V1369 Cen High-resolution Panchromatic Late Nebular Spectra in the Context of a Unified Picture for Nova Ejecta

For each object, the panchromatic data set consists of coordinated optical and UV spectra. Early epochs had the requirement of nearly simultaneous observations, while the late nebular spectra presented herein could be up to 1 month apart for easy scheduling. UV spectra were secured with the Space Telescope Imaging Spectrograph (STIS) on board the Hubble Space Telescope (HST). The adopted instrument setup was generally the same using the medium-resolution echelle gratings E140M centered at 1425 Å and E230M centered at 1978 and 2707 Å on consecutive exposures. The resulting UV range was 1200–2900 Å with spectral resolution R = 45,800 and R = 30,000 for the far-UV (FUV) and near-UV (NUV) band, respectively. The exception was early in the V1369 Cen outburst when the nova was still too bright to be safely observed with the medium echelle in the FUV. Then, the high-resolution echelle was used; see Table 1.

The optical spectra were obtained either at the Nordic Optical Telescope (NOT) using the FIbre-fed Echelle Spectrograph (FIES) for the case of the northern objects (e.g., V339 Del) or with the Fiber-fed Extended Range Optical Spectrograph (FEROS) at the 2.2 m telescope and the Ultraviolet and Visual Echelle Spectrograph (UVES) at the Very Large Telescope (VLT) for the southern objects (V1369 Cen). The covered optical range varied slightly depending on the instrument, the largest being offered by UVES, which is the only one capable of covering the whole visible band from the atmosphere cutoff at 3000–10000 Å. We took advantage of this capability by combining the dichroic setups DIC1/3460 + 5800 Å and DIC2/4370 + 8600 Å. FIES and FEROS have fixed spectral format and cover, respectively, the wavelength range 4000–7500 Å and 4000–9000 Å. All spectra had high resolution: R = 48,000 for FEROS, R = 45,000 or 67,000 for FIES, and R = 40,000 in UVES.

The detailed log of observations is provided in Tables 1–3. Note that, while performed, the V959 Mon STIS observations failed, so no UV spectrum exists for the last epoch of observation of V959 Mon (day 988).

STIS data were reduced with the instrument pipeline. The order merging was, however, performed with the HST Goddard High Resolution Spectrograph script because of its better performance. Instrument pipeline reductions were also used for the optical spectra. We flux-calibrated FEROS and FIES data using our own scripts (IDL and/or IRAF). For each object we observed a standard star that was relatively close in pointing direction. The standard-star spectra (BD +28°4211 for V339 Del at FIES and LTT 4816 + CD –32°9927 for V1369 Cen at FEROS) were taken immediately after the science observation. Although we also observed dedicated standard stars for the UVES runs (HR 2315 for V959 Mon and LTT 4816 for V1369 Cen), we finally adopted the master response function delivered by ESO for its better response below 3500 Å and above 9000 Å. We ascertained that the master response function matched the response function built with the dedicated standard star in the overlap range.

As mentioned in Sections 1 and 3, the nova X-ray light curve was used to aid the planning of the observations and the identification of the nebular spectra. The V1369 Cen light curve obtained from Swift observations is shown in Figure 1, together with the hardness ratio (HR) evolution.

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The Swift-XRT data were processed and analyzed using the standard HEASoft tools. The optical brightness of the nova was such that the pileup of optical photons up to X-ray energies ("optical loading") was a concern. Thus, the light curve was obtained extracting only single-pixel (grade 0) events, which helps to mitigate this problem. In addition, the earliest data (up until 2014 February 18; day 78) were obtained using Windowed Timing (WT) mode, which further decreases the optical loading issues, due to the faster read-out time.

At no point was there any sign of X-ray pileup in the data, so the source light curve and HR bins were extracted using circular regions with radii of 10–20 pixels (1 pixel = 236) depending on the brightness of the source. For the WT data, the background determination was performed using the same size region, offset from, but close to, the source; for Photon Counting mode, a larger circular region was used.

From a series of 12 spectra (FEROS, R = 48,000) taken during early decline, we measured an equivalent width EW = 0.345 ± 0.005 Å for the Na i D2 λ5890 interstellar absorption, corresponding to $E(B-V)$ = 0.15 mag according to the Munari & Zwitter (1997) method. Similarly, measuring the EW of the separate components and adding the individual $E(B-V)$, we obtain $E(B-V)$ = 0.16 mag. However, these $E(B-V)$ may be only lower limits, since the interstellar neutral sodium could have condensed into dust and be depleted in the gas phase. Therefore, for our reddening estimate we also turned to the neutral hydrogen column density. This can be derived by modeling the interstellar Lyα absorption in the day 837 spectrum⁹ by assuming different column densities (Figure 3, top panel). The best Lyα match is obtained for neutral hydrogen column densities of ∼7.2 × 10²¹ cm⁻² corresponding to $E(B-V)$ = 0.15 mag, in agreement with the NaID estimate. We additionally checked that the derived column density is consistent with that computed by integrating the H i 21 cm emission in the LAB and GASS maps (Kalberla et al. 2005; Kalberla & Haud 2015) in the velocity range corresponding to the NaID interstellar absorption profile¹⁰ (Figure 3, bottom panel). We adopt $E(B-V)$ = 0.15 mag and the Cardelli et al. (1989) extinction curve when dereddening our data in the following analysis and measurements.

