<figure><img src="image_1.png" /></figure>

FERMI-LAT GAMMA-RAY DETECTIONS OF CLASSICAL NOVAE V1369 CENTAURI 2013 AND V5668 SAGITTARII 2015

C. C. CHEUNG¹, P. JEAN²,³, S. N. SHORE⁴,⁵, Ł. STAWARZ⁶, R. H. D. CORBET⁷,⁸, J. KNÖDLSEDER²,³, S. STARRFIELD⁹, D. L. WOOD¹⁰, R. DESIANTE¹¹,¹², F. LONGO¹³,¹⁴, G. PIVATO¹⁵, AND K. S. WOOD¹⁰

¹Space Science Division, Naval Research Laboratory, Washington, DC 20375-5352, USA; Teddy.Cheung@nrl.navy.mil

²CNRS, IRAP, F-31028 Toulouse cedex 4, France; Pierre.Jean@irap.omp.eu

³GAHEC, Université de Toulouse, UPS-OMP, IRAP, Toulouse, France

⁴Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, I-56127 Pisa, Italy; steven.neil.shore@unipi.it

⁵Dipartimento di Fisica “Enrico Fermi,” Università di Pisa, Pisa I-56127, Italy

⁶Astronomical Observatory, Jagiellonian University, 30-244 Kraków, Poland

⁷Center for Research and Exploration in Space Science and Technology (CRESST) and NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

⁸University of Maryland Baltimore County, Baltimore, MD 21250, USA

⁹School of Earth and Space Exploration, Arizona State University, P.O. Box 871404, Tempe, AZ 85287-1404, USA

¹⁰Praxis Inc., Alexandria, VA 22303, resident at Naval Research Laboratory, Washington, DC 20375-5352, USA

¹¹Università di Udine, I-33100 Udine, Italy

¹²Istituto Nazionale di Fisica Nucleare, Sezione di Torino, I-10125 Torino, Italy

¹³Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, I-34127 Trieste, Italy

¹⁴Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy

¹⁵Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, I-56127 Pisa, Italy

Received 2016 February 12; revised 2016 May 4; accepted 2016 May 13; published 2016 July 27

ABSTRACT

We report the *Fermi* Large Area Telescope (LAT) detections of high-energy (>100 MeV) γ-ray emission from two recent optically bright classical novae, V1369 Centauri 2013 and V5668 Sagittarii 2015. At early times, *Fermi* target-of-opportunity observations prompted by their optical discoveries provided enhanced LAT exposure that enabled the detections of γ-ray onsets beginning ~2 days after their first optical peaks. Significant γ-ray emission was found extending to 39–55 days after their initial LAT detections, with systematically fainter and longer-duration emission compared to previous γ-ray-detected classical novae. These novae were distinguished by multiple bright optical peaks that encompassed the time spans of the observed γ-rays. The γ-ray light curves and spectra of the two novae are presented along with representative hadronic and leptonic models, and comparisons with other novae detected by the LAT are discussed.

Key words: gamma-rays: stars – novae, cataclysmic variables – radiation mechanisms: general

1. INTRODUCTION

Novae are thermonuclear runaway explosions triggered on the surfaces of white dwarf stars due to mass accretion from the companion in a binary system (Kraft 1964). In their nascent optically thick stage, a transient source of nuclear decay γ-ray emission with signature lines at ~MeV energies will be produced by disintegration of unstable isotopes and positron annihilation (Clayton & Hoyle 1974; Starrfield et al. 1978; Clayton 1981), but no individual novae have yet been detected in this way (Hernanz 2008). Rather, novae have long been recognized visually by their telltale bright optical transient nature (Lundmark 1921; McLaughlin 1939; Payne-Gaposchkin 1957), and contemporary radio, infrared, optical/ultraviolet, and X-ray imaging and spectroscopy studies have revealed different facets of the physics of the ensuing expanding ejecta (Bode & Evans 2008; Woudt & Ribeiro 2014).

The study of novae has undergone a recent resurgence because of the *Fermi* Large Area Telescope (LAT; Atwood et al. 2009) detections of >100 MeV γ-ray emission from three classical novae (Ackermann et al. 2014) following the initial LAT detection of the symbiotic-like recurrent nova V407 Cyg 2010 (Abdo et al. 2010; Cheung et al. 2010). In hindsight, the idea that symbiotic novae can be continuum emitters in >100 MeV γ-rays could have been expected from shock-accelerated particles in the ejecta through interactions with the dense wind of the red giant companion as considered for RS Oph (Tatischeff & Hernanz 2007; Hernanz 2014). However,

the subsequent LAT detections of classical novae were truly unexpected, because they instead involve less evolved (main-sequence or subgiant) companions demonstrating high-energy particle acceleration occurring in the absence of dense wind material. Moreover, the LAT-detected classical novae displayed different optical/ultraviolet properties (e.g., Gehrz et al. 1998) that indicated explosions from white dwarfs with an oxygen–neon (ONe) composition in V959 Mon 2012, while V1324 Sco 2012 and V339 Del 2013 appeared to be carbon–oxygen (CO) types. The key implication of this handful of reported LAT detections in the local volume within ~4–5 kpc is that most novae, if not all, are potential sources of high-energy continuum γ-ray emission.

Here we report two additional classical novae detected with the *Fermi*-LAT following their optical discoveries, the fifth and sixth novae now securely detected in >100 MeV γ-rays. Both novae were discovered by J. Seach, in Australia: V1369 Centauri (V1369 Cen = Nova Cen 2013) on 2013 December 2.692¹⁶ and V5668 Sagittarii (V5668 Sgr = Nova Sgr 2015 No. 2) on 2015 March 15.634 (all times are UT). Spectroscopic observations obtained on 2013 December 3 revealed $H\alpha$ and $H\beta$ emission lines and confirmed V1369 Cen as a nova (see

<footnote n="16">¹⁶ Note the report (http://aavso.org/possible-nova-centaurus) that “Steven Graham in Templeton, NZ, has a webcam set up ... hearing of this nova, he searched his archives and found it was visible on his image at 0945 UT (December 2), but not on the previous dark one at 1330 UT (December 1).” This pre-discovery photo helps constrain the V1369 Cen explosion epoch as 0.28 days earlier than the Seach discovery (Table 1).</footnote>
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Fermi-LAT 1-day bin >100 MeV γ-ray (top panels) and optical (bottom panels) light curves for V1369 Cen (left) and V5668 Sgr (right). For the LAT data, vertical lines indicate $1\sigma$ uncertainties when $\text{TS} \ge 4.0$ and gray arrows indicate $2\sigma$ upper limits when $\text{TS} < 4.0$ (see Appendix A for tabulated fluxes, TS values, and corresponding exposures). The optical discovery measurements (open squares) are shown separately from the subsequent 0.25-day bin averaged data extracted from the AAVSO database (filled circles).</figcaption></figure>

Seach et al. 2013) with a likely progenitor that brightened by ~10 mag (Kornoch 2013) at discovery. For V5668 Sgr, Seach followed up his 2015 March 15 discovery (6.0 mag; it was not detected with a 10.5 mag limit in his previous night's observation) with a bright $H\alpha$ detection hours later (Seach et al. 2015), and the spectroscopic confirmation came the following day (Williams et al. 2015).

