11institutetext:  Department of Astronomy, AlbaNova University Center,
Stockholm University, SE-10691 Stockholm, Sweden
11email<EMAIL_ADDRESS>22institutetext: The Oskar Klein Centre, AlbaNova,
SE-10691 Stockholm, Sweden
33institutetext: Ioffe Institute, Politekhnicheskaya 26, St. Petersburg,
194021, Russia
44institutetext: Peter the Great St. Petersburg Polytechnic University,
Politekhnicheskaya 29, St. Petersburg, 195251, Russia

# Kinematics, structure and abundances of supernova remnant 0540-69.3††thanks:
Based on observations performed at the European Southern Observatory, La Silla
and Paranal, Chile (ESO Programmes 56.C-0731 and 68.D-0394).

P. Lundqvist 1122 N. Lundqvist 1122 Yu. A. Shibanov 3344

(Received ?, ?, 2021; accepted ?, ?, 2021)

###### Abstract

Aims. To investigate the structure, elemental abundances, physical conditions
and the immediate surroundings of supernova remnant 0540-69.3 in the Large
Magellanic Cloud.

Methods. Imaging in [O iIi] and spectroscopic studies through various slits
were utilized using European Souther Observatory’s Very Large and New
Technology Telescopes. Densities, temperatures and abundances were estimated
applying nebular analysis for various parts of the remnant.

Results. Several new spectral lines are identified, both in the pulsar-wind
nebula part of the remnant, and in interstellar clouds shocked by the
supernova blast wave. In the pulsar-wind nebula, all lines are redshifted by
$440\pm 80\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ with respect
to the rest frame of the host galaxy, and a 3D-representation of the [O iii]
emission displays a symmetry axis of ring-like structures which could indicate
that the pulsar shares the same general redshift as the central supernova
ejecta. [O ii], [S ii], [Ar iii] and H$\beta$ share a common more compact
structure than [O iii], and possibly [Ne iii]. The average [O iii] temperature
in the pulsar-wind nebula is $23\,500\pm 1\,800$ K, and the electron density
derived from [S ii] is typically $\sim 10^{3}\rm\leavevmode\nobreak\ cm^{-3}$.
By mass, the relative elemental abundances of the shocked ejecta in the
pulsar-wind nebula are ${\rm O:Ne:S:Ar}\approx 1:0.07:0.10:0.02$, consistent
with explosion models of $13-20\leavevmode\nobreak\ {\rm M}_{\odot}$
progenitors, and similar to that of SN 1987A, as is also the explosive mixing
of hydrogen and helium into the center. From H$\beta$ and He i $\lambda$5876,
the mass ratio of He/H in the center is estimated to be in excess of $\sim
0.8$. The rapid cooling of the shocked ejecta could potentially cause
variations in the relative abundances if the ejecta are not fully
microscopically mixed, and this is highlighted for S/O for the period
1989–2006. [O iii] is also seen in presumably freely coasting photoionized
ejecta outside the pulsar-wind nebula at inferred velocities out to well above
$2\,000\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$, and in
projection [O iii] is seen out to $\sim 10$″ from the pulsar. This is used to
estimate that the pulsar age is $\approx 1\,200$ years. The freely coasting [O
iii]-emitting ejecta have a strictly non-spherical distribution, and their
mass is estimated to be $\sim 0.12\leavevmode\nobreak\ {\rm M}_{\odot}$. A
possible outer boundary of oxygen-rich ejecta is seen in [O ii]
$\lambda\lambda$3726,3729 at $\sim 2\,000-2\,100\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$. Four filaments of shocked interstellar medium
are identified, and there is a wide range in degree of ionization of iron,
from Fe+ to Fe13+. One filament belongs to a region also observed in X-rays,
and another one has a redshift of $85\pm 30\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ relative to the host. From this we estimate
that the electron density of the [O iii]-emitting gas is $\sim
10^{3}\rm\leavevmode\nobreak\ cm^{-3}$, and that the line of the most highly
ionized ion, [Fe xiv] $\lambda$5303, come from an evaporation zone in
connection with the radiatively cooled gas emitting, e.g., [O iii], and not
from immediately behind the blast wave. We do not find evidence for nitrogen-
enriched ejecta in the south-western part of the remnant, as was previously
suggested. Emission in this region is instead from a severely reddened H ii-
region.

###### Key Words.:

ISM: supernova remnants – supernovae: general – pulsars: individual: PSR
B0540-69

##  1 Introduction

Supernova remnant (SNR) 0540-69.3 (henceforth simply 0540) has been observed
at wavelengths ranging from X-rays to the radio. Both in the radio and in
X-rays. the remnant is bounded by an outer shell, which has a radius of $\sim
20-35\arcsec$ (Manchester et al., 1993b; Gotthelf & Wang, 2000). In the
optical, the outer shell coincides with two bright filaments to the west and
southwest (Mathewson et al., 1980), one emitting [O iIi] and the other [N ii],
respectively. As cautioned by these authors, the [N ii] filament may not
belong to the remnant, as it coincides with two bright stars.

Inside the outer shell, the emission from the remnant is concentrated to a
substantially smaller nebula (Mathewson et al., 1980; Kirshner et al., 1989;
Caraveo et al., 1992; Morse, 2003; Serafimovich et al., 2005; Lundqvist et
al., 2011). In [O iii] the diameter of the main emission is $\sim 8\arcsec$
(Caraveo et al., 1992). Henceforth we will refer to this as the ‘central part
of the SNR’ (SNRC), and in [S ii] and H$\alpha$ the observed structures are
even smaller and weaker, decreasing in size and strength in this order.

The SNRC also contains an optical continuum source; this is synchrotron
emission from the pulsar wind nebula (PWN) (Chanan et al., 1984; Serafimovich
et al., 2004; Lundqvist et al., 2011). The synchrotron emission and its
spectral characteristics have been studied throughout the energy range from
radio to X-rays (Serafimovich et al., 2004; Lundqvist et al., 2011; Mignani et
al., 2012; Brantseg et al., 2014; Lundqvist et al., 2020) A PWN is expected
since the remnant harbors the young pulsar (PSR) B0540-69 whose pulsed
emission has been documented in X-rays (Seward et al., 1984), in the UV
(Mignani et al., 2019), in the optical (Middleditch & Pennypacker, 1985), and
in the radio (Manchester et al., 1993a).

The SNRC with its pulsar bears many similarities to the Crab Nebula, and a
detailed discussion and comparison of 0540 with the Crab pulsar and its PWN
can be found in Serafimovich et al. (2004). However, as revealed by spectral
studies in the optical (Mathewson et al., 1980; Dopita & Tuohy, 1984; Kirshner
et al., 1989; Morse et al., 2006), the elemental abundances in 0540 are very
different from those in the Crab. While the Crab is helium-rich, but not
conspicuous in other respects (MacAlpine et al., 1996), 0540 is dominated by
forbidden oxygen and sulphur lines, and is classified as an “oxygen-rich SNR”
(OSNR). The most studied object in this class is undoubtedly Cas A, which,
however, is not pulsar-powered, although it contains a neutron star
(Tananbaum, 1999; Pavlov et al., 2000). SN 1987A is another case that is now
entering its remnant stage, with an oxygen-mass of $\sim
1.8-1.9\leavevmode\nobreak\ {\rm M}_{\odot}$ within its innermost ejecta,
i.e., out to $\sim 2\,000\rm\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}$ (Kozma & Fransson, 1998; Jerkstrand et al., 2011). 0540 makes an
interesting link between pulsar-powered remnants in general and OSNRs.

In all the emission lines, projected images on the sky of the SNRC appear to
be concentrated to a few blobs (e.g., Lundqvist et al., 2011). In addition,
spectroscopy of 0540 by Kirshner et al. (1989) showed that the weighted
emission of the SNRC is redshifted with respect to the LMC rest velocity. This
was further studied by Morse et al. (2006) who, however, also revealed a faint
[O iIi] “halo” between $-1400$ and $+1900\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$, with the center of expansion close to the
systemic velocity of the surrounding H II region. Sandin et al. (2013) used
the the integral field unit (IFU) ESO/VLT/VIMOS to probe the 3D structure of
the whole SNRC and found that [O iIi] the full velocity range between
$-1650\leq v_{[{O\textsc{iIi}}]}\leq+1700\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$, where $v_{[{O\textsc{iIi}}]}$ is relative to
the systemic velocity of local LMC redshift. In the plane of the sky, an [O
iIi] halo can be traced out to $\sim 8\arcsec$ from the pulsar (Morse et al.,
2006) . Williams et al. (2008, who also included infrared observations with
the Spitzer Space telescope) interpreted the halo emission to come from
photoionized unshocked supernova ejecta outside the PWN, but inside the
reverse shock of the SNR. At a distance of 50 kpc, $\sim 8\arcsec$ and
$v_{[{O\textsc{iIi}}]}\approx 1700\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ would imply an age of $\sim 1.1\times 10^{3}$
years for 0540, which is less than the spin down age of the pulsar ($1.6\times
10^{3}$ years, Reynolds, 1985).

Spectroscopy and imaging show that there are clear differences, not only in
the size of the SNRC, but also in the structure of the emitting gas depending
on the emission line traced. In particular, the structures of [O iIi] and [S
Ii] emission have a very low correlation in the bright southwest part of the
SNRC, while the [S Ii] emission correlates well with continuum emission
(Lundqvist et al., 2011). This could be due to differences in the ionization
structure as a function of position angle, or it could be difference in
elemental structure.

Table 1: Log of observations of SNR 0540-69.3.

Imaging of 0540
---
Telescope | Instrument |  | Filter |  | UT | Exp. time |  | sec z | Seeinga
|  |  |  |  |  | (s) |  |  | (arcsec)
NTT | EMMI |  | [O iii]$/$0 |  | 04:24:54b | 900 |  | 1.37 | 1.20
NTT | EMMI |  | [O iii]$/$6000 |  | 05:05:00 | 900 |  | 1.43 | 1.47
NTT | EMMI |  | [O iii]$/$0 |  | 06:27:17 | 900 |  | 1.62 | 1.13
Spectroscopy of 0540
Telescope | Instrument |  | Range |  | UT | Exp. time |  | sec z | Seeinga
|  |  | (nm) |  |  | (s) |  |  | (arcsec)
NTT | EMMI |  | 385-845 |  | 07:26:45c | 2200 |  | 1.89 | 1.35
VLT | FORS1 |  | 360-606 |  | 01:59:32d | 1320 |  | 1.43 | 1.25
|  |  |  |  | 02:23:25 | 1320 |  | 1.42 | 1.30
|  |  |  |  | 02:52:38 | 1320 |  | 1.41 | 1.18
|  |  |  |  | 03:16:31 | 1320 |  | 1.41 | 1.12
|  |  |  |  | 03:42:32 | 1320 |  | 1.41 | 1.24
|  |  |  |  | 04:06:25 | 1320 |  | 1.43 | 1.09
|  |  |  |  | 04:32:42 | 1320 |  | 1.45 | 0.88
VLT | FORS1 |  | 360-606 |  | 02:07:57e | 1320 |  | 1.42 | 1.48
|  |  |  |  | 02:31:50 | 1320 |  | 1.41 | 1.25
|  |  |  |  | 03:39:58 | 1320 |  | 1.42 | 0.92
|  |  |  |  | 04:03:52 | 1320 |  | 1.43 | 0.99
|  |  |  |  | 04:30:26 | 1320 |  | 1.46 | 1.03
|  |  |  |  | 04:54:20 | 1320 |  | 1.49 | 1.03
Spectroscopy of standard star LTT 3864
Telescope | Instrument |  | Range |  | UT | Exp. time |  | sec z | Seeinga
|  |  | (nm) |  |  | (s) |  |  | (arcsec)
NTT | EMMI |  | 385-845 |  | 08:14:55b | 900 |  | 1.91 | 1.02
VLT | FORS1 |  | 360-606 |  | 08:51:03f | 20 |  | 1.03 | 0.67

a FWHM from stellar profiles |  d 2002 Jan 9, slit “1” in Fig. 1, PA=88°
---|---
b 1996 Jan 17 |  e 2002 Jan 10, slit “3” in Fig. 1, PA=51°
c 1996 Jan 17, slit “2” in Fig. 1, PA=22° |  f 2002 Jan 10

Figure 1:  3.2′$\times$2.0′ [O iii] image of SNR 0540-69.3 obtained with
NTT/EMMI in 1996 using the narrow [O iii]$/$0 filter centered at the rest
wavelength of [O iii] $\lambda 5007$. The bright extended object in the center
of the image is the central part of the remnant containing the pulsar. The
white lines marked by numbers show the slit positions used at the spectral
observations of the SNR with NTT/EMMI (2) and VLT/FORS1 (1 and 3). The areas
marked “F1-F5” show the positions of five H II regions identified from the
spectral observations and described in the text. A 100″$\times$100″ black box
outline the region shown in Fig. 2.

Figure 2: The 100″$\times$100″ region of the field around 0540 marked with a
box in Fig. 1. The images are obtained in the [O iii]$/$0 (left) and [O
iii]$/$6000 (middle) bands with NTT/EMMI, and in the 1.5$-$6.4 keV X-ray range
(right) with Chandra/ACIS (Hwang et al. 2001). The positions of all the slits
used in the spectral observations, and of the detected H II regions are marked
as in Fig. 1. A 20″$\times$20″ box marks the inner region of 0540 blown up in
Fig. 4. Note that the H II structures named as “F1”, “F2”, “F4” and “F5” are
projected on regions with strong X-ray emission from the SNR.

The 3D structure probed by Sandin et al. (2013) shows that [S Ii] comes from a
more central part, $-1200\leq
v_{[{S\textsc{ii}}]}\leq+1200\rm\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}$, than [O Iii] with very weak emission in the $-1200\leq
v_{[{S\textsc{ii}}]}\leq-800\rm\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}$ range. Sandin et al. (2013) used the [S Ii] line to make a map of the
electron density, $n_{\rm e}$, and found that the [S Ii] emission mainly comes
from regions with $n_{\rm
e}\\!\\!\\!\phantom{\leq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle<$}\over{\sim}$}}}\,\,750\rm\leavevmode\nobreak\
cm^{-3}$, although there could be “pockets” with $n_{\rm e}\sim 2\times
10^{-3}\rm\leavevmode\nobreak\ cm^{-3}$. In particular, [S Ii] emission is
strong from a specific feature called “the blob” in our previous papers
(Serafimovich et al., 2004, 2005; Lundqvist et al., 2011; Sandin et al.,
2013), located $\sim 1\aas@@fstack{\prime\prime}3$ south-west of the pulsar.
This blob is conspicuous in continuum emission from radio to X-rays (Lundqvist
et al., 2011, 2020), and De Luca et al. (2007) argued for that the blob
appears to change position and continuum brightness between 1995 and 2005.
Lundqvist et al. (2011) offered the alternative explanation, also including
optical polarimetry and X-ray data in their analysis, that a local energy
deposition may have occurred around 1999, and that the emission from that
faded until later epochs. Sandin et al. (2013) suggested that the energy
deposition in the blob region could be due to interaction of the blob with the
pulsar-wind torus.

There are also more recent evidence of time-varying emission from the PWN. Ge
et al. (2019) showed that the sudden change in the spin-down rate in December
2011 could be linked to a gradual brightening of the PWN in X-rays by $\sim
30\%$ in about $\sim 2$ years. Lundqvist et al. (2011) suggested that spatial
changes in polarization angle along an axis in the northeast-southwest
direction, and crossing the blob, point to past changes in activity along this
axis. It is intriguing that the presumed pulsar jet has been suggested to
point nearly orthogonal to this axis (e.g., Gotthelf & Wang, 2000).

Here we report on imaging and spectroscopic observations of 0540 and its
immediate surroundings using NTT/EMMI from 1996 and VLT/FORS from 2002 (Sect.
2 & 3). We also include results from Sandin et al. (2013). Since our data are
deeper than previously reported spectral studies, our aim is to improve the
knowledge about the spatial velocity distribution of various elements, and on
the temperature and ionization of the different parts of the remnant and its
neighborhood (Sect. 4). We summarize our conclusions in Sect.5. A preliminary
version of parts of our work was presented in Serafimovich et al. (2005).

##  2 Observations and data analysis

###  2.1 NTT Observations

Observations of 0540 were performed on 1996 January 17, using the 3.58m
ESO/NTT equipped with the ESO Multi-Mode Instrument (EMMI). Narrow-band images
were obtained in [O iii] $\lambda=5007$ Å at zero velocity using the [O
iii]$/$0 filter111http://www.ls.eso.org/lasilla/Telescopes/NEWNTT/
emmi/emmiFilters.html, and through the [O iii]$/$6000 filter which is shifted
to +6000 km s-1 from the rest wavelength of [O iii]. The pixel size was
0$\aas@@fstack{\prime\prime}$268$\times$0$\aas@@fstack{\prime\prime}$268\. On
the same night we also carried out low-resolution (2.23 Å$/$pixel) long-slit
spectroscopy of 0540 in the 3850-8450 Å range using the EMMI RILD mode with
grism#3222http://www.ls.eso.org/lasilla/Telescopes/NEWNTT/ emmi/emmiRild.html.
The log of the observations is presented in Table 1. The EMMI [O iii]$/$0
image of the 0540 neighborhood is shown in Fig. 4, where we also show the slit
position of the NTT spectral observation (marked by “2”). The position angle
of the slit is PA=22°, and the slit crosses the SNRC containing the pulsar and
the PWN.

