compared with V3890 Sgr.

The optical light curves of these recurrent symbiotic novae evolve quickly following an eruption due to the low mass of material accreted onto the surface of the white dwarf since the last nova eruption, as these systems are known to host massive white dwarfs ( 1.2 M ; see Table 1 ). The ejecta outfows following an eruption are also fast, with velocities 4000 km s -1 measured from emission lines observed during different stages of the spectral evolution (see Table 1 ). The emission lines, ho we ver, become narro wer with time during the early phase of the ejecta evolution, as the nova ejecta sweep up and are decelerated by the wind from the secondary star (e.g. Gonzalez-Riestra 1992 ;Banerjee et al. 2014 ;Mondal et al. 2018 ).

Recurrent novae have short recurrence times of less than a century (see Table 1 ), which are attributed to high accretion rates, Ṁ ≈ 10 -8 M yr -1 (Yaron et al. 2005 ). The high rates rapidly supply enough material to power the subsequent thermonuclear runaway . Theoretically , most recurrent novae also consist of massive white dwarfs, and therefore require less mass to accumulate for hydrogen ignition (e.g. Prialnik & Ko v etz 1995 ;Yaron et al. 2005 ;Wolf et al. 2013 ). In symbiotic systems, the high Ṁ is acquired through mass-loss from the companion red giant, which is accreted either as a wind or through a disc via the inner Lagrangian point (Luna Table 1. Estimated parameters of the symbiotic recurrent novae based on multiwavelength studies of individual systems. Listed parameters include masses of the binary components, the spectral classifcation of the companion star, orbital period ( P orbit ), years of recorded eruptions, the nova recurrence time ( t rec ), velocity of the ejected material ( V ej ), the time it takes for the nova to fade from optical maximum by three magnitudes ( t 3 ), and the distance to the nova ( d ).

M white dwarf M giant Spectral P orbit Years of t rec V ej t 3 d M M type (Days) eruption (yrs) (km s -1 ) (Days) (kpc) T CrB 1.37 (1) 1.12 (1) M4 III (2) 228 (3) 1866, 1946 80 6 (8) 0.81 (4) RS Oph 1.2-0.7-M0-2 III (6) 453.6 (5) 1898, 1907, 1933, 1945 10 4200 (7) 14 (8) 1.6 (9) 1.4 (5) 0.8 (5) 1958, 1967, 1985, 2006, 2021 V745 Sco M4 III (10) 510 (8) 1937, 1963, 1989, 2014 25 > 4000 (11) 9 (8) 7.8 (8) V3890 Sgr 1.35 (12) 1.1 (12) M5 III (10) 747.6 (12) 1962, 1990, 2019 28 4200 (13) 14 (8) 9 (12)

Note. References: (1) Stanishev et al. ( 2004 ), (2) M ürset & Schmid ( 1999 ), (3) Kenyon & Garcia ( 1986 ), (4) Bailer-Jones et al. ( 2018), ( 5) Brandi et al. ( 2009 ), (6) Anupama & Mikołajewska ( 1999 ), ( 7) Mondal et al. ( 2018 ), ( 8) Schaefer ( 2010), ( 9) Hjellming et al. ( 1986 ), (10) Harrison, Johnson & Spyromilio ( 1993 ), (11) Banerjee et al. ( 2014 ), ( 12) Mikołajewska et al. ( 2021), ( 13) Strader et al. ( 2019 ), and ( 14) Munari & Walter ( 2019b ).

2019 ). The mass-loss via the giant's wind also contributes to a dense circumstellar environment, which is impacted by the expanding nova env elope to giv e rise to shocks observ ed at high energies such as X-rays (e.g. Bode & Kahn 1985 ;Sokoloski et al. 2006 ) and γrays (Zheng et al. 2022 ). A combination of high-mass white dwarfs and high-mass accretion rates make the eruptions of these systems relatively gentle, and consequently not all of the accreted material is ejected during eruption (Yaron et al. 2005 ). The white dwarf may therefore grow in mass towards the Chandrasekhar limit. Indeed, the white dwarfs in recurrent no vae hav e been shown to be massive (Osborne et al. 2011 ;Page et al. 2015 ), and these systems have therefore been proposed as progenitors of supernovae type Ia (Maoz, Mannucci & Nelemans 2014 ). Ho we ver, it is not clear whether the underlying white dwarfs in recurrent symbiotic novae are composed of CO or ONe. A CO white dwarf is required for a SN Ia; the fate of an ONe white dwarf that has grown in mass towards the Chandrasekhar limit is instead an accretion-induced collapse into a neutron star (Gutierrez et al. 1996 ).

Based on previous eruptions, the optical evolution of V3890 Sgr is fast, taking less than a day to rise to maximum magnitude ( V ≈ 8 mag) and 14 days for the brightness to drop by 3 mag; it is therefore classifed as a fast no va (P ayne-Gaposchkin 1964 ;Schaefer 2010 ).

The spectral evolution of V3890 Sgr at ultraviolet wavelengths shows the presence of both broad and narrow emission lines (Gonzalez-Riestra 1992 ). The broad lines originate from the expanding nova ejecta, while the narrow lines represent the speed of the red giant wind (e.g. Munari 2019 ). The FWHMs of the hydrogen Balmer lines decrease with time, from 2140 km s -1 to 210 km s -1 within a period of 13 days following the eruption in 1990 (Gonzalez-Riestra 1992 ). Following the 2019 eruption, the nova was observed with the Gemini observatory to obtain near-infrared spectra during the early days after the outburst (Evans et al. 2022 ). During this time, Helium emission lines showed both broad and narrow components. The broad lines emerged on day 3 and narrowed through day 23 (Evans et al. 2022 ). This is interpreted as evidence of the highv elocity no va env elope being decelerated with time as it sweeps up the red giant wind.