V1369 Cen and V5668 Sgr were extensively monitored optically by the AAVSO and ARAS groups<fnref n="17" /> and showed broadly similar multipeaked light curves. Their respective first peaks were 3.6 and 4.1 mag, making them the visually brightest novae observed since V382 Vel 1999 (2.5 mag peak) and since the 2008 launch of Fermi (V339 Del 2013 peaked at 4.5 mag; see Munari et al. 2015). V5668 Sgr was characterized by systematically longer timescales in its brightening and fading (see Figure 1 for an overview, and Table 1). Both rose to their first peaks by ~1.9 mag after discovery, but with different rates of ~0.6 mag day⁻¹ for V1369 Cen and ~0.3 mag day⁻¹ for V5668 Sgr. Following a 2-day decline, a slightly brighter second peak in V1369 Cen was observed ~9 days after its first peak, with three subsequent fainter peaks spaced by 5–14 days. V5668 Sgr declined over a longer 3.5-day interval and rebrightened to a modestly fainter, broader second peak ~15–18 days after its first peak, and it underwent three additional brightening events to ~4.5–5 mag at intervals of 8–13 days (see Waagen 2015).

In the following, we present the LAT observations of the two novae (Section 2), describing the γ-ray light curves coinciding with multipeaked optical activity (Section 2.1; preliminary results were presented in Cheung et al. 2015c), and hadronic and leptonic modeling of their high-energy γ-ray spectra (Section 2.2). The results are discussed in Section 3, and we conclude in Section 4.

## 2. LAT OBSERVATIONS AND ANALYSIS

The Fermi-LAT routinely operates in a sky-survey mode, providing coverage of the entire sky every ~3.2 hr (two spacecraft orbits). We obtained Fermi target-of-opportunity (ToO) observations a few days after each optical nova discovery that resulted in exposures approximately twice what the nominal sky survey would have achieved in both cases. The ToOs were timed for after the optical emission peaked, as previous observations of V339 Del 2013 indicated that the >100 MeV γ-ray onset occurred ~1.5 days later. This strategy led to the successful early detections of the two new novae, while continued Fermi sky-survey observations at later times revealed detectable γ-ray emission out to ~1.5–2 months.

At the time of the V1369 Cen optical discovery, Fermi was operating with a modified sky survey pattern favoring the Galactic center direction<fnref n="18" /> with minimal sky exposure toward Centaurus. This Fermi ToO observation began on 2013 December 6.0, just 0.3 days after V1369 Cen's first optical peak. The initial 5-day ToO sequence resulted in a low-significance cumulative 3-day LAT detection beginning about 1.5 days after its optical peak (Cheung et al. 2013a). On the last day of this ToO sequence, the source brightened in γ-rays as the optical was rising to its second peak (Cheung et al. 2013b). This prompted a return to the ToO pointing for 5 additional days, providing enhanced coverage of the second, brighter, optical peak as well, after 3 days of modified sky survey.

For V5668 Sgr, the Fermi ToO started around March 17.9, while the optical brightness continued to rise after discovery and extended for 18 days in total, ending on April 5; the ToO observation was longer because of the slower rise to optical peak. As the optical brightness climbed, there were no significant LAT detections until the expected onset in γ-rays ~1.5 days after optical peak (Cheung et al. 2015a, 2015b),

<footnote n="17">¹⁷ American Association of Variable Star Observers (http://aavso.org/lcg) and Astronomical Ring for Access to Spectroscopy (http://astrosurf.com/aras/), respectively.</footnote>

<footnote n="18">¹⁸ http://fermi.gsfc.nasa.gov/ssc/observations/types/exposure/</footnote>
<table><caption>**Table 2**
Fermi-LAT >100 MeV γ-ray Spectral and Model Fit Results for the Two Classical Novae</caption><thead><tr><th>Nova</th><th>V1369 Cen 2013</th><th>V5668 Sgr 2015</th></tr></thead><tbody><tr><td colspan="3">Single Power Law</td></tr><tr><td>Flux, F<sub>γ</sub></td><td>25.4 ± 4.1</td><td>11.4 ± 2.2</td></tr><tr><td>Photon index</td><td>2.37 ± 0.09</td><td>2.42 ± 0.13</td></tr><tr><td>TS</td><td>99.9</td><td>70.4</td></tr><tr><td colspan="3">Exponentially Cutoff Power Law</td></tr><tr><td>Flux, F<sub>γ</sub></td><td>21.1 ± 4.2</td><td>10.9 ± 2.4</td></tr><tr><td>Slope, s</td><td>1.84 ± 0.23</td><td>2.27 ± 0.25</td></tr><tr><td>E<sub>c</sub></td><td>2.3 ± 1.0</td><td>9 ± 14</td></tr><tr><td>TS</td><td>110.6</td><td>71.1</td></tr><tr><td colspan="3">Hadronic Model</td></tr><tr><td>Flux F<sub>γ</sub></td><td>20.7 ± 3.6</td><td>8.2<sup>+1.2</sup><sub>-1.4</sub></td></tr><tr><td>Slope, s<sub>p</sub></td><td>3.0<sup>+0.9</sup><sub>-0.4</sub></td><td>3.1<sup>+0.3</sup><sub>-0.9</sub></td></tr><tr><td>E<sub>cp</sub></td><td>>10</td><td>>10</td></tr><tr><td>TS</td><td>115.3</td><td>70.7</td></tr><tr><td colspan="3">Leptonic Model</td></tr><tr><td>Flux, F<sub>γ</sub></td><td>20.0<sup>+2.6</sup><sub>-4.4</sub></td><td>10.1<sup>+3.0</sup><sub>-2.2</sub></td></tr><tr><td>Slope, s<sub>e</sub></td><td>1.3<sup>+1.3</sup><sub>-1.6</sub></td><td>2.8<sup>+0.5</sup><sub>-1.5</sub></td></tr><tr><td>E<sub>ce</sub></td><td>3.2<sup>+7.1</sup><sub>-1.4</sub></td><td>>3.2</td></tr><tr><td>TS</td><td>111.2</td><td>71.1</td></tr></tbody></table>

**Note.** Best-fit parameters from the average spectral fits and the hadronic and leptonic modeling of the LAT data for V1369 Cen and V5668 Sgr. The reported errors on spectral parameters are 1σ statistical uncertainties only with >100 MeV fluxes, F<sub>γ</sub>, in units of 10<sup>-8</sup> photons cm<sup>-2</sup> s<sup>-1</sup> and the cutoff energies, E<sub>c</sub>, in GeV.

gap in the V1369 Cen observations starting at t<sub>s</sub> + 50 days due to an LAT ToO observation of SN 2014J in M82.