Figure 3:  Effective transmission curves for the ESO/[O iii]/0 (red), ESO[O
iii]/6000 (blue) and HST/F502N (green) filters. The velocity is centered on
the rest velocity of [O iii] $\lambda$5007 in the local gas in the LMC, which
we assume has a systemic shift of $+273\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ compared to Earth (cf. Morse et al., 2006). The
red wings of the curves ESO/[O iii]/0 and HST/F502N are due to emission from
[O iii] $\lambda$4959 that enters the filter with a shift of $\sim
2\,870\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$. We have assumed
that this line is a factor of three weaker than [O iii] $\lambda$5007\.

Figure 4:  Central 20″$\times$20″ field of 0540 as viewed by HST/WFPC2/F673N
(left, positive) and NTT/EMMI/[O iii]/0 (right, negative). North is up and
east to the left. The contours of the Chandra/ACIS X-ray fluxes in Fig. 2 are
overlaid in both images. The spatial distribution of the X-ray emission shows
an elongated structure with NW-SE jets, which is associated with the PWN (cf.
Serafimovich et al., 2004; Lundqvist et al., 2011). As seen, the [S ii]
emission dominating in the HST image does not extend outside the PWN, whereas
the [O iii] glow in the NTT image extends far outside the PWN.  Figure 5:
Right: 65″ $\times$ 33″ difference image between NTT/EMMI/[O iii]/0 and
NTT/EMMI/[O iii]/6000 with square root intensity scaling to bring out faint
details. The [O iii]/0 image was smoothed to match the slightly worse seeing
of the [O iii]/6000 image before subtraction. North is up and east is to the
left. The image can trace faint [O iii] emission to large distances from the
pulsar. A blue circle is drawn with radius 10.0″, corresponding to $\sim
2\,150\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ for ejecta
coasting freely for 1 100 years (or $\sim 1\,980\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ for 1 200 years) at at distance of 50 kpc. The
filaments F1, F2, F4 and F5, discussed in the text, are marked. Note PWN
protrusions to the north, presumably in the pulsar jet direction, and to the
southwest, which could be a structure similar to the Crab chimney.  Figure 6:
Right: 20″$\times$20″ difference image between the NTT/EMMI/[O iii]/0 and
NTT/EMMI/[O iii]/6000 images. The blue circle has the same meaning as in
Fig.5. The flux scaling is linear. To highlight the [O iii] glow, red contours
are inserted for intensities up to $23\%$ of the peak surface intensity of the
PWN. Filament F1 has been marked. North is up and east to the left. Middle two
top panels: [O iii] $\lambda 5007$ as viewed by VIMOS/IFU Sandin et al.
(2013). The left of the two middle panels shows the central part, where blue
is for approaching ejecta, and red for receding. The right of the two panels
brings out fainter halo emission. Middle two bottom panels: Same as the two
top panels, but in velocity space. A symmetry axis (also shown in the top
panel) is marked that goes through rings of [O iii] emitting ejecta, and a
possible jet axis is highlighted for the pulsar jet. For the lower right
panel, likely contamination from LMC H II region He i $\lambda 5016$ is
marked, as is also a region with emission on the approaching side
($\leq-750\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$) named the
blue “Wall” (also seen for [O iii] $\lambda 5007$ in Fig. 10). Left: Wavelet
filtered HST/WFPC2/F502N map and contours of a wavelet filtered
HST/WFPC2/F457M map (Lundqvist et al., 2011). Areas where the F502N fails to
detect [O iii] emission are highlighted. To guide the eye, a 1$\arcsec$ slit
with PA $=90$° has been drawn across all top panels. A green line in the
rightmost panel marks how far west the VIMOS field reaches. All images are to
scale.  Figure 7: Top panel: Central 8″$\times$8″ of SNR 0540-69.3 using the
NTT/EMMI difference image with linear intensity scaling in Fig. 6, rotated
$68\degr$ to match the horizontally marked slit 2\. Lower panels: Space-
velocity images along slit 2 for [O iii] $\lambda$5007, H$\alpha$, and [S ii]
$\lambda\lambda$6716,6731. The vertical and horizontal axes show the velocity
(in $\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$, corrected for the
LMC redshift) and the spatial coordinate (in arcseconds) along the slit,
respectively. The horizontal black lines (for H$\alpha$) mark the velocity
spread of H II regions in LMC ($\sim\pm 125\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$). The velocity interval affected by the
subtraction of the uneven LMC background is somewhat larger because of the
finite spectral resolution. H$\alpha$ is more affected by the background
subtraction than other lines, and blended with [N ii]
$\lambda\lambda$6548,6583. The vertical line in the [S ii] image is described
in Sect. 3.2.1.  Figure 8: Top panel: Central $20\arcsec\times$17″ of SNR
0540-69.3 using the NTT/EMMI difference image with square root intensity
scaling in Fig. 5, rotated $68\degr$ to match the horizontally marked slit 2
Bottom panel Space-velocity image along slit 2 for [O iii]
$\lambda\lambda$4959,5007. Velocity, corrected for the LMC redshift, is for [O
iii] $\lambda$5007\. The large dynamic range of the images reveals the faint
glow emission outside the SNRC of 0540.  Figure 9: Same as in Fig. 7, but for
slit 1 (cf. Fig. 2), and for a different set of emission lines, as marked in
the panels. The spatial extent of the images along the slit is 10″. As for
H$\alpha$ in Fig. 7, the H$\beta$ image is corrupted by subtraction of the
uneven LMC background. Note the very different structures in [O ii] and [O
iii].  Figure 10: Same as in Fig. 8, but for slit 1. The spatial extent of the
images along the slit is 20″. Filament F1 is highlighted. Ellipses are drawn
around [O iii]$\leavevmode\nobreak\ \lambda$5007 marking an ejecta velocity of
$+1\,900\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ at 4″ west of
the pulsar, assuming freely coasting ejecta and an age of 1 100 years (blue)
and 1 200 years (red) for 0540. See text for further details.

###  2.2 VLT observations

Further spectral observations were carried out in the 3600–6060 Å range on
2002 January 9 and 10 with the FOcal Reducer/low dispersion Spectrograph
(FORS1) on the 8.2m UT3 (MELIPAL) of ESO/VLT, using the grism
GRIS_600B333http://www.eso.org/instruments/fors1/grisms.html. This has a
dispersion of 50 Å$/$mm, or 1.18 Å$/$pixel. The optical path also includes a
Linear Atmospheric Dispersion Corrector that compensates for the effects of
atmospheric dispersion (Avila et al., 1997). The spatial scale of the FORS1
CCD is 0$\aas@@fstack{\prime\prime}$2 per pixel. On January 9 and 10 we
obtained seven and six exposures of 1320 s each, respectively (see Table 1),
i.e., a total exposure time of 154 and 132 minutes. The position angles,
PA=88° and PA=51°, were the same in all these exposures, and the slit
positions are marked by “1” and “3” in Fig. 1, respectively.

Slits 1 (VLT) and 2 (NTT) were chosen to include the SNRC and the pulsar. Slit
3 (VLT) does not cross the SNRC, but was placed west of it to probe the
emission from the outer shell that is most clearly identified in the Chandra
X-ray images (Hwang et al., 2001, see Fig. 2). All spectroscopic observations
(both NTT and VLT) were performed using a slit width of 1″ and the seeing was
generally about 1″.

###  2.3 NTT and VLT data reduction

The spatial and spectral images were bias-subtracted and flat-fielded using
standard procedures and utilities from the NOAO IRAF package. We used the
averaged sigma clipping algorithm avsigclip with the scale parameter set equal
to none to combine the images. Wavelength calibration for the 2D spectral
images were done using arc frames obtained with a He/Ar lamp and procedure
transform. The spectra of the objects were then extracted from the 2D image
using the apall and background tasks. Flux calibration of the spectra was
accomplished by comparison to the spectrophotometric standard star LTT 3864
(Hamuy et al., 1994) for both the NTT and VLT spectra. Atmospheric extinction
corrections were performed using a spectroscopic extinction table provided by
ESO444http://www.eso.org/observing/dfo/quality/UVES/files/
/atmoexan.tfits.

###  2.4 HST and Chandra observations

The SNR 0540-69.3 field has been imaged with the HST several times in various
bands. In particular, narrow and medium band filters are useful to compare
with our spectral information. The HST data highlighted here are described and
discussed in Morse (2003), Morse et al. (2006) and Lundqvist et al. (2011).

To compare the optical and X-ray data we also discuss data retrieved from the
Chandra archive. In Lundqvist et al. (2011) we discuss these data in greater
detail and how they were reduced.

##  3 Results and Discussion

###  3.1 Imaging

Narrow-band [O iii] images of 0540 obtained with NTT/EMMI through the zero
velocity and +6 000 $\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$
filters ([O iii]/0 and [O iii]/6000, respectively) are shown in the left and
middle panels of Fig. 2, respectively. The FWHM of the transmission curve for
both filters corresponds to 3 300 $\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ (cf. Fig. 3). The +6 000
$\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ image shows no obvious
sign of [O iii] emission in any part of the remnant, confirming the
spectroscopic observations by Kirshner et al. (1989) who did not find any line
emission with redshifts higher than $\sim 3\,000\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$. The only emission seen from the remnant in the
+6 000 $\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ image is the
continuum radiation from the PWN powered by the pulsar B0540-69.3 in SNRC (see
Serafimovich et al., 2004; Lundqvist et al., 2011, for details on the
continuum part).

The zero-velocity [O iii] image of Fig. 2 reveals more extended emission in
accordance with Caraveo et al. (1992). Faint patchy nebulosity from the LMC
background is also seen. A comparison between the [O iii]/0 image and the
X-ray image obtained with Chandra/ACIS (right panel of Fig. 2), where the
shell-like structure associated with the outer SNR shock activity is clearly
detected (Hwang et al., 2001), shows no obvious morphology that connects the
optical to the X-ray emission. As seen in Fig. 4, the slits used for our
spectroscopic observations encapsulate X-ray structures of the SNR. This
enables us to test (see Sect. 3.2) whether or not optical structures projected
on the regions with strong X-ray emission and named “F1”, “F2”, “F4” and “F5”
in Figs. 1 and 2 belong to, or are affected by the SNR.

The high spatial resolution of HST/WFPC2 allows us to resolve in great detail
the filamentary structure of the SNRC. In Fig. 4 we present an image of this
field obtained in the narrow band F673N, centered on [S ii]
$\lambda\lambda$6716,6731. The F637N data, and data for the F502N band,
centered on [O iii] $\lambda$5007, were shown and discussed by Morse et al.
(2006) and Lundqvist et al. (2011).

Although detailed, the HST [S ii] and [O iii] narrow-band images may not fully
reliably reveal the real structure and size of the SNRC. The reason is that
the narrow band filters F502N and F673N may not fully cover the whole line
profiles of the [O iii] and [S ii] emission, respectively. As shown in Morse
et al. (2006), the F502N filter cuts around 5035 Å, which corresponds to
$\sim+1\,415\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ from the
rest wavelength of [O iii] $\lambda$5007 (if we include a systemic shift of
$+273\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ for the local gas
in the LMC), but spectroscopic studies show (Kirshner et al., 1989, Sect. 3.2
of this paper) that the faint [O iii] emission extends up to at least +1 700
$\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ (in the rest frame of
LMC). This can, as pointed out by Morse et al. (2006), mean that F502N image
misses out some high-velocity features of the SNRC (see also below).

The F673N filter cuts around 6770 Å, which corresponds to
$\sim+1\,475\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ from the
rest wavelength of [S ii] $\lambda$6731 (for the same systemic redshift).
Since the [S ii] emitting region is truly more compact than that emitting [O
iii] also along the line of sight (Sandin et al., 2013), the F673N filter (cf.
Fig. 4) should encapsulate most of the [S ii] emission.

Figure 4 demonstrates the difference between the HST/WFPC2/F673N (left) and
NTT/EMMI/[O iii]/0 (right) images. The images are presented for the same
spatial scale and the contours of the Chandra/ACIS X-ray image are overlaid on
each optical image to help us to better compare the sizes and shapes of the
SNRC in both images. In the F673N image the emission from the SNRC in the
optical traces the X-ray emission, and we see no [S ii] emission outside the
X-ray PWN (see also Lundqvist et al., 2011).

One effect not discussed in Morse et al. (2006) is the influence of the [O
iii] $\lambda$4959 line on filter observations centered on [O iii]
$\lambda$5007\. Since the velocities of the remnant are high enough for the
$\lambda$4959 component to be probed by the F502N filter at velocities in the
range $1\,900-4\,000\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$
(including LMC redshift), and since the expected intensity ratio $I_{\lambda
5007}/I_{\lambda 4959}$ is 3, the effective F502N filter transmission of [O
iii] $\lambda\lambda 4959,5007$ looks like the green curve in Fig. 3. From
this we can clearly see that [O iii] $\lambda\lambda 4959,5007$ is not probed
well by F502N for $v_{[{O\textsc{iii}}]}\leq-1\,200\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ and at a redshift between
$1\,300-1\,900\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$,
bottoming at around 5% effective transmission at
$\sim+1\,600\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$, while
emission from gas at higher velocities has about 20% effective transmission.
If we compare with the velocity maps of Sandin et al. (2013) for the VIMOS/IFU
field, the F502N filter mainly misses emission from gas moving away from us at
projected positions $\sim 2\arcsec\ -3\arcsec$ northeast and northwest of the
pulsar, close to the pulsar and $\sim 3\arcsec$ southwest of the pulsar. This
is shown in Fig. 6. As we discuss in Sect. 3.2, there are also regions outside
the VIMOS/IFU field that are not probed well by the F502N filter.

The [O iii]/0 filter used in our NTT/EMMI observations has its peak
transmission at 5009 Å and has 25% transmission of the peak value at 5042 Å.
Including the emission in [O iii] $\lambda$4959, Fig. 3 shows that 20%
effective transmission extends out to $\sim+3500\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ (including LMC redshift), without any dropouts
in transmission like those of the F502N filter. The 20% transmission cutoff on
the blue side of [O iii] $\lambda$5007 is at
$\sim-2\,200\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$. The [O
iii]/0 filter is therefore likely to probe gas with all likely velocities, and
with less bias than the F502N filter. Fig. 3 also shows that the effective
transmission is the same (19 %) for [O iii]/0 and [O iii]/6000 filters at
$\sim 3\,600\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$, and that
the [O iii]/6000 filter only kicks in at velocities
$\\!\\!\\!\phantom{\geq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle>$}\over{\sim}$}}}\,\,3\,000\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$, which is higher than seen in spectra for [O
iii].

A difference image between [O iii]/0 and [O iii]/6000 filter observations
should therefore remove stars and the synchrotron continuum from the PWN, and
in principle provide a cleaner image than using HST/F502N to probe [O
iii]-emitting gas moving at velocities between
$\sim-2\,200\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ and
$\sim+3\,000\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$, albeit at
lower spatial resolution. We show such an image in Fig. 5. The [O iii]/0 image
was smoothed to match the slightly worse seeing of the [O iii]/6000 image
before subtraction. However, some residuals from the image subtraction remain.
The surface intensity has a square root scaling to bring out faint emission.
To guide the eye, we have included a circle, which corresponds to the distance
freely expanding SN ejecta would reach in 1 100 years if moving at
$2\,150\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ (or in 1 200
years if moving at $1\,980\rm\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}$) and for a distance to the LMC of 50 kpc (e.g., Pietrzyński et al.,
2019). Although the nebulous [O iii] emission is complex, there is a hint of
emission associated with the SNRC out to this radius. Fig. 5 also highlights
filaments F1, F2, F4 and F5.

For the PWN part of the SNRC, the ground-based VIMOS/IFU [O iii] images in
Sandin et al. (2013), are superior to the combination of [O iii]/0 and[O
iii]/6000 as it also adds velocity information, but those images only cover
$13\arcsec\times 13\arcsec$. A problem with all the mentioned methods to study
the SNRC, even with the good spectral resolution of the VIMOS/IFU data, is to
clean the images from [O iii], and to a minor extent, He i $\lambda 5016$ (cf.
Fig. 6) emission from H II regions in the LMC.

The [O iii] emission in our NTT image extends outside the X-ray PWN, and the
faint [O iii] glow fills the space out to filament F1. This can certainly not
be explained by worse spatial resolution of the ground-based observations, and
further shows that we are losing some important information in the narrow band
HST filters. Extended [O iii] emission was discussed in Morse et al. (2006),
and was traced out to a radius of $\sim 8\arcsec$. As filament F1 lies at a
projected distance of $\approx 8\aas@@fstack{\prime\prime}5$ from the pulsar,
the [O iii] glow is therefore more extended than argued for by Morse et al.
(2006, see also below). As shown in Fig. 5, there is in particular a broad
region of [O iii] glow to the southwest which extends well outside the ring
with a radius of 10″. We return to this below whether or not this glow is
intrinsic to 0540, or emanates from other nebulae.