The rise, peak, and decay of the optical light curve of V3890 Sgr following the 2019 August eruption is well observed (Sokolovsky et al. 2019 ;Strader et al. 2019 ). The optical evolution of the nova shown in Fig. 1 is similar to previous outbursts (see Fig. 1 ).

The eruption has been observed at γ -ray , X-ray , infrared, UV, optical, and radio wavelengths (Buson, Jean & Cheung 2019 ;Nyamai et al. 2019 ;Polisensky et al. 2019 ;Orio et al. 2020 ;Evans et al. 2022 ;Kaminsky et al. 2022 ;Ness et al. 2022 ). V3890 Sgr was detected in γ -rays and hard X-rays very soon ( ∼2 days) following the eruption (Buson et al. 2019 ;Sokolo vsk y et al. 2019 ), consistent with expectations for a nova erupting in a dense environment.

Presented in this paper are radio observations of V3890 Sgr with MeerKAT at 1.28 GHz and the VLA at radio frequencies between 1.26 GHz and 35 GHz. The observations are used to study the transient phenomena of the system at radio frequencies. In Section 2 , radio observations and measurements including the radio light curve, radio spectral evolution, and H I absorption analysis are presented. The emission from the nova, modelled as synchrotron radiation emanating from the interaction of the ejecta with the red giant wind, is analysed in Section 3 . The conclusions are highlighted in Section 4 .

Monitoring of V3890 Sgr with the MeerKAT telescope started on ( tt 0 ) ≈ 2 days, where t 0 is taken as 2019 August 27.9 (MJD 58722.9). V3890 Sgr is the frst recurrent nova to be studied with MeerKA T. MeerKA T is a radio telescope located in South Africa and consists of 64 dishes each with a diameter of 13.5 m (Jonas & MeerKAT Team 2016 ). Combined, they form an array with a maximum baseline of 8 km. The observations were taken using the MeerKAT L -band receiver, which has a total bandwidth of 856 MHz split into 4096 channels each with a width of 209 kHz. The frequenc y range co v ered is 0.9 to 1.67 GHz centred at 1.284 GHz. In each observation, the time on target was between 15 and 30 min (see Table 2 ). For the frst 15 days after optical discovery, V3890 Sgr was observed daily and then every 2 days afterwards until day 25. Later, the observations were carried out once every week and fnally the cadence was slo wed do wn further to twice every month until the end of the observations on 2020 May 26. For all the epochs, the fux and bandpass calibrator J1939-6342 was observed for ∼5 mins. The complex gain (secondary) calibrator J1911-2006 was observed for 2 min per visit before and after observing the target.

V3890 Sgr was observed with the VLA from 2019 August 30 to 2021 February 13 at observing frequencies between 1 GHz and 37 GHz. Observations were conducted using the L , C , Ku , and Ka band receivers. The total bandwidth was 1 GHz for L band (1-2 GHz), 4 GHz for C band (4-8 GHz), 6 GHz for Ku band (12-18 GHz), and 8 GHz for Ka band . For all epochs, the absolute fux density and bandpass calibrator 3C286 was observed for 2 min per band. The complex gain calibrator J1820-2528 was used for all observations at C , Ku , and Ka bands. For the L band observations, the complex gain calibrator was J1820-2528 during A and B confgurations, and J1833-2103 during C and D confgurations. VLA observations were carried out under programs VLA/19B-313 and VLA/20B-302. The total observing time on target aross all frequency bands varied between 17 mins and 78 mins (see Table 2 ).

Data reduction for MeerKAT was undertaken using CASA (McMullin et al. 2007 ). To remo v e radio-frequenc y interference, the data were fagged using the AOflagger algorithm (Of fringa, v an de Gronde & Roerdink 2012 ). In order to fnd the bandpass corrections, frst the phase-only and antenna-based delay corrections were determined on the primary calibrator. The primary calibrator bandpass corrections were then applied. This was followed by solving for complex gains for both the primary and secondary calibrators. The absolute fux density of the secondary calibrator was estimated by scaling the corrections from the primary to the secondary calibrator. Calibrations and the absolute fux-density scale were consequently transferred to V3890 Sgr (the target).

Imaging of MeerKAT data was performed using WSCLEAN (Offringa et al. 2014 ) using a Briggs weighting with a robust value of -0.7. These steps are summarized in the oxkat pipeline. 1 The fux densities of V3890 Sgr were estimated with the CASA IMFIT task by ftting a Gaussian to the image of the target. Since the nova was very bright, exhibiting a high signal-to-noise ratio, the width of the Gaussian was allowed to vary when obtaining the fux density measurements. For non-detections, the upper limit was calculated as the pixel value at the location of the nova added to 3 × rms value of a region in the image away from the target location. The observations and results are presented in Table 3 and plotted in Fig. 2 . The quoted errors on the fux densities include Gaussian ft errors ( σ Fit ) and 10 per cent calibration errors ( σ cal = 0.1 S ν ; e.g. Hewitt et al. 2020 ) such that

1 https://www. github.com/IanHeywood/oxkat and through the Astrophysics Source Code Library record ascl:2009.003 (Heywood 2020 ).

