# Radio light curves and imaging of the helium nova V445 Puppis reveal seven
years of synchrotron emission

M. M. Nyamai1, L. Chomiuk2, V. A. R. M. Ribeiro3,4, P. A. Woudt1, J. Strader2,
and K. V. Sokolovsky2,5
1Department of Astronomy, University of Cape Town, Private Bag X3, Rondebosch
7701, South Africa
2Department of Physics and Astronomy, Michigan State University, East Lansing,
MI 48824, USA
3Instituto de Telecomunicações, Campus Universitário de Santiago, 3810-193
Aveiro, Portugal
4Departamento de Física, Universidade de Aveiro, Campus Universitário de
Santiago, 3810-193 Aveiro, Portugal
5Sternberg Astronomical Institute, Moscow State University, Universitetskii
pr. 13, 119992 Moscow, Russia nymmir001<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

V445 Puppis is the only helium nova observed to date; its eruption in late
2000 showed high velocities up to 8500 km s-1, and a remarkable bipolar
morphology cinched by an equatorial dust disc. Here we present multi-frequency
radio observations of V445 Pup obtained with the Very Large Array (VLA)
spanning 1.5–43.3 GHz, and between 2001 January and 2008 March (days
$\sim$89–2700 after eruption). The radio light curve is dominated by
synchrotron emission over these seven years, and shows four distinct radio
flares. Resolved radio images obtained in the VLA’s A configuration show that
the synchrotron emission hugs the equatorial disc, and comparisons to near-IR
images of the nova clearly demonstrate that it is the densest ejecta—not the
fastest ejecta—that are the sites of the synchrotron emission in V445 Pup. The
data are consistent with a model where the synchrotron emission is produced by
a wind from the white dwarf impacting the dense equatorial disc, resulting in
shocks and particle acceleration. The individual synchrotron flares may be
associated with density enhancements in the equatorial disc and/or velocity
variations in the wind from the white dwarf. This overall scenario is similar
to a common picture of shock production in hydrogen-rich classical novae, but
V445 Pup is remarkable in that these shocks persist for almost a decade, much
longer than the weeks or months for which shocks are typically observed in
classical novae.

###### keywords:

binaries:close – helium novae, cataclysmic variables – stars : outflows –
radio continuum: individual (V445 Puppis)– white dwarfs

††pubyear: 2019††pagerange: Radio light curves and imaging of the helium nova
V445 Puppis reveal seven years of synchrotron emission–C

##  1 Introduction

Extensive accretion of helium-rich material onto a white dwarf (WD) from a
helium companion star results in increasing density and temperature on the WD
surface, eventually triggering a helium shell flash (known as a helium nova;
Kato et al. 1989). Helium novae occur for mass accretion rates in the range
$\sim 10^{-8}~{}\rm to~{}10^{-7}~{}M_{\odot}$ yr-1 (Woosley & Kasen, 2011;
Piersanti et al., 2013). The thermonuclear runaway ejects the outer accreted
layers analogous to hydrogen-rich classical novae (see e.g., Bode & Evans,
2008; Woudt & Ribeiro, 2014), although more mass is ejected in helium novae
(Kato et al., 1989; Hillman et al., 2016). However, when the helium accretion
rate is lower ($\leq~{}10^{-8}~{}\rm M_{\odot}$ yr-1), it is possible for a
helium ignition on the surface of the WD to trigger an inward shockwave which
leads to an explosion at the core of the WD hence a double detonation (Nomoto,
1982; Shen & Bildsten, 2009). If the detonation occurs on a carbon-oxygen WD,
it could produce a Type Ia supernova (SN Ia; Moll & Woosley 2013; Ruiter et
al. 2014; Piersanti et al. 2014). The study of helium accretion is therefore
important for validating or ruling out helium-donor and WD binary systems as
progenitors of SNe Ia.

In this paper, we present radio observations of the only spectroscopically
confirmed helium nova, V445 Puppis. The nova was discovered in eruption in
late November 2000 at an optical maximum of $V\approx 8.6$ mag (Kato et al.,
2000), substantially brighter than its $V\approx 14.5$ pre-eruption magnitude
(Ashok & Banerjee, 2003). The day of eruption for V445 Pup is unknown and only
constrained to be between 2000 September 26 and 2000 November 28 (Ashok &
Banerjee, 2001; Kato et al., 2000; Woudt et al., 2009). We adopt a $t_{0}$
from Woudt et al. 2009 of 2000 November 02 (MJD = 51850) as the time of
eruption. The nova was unusually rich in carbon and showed helium emission
lines, but lacked hydrogen lines (which are prominent in the spectra of
classical novae; Ashok & Banerjee 2003; Iijima & Nakanishi 2008; Woudt et al.
2009).