The [O iii] glow in 0540 contrasts the situation for the Crab nebula, where
the filamentary structure terminates with a shell-like structure. Observations
of the filamentary ejecta in the Crab (e.g., Blair et al., 1997; Hester, 1998)
suggest that the filaments are the result of Rayleigh-Taylor instabilities at
the interface between the synchrotron nebula and the swept-up ejecta. The
emission comes from the cooling region behind the shock driven into the
extended remnant by the pressure of the PWN. The same most likely applies to
0540 (cf. Williams et al., 2008, see also Section 3.4), but in the Crab there
is no external glow (e.g. Tziamtzis et al., 2009), presumably simply because
of lack of fast SN ejecta (Yang & Chevalier, 2015). Further comparing with the
Crab, the protruded [O iii] glow in the south-western direction in 0540, bears
similarities with the Crab chimney (e.g., Rudie et al., 2008), especially when
viewed through the HST/WFPC2/F502N filter (see Fig. 6).

###  3.2 Two-dimensional spectroscopy

As seen from Fig. 1, slits 1 and 2 cross the SNRC in two almost orthogonal
directions. In both directions the angular sizes of the SNRC are about ten
times larger than the $\sim$1″ seeing value in our NTT and VLT spectral
observations. This enables us to spectrally resolve different spatial parts of
the SNRC projected on the slits, i.e., to create space-velocity maps of the
encapsulated SN ejecta. In these space-velocity maps the continuum emission
was subtracted using the IRAF background task along the spatial axis to reveal
the kinematic structure from the emission lines. We caution that the uneven
LMC background introduces some uncertainty in the derived velocity structure,
especially for H$\alpha$, at velocities embracing the LMC redshift, i.e., at
$\sim 270\pm 150\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$. In
Fig. 6, where we include results for [O iii] from Sandin et al. (2013), we
have used LMC redshift as the reference velocity, and will continue to do so
as default throughout the paper, unless otherwise remarked.

The slit (“slit 2”) in Fig. 7 (top panel) is oriented almost along the
continuum-emitting elongated structure of the central PWN, discussed in detail
by Lundqvist et al. (2011). In Fig. 7 we have used a zoomed-in and rotated
version of our NTT/EMMI [O iii] difference image in the right panel of Fig. 6
for reference, as this image is free from continuum sources, to show how slit
2 probes 0540.

The second panel from the top in Fig. 7 shows the space-velocity distribution
of the [O iii] $\lambda 5007$ emitting material encapsulated by slit 2. The
space-velocity structure of [O iii] $\lambda$5007 is unaffected by
contamination from [O iii] $\lambda$4959 which is shifted in velocity to [O
iii] $\lambda$5007 by $2\,870\rm\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}$.

The [O iii] emission is dominated by a component with an average redshift
velocity of $\sim 400\leavevmode\nobreak\ \rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ (relative to LMC redshift). There is a slight
asymmetry with the northeast part being redshifted with a few hundred
$\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ more than the
southwestern part. From the 3D structure of [O iii] outlined by Sandin et al.
(2013), the dominating centra of [O iii] emission in our space-velocity map
are parts of two separate dominating ring-like structures in the ejecta. They
are clearly displayed in Fig. 6.

To highlight the fainter [O iii] emission, we have constructed a similar plot
to that in Fig. 7, but for wider velocity and spatial ranges. This is shown in
Fig. 8 where we have again used our NTT/EMMI [O iii] difference image, but
this time a rotated version of that in Fig. 5 to highlight fainter emission.
Fig. 8 also includes [O iii] $\lambda$4959, which is $\approx 3$ times fainter
than [O iii] $\lambda$5007, as expected. Both components of the doublet are
shown to more easily evaluate high-velocity features, as well as the structure
of the faint glow outside the SNRC. We have carefully subtracted stars, the
PWN and LMC H ii regions to trace the weakest features. Despite this,
artifacts due to over-subtraction of the LMC background emission are seen, but
are not crucial to conclusions about the space-velocity structure of the [O
iii] glow.

As seen, the faint glow has a completely different structure to that of the
core, as its maximum redshift, close to $+2\,100\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$, occurs in the southwestern part, whereas the
maximum blueshift, $\sim-1\,300\rm\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}$, is in northeastern part. The structures apparent for the two [O iii]
line components do not overlap, and have counterparts in both components that
increase the reliability of the velocity structure. It is evident that the
SNRC emission and the outer [O iii] glow form two distinctly different ejecta
components, which is fully consistent with the findings of Sandin et al.
(2013) (see also Fig. 6), although the 3D cube of Sandin et al. (2013) did not
include the highest velocities on the receding side.

We also note that the $+2\,100\rm\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}$ component has a continuation from $\sim 3-4\arcsec$ southwest of the
pulsar, and further along the slit in the same direction, all the way out to
the edge of the frame at $9\arcsec$ from the pulsar, where the glow has a
velocity just redward of LMC rest velocity, but perhaps also connects to
emission on the blue side. It appears as if the glow is part of an incomplete
shell structure with stronger emission on the receding side to the southwest
and on the approaching side to the northeast. This is also consistent with the
VIMOS/IFU image in Fig. 6. The glow continues further to the southwest, but
the signal-to-noise is too low in the NTT/EMMI spectrum to trace the velocity
outside the frame of Fig. 8. Signal-to-noise was also too low in the study of
Mathewson et al. (1980) to probe possible broad-line emission in this
direction (at PA $=60\degr$).

Turning to [S ii] $\lambda\lambda$6716,6731 in Fig. 7 we note that it has a
smaller extent to the southwest than [O iii], but similar extent to the
northeast. Although not shown here, we see a similarly small extent in [Ar
iii] $\lambda$7136\. The two line components of [S ii] blend together which
makes the real space-velocity structure of each component more difficult to
disentangle than for [O iii]. In Sandin et al. (2013) we devised a way to
separate the components, and at the same time create an electron density map
from the relative intensities of the two [S ii] line components, and we
highlight this here in Sect. 3.2.2. The [S ii] lines follow the trend for [O
iii] in Fig. 7, i.e., there is a general redshift towards the northeast
compared to the southwest. The spectral structure range between a blueshift of
$\sim 800\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ and a redshift
of $\sim 1\,100\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$.

The H$\alpha$ space-velocity structure (second panel from the bottom of Fig.
7) is less organized, mainly due to subtraction of the uneven LMC background
in H$\alpha$, but there is also a hint of subtraction residuals due to [N ii]
$\lambda\lambda$6548,6583. The bright emission between
$700-1\,200\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ actually
falls on top of the [N ii] $\lambda$6583 line from the LMC. H$\alpha$ or [N
ii] was a serious matter of discussion in Kirshner et al. (1989). To underline
this, there is no strong [O iii] or [S ii] emission just north of the pulsar
along the slit reaching out to $\sim+1\,900\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$), whereas the H$\alpha$ plot shows emission
there. We agree with Morse et al. (2006) that [N ii] $\lambda$6583 from 0540
contributes at those wavelengths. That we expect H$\alpha$ from 0540 at all
mainly rests on the results from slit 1 which clearly displays several Balmer
lines (see below). This was reported for the first time in Serafimovich et al.
(2005), and this has led to the interpretation that 0540 stems from a Type II
SN explosion with a zero-age main-sequence mass of $\sim
20\leavevmode\nobreak\ {\rm M}_{\odot}$ (Chevalier, 2006; Williams et al.,
2008; Lundqvist et al., 2011).

Table 2: Dereddened line fluxes relative to [O iii] $\lambda$5007 and line
velocities in SNR 0540-69.3.

| VLT (PA=88°) |  | NTT (PA=22°) |  | Othersd
---|---|---|---|---|---
Line | Measured | fluxa | velocityb |  | Measured | fluxc | velocityb |  | flux | velocityb
| (Å) |  | (km s-1) |  | (Å) |  | (km s-1) |  |  | (km s-1)
[O ii] $\lambda\lambda$3726,3729e | 3735.0 | 59.6 | 600 $\pm$ 90 |  |  |  |  |  | 52/61 | 732 $\pm$ 80
[Fe vii] $\lambda$3759 | 3764.4 | 1.5 | 460 $\pm$ 30 |  |  |  |  |  |  |
[Fe v] $\lambda\lambda$ 3783$-$3797 | 3797.8 | 1.7 | 690 $\pm$ 60 |  |  |  |  |  |  |
[Ne iii] $\lambda$3869$+$H i,He i $\lambda$3889f | 3878.2 | 3.3 | 710 $\pm$ 80 |  |  |  |  |  |  $<$2/7.3) |
[Ne iii] $\lambda$3967$+$H i $\lambda$3970f | 3976.1 | 1.6 | 630 $\pm$ 120 |  |  |  |  |  | -/1.7 |
He i $\lambda$4026 | 4034.0 | 0.4: | 580 $\pm$ 90 |  |  |  |  |  |  |
[S ii] $\lambda\lambda$4069,4076g | 4078.1 | 3.5 | 700 $\pm$ 90 |  |  |  |  |  | 4/4.8 |
H i $\lambda$ 4102 | 4106.0 | 0.9: | 310 $\pm$ 50 |  |  |  |  |  |  |
He i $\lambda$ 4143 | 4154.5 | 0.7: | 780 $\pm$ 200 |  |  |  |  |  |  |
[Fe v] $\lambda$4227 | 4235.7 | 1.6 | 450 $\pm$ 170 |  |  |  |  |  | 6.7/- |
[Fe ii] $\lambda$4287 | 4295.3 | 0.9: | 550 $\pm$ 180 |  |  |  |  |  |  |
[O iii] $\lambda$4363$+$H$\gamma$ | 4368.7 | 5.7 | 380 $\pm$ 190 |  |  |  |  |  | 9.3/4.4 |
[Fe ii] $\lambda$4414 | 4418.2 | 0.3: | 250 $\pm$ 150 |  |  |  |  |  |  |
[Fe ii] $\lambda\lambda$4452,4458,4475 + He i $\lambda$4471 | 4473.6 | 1.4 | 640 $\pm$ 250 |  |  |  |  |  |  |
Mg i] $\lambda$4571 | 4576.8 | 0.4: | 380 $\pm$ 90 |  |  |  |  |  |  |
[Fe iii] $\lambda$4658 | 4665.5 | 1.9 | 480 $\pm$ 100 |  |  $\sim$4670 | ::i |  |  | 2: |
H$\beta$ | 4869.2 | 3.3 | 490 $\pm$ 70 |  |  $\sim$4870 | ::i |  |  |  $<$2/1.9 |
[Fe iii] $\lambda$4881 | 4890.7 | 0.3: | 590 $\pm$ 80 |  |  |  |  |  |  |
[O iii] $\lambda$4959 | 4970.4 | 33.2 | 700 $\pm$ 120 |  | 4970.7 | 37 | 700 $\pm$ 50 |  | 33/33 | 515 $\pm$ 100
[Fe iii] $\lambda$4986 | 4987.6 | 1.4: | 100 $\pm$ 300 |  |  |  |  |  |  |
[O iii] $\lambda$5007 | 5017.9 | 100 | 660 $\pm$ 110 |  | 5016.3 | 100 | 560 $\pm$ 50 |  | 100/100 | 461 $\pm$ 120
[Fe ii] $\lambda$5044 | 5052.6 | 0.3: | 540 $\pm$ 110 |  |  |  |  |  |  |
[Fe ii] $\lambda$5159$+$[Fe vii] $\lambda$5159 | 5171.0 | 1.6 | 700 $\pm$ 200 |  |  $\sim$5160 | 2: | 100 $\pm$ 200 |  |  |
[Fe iii] $\lambda$5270 | 5280.8 | 1.2 | 590 $\pm$ 120 |  |  $\sim$5280 | 2: | 500 $\pm$ 200 |  |  |
[Fe vii] $\lambda$5721 | 5730.6 | 0.8: | 520 $\pm$ 90 |  |  |  |  |  |  |
He i $\lambda$5876 | 5881.7 | 0.8: | 310 $\pm$ 100 |  |  |  |  |  | -/1.3 |
[O i] $\lambda$6300 |  |  |  |  | 6313.2 | 7 | 630 $\pm$ 20 |  | 6.7/4.4 |
[O i] $\lambda$6363 |  |  |  |  | 6374.3 | 4: | 530 $\pm$ 70 |  | -/1.2 |
H$\alpha$h |  |  |  |  | 6577.8 | 17 | 680 $\pm$ 130 |  | 36/19.3 |
[S ii] $\lambda\lambda$6717,6731g |  |  |  |  | 6738.1 | 99 | 320 $\pm$ 50 |  | 67/45.1 |
[Ar iii] $\lambda$7136 |  |  |  |  | 7151.0 | 9 | 630 $\pm$ 40 |  | 10.7/- | 630 $\pm$ 100
[O ii] $\lambda$7325 |  |  |  |  | 7344.7 | 11 | 810 $\pm$ 120 |  | 8/- |
[Ni ii] $\lambda$7378 |  |  |  |  | 7390.5 | 9 | 520 $\pm$ 50 |  | 6.7/- |

a The flux of [O iii] $\lambda$5007 is 4.1 $\times\leavevmode\nobreak\ 10^{-14}$ ergs cm-2 s-1. |  b Not corrected for the LMC redshift ($\sim 270\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$).
---|---
c The flux of [O iii] $\lambda$5007 is 5.0 $\times\leavevmode\nobreak\ 10^{-14}$ ergs cm-2 s-1. |  d Kirshner et al. (1989, PA=77°) / Morse et al. (2006, PA=124°).
e [O ii] $\lambda$3727.5 was used for velocity estimate. |  f Velocity estimated for [Ne iii].
g Velocity for [S ii] $\lambda$4069 and [S ii] $\lambda$6731, respectively. |  h Blended with [N ii] $\lambda\lambda$6548,6583.
i Line detected, flux uncertain. |

Table 3: Dereddened line fluxes relative to H$\beta$ and line velocity in H II
regions along the VLT “slit 1”.