In the γ-ray and optical comparison (Figure 1), we display the interval t<sub>s</sub> − 10 days to +70 days, with the AAVSO data averaged in 0.25-day bins. In the 1-day bin LAT light curves (see Appendix A for corresponding TS and exposure values), the first significant γ-ray detections (defined as TS > 4) of both novae spanned the 2 days from t<sub>s</sub> + 2.0 to +4.0 days, with TS ~ 6–7 in each day for V1369 Cen and TS = 11.5 and 5.3 for V5668 Sgr, confirming the preliminary findings (Cheung et al. 2013a, 2013b, 2015a, 2015b). The respective >100 MeV fluxes were ~ (2.0–2.3) × 10<sup>-7</sup> and ~ (1.3–1.6) × 10<sup>-7</sup> photons cm<sup>-2</sup> s<sup>-1</sup>, both fainter than previously detected novae at similar times. By splitting the data for the first significant 1-day detections into two halves, we found the more significant detection in the latter half-day in V1369 Cen (TS = 1.1 vs. 6.0) and in the first half-day in V5668 Sgr (TS = 9.2 vs. 3.5). Taking these 0.5-day bin results, we can constrain the γ-ray onsets to ~1.8 and 2.0 days after their respective first optical peaks. The LAT ToOs for each nova provided enhanced exposure through the observed γ-ray onsets, suggesting that the γ-ray onset determinations were not exposure artifacts.

The total LAT-detected durations of these two novae are systematically longer than for the previously detected novae, albeit with the detections appearing sporadic because of a combination of the changing LAT exposure and low photon statistics. This limits our statements regarding changes in the γ-ray light curves predominantly to intervals with good exposure

and precludes a meaningful comparison with the optical data when the LAT exposures were low. Considering primarily the 1-day bins with enhanced ToO exposures at early times (i.e., t<sub>s</sub> to t<sub>s</sub> + 15 days), we found only 3/10 days in V1369 Cen with highly significant detections (TS = 19.3–37.6) and 3/15 days in V5668 Sgr with significant detections (TS = 8.5–11.6), with no obvious correlation of TS with exposure. In the three 1-day bins with largest TS in V1369 Cen, the fluxes are a factor of two greater than those in other comparably exposed time bins. These higher γ-ray fluxes were observed both preceding and following its second optical peak at t<sub>s</sub> + 9.3 days (the more limited statistics in V5668 Sgr prevent a similar determination). At later times (after t<sub>s</sub> + 15 days), both novae declined in and out of detectability because of lower exposures when the LAT returned to survey mode. In V1369 Cen, there is only a single TS > 9 point on t<sub>s</sub> + 19.5 days, which amounts to a total detected duration of at least 18 days for this nova (note that the total detected durations include the first significant detections for each nova at t<sub>s</sub> + 2.0 days), and a total detected duration of 39 days is implied if the lower-significance (TS > 4) detections found in 5 of the 21 subsequent bins up to t<sub>s</sub> + 40.5 days are considered. V5668 Sgr was sporadically detected at late times in seven more bins evenly spread over a long interval up to +57.0 days, again, without an apparent correlation with exposure. Its apparent lull in signal (essentially TS = 0) from t<sub>s</sub> + 15.0 to +24 days is difficult to gauge because of minimal exposure at these times. If we take the last day with observed TS > 9 in V5668 Sgr, then the total detected duration is 47 days, and this duration is enlarged slightly to 55 days if we consider the single TS = 8.6 point at t<sub>s</sub> + 56.5 days.

## 2.2. Spectral Analysis, Source Localization, and Modeling

To derive average LAT spectra, we selected data covering the total durations (39 days for V1369 Cen and 55 days for V5668 Sgr) determined from the intervals spanned by the TS ≥ 4 points in the 1-day bin light curves. The spectra were extracted using *gtlike* by fitting the flux from each nova in 12 logarithmic bins from 100 MeV to 100 GeV. As in Ackermann et al. (2014), we fit the data assuming a single PL, with the integrated >100 MeV flux and the photon index as free parameters, and an exponentially cutoff power law (ECPL), which has the cutoff energy as an additional free parameter to gauge spectral curvature. The best-fit PL and ECPL parameters for both novae are presented in Table 2, with Figure 2 (top panels) showing the best-fit analytic curves overlaid onto the extracted LAT spectra. Note that the TS obtained with the ECPL fit in V1369 Cen is only slightly larger than the one obtained with the PL fit, amounting to an improvement of (ΔTS)<sup>1/2</sup> = 3.3σ, while there is a negligible increase in TS in the V5668 Sgr case. In the three previously detected γ-ray classical novae (Ackermann et al. 2014), the spectra were similar with broad spectral peaks that cut off at energies ~1–4 GeV and emission observed up to ~6–10 GeV (the highest energy extension was observed in V1324 Sco), and we remark only that the relatively poor statistics in the new cases presented here do not permit a robust comparison.

To confirm positional coincidences of the γ-ray sources with the novae, the LAT positions were determined by running the *gtfindsrc* tool assuming the single PL spectral model, using the same time interval used in the average spectral analyses. The γ-ray sources were well localized with best-fit LAT 95% localization error radii of 0°.10 (V1369 Cen) and 0°.14 (V5668
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Fermi-LAT >100 MeV average spectra of V1369 Cen (left panels) and V5668 Sgr (right panels) with vertical bars indicating $1\sigma$ uncertainties for data points with $\text{TS} \ge 4$; otherwise, $2\sigma$ upper limits are plotted. Overlaid are the PL and ECPL fits (top panels) and hadronic and leptonic model fits (bottom panels).</figcaption></figure>

Sgr), consistent with their optical positions (Table 1). The smoothed LAT counts maps centered at each novae over the defined total data intervals are shown in Figure 3.

To help gauge whether the γ-ray emission is due to the decay of neutral pions produced by high-energy proton interactions in the ejecta (hadronic model) or due to inverse Compton and bremsstrahlung of high-energy electrons (leptonic model), the parameters of these physical models were also fit to the LAT data. Assuming a single emission region, the spectral distribution of interacting particles is assumed to be an ECPL defined with a slope, a cutoff energy, and a normalization factor. In the hadronic model, the high-energy protons are expected to be uniformly distributed in the expanding shell, where they interact with the nuclei of the ejecta. We followed Ackermann et al. (2014, Section S2 therein) for the leptonic

model, where a typical temperature of 15,000 K with radius $3 \times 10^{12}$ cm for the optically thick surface (equivalent to the nova photosphere in the optical band) was assumed. High-energy electrons are expected to produce γ-ray photons via bremsstrahlung in collisions with atoms in the ejecta, and the emission spectra were calculated assuming a typical ejecta mass of $10^{-5} M_{\odot}$. As in Ackermann et al. (2014), to simplify our estimates, we adopted a spherical geometry for both novae, and the mean radius of the ejecta where high-energy electrons are expected to be accelerated and interact via inverse Compton scattering with photospheric photons is $\sim 4 \times 10^{14}$ cm, assuming a typical ejecta velocity of $\sim 2000 \text{ km s}^{-1}$ at $\sim 50$ days after explosion. The mean density for the bremsstrahlung emission was obtained by dividing the ejecta mass by its mean volume (averaged over the γ-ray emission duration), assuming that it is
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Fermi-LAT γ-ray adaptively smoothed count maps centered on the optical positions of the two classical novae (marked with yellow 1° radius circles). The maps used 0.1° × 0.1° pixels with 39 days of >100 MeV data for V1369 Cen (left) and 55 days of >300 MeV data for V5668 Sgr (right). The slightly higher energy threshold for V5668 Sgr was chosen for this figure alone in order to help suppress the visual prominence of the surrounding steep-spectrum diffuse Galactic emission.</figcaption></figure>

a shell with a relative thickness of $\Delta R/R = 0.4$. Note that the adopted value of the ejecta velocity was chosen to be consistent with strict lower limits of ~1500–2000 km s⁻¹ indicated by the half-widths at zero intensity of the hydrogen lines in late-time optical spectra (≥50 days after optical discovery; Shore et al. 2014; Garde & Buil 2015).

