Could the recent rebrightening of the GW170817A afterglow be caused by a counter jet?

Binary neutron star (BNS) mergers have long been believed to be a strong candidate for multimessenger astrophysics. On 2017 August 17, GW170817 (and GRB170817A) became the first such event to be detected directly. It provided unprecedented insights into the physical properties of pre-merger (GW) and post-merger (EM) BNS. The event was quickly localized (Coulter et al., 2017) to a nearby galaxy at 40.7 Mpc (Cantiello et al., 2018). The initial EM spectrum ($\sim$ days) was powered by thermal emission from the merger ejecta (also known as the kilonova) and the nonthermal synchrotron emission dominating in the X-ray and radio bands.

The early kilonova emission, powered largely by radioactive decay of heavy chemical elements, was in agreement with theoretical predictions (Metzger, 2017). Meanwhile, the nonthermal emission in the first $\sim$900 days has been associated with synchrotron emission from a GRB afterglow due to an ultrarelativistic jet pointing away from us (Mooley et al., 2018a; Ghirlanda et al., 2019; Hotokezaka et al., 2019; Nathanail et al., 2021). The initial observations during this period did not show any spectral evolution across nine orders of magnitude of frequency, and they were characterized as synchrotron emission with power-law spectrum $F_{\nu}\propto\nu^{-(p-1)/2}$, with $p=2.166\pm 0.026$ (Fong et al., 2019; Hajela et al., 2019; Troja et al., 2020). More recent observations, after 900 days since the merger, have found evidence for an excess in X-ray emission. The excess X-ray emission was measured with $L_{X}\approx 5\times 10^{38}\mbox{ erg s}^{-1}$ at 1234 days. However, similar observations at 3GHz (radio) and 5keV (X-ray) lacked such a strong excess (Hajela et al., 2022; Troja et al., 2021).

The GRB afterglow has been studied extensively, and the physical parameters are constrained by several lightcurve and spectral fits (Zhang & MacFadyen, 2009; Piran, 2005) for $\delta t<900$ days. Several simple and complex models of jets have also been employed to explain the behavior of synchrotron emission from GW170817A. Top-hat jet models, formed by angular truncation of a spherical Blandford-McKee blast wave solution (Blandford & McKee, 1976), cannot account for the mild and steady rise of the nonthermal emission (Troja et al. (2017), and references therein). More complex models include, a jet-less fireball model (Salafia et al., 2017; Wu & MacFadyen, 2018), the choked jet-cocoon model (Nakar & Piran, 2018), and the choked jet-cocoon model with a fast tail (Hotokezaka et al., 2018) characterized by a mildly relativistic quasi-spherical outflow. Other models include a structured jet with wide-angle wings viewed off-axis (e.g. Kathirgamaraju et al. (2017), Margutti et al. (2018) and other), like the Gaussian shaped jet model (Troja et al. (2018) and references therein), the successful jet-cocoon model (Duffell et al., 2018), and the boosted fireball model (Wu & MacFadyen, 2018). These complex models have been successful in explaining the spectral and temporal evolution of the synchrotron emission from GW170817A, but in the context of successful jet breakout, they are indistinguishable from each other (Wu & MacFadyen (2018) and references therein). However, the lightcurves show significant statistical deviation from the recent X-ray excess observed at 1keV. This excess emission has been associated with kilonova ejecta (Kathirgamaraju et al., 2019), and also compact object remnants like hypermassive NS, or a prompt collapse to a BH, or a spinning-down NS (Hajela et al. (2022) and references therein).

In this paper, we adopt the boosted fireball model (Duffell & MacFadyen, 2013). We then revisit the parameter space for the standard external shock and ISM interaction model of GRB afterglows (Sari et al., 1999; Granot & Sari, 2002) and include the most recent observations (up to <1300 days). One should note that the existing best fit parameters are based on observations for $\delta t<900$ days, and the lightcurves deviate beyond that epoch. We compare the re-evaluated jet and afterglow microphysical parameters with the existing best fits and the MCMC results. Motivated by the association of late-time bumps in afterglow lightcurves to counter jet re-brightening (Granot & Loeb, 2003; Li & Song, 2004; Wang et al., 2009; Zhang & MacFadyen, 2009), we revisit this scenario as a probable source of the excess flux in the recent observations of GRB170817A. We further make predictions for later behaviour. We also explore the correlation between the ratio of the global peak flux to the counter jet bump and the observer angle.