| (F1) 8″ from pulsar |  | (F2) 25″ from pulsar |  | (F3) 62″ from pulsar
---|---|---|---|---|---
Line | Measured | fluxa | velocityb |  | Measured | fluxc | velocityb |  | Measured | fluxd | velocityb
| (Å) |  | (km s-1) |  | (Å) |  | (km s-1) |  | (Å) |  | (km s-1)
[O II] $\lambda\lambda$3726, 3729e | 3730.8 | 478.3 | 270 $\pm$ 70 |  | 3729.7 | 756.3 | 180 $\pm$ 10 |  | 3730.6 | 529.8 | 250 $\pm$ 60
H I $\lambda$3771 |  |  |  |  |  |  |  |  | 3773.5 | 5.2 | 230 $\pm$ 90
H I $\lambda$3798 |  |  |  |  | 3799.7 | 20.1 | 140 $\pm$ 50 |  | 3800.7 | 5.6 | 220 $\pm$ 90
H I $\lambda$3835 |  |  |  |  | 3838.7 | 23.2 | 260 $\pm$ 50 |  | 3838.7 | 8.0 | 260 $\pm$ 80
[Ne III] $\lambda$3869 | 3872.9 | 37.1 | 320 $\pm$ 60 |  | 3871.8 | 146.3 | 230 $\pm$ 50 |  | 3872.1 | 21.1 | 260 $\pm$ 10
H I $+$He I$\lambda$3889 | 3894.6 | 28.0 | 430 $\pm$ 150 |  | 3892.2 | 26.9 | 260 $\pm$ 20 |  | 3892.3 | 20.6 | 270 $\pm$ 10
Ca II $\lambda$3934 | 3939.2 | 26.3 | 420 $\pm$ 110 |  | 3941.3 | 12.5 | 580 $\pm$ 180 |  | 3937.6 | 4.3: | 120 $\pm$200
[Ne III] $+$ Ca II $+$ H If | 3972.6 | 35.9 | 300 $\pm$ 70 |  | 3971.5 | 68.9 | 210 $\pm$ 40 |  | 3972.9 | 25.1 | 320 $\pm$ 50
He I $\lambda$4026 |  |  |  |  |  |  |  |  | 4031.2 | 4.2: | 370 $\pm$ 90
[S II] $\lambda$4069g | 4072.6 | 26.8 |  |  | 4072.9 | 11.9 |  |  | 4072.6 | 4.0 |
[S II] $\lambda$4076g | 4082.9 | 13.9 |  |  | 4080.9 | 5.5 |  |  | 4080.9 | 2.3 |
H$\delta$ | 4107.3 | 24.3 | 410 $\pm$ 50 |  | 4105.2 | 34.6 | 260 $\pm$ 30 |  | 4105.7 | 26.8 | 300 $\pm$ 30
[Fe V] $\lambda$4227 | 4231.7 | 10.0 | 320 $\pm$ 70 |  | 4231.0 | 17.6 | 270 $\pm$ 40 |  |  |  |
[Fe II] $\lambda$4244 | 4248.3 | 8.0 | 250 $\pm$ 100 |  |  |  |  |  |  |  |
[Fe II] $\lambda$4287 | 4293.2 | 7.3 | 400 $\pm$ 90 |  |  |  |  |  | 4291.5 | 2.3: | 290 $\pm$ 90
H$\gamma$ | 4346.2 | 44.4 | 400 $\pm$ 50 |  | 4344.2 | 55.7 | 260 $\pm$ 20 |  | 4344.8 | 47.1 | 300 $\pm$ 40
[O III] $\lambda$4363 | 4367.1 | 25.5 | 270 $\pm$ 50 |  | 4367.0 | 79.3 | 270 $\pm$ 10 |  | 4367.2 | 6.3 | 280 $\pm$ 70
He I $\lambda$4471 | 4478.7 | 11.9: | 480 $\pm$ 100 |  |  |  |  |  | 4476.2 | 4.9 | 320 $\pm$ 60
[Mg I] $\lambda$4563 |  |  |  |  |  |  |  |  | 4567.5 | 2.4: | 320 $\pm$ 90
Mg I] $\lambda$4571 | 4574.4 | 6.4 | 220 $\pm$ 100 |  |  |  |  |  | 4576.0 | 2.2: | 320 $\pm$ 110
[Fe III] $\lambda$4658 | 4663.2 | 19.0 | 330 $\pm$ 80 |  | 4661.8 | 16.3 | 250 $\pm$ 30 |  | 4662.7 | 11.5 | 300 $\pm$ 40
He II $\lambda$4686 | 4691.3 | 14.3 | 360 $\pm$ 90 |  | 4690.1 | 36.3 | 280 $\pm$ 50 |  |  |  |
[Fe III] $\lambda$4702 |  |  |  |  |  |  |  |  | 4706.5 | 3.4 | 320 $\pm$ 60
[Fe III] $+$ [Ar IV] $+$ [Ne IV]j | 4713.8 | 14.9 | 300 $\pm$ 70 |  | 4717.3 | 15.0 | 380 $\pm$ 90 |  |  |  |
He I $\lambda$4713 |  |  |  |  |  |  |  |  | 4718.6 | 1.5: | 340 $\pm$ 90
[Ne IV] $\lambda$4726 |  |  |  |  | 4730.2 | 8.3 | 290 $\pm$ 30 |  |  |  |
[Fe III] $\lambda$4734 | 4738.2 | 16.5 | 270 $\pm$ 80 |  |  |  |  |  | 4738.9 | 1.0: | 320 $\pm$ 100
[Ar IV] $\lambda$4740 |  |  |  |  | 4744.3 | 8.8 | 260 $\pm$ 30 |  |  |  |
[Fe III] $\lambda$4755 | 4760.6 | 6.0 | 360 $\pm$ 110 |  |  |  |  |  | 4759.2 | 2.0: | 290 $\pm$ 50
[Fe III] $\lambda$4769 |  |  |  |  |  |  |  |  | 4774.8 | 1.8: | 340 $\pm$ 60
[Fe III] $\lambda$4778 | 4781.7 | 7.0 | 240 $\pm$ 100 |  |  |  |  |  | 4782.4 | 0.9: | 290 $\pm$ 80
[Fe II] $\lambda$4814 | 4820.8 | 7.1 | 400 $\pm$ 90 |  |  |  |  |  |  |  |
H$\beta$ | 4867.9 | 100 | 410 $\pm$ 60 |  | 4865.4 | 100 | 260 $\pm$ 10 |  | 4866.2 | 100 | 310 $\pm$ 20
[Fe III] $\lambda$4881 | 4886.6 | 6.9 | 350 $\pm$ 80 |  | 4885.0 | 7.1 | 250 $\pm$ 50 |  | 4885.9 | 3.4: | 300 $\pm$ 70
He I $\lambda$4922 |  |  |  |  |  |  |  |  | 4927.4 | 3.0: | 340 $\pm$ 70
[O III] $\lambda$4959 | 4965.0 | 121.1 | 370 $\pm$ 20 |  | 4963.4 | 455.0 | 270 $\pm$ 10 |  | 4963.9 | 75.6 | 300 $\pm$ 30
[Fe III] $\lambda$4986 | 4991.9 | 8.2 | 350 $\pm$ 50 |  | 4990.3 | 15.8 | 260 $\pm$ 60 |  | 4990.9 | 14.5 | 300 $\pm$ 50
[O III] $\lambda$5007 | 5013.2 | 358.8 | 390 $\pm$ 20 |  | 5011.5 | 1370.2 | 290 $\pm$ 10 |  | 5011.9h | 222.2 | 310 $\pm$ 10
[Fe II] $\lambda$5112 | 5120.2 | 9.9 | 500 $\pm$ 90 |  |  |  |  |  |  |  |
[Fe II] $\lambda$5159 | 5165.4 | 16.9 | 390 $\pm$ 100 |  |  |  |  |  | 5162.9 | 2.5: | 240 $\pm$ 100
[N I] $\lambda\lambda$5198-5200 | 5211.0 | 8.7: | 680 $\pm$ 240 |  |  |  |  |  | 5201.9 | 2.5: | 160 $\pm$ 140
[Fe III] $\lambda$5270 | 5274.6 | 19.2 | 240 $\pm$ 80 |  | 5276.0 | 7.6 | 320 $\pm$ 70 |  | 5275.9 | 6.4 | 310 $\pm$ 80
[Fe XIV] $\lambda$5303$+$[Ca V] $\lambda$5309 | 5311.3 | 9.8 | 300 $\pm$ 100 |  |  |  |  |  |  |  |
[Fe II] $\lambda$5334 | 5340.2 | 5.9 | 380 $\pm$ 90 |  |  |  |  |  |  |  |
[Ar X] $\lambda$5534 | 5537.9 | 8.0 | 210 $\pm$ 60 |  |  |  |  |  |  |  |
[Fe VII] $+$[Fe II] $\lambda$5721 | 5724.6 | 15.2 | 270 $\pm$ 80 |  |  |  |  |  |  |  |
He I $\lambda$5876 | 5883.4 | 13.5 | 400 $\pm$ 70 |  | 5881.2 | 11.9 | 290 $\pm$ 60 |  | 5881.8 | 12.2 | 310 $\pm$ 70

a The flux of H$\beta$ is 3.4 $\times\leavevmode\nobreak\ 10^{-16}$ ergs cm-2 s-1 |  b Not corrected for the LMC redshift ($\sim 270\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$)
---|---
c The flux of H$\beta$ is 8.1 $\times\leavevmode\nobreak\ 10^{-16}$ ergs cm-2 s-1 |  d The flux of H$\beta$ is 2.1 $\times\leavevmode\nobreak\ 10^{-15}$ ergs cm-2 s-1
e [O II] $\lambda$3727.5 was used for velocity estimate |  f For velocity estimate used $\lambda$3968.67
g Deblending for [S II] was carried out assuming |  h He I $\lambda$5015 detected in the red wing of [O III] $\lambda$5007,
Gaussian line profiles | but flux is uncertain.

Table 4: Dereddened line fluxes relative to H$\beta$ and line velocities in H
II regions along the VLT “slit 3”.

| (F4) |  | (F5)
---|---|---|---
Line | Measured | fluxa | velocityb |  | Measured | fluxc | velocityb
| (Å) |  | (km s-1) |  | (Å) |  | (km s-1)
[O II] $\lambda\lambda$3726, 3729d | 3729.2 | 299.6 | 140$\pm$ 50 |  | 3729.5 | 377.1 | 160$\pm$ 60
H I $\lambda$3798 | 3802.1 | 12.6 | 330$\pm$ 80 |  | 3802.0 | 7.4 | 330$\pm$ 50
H I $\lambda$3835 | 3837.7 | 7.1 | 180$\pm$ 90 |  |  |  |
[Ne III] $\lambda$3869 | 3871.6 | 48.1 | 220$\pm$ 20 |  | 3871.5 | 80.3 | 210$\pm$ 20
H I $+$ He I $\lambda$3889 | 3891.7 | 18.8 | 220$\pm$ 30 |  | 3892.7 | 24.9 | 290$\pm$ 30
[Ne III] $+$ H I $+$ Ca IIe | 3971.9 | 31.5 | 240$\pm$ 50 |  | 3971.4 | 38.3 | 210$\pm$ 40
[S II] $\lambda\lambda$4069, 4076 | 4072.5 | 10.6 |  |  | 4071.5 | 8.3 |
H$\delta$ | 4104.8 | 29.8 | 230$\pm$ 40 |  | 4104.9 | 24.3 | 230$\pm$ 40
[Fe V] $\lambda$4227 | 4230.5 | 3.3: | 230$\pm$ 110 |  | 4230.0 | 6.7 | 200$\pm$ 90
H$\gamma$ | 4343.9 | 46.3 | 250$\pm$ 20 |  | 4343.9 | 44.4 | 240$\pm$ 20
[O III] $\lambda$4363 | 4366.5 | 17.0 | 230$\pm$ 30 |  | 4366.6 | 41.2 | 240$\pm$ 30
He I $\lambda$4471 | 4475.2 | 4.0 | 250$\pm$ 90 |  | 4472.6 | 5.4 | 80$\pm$ 140
[Fe III] $\lambda$4658 | 4661.5 | 8.0 | 230$\pm$ 80 |  | 4661.7 | 10.5 | 230$\pm$ 50
He II $\lambda$4686 | 4690.1 | 8.3 | 290$\pm$ 80 |  | 4689.8 | 13.6 | 270$\pm$ 60
[Ar IV] $\lambda$4711 $+$ [Ne IV] $\lambda$4714f |  |  |  |  | 4716.5 | 5.7 | 240$\pm$ 70
[Ar IV] $\lambda$4740 |  |  |  |  | 4743.3 | 3.3 | 200$\pm$ 100
[Fe III] $\lambda$4756 |  |  |  |  | 4758.1 | 3.2 | 210$\pm$ 110
H$\beta$ | 4865.1 | 100 | 240$\pm$ 10 |  | 4865.1 | 100 | 240$\pm$ 10
[O III] $\lambda$4959 | 4963.3 | 186.0 | 260$\pm$ 10 |  | 4963.1 | 282.2 | 260$\pm$ 20
[Fe III] $\lambda$4986 | 4989.9 | 7.1 | 230$\pm$ 80 |  | 4990.8 | 10.3 | 290$\pm$ 60
[O III] $\lambda$5007 | 5011.2 | 553.9 | 270$\pm$ 10 |  | 5011.1 | 851.8 | 260$\pm$ 10
[Fe II] $\lambda$5159 | 5163.4 | 2.5: | 270$\pm$ 100 |  | 5163.7 | 4.2 | 290$\pm$ 90
[Fe III] $\lambda$5270 | 5276.3 | 3.3: | 330$\pm$ 120 |  | 5275.6 | 4.8 | 290$\pm$ 80
[Fe XIV] $\lambda$5303 $+$ [Ca V] $\lambda$5309 | 5312.8 | 11.5 | 380$\pm$ 110 |  | 5308.9 | 7.3 | 170$\pm$ 90
He I $\lambda$5876 | 5880.3 | 12.0 | 240$\pm$ 50 |  | 5880.8 | 12.4 | 270$\pm$ 40

a The flux of H$\beta$ is 1.8 $\times\leavevmode\nobreak\ 10^{-15}$ ergs cm-2 s-1 |  b Not corrected for LMC redshift ($\sim 270\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$)
---|---
c The flux of H$\beta$ is 1.0 $\times\leavevmode\nobreak\ 10^{-15}$ ergs cm-2 s-1 |  d [O II] $\lambda$3727.5 was used for velocity estimate
e Velocity estimated using 3968.67 |  f Velocity estimated using mean value

Moving to the space-velocity diagrams for slit 1, these are shown in the
images in Fig. 9. We have again used a zoomed-in and rotated (this time by 2°)
version of our NTT/EMMI [O iii] difference image in the right panel of Fig. 6
for reference. The [O iii] $\lambda$5007 VLT/FORS image along slit 1 (Fig. 9)
has a “pepper-slice”-like shape that also reflects the expansion of the SNRC.
Like for slit 2, the emission is heavily redshifted, but less skewed in the
space-velocity diagram. The line can be traced between about
$-700\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ and
$+1\,400\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$. It is easy to
imagine a relatively symmetric (but redshifted) shell with filamentary
structures reaching inward toward the center around the average velocity of
the shell, i.e., $\sim 400\rm\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}$. However, judging from the 3D structure derived by Sandin et al.
(2013) and shown in Fig. 6, the eastern and western parts of the “pepper” come
from the same two ring-like features for the SNRC discussed for slit 2 above.

H$\beta$ (panel two from the bottom of Fig. 9) is partly corrupted by the LMC
background subtraction, but can be seen to have a surprisingly similar
structure to that of [O ii] $\lambda\lambda$3727,3729 (bottom panel of Fig. 9
in which the velocity scale is centered on $3727.5\AA$). Both H$\beta$ and the
[O ii] lines lack emission at the highest velocities
($\\!\\!\\!\phantom{\geq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle>$}\over{\sim}$}}}\,\,1\,200\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$) west of the pulsar. The different structures
in [O ii] and [O iii] reveal different ionization conditions, especially in
the western part along the slit. As a matter of fact, the [S ii] 3D structure
of Sandin et al. (2013) resembles those of H$\beta$ and [O ii] in Fig. 9,
which may argue for that the differences between the [O iii] and [S ii] are
more likely to be due to an effect of different levels of ionization rather
than abundance effects. Moreover, the similarity between H$\beta$ and [O ii]
further argues for contamination of [N ii] in the H$\alpha$ image in Fig. 7.

Like the NTT data in Fig. 8, the VLT data in Fig. 10 show a glow of [O iii]
$\lambda$5007 emission outside the inner part of the SNRC. The glow extends
out to a radius of about $8\arcsec-10\arcsec$, and seems to connect to
filament F1 in the west, which in turn appears to emit at a velocity close to
LMC rest velocity. The blue circle in the upper panel marks a 10″ radius from
the pulsar. The space-velocity plot in Fig. 10 reveals four interesting
features: fast blueshifted (at least to $-1\,600\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$) faint emission around the pulsar position,
fast redshifted (at least to $+1\,800\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$) faint emission to the west of the pulsar, no
redshifted emission at the pulsar position that was not already revealed by
the bright emission in Fig. 9, and an intricate low-velocity structure which
seems to form a loop to the east and a stream to the west possibly connecting
to regions around filament F1. F1 itself stands out clearly, which could
indicate that it is just an H II-region projected onto 0540. However, as we
will see in Sect. 3.3.2, this is not the correct interpretation. In Section
3.3.2. we will also discuss [Fe iii] $\lambda$4986, which would introduce
emission in Fig. 10 at $\sim-1\,250\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$. Contamination by He i $\lambda$5016 would
introduce emission at $\sim+530\rm\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}$, and could be responsible for the “horn” sticking out on the eastern
side in the space-velocity plot, but a similar feature is seen for [O iii]
$\lambda$4959, so background subtractions do not leave imprints from He i
$\lambda$5016 in Fig. 8, contrary to the VLT/VIMOS/IFU images of Sandin et al.
(2013, cf. Fig. 6). We highlight that the VLT/VIMOS/IFU images neither cover
F1 nor the low-velocity feature to the east.

The impression from slit 1 is the same as from slit 2, i.e, there appears to
be glow from fast [O iii]-emitting ejecta with a tilt towards red on the
western side and towards the blue on the eastern side. ”Glow” (or at least
fast [O iii]-emitting ejecta) can be seen in the VIMOS/IFU image in Fig. 6 to
be more pronounced for ejecta moving towards us than away from us, and this
agrees with the fast blue-shifted ejecta in Fig. 10 with a projected center
slightly to the east of the pulsar position.

The blue circle drawn in, e.g., Fig. 10 has a radius of 10″ and corresponds to
a maximum velocity of freely coasting [O iii]-emitting ejecta with velocity

$v_{\rm max}([{O\textsc{iii}}])=2150\leavevmode\nobreak\ \left(\frac{D_{\rm
LMC}}{50}\right)\leavevmode\nobreak\ \left(\frac{t_{\rm
yr}}{1100}\right)^{-1}\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1},$
(1)

where $D_{\rm LMC}$ is the distance to 0540 in kpc and $t_{\rm yr}$ is the age
of 0540 in years. As the space-velocity spectra do not really reveal [O iii]
at velocities $\\!\\!\\!\phantom{\geq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle>$}\over{\sim}$}}}\,\,2\,000\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ (taking the spectral resolution into account),
one may come to the conclusion that there is no support for space motions of
[O iii]-emitting gas much in excess of $2\,000\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ (relative to LMC). However, for both slits 1
and 2, the maximum velocity on the red side occurs $\sim 4\arcsec$ west and
southwest of the pulsar, respectively. The true space motion of ballistic
ejecta, $v_{\rm true}$, if originating from a central position in the SNRC, is
therefore

$v_{\rm true}=\sqrt{v_{\rm obs}^{2}+\left(\frac{r_{\rm obs}}{t}\right)^{2}},$
(2)

where $r_{\rm obs}$ is the projected distance from the pulsar at which the
maximum observed redshift velocity, $v_{\rm obs}$, of [O iii], emission
occurs, and $t$ is the age since explosion. With $D=50$ kpc and $r_{\rm
obs}\approx 3.0\times 10^{18}$ cm (corresponding to $4\arcsec$), one obtains
$v_{\rm true}([{O\textsc{iii}}])\sim 2\,090\leavevmode\nobreak\
(2\,060)\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ for $t_{\rm
yr}=1\,100\leavevmode\nobreak\ (1\,200)$ and $v_{\rm
obs}=1\,900\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ for slit 1,
and $v_{\rm true}([{O\textsc{iii}}])\sim 2\,270\leavevmode\nobreak\
(2\,240)\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ for $t_{\rm
yr}=1\,100\leavevmode\nobreak\ (1\,200)$ and $v_{\rm
obs}=2\,100\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ for slit 2,
respectively. This is several hundred $\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ faster than $v_{\rm max}([{O\textsc{iii}}])$
for the SNRC on the red side, and also faster than the glow on the blue side,
although confusion with [O iii] $\lambda$4959 causes uncertainty there.

