A compact symmetric ejection from the low mass AGN in the LINER galaxy NGC 4293

Stellar-mass black holes (SBHs), formed from the direct collapses of massive stars (Mirabel, 2017), are widely observed in the Universe. Supermassive black holes (SMBHs, $10^{6}-10^{10}\,M_{\odot}$) are also universally found in the centers of galaxies with bulges (Kormendy & Ho, 2013). However, the gap between two classes of black holes, i.e. the so-called intermediate-mass black holes (IMBHs, $10^{2}-10^{6}\,M_{\odot}$, see review by Greene et al., 2020), remains unfilled (especially $10^{3}-10^{4}\,M_{\odot}$). The necessity for the existence of IMBHs is strongly suggested by SMBHs with masses up to $10^{10}\,M_{\odot}$ (Wu et al., 2015; Bañados et al., 2018) in the early Universe, when the Universe was only $5\%$ of its current age. These discoveries pose challenges to the formation of SMBHs, and intermediate-mass (seed) black holes are required to form SMBHs at such an early age.

Based on the expected formation and evolution scenarios, observational searches for IMBHs have typically focused on the following habitats: globular clusters, ultra/hyper-luminous X-ray sources, and dwarf galaxies, there is growing evidence for the abundance of $10^{5}\,M_{\odot}$ IMBHs in dwarf galaxies with stellar masses ranging from $10^{7}-10^{10}\,M_{\odot}$ (e.g. Greene & Ho, 2004, 2007; Dong et al., 2012; Reines et al., 2013; Liu et al., 2018; Chilingarian et al., 2018; Mezcua et al., 2018). Moreover, black holes with $10^{4}-10^{6}$ solar masses discovered in the centers of nearby dwarf galaxies are thought to be formed in the early Universe (Volonteri, 2010; Greene, 2012). These dwarf galaxies have undergone few merger events in their evolutionary history and therefore have not grown significantly since their birth. Thus, the central black holes in dwarf galaxies still retain the footprints of the seed black holes, providing valuable clues for our study of the formation and evolution of SMBHs in the early Universe (Volonteri, 2010; Inayoshi et al., 2020).

Radio jets/outflows are the fundamental parts of both SBHs and SMBHs which maintain accretion process (e.g. Faucher-Giguère & Quataert, 2012; King & Pounds, 2015). Continuum imaging and spectral studies can be used to infer the observational signatures of mildly relativistic to relativistic outflows (0.1 – 1.0 $c$ respectively, e.g. Nyland et al., 2017; Saikia et al., 2018; Hwang et al., 2018; Yang et al., 2021) and hence, the activity of IMBHs that are hosted in Active Galactic Nuclei (AGNs). A pilot radio survey and study of low-mass AGNs with high accretion rates by Greene et al. (2006) indicates that these sources are predominantly radio-quiet. These signatures may be explained by comparison with Galactic X-ray binaries (hosting stellar mass black holes) where the high/soft X-ray state is characterized by a quenched radio emission (e.g. McClintock & Remillard, 2006). It is generally believed that the accretion process in SMBHs and SBHs are similar and scale independent (e.g. Svoboda et al., 2017). Simultaneously, the high/soft state in Galactic X-ray binaries is radio quiet, while the transition from a low/hard state to a high/soft state is often associated with transient jets/outflows. On studying of a sample of high accretion rate IMBHs show that the ejection process in IMBHs is likely episodic, and in some cases the radio core is visible and in other cases, it is not (Yang et al. 2022, In preparation). A recent study of the IMBH candidate NGC 4395 reveals both fossil radio ejecta and diffuse and flat-spectrum radio emission in the nucleus (Yang et al., 2022), and a thermal mechanism in the nucleus is proposed correspondingly.

Very Long Baseline Interferometry (VLBI) observations offer high angular resolutions (at the milli-arcsec scale) in radio band, surpassing other imaging techniques in astronomy. The VLBI detection of compact pc-scale radio-emitting structures (core/core-jet/jet-knot) in the nuclear regions of dwarf galaxies can directly probe the jet/outflow activity enabled by an accreting, potential IMBH. To date, high-resolution VLBI observational studies are limited to only a few IMBH candidate hosts: NGC 4395 (Wrobel & Ho, 2006; Yang et al., 2022), Henize 2-10 (Reines & Deller, 2012), NGC 404 (Paragi et al., 2014) and RGG 9 (Yang et al., 2020a). In order to understand the ejection process in actively accreting IMBHs, we present an observational study of an IMBH candidate in NGC 4293.