Within one month of the eruption, dust was detected from the nova using
infrared spectroscopy (Lynch et al., 2004). By $\sim$8 months after the nova
eruption, the optical brightness had dropped below pre-eruption levels (Ashok
& Banerjee, 2003; Woudt et al., 2009), attributed to a strong dust formation
episode. Six years following the eruption, the optical light had still not
returned to pre-eruption levels (Woudt et al., 2009), and the dust mass was
determined to be $>10^{-5}~{}\rm M_{\odot}$ (Shimamoto et al., 2017).

V445 Pup was spatially resolved using near-infrared adaptive optics imaging
with the Very Large Telescope (VLT), revealing an expanding bipolar shell
confined by an equatorial dust disc and with polar knots on both ends of the
bipolar ejecta (Woudt et al. 2009; see their Figure 2). Woudt et al. (2009)
determined a distance of $8.2~{}\pm~{}0.5~{}{\rm~{}kpc}$ to the nova using
expansion parallax techniques.

Presented in this paper are multifrequency observations of the nova obtained
in the years following eruption using the Very Large Array (VLA) radio
telescope. The radio data reveal an unprecedented, near decade-long,
synchrotron-powered radio light curve. In §2, we discuss the radio
observations and our data analysis procedure. In §3, we present the multi-
frequency radio light curve, radio spectral evolution, and spatially-resolved
radio imaging. In §4, we present the results, and in §5 we highlight our
conclusions.

##  2 Observations and data analysis

Radio observations of V445 Pup were obtained with a variety of VLA programs,
most of which were led by M. Rupen. The data were retrieved from the VLA
archive (see Table 1 for a log of the observations). The first radio
observations of V445 Pup were taken on 2001 January 18 and 30 ($t-t_{0}$ = 77
and 89 days). On day 77, the nova was not detected at 8.4 GHz (Rupen et al.,
2001), and there was a marginal detection on day 89. After day 89,
observations were paused until 2001 September 9 (day 312 day), when the nova
was strongly detected at 8.4 GHz (Rupen et al., 2001). V445 Pup was
subsequently observed with the VLA from September 2001 to March 2008 (between
day $312-2704$), resulting in a detailed radio light curve spanning almost a
decade following the eruption (Figure 1).

Observations were obtained in continuum mode, at different frequency bands
with two 50 MHz-wide frequency channels. The observations were conducted at L
(1.46 GHz), C (4.86 GHz), X (8.46 GHz), U (14.94 GHz), K (22.46 GHz) and Q
(43.34 GHz) bands, and are used to trace the nova emission throughout all of
the VLA’s configurations. The VLA A configuration provides the highest
resolution (synthesized beam FWHM of $2\arcsec$ at 1.5 GHz and $0.3\arcsec$ at
8.5 GHz), and has the potential to provide resolved images (see § 3.3). At
each frequency, observations of the target are obtained together with
observations of gain calibrators (see Table 2). The most common gain
calibrator used was 0804-278, for which we took the ICRS coordinates RA =
08h04m51.451s and Dec = $-27^{\circ}49^{\prime}11.32^{\prime\prime}$. We note
that a slightly different RA position was used by National Radio Astronomy
Observatory (NRAO) for this calibrator in 2001–2002 (RA = 08h04m51.440s); we,
therefore, shifted the data so that all observations take RA = 08h04m51.451s
(this is particularly relevant for our imaging results; §3.3). Flux density
calibrators 0137$+$331 (3C48), 0542$+$498 (3C147) or 1331$+$305 (3C286) were
observed to set the absolute flux density scale. Some observations were
obtained without a flux density calibrator; in most cases, we do not include
these observations in this work. For the ones included, we used a flux
calibrator of an adjacent epoch to set the flux density of the secondary
calibrator.

Table 1: Log of VLA observations of V445 Pup.

Observation | $t$ | $t-t_{0}$ | Configuration | Observation time on target (min)
---|---|---|---|---
Date | (MJD) | (Days) |  | 1.43 GHz | 4.86 GHz | 8.46 GHz | 14.94 GHz | 22.46 GHz | 43.34 GHz
2001 Jan 18 | 51927 | 77 | A | … | … | 3.7 | … | … | …
2001 Jan 30 | 51939 | 89 | A | … | … | 6.4 | … | … | …
2001 Sept 09 | 52162 | 312 | C | … | … | 6.7 | … | … | …
2001 Sept 11 | 52164 | 314 | C | 15.6 | 3.7 | … | 5.2 | 4.6 | 4.4
2001 Sept 12 | 52165 | 315 | C | 10.9 | 3.9 | 3.7 | 5.2 | 4.4 | …
2001 Sept 14 | 52167 | 317 | C | … | 4.1 | … | … | … | …
2001 Sept 15 | 52168 | 318 | C&D | … | 1.9 | 3.1 | … | … | …
2001 Sept 16 | 52169 | 319 | C&D | 5.2 | 6.9 | 6.9 | 4.9 | … | …
2001 Sept 17 | 52170 | 320 | C&D | 10.4 | 11.2 | … | 11.9 | … | …
2001 Sept 20 | 52173 | 323 | C&D | 3.7 | 4.2 | 4.2 | 4.2 | 4.2 | …
2001 Sept 25 | 52178 | 328 | C&D | … | 11.7 | 12.7 | 14.8 | … | …
2001 Sept 26 | 52179 | 329 | C&D | … | 3.2 | 4.7 | 6.2 | 6.2 | …

  * •

‘…’ indicates no observations for this epoch at that frequency. Here, $t_{0}$
is taken as 2000 November 02 (MJD = 51850). This table is continued in
Appendix C Table 5.