To guide the eye, we have inserted two ellipses in Fig. 10. Both are for
constant $v_{\rm true}$ in all azimuthal directions carved out by the slit,
and they are both tuned to give $v_{\rm obs}\pm 1\,900\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ at $4\arcsec$ west of the pulsar (as for slit
1). The blue and red curves are for $t_{\rm yr}=1\,100$ and $t_{\rm
yr}=1\,200$, respectively, and $D_{\rm LMC}=50$. Both curves encapsulate F1,
but reach zero velocity at $\pm 9\aas@@fstack{\prime\prime}7$ and $\pm
10\aas@@fstack{\prime\prime}4$, respectively. If $v_{\rm true}$ is indeed the
same for the full region encapsulated by the slit west of the SNRC, Figs. 5
and 10 point to an age of
$1\,100\\!\\!\\!\phantom{\leq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle<$}\over{\sim}$}}}\,\,t_{\rm
yr}\\!\\!\\!\phantom{\leq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle<$}\over{\sim}$}}}\,\,1\,200$. At the position of
F1 (i.e., at $\sim 8\aas@@fstack{\prime\prime}5$), the red side of [O iii]
$\lambda$5007 should reach $800\rm\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}$ for $t_{\rm yr}=1\,100$, and $1\,200\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ for $t_{\rm yr}=1\,200$. For a non-accelerating
scenario determining $v_{\rm true}$ (as in Eq. 2), the pulsar seems to be
significantly younger than the spin-down age, i.e., $\sim 1600$ years. We
return to the pulsar age in Section 3.4.3.

Looking at other parts of the space-velocity structure of the [O iii]
$\lambda$5007 glow for slit 1, we note that $v_{\rm true}$ appears to be
significantly lower than for the receding region west of the SNRC, perhaps
except for the very eastern part, and towards the center of the SNRC on the
blue side. The absence of [O iii] $\lambda$5007 at high velocities on the red
side towards the SNRC is remarkable, This could be due real differences in the
azimuthal distribution of [O iii]-emitting gas, but it could in principle also
be due dust absorption screening of the red side behind the SNRC. We find this
explanation less likely though, since the dust would have to be located
between the SNRC and fast (unseen due to dust) ejecta on the blue side, while
there is no dust counterpart on the approaching side. Moreover, one does not
see this effect in the Crab, despite it containing large amounts of dust
(Gomez et al., 2012). In the Crab the dust is concentrated to filaments with
modest filling factor which in the optical are notably strong in [O iii].

The picture that emerges for the [O iii] glow seen through slits 1 and 2 is
that it does not come a spherically symmetric shell surrounding the SNRC, but
from a much less complete structure. On the blue side it appears to be
concentrated to the “wall”-like structure centered just west of the pulsar
position and reaching out to $\sim-1\,600\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ seen and marked as “Blue Wall” in Fig. 6 and
shown by Sandin et al. (2013). On the red side, the fastest glow is in the
southwestern and western parts $\sim 4\arcsec$ from the pulsar reaching space
velocities well in excess of $2\,000\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$. In the eastern part, velocities covered by
slits 1 and 2 are less extreme, especially on the receding side. However, our
slits do not cover the southeastern part. Here we make use of the long-slit
observations by Morse et al. (2006) (described more in Section 3.3.1) as they
cover the southeastern and northwestern parts of the [O iii] glow region.
Figure 5a of Morse et al. (2006) shows a clear asymmetry for the [O iii] glow
not covered by our slits 1 and 2, or the VIMOS/IFU data of Sandin et al.
(2013). The figure of Morse et al. (2006) shows strong [O iii] glow on the
approaching side to the northwest, as well to the southeast for the receding
side. Apart from the “wall”-like structure on the blue side (which is also
evident as the blue-ward emission in the VIMOS/IFU spectrum in. Fig 19), it
appears as if the incomplete shell of [O iii] glow is devoid of emission on
the receding northern side, and on the approaching southern side.

Figure 11: Spectrum of the central part of the SNR 0540-69.3 obtained with
ESO$/$NTT (PA=22°). The lower panel has an expanded flux scale to highlight
weaker lines. The spectrum has been dereddened using $E(B-V)=0.19$ and R=3.1.
“H$\alpha$” is a blend of H$\alpha$ and [N ii] $\lambda\lambda$6548,6583.
Figure 12: Spectrum obtained with ESO$/$VLT (PA=88°), and again (like in the
Fig. 11) the lower panel is plotted to bring out weaker lines. The spectrum
has been dereddened using $E(B-V)=0.19$ and R=3.1. Note the significantly
higher signal-to-noise in the VLT spectrum compared to Fig. 11, which made it
possible to detect new lines in SNR 0540-69.3 as reported in Serafimovich et
al. (2005) and here. Of particular importance are the [Ne iii] lines and
H$\beta$ (see text).

####  3.2.1 Density from [S ii] $\lambda\lambda$6716,6731

The two components of the [S ii] doublet in Fig. 7 have a difference in
wavelength corresponding to a velocity shift of $\approx
640\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$. In 0540 they blend
together because of the velocity broadening of the emitting gas. There are,
however, a few positions along the slit for which the blend is small. One such
position is marked with a vertical solid line in Fig. 7, along detector row 29
in our notation. We discussed the deblending of [S ii]
$\lambda\lambda$6716,6731 along this row in Serafimovich et al. (2005),
assuming that the line intensity ratio
$R_{\rm[{S\textsc{ii}}]}=\frac{I(\lambda 6716)}{I(\lambda 6731)}$ is the same
for all parts of the supernova remnant encapsulated by the slit row. As
$R_{\rm[{S\textsc{ii}}]}$ is density sensitive (e.g., Osterbrock & Ferland,
2006), we effectively assumed that the density is constant in this part of the
remnant. The debelendig in Serafimovich et al. (2005) resulted in
$R_{\rm[{S\textsc{ii}}]}=0.7$, and the multilevel model for [S ii] described
in Maran et al. (2000) was used to obtain $n_{\rm e}=(1.4-4.3)\times
10^{3}\rm\leavevmode\nobreak\ cm^{-3}$ for the temperature $T=10^{4}$ K, and
$n_{\rm e}=(1.8-5.3)\times 10^{3}\rm\leavevmode\nobreak\ cm^{-3}$ for
$T=2\times 10^{4}$ K.

As we discuss in Sect. 3.4, the temperature in [S ii]-emitting gas is probably
$T\sim 15\,000$ K. In addition, a more careful background subtraction along
row 29 than the preliminary one in Serafimovich et al. (2005) gives
$R_{\rm[{S\textsc{ii}}]}=0.85\pm 0.10$, translating into $n_{\rm
e}=(0.9-2.0)\times 10^{3}\rm\leavevmode\nobreak\ cm^{-3}$. This is fully
consistent with densities found in the Crab Nebula for which [O ii] and[S ii]
line ratios indicate electron densities in the range $4\times 10^{2}-4\times
10^{3}\rm\leavevmode\nobreak\ cm^{-3}$ for the various filaments observed
(Davidson & Fesen, 1985). For the region mapped out by our detector row 29,
Sandin et al. (2013) estimate $n_{\rm
e}\\!\\!\\!\phantom{\leq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle<$}\over{\sim}$}}}\,\,1\times
10^{3}\rm\leavevmode\nobreak\ cm^{-3}$. As emphasized by these authors there
are, however, pockets of ejecta with $n_{\rm e}\sim(1-2)\times
10^{3}\rm\leavevmode\nobreak\ cm^{-3}$ in the SNRC when spectra from
individual fibers are studied; their density plot was smoothed over a $2\times
2$ pixel kernel. Inspection of the individual fibre spectra of Sandin et al.
(2013) also reveals background LMC residuals, which introduces a bias to
underestimate electron densities from [S ii]. The reason is the small field of
view of VIMOS which makes background subtraction cumbersome. Our estimate of
$n_{\rm e}\sim(1-2)\times 10^{3}\rm\leavevmode\nobreak\ cm^{-3}$ for detector
row 29 are therefore not in conflict with Sandin et al. (2013). For a more
complete discussion about the variation of electron density from [S ii] within
the SNRC we refer to Sandin et al. (2013), with the caveat in mind that the
electron densities in that paper coud be somewhat underestimated in general.
In addition, we emphasize that the densities derived for detector row 29 and
in Sandin et al. (2013) are average densities along the line-of-sight for the
SNRC, unlike the situation in the Crab for which more detailed 3D studies can
be done more easily due its proximity (e.g., Charlebois et al., 2010; Martin
et al., 2021). In the analysis in Sect. 3.4 for the SNRC we will use $n_{\rm
e}=10^{3}\rm\leavevmode\nobreak\ cm^{-3}$ unless otherwise specified.

###  3.3 One-dimensional spectroscopy

####  3.3.1 The central part of 0540

Previous optical spectroscopic studies of the SNRC were carried out by
Mathewson et al. (1980), Kirshner et al. (1989) and Morse et al. (2006), and
we reported preliminary results of our NTT/EMMI and VLT/FORS observations in
Serafimovich et al. (2005). We will mainly compare with Kirshner et al. (1989)
and Morse et al. (2006). Kirshner et al. (1989) used a slightly larger slit
($1\aas@@fstack{\prime\prime}5$) than us, and positioned their slit to cross
the SNRC at PA $=77\degr$. Morse et al. (2006) used an even wider slit
($2\arcsec$) at PA$=124\degr$, and we discussed some of their results already
in Sect. 3.2.

We extracted 1D spectra of the SNRC from our spectral images using the IRAF
procedure apall and spatial extents of 10″ and 8″ centered on the pulsar for
slits “1” and “2”, respectively. The extracted windows correspond to the
observed extents of the SNRC along the respective slit directions. The
extracted spectra are shown in Fig. 11 and 12.

Line fluxes were derived by integrating over each line profile. (No Gausian
fitting can be done since the line profiles are strongly non-Gaussian.) This
gives accurate fluxes for strong lines like [O ii] and [O iii] as found from a
test where we varied the background level up and down by $1\sigma$ from the
mean value; the statistical error of the strongest lines is less than 5%. For
faint lines like the [Fe ii] lines and Mg i] the flux uncertainty can be up to
40%. In Table 2 we have marked the fluxes of such lines by a colon.

A list of identified lines and their measured fluxes, central wavelengths and
velocities is presented in Table 2. The results of Kirshner et al. (1989) and
Morse et al. (2006) are also included for comparison. All our fluxes have been
dereddened using $E(B-V)=0.19$ and R=3.1, as was also done by Kirshner et al.,
while Morse et al. (2006) used $E(B-V)=0.20$. A detailed discussion on the
extinction towards 0540 can be found in Serafimovich et al. (2004). The fluxes
were then normalized to [O iii]$\leavevmode\nobreak\ \lambda 5007$. We note
that Kirshner et al. (1989) and Morse et al. (2006) normalized to the sum of
[O iii]$\leavevmode\nobreak\ \lambda 4959$ and [O iii]$\leavevmode\nobreak\
\lambda 5007$. In Table 2 we therefore simply assumed a $1:3$ line ratio of
those two components, and renormalized all fluxes in Kirshner et al. (1989)
and Morse et al. (2006) to [O iii]$\leavevmode\nobreak\ \lambda 5007$. Guided
by the VIMOS/IFU observations of Sandin et al. (2013), who concentrated on the
two doublets [O iii]$\leavevmode\nobreak\ \lambda\lambda 4959,5007$ and [S
ii]$\leavevmode\nobreak\ \lambda\lambda 6716,6731$, one expects line fluxes
for the various slit orientations shown in Table 2 to be different just
because of different parts of the SNRC being caught by the slits.

Our 1D spectra of the SNRC are consistent with those of the other studies but
also reveal many differences. The higher sensitivity of the VLT observations
allowed us in Serafimovich et al. (2005) to report many new lines not detected
in previous studies, and we report more here. The most important findings in
Serafimovich et al. (2005) were [Ne iii]$\leavevmode\nobreak\
\lambda\lambda$3869,3967 and Balmer lines of hydrogen all the way down to H i
$\lambda$3889 (H$\zeta$). While the neon lines constrain the supernova, the
Balmer lines show that the previously detected emission around H$\alpha$ is at
least partly due to H$\alpha$, and not only to [N ii] $\lambda$6583, or any
other line as discussed by Caraveo et al. (1998). We do not try to separate
H$\alpha$ from [N ii]$\leavevmode\nobreak\ \lambda\lambda$6548,6583. However,
from the H$\alpha$ panel of Fig. 7 it is clear that [N ii] is present with a
velocity structure that looks similar to that of [S ii], and with a velocity
for [N ii]$\leavevmode\nobreak\ \lambda$6583 that reaches at least
$+1\,000\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ in the LMC rest
frame. Morse et al. (2006) estimated an intensity ratio of $I_{{\rm
H}\alpha}/I_{[{N\textsc{ii}}]}\sim 1.1$ for their slit position.

The [Ne iii]$\leavevmode\nobreak\ \lambda\lambda$3869,3967 lines, and [O iii]
$\lambda$4363 are all contaminated by H i lines, which leads to an
overestimate of the fluxes of these lines not accounted for in Table 2, and
for [O iii] $\lambda$4363 fluxes in previous investigations. Another
complication is that all H i lines suffer from influence of the uneven LMC
background which must be compensated for. We discuss this further Sect. 3.4.

Using unblended lines we estimate that the mean velocity of the central region
of the 0540 system is +500$\pm$55 $\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ for slit “1” and +380$\pm$60
$\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ for slit “2”,
respectively, when the LMC redshift of $270\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ is accounted for. Within errors both values are
consistent with each other, and a mean velocity of the two gives +440$\pm$80
$\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$. This is $\sim
100\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ higher than the
value of Kirshner et al. (1989), but the two investigations are consistent
with each other, despite different slit orientations.

The redshift of the SNRC of 0540 is indeed large. An explanation could be that
the 0540 system is the result of an asymmetric explosion, as discussed by
Serafimovich et al. (2004). The SNRC of 0540 is not unique in that sense.
Balick & Heckman (1978) found that the oxygen-rich SNR NGC 4449 also moves at
a velocity of $\sim 500\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$
relative to its surrounding H II regions. Like 0540, this remnant is also
oxygen-rich. Over a larger scale, 0540 may not be all that asymmetric as
revealed by the [O iii] glow from ejecta moving at high speed
($\\!\\!\\!\phantom{\geq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle>$}\over{\sim}$}}}\,\,1\,500\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$) both towards and away from us discussed in
Sect. 3.2. (see also Morse et al., 2006; Sandin et al., 2013).

Figure 13: Spectrum of filament F1 in the vicinity of SNR 0540-69.3. The
filament is situated only 8″ west of the pulsar (see Figs.1 and 2). As in
Figs. 11 and 12, we have also plotted the spectra with expanded flux scales to
highlight weaker lines. The spectrum was dereddened using $E(B-V)=0.19$ and
R=3.1. Note the broad base of the [O iii] $\lambda\lambda$4959,5007 lines
skewed to the red as compared to the narrow components, reaching at least +1
700$\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$. No such features
are seen in spectra of the emission from filaments F2, F3, F4 or F5 (see Fig.
14) as marked in Fig. 1. Line fluxes of all filaments are given in Tables 3
and 4.  Figure 14: Spectrum of an H II region along the VLT slit “3” at a
projected distance of 25″ to the west of the pulsar (called filament F5 in
Figs. 1 and 2). As in Fig. 11, we have also plotted spectra with expanded flux
scales to highlight weaker lines. The spectrum have been dereddened using
$E(B-V)=0.19$ and R=3.1.

####  3.3.2 Filaments

SNR 0540-69.3 is near the LMC H II region DEM 269 and the OB association LH
104 (see Kirshner et al., 1989, and references therein, as well as below.)
This is consistent with that we detect narrow emission lines that vary
spatially in strength along our slits. The lines are spectrally unresolved
(except for one case, see below).

To study whether or not some of these emitting regions are affected by the SNR
activity, we looked at filaments detected along the slits. We mainly
considered those with an [O iii] temperature in clear excess of $10^{4}$ K, as
is usually observed in shocks or photoionization heated regions of known SNRs.
We assumed the same extinction for the filaments as for the remnant, and used
the standard ratio $R_{\rm[{O\textsc{iii}}]}=\frac{I(\lambda 4959)+I(\lambda
5007)}{I(\lambda 4363)}$ for the temperature (e.g., Osterbrock & Ferland,
2006). We also looked for lines of highly ionized ions as tracers of influence
by the SNR. We detected a few filaments of interest along the VLT slits “1”
and “3”, and they are marked as F1, F2, F4 and F5 in Fig. 1. We also mark
filament F3, and use this as reference for a presumed LMC H II region.