The best-fit parameters for the physical models obtained with *gtlike* along with their TS values are summarized in Table 2, with Figure 2 (bottom panels) showing the model curves compared to the LAT spectra. The slopes and the cutoff energies are not well constrained (see Figure 4 for the likelihood contours), which means that a single PL spectrum can explain the LAT data. With only small differences in TS values (ΔTS ~ 2σ for V1369 Cen), the hadronic and leptonic model fits were statistically indistinguishable, as they were in the three previously detected classical novae. The values of the best-fit physical parameters are similar to those obtained from the spectral analyses of the previous classical novae detected by Fermi-LAT, taking into account their uncertainties (cf. Ackermann et al. 2014, supplementary Figures S3 and S4 therein). The similarity of these results suggests that a common mechanism is responsible for the γ-ray emission of classical novae, with only the emissivity differing significantly between them.

In the hadronic model, the spectral fits to the LAT data allow us to estimate the total energy in high-energy protons, $\epsilon_p$, and the conversion efficiency, $\eta_p \equiv \epsilon_p/\epsilon_{ej}$, where $\epsilon_{ej}$ is the kinetic energy of the ejecta. Here the conversion efficiencies were calculated with $\epsilon_p$ based on the proton spectrum parameters that best fit the observed γ-ray spectral data, and they differ from the cosmic-ray (CR) proton production conversion efficiency, which is the ratio of the total energy of the CR protons accelerated at the shock front, $\epsilon_{cr}$, to the kinetic energy of the ejecta (see Appendix B). Estimating the conversion efficiency of the shock-accelerated CR proton production requires an

accounting of the propagation and energy-loss rate of protons in the expanding ejecta and an assumption of how they were injected (e.g., as a single burst, repeated shock events, at a continuous rate, or through wind-wind interactions). For simplicity, we assume that high-energy protons collide with target hydrogen atoms in the ejecta volume with a density averaged over the source lifetime taken to be the LAT-observed emission duration producing the mean observed γ-ray rate (see the online supplements of Abdo et al. 2010; Ackermann et al. 2014, for the details of the calculation method). Under these conditions, with a typical ejecta mass of $10^{-5} M_{\odot}$ and velocity of 2000 km s⁻¹, the total energies in protons are ~3.2 × $10^{43}$ erg and ~2.3 × $10^{43}$ erg with $\eta_p$ ~ 8% and ~6% for V1369 Cen and V5668 Sgr, respectively. Note that $\epsilon_p$ and $\eta_p$ scale with the inverse of the ejecta mass and with the square of the distance, which we have assumed to be uncertain to ±0.5 kpc. These values are slightly larger than (but of the same order of magnitude as) the ones obtained for the previous novae, $\epsilon_p$ ~ (0.7–2) × $10^{43}$ erg and $\eta_p$ ~ 0.1%–7% (see Table S3 of Ackermann et al. 2014). From the leptonic model fits, the total energy in electrons $\epsilon_e$ ~ 3.6 × $10^{41}$ erg and ~3.8 × $10^{41}$ erg for V1369 Cen and V5668 Sgr, respectively, with conversion efficiencies $\eta_e$ ~ 0.1% for both novae. Here again, these values are similar to the ones obtained for previous novae (see Table S4 of Ackermann et al. 2014). Modeling the acceleration and propagation of protons including detailed parameterization of the evolving ejecta (see, e.g., Martin & Dubus 2013, in the case of V407 Cyg) with a more realistic geometry could change these estimates, but these calculations are beyond the scope of this paper.

### 3. DISCUSSION

The two optically bright novae are part of an emergent class of transient Galactic γ-ray sources discovered with the Fermi-
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Confidence intervals for the hadronic (top panels) and leptonic (bottom panels) model fits to the *Fermi*-LAT data for V1369 Cen (left panels) and V5668 Sgr (right panels). The best-fit values of the slopes and cutoff energies (GeV) in the hadronic ($s_p, E_{cp}$) and leptonic ($s_e, E_{ee}$) models (Table 2) are indicated in each panel with an asterisk.</figcaption></figure>

LAT. Together with the first LAT-detected symbiotic-like recurrent nova V407 Cyg and the three classical novae reported in Ackermann et al. (2014), this brings the total to six secure detections thus far. This total does not count the marginal $2\sigma$-3$\sigma$ LAT observations of the recurrent symbiotic-like nova V745 Sco in the 1-day intervals on February 6 and 7 (Cheung et al. 2014), coincident with the optical peak discovery on 2014 February 6.694 (Stubbings & Pearce 2014) or the current pending candidates from the LAT Pass 8 analysis of all known optical novae observed since *Fermi*'s launch (Franckowiak et al. 2015). The earliest LAT nova detections were serendipitously enabled through the *Fermi*-LAT's all-sky monitoring mode, but the most recent examples were enabled by transitioning to deeper ToO observations following their optical discoveries by the amateur community. These two new LAT detections keep the γ-ray nova detection rate over the first ~7 yr of the *Fermi* mission at pace with the early rate of ~1 yr⁻¹, consistent with the estimated rate of Galactic novae at ~4–5 kpc distances (Ackermann et al. 2014).

The average >100 MeV γ-ray flux of V5668 Sgr, ~1 × 10⁻⁷ photons cm⁻² s⁻¹, is the lowest so far for any LAT-detected nova, being ~2× smaller than for V1369 Cen and V339 Del, and ~5–6× smaller than the other three LAT-detected novae. The corresponding >100 MeV luminosities are 1 × 10³⁵ (D/2.5 kpc)² erg s⁻¹ for V1369 Cen and 3 × 10³⁴ (D/

2.0 kpc)² erg s⁻¹ for V5668 Sgr. The adopted distances are scaled to V339 Del (Shore et al. 2014) for V1369 Cen, and the suggested range is D = 1.5–2.0 kpc for V5668 Sgr (Banerjee et al. 2015). Such small distances are supported by the low extinctions, $E(B-V)$ ~ 0.10–0.14 for V1369 Cen (Izzo et al. 2013; Shore et al. 2014) and $E(B-V)$ ~ 0.2–0.3 for V5668 Sgr (Kuin et al. 2015). The implied >100 MeV γ-ray luminosities are thus, systematically, up to a factor of 10 smaller than the observed range of the previously detected novae of (3–9) × 10³⁵ erg s⁻¹ and suggest that more distant analogs will be difficult to detect with *Fermi*-LAT. Overall, these two new LAT detections suggest a wider range of γ-ray luminosities than observed in the first reported γ-ray detections, albeit with the inherent uncertainties in their distance determinations (see Cheung et al. 2015c).