NGC 4293, at redshift $z=0.003$, was identified as a late-type spiral galaxy with a low-ionization nuclear emission-line region (LINER, Ho et al., 1997a; Decarli et al., 2007). The black hole mass of its AGN was estimated as $\log{(M_{\mathrm{BH}}/M_{\odot})}=7.7$ through the black hole mass ($M_{\mathrm{BH}}$) and velocity dispersion ($\sigma$) relation (Chiaberge et al., 2005). Another work obtained a similar black hole mass $\log{(M_{\mathrm{BH}}/M_{\odot})}=7.5$ by taking the black hole mass - $K_{s}$-band bulge luminosity relation (Dong & De Robertis, 2006). Recently, Chilingarian et al. (2018) used the single-epoch broad H$\alpha$ emission to measure the black hole mass of NGC 4293. This source was re-weighted as $\log{(M_{\mathrm{BH}}/M_{\odot})}=5.30\pm 0.06$, and hence an IMBH candidate. Nagar et al. (2002); Nagar et al. (2005) observed NGC 4293 at 15 GHz with Very Large Array (VLA) A-array, they obtained a resolution of 0.15 arcsec and yielded a integrated flux density of $\sim 1.4$ mJy (with merely a signal-to-noise ratio of $\sim 5$). With the VLA A-array 15 GHz observation and VLA archive data at 1.5 and 5 GHz, Nagar et al. (2002) measured a steep radio spectrum ($\alpha<-0.3$ according to their definition and $S\propto\nu^{+\alpha}$, while in this work, a spectrum is termed as steep, flat or inverted when $\alpha<=-0.5$, $>-0.5$ or $>0$, respectively) in NGC 4293. While comparing with the 15 GHz observation and a Multi-Element Radio Linked Interferometer Network (MERLIN) 5 GHz observation, Filho et al. (2006) conclude a flat radio spectrum. In order to investigate the nuclear (parsec and sub-parsec scale) outflows of NGC 4293, in this work, we report the Very Long Baseline Array (VLBA) observation of the nuclear region in NGC 4293 and we also analyse the archival data from VLA and MERLIN. This paper is organised as follows. In Section 2, we describe multi-band observations and data reduction of the target NGC 4293. In Section 3, we present imaging, spectral and model-fitting results of NGC 4293. In Section 4, we discuss the radio identification of NGC 4293, describe the interpretation of the multi-band properties, and estimate black hole mass. Finally, we give our conclusions in Section 5. Throughout this work, we adopt the standard $\Lambda$CDM cosmology with $H_{0}=71$ km s^-1 Mpc^-1, $\Omega_{\Lambda}=0.73$, $\Omega_{m}=0.27$ and the corresponding physical scale is 0.061 pc mas^-1 in NGC 4293.

We observed NGC 4293 with eight VLBA antennas from 2021 July 08 to 09 (UT, the project ID: BA146). The antennas at Kitt Peak (KP) and North Liberty (NL) were unavailable due to equipment failure. The observation was scheduled at L-band (the central frequency is 1.545 GHz, hereinafter using 1.5 GHz for short), with a total observation time of 3 h and a data recording rate of 2 Gbits per second. Phase-reference mode was used and the quasar 1216$+$179 (R.A. $=\mathrm{12^{h}18^{m}46^{s}.6045}$, DEC. $=+17^{\circ}38^{\prime}17^{\prime\prime}.268$) was chosen as the phase-reference calibrator. The observation was scheduled with a dual polarization mode and a total bandwidth of 320 MHz with 1 min on calibrator and 5 min on target in each observing cycle. The correlated data was processed using the Astronomical Image Processing System (AIPS, Greisen, 2003) developed by the National Radio Astronomy Observatory (NRAO) of the USA. A prior amplitude calibration was performed using the system temperatures and the antenna gain curves provided by each VLBA station. The Earth orientation parameters were obtained and calibrated using the measurements from the U.S. Naval Observatory database, and the ionospheric dispersive delays were corrected from a map of the total electron content provided by the Crustal Dynamics Data Information System (CDDIS) of NASA ¹¹1https://cddis.nasa.gov. The opacity and parallactic angles were also corrected using the auxiliary files attached to the data. A global fringe-fitting on the phase-reference calibrator 1216$+$179 was performed, taking the calibrator’s model to solve miscellaneous phase delays of the target.

