Transient Events in the Circumnuclear Regions of AGNs and Quasars As Sources of Imitations of Proper Motions

Abstract

This paper is an extension of the study by Khamitov et al. (2022) with regard to the catalog and the astrophysical interpretation of the imitation of significant proper motions in active galactic nuclei (AGNs) and quasars based on data from the Gaia space observatory. We present a sample of SRG/eROSITA X-ray sources in the eastern Galactic hemisphere (${0^{\circ}<l<180^{\circ}}$) having significant proper motions in the Gaia EDR3 measurements with the confirmed extragalactic nature of the objects. The catalog consists of 248 extragalactic sources with spectroscopically measured redshifts. The catalog includes all of the objects available in the SIMBAD database and coincident with the identified optical counterpart within 0.5 arcsec. Eighteen sources with spectroscopically measured redshifts from observations with the Russian–Turkish 1.5-m telescope RTT-150 (Khamitov et al. 2022) have been additionally included in the catalog. The sources in the catalog are AGNs of various types (Sy1, Sy2, LINER), quasars, radio galaxies, and star-forming galaxies. The imitation of significant proper motions can be explained (by the VIM effect previously known in astrometry) by the presence of transient events on the line of sight in the vicinity of AGNs and quasars (within the Gaia optical resolution element). Among such astrophysical events are supernova outbursts, tidal disruption events in binary AGNs, the variability of high-mass supergiants, the presence of OB associations against the background of AGNs with a variable brightness, etc. The model of outbursts with a fast rise–exponential decay profile allows the variable positional parameters of most sources observed in Gaia to be described. This approach can be used as an independent way of detecting transient events in the vicinity of AGNs (on scales of several hundred parsecs in the plane of the sky) based on data from the SRG/eROSITA catalogs of X-ray sources and the optical Gaia catalog.

APPENDIX

Determining the Photocenter in the Case of a Transient Event

We considered the shift of the photocenter with time and the ‘‘Gaia data’’ for two objects: (i) a quasi-stationary one and one that flared up for a short time (year) with a given light curve; (ii) a quasi-stationary one and one with an apparent linear motion. The objects are treated as point-like ones.

In both cases, the analysis can be reduced to a one-dimensional model. In the plane of the sky we will tie the origin of coordinates to the AGN position, i.e., $X_{\textrm{AGN}}=0$, and direct the $X$ axis from the AGN toward the transient event (TE). Obviously, the photocenter with a TE at a distance $X_{T}$ from the AGN position is defined as

$$X_{C}=\frac{X_{T}F_{T}}{F_{T}+\langle F_{\textrm{AGN}}\rangle+\xi(t)},$$

(1)

where $\langle F_{\textrm{AGN}}\rangle$ is the mean flux from the AGN, $F_{T}$ is the flux from the TE recorded at a given time, and $\xi(t)$ is the stochastic AGN variability relative to the mean.

Consequently, we have two limiting values of $X_{C}$:

$$X_{C}\begin{cases}X_{T},&\quad\text{if }\quad F_{T}\gg F_{\textrm{AGN}}\\ 0,&\quad\text{if }\quad F_{T}\ll F_{\textrm{AGN}}.\end{cases}$$

(2)

Fig. 5

Shift of the photocenter during an outburst with a FRED profile occurred 100 days before the beginning of the Gaia survey (the model parameters are $X_{T}=60$ mas, $R_{0}=1$, $\alpha=110^{\textrm{d}}$, and $\sigma=10^{\textrm{d}}$). The negative proper motion in the one-dimensional model corresponds to the direction from the outburst toward the nucleus.