The question we ask here is, being agnostic of the observer angle, is it possible to correlate the re-brightening timescale with the emergence of counter jet emissions? If so, what are the required conditions for it? The paper is presented as follows. In section 2, we discuss the theoretical aspects behind the problem. This is followed by section 3, which describes the numerical implementations. Here we also introduce our new synchrotron radiation code Firefly. This includes how we use Firefly to map the flux distribution along the plane perpendicular to the observer’s line of sight. We discuss our findings and overall line of thought in section 4. Section 4.1 discusses the empirical scaling law between the time scales of the forward jet peak emission and the counter jet peak emission. This is followed by a discussion comparing our simulated lightcurves to the observations in section 4.2 and the spectrum in section 4.3. Finally, we estimate the apparent superluminal motion for the brightest region of the GRB170817A afterglow through the sky in section 4.4. We summarize and discuss our findings and their implication in the conclusions (section 5).

In this work, we use the boosted fireball jet model. The boosted fireball is a two-parameter model (Duffell & MacFadyen, 2013) that generates a family of outflows after they have expanded many orders of magnitude larger than the merger scale. The two input parameters are $\eta_{0}\sim E/M$ which is the fluid frame Lorentz factor of a blast with energy E and mass M, and $\gamma_{B}\sim\frac{1}{\theta_{0}}$ being the boost (in lab frame or blast frame) given to the said blast, and $\theta_{0}$ is the jet opening angle. In contrast to a conventional fireball which expands isotropically (with the Lorentz factor $\eta$ ,as per our convention), the boosted fireball has gets an external kick in a particular direction with Lorentz factor $\Gamma_{B}$. In the extreme limit $\Gamma_{B}\rightarrow 1$, the boosted fireball is the same as an conventional fireball. While on the other end for $\Gamma_{B}\rightarrow\infty$ it corresponds to an ultra-relativistic jet with a negligible jet opening angle ($\theta_{0}\approx 1/\Gamma_{B}$). The explosion energy per fireball is $E_{0}\sim\gamma_{B}\eta_{0}E$. Thus for a double sided jet, the total energy will be $2E_{0}$, which is related to the isotropic equivalent energy ($E_{iso}$) by the relation

A single fireball has previously been used to simulate the forward jet, and its dynamics are comparable to other standard jet models (Wu & MacFadyen, 2018). In this work we consider two symmetrically reflected fireballs along the jet axis, but they are boosted in the opposite directions. This simulates the joint evolution of the forward jet and the counter jet. We assume a constant and equal boost in both the directions. This is justified because the merger’s spatial and temporal scales are much smaller than the afterglow’s spatial and temporal scales.

For this study, we have used the standard GRB afterglow theory (Sari et al., 1998; Granot & Sari, 2002). This refers to models based on synchrotron radiation from a decelerating relativistic blast wave interacting with the interstellar medium. It assumes the radiation is generated by non-thermally distributed electrons accelerated by the forward shock. These electrons are further assumed to be distributed as a power-law of their Lorentz factor $n^{\prime}_{e}=C_{e}fn^{\prime}\gamma_{e}^{\prime-p},\mbox{ where }\gamma^{\prime}_{e}>\gamma^{\prime}_{m}$ (van Eerten, 2013). Where primed quantities are expressed in the fluid comoving frame, and f is the fraction of electrons radiating ($n’$). Assuming electrons are accelerated to $\gamma’_{e}\rightarrow\infty$ this equation can be integrated to obtain the normalization constant $C_{e}$ as, $C_{e}=\frac{1}{f}(p-1)\gamma_{m}^{p-1}$. We found a marginal change in f has no significant effect on the lightcurves. It was hence fixed at 1 for the rest of the analysis. The minimum electron Lorentz factor at which the accelerated electrons are radiating ($\gamma^{\prime}_{m}$) is given by Eq. 5. Similarly, the cooling break can be solved as in Eq. 7, where $\epsilon_{e}$ and $\epsilon_{B}$ are the fraction of total energy ($\epsilon_{\rm{th}}$) converted to kinetic and magnetic energy respectively. Further, due to the relativistic nature of the blast wave, most of the density is concentrated in a very thin shell behind the forward shock. The radiation is dominated by electrons present in this shocked shell of width $\Delta R/R\sim 1/(12\Gamma^{2})$, where $\Gamma$ is the jet head Lorentz factor.