The VLA data were calibrated using the VLA CASA calibration pipeline versions 5.4.2 and 5.6.2. Additional fagging was done in AIPS (Greisen 2003 ) and fnal imaging was done using Difmap (Shepherd 1997 ). The VLA data for each band were split into two subbands for imaging to increase spectral co v erage. When possible, phase self-calibration was performed in Difmap as part of the imaging process. All images where the nova was detected were then loaded into AIPS and fux density measurements were made using the JMFIT task. As with the MeerKAT data, we include 10 per cent calibration uncertainty for the VLA fux density values, added in quadrature with the statistical uncertainty from JMFIT . In the cases of non-detections, we recorded the fux density value at the location of the nova and obtained the image rms in a re gion a way from the nova. The upper limit values presented for the VLA are the fux density value at the nova location plus 3 × the off-source image rms.

The 1 to 37 GHz light curves are plotted in Fig. 2 . Initially, during day 2 to day 5 after eruption, the nova was not detected, with 3 σ upper limits of < 0.2 mJy. V3890 Sgr then shows a rapid increase in fux density, which peaked frst on day 19 and again on day 60, forming a double peaked radio light curve. The fux density varies with frequency, such that the light curve peaks frst at higher frequencies ( > 5 GHz). During this time, the fux is still rising at lower frequencies ( < 2 GHz), which peak later. During the frst peak, (day 19), the brightness of the nova remains the same at all observed frequencies. Ho we ver, during the second peak, (day 60), the nova is brighter at lower frequencies. After the secondary peak, the nova faded to fux densities below 0.1 mJy.

To determine the spectral evolution of V3890 Sgr, the data are ft assuming a simple power law using the method of least-squares. Measurements of the spectral index ( α where S ν ∝ ν α ) are presented in Figs 2 and 3 . During the early times (e.g. on day 11.2), the fux density rises towards higher frequency, giving α = 0.29, an indicator of optically thick emission. Around the radio light curve maximum, e.g. on day 21 the spectrum switches to rising towards lower frequency, and is well described by a power law with slope α = -0.2.

The spectrum continues to steepen ( α becomes more ne gativ e,) with time, as shown on day 67 where α = -0.4. On day 327, the spectrum appears to fatten ( α = -0.1), which could indicate some contribution from optically thin free-free emission. Ho we ver, the fux densities on day 327 were quite low with signifcant uncertainty at the lowest and highest frequencies. Also, on day 534, the spectrum rises steeply again towards lower frequencies and can be ft with a single power law such that α = -0.6, an indication of optically thin synchrotron emission. A mixture of optically thin free-free emission and synchrotron emission has also been observed in other novae such as V445 Pup (Nyamai et al. 2021 ) and V1535 Sco (Linford et al. 2017 ).

The distance to V3890 Sgr is not well constrained, with estimates ranging from 4.4 kpc to 9.0 kpc using different methods (Schaefer 2010 ;Munari & Walter 2019a ;Orio et al. 2020 ;Mikołajewska et al. 2021 ). Following the latest eruption, Munari & Walter ( 2019a ) Note. Here, t 0 is taken as 2019 August 27.9 UT (MJD = 58722.9).

determined a reddening of E ( B -V ) = 0.56 mag using absorption features of optical spectral lines. Comparing this value with the threedimensional interstellar reddening maps of Green et al. ( 2019 ) and Lallement et al. ( 2014 ), they estimate a distance of > 4.5 kpc. Using the surface temperature and the size of the companion star, a black body distance of 7 kpc is derived to the nova (Schaefer 2010 ). This method relies on the orbital period of the system and assumes that the companion star flls its Roche lobe (which is far from certain in the case of a symbiotic binary).

Since estimates of the distance to V3890 Sgr vary based on dif ferent observ ations, an attempt is made here to further constrain the distance using H I absorption along the line-of-sight to the nova (see Chauhan et al. 2021 for more details about H I absorption with MeerKAT). The epochs used to obtain the H I spectrum towards V3890 Sgr include radio detections of the nova when it was at its brightest ( > 30 mJy). Fig. 4 shows the average MeerKAT H I spectrum towards V3890 Sgr, compared with the average of seven reference sources (indicated by the blue spectrum in Fig. 4 ) that have been offset for clarity. These reference sources are presumably background extragalactic sources, and their spectra were averaged together to yield optimal S/N. These spectra were constructed by taking an inverse-variance weighted av erage o v er spectra from sev en epochs observ ed with MeerKAT.

Line-of-sight absorption through Galactic H I clouds is detected towards V3890 Sgr. By identifying distinct kinematic components in the H I spectrum, and comparing with the spectrum of reference sources, an attempt is made to determine the distance to V3890 Sgr.

H I absorption at the level of 12 per cent is clearly detected in both the spectra of V3890 Sgr and the reference sources. In both cases, the absorption is at a velocity of 14 ± 22 km s -1 , but is unfortunately unresolved by the data obtained in the MeerKAT 4k correlator mode. At the time of the observations, the 32k correlator mode was not yet available. Absorption is detected at velocities We take MJD = 58722.9 as the date of the eruption ( t 0 ). Bottom: spectral indices obtained by ftting a single power-law to multiband data (1.26-35) GHz. The dash-dotted line in the lower panel represents α = -0.1, the theoretically expected index of optically thin free-free emission. The dotted line represents α = -0.5, the expected index of optically thin synchrotron emission. lower than 36 km s -1 , corresponding to kinematic distances greater than 4 . 44 + 0 . 34 -0 . 31 kpc (using a Monte Carlo technique by Wenger et al. 2018 ). This estimate is similar to the distance value obtained using interstellar reddening as discussed earlier. Therefore, the distance constraint for this nova is consistent with being greater than 4.4 kpc. The absolute magnitude in the V flter and bolometric magnitude measurements give distance estimates of 8.75 and 9 kpc, respectively (Mikołajewska et al. 2021 ). A distance of 9 kpc is thus adopted for calculations in this work.