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We computed the electron density, n_e, and derived its variation over time. Despite the optimal wavelength coverage of our spectra, we are often impeded in the use of the classic diagnostics because of the heavy blends or small gaps in spectral coverage. We could not use the [Ne v] and [Ne iii] because we do not observe the [Ne v] λ2975 emission, and for [Ne iii] we are unable to deblend the [Ne iii] λ3342 from the λ3346 owing to superposed emission from O iii λ3341 (all epochs). We could not use the [N ii] diagnostic even when the λλ6548, 6583 doublet was separable from Hα because the [N ii] λ5755 emission line falls in the gap of the UVES red CCD mosaic in the VLT observations. Instead, we used the [O iii] diagnostic, deblending the λ4363 from the Hγ line (by scaling Hβ to the blue wing of Hγ as in our previous studies).

Unlike previous analyses in the literature, our method does not use the integrated line flux. We computed the electron density for each velocity resolution element. The advantage is that of retaining information about the ejecta projected geometry and kinematics and revealing different local conditions. We plot in Figure 4 the electron density in velocity space at the four epochs of Table 1, as derived from the [O iii] emission lines. The plot shows how the electron density decreases from ∼10⁷ cm⁻³ to less than 10⁶ cm⁻³ between days 242 and 835, at least for the low-velocity $(| {v}_{\mathrm{rad}}| \leqslant 800\,\mathrm{km}\,{{\rm{s}}}^{-1})$ portion of the ejecta. The high-velocity gas (i.e., $| {v}_{\mathrm{rad}}| \geqslant 800\,\mathrm{km}\,{{\rm{s}}}^{-1}$) in [O iii] is too weak to allow density computations. The low-velocity gas, however, is not uniform in density, and the portions between −700 km s⁻¹ ≤ v_rad ≤ −500 and 400 km s⁻¹ ≤ v_rad ≤ 600 km s⁻¹ have somewhat higher density than the line "center" (−500 km s⁻¹ < v_rad < 400 km s⁻¹). The contrast increases from day 242 to day 835 up to a factor of 2. The innermost portion of the ejecta follows the density decrease expected for ballistic expansion (i.e., n_e ∝ t⁻³), while the intermediate portion of the ejecta follows a less steep decrease in time (n_e ∝ t^−2.4; see the bottom right panel of Figure 4). This does not imply that the ejecta is following different expansion laws in different portions, but that the intermediate-velocity portion of the ejecta is not yet in the collisionless limit.

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In addition, the profile of the UV transitions in the last epoch (day 837) has evolved in such a way that the two doublets C iii] λλ1906, 1908 and N iv] λλ1483, 1486 are no longer blended and also can be used as density diagnostics. This is a first for novae, although the diagnostic is standard for H ii regions, planetary nebulae, and symbiotic stars. Note that these ratios are independent of reddening. Figure 5 shows (left panels) V1369 Cen C iii] and N iv] line profiles and, for comparison (right panels), the same transitions in the last spectrum of V339 Del (day 866). The doublets are blended in V339 Del, even at the last epoch, and the line profile shows an obvious asymmetry of the ejecta. We will return to this in Section 6 when discussing the geometry.

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Nussbaumer & Schild (1981) plot the N iv] line ratio for pure recombination as a function of the electron density for a range of temperatures. We measured the N iv] line ratio for the blue and red peaks separately and ascribe any difference to noise. We obtain an average line ratio of 0.52 ± 0.06 so that n_e ≃ 5.2 × 10⁵ cm⁻³, compared with the average value of 5.6 × 10⁵ cm⁻³ from the [O iii] density diagnostic at the blue and red peaks. Note that the [O iii] and N iv] peaks yield both comparable densities and density decline rates (as computed for the N iv from the last two epochs). The C²⁺ recombination coefficient and line ratio as a function of density have been computed by Nussbaumer & Schild (1979). We measured the average flux ratio 0.30 ± 0.05 from the blue and red peaks of the C iii] transition in the day 837 spectrum (after a boxcar smoothing of 15 resolution elements). Assuming an electron temperature T_e = 10,000 K, we derive from Nussbaumer & Schild (their Figure 5(a)) n_e ∼ 1.4 × 10⁵ cm⁻³.

