Angular Expansion of Nova Shells

Novae are the result of the interaction of stars in close binary systems, where a white dwarf (WD) accretes H-rich material from a companion, typically a giant or subgiant low-mass star (Bode & Evans 2008). When the accreted material reaches a critical mass, a thermonuclear runaway occurs. Temperatures can reach values of ∼1–4 × 10⁸ K in a few seconds (Starrfield et al. 2016) and up to ∼2 × 10⁻⁴ M_⊙ (Gehrz et al. 1998) of highly processed material is ejected at velocities ∼1000 km s⁻¹ (Bode 2010) in a classical nova (CN) event. With time, the nova remnants will expand and mix into the interstellar medium (ISM).

The morphology and expansion of a nova remnant depend on the details of the nova event, and on the interactions of the ejecta with the stellar companion and the pre-existing circumstellar material, which may consist of an accretion disk and a common envelope. A typical CN outburst includes an initial slow (500–2000 km s⁻¹) wind followed by a longer phase with a faster (1000–4000 km s⁻¹) wind (Bode & Evans 2008). The interaction of these two winds forms a double shock structure, with the fast wind passing through the slow one until it dissipates and cools adiabatically as it expands (O'Brien & Lloyd 1994).

Additionally, the interaction of the ejecta with the binary companion and material in a common envelope has effects on the asphericity of the nova shell (Livio et al. 1990) and dynamics of the ejecta (Shankar et al. 1991). The effects of these interactions vary among novae of different speed classes (Lloyd et al. 1997), which are basically associated with the different timescales of the slow and fast wind phases, providing an interpretation for the larger asphericities of the remnants of slow novae with respect to those of fast novae (Slavin et al. 1995). Finally, the WD rotation may also feed the ejecta with angular momentum, which can produce noticeable effects on the structure of nova shells (Porter et al. 1998).

The late expansion of nova shells can provide insights into the plasma physics and shock phenomena associated with the blast produced by the interaction of hydrogen-poor, metal-rich ejecta with the circumstellar environment and to investigate the ingestion of this ejecta by the ISM. The complete dynamical evolution of a nova occurs on timescales comparable to that of human life, thus it provides a first class comparison to investigate the much slower evolution of planetary nebulae (PNe), or the processes involved in the evolution of supernova remnants (SNR), which are rare. The timescale for a nova dispersal is an important parameter to assess the duration of the different stages of hibernation between a CN eruption and their parents' cataclysmic variables (Shara et al. 2017).

Very little attention has been paid to the late expansion of nova shells, however. Duerbeck (1987) conducted a heroic investigation of the angular expansion of nova shells using images of limited quality and concluded that they have mean half-times of 75 yr, noting that this deceleration is most noticeable for novae with higher expansion velocities. Since then, very few detailed studies of the angular expansion of nova shells have been conducted, including studies of GK Per, perhaps the most known nova shell (Liimets et al. 2012; Takei et al. 2015; Harvey et al. 2016), DQ Her (Herbig & Smak 1992; Vaytet et al. 2007; Harrison et al. 2013), FH Ser (della Valle et al. 1997; Esenoglu 1997), and recently IPHASX J210204.7+471015 (Santamaría et al. 2019). The multiple knots in GK Per expand isotropically at an angular velocity of 03–05 yr⁻¹, which has been kept unchanged since their ejection a century ago (Liimets et al. 2012; Shara et al. 2012). This is somehow surprising, because detailed analyses of individual knots reveal notable interaction between the knots and with the ISM (Harvey et al. 2016). On the other hand, a noticeable deceleration of the bow-shock component of the nova IPHASX J210204.7+471015 has been recently reported (Santamaría et al. 2019).