The radio emission of novae embedded in the winds of giant stars is dominated by synchrotron emission, as observed in systems such as RS Oph (Taylor et al. 1989 ;O'Brien et al. 2006 ;Rupen, Mioduszewski & Sokoloski 2008 ;Sokoloski, Rupen & Mioduszewski 2008 ;Eyres et al. 2009 ), V745 Sco (Kantharia et al. 2016 ), and V1535 Sco (Linford et al. 2017 ). The non-thermal radio emission is the result of the ejecta interacting with the pre-existing circumstellar medium. A nova shock wave moving outwards populates a thin region of shocked circumstellar material with accelerated particles required for non-thermal emission. The evolution of the shock wave in symbiotic novae is similar to that of supernovae (SNe) following an explosion (e.g. Che v alier 1982b ; O' Brien et al. 2006 ). The radio luminosity increases as the optically thick emitting region expands. As the emitting re gion e xpands, the free-free optical depth from the ionized red giant wind ahead of the shock decreases, and the emission becomes optically thin. The radio luminosity peaks when τ = 1, and then decays as the expanding shock wave decelerates in velocity and the surrounding medium drops in density (Che v alier 1982b ).

The radio light curve of V3890 Sgr evolves through the three phases of rise, peak, and decay within months following the nova eruption, and is similar to V745 Sco (e.g. Kantharia et al. 2016 ). The radio spectra of V3890 Sgr during the rise phase of the light curve yield a spectral index of α ≈ 1.3, consistent with optically thick emission. After the radio peak, the spectral index is steep and converges to α = -0.3 at late times of light curve evolution (see Fig. 2 and Table 3 ), an indication of optically thin synchrotron emission. Similar values of α are observed in sources that are strong synchrotron emission emitters such as SNe and SN remnants (Weiler et al. 2002 ;Green et al. 2019 ) and the helium nova V445 Pup (Nyamai et al. 2021 ). To further constrain the type of emission from V3890 Sgr, the brightness temperature is determined by estimating the size of the emitting region (Nyamai et al. 2021 ;Chomiuk et al. 2021b ). To determine the angular size of the emitting region, a spherically symmetric shock wave expanding at ≈ 4200 km s -1 since t 0 is assumed (Strader et al. 2019 ). Using fux densities observed at 1.28 GHz (23 cm), the estimated brightness temperatures on the frst Figure 5. Brightness temperature of V3890 Sgr following the 2019 eruption, estimated assuming a constant shock velocity of 4200 km s -1 , a distance of 9 kpc to the nova and fux densities determined at 1.28 GHz observing frequency. The actual radius of the emitting region is less than the calculated shock radius since the shock is decelerating as it interacts with the red giant wind. Consequently, the brightness temperatures derived by assuming a constant shock velocity are lower limits. 200 days are 10 5 K as shown in Fig. 5 , a strong indicator of nonthermal emission (Chomiuk et al. 2021b ). The brightness temperature after day 200 declines to ≈10 4 K. Ho we ver, we note that the actual angular size of the emitting region may be substantially smaller than our estimated size of the emitting region, since the shock wave decelerates as it interacts with the red giant wind. The implication MNRAS 523, 1661-1675 (2023) is that the brightness temperatures shown in Fig. 5 are lower limits. The spectral evolution and brightness temperatures indicate that the radio emission from V3890 Sgr is synchrotron-dominated, produced in a manner similar to that in SNe, where the radio light curve also evolves on time-scales of weeks to months (Weiler et al. 2002 ).

In an environment where the nova ejecta interact with a dense surrounding medium, radio emission can be used to probe the external surrounding medium and determine its density profle, as is commonly done in radio SNe (e.g. Weiler et al. 2002 ). The radial profle depends on the mass-loss from the companion star and its shaping by binary interaction (e.g. Ji et al. 2013 ;Mohamed et al. 2015 ). An interaction of the nova ejecta with the companion's wind will accelerate particles to high energies through dif fusi ve shock acceleration (Bell 1978 ;Blandford & Ostriker 1978 ) and amplify the shock magnetic feld (Bell 2004 ), producing synchrotron radiation. The interaction produces a forward shock, which drives into the pre-existing circumstellar material and a reverse shock driving into the ejecta (Che v alier 1982a ; Reynolds 2017 ). The radius of discontinuity R cd separates the forward-and reverse-shocked regions. The evolution of the shock fronts depends on the density structure of the nova ejecta ( ρ ej ) and that of the surrounding medium ( ρ CSM ; Che v alier 1982a ; Tang & Che v alier 2017 ).

To interpret the radio luminosity from V3890 Sgr, this double shock system is considered. Shock wave dynamics have been observed in X-rays for recurrent novae, where the most notable characteristics of the shocked ejecta are high temperatures, 10 7 K, which decrease with time as the shock decelerates (e.g. Bode et al. 2006 ;Sokoloski et al. 2006 ). Immediately following its 2019 eruption, V3890 Sgr produced hard X-rays that were attributed to the nova outfow impacting the red-giant wind (Sokolo vsk y et al. 2019 ;Orio et al. 2020 ;Page et al. 2020 ;Singh et al. 2021 ). More evidence of shocks in V3890 Sgr comes from the presence of high-ionization emission lines in optical and infrared spectra (Munari & Walter 2019b ;Evans et al. 2022 ).