Table 2: Log of gain calibrators used at different configurations and
observing frequencies.

Observation |  | Gain calibrators |
---|---|---|---
Date range | Configuration | 1.43 GHz | 4.86 GHz | 8.46 GHz | 14.94 GHz | 22.46 GHz | 43.34 GHz |
2001 Jan 18–2001 Jan 30 | A | … | … | 0804-278 | … | … | … |
2001 Sep 09–2001 Sep 14 | C | 0738-304 | 0804-278 | 0804-278 | 0804-278 | 0804-278 | 0804-278 |
2001 Sep 15–2001 Oct 10 | C&D | 0735-175 | 0804-278 | 0804-278 | 0804-278 | 0804-278 | 0804-278 |
|  | 0806-268 | 0738-304 |  |  |  |  |
|  | 0706-231 |  |  |  |  |  |
2001 Oct 12– 2002 Jan 13 | D | 0706-231 | 0738-304, | 0804-278 | 0804-278 | 0804-278 | 0804-278 |
|  | 0806-268 | 0804-278 |  |  |  |  |
2002 Feb 07– 2002 Jun 07 | A, A&B | 0804-278 | 0804-278 | 0804-278 | 0804-278 | 0804-278 | … |
2002 Jun 17– 2002 Oct 31 | B | 0804-278 | 0804-278 | 0804-278 | … | … | 0804-278 |
2002 Dec 09– 2003 Jan 29 | C, C&D | … | 0804-278 | 0804-278 | … | … | … |
2003 Feb 06– 2003 Apr 18 | D | … | 0804-278 | 0804-278 | … | … | … |
2003 May 30– 2003 Oct 08 | A, A&B | 0735-175 | 0804-278 | 0804-278 | … | … | … |
|  | 0804-278 |  |  |  |  |  |
2003 Oct 21– 2004 Mar 02 | B, B&C | 0804-278 | 0804-278 | 0804-278 | 0804-278 | 0804-278 | 0804-278 |
2003 Mar 10– 2004 June 12 | C, C&D | 0738-304 | 0804-278 | 0804-278 | … | 0804-278 | … |
|  | 0706-231 |  |  |  |  |  |
2004 Jun 25– 2004 Aug 21 | D | … | 0804-278 | 0804-278 | 0804-278 | … | … |
2004 Sep 09– 2005 Feb 03 | A, A&B | … | 0804-278 | 0804-278 | 0804-278 | … | … |
2005 Feb 26– 2005 Jul 02 | B, B&C | 0804-278 | 0804-278 | 0804-278 | … | … | … |
2005 Jul 09– 2005 Oct 31 | C, C&D | … | 0804-278 | 0804-278 | … | 0804-278 | … |
2005 Nov 08– 2006 Jan 22 | D | … | 0738-304 | 0804-278 | … | … | … |
2006 Mar 15– 2006 May 10 | A | … | … | 0804-278 | … | … | … |
2006 Jun 25– 2006 Sep 11 | B | … | 0804-278 | 0804-278 | … | … | … |
2007 Sep 30–2008 Jan 17 | A&B, B | … | … | 0804-278 | … | … | … |
2007 Jan 23, 2008 Mar 28 | C&D, D | … | … | 0804-278 | … | … | … |

  * •

‘…’ indicates no observations at that date range and frequency.

All data were processed using the Common Astronomy Software Applications
(CASA; McMullin et al. 2007). The AOflagger algorithm (Offringa et al., 2012)
was used to flag data corrupted by radio frequency interference. Standard
calibration procedures were applied to each observation, and calibration
solutions were applied to the target data before imaging. Starting in 2006,
the VLA antennas were gradually upgraded to Jansky VLA capabilities, and we
therefore found baseline-based calibration solutions using the flux
calibrator.The CASA task clean was used for imaging, utilising Briggs
weighting with a robust value of 1. Self-calibration was not performed.

To measure the flux densities of V445 Pup, the CASA task imfit was used to fit
a Gaussian to the nova in each resulting image. In most measurements the width
of the Gaussian is allowed to vary, and the integrated flux density was
recorded. However, in cases of low signal-to-noise, the size of the Gaussian
was fixed to the size of the synthesized beam. The uncertainty in flux density
includes the error from the Gaussian fit added in quadrature with estimates of
the uncertainty on the absolute flux calibration (5$\%$ of the flux for 1–10
GHz and 10$\%$ of the flux for frequencies greater than 10 GHz). In epochs
where there is a non-detection, the task imstat was used to determine the
noise of the image. An upper limit on the flux density is determined as three
times the image rms plus the value of the pixel at the target location.