Interestingly, V1369 Cen and V5668 Sgr also appear to have longer γ-ray emission durations than previous examples. Because they are fainter in γ-rays on average than the previous LAT-detected novae, their light curves are more difficult to characterize, but nevertheless appear sporadic in nature with low-significance 1-day detections extended over moderately longer durations (up to ~1–2 months). Specifically, during times of enhanced LAT exposures due to the ToOs, we found the γ-ray onsets delayed with respect to the first optical peaks by ~2 days (Section 2.1) and ~5–8 days after their optical
<figure><img src="image_6.png" /><figcaption>**Figure 5.** For the five classical novae with reported *Fermi*-LAT detections (thus excluding the symbiotic-like recurrent nova V407 Cyg), the total number of >100 MeV γ-ray photons emitted (left panel) and total emitted energies (right panel) are plotted vs. the LAT-measured γ-ray durations.</figcaption></figure>

<table><caption>**Table 3**
Parameters of Classical Novae Detected by the *Fermi*-LAT</caption><thead><tr><th>Nova</th><th>Distance (kpc)</th><th>Duration (days)</th><th>Fluence (photons cm<sup>-2</sup>)</th><th>Number of Photons (10<sup>45</sup>)</th><th>Total Energy (10<sup>42</sup> erg)</th></tr></thead><tbody><tr><td>V1324 Sco 2012</td><td>4.5</td><td>17</td><td>0.72 ± 0.04</td><td>1.77 ± 0.40</td><td>1.27 ± 0.29</td></tr><tr><td>V959 Mon 2012</td><td>3.6</td><td>22</td><td>0.79 ± 0.12</td><td>1.23 ± 0.39</td><td>0.67 ± 0.21</td></tr><tr><td>V339 Del 2013</td><td>4.2</td><td>27</td><td>0.45 ± 0.07</td><td>0.96 ± 0.27</td><td>0.57 ± 0.16</td></tr><tr><td>V1369 Cen 2013</td><td>2.5</td><td>39</td><td>0.71 ± 0.14</td><td>0.54 ± 0.24</td><td>0.30 ± 0.13</td></tr><tr><td>V5668 Sgr 2015</td><td>2.0</td><td>55</td><td>0.52 ± 0.11</td><td>0.25 ± 0.14</td><td>0.12 ± 0.07</td></tr></tbody></table>

**Note.** Durations of the >100 MeV γ-ray emission, fluences, total number of photons, and total energy emitted by classical novae as derived from LAT data analysis. For the three previously detected classical novae, the distances adopted were taken from Ackermann et al. (2014). The 1σ uncertainties of the total number of photons and total energies take into account an adopted uncertainty of 0.5 kpc for all the distances.

discoveries. This delay could indicate the timescale for particle acceleration in the ejecta or γ-ray absorption at early times when the ejecta are most dense (Abdo et al. 2010; Ackermann et al. 2014; Chomik et al. 2014; Metzger et al. 2015). These explanations could have distinct signatures in early, time-resolved LAT spectra, with, e.g., the latter scenario predicting progressively harder γ-ray spectra due to increased transmission of higher-energy photons, but the limited statistics in these cases prevent such an analysis. Moreover, the overall low statistics make it difficult to associate the later individual γ-ray detections with subsequent optical peaks, although we note that the brighter, second optical peak of 3.3 mag in V1369 Cen appears to be followed by a 2-day-long γ-ray brightening (centered at $t_s + 12$ days) that is also delayed by ~2 days (see below). The LAT detections overall span the duration of the multipeaked optical activity in each nova (Section 1; Figure 1) and indicate that future γ-ray novae require dedicated long-term increased LAT exposures to establish any possible correlations with optical activity (see discussions of previous cases in, e.g., Metzger et al. 2015).

That the LAT-observed durations of these two classical novae are longer than in the three previously detected examples is of interest, particularly with the lower γ-ray luminosities of the former. We can thus remark on a plausible relation between the total emission durations of the >100 MeV emission found in our LAT-based studies and the mean γ-ray luminosity in the same band (in photons s⁻¹). Because the mean luminosity logically decreases with the integration period for transient

events, we estimated the total number of >100 MeV photons emitted, as well as the total energies over the emission duration, and found that the longer the γ-ray duration, the smaller the total number of emitted photons and total energies (Figure 5, Table 3). As an intermediate step, the fluences were calculated by multiplying the best-fit average >100 MeV fluxes from the ECPL fits (see Tables 2 and S1 of Ackermann et al. 2014) by the total durations. Note that the total energies for the three previously detected classical novae were presented in Ackermann et al. (2014) assuming the PL fits and are consistent with the values presented here. The two new LAT-detected classical novae probe systematically lower values of total energies than the previous examples, as well as total number of emitted photons. Despite the intriguing apparent inverse relationship of these quantities with γ-ray durations, we cannot rule out selection effects related to the *Fermi*-LAT sensitivity (e.g., some photons are missing because the flux is too low to be detected) or conclude whether there is a relationship at all due, e.g., to the uncertain distances.<fnref n="23" /> A more extensive sample of *Fermi*-LAT-detected novae could test whether this relation is due to physics of the outbursts, particle acceleration, and ejecta parameters—e.g., for short emission durations, the putative shocks cross more compact ejecta (i.e., with higher density) and for longer emission durations the shock goes through ejecta

<footnote n="23">²³ For example, taking the larger distance of >6.5 kpc for V1324 Sco (Finzell et al. 2015) than the 4.5 kpc we adopted, the number of emitted photons increases from $1.8 \times 10^{45}$ to $>3.8 \times 10^{45}$.</footnote>
with larger radii (with lower density) and is less efficient in producing γ-rays.

There has been a long history of predictions (Section 1) for MeV line emission promptly after the thermonuclear runaway when the explosion is optically thick, i.e., as the optical brightness peaks and before the GeV emission onset. Specifically, line emission will be expected at 478 and 1275 keV for CO and ONe novae, respectively, together with positron annihilation line emission at 511 keV and continuum down to 20–30 keV due to Comptonization and positronium emission. The multiple optical peaks observed in V1369 Cen and V5668 Sgr, with apparent concomitant >100 MeV band emission, could signal renewed outbursts, originating from either repeated shock events in the ejecta or distinct outbursts from the white dwarf surface. In the former, the γ-ray observations probe the density profile of the ejecta where the shock could interact with different density material, resulting in varying rates of particle injection for acceleration processes and/or different target density material for interactions producing γ-rays. In the latter case, any accompanying radioactive decay emission will depend on ejecta mass and ejecta velocity for a given white dwarf mass (Hernanz et al. 2002), which can be different for each subsequent outburst. Previous observations of emission up to 70 keV with Suzaku (Takei et al. 2009) and the likely ~0.1 MeV Compton/ OSSE detection of V382 Vel 1999 (Cheung et al. 2015c) suggest extended timescale emission in classical novae and should motivate continuum emission searches with INTEGRAL (Winkler et al. 2003) and ASTRO-H (Takahashi et al. 2012; Coppi et al. 2014) at later times than so far considered for the nuclear decay emission.