A formalism for predicting synchrotron emission from shocks is put forward by Che v alier ( 1982b ). Abo v e a minimum energy E min , the energy spectrum of relativistic electrons can be described by a power -law distrib ution, N ( E ) = N 0 E -p , where N 0 is a constant, N ( E ) is the number of particles with energy E , and p is the power-law index of the energy spectrum. The energy of a relativistic electron is E = γ m e c 2 , where γ and m e are the Lorentz factor and mass of an electron, respectiv ely. F or the non-relativistic shock v elocities observed in V3890 Sgr, we assume that E min is the rest-mass of the electron ( γ min = 1; Che v alier 1998 ). The optically thin synchrotron spectrum produced by a power-law distribution of electrons is also a power law, L ν ∝ ν -( p -1)/2 , so that the spectral index α = -( p -1)/2. For V3890 Sgr, an average value of α ≈ -0.3 is measured in the optically thin limit of the radio light curve. This translates to p = 1.6. Theoretically, in dif fusi ve shock acceleration, the spectral index of relativistic particles p is predicted to be between 2 and 2.5 (Bell 1978 ;Blandford & Ostriker 1978 ). Ho we v er, for no vae, p is observed in the range of 1.2 and 2 (Eyres et al. 2009 ;Finzell et al. 2018 ;Nyamai et al. 2021 ). This could imply a shallower electron energy distribution, or the magnetic felds and particle density are not uniformly distributed leading to complex optical depth effects (Vlasov, Vurm & Metzger 2016 ). The post-shock energy density is described as U shock ≈ ρ CSM V 2 shock , where ρ CSM is the density of the material being shocked and V shock is the velocity of the forward shock. In Che v alier's model, it is assumed that a fraction of the post-shock energy density is transferred to the accelerated electrons and the amplifed magnetic feld. Therefore, the energy density in relativistic electrons is U e = e ρ CSM V 2 shock and the energy density in the magnetic feld is U B = B ρ CSM V 2 shock . The effciency factors e and B are used to describe the fraction of the post-shock energy in the form of relativistic electrons and amplifed magnetic felds, respectively. The normalization for the electron energy spectrum can be expressed as follows:

in cgs units; this expression is valid for p > 2.

Che v alier ( 1998 ) expresses the fux density of synchrotron emission at frequency ν as follows:

Constants C 5 and C 6 are determined as a function of p (Pacholczyk 1970 ). For V3890 Sgr, we take p = 2.1 as this modelling formalism requires p > 2.1. Therefore, the values C 5 = 1.37 × 10 -23 and C 6 = 8.61 × 10 -41 for p = 2.1 are used here. R is the radius of the blast wave and D is the distance to the nova. B is the post-shock magnetic feld strength and is given by B = √ 8 π U B . ν 1 is the frequency at which the optical depth to synchrotron self-absorption (SSA) is equal to unity, given as

Hz .

The synchrotron emitting region is assumed to be between the forward shock and the contact discontinuity; its volume-flling factor is quantifed as f . We estimate the value of f = 0.88 using the approximations of the forward shock radius and the contact discontinuity radius given in Tang & Che v alier ( 2017 ). Based on the authors' approximations, the forward shock radius is twice that of the contact discontinuity.

Radio synchrotron luminosity may increase at early times due to decrease in SSA or free-free absorption by the ionized gas ahead of the forward shock, depending on the amplifed magnetic feld, the density of the external medium, and the shock wave velocity (Weiler et al. 1986 ;Che v alier 1998 ). It has been shown that free-free absorption is dominant for slow shock wave velocities ( 10 4 km s -1 ), while SSA is the dominant source of opacity for f aster blast w aves (Che v alier 1998 ; Panagia et al. 2006 ). In cases where the optical depth is dominated by an ionized wind-like medium (as described in Section 3.3.2 ) ahead of the shock, the free-free optical depth is defned by Che v alier ( 1981 ) as

To predict the radio luminosity of a nova interacting with circumbinary material, we must know the radius and velocity of the blast wave. These depend on the density and velocity structure of the nova ejecta, along with the density profle of the circumbinary material.

The unshocked material of the nova envelope is commonly described as expanding freely and homologously, such that V ( r ) ∝ r where V is the expansion velocity and r is the radial distance from the white dwarf. In this case, the ejecta would show a range of velocities with the inner ejecta characterized by low velocities and the outer ejecta expanding fastest. Based on the modelling of nova remnants, the density profles of the ejecta can be described by a power-law distribution, ρ ej ∝ r -n with inner ejecta having n = 2 or 3 and outer ejecta having n between 10 and 20 (e.g. Hauschildt et al. 1997 ).

Only a tiny fraction of the ejecta mass is found in the outer parts characterized by a steep power law (and this mass will be swept up very quickly, in just a few hours), so a shallo w po wer law is adopted to describe the ejecta density profle of V3890 Sgr, such that n = 2. The kinetic energy of the nova ejecta is, therefore, the integral of the density profle with a homologous expansion such that

where M ej is the mass of the nova ejecta, V max is the maximum ejecta velocity, and V min is the minimum ejecta velocity.

Observationally, the ejected masses of symbiotic recurrent novae are in the range of 10 -7 -10 -6 M (O'Brien, Bode & Kahn 1992 ;Anupama & Sethi 1994 ;Sokoloski et al. 2006 ;Orlando, Drake & Miceli 2017 ). After the 1990 eruption of V3890 Sgr, the optical light curve at V band declined by three magnitude in 14 days (Schaefer 2010 ). After the 2019 eruption, the optical light curve also shows a fast decline (see Fig. 1 ). Such a fast decline is expected for nova envelopes with mass of < 10 -6 M (Yaron et al. 2005 ). Furthermore, the same rapid decay of the optical light curve is observed in RS Oph, where its ejected no va env elope is estimated to be (10 -7 ≤ M ej ≤ 10 -6 ) M (e.g. O'Brien et al. 1992 ;Sokoloski et al. 2006 ). More evidence of a low-mass ejected envelope in V3890 Sgr is based on the fast nov a e volution where high-ionization lines appear in the spectra ≈18 days following the 1990 eruption (Anupama & Sethi 1994 ).