The flux densities of V445 Pup for each frequency band are given in Table 3;
the first ten epochs are presented in this manuscript and others are available
in the electronic materials.

##  3 Results

###  3.1 Radio light curves

Multi-frequency observations, spanning 1.5–43.3 GHz, reveal an unusual radio
light curve for the eruption of V445 Pup between 2001–2008 presented in Figure
1. The radio light curve shows four distinct flares throughout its evolution.

In the earliest radio observation following the eruption of V445 Pup, around
day 77, no radio emission was detected, with a 3$\sigma$ upper limit of 0.34
mJy at 8.4 GHz. However, on day 89, a 4$\sigma$ detection of 0.35 mJy was
obtained at 8.4 GHz. Unfortunately, following the day 89 detection there were
no radio observations of the nova until 312 days after eruption. As a result
of very limited coverage during the first 300 days after eruption, these early
points are not shown in Figure 1. On day 312, it became clear that V445 Pup
had brightened at radio frequencies since day 89 by a factor of $\sim 26$ to
9.4 mJy at 8.4 GHz. Over the next $\sim$3 months (see Figure 2), the light
curve shows flux densities declining from a radio maximum, which presumably
occurred before day 312.

Other flares are superimposed on the decline, like the steep peak on day 337
(at 4.9/8.5/14.9 GHz; Figure 2). Another flare peaked between days 450 to 460
(at 4.86/8.46/14.94 GHz bands). We note that, for the lowest frequency (1.43
GHz) light curve, these peaks occur later, at days 341 and 493 (Figure 2).

The radio peaks observed between day 300–700, indicated by vertical dashed
lines in Figure 2, have sharp, rapid rises and falls in flux density, compared
to the last broad peak which occurs between days 700 and 3000 (Figure 1).
Furthermore, the flux density at the peak of the last flare is a factor of
five fainter than the early-time peaks.

Table 3: Flux densities and spectral indices of V445 Pup

$t$ | $t-t_{0}$ | Radio flux densities (mJy) | $\alpha$
---|---|---|---
(MJD) | (Days) | 1.43 GHz | 4.86 GHz | 8.46 GHz | 14.94 GHz | 22.46 GHz | 43.34 GHz |
51927 | 77 | … | … |  $<$ 0.34 | … | … | … | …
51939 | 89 | … | … | 0.354 $\pm$ 0.064 | … | … | … | …
52162 | 312 | … | … | 9.39 $\pm$ 0.54 | … | … | … | …
52164 | 314 | 21.27 $\pm$ 1.22 | 12.66 $\pm$ 0.71 | … | 4.83 $\pm$ 0.82 | 3.71 $\pm$ 0.50 | 3.87 $\pm$ 1.03 | $-0.57~{}\pm~{}0.08$
52165 | 315 | 20.47 $\pm$ 1.24 | 11.59 $\pm$ 0.64 | 8.00 $\pm$ 0.54 | 5.96 $\pm$ 0.90 | 3.29 $\pm$ 0.72 | … | $-0.54~{}\pm~{}0.05$
52167 | 317 | … | 11.18 $\pm$ 0.62 | … | … | … | … | …
52168 | 318 | … | 9.99 $\pm$ 0.66 | 6.77 $\pm$ 0.45 | … | … | … | …
52169 | 319 | 18.86 $\pm$ 1.24 | 9.52 $\pm$ 0.55 | 5.74 $\pm$ 0.38 | 4.54 $\pm$ 0.57 | … | … | $-0.64~{}\pm~{}0.06$
52170 | 320 | 17.55 $\pm$ 1.26 | 9.30 $\pm$ 0.50 | 6.03 $\pm$ 0.41 | 4.48 $\pm$ 0.57 | 2.62 $\pm$ 0.62 | … | $-0.61~{}\pm~{}0.05$
52173 | 323 | 17.25 $\pm$ 1.07 | 9.07 $\pm$ 0.62 | 6.48 $\pm$ 0.76 | 4.90 $\pm$ 0.72 | 4.44 $\pm$ 0.79 | … | $-0.52~{}\pm~{}0.02$
52178 | 328 | 11.71 $\pm$ 0.82 | 8.44 $\pm$ 0.45 | 7.40 $\pm$ 0.39 | 5.46 $\pm$ 0.69 | … | … | $-0.28~{}\pm~{}0.03$
52179 | 329 | … | 8.89 $\pm$ 0.48 | 8.50 $\pm$ 0.46 | 6.58 $\pm$ 0.73 | 4.63 $\pm$ 0.64 | … | $-0.33~{}\pm~{}0.13$

  * •

‘…’ indicates no measurements for flux density for the epoch at that
frequency. This table is continued in Appendix C Table 9.