A striking important result can be obtained from the comparison of the discrete absorption features for N v λλ1238, 1242 and C iv λλ1548, 1550. In V1369 Cen we observe a significant number of coincident (in velocity) N v and C iv absorptions, whose EWs were used to obtain the N⁴⁺/C³⁺ column density ratio as follows:

$$\begin{eqnarray*}&&{({\rm{N}}/{\rm{C}})}_{{v}_{\mathrm{rad}}}=({\mathrm{EW}}_{{\rm{N}}}/{\mathrm{EW}}_{{\rm{C}}}){({\lambda }_{{\rm{C}}}/{\lambda }_{{\rm{N}}})}^{2}({f}_{{\rm{C}}}/{f}_{{\rm{N}}})\sim 1.8({\mathrm{EW}}_{{\rm{N}}}/{\mathrm{EW}}_{{\rm{C}}}),\end{eqnarray*}$$

where λ is the rest wavelength and f is the oscillator strength. The common velocity components were at −1840, −1570, −1345, and −1150 km s⁻¹ (see Figure 6), and the derived N⁴⁺/C³⁺ column density ratio was 270, 200, 233, and >120, respectively, with an uncertainty of about 10%. Thus, excluding the lower limit and assuming that the measured resonance lines represent the dominant ion state, the ratio of nitrogen to carbon was ≥200. The solar ratio is 0.31 (Asplund et al. 2009), implying that V1369 Cen was enormously enhanced in nitrogen relative to carbon. The ratio is more extreme than published nucleosynthetic yields of the TNR of massive white dwarfs (WDs; e.g., Downen et al. 2013; Casanova et al. 2016; Starrfield et al. 2016).

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A similar analysis applied to T Pyx and V339 Del produced different values. In particular, we found an N/C ratio in the range of [1, 6] for the case of V339 Del¹¹ and N/C ≃ 2.3 ± 0.2 for T Pyx. In both cases, the values are not as different relative to the solar value as for V1369 Cen, and they are compatible with theoretical TNR predictions.

Note that in all cases no information is available for the isotopic composition of the clumps. Although consistent with the general expectation for the explosive yields, these abundance ratios cannot place precise constraints on the thermodynamic condition at the peak of the TNR.

The first STIS spectra were taken at the highest echelle resolution when the nova was especially bright. This affords the best interstellar absorption line profiles, and we have used the O i λ1302, Si ii λ1260, C i λ1561, and Al ii λ1670 lines to provide a range of ionizations and line strengths. Except for O i, all are strong but unsaturated. The interval covered by the profiles was −11 km s⁻¹ ≤ v_rad,helio ≤ 14 km s⁻¹ with a mean velocity of 1.4 km s⁻¹ (weighted flux distribution), corresponding to v_rad,LSR = −2.4 km s⁻¹ in the local standard of rest (LSR). Using the IAU standard Oort constants and distance to the Galactic center, this velocity implies a distance 1.8 ≤ D(kpc) ≤ 2.4. We adopt 2 kpc in what follows. This is also consistent with the extinction. The distance is independent of any maximum magnitude versus rate of decline (MMRD) assumptions. As we discussed, V1369 Cen did not resemble either V959 Mon (or other ONe classical novae) or V339 Del, so we cannot scale the spectra relative to previously observed exemplars.

For mass determination, we take advantage of the multiple determinations of the n_e from the last-epoch optical and UV spectrum (day 835/837). The measured Hβ flux was $F({\rm{H}}\beta )=1.47\,\times \,{10}^{-12}$ erg s⁻¹ cm⁻². With a reddening $E(B-V)$ = 0.15 applied and for a distance of 2 kpc, the line luminosity was L(Hβ) = 1.2 × 10³²(D/2 kpc)² erg s⁻¹. The range of n_e obtained from the C iii] λ1908, N iv] λ1486, and [O iii] nebular lines is 1 < (n_e/10⁵) cm⁻³ < 6, giving a predicted range 0.5 < L(Hβ)/(10³⁵ erg s⁻¹) < 12 with a choice of v_max = 2500 km s⁻¹. Although this is a broad range, other quantities are fairly well constrained: the solid angle of the aspherical ejecta as provided by the bipolar models (see Section 6.2) is (ΔΩ/4π) ≈ 1/3, and the filling factor is in the range of 0.1 < f < 0.2. Combined with the electron density, the ejecta mass resulted in approximately (1.1 ± 0.4) × 10⁻⁴ M_⊙ adopting a solar He/H ratio. Although some novae appear to have either hydrogen deficiencies or enhanced helium abundances (e.g., José & Shore 2008; Schwarz 2014), the electron density is obtained directly from the plasma diagnostics and not from the Hβ flux, which was used only to derive the filling factor. The filling factor scales as f ∼ [1 + n(He)/n(H)]⁻¹, and the mass scales as (μ/1.6)f. The independent determination of the helium abundance is only possible with detailed modeling of the recombination and ionization structure of the ejecta and applies only during the photoionization-dominated stage before SSS turnoff. We note, alternatively, that the mass scales as ${M}_{{ej}}\sim {v}_{\max }^{-3/2}{{Dn}}_{e}{[E(B-V)]}^{1/2}$.