Anupama & Sethi use Balmer emission line fuxes to estimate the mass of the no va env elope as ≈ 10 -7 M . In addition, Evans et al. ( 2022 ) used Paschen emission line fuxes to estimate the mass of the ejected envelope following the 2019 eruption as 5 × 10 -7 M . In our analysis, we consider ejecta masses in the range of 10 -7 -10 -5 M .

The simplest model for the circumstellar material is to assume the companion star is expelling a spherically symmetric wind with constant velocity and mass-loss rate. The density distribution of the medium is then described as

where Ṁ is the mass-loss rate, V wind is the velocity of the red giant wind, and r is the distance from the companion binary. Without prior knowledge of the distribution of circumstellar material, this spherical distribution of the red giant wind is assumed for V3890 Sgr. It is, ho we ver, noted that non-spherical distribution of material is common in symbiotic recurrent systems (Walder, Folini & Shore 2008 ;Booth, Mohamed & Podsiadlowski 2016a ). Furthermore, the two components observed in the emission-line profles of V3890 Sgr following the 1990 and 2019 eruptions indicate that the nova remnant is non-spherical (Anupama & Sethi 1994 ;Evans et al. 2022 ).

A spherical assumption considered here is, therefore, a simplistic approach.

The time evolution of a shock wave propagating through the red giant wind is divided into two phases. During the frst phase, when the mass of the nova envelope ( M ej ) is much larger than that of the swept-up surrounding medium ( M sw ), the shock is in free expansion.

As the mass of the swept-up material increases, such that M sw > M ej , the no va env elope enters a second phase of evolution referred to as the Sedov-Taylor phase. For spherical nova ejecta with a power-law density profle ( ρ ej ∝ r -2 ) interacting with circumstellar medium of density, ρ CSM ∝ r -2 , self-similar solutions are determined for the evolution from a free expansion phase to the adiabatic expansion phase, as shown in Table 1 of Tang & Che v alier ( 2017 ). For the purposes of this analysis, we assume that the red giant and white dwarf are co-located at the centre of the red giant wind, a valid assumption o v er the course of the radio light curv e because the shocked ejecta expand outside the binary system within the frst day of eruption.

Tang & Che v alier ( 2017 ) present expressions for the radius and velocity of the forward shock with time, given as

Here R ch , V ch , and t ch are the characteristic radius, velocity, and time, respectively, as follows:

V wind 10 km s -1 pc (7)

R * b and V * b are analytical dimensionless quantities defned by Tang & Che v alier ( 2017 ), and can be written as a function of t * = t / t ch as follows:

The predicted radius ( R shock ) and velocity ( V shock ) of the blast wave are shown in Fig. 6 . The radius and velocity of the shock depend on the ejecta mass ( ≈10 -5 -10 -7 M ) and kinetic energy of the nova ejecta, along with the density of the circumbinary material (i.e. Ṁ /V wind ). The shock radius frst grows linearly with t and later as t 0.67 . Similarly, the shock wav e v elocity frst remains at a near-constant value but decreases as t -0.33 at later times. The fux densities depend not only on these quantities, but also on the distance to the nova, e and B . For a given M ej , we iterate to fnd which E yields maximum expansion velocities at early times (i.e. during free expansion; Fig. 6 ) consistent with the maximum ejecta velocity of ≈4200 km s -1 , as estimated from optical spectroscopy (Strader et al. 2019 ).

Figure 6. Top: Radial evolution for a nova forward shock interacting with a circumstellar material, assuming ejecta mass of 10 -6 M , kinetic energy E = 6 × 10 45 erg and Ṁ = 10 -7 M yr -1 for V wind = 10 km s -1 . This represents the free expansion ( R shock ∝ t ) and the Sedov-Taylor phase of the evolution ( R shock ∝ t 2/3 ). Bottom: Velocity evolution of the forward shock as it interacts with the surrounding medium. At the beginning of the evolution, during the free expansion phase, the velocity is constant. Later, the shock enters the Sedov-Taylor phase of evolution and V shock ∝ t -1/3 . The vertical dashed line represents the initial maximum velocity of ≈4200 km s -1 of the nova ejecta on day 1.2 after the nova eruption.

The radio light curve of V3890 Sgr is compared to the model used to explain non-thermal emission in supernova explosions (Section 3.2 ; Che v alier 1998 ). The model depends on various input parameters, including: p = 2.1, V wind = 10 km s -1 , and the distance to the nova (9 kpc). The velocity and radial profle of the expanding material are as discussed in Section 3.3.3 .