The lack of agreement between these results most likely implies that the expansion of a nova shell depends on the details of the nova outburst and the local properties of the ISM. The availability of high-quality archival images of nova shells allows a precise investigation of the expansion of a meaningful sample of sources. Using the sample of images presented by Slavin et al. (1995), we have selected five nova shells with multi-epoch high-quality images, namely DQ Her, FH Ser, T Aur, V476 Cyg, and V533 Her, to carry out a pilot study of the investigation of the angular expansion of nova shells. Basic information on these novae, including their Galactic coordinates, type, outburst date, distance (as adapted from Schaefer 2018), height over the Galactic Plane, and expansion velocity derived from spectroscopic observations, is compiled in Table 1. The latter is provided for the major and minor axes of FH Ser.

Table 1.  Sample of Novae

Object	$l,b$	Nova Type	Outburst Date	Distance	z	Angular Size	${v}_{\exp }^{\mathrm{sp}}$	References
						major × minor	major × minor
	(°)			(pc)	(pc)	('')	(km s−1)
T Aur	177.14 − 1.70	fast	1891 Dec	880${}_{-35}^{+50}$	25	25.4 × 18.6	655	1
V476 Cyg	87.37 + 12.42	very fast	1920 Aug	670${}_{-50}^{+110}$	145	14.6 × 13.4	725	2
DQ Her	73.15 + 26.44	slow	1934 Dec	501${}_{-6}^{+6}$	220	32.0 × 24.2	370	3
V533 Her	69.19 + 24.27	slow	1963 Feb	${1200}_{-40}^{+50}$	495	16.8 × 15.2	850	4
FH Ser	32.91 + 5.79	slow	1970 Feb	${1060}_{-70}^{+110}$	105	12.4 × 10.6	490 × 385	4

Note. Distances were obtained from Gaia Data Release 2 (DR2) (Schaefer 2018). References for spectroscopic expansion velocities: (1) Cohen & Rosenthal (1983), (2) Duerbeck (1987), (3) Vaytet et al. (2007), (4) Gill & O'Brien (2000).

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2.1. Contemporary Imaging

Present-day (2016–2019) images of the nova shells in Table 1 were obtained using the Alhambra Faint Object Spectrograph and Camera (ALFOSC) at the 2.5 m Nordic Optical Telescope (NOT) of the Roque de los Muchachos Observatory in La Palma, Spain. The E2V 231-42 2k × 2k CCD was used with pixel size 15.0 μm, providing a plate scale of 0211 pix⁻¹ and a field of view (FoV) of 72 arcmin. The images used to investigate the angular expansion of these novae were obtained through Hα filters with FWHMs of 33 Å for the 2016 run of T Aur and 13 Å for the others. Total exposure times and spatial resolutions, as determined from the FWHM of field stars, are listed in Table 2.

Table 2.  Details of the Imaging Observations

Object	Date	Telescope and	Filter	Exposure	Pixel	Spatial
		Instrument		Time	Scale	Resolution
				(s)	(''pix−1)	('')
T Aur	1956 Dec	PO and 103aE	Red	⋯	1.7	⋯
	1978 Mar	KPNO and ISIT	Hα	1800	⋯	⋯
	1989 Nov 22	POSS2	Red RG610	4800	1.0	⋯
	1998 Nov 2	HST and WFPC2	F656N	5400	0.05	0.2
	2016 Nov 28	NOT and ALFOSC	NOT #21 Hα	1800	0.21	0.6
	2018 Jan 3	NTT and EFOSC2	Hα	1440	0.12	0.5
	2019 Oct 11	NOT and ALFOSC	OSN H01 Hα	2700	0.21	0.9
V476 Cyg	1944 Jan–Jun	MW and 100-inch	Hα	⋯	⋯	⋯
	1993 Sep 12	WHT and Aux. Port	Hα 6569	900	0.25	1.2
	2018 Jun 8	NOT and ALFOSC	OSN H01 Hα	2700	0.21	0.7
DQ Her	1977 May 15	BokT and ITT 40 mm	Hα	⋯	⋯	⋯
	1993 Jul 31	JKT and AGBX	Hα	7200	0.33	2.0
	1995 Sep 4	HST and WFPC2	F656N	2000	0.05	0.1
	1997 Oct 25	WHT and Aux. Port	Hα 656	1200	0.11	0.4
	2012 Aug 15	WHT and ACAM	T6565	40	0.25	0.7
	2017 May 27	NOT and ALFOSC	OSN H01 Hα	2700	0.21	0.8
	2018 Jun 5	NOT and ALFOSC	OSN H01 Hα	2700	0.21	0.8
V533 Her	1993 Sep 11	WHT and Aux. Port	Hα 6569	1800	0.25	1.0
	1997 Sep 3	HST and WFPC2	F656N	2600	0.05	0.2
	2018 Jun 6	NOT and ALFOSC	OSN H01 Hα	4800	0.21	0.6
FH Ser	1996 Mar 18	NTT and SUSI	Hα	720	0.13	0.9
	1997 May 11	HST and WFPC2	F656N	4800	0.05	0.1
	2017 May 29	NOT and ALFOSC	OSN H01 Hα	2700	0.21	0.6
	2018 Jun 6	NOT and ALFOSC	OSN H01 Hα	3600	0.21	0.7