This mass is higher than we found for V339 Del ((2–3) × 10⁻⁵ M_⊙; Shore et al. 2016) and V959 Mon (≲6 × 10⁻⁵ M_⊙; Shore et al. 2013a), but not excessively so, and is around the values expected from the models of the TNR (Downen et al. 2013).

One must never forget that the emission-line profile is the result of a line-of-sight velocity projection effect. For optically thin gas, we see everything that has a sufficient emission measure in a given radial velocity bin, so we measure the sum of the contributions from individual clumps, each of which may have different density conditions. Hence, even the density in velocity space, as in Figure 4, is an average per velocity bin. The diverse local conditions of the clumps imply that different parts of the ejecta might develop differently depending on their different outward velocity relative to the WD. However, once each clump is in pure recombination for a given ion, the line profile is "frozen" and the line flux simply decreases with time with no change in v_rad. With this in mind, we can compare lines produced by different mechanisms (e.g., recombination, collisions exciting a metastable level, or intercombination transitions) and by different ions of the same element. These comparisons yield the boundaries of the distribution of various ions, i.e., the ionization structure, and help disentangle abundance from ionization effects in the observed line profiles.

To illustrate this for the V1369 Cen ejecta, we compare (1) the temporal evolution of three forbidden transitions of oxygen from different ionization stages (O⁰ to O²⁺); (2) the different profiles of recombination, intercombination, and forbidden transitions from low- and high-ionization energy ions at epoch ∼566 days; and (3) the profiles of recombination lines from different ions at day 835.

The evolution of the oxygen ions is shown in Figure 7. Since this treats a single element in various ionization stages, it shows the development of the ionization structure unbiased by abundance. It is interesting to note here that in the first epoch (day 242/252), [O ii] and [O iii] both have very pronounced wings $(800\,\mathrm{km}\,{{\rm{s}}}^{-1}\lt | {v}_{\mathrm{rad}}| \lt 1600\,\mathrm{km}\,{{\rm{s}}}^{-1})$, which quickly disappear for the [O ii] transitions but persist (although weakened) in [O iii]. Hence, in that velocity range the densities are low enough that O²⁺ no longer recombines to O⁺ as easily. Oxygen exists mostly in the double ionized state, which is excited from the ground level by collisions (and the collisional excitation cross section is larger than the collisional recombination cross section). Similarly, the neutral O is confined to higher-density regions that correspond to the lower-velocity bins. By projection, the peak intensity of the [O i] transition occurs at −400 km s⁻¹ and +300 km s⁻¹, while the [O iii] emissions have their peak intensity at −600 km s⁻¹ and +550 km s⁻¹.¹² At those velocities the [O i] shows only a weak shoulder. This implies that the O²⁺ concentrates, on average, at larger velocities with respect to O⁰, i.e., the O²⁺/O⁰ ratio increases at higher velocity. The lowest v_rad portion of the emission lines (velocity range −300 km s⁻¹ < v_rad < 200 km s⁻¹) shows relatively higher flux in the [O iii] transition than in the [O ii] and [O i], especially at epochs 458 and 566, indicating that there are projected low-velocity regions where O²⁺ does not recombine. In other words, the oxygen is mostly in the O²⁺ state everywhere across the ejecta but is relatively more abundant—compared to O⁺ and O⁰—in the outer portion of the ejecta (those with the higher velocity), where the density must be lower for the recombination rate to be consequently lower. The O⁺ tracer, [O ii]λ2470, disappears earlier (at day 837 it is almost completely gone) because of the higher energy of its upper level.

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Figure 8 shows forbidden, intercombination, and recombination transitions from different ions observed on day 566. In particular, the left panel compares line profiles from low-energy oxygen ions, including the O iii]λ1666 line, which is an intercombination transition and shows where O³⁺ recombines to O²⁺. The transition shows emission at the −600 and +500 km s⁻¹ peaks and is undetectable everywhere else, i.e., the emission measure is larger where the density is not too low to prevent the O³⁺ recombination and not too high to favor the recombination of lower ions. The right panel compares forbidden and recombination transitions from high-energy ions (67 eV ≤ IP ≤ 113 eV, where IP is the ionization potential), showing that their profiles are similar, i.e., the ions are co-spatial. We note that the O v λ1371 line and similar recombination transitions (e.g., N iv λ1718) are frozen since high-energy ionizing photons are no longer dominant. The highest-energy ions provide information about the spectral energy distribution of the underlying photoionizing source: the detection of O v and [Fe vii] lines and the lack of [Fe x] constrain the SSS (when on) to temperatures >100–130 eV and <200 eV.