The target source’s data were exported into DIFMAP (Shepherd, 1997) for imaging and model-fitting. The final image was created with natural weighting through the task ‘CLEAN’, see Figure 1. We estimate flux density uncertainties following the instructions described by Fomalont (1999). In this work, the integrated flux densities $S_{i}$ were extracted from Gaussian model-fit in DIFMAP with the task ‘MODELFIT’, where a standard deviation in model-fit was estimated for each component and considered as the fitting noise error. Additionally, we assign the standard 5% errors originating from amplitude calibration of VLBA (see VLBA Observational Status Summary 2021A ²²2https://science.nrao.edu/facilities/vlba/docs/manuals/oss2021A). The final image gives a $1-\sigma$ rms noise of 0.03 mJy beam^-1 and a beam size of $13\times 4.52$ mas at a position angle of $-8.58^{\circ}$.

Furthermore, we also retrieved MERLIN data from MERLIN archive ³³3http://www.merlin.ac.uk/archive/acknowledge.html
[email protected] and VLA data from the NRAO data archive ⁴⁴4https://archive.nrao.edu/archive/advquery.jsp. The MERLIN 5 GHz data was observed on June 12th, 2004 and it is likely the same observation that was published by Filho et al. (2006), the total bandwidth of MERLIN observation is 15 MHz. In this work, we used the reduced data from the MERLIN archive. A manual deconvolution and two-dimensional Gaussian model-fitting were done in DIFMAP with the DIFMAP task ‘CLEAN’ and ‘MODELFIT’, respectively. The final image gives a $1-\sigma$ rms noise of 0.1 mJy beam^-1 and a beam size of $79\times 49$ mas at a position angle of $26^{\circ}$. The radio observation at 4.86 GHz and 8.46 GHz were taken from VLA archive project AS0806 (PIs or Observers are Schmitt et al.), which were carried out with a configuration of VLA A-array and a total bandwidth of 50 MHz, on 2004 October 23. We obtained the reduced data from the NRAO archive and performed a manual deconvolution and two-dimensional Gaussian model-fitting in DIFMAP to retrieve the information of a central compact component, the results are shown in Table 1, where the $1-\sigma$ rms noise is 0.06 and 0.04 mJy beam^-1, respectively. The flux density uncertainties for MERLIN and VLA data are estimated following the same method described in Yang et al. (2020b).

In Figure 1, we show the naturally weighted VLBA L-band (1.5 GHz) image. The source shows a symmetric structure with two discrete lobes, where we mark the North-West component as ‘N’ and the South-East component as ‘S’. The peak flux densities of N and S are $2.70\pm 0.17$ and $0.72\pm 0.05\,\mathrm{mJy\,beam^{-1}}$, respectively, yielding an SNR of $40$ and $10$, respectively, indicating clear detections. Both components N and S have counterparts in the MERLIN 5 GHz image, see black contours in panel $c$ of Figure 2. We performed two-dimensional Gaussian model fittings on the VLBA L-band and MERLIN C-band uv-visibilities. Especially, in order to match the resolution between VLBA L and MERLIN C-band, here we downward the resolution of VLBA L-band data by using an uv-taper. The model-fitting results are listed in Table 2. We take the integrated flux density to measure the non-simultaneous radio spectral indices $\alpha$ between 1.5 and 5 GHz for components N and S, which are $-0.64\pm 0.09$ and $0.33\pm 0.09$, respectively.

