantly small flux densities of ≲100 mJy at ∼3–25 Gλ, with the tightest constraint given by the phased JVLA to SRT baselines at ∼15.8 Gλ with an upper limit of ∼70 mJy upper limit (Table 5). Also, we emphasize that these nondetections were presented in various epochs during 2013–2016 as well as different baseline position angles. This indicates that the jet of M87 at 22 GHz persistently lacks compact features that could be detected by the long space baselines.

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Table 5. Upper Limits on the Flux Densities of M87 at 22 GHz for Space Baselines to RadioAstron, in Order of Increasing Baseline Length

Tobs	Expr. Code	Station	Tsolint	S/N	${\rm{S}}/{{\rm{N}}}_{\det }$	B	PA	Fupper
			(sec)			(Gλ)	(deg)	(Jy)
2014-02-05 11:10:00	gs032	FD	570	5.42	6.1	0.264	156.7	0.319
2014-02-05 11:00:00	gs032	FD	570	4.89	6.1	0.289	−170.2	0.32
2014-02-05 11:00:00	gs032	KP	570	4.76	6.1	0.294	179.0	0.333
2014-02-05 11:10:00	gs032	KP	570	4.96	6.1	0.298	147.7	0.331
2014-02-01 04:15:05	raks01sr	YS	864	6.14	6.83	25.193	80.7	0.279
2014-02-01 04:00:01	raks01sr	EF	868	5.65	6.83	25.234	80.6	0.126
2014-02-01 04:15:02	raks01sr	EF	839	5.67	6.83	25.251	80.6	0.132

Notes. For each column (from left to right), (1) T_obs is the starting time of the scans in year-month-date and hour-minute-second in UTC, (2) experiment code for each observation (gs032 for the imaging experiment and others for the AGN survey observations), (3) name of the ground station, (4) solution interval used in the estimates of the S/N in seconds, (5) and (6) observed and detection-threshold S/N values, respectively, (7) baseline length in Gλ, (8) baseline position angle measured from north to east in degrees, and (9) upper limits on the flux density in janskys. Additional stations that participated in the AGN survey but not in the imaging observation (Table 1) are DSS63 and VLA-N8, which are the Deep Space Station 63 antenna (Robledo 70 m; geodetic code RO) and the phased JVLA (Y27; N8 for the phase center location).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Figure 10 shows the image of M87 from the quasi-simultaneous VLBA observations at 43 GHz, made using uniform weighting (because of higher-S/N fringe detections at the long baselines than at 22 GHz). Detailed properties of this image are given in Table 3. The 43 GHz image shows the compact core and edge-brightened approaching jet, similar to typical VLBA 43 GHz maps of M87 over the last decade (Walker et al. 2018) and the one obtained on 2014 March 26 (see Figure 6 of Hada et al. 2016), which is close in time to our observation (49 days later). Our 43 GHz image does not clearly reveal the counterjet emission (Section 4.1), which can be due to a combined effect of the limited image dynamic range as well as fainter jet emission at the higher observing frequency. Therefore, we set a lower limit on the jet to counterjet BR by following the same BR calculations in Section 4.1 and at the 0.20–0.45 mas core distances. From this, we obtain BR > 6 at 43 GHz. If there is no frequency dependence for the jet to counterjet BR, we can combine the results at 22 and 43 GHz, which yields BR ∼6–11. This value is consistent with results of Hada et al. (2016), who reported BR ∼5–20 at the 43–86 GHz frequency band and within 1 mas from the core in the same 2014 February epoch, as well as Kim et al. (2018b), who also suggest BR ≲20 within ∼0.3 mas from the core at 86 GHz.

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Since the 22 and 43 GHz observations are interleaved to each other, we can compute the spectrum of the jet in M87 with negligible time-variability effect. A more comprehensive analysis of the jet spectrum, also including the 4.8 GHz RadioAstron image (E. V. Kravchenko et al. 2023, in preparation), can be done with precise alignment of the multifrequency jet images and is planned for a future work. In this work, we instead provide the integrated spectrum of the core for later discussions. The spectral index of the nuclear region is estimated by matching the angular resolutions of the 22 and 43 GHz maps and computing the ratio of the peak intensities by $\alpha =\mathrm{log}({I}_{43}/{I}_{22})/\mathrm{log}(43/22)$. For this, we adopt for both images a common convolving beam of 0.47 × 0.15 mas at 0^◦ position angle and obtain the peak intensities of 0.52 and 0.49 mJy beam⁻¹ at 22 and 43 GHz, respectively. Assuming ∼10% absolute flux calibration errors, the core spectral index α = −(0.1 ± 0.2). This result is consistent with earlier studies of the partially optically thick nucleus at ≲43 GHz (e.g., Ly et al. 2007; Hada et al. 2012; Kim et al. 2018a; Kravchenko et al. 2020a).