The quantities upstream (ahead of the shock, in the ISM) and downstream of the shock are related as, $n’_{e}=4\Gamma n_{e}$ and $e’_{\rm{th}}=(\Gamma-1)n’_{e}m_{p}c^{2}$. Thus the above equation after integrating and some algebra, can be solved to give,

and,

The corresponding break frequencies can be found using Eq. 6.

Where $\gamma^{\prime}_{i}$ is the Lorentz factor in the local fluid frame, and i corresponds to either cooling break or minimum Lorentz factor cut off. However beyond a certain critical Lorentz factor ($\gamma^{\prime}_{c}$), the electrons starts loosing energy by cooling over a timescale $t^{\prime}$ (in lab frame $t=\gamma t^{\prime}$). The frequency at which this happens is hence called the cooling frequency, $\nu_{c}^{\prime}$. This can be estimated by equating the power lost over some expansion time ($t’$) to the rest mass energy, and it comes out to be (see van Eerten et al. (2010) for detailed calculations):

The characteristic frequencies, $\nu_{m}$ and $\nu_{c}$, can be observed as two break frequencies in the spectrum. Thus in the local fluid frame, a given fluid element has monochromatic emissivity per unit volume:

where,

Since most of the mass for a relativistic blast wave is concentrated in a very thin shell behind the shock, the observed emission comes only from this optically thin shell. This has a volume element given by:

This converts to observed flux from the lab frame for a fluid element having doppler factor $\delta$ as:

Where z is the cosmological redshift, and $D_{L}$ is luminosity distance of the source. And the local fluid frame frequency ($\nu^{\prime}$) and time (t^′) are related to the observer frequency ($\nu_{\rm{obs}}$) and observer time ($t_{\rm{obs}}$) as:

At any given time and frequency, the observed flux is a result of the total light collected from all the photons arriving at the same time to the observer. In the lab frame (or the center of blast frame), these contours are known as “Equal Arrival Time Surfaces” and are spread over the entire jet at all times. The two frames, lab frame and observer frame, can be bridged by taking a projection of the local fluid element ($\vec{r}$) (with respect to the center of blast), along the line of sight of the observer ($\hat{n}$).

The entire process of generating lightcurves and spectra from jets can be divided into two parts. First we hydrodynamically evolve two oppositely directed relativistic jets through a constant density interstellar medium (ISM) originating from the center of our domain. The domain is assumed to be in the BNS merger rest frame, and the fireballs are boosted with respect to this frame by Lorentzian transformations (see Duffell & MacFadyen (2013) for the detailed calculations). This was carried out using the two-dimensional relativistic hydrodynamics moving mesh code, JET (Duffell et al., 2018).

Each jet is initiated as a boosted fireball with a given fluid frame Lorentz factor $\eta_{0}$ and boosted with a Lorentz factor $\gamma_{B}$. The hydrodynamic simulations are carried out in code units normalized by setting the Sedov radius, $l\equiv(E/\rho_{0})^{1/3}$, to unity, in the center of blast frame. This translates to the total blast energy E and a constant ISM density ($\rho_{0}$) set to unity. These are scaled to physical units during the afterglow calculations. The input for $\eta_{0}\sim E/M$ sets the total ejected mass in the jet, and $\gamma_{B}\sim 1/\theta_{0}$ sets the jet opening angle ($\theta_{0}$), both in code units. The simulation begins around the time the fireball enters BM self similar phase, $t_{\rm{BM}}\sim(E/(\rho_{0}c^{5}\Gamma^{2}))^{1/3}$, this sets the initial time $t_{\rm{min}}=0.06t_{\rm{BM}}$ (where $c=1$ in code units). This ensures that the blast wave evolution begins before the radiation is dominated by the ejecta swept up by the forward shock. The system is evolved until it expands to 20 times its Sedov radius (that is, $t_{\rm{final}}=20l/c$), where it becomes subrelativistic. The system stratifies to a density profile given by Eq. 15. A homologus expansion of the ejecta ($v=r/t$) is assumed.