By evaluating the radio spectrum compiled from the non-simultaneous data, we check the variability of NGC 4293 through observations with the same configurations, i.e. at the same frequencies with identical resolutions. Both the two TGSS and VLASS observations satisfy this purpose (see Table 1). These two TGSS observations were conducted in the frequency of 0.147 GHz and an angular scale of 25 arcsec, which results in no significant variability higher than 35% within 6 years from 2010 to 2016. Again, these two VLASS observations were conducted in the frequency of 3 GHz and the angular scale of $\sim$2.6 arcsec. A marginal variability of 8.7% can be inferred with a significance of only $2\sigma$ within 2.6 years from 2019 to 2021. Therefore, as a conclusion, no clear variability is detected in NGC 4293. The target is unresolved at a resolution poorer than 1 arcsec (see panels $b$ and $c$ of Figure 2), while combing the high-resolution data with low-resolution ones may still result in the loss of diffuse emission. Figure 3 shows the L (1.4) and S-band (3 GHz) observations at different resolutions, where combing the Arecibo 2.38 and Effelsberg 4.85 GHz data, we measured the 3 GHz flux density in $\sim$150 arcsec. The plot implies a positive correlation (possibly a power law) between radio flux densities and collection areas, and it likely hints at a similar trend at different frequencies.

We follow the equation described in e.g. Callingham et al. (2017) to model the entire spectrum of NGC 4293. Additionally, here we assume a power-law distribution of radio flux density along angular size according to the observational hints (see Figure 3).

where $S_{\nu}$ is the flux density at frequency $\nu$ and angular size $\theta$, $\nu_{p}$ is the frequency at which the spectrum peaks, $S_{p}$ is the flux density at the frequency $\nu_{p}$ and an unit angular size (i.e. $\theta$=1 arcsec), $\alpha_{\mathrm{thick}}$ and $\alpha_{\mathrm{thin}}$ are the spectral indices in the optically thick and optically thin regimes of the spectrum, respectively.

A Markov chain Monte Carlo algorithm is used to fit the spectrum, and only the observations with beam size larger than 2 arcsec are taken in the fitting. In Figure 4, we show the posterior probability distributions of each parameter, and we take 16% and 84% of the distributions as the lower and upper limits, respectively, thus representing $1\sigma$ confidence ranges. The fitting yields a peak flux density $S_{p}=15.65^{+2.04}_{-1.63}$ mJy at frequency $\nu_{p}=0.44^{+0.14}_{-0.11}$ GHz and the angular size $\theta=1$ arcsec, with optically thin and thick spectral index $\alpha_{\mathrm{thin}}=-0.66^{+0.05}_{-0.06}$ and $\alpha_{\mathrm{thick}}=1.29^{+0.58}_{-0.33}$, respectively. Furthermore, the power-law index of flux density distribution along angular size $\alpha_{\mathrm{size}}=0.14\pm 0.02$. The spectrum of NGC 4293 is plotted in Figure 5, where the black solid line represents the best fit of equation 1 to the integrated radio spectrum at the typical angular size of $20$ arcsec. The thin and thick radio spectral indices are consistent with the typical peaked spectrum radio sources (O’Dea, 1998). Furthermore, NGC 4293 is resolved and shows diffuse emission along east-west direction in an angular scale of 1 arcsec (see panel $c$ of Figure 2). It shows that the spectrum of the central compact component in VLA A-array 4.86 and 8.46 GHz aligns the integrated spectrum (optically thin part, see Figure 5), which indicates the core dominance in this scale. Assuming a similar flux density distribution along frequencies and sizes, i.e. equation 1 is still applicable in an angular scale of $\sim 0.5$ arcsec, the equation gives a flux density of $4.67\pm 1.19$ and $3.10\pm 0.85$ mJy beam^-1 for VLA A-array 4.86 and 8.46 GHz respectively and this is approximately consistent with the observations.

The brightness and compactness of radio components can be parameterized by taking the brightness temperatures, measured using the formula (e.g. Ulvestad et al., 2005)

where $S_{i}$ is the integrated flux density of each Gaussian model component in mJy (column 2 of Table 2), $\theta$ is $\mathrm{FWHM}$ of the Gaussian model in mas (column 4 of Table 2), $\nu$ is the observing frequency in GHz, and $z$ is the redshift. The estimated brightness temperatures are listed in column 5 of Table 2. The radio brightness temperatures are inversely proportional to the measured component sizes. Since the measured component sizes are only upper limits, the radio brightness temperatures should be considered as lower limits.