## 4. CONCLUSIONS

The newly reported >100 MeV γ-ray detections of V1369 Cen and V5668 Sgr add to the four previously detected novae by the Fermi-LAT. These recent detections may be revealing a wider diversity in γ-ray properties, being fainter and seemingly characterized by longer total durations. Further serendipitous and targeted γ-ray detections through the continued Fermi mission, as well as studies of non-LAT-detected novae (Cheung 2012; Franckowiak et al. 2015), could further broaden the range of observed γ-ray properties. While observationally based scenarios have been developed for symbiotic systems (Tatischeff & Hernanz 2007), and V407 Cyg in particular (Abdo et al. 2010; Chomiuk et al. 2012; Nelson et al. 2012; Orlando & Drake 2012; Martin & Dubus 2013; Pan et al. 2015), understanding the particle acceleration revealed in the classical novae is still an open problem. Thus, future Fermi-LAT observations of novae (where deep pointed observations are imperative to study the brightest γ-ray-emitting novae in detail) can be exploited with multiwavelength observations and modeling to test scenarios for how, when, and where the putative shocks are generated, e.g., in internal shocks or strong turbulence driven in the ejecta (Ackermann et al. 2014) or in wind–wind interactions (Chomiuk et al. 2014), and can implicate the underlying γ-ray emission mechanism (see, e.g., Metzger et al. 2015).

At the highest energies, one can anticipate very high energy (VHE; >0.1 TeV) emission and a transient neutrino signal in the pion-decay scenario for symbiotic novae (Razzaque et al. 2010; Aliu et al. 2012; Bednarek 2013) and for classical novae (Ahnen et al. 2015; Metzger et al. 2016). Among the

recurrent novae with shorter recurrence times (Schaefer 2010), we may anticipate an explosion from RS Oph during the Fermi mission and in the era of the upcoming Cerenkov Telescope Array. Naively scaling by distance, we may expect the even more nearby system, $T \text{CrB}$ ($D \sim 0.8$ kpc), to produce an order of magnitude brighter GeV source than V407 Cyg ($D \sim 2.7$ kpc), with emission extending below MeV and up to VHE energies. Any particularly nearby ($D \lesssim 1–2$ kpc) classical nova in the future will provide a useful contrasting case to the symbiotic/recurrent systems.

With the study of novae now expanded into the γ-ray regime, the words of Payne-Gaposchkin (1957, p. VII) ring even more true today: “I have become convinced that the whole nova phenomenon must be studied; the variations of total light and continuum, of radial velocity, and of the intensities and profiles of absorption and emission lines must be seen as connected parts of one physical phenomenon, rather than as isolated data that can be understood separately.” With the expanding number of LAT-detected novae, existing models are open to a greater level of scrutiny, and the opportunities with Fermi should be pursued in earnest.

The Fermi-LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT, as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States; the Commissariat à l'Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France; the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy; the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK), and Japan Aerospace Exploration Agency (JAXA) in Japan; and the K.A. Wallenberg Foundation, the Swedish Research Council, and the Swedish National Space Board in Sweden.

Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d'Études Spatiales in France.

We thank the Fermi operations team at the Science Support Center for their prompt scheduling of the ToO observations. We acknowledge with thanks the variable star observations from the AAVSO International Database contributed by observers worldwide and used in this research, as well as the dedicated observers of the ARAS group. We are grateful to G. Dubus for detailed comments that helped improve the manuscript and the anonymous referee for interesting comments.

C.C.C. was supported at NRL by a Karles' Fellowship and by NASA through Guest Investigator programs 12-FERMI12-0026 and 13-FERMI13-0008. Ł.S. was supported by Polish NSC grant DEC-2012/04/A/ST9/00083. S.S. acknowledges partial support from NSF and NASA grants to ASU.

Facilities: Fermi, AAVSO, ARAS.

## APPENDIX A
Fermi-LAT LIGHT CURVES

The Fermi-LAT 1-day bin light-curve data, TS, and exposure values are presented in Figure 6, with the fluxes and TS values tabulated in Table 4.
<figure><img src="image_7.png" /><figcaption>**Figure 6.** Fermi-LAT 1-day bin >100 MeV γ-ray data for V1369 Cen (left) and V5668 Sgr (right). The light curves (top panels) are as presented in Figure 1, along with the corresponding TS (middle panels) and exposure values (bottom panels). The corresponding panels for the two novae show the same range to ease comparison. In the middle panels, horizontal lines indicate values of TS = 4 (dotted) and TS = 9 (dashed). With the range chosen in the middle panel, three larger TS values in V1369 Cen were cropped (TS = 37.6, 20.3, and 19.3 centered, respectively, on t_s + 5.5, +11.5, and +12.5 days).</figcaption></figure>

## APPENDIX B
CR PROTON ENERGETICS

Assuming that CR protons are injected at the shock front of a nova explosion at a constant rate with an energy spectrum $\dot{Q}(E)$, the total energy stored in CR protons over the source lifetime of the ejecta, $\tau_{ej}$, is

$$ \epsilon_{cr} = \int_{0}^{\tau_{ej}} dt \int dE E \dot{Q}(E) = \tau_{ej} \times \int dE E \dot{Q}(E) \equiv \tau_{ej} \times \dot{Q}_{cr}. \qquad (1) $$

We define the CR proton production efficiency factor:

$$ \eta_{cr} \equiv \frac{\epsilon_{cr}}{\epsilon_{ej}}, \qquad (2) $$

where $\epsilon_{ej}$ is the total kinetic energy of the ejecta; hence,

$$ \dot{Q}_{cr} = \frac{\eta_{cr} \epsilon_{ej}}{\tau_{ej}}. \qquad (3) $$

CR protons injected at the shock front are advected downstream, where they interact with the ambient plasma through proton-proton (pp) interactions, and may eventually escape diffusively. The characteristic timescales for these processes are $\tau_{pp}$ and $\tau_{esc}$, respectively. Therefore, the CR proton energy spectrum, $N(E, t)$, evolves accordingly to

$$ \frac{\partial N(E, t)}{\partial t} + \frac{N(E, t)}{\tau_{\min}} = \dot{Q}(E), \qquad (4) $$

where $\tau_{min} \equiv \min(\tau_{pp}, \tau_{esc})$. Note here that pp interactions are modeled as “catastrophic” energy losses, and CR proton diffusion in the downstream is approximated by a simple “escape” term. The solution to the above equation at a given moment of time $t = \tau_{ej}$ reads then as

$$ N(E, \tau_{ej}) = \tau_{\min} (1 - e^{-\tau_{ej}/\tau_{\min}}) \times \dot{Q}(E), \qquad (5) $$

assuming that $\tau_{min}$ is independent of time.

The pp interactions lead to the production of γ-ray photons with energies $\epsilon \simeq 0.2 E$ (see Abdo et al. 2010), with a monochromatic luminosity at a given moment $t = \tau_{ej}$ approximately

$$ [\epsilon L_{\epsilon}] \simeq \eta_{\gamma} \frac{E^2 N(E, \tau_{ej})}{\tau_{pp}}, \qquad (6) $$

where the numerical factor $\eta_{\gamma}$ is of the order of $\sim 0.1$ ($\eta_{\gamma} < 1$ because, in addition to γ-rays, secondary $e^{\pm}$ pairs and neutrinos are also produced in pp interactions). Hence, around the peak photon energies for which $[\epsilon L_{\epsilon}] \simeq L_{\gamma}$, with corresponding $E^2 \dot{Q}(E) \simeq \dot{Q}_{cr}$, one has

$$ L_{\gamma} \sim \eta_{\gamma} \eta_{cr} \epsilon_{ej} \frac{\tau_{\min}}{\tau_{ej} \tau_{pp}} (1 - e^{-\tau_{ej}/\tau_{\min}}) \qquad (7) $$

(Equations (3), (5), and (6)).