The second limiting value is reached fairly quickly, for example, for a supernova event or a tidal disruption event. Consequently, for the known values of the proper motion ($\mu$) measured in the Gaia catalog and the estimated flux from the AGN, in the cases of a TE we can estimate a lower limit for the peak flux from the transient in the interval of Gaia observations:

$$F_{T}=\frac{\mu t_{\textrm{gaia}}}{X_{T}-\mu t_{\textrm{gaia}}}F_{\textrm{AGN}},$$

(3)

where $t_{\textrm{gaia}}$ is the time base of the Gaia EDR3 catalog based on which the proper motions of the sources were determined, i.e., 2.8 years. Since both sources are at the same distance, the fluxes in Eq. (3) can be replaced with the luminosities of the sources. Adopting the conservative limitation on the maximum possible value of $X_{T}$ by the Gaia detector resolution element, i.e., 60 mas, we calculated a lower limit for the transient luminosity. The results are presented in Tables 2–10 in the ninth column ($L_{T}$).

Fig. 6

Change of the model curves as a function of the distance of the transient from the nucleus $X_{T}$ ($R_{0}=1,\alpha=110^{\textrm{d}},\sigma=10^{\textrm{d}}$). The numbers indicate the values of these distances in mas.

In addition to the proper motion parameter, there is also the astrometric excess noise parameter $\epsilon$ (astrometric_excess_noise) in the Gaia catalog. Introducing a new variable $R$ as the ratio of the TE fluxes to the mean AGN flux and taking the ratio of $\xi(t)$ to the sum of the TE and AGN fluxes on the time base of the Gaia catalog to be less than unity and, basically, in the time interval when the TE can be recorded by the Gaia detectors, (1) takes the form

$$X_{C}=\frac{R}{R+1}X_{T}-\frac{R}{(R+1)^{2}}\xi^{\prime}(t)X_{T},$$

(4)

where $\xi^{\prime}(t)={\xi(t)}/{\langle F_{\textrm{AGN}}\rangle}$. The second term of the sum in (4), with a chaotic behavior, gives an additional small contribution to the astrometric excess noise dependent on the amplitude of the intrinsic relative AGN variability on the outburst detection scale.

The Case with a Quasi-stationary Object and an Object Flaring up at a Given Distance

We considered a simple model of the influence of an outburst with a fast rise–exponential decay (FRED) profile occurred at some distance from the nucleus ($X_{T}$). The fast rise is provided by a Gaussian:

$$R_{i}=R_{0}\begin{cases}e^{-(t_{i}-t_{\textrm{peak}})^{2}/2\sigma^{2}},&\quad\text{if }\quad t_{i}\leq t_{\textrm{peak}}\\ e^{-(t_{i}-t_{\textrm{peak}})/\alpha},&\quad\text{if }\quad t_{i}>t_{\textrm{peak}},\end{cases}$$

(5)

where $t_{\textrm{peak}}$ is the time of the outburst peak flux, $R_{0}$ is the ratio of the TE and AGN fluxes at $t_{\textrm{peak}}$, $\sigma$ is the root-mean-square (rms) deviation of the Gaussian, $\alpha$ is the exponential decay parameter, and $t_{i}$ are the times of observations in the Gaia catalog that were used in the model with some arbitrariness. According to the Gaia motion parameters, each source in a five-year all-sky survey, on average, is observed 70 times, i.e., at least one measurement in 30 days. Thus, for our modeling we assumed that at least 39 photometric and position measurements of extragalactic objects were carried out in the survey time $t_{\textrm{gaia}}$.

Fig. 7

Change of the model curves as a function of the ratio of the TE and AGN fluxes at $t_{\textrm{peak}}$, $R_{0}$ ($X_{T}=60$ mas, $\alpha=110^{\textrm{d}}$, and $\sigma=10^{\textrm{d}}$). The numbers indicate the values of $R_{0}$ corresponding to the curves.

Next, having estimated the photocenter position $X_{C}$ from Eqs. (4) and (5), the proper motion $\mu$ and the rms deviation from the line $\epsilon$ ($\epsilon$ does not include the contribution from the stochastic AGN variability) are calculated by linear interpolation from all points. Depending on the shift ($LAG$) of the outburst peak time $t_{\textrm{peak}}$ relative to the beginning of the Gaia survey, these discrete measurements will occur in different outburst segments. We can distinguish two cases, depending on the sign of $LAG$. In the first case, at negative values the outburst peak is within the survey period (Fig. 4). Some of the pre-outburst photocenter measurements will correspond to unshifted values irrespective of the AGN variability, i.e., equal to zero. In the second case, at positive values the outburst peak is before the beginning of the survey (Fig. 4) and all of the photocenter measurements will be shifted. In these examples we ignored the intrinsic AGN variability, $X_{T}$ is 60 mas, $R_{0}=1$, and $\sigma=10^{\textrm{d}}$.