First, we consider a range of M ej between M ej = 10 -5 M and 10 -7 M . Fig. 7 shows model radio light curves for three different ejecta masses: M ej = 10 -5 M , 10 -6 M , and 10 -7 M . In all three cases, we assume Ṁ = 3 . 2 × 10 -8 M yr -1 for V wind = 10 km s -1 . By studying supernov a shocks, Che v alier & Fransson ( 2006 ), established that microphysical shock parameters e = B = 0.1. Similar v alues are deri ved from simulations of relativistic shocks (Sironi, Keshet & Lemoine 2015 ). However, observations of shocks in novae at γ -ray wavelengths determine e = 0.01 (Chomiuk, Metzger & Shen 2021a ) and simulations of nonrelativistic shocks show B ≈ 0.01 (Caprioli & Spitko vsk y 2014 ). F or our fducial M ej value of 10 -6 M , we fnd Ṁ that produces the radio light curve. Model A and C are demonstrating what happens when we change M ej . For a particular value of M ej , the kinetic energy is chosen to yield a maximum velocity of ≈4200 km s -1 on day 1.2, see Fig. 6 . Model parameters are listed in Table 4 . For model A (left panel of Fig. 7 ), the synchrotron emission is signifcantly more luminous and longer lasting than the observations. With the parameters given in model B in Table 4 , M ej = 10 -6 M agrees well with the data during the rise and peak of the radio emission (middle panel of Fig. 7 ). For model C, the right panel of Fig. 7 , the radio light curve is less bright and the radio emission does not last very long. None of the models predict the decay phase of the radio light curve accurately. A discussion of why this is the case is included in Section 3.4.2 .

For the more massive ejection ( M ej = 10 -5 M ) to not overpredict the radio fux densities, the model would require less energy in accelerated particles and amplifed magnetic felds, such that e = B = 0.004. This is consistent with estimates of particle acceleration implied by modelling of γ -ray emission from a symbiotic nova (e.g. Abdo et al. 2010 ). Additionally, Sarbadhicary et al. ( 2017 ) have also shown e to be lower than 0.01 in non-relativistic shocks. Adopting these values of e and B produces a model D shown in Fig. 8 and tabulated in Table 4 .

For the less massive ejection ( M ej = 10 -7 M ) to not underpredict the radio fux densities, the model requires a high effciency of either accelerating particles or amplifying magnetic felds, if not both. As B is the more poorly constrained parameter (e.g. Che v alier & Fransson 2006 ;Lundqvist et al. 2020 ), we let it vary while holding e fxed, fnding a good match to the observed light curve with e = 0.01 and B = 0.1 (Fig. 9 ; Model E in Table 4 ). This produces a better ftting model compared to model C. Ho we ver, since B has been shown to vary signifcantly with values as low as 3 × 10 -3 (Lundqvist et al. 2020 ), this less massive ejection model should be considered with caution.

The most likely mass of the ejecta envelope is, therefore, between 10 -5 M and 10 -6 M . These values of ejecta mass are similar to those estimated in recurrent novae T Pyx (Nelson et al. 2014 ) and RS Oph (P ande y et al. 2022 ).

The model of the frst radio peak is compared to the VLA radio light curves at frequencies between 1.78 GHz and 7 GHz as shown in Fig. 10 .

At higher frequencies, the ejected material becomes optically thin faster and a line of sight can penetrate deeper into the ejecta (compared to observations at lower frequencies), thus providing information at smaller radii. By keeping the ejected mass and Ṁ at constant values of 10 -6 M and Ṁ = 3 . 2 × 10 -8 M yr -1 , the MeerKAT model does not provide proper fts for any of the VLA radio light curves (see Fig. 10 ). This implies that the CSM profle cannot be described with ρ CSM ∝ r -2 at the regions closest to the compact object.

Even though the prediction of synchrotron luminosity is sensitive to the assumptions made, in all the cases presented abo v e, the radio light curve provides an estimate of the mass-loss rate of the red-giant companion of 3 . 2 × 10 -8 M yr -1 , taking the velocity of the red giant wind as 10 km s -1 . Using radio observations and assuming spherically distributed ionized circumstellar material in symbiotic systems, Seaquist & Taylor ( 1990 ) determined • M wind = 10 -7 M yr -1 for most red giant stars assuming V wind = 10 km s -1 . Ho we ver, studies of the most studied recurrent nova RS Oph imply a mass-loss rate of 10 -8 M yr -1 (Vaytet, O'Brien & Bode 2007 ;Van Loon 2008 ). The mass-loss rate of V3890 Sgr estimated from its radio light curve is in the range of those found for red giants in symbiotic systems and RS Oph.

Although the early shape of the MeerKAT 1.28 GHz radio light curve can be described with a simple model of a ρ CSM ∝ r -2 circumstellar medium, the light curve then plateaus around days ∼30-60, in excess

Downloaded from https://academic.oup.com/mnras/article/523/2/1661/7176084 by Michigan State University-College of Law user on 02 July 2023 4 . For a particular value of M ej , the kinetic energy is varied to yield a maximum velocity on day 1.2. For model A (left panel) with M ej = 10 -5 M , the synchrotron emission is signifcantly more luminous and longer lasting than the observations. The middle plot shows model B for M ej = 10 -6 M and is a good match to the observations during the rise and peak of the radio emission. The right plot represents model C for M ej = 10 -7 M and is not luminous enough to match the observations. Note. Here we assume a wind velocity, V wind = 10 km s -1 .