The typical size of the filaments along the slit is $\sim 3\arcsec$. As in the
case of the SNRC we have constructed 1D spectra for each filament. The
dereddened spectra of F1, which is closest to the SNRC in projection, and F5,
which appears close to the outer shock front detected in X-rays, are shown in
Figs. 13 and 14, respectively. Spectra of the other filaments are similar to
the ones presented. Lists of identified spectral lines for F1-F5 with measured
fluxes, central wavelengths and velocities, are presented in Tables 3 and 4.
We return to a more detailed discussion of the filaments in Sect. 3.4.2.

###  3.4 Line profiles and intensities

####  3.4.1 The central part

Supernova remnants are good laboratories to test the theory of stellar
evolution, explosive nucleosynthesis, radiation processes and shock physics.
To test the first two items, an estimate of elemental abundances of the ejecta
is essential. As the information from SNRs mainly rests on collisionally
excited lines, we therefore also require knowledge about the density and
temperature of the emitting gas.

The observed strength of the spectral lines allow us to deduce this
information. The prime thermometer is $R_{\rm[{O\textsc{iii}}]}$. Because we
see [O iii]$\leavevmode\nobreak\ \lambda\lambda 4959,5007$ and [O
iii]$\leavevmode\nobreak\ \lambda$4363 in all VLT spectra of 0540 and the
filaments, we are able to estimate the temperature of the [O iii] emitting
plasma in both the SN ejecta and the filaments.

Figure 15: Line profiles of the Balmer lines from 0540 in velocity space
relative to LMC for the VLT spectrum in Fig. 12. Top panel: H$\zeta$ blended
with [Ne iii]$\leavevmode\nobreak\ \lambda$3869, Middle panel: H$\epsilon$
blended with [Ne iii]$\leavevmode\nobreak\ \lambda$3967, and bottom panel:
H$\gamma$ blended with [O iii]$\leavevmode\nobreak\ \lambda$4363\. In all
panels we also show H$\beta$ (grey) and the continuum level (black). H$\beta$
was used as a template to subtract the expected emission from H$\gamma$,
H$\epsilon$ and H$\zeta$ using Case B line ratios (Brocklehurst, 1971). The
blue and red solid lines show [O iii]$\leavevmode\nobreak\ \lambda$4363 and
[Ne iii]$\leavevmode\nobreak\ \lambda\lambda$3869,3967 before and after
deblending, respectively.  Figure 16: Line profiles of [O iii]
$\lambda\lambda$4959,5007 and [O iii]$\leavevmode\nobreak\ \lambda$4363 of the
emission from 0540 as observed through the VLT slit. The velocity is relative
to LMC. The [O iii] $\lambda\lambda$4959,5007 profile was created from a
cleaning procedure described in the text, and is for the sum of the two line
components. The [O iii]$\leavevmode\nobreak\ \lambda$4363 is the blue-red
profile in the bottom panel of Fig. 15. The flux of [O
iii]$\leavevmode\nobreak\ \lambda$4363 has been multiplied by 28 and 34 to
match the various parts of the line profiles. There is a tendency of
relatively weaker [O iii]$\leavevmode\nobreak\ \lambda$4363 on the blue side,
which could mean hotter [O iii]-emitting plasma on the receding side of 0540
(see text).  Figure 17: Sum of the “cleaned” [O iii]$\lambda\lambda$4959,5007
profiles (cf. Fig. 16) of the emission from 0540 (black) compared to the
observed emission (blue). The velocity scale is for the $\leavevmode\nobreak\
\lambda$5007 component relative to LMC. The difference (red) is attributed to
[Fe iii]$\leavevmode\nobreak\ \lambda$4986\. The maximum velocity on the red
side of [O iii] $\leavevmode\nobreak\ \lambda$5007 is
$\approx+1\,800\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$, which
may be less than on the blue side ($\approx-1\,900\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$, see Fig. 16).  Figure 18: Same profile for [O
iii] as in Fig. 16, but only for [O iii] $\lambda$5007 (blue) together with
the “cleaned” [Ne iii] $\lambda$3869 profile in Fig. 15. The [Ne iIi] profile
was multiplied by a factor of 30 to match [O iii] $\lambda$5007\. Note the
similar widths and structures of the two profiles. Noise is too high for the
[Ne iii] line to trace it out the highest velocities on the blue side.  Figure
19: Same profile for [O iii]$\lambda\lambda$4959,5007 as in Fig. 16 (blue)
together with the [O iii]$\lambda\lambda$4959,5007 profile for the full
$13\arcsec\times 13\arcsec$ field as observed by Sandin et al. (2013). The
slit 1 profile was multiplied by a factor of 7.2 to match the integrated
emission at $\geq-750\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$.
Note the strong [O iii] emission for $\leq-750\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ for the larger field-of-view compared to the
slit 1 observations. This emission corresponds to about 10% of the total [O
iii] emission. A minor fraction ($\sim 10\%$) of the emission at
$\leq-750\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ could be due
to [Fe iii] $\lambda$4986, as displayed in Fig. 17, but most of it comes from
the approaching “wall” described in Sect. 3.2.  Figure 20: Same profile for [O
iii]$\lambda\lambda$4959,5007 as in Fig. 16 (blue) together with the combined
[O ii] $\lambda\lambda$3726,3729 profile. The velocity for the [O ii] lines is
centered on 3727.5 Å. The [O ii] profile was multiplied by a factor of 2 to
match $1.33\times$ [O iii] $\lambda$5007\. Note that [O ii] $\lambda$3726 only
reaches $\approx-1\,400\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$
on the blue side (when the $118\rm\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}$ difference between [O ii] $\lambda$3726 and 3727.5 Å is accounted
for). On the red side of [O ii] $\lambda$3729 the emission is blended with [Fe
vii] $\lambda$3759 as shown by the inset. The red curve is Savitzky-Golay
fitting to the noisy [Fe vii] line profile.  Figure 21: Same in Fig. 18, but
for [S ii] $\lambda$$\lambda$4069,4076 (black, and smoothed in red) instead of
[Ne iii] $\lambda$3869\. The [O iIii] profile was multiplied by a factor of
0.03 to match [S ii]. The sulphur doublet was velocity-centered on the
$\lambda$4069 component. LMC rest frame velocities for both components are
marked by vertical thin lines. The red side of the [S ii] doublet is affected
by H$\delta$. (The dip in H$\delta$ is due to over-subtraction of the LMC
background.)  Figure 22: Same in Fig. 18, but for He i $\lambda$5876 (black,
and smoothed in red) instead of [Ne iii] $\lambda$3869\. The [O iIii] profile
was multiplied by a factor of 0.01 to match the He i line. LMC rest frame
velocitiy is marked by a vertical thin line. The red side of the He i line
appears depreciated compared to [O iIii], similar to H$\beta$ in Fig. 15.

Unfortunately, for the SNRC with its broade lines, [O
iii]$\leavevmode\nobreak\ \lambda$4363 is blended with H$\gamma$. This may
lead to over-estimating the [O iii] temperature. To get the real [O iii]
temperature we subtracted H$\gamma$ from the line profile of the observed [O
iii]$\leavevmode\nobreak\ \lambda$4363$+$H$\gamma$ blend. As a template
profile for all H i lines we used H$\beta$. As shown in Fig. 15, the H$\beta$
template is affected by [Fe iii]$\leavevmode\nobreak\ \lambda$4481, but this
has very small impact on the process of removing the bluer Balmer lines. A
further complication is that all hydrogen lines suffer from background
contamination of emission around LMC rest velocity. We approximated this for
all H i lines by a linear approximation of the flux across the corrupted
frequency range.

The expected flux of H$\gamma$ relative to H$\beta$ was estimated from Case B
theory (Brocklehurst, 1971). The bottom panel of Fig. 15 shows how we were
able to remove H$\gamma$ from the [O iii]$\leavevmode\nobreak\
\lambda$4363$+$H$\gamma$ blend. As a spin-off, the line subtraction confirms
the values we used for the dereddening, i.e., $E(B-V)=0.19$ and $R=3.1$; when
the Balmer line was removed, continuum level was attained.

After the H$\gamma$ subtraction, the flux of [O iii]$\leavevmode\nobreak\
\lambda$4363 relative to [O iii]$\leavevmode\nobreak\ \lambda$5007 (set to
100) is $\sim 4.3$ (instead of 5.7, if H$\gamma$ is unaccounted for). This
gives $R_{\rm[{O\textsc{iii}}]}\sim 31$. We can, however, refine this analysis
by comparing the deblended profile of [O iii]$\leavevmode\nobreak\
\lambda$4363 to that of a template profile for [O iii]$\leavevmode\nobreak\
\lambda\lambda$4959,5007. The template for the latter was made from a similar
procedure to what was done in Sandin et al. (2013), i.e., the blue part of [O
iii]$\leavevmode\nobreak\ \lambda$4959 and the red part of [O
iii]$\leavevmode\nobreak\ \lambda$5007 were used as initial guesses for the
template. With the known intensity ratio of 3 for $I(\lambda 5007)/I(\lambda
4959)$, we constructed the combined [O iii]$\leavevmode\nobreak\
\lambda\lambda$4959,5007 template shown in red in Fig. 16. The template is for
the sum of the two line components. In the same figure we have also included
the “clean” [O iii]$\leavevmode\nobreak\ \lambda$4363 profile from Fig. 15.
Once multiplied by a factor of 28, and once by 34. In general, the [O
iii]$\leavevmode\nobreak\ \lambda$4363 profile is similar to that of the [O
iii]$\leavevmode\nobreak\ \lambda\lambda$4959,5007 template, although noise
limits the usefulness of the [O iii]$\leavevmode\nobreak\ \lambda$4363 profile
in its wings.

We thus find $R_{\rm[{O\textsc{iii}}]}=31\pm 3$, with a tendency for a lower
ratio in the blue part of the line profile compared to the red. The
corresponding [O iii] temperature range for the SNRC is $23\,500\pm 1\,800$ K
(cf. Table 5). This is less than $\sim 34\,000$ K, but consistent with
$\approx 25\,500$ K estimated by Kirshner et al. (1989) and Morse et al.
(2006), resepctively. In neither of those two studies H$\gamma$ was accounted
for. The slightly larger ratio we find for $R_{\rm[{O\textsc{iii}}]}$ for the
receding side of the remnant (compared to LMC rest velocity) could be due to a
lower temperature in this part of the SNRC, or intrinsic dust reddening. The
latter would not be surprising considering that dust in the Crab nebula is
concentrated to [O iii]-emitting filaments, and the pathlength through dust to
the receding side of the SNRC is likely to be longer than to ejecta moving
toward us. To compensate for the factor $\sim 1.2$ in larger
$R_{\rm[{O\textsc{iii}}]}$-value for the red side, $E(B-V)$ would have to be
$\sim 0.5$ instead of 0.19. This would depress the red side of the line
profiles severely, which is not what we see. Dust is therefore not a likely
reason for the large $R_{\rm[{O\textsc{iii}}]}$-value on the red side of the
[O iii] lines.

Fig. 16 shows that the blue sides of [O iii]$\leavevmode\nobreak\ \lambda$4959
and [O iii]$\leavevmode\nobreak\ \lambda$5007 nearly reach
$-1\,900\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$, which was
difficult to disentangle from Fig. 10 due to blending. For the red side, the
maximum velocity is $+1\,700\rm\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}$, which is consistent with the space- velocity results. Fig. 17 shows
that the construction of the [O iii]$\leavevmode\nobreak\
\lambda\lambda$4959,5007 template reveals a residual that we attribute to [Fe
iii]$\leavevmode\nobreak\ \lambda$4986, a line that is also seen in the
spectra of the filaments and other SNRs (Fesen & Hurford, 1996).

The [Ne iii]$\leavevmode\nobreak\ \lambda\lambda$3869,3967 doublet is also
affected by blending with Balmer lines. The same subtraction routine was
applied for both components of [Ne iii], and in Fig. 15 we show how the Balmer
lines H$\zeta$ and H$\epsilon$ were removed from their blends with [Ne
iii]$\leavevmode\nobreak\ \lambda$3869 and [Ne iii]$\leavevmode\nobreak\
\lambda$3968, respectively. As seen from the figure, [Ne
iii]$\leavevmode\nobreak\ \lambda$3869 is insignificantly contaminated by
Balmer line emission, whereas [Ne iii]$\leavevmode\nobreak\ \lambda$3967 is
more affected.

Figure 23: Same in Fig. 22, but for several forbidden iron lines (black, and
smoothed in red) instead of He i $\lambda$5876\. The velocities are centered
on LMC rest frame velocities of [Fe ii] $\lambda$5159 (upper left panel), [Fe
iii] $\lambda$5270 (lower left), [Fe v] $\lambda$4227 (upper right) and [Fe
vii] $\lambda$721 (lower right). In each panel grey arrows mark velocities for
other nebular lines seen in SNRs (Fesen & Hurford, 1996). In particular, [Fe
ii] $\lambda$5159 could be blended with (and even dominated by) [Fe vii]
$\lambda$5159\. Note the broad wings of [Fe v] $\lambda$4227, possibly
reaching $\pm 2\,000\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$.

A direct comparison between [Ne iii]$\leavevmode\nobreak\ \lambda$3869 and [O
iii]$\leavevmode\nobreak\ \lambda$5007 is shown in Fig. 18. The profile of the
neon line is fairly noisy, but it is consistent with the general features and
maximum velocities of [O iii]$\leavevmode\nobreak\ \lambda$5007\. The ratio of
the two lines is $I_{[{O\textsc{iii}}]\leavevmode\nobreak\ \lambda
5007}/I_{[{Ne\textsc{iii}}]\leavevmode\nobreak\ \lambda 3869}\sim 30$. With a
temperature in the $23\,500\pm 1\,800$ K, and assuming similar ionization
structures of O2+ and Ne2+, our multilevel atom models (e.g., Maran et al.,
2000; Mattila et al., 2010), updated with the recent atomic data in the
CHIANTI database (Del Zanna et al., 2021), result in a mass ratio $M_{\rm
Ne}/M_{\rm O}\sim 0.07$, which should probably be considered a lower limit
since the ionization zone of O2+ is likely to be wider than that of Ne2+. In
this context, we highlight the observations of Morse et al. (2006). They
detected [Ne iii]$\leavevmode\nobreak\ \lambda$3869, but neither got a
$3\sigma$ detection of [Ne iii]$\leavevmode\nobreak\ \lambda$3967, nor
corrected for Balmer line contamination. Their flux values translate into
$M_{\rm Ne}/M_{\rm O}\sim 0.13$ for the temperature we find from [O iii].

Williams et al. (2008) modeled the emission from 0540, and in those models
they assumed the abundance ratio Ne/O $=0.2$ (i.e., a mass ratio of 0.25), and
obtained $I_{[{Ne\textsc{iii}}]\leavevmode\nobreak\ \lambda
3869}/I_{[{O\textsc{iii}}]\leavevmode\nobreak\ \lambda 5007}=0.093$. This is
almost three times the value we obtain from our observations; if the $M_{\rm
Ne}/M_{\rm O}$ ratio in their model is lowered to 0.085 (i.e., close to our
value of 0.07), their predicted line ratio should agree with our observations.
The question is how likely a value of $M_{\rm Ne}/M_{\rm O}\sim 0.1$ could be.
It is, for example, about half the mass ratio for the inner ejecta found in a
recent model for the nucleosynthesis yields for the central part of an
exploding $11.8\leavevmode\nobreak\ {\rm M}_{\odot}$ star (Sieverding et al.,
2020), but the models of Chieffi & Limongi (2013), which take rotation of the
progenitor into account, yield $M_{\rm Ne}/M_{\rm O}=0.063\leavevmode\nobreak\
(0.053)\leavevmode\nobreak\ (0.21)\leavevmode\nobreak\ {\rm M}_{\odot}$ for
progenitor masses of $13\leavevmode\nobreak\ (15)\leavevmode\nobreak\
(20)\leavevmode\nobreak\ {\rm M}_{\odot}$. For non-rotating progenitors
Chieffi & Limongi (2013) find $M_{\rm Ne}/M_{\rm O}=0.22\leavevmode\nobreak\
(0.46)\leavevmode\nobreak\ (0.32)\leavevmode\nobreak\ {\rm M}_{\odot}$.
Judging from this, rotation could be important as $M_{\rm Ne}/M_{\rm O}$ in
those models agree with the values derived from observations.