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Finally, we show in Figure 9 the profiles of the recombination transitions He ii λ4686 and the singlet He i λ6678, together with Hβ λ4861 at day 835. The two He lines show the distribution of singly and doubly ionized He; since H is the most abundant element, Hβ shows the projected geometry of the ejecta. The He i profile resembles the [O i] line, but with more pronounced peaks at −400 and +300 km s⁻¹. In contrast, He ii has peaks at −600 and +500 km s⁻¹ that are very similar to [O iii], although the two He ii peaks have greater contrast relative to the rest of the line than those in the [O iii] line profile. The similarity is not surprising, since He ii and [O iii] trace the distribution of the highly ionized gas, while He i and [O i] trace the neutral gas. The individual different contrasts in each line result from the fact that recombination lines have much higher transition probability than forbidden lines, and these also depend on their collisional cross section and the electron energy distribution for the population of their upper level.

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In this section we apply the Monte Carlo simulation already used for T Pyx, V959 Mon, and V339 Del, to reproduce the observed line profiles in the V1369 Cen spectra. The code uses random particles confined in a biconical geometry to reproduce the gross characteristics of the line profiles. The random particles have a linear velocity law within a range matching the observations, constant mass, and emissivity corresponding to the evolutionary stage of the nova (recombination). Given the frozen state of the ejecta, it would be physically inconsistent to adopt any photoionization code to reproduce the observed line profile. Photoionization codes assume equilibrium (which is not physically appropriate) and do not account for expansion. The simulation reproduces the global line profile but not specific substructures: these result from the simulation noise but correspond to individual clumps overlapping in the projected velocity space, in real ejecta. Modeling of individual substructures would require adopting specific particle distributions, an assumption that is not relevant to the purpose of our work.

A variety of profiles can result from our code, including the most common, so-called "saddle"- and "castellated"-shaped profiles. They are produced by a combination of opening angles, cone thickness, and inclination with respect to the line of sight. Figure 10 shows the effect of the cone opening angle in shaping the line profile for a fixed inclination. Less collimated ejecta produce more "rectangular" (or "flat-top") profiles, while a "saddle"- or V-shaped profile is obtained with more collimated ejecta. In the case of V1369 Cen we could reproduce its "horned" line profiles of width ∼1200–1500 km s⁻¹ adopting a biconical geometry with opening angle up to 140°, thickness 0.75R (where R is the maximum radius of the ejecta), and maximum expansion velocity v = 2500 km s⁻¹ viewed at an inclination of ∼40°. Figure 11 displays the Hβ profile for T Pyx, V959 Mon, V339 Del, and V1369 Cen, together with the biconical geometry that best mimics their profile and the corresponding Monte Carlo simulation predicted profile. The figure shows the gross similarities and the specific differences characteristic of each ejecta. The emission lines of a given nova can be broader or narrow and more or less rectangular in shape. They can also display extended wings as in the case of T Pyx. All trace back to the specific characteristic of the biconical ballistic ejecta.

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Note that the simulations are not fitting each profile but providing a tool for interpreting the data. In particular, (1) for each nova, the opening angle varies with the transition as different ions have different structures (e.g., [O iii] typically suggests a slightly wider opening angle than [O i] given that the most external regions are less dense and, therefore, more highly ionized; see Section 6.1); (2) there might be degeneracies in the simulation (see Shore et al. 2013b); (3) the line widths and the emission measure decreases with time; and (4) the simulations produce globally symmetric profiles. Asymmetries such as those observed in V339 Del at each epoch and in all transitions (see Shore et al. 2016) likely reflect intrinsic characteristics of the ejecta whose origins remain to be investigated. Hence, the takeaway result from the simulation is that all of the gross features of the observed profiles for each nova can be reproduced by a biconical geometry with relatively wide opening angles and relatively large thickness. Features resembling rings, equatorial belts, and polar caps also result from projection effects of the biconical geometry onto the sky plane (see, e.g., Figure 10 in Shore et al. 2013b; Figures 16 and 20 in Shore et al. 2013a). Thus, bipolar ejection seems to be common to all novae without requiring additional specially tailored structures such as equatorial rings or jets.