Figure 1: Top: Observed flux densities of V445 Pup spanning from day 300 to
day 2700 after the nova eruption. We take 2000 November 02 as the date of the
eruption ($t_{0}$). Bottom: spectral indices obtained by fitting a single
power-law to the data. The dashed line in the lower panel represents
$\alpha=-0.1$, the theoretically expected index of optically thin free-free
emission. Figure 2: Observed flux densities of V445 Pup spanning from day 300
to day 700 after the nova eruption. Data are the same as those plotted in
Figure 1, but zoomed in to show detail of the radio flares indicated with
vertical dashed lines.

The last recorded flux density of the nova with the VLA was 0.19 mJy at 8.46
GHz on 2008 March 29 (day 2704). On 2009 October 29 and December 29 (days 3283
and 3325 respectively), V445 Pup was observed using the Giant Metrewave Radio
Telescope (GMRT) at 1.28 GHz and 1.40 GHz (Kantharia, 2012). Radio emission
was present in the first GMRT observation, with a flux density $\sim 0.3\pm
0.08$ mJy. The second epoch yields a non-detection with a 3$\sigma$ upper
limit of 60 $\mathrm{\SIUnitSymbolMicro}$Jy (Kantharia, 2012).

###  3.2 Radio spectral evolution

We determine the spectral index for each observation ($\alpha$, defined as
$S_{\nu}~{}\propto~{}\nu^{\alpha}$, where $S_{\nu}$ is the flux density and
$\nu$ is the observing frequency), from the slope of the line fit to the data
in log-log scale. The python function curve-fit in the scipy package is used
to perform the least-squares fit. Detections separated by less than a day are
combined into one spectral index fit. Selected spectra are plotted in Figure
3, while the lower panel of Figure 1 shows how the spectral index varies with
time.

During the first decay of the radio flux density (days $\sim$312–400), the
spectrum has a form that rises steeply toward low frequencies and is well fit
with a single power law. For example, on day 314, $\alpha=-0.6$ (top left
panel of Figure 3), an indication of optically-thin synchrotron emission (see
§4.1 for more discussion). Sometimes the spectrum appears to flatten toward
low frequency (such as on day 337) and afterwards the spectrum switches back
to being well fit with a single power law (e.g., day 383)

On days 429 and 447, the spectrum becomes inverted and rises towards higher
frequencies, with $\alpha\approx 0.4$ (Figure 3), an indication of optically-
thick emission. On days 462 and 469, the radio spectrum is transitioning back
to an optically-thin state, exhibiting a combination of inverted/flat spectral
index at lower frequencies and steep spectral index at higher frequencies. By
day 493, the radio spectrum has returned to optically thin, hovering around
$\alpha\approx-0.5$. We discuss likely causes of these changes in the radio
spectrum in §4.3.

Figure 3: Selected VLA radio spectra of of V445 Pup, with linear fits
overplotted. The time after eruption (since 2000 November 2) and the value of
the spectral index is given for each spectrum. The data points marked with red
stars represent flux densities in L-band (1.4 GHz) or C-band (4.9 GHz) which
are relatively flat and thus not included in the fit.

(a)  (b)

Figure 4: High-resolution images of V445 Pup observed at radio (left) and
near-infrared (right) wavelengths. The red circles are the positions of the
two Gaussian components fit to the 2004 Oct–Nov A configuration data in the uv
plane, and have diameters of $0.12^{\prime\prime}$. The left panel shows our
8.4 GHz image representing the average of data obtained between 2004 Sep 23
and 2004 Nov 29 (days 1402–1488). The ellipse in the bottom left corner shows
the FWHM extent of the synthesized beam ($0.48^{\prime\prime}\times
0.23^{\prime\prime}$, PA= $165^{\circ}$). The right panel shows a near-IR
K-band image obtained on 2005 Mar 26 (day 1605), with the same positions of
the radio counterparts marked as red circles. In these images, north is up and
east is to the left; and the fields-of-view are matched to be
$2.4^{\prime\prime}\times 1.7^{\prime\prime}$. The grey scale is linear in
both cases.

###  3.3 Radio Images

In its most extended A configuration, the VLA achieves angular resolution
sufficient to constrain the morphology of radio emission from V445 Pup. The
dates of these high-resolution observations are listed in Table 4, along with
a brief description of the resulting images and the central position of the
emission region (more details below). We fit the morphology of V445 Pup in the
uv-plane, using the UVFIT task in AIPS (Greisen, 2003a) and Difmap (Shepherd
et al., 1994; Shepherd, 1997a).