Where $\rho_{\rm{max}}\sim E/4\pi c^{3}t^{3}$ is the maximum blast wave density at the shock and follows from $E=4\pi\rho_{\rm{max}}(ct)^{3}c^{2}$. The shock radius ($R_{\rm{sh}}$) is given by $R_{\rm{sh}}=t(1-1/2\eta_{0}^{2})$. The pressure is set to be very low ($10^{-5}\rho$) initially. An adiabatic equation of state is used with a constant adiabatic index of 4/3 for relativistic fluids. Although, by the end of our simulation the flow becomes subrelativistic, the afterglow emissions are dominant in the relativistic phase. The relativistic adiabatic constant holds true for marginally relativistic flow as well. Hence, a single value for the adiabatic constant does not affect the results significantly. The counter jet is implemented by reflecting the forward jet about the plane perpendicular to the jet axis. Lastly, the fireball is expanded in an interstellar medium of constant density normalized to unity. A snapshot of the evolution is shown in Fig 1.

Since the problem is axisymmetric, the domain is set in a two-dimensional $r-\theta$ plane polar mesh. The $\theta$ coordinate varies from 0 to $\pi$, and is split into 3200 zones. The radial coordinate is initiated with $R_{\rm{min}}=0.006l$ and $R_{\rm{max}}=0.061l$, and is split into 6400 zones. These resolutions capture both the radial and angular features well enough keeping the run time feasible. A smaller initial radial domain (as compared to the entire radial range of the problem) helps capture the shock at a higher Lorentz factor. The radial mesh eventually expands, moving the inner and outer boundaries using the moving mesh feature of the Jet Code, and dynamically captures the entire radial range of the jets with temporal evolution. This is achieved by fixing the ratio of the inner to outer domain with respect to the shock front. We use a logarithmic time grid varying from 0.06 code units to 20 code units split in $10^{5}$ time steps.

We developed a code, Firefly, to post-process the hydro simulations from the JET code. The Firefly code takes the complete two dimensional hydrodynamical evolution as its input and computes the three-dimensional synchrotron radiation using the standard afterglow model as described in the previous section. The 2D hydro data is extended to three dimensions by Firefly using the rotational symmetry about the jet axis. The radial and $\theta$ resolution for the afterglow calculations assumes the same resolution as the Jet Code output, while the $\phi$ axis is divided into 64 zones from 0 to $\pi$. The hydrodynamical parameters thus have the same value for all $\phi$ zones at a given ($r,\theta$). The hydro checkpoints are then binned over temporal resolution for the observer $t_{\rm{obs}}/dt_{\rm{obs}}=0.03$. The binning ratio is a user choice, we choose the mentioned ratio to generate a smooth lightcurve without the loss of any physical features. Firefly has three user input modes; to calculate the lightcurve, spectrum, or sky map. For each mode, it takes the total energy ($E_{\rm{tot}}$, interstellar nucleon density ($n_{\rm{\small{ISM}}}$), which is the same as $n_{e}$ in 2), and other micro-physical parameters ($\epsilon_{B},\epsilon_{e}$, spectral index $p$) as user inputs. The total energy for a two jet system is related to the isotropic equivalent energy by Eq. 18. The quantities $E_{\rm{tot}}$ and $n_{\rm{ISM}}$ are scaled in the Firefly code as their code unit values in the hydrodynamical evolution. Since in the Jet code these values are scaled to unity in code units, the input values in the Firefly code are the absolute values (corresponding to actual units, i.e. cgs or SI) pertaining to the problem. An observer is placed at luminosity distance ($d_{L}$) with a redshift ($z$) at an angle $\theta_{\rm{obs}}$. Firefly can then be used to calculate the lightcurve (at any given observer frequency). Firefly computes the cooling break and minimum break frequencies to correctly generate the broken power law spectrum of the GRB afterglow. It however does not account for the synchrotron self-absorption.

Additionally, Firefly can also be used to track the apparent motion of the object in the sky (as seen by the observer). This is achieved by computing the flux distribution (for a user-given frequency) along a plane perpendicular to the line of sight of the observer and the merger (hereon referred to as sky map, see Fig. 2), as a function of its distance from the merger center. This provides a more realistic approach to tracking the entire shock-ISM interaction region through the sky, and not just the jet head. This is especially relevant for off-axis observations and structured jets. The brightest emitting region from such a plot at multiple observer times can then be used to calculate the apparent motion of the object through the sky.