Let us now consider the three possible cases:

i. $\tau_{ej} \ll \tau_{min}$, where the source lifetime is much shorter than either the pp interaction timescale or the CR proton escape timescale. Under such conditions, $(1 - e^{-\tau_{ej}/\tau_{min}}) \sim \tau_{ej}/\tau_{min}$; thus,

$$ L_{\gamma} \sim \eta_{\gamma} \eta_{cr} \frac{\epsilon_{ej}}{\tau_{pp}}. \qquad (8) $$

This case describes a young system where CR protons injected downstream have yet to escape and only some fraction ($\tau_{ej}/\tau_{pp} \ll 1$) of the total energy stored in CR protons at the shock front could be transferred to the γ-ray emission (depending on $\tau_{pp}$ and regardless of $\tau_{esc}$).

ii. $\tau_{pp} \ll \tau_{esc}$ and $\tau_{pp} \ll \tau_{ej}$, where the pp interaction timescale is much shorter than both the CR proton escape timescale and the source lifetime. Under such conditions,
<table><caption>**Table 4**
Fermi-LAT >100 MeV γ-ray Light-curve Data</caption><thead><tr><th rowspan="2">Days since<br>Start</th><th colspan="2">V1369 Cen 2013</th><th colspan="2">V5668 Sgr 2015</th></tr><tr><th>TS</th><th>F<sub>γ</sub></th><th>TS</th><th>F<sub>γ</sub></th></tr></thead><tbody><tr><td>-9.5</td><td>0.0</td><td>&lt;2.6</td><td>2.4</td><td>&lt;4.3</td></tr><tr><td>-8.5</td><td>0.2</td><td>&lt;4.3</td><td>0.0</td><td>&lt;1.1</td></tr><tr><td>-7.5</td><td>0.3</td><td>&lt;4.3</td><td>0.0</td><td>&lt;1.5</td></tr><tr><td>-6.5</td><td>0.0</td><td>&lt;2.3</td><td>0.0</td><td>&lt;1.6</td></tr><tr><td>-5.5</td><td>0.0</td><td>&lt;3.1</td><td>0.8</td><td>&lt;3.4</td></tr><tr><td>-4.5</td><td>0.1</td><td>&lt;4.0</td><td>0.9</td><td>&lt;3.6</td></tr><tr><td>-3.5</td><td>0.0</td><td>&lt;2.2</td><td>0.0</td><td>&lt;1.8</td></tr><tr><td>-2.5</td><td>0.0</td><td>&lt;2.9</td><td>0.0</td><td>&lt;0.7</td></tr><tr><td>-1.5</td><td>0.0</td><td>&lt;2.4</td><td>0.0</td><td>&lt;0.6</td></tr><tr><td>-0.5</td><td>0.0</td><td>&lt;1.9</td><td>0.5</td><td>&lt;1.5</td></tr><tr><td>0.5</td><td>0.0</td><td>&lt;3.4</td><td>0.7</td><td>&lt;1.9</td></tr><tr><td>1.5</td><td>0.4</td><td>&lt;2.3</td><td>0.9</td><td>&lt;2.2</td></tr><tr><td>2.5</td><td>6.7</td><td>2.0 ± 1.0</td><td>11.5</td><td>1.6 ± 0.7</td></tr><tr><td>3.5</td><td>6.1</td><td>2.3 ± 1.1</td><td>5.3</td><td>1.3 ± 0.7</td></tr><tr><td>4.5</td><td>1.9</td><td>&lt;3.4</td><td>0.0</td><td>&lt;1.0</td></tr><tr><td>5.5</td><td>37.6</td><td>5.1 ± 1.3</td><td>4.0</td><td>1.2 ± 0.7</td></tr><tr><td>6.5</td><td>8.0</td><td>7.2 ± 3.2</td><td>11.6</td><td>1.8 ± 0.8</td></tr><tr><td>7.5</td><td>0.9</td><td>&lt;5.4</td><td>1.1</td><td>&lt;2.4</td></tr><tr><td>8.5</td><td>0.0</td><td>&lt;3.2</td><td>2.3</td><td>&lt;2.7</td></tr><tr><td>9.5</td><td>1.6</td><td>&lt;3.7</td><td>0.0</td><td>&lt;1.1</td></tr><tr><td>10.5</td><td>5.2</td><td>2.3 ± 1.2</td><td>5.0</td><td>1.1 ± 0.7</td></tr><tr><td>11.5</td><td>20.3</td><td>4.9 ± 1.5</td><td>0.1</td><td>&lt;1.9</td></tr><tr><td>12.5</td><td>19.3</td><td>4.6 ± 1.4</td><td>3.1</td><td>&lt;2.3</td></tr><tr><td>13.5</td><td>3.7</td><td>&lt;5.3</td><td>2.8</td><td>&lt;3.1</td></tr><tr><td>14.5</td><td>1.6</td><td>&lt;7.3</td><td>8.5</td><td>1.9 ± 0.9</td></tr><tr><td>15.5</td><td>0.1</td><td>&lt;4.8</td><td>0.0</td><td>&lt;3.9</td></tr><tr><td>16.5</td><td>0.0</td><td>&lt;3.7</td><td>0.5</td><td>&lt;5.0</td></tr><tr><td>17.5</td><td>3.6</td><td>&lt;7.4</td><td>0.2</td><td>&lt;5.6</td></tr><tr><td>18.5</td><td>1.6</td><td>&lt;7.2</td><td>0.0</td><td>&lt;1.6</td></tr><tr><td>19.5</td><td>9.4</td><td>5.1 ± 2.2</td><td>0.0</td><td>&lt;2.7</td></tr><tr><td>20.5</td><td>2.6</td><td>&lt;7.8</td><td>0.1</td><td>&lt;4.0</td></tr><tr><td>21.5</td><td>0.0</td><td>&lt;3.0</td><td>0.0</td><td>&lt;2.7</td></tr><tr><td>22.5</td><td>1.2</td><td>&lt;3.8</td><td>0.1</td><td>&lt;4.6</td></tr><tr><td>23.5</td><td>0.0</td><td>&lt;3.0</td><td>0.0</td><td>&lt;3.3</td></tr><tr><td>24.5</td><td>3.3</td><td>&lt;6.8</td><td>3.4</td><td>&lt;7.3</td></tr><tr><td>25.5</td><td>0.3</td><td>&lt;5.2</td><td>0.7</td><td>&lt;6.0</td></tr><tr><td>26.5</td><td>2.7</td><td>&lt;9.8</td><td>1.8</td><td>&lt;5.8</td></tr><tr><td>27.5</td><td>0.0</td><td>&lt;2.5</td><td>0.6</td><td>&lt;6.3</td></tr><tr><td>28.5</td><td>4.2</td><td>2.5 ± 1.9</td><td>2.9</td><td>&lt;7.5</td></tr><tr><td>29.5</td><td>0.0</td><td>&lt;3.9</td><td>0.5</td><td>&lt;4.7</td></tr><tr><td>30.5</td><td>0.3</td><td>&lt;5.3</td><td>10.2</td><td>5.3 ± 2.3</td></tr><tr><td>31.5</td><td>5.4</td><td>3.5 ± 2.3</td><td>1.6</td><td>&lt;6.2</td></tr><tr><td>32.5</td><td>3.7</td><td>&lt;8.4</td><td>6.0</td><td>2.1 ± 1.6</td></tr><tr><td>33.5</td><td>0.1</td><td>&lt;4.6</td><td>1.4</td><td>&lt;4.0</td></tr><tr><td>34.5</td><td>4.0</td><td>3.1 ± 2.2</td><td>3.4</td><td>&lt;3.9</td></tr><tr><td>35.5</td><td>0.0</td><td>&lt;6.4</td><td>0.0</td><td>&lt;3.0</td></tr><tr><td>36.5</td><td>4.3</td><td>3.8 ± 2.5</td><td>2.3</td><td>&lt;5.3</td></tr><tr><td>37.5</td><td>3.0</td><td>&lt;9.8</td><td>0.0</td><td>&lt;2.7</td></tr><tr><td>38.5</td><td>0.0</td><td>&lt;5.2</td><td>2.9</td><td>&lt;5.8</td></tr><tr><td>39.5</td><td>0.0</td><td>&lt;4.8</td><td>8.0</td><td>3.6 ± 1.6</td></tr><tr><td>40.5</td><td>4.5</td><td>5.7 ± 3.4</td><td>1.4</td><td>&lt;3.9</td></tr><tr><td>41.5</td><td>2.4</td><td>&lt;10.6</td><td>7.1</td><td>2.5 ± 1.3</td></tr><tr><td>42.5</td><td>0.4</td><td>&lt;7.3</td><td>1.8</td><td>&lt;3.1</td></tr><tr><td>43.5</td><td>2.3</td><td>&lt;8.1</td><td>0.0</td><td>&lt;2.0</td></tr><tr><td>44.5</td><td>0.0</td><td>&lt;4.3</td><td>0.0</td><td>&lt;2.0</td></tr><tr><td>45.5</td><td>2.5</td><td>&lt;9.3</td><td>0.0</td><td>&lt;1.3</td></tr><tr><td>46.5</td><td>0.0</td><td>&lt;2.2</td><td>1.2</td><td>&lt;3.5</td></tr><tr><td>47.5</td><td>2.1</td><td>&lt;6.7</td><td>0.0</td><td>&lt;2.0</td></tr><tr><td>48.5</td><td>0.7</td><td>&lt;5.6</td><td>9.7</td><td>2.8 ± 1.2</td></tr><tr><td>49.5</td><td>0.0</td><td>&lt;2.8</td><td>0.8</td><td>&lt;3.2</td></tr><tr><td>50.5</td><td>...</td><td>...</td><td>0.9</td><td>&lt;3.1</td></tr><tr><td>51.5</td><td>...</td><td>...</td><td>6.1</td><td>3.2 ± 1.5</td></tr><tr><td>52.5</td><td>...</td><td>...</td><td>0.0</td><td>&lt;2.1</td></tr></tbody></table>