Table 4: High-Resolution A-configuration observations of V445 Pup. Observation | $t-t_{0}$ | Description | RA (J2000.0) | Dec (J2000.0)
---|---|---|---|---
Date Range | (Days) |  | (07h37m56.XXXs) | ($-25^{\circ}56^{\prime}58^{\prime\prime}.$XX)
2001 Jan 18–Jan 30 | 77–89 | Marginally detected | – | –
2002 Feb 7–May 15 | 462–559 | Unresolved, FWHM $<0.1^{\prime\prime}$ | $.885\pm.001$ | $.86\pm.01$
2003 May 17–Sep 19 | 926–1051 | Marginally resolved, $0.3^{\prime\prime}\times<0.1^{\prime\prime}$ | $.880\pm.001$ | $.85\pm.02$
2004 Sep 23–2005 Jan 6 | 1408–1526 | Two components separated by $0.2^{\prime\prime}$ | NE: $.890\pm.002$ | $.80\pm.03$
|  |  | SW: $.875\pm.002$ | $.88\pm.03$
2006 Feb 9–May 10 | 1925–2015 | One component, $0.3^{\prime\prime}\times<0.2^{\prime\prime}$ | $.883\pm.002$ | $.85\pm.04$
2007 Jul 15–Jul 28 | 2446–2459 | Marginally detected | – | –

The VLA was in A configuration during the first observations of V445 Pup in
2001 Jan. They yielded a non-detection (Jan 17, $t-t_{0}~{}=~{}77$ days) and a
marginal detection (Jan 30, $t-t_{0}~{}=~{}89$ days). The S/N was not
sufficient to constrain the morphology of V445 Pup at this time.

During the 2002 A configuration (462–559 days after eruption), V445 Pup was
radio bright. At 8.4 GHz, it is unresolved; model fitting with an elliptical
Gaussian in the uv plane implies FWHM $<0.1^{\prime\prime}$.

During the 2003 A configuration (926–1051 days after eruption), V445 Pup is
marginally resolved. We model the 8.4 GHz data in the uv plane with an
elliptical Gaussian with a major axis of $0.25^{\prime\prime}\pm
0.04^{\prime\prime}$, unresolved minor axis ($<0.1^{\prime\prime}$), and
position angle of $92^{\circ}\pm 14^{\circ}$ (degrees east from north).
Subtracting this Gaussian in the uv plane and imaging the residuals, there is
some structure remaining which implies that the source is not fully described
as a single Gaussian. The central position of the 2003 emission is near the
2002 position, although not consistent within the formal errors (Table 4).
Inspection of the images implies that they likely share a common position, but
the more complex morphology of the 2003 image leads to a slight apparent
offset.

During the first months of the 2004 A configuration (1408–1488 days after
eruption), V445 Pup is resolved into two distinct regions of emission that are
roughly aligned with the major axis of the 2003 elliptical Gaussian fit. In
the 8.4 GHz observations, the structure of V445 Pup can be fit with two
circular Gaussian components separated by $0.22^{\prime\prime}\pm
0.02^{\prime\prime}$. No significant motion of the components could be seen
over $\sim$4 months of observations. The north-eastern (NE) component’s ICRS
coordinates are RA = 7h37m56.890s, Dec =
$-25^{\circ}56^{\prime}58.80^{\prime\prime}$, and the coordinates of the
south-western (SW) component are RA = 7h37m56.875s, Dec =
$-25^{\circ}56^{\prime}58.88^{\prime\prime}$. The components themselves are
marginally resolved, with the NE component’s FWHM $=0.16^{\prime\prime}\pm
0.05^{\prime\prime}$ and the SW component measured to have a FWHM
$=0.12^{\prime\prime}\pm 0.03^{\prime\prime}$. The 2004 components are located
on either side of the radio emission imaged in 2002/2003, consistent with them
moving away from this origin position. The two 2004 components are similar in
brightness, with flux densities of $0.7\pm 0.1$ mJy (NE) and $0.5\pm 0.1$ mJy
(SW). The NE component gradually fades while the SW component gradually
brightens and remains the only visible component by the end of 2004.

Figure 4 compares a VLA image produced by stacking the 8.4 GHz observations
obtained during the 2004 A configuration with the near-IR high-resolution
image, obtained by Woudt et al. (2009) on 2005 Mar 26 using the NAOS/CONICA
adaptive optics system of the VLT. To make the near-IR K-band image, we
downloaded several K-band exposures from the European Southern Observatory
(ESO) Science Archive Facility (request #543179), stacked them to remove
cosmic rays and artifacts, and applied a world coordinate system (WCS) using
six stars in the image with _Gaia_ Data Release 2 (DR2) positions (estimated
error on our WCS is $0.02^{\prime\prime}$). The near-IR K-band emission is a
composite of emission lines from warm gas (e.g., He i) and warm dust continuum
emission (Woudt et al., 2009).

From Figure 4, it is clear that the radio emission is emanating from the same
bipolar regions of the V445 Pup ejecta that are dominating the near-IR
emission. The two images were obtained around the same time (day $\sim$1445 at
8.4 GHz, and day 1605 at near-IR K-band), and to first order, the two radio
components are aligned with the peaks of the near-IR emission. Woudt et al.
(2009) show that the thermal ejecta expand with a range of velocities in the
polar (NE–SW) direction, while expansion in the equatorial plane is confined
by a dense dust disc. It is the ejecta nearest to the dust disc that is
densest and brightest in the near-IR—and also in radio emission.