Our fitting of the observed parameters ($\mu,\epsilon$) by a FRED outburst is a multi-parameter problem. Indeed, a decrease in the parameter $X_{T}$ or a decrease in the parameter $R_{0}$ leads to a horizontal displacement of the solutions in the direction of decreasing $\epsilon$ (Figs. 6 and 7), while a decrease in the exponential decay parameter $\alpha$ leads to a vertical displacement in the direction of decreasing ratio of the proper motions to the astrometric excess noise (Fig. 8). The horizontal branches of our model estimates correspond to the periods when the TE flux peak occurred before the beginning of the Gaia catalog, whereas the vertical part occurs at the times when the outburst occurred within the time interval covered by the Gaia catalog. Lower values of $\epsilon$ on the horizontal branch correspond to larger $LAG$, while on the vertical curve lower values of $2.8\mu/\epsilon$ correspond to lower $LAG$.

Fig. 8

Change of the model curves as a function of the exponential decay parameter $\alpha$ ($R_{0}=1$, $X_{T}=60$ mas, $\sigma=10^{\textrm{d}}$). The numbers indicate the values of this parameter in days.

Apart from the case with a quasi-stationary object and an object flaring up at a given distance, the case of two quasi-stationary objects (the distance between the objects is $X_{T}$), with a TE occurring in the vicinity of one of them, is possible. In that case, (1) takes the form

$$X_{C}=\frac{X_{T}F_{2}+X_{T}F_{T}}{F_{1}+F_{2}+F_{T}},$$

(6)

where $F_{1}$ and $F_{2}$ are, respectively, the fluxes from the first object and the second one, in the vicinity of which the TE took place. Introducing a variable $R={F_{T}}/{(F_{1}+F_{2})}$, (6) takes the form

$$X_{C}=\frac{X_{0}+X_{T}R}{1+R},$$

(7)

where $X_{0}={X_{T}F_{2}}/{(F_{1}+F_{2})}$ is the mean coordinate of the photocenter of the binary system in the absence of a TE. $X_{C}$ and $R$ are the observational Gaia parameters from which we can estimate the distance between the objects and reconstruct the TE light curve.

The Case with a Quasi-stationary Object and Object of Variable Brightness with an Apparent Linear Motion

Such cases take place with blazars that exhibit luminous optical jets directed toward the observer at a small angle. Such optically bright ($R\sim 0.01$) jets with superluminal speeds were observed in the nearest luminous radio galaxy M87 (Biretta et al. 1999), where the Hubble Space Telescope observed the motions of features in the jet image with apparent power motions ($\mu_{\textrm{jet}}$) $\sim 20$ mas yr${}^{-1}$. In our calculation of the distribution of ($\mu,\epsilon$) the coordinate $X_{T}$, in contrast to the previous case, changes linearly with time: $X_{T}=X_{T0}+\mu_{\textrm{jet}}t$, where $X_{T0}$ is the TE coordinate at the initial time of the Gaia catalog. Then, from Eq. (4) the apparent proper motion recorded by Gaia is calculated as

$$\mu=\frac{R}{(R+1)}\mu_{\textrm{jet}}+o(\xi^{\prime}),$$

where $o$-small is of the linear part of the random parameter $\xi^{\prime}$, which, apart from the relative AGN variability, also includes the relative jet variability, while $\epsilon$ is a function of the TE-to-AGN flux ratio ($R$), the relative intrinsic AGN and jet variability ($\xi^{\prime}$), the TE coordinate at the initial time of the Gaia catalog ($X_{T0}$), and the apparent TE proper motion ($\mu_{\textrm{jet}}$). Calculating this parameter is beyond the scope of this study.