In the models of Williams et al. (2008), infrared lines observed with Spitzer
Space Telescope were included. To compare the IR lines to optical lines, these
authors multiplied the fluxes in Morse et al. (2006) by a factor of 4 to
account for the 2″ slit in the optical as the infrared observations observed
the full region. We use the same procedure, but to put the slit compensation
on firmer footing, we make use of the VLT/VIMOS observations of Sandin et al.
(2013). In Fig. 19 we show the line profile of [O iii]$\leavevmode\nobreak\
\lambda$5007 for the full $13\arcsec\times 13\arcsec$ field observed with
VIMOS, and compare this to $7.2\times$ the template [O
iii]$\leavevmode\nobreak\ \lambda$5007 profile from our slit 1 observations.
With the 7.2 factor, the integrated emission of the two profiles is the same
for velocities $\\!\\!\\!\phantom{\geq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle>$}\over{\sim}$}}}\,\,-750\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$. About 10% of the VIMOS [O
iii]$\leavevmode\nobreak\ \lambda$5007 flux falls at velocities below
$-750\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$, and is mainly
attributed to [O iii] glow not captured efficiently by the slits used by Morse
et al. (2006) and us. We therefore use the factor of 7.2 for most lines For
lines with suspected glow we use 8.0 since the Spitzer field-of-view is likely
to capture much of the glow. (The corresponding numbers for our NTT/EMMI slit,
i.e., slit 2, is 6.3 and 6.6, respectively.) As Morse et al. (2006) obtain
$\approx 1.6$ times larger [O iii]$\leavevmode\nobreak\ \lambda$5007 flux
through their $2\arcsec\times 11\arcsec$ slit than we do through our
$1\arcsec\times 10\arcsec$ slit, the conversion factor Williams et al. (2008)
should have used for most lines is 4.5, instead of their 4. For [O
iii]$\leavevmode\nobreak\ \lambda$5007, and other possible lines with glow, a
conversion factor of 5 would have been more appropriate.

Williams et al. (2008) measure $(7.29\pm 0.56)\times 10^{-14}$ erg cm-2s-1 for
[Ne iii] 15.6$\mu$. If we use our VLT observations, multiplied by 8, the [Ne
iii]$\leavevmode\nobreak\ \lambda$3869 flux is $1.1\times 10^{-14}$ erg
cm-2s-1, i.e., $I_{[{Ne\textsc{iii}}]\leavevmode\nobreak\
15.6\mu}/I_{[{Ne\textsc{iii}}]\leavevmode\nobreak\ \lambda 3869}\sim 6.7$,
which is twice as high as in the model of Williams et al. (2008). From our
multilevel modeling it is obvious that the [Ne iii] 15.6$\mu$ flux cannot come
from the same hot gas as the [O iii] lines we observe, since the ratio for
this at 23 000 K is $I_{[{Ne\textsc{iii}}]\leavevmode\nobreak\
15.6\mu}/I_{[{Ne\textsc{iii}}]\leavevmode\nobreak\ \lambda 3869}\sim 0.14$. An
intensity ratio of 6.7 is only obtained for temperatures
$\\!\\!\\!\phantom{\leq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle<$}\over{\sim}$}}}\,\,7\,000$ K. Although there
are several uncertainties, the main explanation must be that [Ne iii]
15.6$\mu$ predominantly comes from regions with much lower temperatures than
that emitting the optical [O iii] and [Ne iii] lines. The most likely region
is gas heated by photionization rather than by shocks, as shock-heated
material would be hotter. Extinction due to internal dust may be a
complementary explanation as this would not affect the IR line.

Fig. 19 emphasizes the redshift of all [O iii] emission from the full SNRC,
and shows that the line profile through slit 1 surprisingly well represents
the emission at most velocities. The most obvious difference is the strong
emission at velocities $\\!\\!\\!\phantom{\leq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle<$}\over{\sim}$}}}\,\,-750\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ (which is also evident from Fig. 6, and which
is mainly due to the approaching “wall” described in Sect. 3.2) as well as
slightly more emission at $\\!\\!\\!\phantom{\geq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle>$}\over{\sim}$}}}\,\,+750\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$. The peak around LMC rest velocity is at least
to some extent artificial due to difficulty with removing LMC background
emission due to the small field-of-view of VIMOS. The VIMOS data are not
sensitive enough to trace velocities
$\\!\\!\\!\phantom{\geq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle>$}\over{\sim}$}}}\,\,\mid{\pm
1\,500}\mid\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$.

Turning to ions of lower degree of ionization observed through slit 1, we show
[O ii]$\leavevmode\nobreak\ \lambda\lambda$3726,3729 in Fig. 20, [S
ii]$\leavevmode\nobreak\ \lambda\lambda$4069,4076 in Fig. 21, and He
i$\leavevmode\nobreak\ \lambda$5876 in Fig. 22. For [O ii] and [S ii] we have
centered the velocity on 3727.5 Å and the strongest component of [S ii] (i.e.,
$\leavevmode\nobreak\ \lambda$4069), respectively. As already discussed in
Sect. 3.2, [O ii] has a profile similar to that of H$\beta$, and [S
ii]$\leavevmode\nobreak\ \lambda\lambda$4069,4076 is similarly narrow, i.e.,
primarily extends from $\sim-700\rm\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}$ to $\sim+1\,000\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$,
although there is a blue wing of [O ii] that reaches
$\sim-1\,400\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$. This is
not seen for [S ii]$\leavevmode\nobreak\ \lambda\lambda$4069,4076 in Fig. 21,
but the low signal-to-noise does not allow us to draw firm conclusions on that
part of the line profile. Interestingly enough, the full view SNRC
observations of [S ii]$\leavevmode\nobreak\ \lambda\lambda$6716,6731 by Sandin
et al. (2013, their Figure 2) does show a blue wing between
$-1\,200\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ and
$-700\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$. Our choice to
center the [O ii] doublet on 3727.5 Å is because this does not introduce any
bias for either of the two doublet components. What is intrinsically assumed
by centering on 3727.5 Å is that we assume that
$I_{[{O\textsc{ii}}]\leavevmode\nobreak\ \lambda
3729}/I_{[{O\textsc{ii}}]\leavevmode\nobreak\ \lambda 3726}\approx 1.11$,
which means $n_{\rm e}\sim 350\leavevmode\nobreak\
(400)\rm\leavevmode\nobreak\ cm^{-3}$ for $T\sim 20\,000\leavevmode\nobreak\
(30\,000)$ K. According to our multilevel model, the intensity ratio decreases
from $\approx 1.35$ to $\approx 0.38$ as electron density increases from
$10^{2}\rm\leavevmode\nobreak\ cm^{-3}$ to $10^{4}\rm\leavevmode\nobreak\
cm^{-3}$.

Our observed $I_{[{S\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda
4069,4076}/I_{[{O\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda 3726,3729}$
ratio is $\sim 0.06$. For the temperature interval $10\,000-15\,000$ K and
density interval $500-1\,000\rm\leavevmode\nobreak\ cm^{-3}$, our multilevel
model atoms translate the observed ratio into an abundance ratio of
S/O$=0.05\pm 0.01$, and thus a mass ratio $M_{\rm S}/M_{\rm O}=0.10\pm 0.02$.
The models of Chieffi & Limongi (2013) predict a ratio of $0.05-0.06$ for
rotating progenitors for progenitor masses between $13-20\leavevmode\nobreak\
{\rm M}_{\odot}$, and between $0.05-0.13$ for non-rotating (with 0.05 for
$20\leavevmode\nobreak\ {\rm M}_{\odot}$). The more recent model of Sieverding
et al. (2020) predicts $M_{\rm S}/M_{\rm O}=0.085$ from their
$11.8\leavevmode\nobreak\ {\rm M}_{\odot}$ model for the inner ejecta and
$0.12\leavevmode\nobreak\ {\rm M}_{\odot}$ for all ejecta. Williams et al.
(2008) assumed $M_{\rm S}/M_{\rm O}=0.05$ in their models, and underproduced
[S iii] 18$\mu$ and [S iv] 10$\mu$ by factors of $\sim 1.4$ and $\sim 2.8$,
respectively, when we adjust their results with more accurate slit
compensations. It therefore appears as if their model would fit the Spitzer
data better with $M_{\rm S}/M_{\rm O}\sim 0.1$, which is consistent with both
Chieffi & Limongi (2013) and Sieverding et al. (2020), albeit perhaps not for
non-rotating low-mass progenitors in the case of Chieffi & Limongi (2013).
However, the model of Williams et al. (2008) gives an
$I_{[{S\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda
4069,4076}/I_{[{O\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda 3726,3729}$
ratio which is $\sim 0.09$, and that is on the high side compared to our
observations already with $M_{\rm S}/M_{\rm O}=0.05$.

$M_{\rm S}/M_{\rm O}$ can also be estimated from our slit 2 data for which we
have $I_{[{S\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda
6716,6731}/I_{[{O\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda
7319-7331}\sim 9.0$. This is similar to $\approx 8.4$ by Kirshner et al.
(1989), and 10 in the model of Williams et al. (2008) assuming S/O $=0.1$).
Our multilevel atom modeling shows that a temperature
$\\!\\!\\!\phantom{\geq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle>$}\over{\sim}$}}}\,\,20\,000$ K is needed to
excite O+ to emit [O ii]$\leavevmode\nobreak\ \lambda\lambda$7319-7331 at the
observed relative intensity. In particular, for the [O iii] temperature $T\sim
23\,000$ K, $I_{[{S\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda
6716,6731}/I_{[{O\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda
7319-7331}\sim 7$ for S/O $=0.1$ and electron densities estimated by Sandin et
al. (2013). The ratio rises steeply below 20 000 K.

Another way to estimate a temperature in the [O ii]-emitting regions is from
the ratio $I_{[{O\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda
3726,3729}/I_{[{O\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda 7319-7331}$,
but for this we have to combine slits 1 and 2. Using the slit correction
factors 7.2 and 6.3, respectively, we obtain $\sim 6.2$, which is very close
to $\sim 6.5$ by Kirshner et al. (1989), but very different from the modeled
flux by Williams et al. (2008), which is $\approx 14.7$. Our multilevel model
suggests very high temperatures (well above $30\,000$ K) to get a ratio below
8.0, which appears unlikely. Since our flux agrees with that of Kirshner et
al. (1989), a possible explanation could be that [O ii]$\leavevmode\nobreak\
\lambda\lambda$7319-7331 is contaminated by [Ca ii] in both our slit 2 and the
data in Williams et al. (2008). Such contamination (at 20% level) was already
discussed by Kirshner et al. (1989).

Figure 24: Spectra of forbidden lines from F1 (cf. Figs. 5 and 13). All
spectra are in the LMC rest frame and the velocities are for [O iii]
$\lambda$5007 (left), 3727.5 Å (middle), [Fe ii] $\lambda$5159 (upper right)
and [Fe xiv] $\lambda$5303 (lower right). For the oxygen lines, the line
profiles of the emission from the SNSC in Figs. 16 and 20, multiplied by a
factor of 0.01, have been included for comparison (in red). The narrow
spectral lines are unresolved, as highlighted for [O iii] $\lambda$5007 and
the [O ii] doublet, where the solid black lines show Gaussians with the
expected FWHM of the instrument at 5007 Å and 3727.5 Å, i.e., $\sim
355\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ and $\sim
476\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$, respectively. Note
the broad bases seen for [O iii] and possible broad base wings for [O ii]
$\lambda\lambda$3726,3729. Lines of the H i Balmer series are marked in the
middle panel. For the iron lines, Gaussians have also been drawn (in blue)
according to the expected resolution. Several other lines have also been
marked/indicated. Red marks Savitzky-Golay fitting to the spectrum.

A combination of slits 1 and 2 can also be used to estimate an [S ii]-
temperature from $I_{[{S\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda
6716,6731}/I_{[{S\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda 4069,4076}$,
which with our slit compensations is $\sim 30$. This is much higher than $\sim
17$ by Kirshner et al. (1989), and inconsistent with $\sim 9.4$ by Morse et
al. (2006) as well as the model by Williams et al. (2008) which predicts $\sim
7.4$. Our multilevel models show some density dependence, but intensity ratios
such as those by Morse et al. (2006) and Williams et al. (2008) require
temperatures at least as high as our derived [O iii] temperature from slit 1,
whereas our ratio and that of Kirshner et al. (1989) indicate temperatures of
well below $10\,000$ K and around $15\,000$ K, respectively. Comparing
observations through different slits, and at different epochs, admittedly
increases the risk of systematic errors, so to make a consistency check we
have used the full SNRC [S ii] spectra of Sandin et al. (2013) to make
artificial observations of [S ii] through slits 1 and 2. From this exercise we
find that the slit compensation for [S ii]$\leavevmode\nobreak\
\lambda\lambda$6716,6731 is 6.5 for slit 1 and 7.7 for slit 2 (instead of the
values 7.2 and 6.3, as indicated by [O iii]). This is not large enough to
change our $I_{[{S\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda
6716,6731}/I_{[{S\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda 4069,4076}$
ratio by much (and actually makes it even larger).

The source of inconsistency for $I_{[{S\textsc{ii}}]\leavevmode\nobreak\
\lambda\lambda 6716,6731}/I_{[{S\textsc{ii}}]\leavevmode\nobreak\
\lambda\lambda 4069,4076}$ could either lie in the large relative [S
ii]$\leavevmode\nobreak\ \lambda\lambda$6716,6731 flux we get for slit 2
compared to others (cf. Table 2), and/or the lower flux we measure for [S
ii]$\leavevmode\nobreak\ \lambda\lambda$4069,4076. The latter is not
unreasonable since [S ii]$\leavevmode\nobreak\ \lambda\lambda$4069,4076 is
affected by H$\delta$. From Brocklehurst (1971) we estimate that H$\delta$
would amount to $\sim 25\%$ of H$\beta$, which would decrease the
$I_{[{S\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda
6716,6731}/I_{[{S\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda 4069,4076}$
ratio accordingly, if not corrected for. This effect, of course, does not
affect the modeled results of Williams et al. (2008). Regarding [S
ii]$\leavevmode\nobreak\ \lambda\lambda$6716,6731 we can do a direct test
against the VIMOS observations of Sandin et al. (2013) by placing artificial
slits on the VIMOS images to simulate slits 1 and 2. From figure 3 of Sandin
et al. (2013) it can be seen that $I_{[{S\textsc{ii}}]\leavevmode\nobreak\
\lambda\lambda 6716,6731}/I_{[{O\textsc{iii}}]\leavevmode\nobreak\ \lambda
5007}$ is never higher than $\sim 0.8$, and for slits 1 and 2 we get $\sim
0.47$ and $\sim 0.35$, respectively. Even if we allow for slight displacement
of slit 2 due to atmospheric dispersion (which was not accounted for in the
NTT/EMMI observations), the ratio will not increase by more than $\sim 20\%$.
Careful check of possible erroneous background subtraction of [S
ii]$\leavevmode\nobreak\ \lambda\lambda$6716,6731, together with the fact that
the flux of other lines through slit 2 agrees with the results of Kirshner et
al. (1989) and Morse et al. (2006), leaves us no choice other than to suggest
that the [S ii$]\leavevmode\nobreak\ \lambda\lambda$6716,6731 flux could vary
with time. If we use a ratio of 0.35 from a simulated slit 2, we obtain
$I_{[{S\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda
6716,6731}/I_{[{S\textsc{ii}}]\leavevmode\nobreak\ \lambda\lambda
4069,4076}\sim 12$, which is more aligned with what other groups get, and
would suggest an [S ii] temperature of $\sim 20\,000$ K. The question remains
regarding our high [S ii$]\leavevmode\nobreak\ \lambda\lambda$6716,6731 flux.
We note that there are NTTT/EMMI spectra covering [S ii$]\leavevmode\nobreak\
\lambda\lambda$6716,6731 from 1995 January, i.e., only one year before our NTT
spectrum, which were shown in Caraveo et al. (1998). Unfortunately, these
authors did not provide any fluxes. As there is activity going on in the
south-western part of the PWN, at least between 1999-2007, the NTT spectra of
Caraveo et al. (1998) could prove decisive regarding temporal variations in [S
ii$]\leavevmode\nobreak\ \lambda\lambda$6716,6731. As discussed in Sect.
3.4.2, variations of elements other than oxygen on relative short time scale
are conceivable.

Figure 22 shows that He i $\lambda$5876 is very concentrated to within $\pm
500\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$, in a fairly similar
fashion to H$\beta$ and [S ii]. This means that hydrogen was deeply mixed into
the core region during the explosion. Such mixing is expected from 3D
explosion models (e.g., Hammer et al., 2010), and the amount of hydrogen mixed
into the SNRC is sensitive to hydrodynamic instabilities at the composition
interfaces (e.g., Wongwathanarat et al., 2015). A crude He/H ratio for the
SNRC can be estimated from recombination theory, assuming similar ionization
zones for H and He. The observed flux ratio of He i $\lambda$5876 to H$\beta$
for our slit 1 is $\sim 0.24$, with at least 40% uncertainty. For a
temperature in the range $10\,000-20\,000$ K this translates into a mass ratio
of He+/H+ which is $\sim 0.8$. As He0 roughly has the same ionization
potential as S+, and [S ii] emission dominates over [S iii] in 0540 (Kirshner
et al., 1989), a larger fraction of helium is likely to be neutral than that
of hydrogen, and $M_{\rm He}/M_{\rm H}$ is likely to be larger than 0.8 for
the SNRC of 0540. The fraction of fully ionized helium could in principle be
tested with He ii $\lambda$4686, but it sits in a spectral range with strong
[Fe iii] lines, and is not detected. SN 1987A may serve as interesting
comparison for $M_{\rm He}/M_{\rm H}$, and we note that Jerkstrand et al.
(2011) estimate that both H and He have $\sim 1.2\leavevmode\nobreak\ {\rm
M}_{\odot}$ each in the central $2000\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ region of SN 1987A, i.e., the mass ratio is
$M_{\rm He}/M_{\rm H}\approx 1$, which is consistent with what we estimate for
the SNRC of 0540.