We estimate the velocity at which the radio components are traveling apart
from one another, assuming they were expelled on $t_{0}=51850$ MJD and V445
Pup is at a distance of 8.2 kpc. In convenient units, where $V$ is the
expansion velocity in km s-1 (assumed to be symmetric from a central
location), $d$ is in kpc, $t$ is in units of 100 days, and $\theta$ is the
angular separation in arcsec:

$V=8,660\ {\rm km\ s^{-1}}\ \left(\frac{d}{\rm kpc}\right)\
\left(\frac{\theta}{\rm arcsec}\right)\ \left(\frac{\rm 100\ days}{t}\right)$
(1)

The component separation of $0.22^{\prime\prime}$ on day 1445 implies that the
blobs were expanding at 1080 km s-1. If we estimate that both components have
FWHM of $0.12^{\prime\prime}$, then the outer portions of the blobs would be
separated by $0.34^{\prime\prime}$, implying expansion velocities of 1670 km
s-1. Given these expansion velocities, it is not surprising that we do not
observe significant motion during the 2004 A configuration; between 1408 and
1526 days after eruption, we would only expect the two components to move by
$0.02-0.03^{\prime\prime}$—substantially less than our observational errors
(Table 4). The velocities of 1000–2000 km s-1 implied by the radio imaging are
faster than the velocities of the P Cygni absorption troughs observed in
optical spectroscopy a few months after eruption (Iijima & Nakanishi, 2008),
but are slower than the fastest expanding ejecta imaged in the near-IR by
Woudt et al. (2009).

We note that the high-velocity infrared “knots" pointed out at the extremities
of the bipolar V445 Pup nebula by Woudt et al. (2009)111They are not visible
in the K-band image presented in Figure 4; this may be because we did not
stack all the exposures from 2005 Mar 26, and so our image is shallower than
the one published by (Woudt et al., 2009). We also did not deconvolve the
K-band image as done by Woudt et al., seen to expand at a remarkable 8,450 km
s-1, would have been easily resolved in our radio images if they were radio
bright. The high-velocity knots are not detected in our 2004 A configuration
radio image—a clear demonstration that they are not the source of the bulk of
the radio emission $\sim$1500 days after eruption. Woudt et al. (2009)
estimate that the high-velocity knots were ejected 345 days after $t_{0}$ (a
few months before the 2002 A configuration imaging campaign). If the high-
velocity knots had been radio-emitting during our 2003 A configuration
campaign, they would have been separated by $\sim 0.7-0.8^{\prime\prime}$,
easily resolvable with our high-resolution radio images. We therefore conclude
that it is not the fastest-expanding material in V445 Pup that is dominating
the radio emission at any time. Instead, our radio images imply that it is the
densest material that is the site of the radio synchrotron emission.

In the 2006 A configuration (day 1925–2015), V445 Pup has substantially faded,
and its morphology has reverted to a similar structure as in 2003 (as best we
can tell, given the relatively low S/N). We averaged in the uv-plane all 8.4
GHz data obtained in this A configuration, and found the data can be well-
described by a single elliptical Gaussian with a major axis of
$0.32^{\prime\prime}\pm 0.08^{\prime\prime}$, unresolved minor axis ($\lesssim
0.2^{\prime\prime}$), and position angle of $68^{\circ}\pm 42^{\circ}$
(degrees east from north). The center of this emission region is consistent
with the position of the 2003 emission; it is located between the 2004
components.

By the time of the 2007 A configuration, V445 Pup had faded too much for its
morphology to be constrained by our VLA images.

##  4 Discussion

###  4.1 Radio Emission from V445 Pup is Synchrotron-Dominated

Historically, radio emission from hydrogen-rich classical novae was thought to
be dominated by thermal free-free radiation from expanding ionized ejecta
(Seaquist & Palimaka, 1977; Hjellming et al., 1979; Seaquist & Bode, 2008). At
early times, while the radio luminosity is increasing, the radio-emitting
region is optically thick. As the ejecta expand and drop in density, the radio
light curve peaks and turns over, as the radio photosphere recedes through the
ejecta and the radio emission transitions to an optically thin state. During
the optically thick phase of a thermal-dominated radio light curve, the
spectral index $\alpha$ is expected to be equal to 2, as for blackbody
emission in the Rayleigh-Jeans long-wavelength limit. When the emitting region
is optically thin, the spectral index is flat ($\alpha=-0.1$), as expected for
bremsstrahlung emission (e.g. § 6.2 in Pacholczyk, 1970). The radio light
curve rise, peak, and decay occur on timescales of months to years—much slower
than the evolution of optical light curves of novae.