<table><caption>**Table 4**
(Continued)</caption><thead><tr><th rowspan="2">Days since<br>Start</th><th colspan="2">V1369 Cen 2013</th><th colspan="2">V5668 Sgr 2015</th></tr><tr><th>TS</th><th>F<sub>γ</sub></th><th>TS</th><th>F<sub>γ</sub></th></tr></thead><tbody><tr><td>53.5</td><td>...</td><td>...</td><td>0.0</td><td>&lt;1.4</td></tr><tr><td>54.5</td><td>...</td><td>...</td><td>0.0</td><td>&lt;2.6</td></tr><tr><td>55.5</td><td>...</td><td>...</td><td>1.6</td><td>&lt;3.8</td></tr><tr><td>56.5</td><td>...</td><td>...</td><td>8.6</td><td>2.9 ± 1.3</td></tr><tr><td>57.5</td><td>...</td><td>...</td><td>1.4</td><td>&lt;4.3</td></tr><tr><td>58.5</td><td>...</td><td>...</td><td>0.0</td><td>&lt;1.2</td></tr><tr><td>59.5</td><td>...</td><td>...</td><td>0.4</td><td>&lt;2.9</td></tr><tr><td>60.5</td><td>...</td><td>...</td><td>0.0</td><td>&lt;2.4</td></tr><tr><td>61.5</td><td>...</td><td>...</td><td>1.0</td><td>&lt;3.2</td></tr><tr><td>62.5</td><td>1.6</td><td>&lt;7.9</td><td>0.0</td><td>&lt;2.5</td></tr><tr><td>63.5</td><td>0.7</td><td>&lt;6.3</td><td>0.0</td><td>&lt;3.5</td></tr><tr><td>64.5</td><td>0.0</td><td>&lt;2.6</td><td>0.0</td><td>&lt;2.3</td></tr><tr><td>65.5</td><td>0.0</td><td>&lt;3.0</td><td>0.0</td><td>&lt;2.6</td></tr><tr><td>66.5</td><td>0.3</td><td>&lt;5.3</td><td>0.7</td><td>&lt;4.5</td></tr><tr><td>67.5</td><td>0.0</td><td>&lt;2.0</td><td>0.0</td><td>&lt;2.7</td></tr><tr><td>68.5</td><td>0.0</td><td>&lt;3.9</td><td>0.0</td><td>&lt;2.6</td></tr><tr><td>69.5</td><td>1.5</td><td>&lt;5.5</td><td>0.8</td><td>&lt;5.5</td></tr></tbody></table>

**Note.** Days indicated are the centers of the 1-day bins relative to the defined start times ($t_s$). TS values and >100 MeV fluxes, $F_γ$, in units of $10^{-7}$ photons cm$^{-2}$ s$^{-1}$ (2σ upper limits when TS < 4) are presented. The gap in observations of V1369 Cen from $t_s$ + 50.0 to +62.0 days is due to an LAT ToO on SN 2014J in M82.

$$ \tau_{\min} = \tau_{pp} \text{ and } (1 - e^{-\tau_{ej}/\tau_{pp}}) \sim 1; \text{ thus,} $$

$$ L_{\gamma} \sim \eta_{\gamma} \eta_{cr} \frac{\epsilon_{ej}}{\tau_{ej}}. \qquad (9) $$

Here CR protons injected downstream produce γ-rays so efficiently that all the energy stored in CR protons at the shock front is transferred immediately to γ-ray emission. iii. $\tau_{esc} \ll \tau_{pp}$ and $\tau_{esc} \ll \tau_{ej}$, where the escape timescale is much shorter than both the pp interaction timescale and the source lifetime. Under such conditions, $\tau_{min} = \tau_{esc}$ and $(1 - e^{-\tau_{ej}/\tau_{esc}}) \sim 1$; thus,

$$ L_{\gamma} \sim \eta_{\gamma} \eta_{cr} \frac{\epsilon_{ej}}{\tau_{ej}} \frac{\tau_{esc}}{\tau_{pp}}. \qquad (10) $$

Here CR protons injected downstream escape so efficiently that only a very small fraction ($\tau_{esc}/\tau_{pp} \ll 1$) of the total energy stored in CR protons at the shock front is transferred to the γ-ray emission over the source lifetime.

For the hadronic scenario considered in the main text, the condition $\tau_{ej} \ll \tau_{min}$ described in case (i) is applicable.

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