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Images were also acquired in other filters, as described in the caption of Figure 1, to obtain color-composite pictures of these novae. All images were processed using standard iraf routines.

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2.2. Archival Imaging

We present in the left and middle columns of Figure 1 archival and present-day images of the nova shells in our sample, respectively. These images reveal all nova shells in our sample to have elliptical morphologies with different degrees of ellipticity. T Aur and DQ Her have similar knotty morphologies, with cometary knots showing remarkable tails mainly along the major axis. V476 Cyg also seems to have a broken, clumpy morphology, whereas the shells of FH Ser and V533 Her have smoother appearances. A comparison of present-day images (Figure 1 middle column) with representative archival images (Figure 1 left column) unveils clear expansion patterns. A careful examination of multi-epoch images also discloses small-scale morphological variations, including changes in the size and distribution of clumps. A detailed study is deferred to a subsequent work (E. Santamaría et al. 2020, in preparation).

To investigate and quantify the expansion of these nova shells, radial spatial profiles across individual discrete features have been extracted from the images at the different epochs listed in Table 2. The distance of these features to the central star has been determined by measuring their position using Gaussian fits. The angular sizes along different directions have then been normalized to the minor axis using an elliptical fit to the shape of the nova shell, and an averaged value for the size of the minor axis and its 1σ dispersion derived for each epoch. These are shown in Figure 2, together with linear fits for all the nova shells in our sample, where the time is computed from the nova outburst date and the angular size of the semiminor axis has been converted to linear size using the nova distance. The increase of the size of these nova shells with time can be described by linear fits (Figure 2) with correlation coefficients ≥0.98, implying t-test significance probabilities ≥98% for V533 Her and V476 Cyg, >99% for FH Ser, and >99.9% for DQ Her and T Aur. The slopes of these fits correspond to the angular expansion rates along the minor axis of these nova shells (column 2 of Table 1).

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We note that the angular expansion rates derived from these fits are consistent with previously reported ones.

Vaytet et al. (2007) derived angular expansion rates of 0205 ± 0014 yr⁻¹ and 0165 ± 0012 yr⁻¹ along the major and minor axes of DQ Her, respectively, whereas angular expansion rates of 0128 yr⁻¹ (Seitter & Duerbeck 1987), 0136 yr⁻¹ (Duerbeck 1992), and 0104–0146 yr⁻¹ (della Valle et al. 1997) have been reported for FH Ser. Similarly, (Harvey 2018) provides angular expansion rates ≈012 yr⁻¹ and ≈0088 yr⁻¹ along the major and minor axes of T Aur, respectively, and ≈0075 yr⁻¹ for V476 Cyg.