Through slit 2 we also detect [Ar iii] $\lambda$7136 and [Ni ii] $\lambda$7378
with intensities relative to [O iii]$\leavevmode\nobreak\ \lambda$5007 similar
to what was reported by Kirshner et al. (1989) (cf. Table 2). On the other
hand, the modeled [Ar iii] $\lambda$7136 flux by Williams et al. (2008) was
more than twice as high as the observed relative fluxes of the line. This
could suggest that Ar/O is less than the value of 0.1 assumed by Williams et
al. (2008). Tuning the model results of Williams et al. (2008) with the
observed [Ar iii] $\lambda$7136 fluxes then suggest $M_{\rm Ar}/M_{\rm O}\sim
0.02$. The nucleosynthesis yields in the model of Sieverding et al. (2020)
give the same value, i.e., $M_{\rm Ar}/M_{\rm O}\sim 0.02$ for the total yield
of Ar and O. The ratios in Chieffi & Limongi (2013) are $\sim 0.01$ for
$13-20\leavevmode\nobreak\ {\rm M}_{\odot}$ rotating, and
$20\leavevmode\nobreak\ {\rm M}_{\odot}$ for non-rotating progenitors, whereas
the ratio is higher, $\sim 0.02$, for $13\leavevmode\nobreak\ {\rm M}_{\odot}$
non-rotating progenitors. Our multilevel model atoms suggest $M_{\rm
Ar}/M_{\rm O}=0.015(0.030)$ for equal ionization zones of Ar2+ and O2+ in the
SNRC and for temperatures of 20 000 (30 000) K. The observed level of [Ar iii]
$\lambda$7136 is therefore consistent with that expected from elemental yields
in progenitor models and with [O iii] temperatures.

As shown in Fig. 17 ([Fe iii]$\leavevmode\nobreak\ \lambda$4986), Fig. 20 ([Fe
v]$\leavevmode\nobreak\ \lambda$3726) and Fig. 23 ([Fe
ii]$\leavevmode\nobreak\ \lambda$5159, [Fe iii]$\leavevmode\nobreak\
\lambda$5270, [Fe v]$\leavevmode\nobreak\ \lambda$4227 and [Fe
vii]$\leavevmode\nobreak\ \lambda$5721) we detect several forbidden iron lines
through slit 1, with decent signal-to-noise. We also detect [Fe ii]
$\lambda\lambda$4287,4414,5044, [Fe iii] $\lambda$4658,4881,4986, [Fe v]
$\lambda\lambda$3783-3797 and [Fe vii] $\lambda$5721\. The strongest line is
[Fe iii]$\leavevmode\nobreak\ \lambda$4658, but it blends with several other
[Fe iii] lines, as do also several [Fe ii] lines around $\sim
4474\leavevmode\nobreak\ \AA$. Through slit 2 we detect [Fe
ii]$\leavevmode\nobreak\ \lambda$5159 and [Fe iii]$\leavevmode\nobreak\
\lambda\lambda$4658,5270, but with poor signal-to-noise.

We have chosen to concentrate on presumably unblended lines observed through
slit1. In general, the line profiles are similar to those of the [O ii] lines.
In particular this is the case for [Fe iii] $\lambda$5270 and the core of [Fe
v] $\lambda$4227, whereas [Fe vii] $\lambda$5721 is noisy, and perhaps also
affected by [N ii] $\lambda$5755 in the far red wing. In Fig. 23 we have
marked the velocities corresponding to other lines detected in SNRs (Fesen &
Hurford, 1996) which could perhaps contribute to the lines we have
highlighted. For example, [Fe ii] $\lambda$4247 could contribute to the red
wing of [Fe v] $\lambda$4227, and our identification of [Fe ii] $\lambda$5159
could instead be dominated by [Fe vii] $\lambda$5159, in particular since we
also detect [Fe vii] $\lambda$5721\. To test this we have used our nine-level
model atom for Fe${{}^{6}+}$, including data from Berrington et al. (2000) and
Del Zanna et al. (2021, and references therein). For $n_{\rm
e}=10^{3}\rm\leavevmode\nobreak\ cm^{-3}$ and $T=30\,000$ K, the expected
strongest [Fe vii] lines are (in order and normalized to [Fe vii]
$\lambda$5721): [Fe vii] $\lambda$6089, [Fe vii] $\lambda$3759, [Fe vii]
$\lambda$3587, [Fe vii] $\lambda$4990 and [Fe vii] $\lambda$5159 with relative
strengths 1.9, 1.4, 1.0, 0.7 and 0.5, respectively. Unfortunately, [Fe vii]
$\lambda$3587 and [Fe vii] $\lambda$6089 are outside the spectral range of our
slit 1 observations, although the latter line can, after smoothing, be hinted
in the NTT/EMMI spectrum. [Fe vii] $\lambda$3759 is clearly detected through
slit 1, and [Fe vii] $\lambda$4990 may add to [Fe iii]$\leavevmode\nobreak\
\lambda$4986 in Fig. 17. Judging from the weak measured flux of [Fe vii]
$\lambda$5721, and that [Fe vii] $\lambda$5159 is not expected to be stronger,
we conclude that the spectral line at $\sim 5171$ Å (and $\sim 5160$ Å through
slit 2) is dominated by [Fe ii] $\lambda$5159\. The line has a possible broad
blue wing, which is also hinted for [Fe v] $\lambda$4227 (cf. Fig. 23).
However, since no such wing is expected for [Fe ii] lines, it is probably not
real. Deeper observations are needed to check the wing of the [Fe v] line.

####  3.4.2 Masses and abundances - a summary

In the previous section we estimated the relative abundances in 0540. We now
summarize this and estimate the total ejecta mass of the elements we have
discussed. The mass of O2+ ions in the SNRC emitting [O iii] $\lambda$5007 is

$\begin{split}M({\rm O}^{2+})\approx 3.2\times 10^{-5}\leavevmode\nobreak\
\left(\frac{f_{[{O\textsc{iii}}]\lambda 5007}}{10^{-13}\leavevmode\nobreak\
{\rm erg\leavevmode\nobreak\ cm}^{-2}\leavevmode\nobreak\ {\rm
s}^{-1}}\right)\left(\frac{D}{50\leavevmode\nobreak\ {\rm kpc}}\right)^{2}\\\
\left(\frac{n_{\rm e}}{10^{3}\leavevmode\nobreak\ \rm\leavevmode\nobreak\
cm^{-3}}\right)^{-1}\left(\frac{j_{[{O\textsc{iii}}]\lambda
5007}}{10^{-21}\leavevmode\nobreak\ {\rm erg\leavevmode\nobreak\
cm}^{3}\leavevmode\nobreak\ {\rm s}^{-1}\leavevmode\nobreak\ {\rm
sr}^{-1}}\right)^{-1}\leavevmode\nobreak\ \leavevmode\nobreak\ {\rm
M}_{\odot}.\end{split}$ (3)

Here $f_{[{O\textsc{iii}}]\lambda 5007}$ is the dereddened flux for one of the
slit positions with a slit correction included to account for the full SNRC.
For the SNRC we get $f_{[{O\textsc{iii}}]\lambda 5007}\sim 3.0\times
10^{-13}\leavevmode\nobreak\ {\rm erg\leavevmode\nobreak\
cm}^{-2}\leavevmode\nobreak\ {\rm s}^{-1}$. $j_{[{O\textsc{iii}}]\lambda
5007}$ is the emissivity of the $\lambda$5007 transition, which for
$T=23\,500$ K is $\sim 1.1\times 10^{-21}\leavevmode\nobreak\ {\rm
erg\leavevmode\nobreak\ cm}^{3}\leavevmode\nobreak\ {\rm
s}^{-1}\leavevmode\nobreak\ {\rm sr}^{-1}$. For $n_{\rm
e}=10^{3}\leavevmode\nobreak\ \rm\leavevmode\nobreak\ cm^{-3}$ one then gets
$M({\rm O}^{2+})\sim 9\times 10^{-5}\leavevmode\nobreak\ {\rm M}_{\odot}$.

A similar estimate for $M({\rm O}^{+})$ from [O ii] $\lambda\lambda$3726,3729
gives $M({\rm O}^{+})\sim 5\times 10^{-5}\leavevmode\nobreak\ {\rm M}_{\odot}$
when we use $T=20\,000$ K (and from this $j_{[{O\textsc{iii}}]\lambda\lambda
3726,3729}\sim 1.1\times 10^{-21}\leavevmode\nobreak\ {\rm
erg\leavevmode\nobreak\ cm}^{3}\leavevmode\nobreak\ {\rm
s}^{-1}\leavevmode\nobreak\ {\rm sr}^{-1}$). A combined mass of $M({\rm
O}^{+})+M({\rm O}^{2+})\sim 1.4\times 10^{-4}\leavevmode\nobreak\ {\rm
M}_{\odot}$ may seem like a surprisingly low mass considering that about two
solar masses of oxygen should be present in 0540 (if similar to, e.g., SN
1987A). However, this estimate is only for the amount of oxygen in the SNRC
that has been recently shocked. Those shocks are thin due to intense radiative
cooling. The cooling time, calculated from a simple six-level model atom of
pure O2+ at $T=30\,000$ K with $n_{\rm e}=10^{3}\leavevmode\nobreak\
\rm\leavevmode\nobreak\ cm^{-3}$, is $\sim 0.02$ years, and at $T=50\,000$ K
it is $\sim 0.024$ years. The similar numbers for pure O+ at $T=20\,000$ K and
$T=30\,000$ K are $\sim 0.023$ years and $\sim 0.02$ years. The real cooling
time is longer if the shocked gas starts out hotter than $T=50\,000$ K,
although this is not so important since the cooling function for pure oxygen
peaks around $\sim 2\times 10^{5}$ K (cf. Borlowski & Shull, 1990), and falls
monotonically towards lower temperatures. More important is that the cooling
is counteracted by photoionization of ambients photons from the PWN. With this
in mind, a lower limit on the cooling time is $\sim 0.05$ years. Thus, $\sim
1.4\times 10^{-4}\leavevmode\nobreak\ {\rm M}_{\odot}$ has to be replenished
every $\\!\\!\\!\phantom{\geq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle>$}\over{\sim}$}}}\,\,0.05$ years, which means
$\sim 0.3\leavevmode\nobreak\ {\rm M}_{\odot}$ of shocked oxygen in
$\\!\\!\\!\phantom{\geq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle>$}\over{\sim}$}}}\,\,100$ years.

Williams et al. (2008) did shock modeling for a similar situation where they
assumed a low-velocity shock of $20\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ aided by photoionization of PWN photons to
account for the heavy-element ejecta lines. This is much lower than the shock
velocity in Borlowski & Shull (1990) for Cas A, although that study only
included preionization by photons produced by the shock. The oxygen column
density of the emitting region in Williams et al. (2008) is $\sim 10^{14}$
cm-2, and the mass flux of ejecta flowing into the low-velocity shocks is
$\sim 0.01\leavevmode\nobreak\ {\rm M}_{\odot}$ yr-1, which appears consistent
with our estimate of $\\!\\!\\!\phantom{\leq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle<$}\over{\sim}$}}}\,\,0.003\leavevmode\nobreak\
X_{\rm other}\leavevmode\nobreak\ {\rm M}_{\odot}$ yr-1, where $X_{\rm
other}>1$ is the correction factor to include all elements, and not only
oxygen.

The mass fractions we estimated in Sect. 3.4.1 for the SNRC of 0540, namely
${\rm O:Ne:S:Ar}=1:0.07:0.10:0.02$ and ${\rm
H:He}=1:\\!\\!\\!\phantom{\geq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle>$}\over{\sim}$}}}\,\,0.8$, are thus sampled over
a very small fraction of the inner ejecta at any given time. How
representative these numbers are for all inner ejecta is not very clear.
However, one could imagine that there could be fluctuations on moderate time
scales if the low-velocity shocks run into regions which are not fully
microscopically mixed. This could be the reason for the apparent elevated
sulphur abundance indicated by our NTT/EMMI observations.

Figure 25: Velocities estimated for emission lines from Filament F1. No
doublets/multiplets are included except [O ii]$\leavevmode\nobreak\
\lambda\lambda$3726,3729. As can be seen, the wavelength calibration is stable
across the spectrum. Interestingly, there is a group of lines with LMC
redshift, although the majority has a redshift close to
$\sim+120\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ compared to
LMC redshift. See Table 3 and text for further details.

####  3.4.3 The halo and beyond

Added to the mass of the SNRC is the mass of ejecta in the unshocked freely
moving supernova ejecta. According to Williams et al. (2008), the inner part
of this is photoionized to O2+, so we use Equation 3 with $n_{\rm
e}=1\rm\leavevmode\nobreak\ cm^{-3}$ and $f_{[{O\textsc{iii}}]\lambda
5007}\sim 1.5\times 10^{-13}\leavevmode\nobreak\ {\rm erg\leavevmode\nobreak\
cm}^{-2}\leavevmode\nobreak\ {\rm s}^{-1}$, which corresponds to the
integrated broad base of [O iii] emission in Fig. 19, and assuming that the
VIMOS/IFU field-of-view misses roughly one third of the halo emission. For the
photoionized halo we further assume a temperature of $\sim 12\,000$ K, so that
$j_{[{O\textsc{iii}}]\lambda 5007}\sim 4\times 10^{-22}\leavevmode\nobreak\
{\rm erg\leavevmode\nobreak\ cm}^{3}\leavevmode\nobreak\ {\rm
s}^{-1}\leavevmode\nobreak\ {\rm sr}^{-1}$. With these assumptions, the mass
of O2+ in the halo, $M({\rm O}^{2+})_{\rm halo}\sim 0.12\leavevmode\nobreak\
{\rm M}_{\odot}$. The mass is most likely higher since $n_{\rm
e}=1\rm\leavevmode\nobreak\ cm^{-3}$ only stems from the 4 a.m.u. at the inner
boundary of the unshocked SN ejecta estimated by Williams et al. (2008). The
average electron density could be $n_{\rm e}<1\rm\leavevmode\nobreak\ cm^{-3}$
in the unshocked [O iii] emitting halo. According to Williams et al. (2008),
enough ionizing photons are produced to ionize $\sim 1\leavevmode\nobreak\
{\rm M}_{\odot}$ halo ejecta. In a mixed abundance model by Blinnikov et al.
(2000) for SN 1987A, which contains $\sim 2.0\leavevmode\nobreak\ {\rm
M}_{\odot}$ of oxygen with a drop in mass fraction just short of
$2\,000\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$, the mass
fraction of oxygen falls from $\sim 0.3$ from $\sim
1\,300\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ to well below 0.1
at $2\,000\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$. Choosing 0.1
for the 0540 halo makes our estimate for $M({\rm O}^{2+})_{\rm halo}$
consistent with the ionized mass estimated by Williams et al. (2008), and if
the total oxygen mass is similar to that in SN 1987A, roughly half of the
oxygen is now confined to the filaments in the SNRC.

In SN 1987A, the total mass inside $2\,000\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ is dominated by He, O and H (cf. Blinnikov et
al., 2000). We may assume the same situation for 0540. For a density of 4
a.m.u. at the inner boundary of the halo, corresponding to $V_{\rm
halo,inner}\sim 1\,200\rm\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$,
and an outer velocity for the ionized halo of $V_{\rm
halo,outer}\\!\\!\\!\phantom{\geq}\smash{\buildrel\over{\lower
2.67502pt\hbox{$\buildrel\lower
2.14001pt\hbox{$\displaystyle>$}\over{\sim}$}}}\,\,1\,900\rm\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}$ (as is indicated by our results here), the
total mass in this shell is $\sim 6.8\leavevmode\nobreak\ {\rm M}_{\odot}$,
assuming a flat density profile of the unshocked ejecta (cf. Williams et al.,
2008). This compares well with the mixed model for SN 1987A by Blinnikov et
al. (2000) in which the total mass inside the radius corresponding to this
velocity is about $5-6\leavevmode\nobreak\ {\rm M}_{\odot}$. It therefore
seems that 0540 and SN 1987A could be fairly similar, and perhaps stem from
progenitors with roughly similar zero-age-main sequence masses. The main
difference between the dynamics in these events is of course the influence of
a pulsar, which, if existent in SN 1987A (e.g., Cigan et al., 2019; Greco et
al., 2021; Alp et al., 2021), plays a much smaller role than in 0540. On top
of that, one has the 3D effects stemming from the explosion hydrodynamics, and
possibly pre-explosion rotation. In our mass estimates for the halo we have
compared with models assuming 1D, but from Sect. 3.1.1. it is evident that the
halo is far from spherically symmetric. This obviously introduces
uncertainties in our mass estimates for the halo.

Moving further away from the SNRC, we introduced in Sect. 3.3.2 five
interesting filaments which we have named F1-F5. For all filaments, the
spectral lines are unresolved, except for F1, which displays broad bases of