The sky map is computed by integrating the projected flux along a line on the plane perpendicular to the observer axis from different emitting regions of the jet-ISM interaction. To do this, we consider the x-z plane containing the jet axis and observer. A small emitting region of the jet at $\vec{r}$ from the blast center is projected on this plane containing the jet axis and the vector ($\hat{n}$), connecting the blast center and the observer, by removing the $\hat{y}$ component (axis into the plane of the paper). This gives the position vector of the projected region:

We then calculate its shortest distance ($\omega$) along the plane perpendicular to $\hat{n}$. This is given by the cross product of the remaining vector with the observer axis ($\hat{n}$).

. Since the resulting quantity is a vector, we project it along $\hat{y}$. The geometry can be expressed mathematically as Eq. 20, and pictorially as Fig. 2. This scheme is then repeated over the entire computation domain at a given observer time.

For this study, we explore the parameter space ${E_{iso},\gamma_{B},\eta_{0},\theta_{\rm{obs}},n_{\rm{\small{ISM}}},p,\epsilon_{e},\epsilon_{B}}$. We carried out several runs of the hydrodynamical code for the boosted fireball model (Duffell & MacFadyen, 2013) varying $\eta_{0}$, and $\gamma_{B}$. Values were selected from a parameter range of $\eta_{0}\in[4,12]$ and $\gamma_{B}\in[4,12]$ (inspired by Wu & MacFadyen (2018)). The temporal evolution of the angular energy profile and Lorentz factor for the fireball are plotted in Fig. 3 and 4 respectively. We fixed the luminosity distance $d_{L}$ = 40 Mpc, which corresponds to a cosmological redshift of z = 0.00998. Since the Blandford-McKee solution for relativistic blastwave holds for most of the evolution, we fix the adiabatic index to 4/3.

For a given set of hydrodynamics parameters, we fix all the microphysical afterglow parameters except $\theta_{\rm{obs}}$ and generate lightcurves as in Fig. 5. We observe the late time bump in the lightcurve due to the counterjet as expected (Li & Song, 2004; Granot & Loeb, 2003; Zhang et al., 2013; Li et al., 2019). The counter jet excess flux of the afterglow lightcurves indicates a similar re-brightening timescale for off-axis observations, except for far off-axis ($\gtrsim 1.2$ rad). For these large off-axis observer angles, the re-brightening initiates at earlier times. Fig. 5 shows the same. This also shows that the second bump is indeed associated with the counter jet. Emission from the counter jet shares the same profile in the afterglow lightcurve as the forward jet, but with a very significantly delayed $t_{\rm{obs}}$, due to its orientation pointing and moving away from the observer. While all of the initial afterglow is due to the forward jet, once the jet spreads out and is spherical enough, the counter-jet eventually becomes visible to the observer. Flux from the counter jet gradually increases as the forward jet did, and it eventually outshines the forward jet. This occurs because the observer time $t_{\rm obs}$ for the counter-jet corresponds to an earlier lab-frame time than for the forward jet. The forward jet eventually spreads out and slows down, leading to a steeply declining lightcurve, while the counter jet is still effectively beamed and relativistic at the same observer time. For a brief period, this leads to a higher flux from the counter jet. This effect is also captured in the sky map $\sim 900$ days, Fig. 7. The flux from the counter jet also eventually peaks and is briefly brighter than the forward jet before it declines. The flux from both the jets converge asymptotically and eventually contribute the same flux as the jets spread and eventually become an isotropic system.

GRB170817A is one of the most crucial transients in recent years. While it was the first off-axis sGRB afterglow observed it has reignited multiple questions in the field of gamma-ray bursts and afterglow. The afterglow from GRB170817A has also shown a significant agreement with a structured jet interaction with a constant ISM. In this study, we re-evaluated the parameters to investigate the conditions under which the excess flux could be due to the counter jet.

We ran multiple hydrodynamic simulations for a double sided boosted fireball jet model, varying $\gamma_{B}$, and $\eta_{0}$. The first peak in the afterglow lightcurves was used to constrain the jet opening angle at $\theta_{0}=1/\gamma_{B}=0.125$ rad ($\gamma_{B}=8.0$). The fireball spread parameter, quantified by $\eta_{0}$ was similarly constrained to be 6.5. Wu & MacFadyen (2018) find asymptotic Lorentz factor $\gamma_{B}\sim 11$ and $\eta_{0}\sim 8$ (Fig. 9). Fixing $\gamma_{B}$, and $\eta_{0}$, we constructed lightcurves at 3 GHz radio and 1 keV X-ray for 11 observer angles each. In our model, there is no additional source for excess flux. Thus the second peak observed in Fig. 8 is purely due to the counter-jet interactions. We also observe that at later times, since the counter jet has longer $t_{\rm{obs}}$, it becomes brighter than the forward jet. After this turnover time, the contributions from the counter jet leads to the second peak in the lightcurves. We then computed an empirical scaling law between the jet and counter-jet peak emission time scales, with the observer angle Eq. 22.