Figure 8. Model of radio emission produced by synchrotron emission undergoing free-free absorption (represented as the red solid line), superimposed on the MeerKAT light curve (blue points) for a massive ejection M ej = 10 -5 M with a shock that is less effcient at accelerating electrons and amplifying magnetic felds; see model D in Table 4 for details.

of the model (Figs 7 -10 ; see also Fig. 2 ). We call this excess emission the 'second peak' of the radio light curve. Before day 17, the radio fux is rising. During the decay phase of the radio light curve of V3890 Sgr, the fux densities can be described by a power-law relationship with time such that S ν ∝ t β . Between days 17 and 40, the radio emission fattens such that β = -0.5. After the second peak, from day 60 onwards, the radio fux density rapidly declines as β = -2.8, which is a steeper decay than predicted by our model with a ρ CSM ∝ r -2 circumstellar medium. This standard model is described by β = -1.3 for the decline phase (Che v alier & Fransson 2006 ). The synchrotron luminosity produced when a nova remnant interacts with the circumstellar medium is expected to rise, peak, and decay in a span of a few months (Kantharia et al. 2016 ). The radio luminosity in this framework decays during the optically thin phase of the radio light curve due to a decrease in both the circumbinary density and shock wave velocity (Weiler et al. 2002 ). The second radio peak we observe cannot be explained by a single interaction with a spherically distributed wind-like circumstellar medium. 4 ). Double-peaked radio light curves have been observed previously in novae with giant companions, but on different time-scales. For example, the radio light curve of the 2006 eruption of nova RS Oph showed a frst peak around day 8, which was followed by a second peak on day 40 (Eyres et al. 2009 ). Based on its spectral evolution, the authors concluded that the radio emission from the no va is mix ed thermal and non-thermal radiation. V1535 Sco is another symbiotic nova where the radio light curve shows several radio peaks with the frst one recorded on day 25 (Linford et al. 2017 ). The spectral evolution of V1535 Sco is also consistent with a mixture of thermal and non-thermal emission (Linford et al. 2017 ).

V3890 Sgr is the frst symbiotic recurrent nova where the second radio bump is clearly dominated by non-thermal emission, given that the spectral index is predominantly negative with values of α ranging between -0.3 and -0.4, see Table 3 . The brightness temperature also remains high ( 10 5 K) even at day 100 (Fig. 5 ).

So what might explain the second radio peak and the subsequent fast decay of V3890 Sgr? The luminosity remaining bright compared to the model translates to either an excess of shock velocity or an excess density of material being shocked, relative to our simple model. While man y no v ae sho w multiple ejections and increases in ejecta velocity as an eruption proceeds (Aydi et al. 2020 ), the fast eruptions of symbiotic recurrent novae can generally be described as a single ejection decelerating as it sweeps up circumstellar material (e.g. Walder et al. 2008 ;Orlando, Drake & Laming 2009 ;Munari et al. 2011 ). We therefore interpret V3890 Sgr's deviations from our simple model as complex structure in the circumstellar material (i.e. the density distribution does not just decrease as r -2 , as expected if the red giant companion powered a wind with constant velocity and mass-loss rate).

In fact, it has been shown that the surrounding medium in systems like V3890 Sgr is likely to be structured and aspherical. For example, simulations of RS Oph show that material lost from the companion star ends up concentrated in the orbital plane during the mass transfer process (Walder et al. 2008 ;Booth, Mohamed & Podsiadlowski 2016b ). Mass-loss from the outer Lagrangian points imposes spiral waves on circumstellar material and can create complex structure as the spirals interact. In addition, a non-uniform distribution of material may arise due to changes in the mass-loss rate or wind velocity from the companion star. Finally, recurrent nova eruptions likely sweep up circumstellar material, leading to shells bounded by lower density cavities (Moore & Bildsten 2012 ;Darnley et al. 2019 ).

The excess in radio emission between days ∼30 and 60 therefore implies a relatively dense 'shell' of CSM at ∼10 15 cm from the binary (see the radius evolution in Fig. 6 ). The rapid decline of the radio light curve after day 60 implies circumstellar material whose density declines more steeply than ∝ r -2 (see equation 3 in Nyamai et al. 2021 ), which can be pictured as a lower density region at radii 1.3 × 10 15 cm. Similar low-density material at ≈10 15 cm is implied in another symbiotic nova V407 Cyg (Chomiuk et al. 2012 ). While such a shell/cavity structure is tempting to blame on past nova eruptions sweeping up the giant's wind, this is unlikely since the material ejected during V3890 Sgr's 1992 eruption should be at a radii of ∼10 16 cm based on Fig. 6 . Unless the 1992 eruption was quite different from the 2019 eruption (contrary to the fndings of Schaefer 2010 , who fnd that eruptions in the same recurrent nova system generally match each other well), it is diffcult to imagine how the 2019 ejecta could 'catch up' to the 1992 ejecta. The most likely cause of the structure in the circumstellar material is, therefore, the mass transfer/accretion process itself (Mohamed & Podsiadlowski 2007 ;Walder et al. 2008 ).

Radio observations are not the only evidence for complex structure in the circumstellar material around V3890 Sgr. Chandra High Energy Transmission Grating observations of V3890 Sgr on day 7 showed X-ray emission lines that are asymmetric, blue-shifted, and indicating multiple plasma temperatures (Orio et al. 2020 ). Orio et al. suggest that a non-uniform distribution of the circumbinary medium could be the source of the different emission region temperatures. The H α emission line of V3890 Sgr obtained using the Asiago 1.22 m telescope shows a broad component observed from day 1 following the 2019 eruption. A narrow component appears at least 13 days after the eruption (Munari & Walter 2019c ). This implies presence of both fast and slow outfows of the ejecta. Evolution of emission lines at infrared wavelengths indicates both fast uninterrupted polar outfow and a slow equatorial outfow as a result of encounter with surrounding medium (Evans et al. 2022 ). Binary interaction simulations of systems similar to V3890 Sgr reveal asymmetries in the distribution of circumbinary material, such that the dense material is concentrated at the orbital plane and the less dense material is concentrated at the polar directions of the binary systems (Booth et al. 2016b ). The radio emission is, therefore, possibly originating from the interaction of the shock with dense material. The shock interaction in the equatorial region, therefore, dominates the radio luminosity as the less dense polar outfow expands without much deceleration.