Assuming minimum energy (approximately equipartition) conditions in synchrotron emission, we can estimate the magnetic field $B_{\mathrm{min}}$ in Gauss (G) through the formula (e.g. Patil et al., 2022)

$S_{i}$ (in mJy) is the integrated flux density of the source measured at frequency $\nu$ (in GHz) and angular size $\theta$ (in mas), $\alpha$ is the spectral index, $z$ is the redshift of the source, and $r$ is the comoving distance in Mpc. Here we take $p=0.5$, $\alpha=\alpha_{\mathrm{thin}}$ in the optically thin part of the spectrum from $\nu_{1}\sim 1$ GHz to $\nu_{2}\sim 10$ GHz, a filling factor for the relativistic plasma $f_{rl}=1$, a relative contribution of the ions to the energy a = 2, and the comoving distance $r$ in Mpc. By adopting the standard $\Lambda$CDM cosmology and using the cosmology calculator provided by NED ⁵⁵5https://www.astro.ucla.edu/~wright/CosmoCalc.html, $r=12.7\,\mathrm{Mpc}$ in this case. Here we use the integrated flux density of 19.83 mJy estimated through formula 1 and fitting parameters, at the typical frequency of 1 GHz and angular size of 20 arcsec, which yield $B_{\mathrm{min}}=3\times 10^{-4}\,\mathrm{G}$. The magnetic field is consistent with the typical value of PS sources, e.g. gigahertz peaked-spectrum (GPS, $B\sim 10^{-3}\,\mathrm{G}$) and compact steep spectrum (CSS, $B\sim 10^{-4}\,\mathrm{G}$) radio sources (O’Dea, 1998).

The electron lifetime for a turnover-type spectral radio source can be estimated as follow (O’Dea, 1998)

where $B$ is the magnetic field in $\mathrm{G}$, $B_{\mathrm{R}}\simeq 4(1+z)^{2}\times 10^{-6}\,\mathrm{G}$ is the equivalent magnetic field of the microwave background, and $\nu_{p}$ is the break frequency in GHz. For NGC 4293, using these values estimated above, i.e. $B=3\times 10^{-4}\,\mathrm{G}$ and $\nu_{p}=0.44\,\mathrm{GHz}$, we find the electron lifetime is $\sim 1\times 10^{6}$ years.

In summary, we performed a Very Long Baseline Array (VLBA) L-band (1.5 GHz) observation of the IMBH candidate in the nucleus of the LINER galaxy NGC 4293 ($z=0.003$). By cooperating with the archive VLA and MERLIN data, we find (1) the source has two radio blobs with a projected distance of $\sim 7$ parsec apart from each other and its integrated spectrum has a turnover at $\sim 0.44$ GHz. Therefore it can be allocated as a typical compact symmetric object (CSO). We also find evidence that the lobes are interacting with the dense medium. Despite different mass estimations, the source stands out as one of the lightest and nearest CSOs; (2) We estimate the black hole mass of NGC 4293 through the fundamental plane of black hole activity and constrain it to be $\lesssim 10^{6}\,M_{\odot}$. The result supports that NGC 4293 has a less massive AGN; (3) The discovery of compact symmetric ejecta in the less massive (or intermediate-mass) AGN, NGC 4293, can be reasonably explained as the source is maintaining an episodic ejection.

X.-L.Y. designed the VLBA observations, made the VLBI data reduction and model-fitting, and interpret the results, R.-L.W. contribute to drafting the manuscript, interpret the results and proof correction, and Q.G. provided useful comments on the manuscript. This work is supported by the Shanghai Sailing Program (21YF1455300) and China Postdoctoral Science Foundation (2021M693267). XLY thanks for the support from the National Science Foundation of China (12103076). We thank Luis C. Ho from the Kavli Institute for Astronomy and Astrophysics at Peking University (KIAA-PKU), he shared important experiences and matters that need attention in measuring black hole masses of LINER galaxies. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. $e$-MERLIN is a National Facility operated by the University of Manchester at Jodrell Bank Observatory on behalf of STFC. This work has made use of data from the Pan-STARRS1 Surveys (PS1) and the PS1 public science archive. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium).

Scientific results from data presented in this publication are derived from the VLBA project BA146. The correlated data are available in the NRAO Science Data Archive (https://data.nrao.edu).