For the excess flux of GRB170817A to correspond with the emissions from the counter-jet, we can place a lower bound of $\frac{t_{p}^{j}}{t_{p}^{cj}}>10^{-0.85}$ from observations (sec 4.1). Comparing simulations with the observations (Fig. 8) we constrain our observer angle to be $49.8^{\circ}$. In contrast, previous attempts studies have found $\theta_{\rm{obs}}\sim 27^{\circ}$ (Resmi et al., 2018; Lazzati et al., 2018; Mooley et al., 2018b; Wu & MacFadyen, 2018). Using the relation Eq. 22 we estimate the peak of this second component to occur around 1268 days since explosion. The afterglow lightcurve shall then decay sharply, with a temporal slope faster than before the excess started.

Using this observer angle, we fit the 3 GHz and 1 keV lightcurves, to constrain the microphysical parameters associated with the standard afterglow model. The best match between observations and our calculations from the Firefly code fixed the parameters $\epsilon_{e}=0.4$, and $\epsilon_{B}=0.001$. Resmi et al. (2018) and Wu & MacFadyen (2018) report $\epsilon_{e}\sim 0.2$ and 0.3 respectively. Further typical values for $\epsilon_{B}$ lie within the range $\sim 10^{-5}-10^{-1}$ (Wu & MacFadyen (2018) and references therein). Thus, we find both afterglow parameters agree closely with previous attempts at modelling this afterglow. While the inherent degeneracy of $E_{iso}/n_{\rm{\small{ISM}}}$ remains, owing to the Blandford-McKee solution of blastwave. To break this degeneracy, we fix our isotropic equivalent energy closer to the realistic scales of such BNS mergers. We fix $E_{iso}\approx 1.98\times 10^{51}$, with total jet energy $E_{tot}=1.6\times 10^{49}$. This constraints the circumburst medium density $n_{\rm{\small{ISM}}}=0.1$/cm³. The value is significantly much larger than $10^{-5}-10^{-3}$, suggested by previous studies (Margutti et al., 2018; Mooley et al., 2018b; Lazzati et al., 2018), but in agreement with the expected value for such a medium. In contrast, Wu & MacFadyen (2018) fix $n_{\rm{\small{ISM}}}=10^{-3}$ and obtain $E_{\rm{tot}}=2\times 10^{49}$ erg for a similar model. Table 1 summarizes the parameter values obtained.

Narrowing down all the parameters for the jet-ISM interaction, we then used the sky map feature of Firefly. Tracking the most luminous region of 170817A afterglow along the plane perpendicular to the observer. We get an apparent velocity of the afterglow through the sky as 2.12c in the initial days, slowing down to 1.6c later after the first peak. However, Mooley et al. (2018a) report the apparent velocity observed as seven times the speed of light. This contradicts our model and implies a smaller viewing angle. (Wang et al., 2024) also found larger viewing angle ($\sim 50^{\circ}$) fit to the afterglow, which reduced to $\sim 18.16^{\circ}$ after correcting for the superluminal motion. Other attempts at modeling the re-brightening with $\theta_{\rm{obs}}\sim 27^{\circ}$, include power law momentum distribution in the kilonova (Kathirgamaraju et al., 2017), a fast moving tail in the dynamical ejecta and central engine powered radiation from the compact object (see, Hajela et al. (2019) and references therein for detailed discussion).

We conclude that it is possible to associate a re-brightening time with the counter jet visibility time and constrain the observer angle from that. For GRB170817A/ GW170817 we can further fine-tune the model to match the radio and X-ray lightcurves for that observer angle. However, although the association of counter jet visibility with excess flux time scale and lightcurve matching indicates a possible solution to the X-ray excess, and not for the radio band. Only by comparing the apparent motion of the object through the sky, we can nullify this seeming correlation. Hence we propose,that jet and counter jet re-brightening timescales can also be used to constrain the observer’s orientation with respect to the jet. Further, full diagnostics including the apparent (superluminal) motion along with parameter estimation with lightcurve fitting is required to narrow down the geometrical orientation for such beamed emissions observed off-axis.