For the absorption structures, we see only what is along the line of sight, i.e., any structure that is lying between us and the hot receding surface of the WD. During maximum and early decline when we see the P Cyg profiles, the absorbing gas and the pseudo-photosphere illuminating it are contiguous since the latter is part of the ejecta themselves (or their bottom layer) and subtends a large solid angle that intercepts numerous structures along the line of sight. As the pseudo-photosphere recedes, the number of intercepted structures (i.e., clumps) decreases. Our ability to detect them depends on the inclination and the ejecta characteristics (given sufficient S/N and spectral resolution of the data). Ejecta viewed along the symmetry axis will show a larger number of absorption features. The larger the filling factor, the more absorbing structures are intercepted along the line of sight. The same holds for geometrically thicker ejecta.

V1369 Cen, which is the nova with the best S/N and sampling, shows complex absorptions for the four UV resonance transitions C ii λ1334, Si iv λ1393, C iv λ1548, and N v λ1238, whose ions have different ionization potential energy: ∼11 eV for C⁺, 33 eV for Si³⁺, 47 eV for C³⁺, and 77 eV for N⁴⁺. Figure 12 shows the different absorption patterns produced by each resonant transition at each epoch. Each ion recombines and absorbs where conditions are suitable for it to do so. At early epochs (day 252 in the figure) the densities are sufficiently high that even low ions such as C²⁺ can recombine to C⁺ (and therefore absorb from the ground states) up to relatively high velocities, i.e., up to the outskirts of the ejecta. Si iv, whose absorptions are superposed on a blending emission in the figure, are distributed up to −1750 km s⁻¹ like C ii. In contrast, N v and C iv at that same epoch show absorption troughs (very much like H⁰ or Fe⁺ during the early-decline/iron curtain phase): C and N are four and five times ionized everywhere, but only in the innermost portion of the ejecta is the density high enough for them to recombine to C³⁺ and N⁴⁺. The number of clumps where this can occur is numerous and blending, and only later on (i.e., from day 458 on) do they appear separately. The range of velocity they cover seems to increase, stretching to both lower and higher velocity limits. The appearance of the low-velocity structures at later epochs is because they are seen against the stellar continuum, while earlier they lie on the emission line and conflate with the emission structures. The structures at the higher velocities (i.e., ∼−2000 km s⁻¹) appear as soon as the C⁴⁺ and N⁵⁺ have recombined to C³⁺ and N⁴⁺, respectively (the recombination time for ${{\rm{N}}}^{5+}\to {{\rm{N}}}^{4+}$ is slow), and on day 252 the nitrogen is still 5 times ionized at v_rad < −1700 km s⁻¹. The same holds for C and its recombination ${{\rm{C}}}^{4+}\to {{\rm{C}}}^{3+}$; see also the end of Section 6.5.

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This is consistent with the lack of C⁺ absorptions in the last-epoch spectrum: the majority of C is trapped in high-ionization states, and the fraction of C in low-ionization states is not enough to produce a sufficient contrast against the continuum for detection. The particular absorption pattern produced by a given ion also depends on the clumps' alignment with respect to the changing (decreasing) solid angle subtended by the WD photosphere. Note that most of the structures we see are, in fact, blends even at day 837. The velocity width of individual structures might be as low as 10 km s⁻¹, corresponding to radial thickness of only a few percent or less of R (the cone/ejecta maximum radius).

As a novel feature of our approach, we can also check whether the same approximation used to interpret the emission-line profile reproduces the absorption features observed in these late stages. Hence, we used the same Monte Carlo code, with the same set of parameters and geometry as for the emission profiles (see Figure 10 and Section 6.2), to simulate the absorption features. In this case, each density point along a selected line of sight is used to compute the opacity. Screening effects between clumps have been ignored, although superposition is included. This approximation is valid for the late nebular phase spectra, since the velocity separation between clumps along the line of sight is larger than the velocity width of the individual clumps. The result is shown in Figure 13. The figure shows that decreasing the covering factor reduces the number of absorption features, as discussed above.

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The UV resonance line absorptions were first observed in T Pyx (day 834 spectrum; Shore et al. 2013b) in the very late observations of the recurrent nova and only in N v λ1238 and C iv λ1548 absorptions but with only two structures per transitions. This is consistent with a lower mass for the T Pyx ejecta and with a low filling factor. Unfortunately, we do not have late UV spectra of V959 Mon, so we cannot say anything about its absorption structures in the UV resonance transition. The V339 Del absorptions are shown in Figure 14. The overall evolution of the absorptions in the four resonance transitions is very similar to V1369 Cen, but with a few notable differences: (1) The C ii λ1334 absorptions persist to the end, unlike V1369 Cen, indicating that at similar epochs V1369 Cen reaches lower densities than V339 Del, too low for C²⁺ to recombine to C⁺ (the recombination cross section of C²⁺ is smaller than that of C³⁺ and hence is favored in higher-density environments). (2) The C iv and N v absorptions in V339 Del are never as fragmented as in V1369 Cen, indicating a different distribution of the clumps along the line of sight (the cumulated EWs are comparable in the two novae).