The main result from the investigation of the angular expansion of this sample of nova shells is their linear expansion with time (Figure 2). This linear increase of size with time implies a free expansion, where the initial velocity of the ejecta remains the same since the nova event with no sign of deceleration. Thus, we should expect the expansion velocity of a nova shell derived from its angular expansion rate and distance (${\bar{v}}_{\exp }$, column 3 of Table 3), which is the averaged expansion velocity of the ejecta since the nova outburst projected on the plane of the sky, to be consistent with the expansion velocity derived from spectroscopic observations (${v}_{\exp }^{\mathrm{sp}},$ column 8 of Table 1), which is the expansion velocity along the line of sight at the time of the observation.⁶ These two expansion velocities are found to be in excellent agreement for DQ Her and V533 Her, and within the uncertainties for FH Ser, whose ${v}_{\exp }^{\mathrm{sp}}$ have been derived from spatiokinematic models. Remarkable discrepancies are found, however, for T Aur and V476 Cyg, whose spectroscopic observations are of low quality (Cohen & Rosenthal 1983; Duerbeck 1987). An orientation of the major axis of these nova shells close to the line of sight cannot explain the much larger spectroscopic velocities of T Aur and V476 Cyg compared to the expansion velocities on the plane of the sky along the minor axis. We note that recent high-dispersion spectra of T Aur imply expansion velocities similar to those found here (Harvey 2018).

Table 3.  Flux and Mass of the Nova Shells

Object	Angular Expansion	${\bar{v}}_{\exp }$	${M}_{\mathrm{swept}}\times (\tfrac{{n}_{\mathrm{ISM}}}{1\,{\mathrm{cm}}^{-3}})$	${M}_{\mathrm{shell}}\times {\left(\tfrac{\epsilon }{0.1}\right)}^{0.5}$	${F}_{{\rm{H}}\alpha }$	${E}_{\mathrm{kin}}$
	(''yr−1)	(km s−1)	(${M}_{\odot }$)	(${M}_{\odot }$)	(erg cm−2 s−1)	(erg)
T Aur	(0.097 ± 0.004) × (0.072 ± 0.001)	(410 ± 40) × (315 ± 22)	1.3 × 10−5	3.6 × 10−4	2 × 10−13	4.2 × 1044
V476 Cyg	(0.073 ± 0.008) × (0.067 ± 0.007)	(230 ± 60) × (200 ± 50)	1.7 × 10−6	2.2 × 10−5	1 × 10−14	1.1 × 1043
DQ Her	(0.188 ± 0.008) × (0.139 ± 0.005)	(460 ± 25) × (325 ± 16)	5.2 × 10−6	2.3 × 10−4	7 × 10−13	3.3 × 1044
V533 Her	(0.152 ± 0.006) × (0.139 ± 0.007)	(850 ± 70) × (770 ± 70)	1.3 × 10−5	9.0 × 10−5	7 × 10−15	5.9 × 1044
FH Ser	(0.125 ± 0.002) × (0.109 ± 0.002)	(630 ± 80) × (540 ± 70)	3.5 × 10−6	1.4 × 10−4	9 × 10−14	4.7 × 1044

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The linear expansion with time of the nova shells in this sample strengthens the idea that the ejecta have kept expanding at its initial velocity since the nova event. This result confirms previous results presented for T Aur and V476 Cyg, but also for V1500 Cyg and V4362 Sgr (Harvey 2018). Apparently, the circumstellar medium around these novae has not been able to slow down their expansion, which can be expected if the mass of the ISM material swept up by the nova shell is much smaller than the mass of the nova ejecta. This can be tested by computing their values and assuming an ISM density.⁷

n_ISM = 1 cm⁻³, the volume evacuated by the nova shell implies swept-up masses of 10⁻⁶–10⁻⁵ M_⊙ (column 4 in Table 3). These can be compared with the nova masses 2 × 10⁻⁵–3 × 10⁻⁴ M_⊙ (column 5 in Table 3). The latter have been derived following Mustel & Boyarchuk (1970), using the unabsorbed Hα fluxes listed in column 6 and assuming a filling factor  = 0.1. The Hα fluxes are computed from our Hα narrowband images using intermediate-dispersion flux-calibrated spectra of DQ Her to derive a count-to-flux conversion factor and corrected for absorption using the extinction values given by Slavin et al. (1995) for T Aur and V476 Cyg, Selvelli & Gilmozzi (2013) for DQ Her and V533 Her, and Gill & O'Brien (2000) for FH Ser. The masses of the nova ejecta are indeed much greater than the masses of the swept-up ISM, by factors from 7 to 45, which is consistent with their free expansion. At their present expansion rates, the free expansion can be expected to last from ≃100 yr for V533 Her up to ≃400 yr for T Aur, until the time when the swept-up ISM mass equals that of the nova ejecta. Since the nova ejecta is not slowed down, it reduces the time for dispersal of nova shells into the ISM.