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Global commonalities that we should note are as follows: (i) the velocity ranges spanned by the absorptions are comparable among novae, and (ii) a number of absorption structures persist at the same velocity through all epochs. To better illustrate this, we plot in Figure 15 the absorption structures observed in the low ionization potential metals at early time and in the high-ionization-energy species at late epochs for all the novae studied in panchromatic high-resolution spectroscopy. The figure shows that structures are common to all of them at early decline as soon as the pseudo-photosphere has begun to recede and that similar structures are still visible at very late epochs once the ejecta is frozen in a high-ionization state. There is no one-to-one correspondence of the structures at the two epochs for the following: (1) the opacity of the ejecta is very different and at early phases is rapidly varying as the ejecta expand, and (2) the photosphere against which the absorptions are detected is different at the two epochs and is, in particular, much smaller (being no longer within the ejecta but matching instead the bloated WD photosphere) in the late nebular phase. Nonetheless, one can notice that the structure visible at −1450 km s⁻¹ in the T Pyx 37 day spectrum is the same as the 834 day spectrum. More generally, where we detect bands of absorbing structures at early epochs we detect absorbing structures later on. The largest velocities observed at the two epochs are comparable to those observed in the wings of the emission lines when their emission measure was sufficient. We are, therefore, always seeing the same unchanged distribution of clumps under different illumination, i.e., ionization degrees compatible with their local density and the light source underneath. Their absolute position in space is stretching linearly with time as the ejecta expand. This matches a Hubble flow, i.e., the structures are in ballistic expansion.

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Another important feature of ballistic expansion is that the timescale is unique, independent of the radial distance within the ejecta. Since the recombination time depends on the electron density as ${n}_{e}^{-1}$, and the electron density varies as ${n}_{e}\sim {r}^{-3}\sim {v}_{\mathrm{rad}}^{-3}$, at any epoch after the ejection there is a unique radial velocity (in the observer's frame) that corresponds to that density. It is an expected consequence that the dominant ionization stage of any species is confined at any time in a range of velocities that depends only on the maximum velocity of the ejecta and its mass. Hence, the radial velocity interval in which the discrete absorption features will be observed for any ion will always be about the same, among novae, even if the individual structures are different. For example, for n_e ∼ 10⁵ cm⁻³, as we have in the last epoch of V1369 Cen, the N v and C iv should be observed at around v_rad ≈ −1500 km s⁻¹.

The observational fact emerging from the analysis of the data sets presented in this and the previous works of the series is the presence of persistent absorption structures that do not move, in velocity space, with time. This is evident when comparing late nebular spectra of the same nova (e.g., Figure 30 in De Gennaro Aquino et al. 2014; Figures 12 and 14 in this paper). The persistence of the absorption structures is also shown by comparison of the spectra taken during early decline with those taken during late nebular stages (e.g., Figure 15), and by the evolution of the line profiles across time (e.g., Figure 16; Figures 2 and 4 in Shore et al. 2011; Figures 2 and 3 in Shore et al. 2016). The absorptions from low ionization energy ions visible in a given velocity interval at early stages are also present at later epochs in the resonance transitions of high ionization energy ions. They indicate clumps that have only changed their ionization state, while following the global expansion of the ejecta. The absorption troughs observed during the initial phases of the outburst break into complex absorption structures and tend to shift toward higher v_rad. This matches a clumpy ejecta whose outer portions cool and recombine as the ejecta expand, and as the pseudo-photosphere recedes, the line of sight intercepts progressively fewer structures. Note that these absorptions can also display apparent inward motion or oscillations (e.g., McLaughlin 1957; Figure 1 in Williams et al. 2008; our Figure 16) depending on the nova characteristics and the cadence of the monitoring: each clump absorbs (at a given wavelength) when its density and the incident radiation from behind allow it.

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Persistent structures that do not move in velocity space are, by definition, a Hubble/radial flow (or in ballistic expansion). That they are stationary at velocities well below the maximum velocity observed during early phases of the expansion is not compatible with a wind (e.g., Lamers & Cassinelli 1999). Therefore, a major conclusion of our works is that, in the formation of the observable ejecta, there is no wind ejection at any phase and the ejecta are expanding undisturbed.

In the past, the absorption features observed at early stages in view of their apparent acceleration (despite some exceptions) were interpreted as subsequent shells ejected with increasing velocity. Were that the case, we would not be observing the same structures years after the outburst. It is interesting to note that Liimets et al. (2012) reach similar conclusions (ballistic expansion and little or no deceleration) analyzing the resolved clumps over the past 25 yr of the >100 yr old nova GK Per.

Our monitoring shows that the measured line flux and the derived density in the late nebular spectra of our data sets match the evolution expected for a ballistic expansion. This same conclusion was previously reached by Shore et al. (1996) by analyzing the UV line flux of V1974 Cygni together with its X-ray light curve.

An undisturbed ballistic expansion is incompatible with multiple ejections of shells or structures having increasing velocity (e.g., McLaughlin 1957; Friedjung 1987; Kimeswenger et al. 2008; Tanaka et al. 2011; Chomiuk et al. 2014; Arai et al. 2016). In addition, the velocity field of a ballistic expansion is incompatible with any geometry that implies acceleration or deceleration of the ejecta (e.g., an hourglass geometry).

It is known from imaging that nova ejecta are not spherical but elongated (e.g., Hjellming 1995; Slavin et al. 1995; Gill & O'Brien 2000; Harman & O'Brien 2003; Lane et al. 2007; Chesneau et al. 2011; Liimets et al. 2012; Chomiuk et al. 2014; Schaefer et al. 2014; Linford et al. 2015; Shara et al. 2015; Healy et al. 2017), yet the exact geometry is far from certain. The simplest geometry compatible with a nonspherical radial expansion is polar caps or a biconical form (the difference between the two depending on the thickness one considers). Combining this consideration with the clumpiness of the ejecta, we used a simple Monte Carlo code to mimic the observed line profiles. We adopt a biconical geometry with random clumps that obey a velocity and density distribution matching the ballistic expansion, and emissivity from recombination as appropriate for the late nebular spectra. Our series of papers has shown that such a geometry suffices in reproducing the gross line profiles we observe in high-resolution spectroscopy. Therefore, at this stage, there is no need to consider more complex geometries. The detailed reproduction of individual features would require real dynamical models, which are beyond the scope of this series.

An interesting test of the validity of our approach comes from the use of the adopted geometry in the computation of the ejecta mass and filling factor. They are computed adopting the identified emitting volume and integrating the n ∼ 1/r³ density within such volume. Each epoch is treated independently, providing ejecta mass estimates that are the same within the uncertainties (e.g., Figure 14 of Shore et al. 2016).

The observed spectral evolution is a further validation of the proposed picture. At late phases the highest ions sample the outermost regions of the ejecta because the lower density there prevents recombination. Neutral or singly ionized transitions are favored in the densest region of the ejecta and are expected to be observable for several years in the inner regions of the most massive ejecta. Were the density following a different distribution, we would not have observed such an ionization structure.

Observations by the Fermi/LAT satellite have revealed that novae are capable of emitting γ-rays with energy ≥100 MeV that are evidence of shocks among accelerated particles (Fermi Collaboration 2014; Cheung et al. 2016). Metzger et al. (2014) propose that the 100 MeV emission arises from the collision of distinct ejections of gas having mass differences within an order of magnitude and relative velocity in the range 0.15–0.60. These conditions match the observed range of velocities (from a few hundred to a few thousand kilometers per second; Figures 12, 14, and 15; see also Figures 29 and 30 of De Gennaro Aquino et al. 2014) and the measured local projected densities at any given time (e.g., Figure 4). Hence, collisions between clumps during the ejection and the initial expansion could explain the 100 MeV emission. More than that, intraclump collisions are expected in a single short-duration explosion that generates a stochastic range of clump velocities. The orientation and porosity of the ejecta and the density of individual clumps would then power the γ-ray and X-ray light curves. The modeling of those curves, like precise line profile fitting, would require assuming clump distributions, which are beyond the scope of this paper.

Centimeter-wavelength radio observations have shown morphological changes of the ejecta in resolved images (e.g., Hjellming 1996, and references therein; Chomiuk et al. 2014; Wendeln et al. 2017). Different morphologies observed in different epochs at different frequencies can be explained by differential evolution of the opacity in the spatially resolved nonspherical inhomogeneous sources, similarly to the changes in the line profiles during early stages of the outburst. Indeed, the "varying" radio images during the optically thick phase of the novae were explained by nonspherical single ejecta having a velocity gradient (e.g., Hjellming 1996, 1995). Global density gradients and inhomogeneous ejecta were instead inferred from radio observations deviating from the theoretical distribution expected for a uniform optically thick and isothermal gas (e.g., Seaquist & Palimaka 1977). Morphological difference in resolved radio images of an optically thin gas (e.g., Chomiuk et al. 2014) maps the different emissivity of each region at a given frequency, similarly to the profile difference we observe in the optical in the late nebular phase (e.g., Figure 17, bottom panel; compare N iv] to Hβ for an example of a dramatic difference).

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