The free expansion is supported by the large kinetic energy ($\tfrac{1}{2}\,{M}_{\mathrm{shell}}\,{v}_{\exp }^{2}$) of the nova shells, which have been computed by adopting a weighted expansion velocity among the polar and equatorial velocities. The kinetic energies listed in column 7 of Table 3 are in the range of a few times 10⁴⁴ erg, except for V476 Cyg, which is 1 × 10⁴³ erg.

The free expansion of the nova shells in our sample is in sharp contrast with the conclusions drawn by Duerbeck (1987), who proposed that the expansion velocity of a nova shell reduces to half every 75 yr. This is particularly shocking for DQ Her and V476 Cyg (this work), and GK Per (Liimets et al. 2012; Shara et al. 2012), which were proposed to have deceleration half-times of 67, 117, and 58 yr, respectively. The free expansion of nova shells applies to different nebular morphologies, from the smooth elliptical morphology of FH Ser, V476 Cyg, and V533 Her, the mildly broken elliptical structure of T Aur and DQ Her, and the knotty morphology of GK Per. Only the faint bow-shock structural component of IPHASX J210204.7+471015 seems to have experienced a notable braking in its interaction with the ISM (Guerrero et al. 2018; Santamaría et al. 2019).

A comparison between multi-epoch suitable broadband and narrowband images of the nova shells DQ Her, FH Ser, T Aur, V476 Cyg, and V533 Her has been used to derive their angular expansion rates. These are found to be unchanged since the nova event, i.e., the nova shells in this sample are still in a free expansion phase. This is expected, as the mass of the ejecta is 7–45 times larger than the mass of the swept-up circumstellar medium.

The images of the nova shells in our sample illustrate a time lapse since the nova event from 20 to 130 yr.

Given the large ratio between the mass of the ejecta and that of the swept-up circumstellar medium, the free expansion phase can be expected to last for a few hundred years, during most (if not all) of the visible phase.

E.S., G.R., and J.A.Q.M. acknowledge support from CONACyT and Universidad de Guadalajara. M.A.G. and E.S. acknowledge financial support by grants AYA 2014-57280-P and PGC 2018-102184-B-I00, cofunded with FEDER funds. M.A.G. acknowledges support from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award for the Instituto de Astrofísica de Andalucía (SEV-2017-0709). E.S. acknowledges the hospitality of the IAA during a short-term visit. G.R.L. acknowledges support from CONACyT and PRODEP (Mexico). L.S. acknowledges support from UNAM DGAPA PAPIIT project IN101819. M.A.G. and J.A.T. acknowledge support from the UNAM DGAPA PAPIIT project IA 100318. We appreciate the valuable comments of the referee, Dr Nye Evans. Finally, we thank Alessandro Ederoclite for useful discussions and comments. The data presented here were obtained in part with ALFOSC, and provided by the Instituto de Astrofísica de Andalucía (IAA) under a joint agreement with the University of Copenhagen and NOTSA. This research made use of iraf, distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. We acknowledge the use of the ESO Science Archive Facility developed in partnership with the Space Telescope European Coordinating Facility (ST-ECF). We also acknowledge the ING archive, maintained as part of the CASU Astronomical Data Centre at the Institute of Astronomy, Cambridge and finally, the STScI, operated by the Association of Universities for research in Astronomy, Inc., under NASA contract NAS5-26555.

Facilities: HST(STIS) - Hubble Space Telescope satellite, NOT:2.5 m - .

Software: astropy (Astropy Collaboration et al. 2013), iraf (Tody 1986).