The other possible source of nova radio emission is synchrotron radiation. The
spectral index for optically thin synchrotron emission is set by the energy
spectrum of relativistic electrons; if the number of relativistic electrons
per unit energy is $N(E)\propto E^{-p}$, then the spectral index is
$\alpha=(1-p)/2$. For classic diffusive shock acceleration of relativistic
particles, $p=2-2.5$, and so $\alpha=-0.5$ to $-0.75$ (Bell, 1978; Blandford &
Ostriker, 1978). Indeed, $\alpha\approx-0.7$ is commonly observed in
synchrotron-emitting SNe and SN remnants. (Chevalier, 1982; Weiler et al.,
2002). However, several novae that are strong candidates for synchrotron
emitters have unusually shallow spectral indices of $\alpha\approx-0.1$ to
$-0.5$ (Taylor et al., 1987; Eyres et al., 2009; Weston et al., 2016a; Finzell
et al., 2018). This could imply shallower energy spectra for relativistic
electrons in novae (compared to e.g., SNe), or that the synchrotron emitting
region is inhomogeneous in terms of particle density and magnetic field
strength (Vlasov et al., 2016). Optical depth effects could also flatten the
spectrum; in the jets of active galactic nuclei, partially self-absorbed
synchrotron emission routinely produces flat or inverted spectra of the “radio
core”, while the more extended transparent regions of the jet display the
usual steep spectrum with $\alpha=-0.7$ (Eckart et al., 1986; Blandford et
al., 2019).

The radio spectra of V445 Pup from $\sim$1–4.5 years after optical discovery
generally show higher flux densities at lower frequencies (Figure 3; with the
exception of a few epochs which appear optically thick because of their
inverted spectra). Spectral indices of V445 Pup are in the range
$\alpha\approx 0$ to $-1$ (Figure 1). In the first three years of V445 Pup’s
evolution, its radio spectral index hovers around $\alpha=-0.5$: slightly
shallower than that observed for SNe, but well within expectations of
synchrotron emission (especially when taking into account the relatively
shallow spectral indices observed for other synchrotron-emitting novae). After
day $\sim$1000, the spectral index flattens to $\alpha\approx-0.2$.

To further constrain the radio emission mechanism, we determine the brightness
temperature ($T_{b}$; a parameterization of surface brightness). Nova ejecta
typically have temperatures $\sim 10^{4}$ K, as a direct result of the
photoionization of the ejecta by the central hot white dwarf (Cunningham et
al., 2015). We therefore expect the brightness temperature to be $\sim 10^{4}$
K for a nova in the optically-thick thermal phase of its radio evolution. As
thermal radio emission transitions to optically thin, the brightness
temperature is expected to drop well below $10^{4}$ K (Weston et al., 2016a;
Finzell et al., 2018). Synchrotron emission, on the other hand, can reach much
higher brightness temperatures, up to $\sim 10^{11}$ K (Readhead, 1994).
Therefore, if the nova’s radio brightness temperature is substantially in
excess of $10^{4}$ K, this is a promising indication that it is emitting non-
thermal radiation.

To estimate the brightness temperature, we must constrain the angular diameter
of the object ($\theta$) and measure its flux density ($S_{\nu}$). We can then
calculate the brightness temperature using the formula:

$\frac{T_{b}}{\rm K}=1.36\times\bigg{(}\frac{\lambda}{\rm
cm}\bigg{)}^{2}\times\bigg{(}\frac{S_{\nu}}{\rm
mJy}\bigg{)}\times\bigg{(}\frac{\theta_{a}\theta_{b}}{\rm
arcsec^{2}}\bigg{)}^{-1}$ (2)

where $\lambda$ is the observing wavelength, $\theta_{a}$ is the major axis
diameter, and $\theta_{b}$ is the minor axis diameter. We can estimate
$\theta$ if we know the speed at which the nova ejecta are expanding ($V$;
equation 1) as a function of time ($t$; Seaquist & Bode 2008). We take $t$ as
the time since $t_{0}$ and estimate the expansion velocity $V=1600$ km s-1
along the major axis and $V<800$ km s-1 along the minor axis (inferred from
radio imaging; §3.3). We use the observed flux densities at 1.43 GHz (21 cm),
which place the strongest constraints on the brightness temperature (compared
to higher frequencies).

As seen in Figure 5, the brightness temperature of V445 Pup starts high, $\sim
10^{7}$ K on day $\sim 300$, implying that it is undeniably synchrotron
emission. The brightness temperature declines with time, to $\sim 10^{5}$ K by
day $\sim 600$, and finally to $\sim 10^{4}$ K by day $\sim 2,000$. Despite a
relatively low (for synchrotron emission) brightness temperature of few
$\times 10^{4}$ K after $\sim 1000$ days, we conclude that this emission is
non-thermal, since the spectral index implies that the emission is optically-
thin. If the emission were optically-thin thermal, its brightness temperature
should be substantially lower than the $\sim 10^{4}$ K electron temperature.
Therefore, we conclude that the radio light curve of V445 Pup is dominated by
synchrotron emission over $\sim$7 years of its evolution.

Figure 5: Surface brightness temperature for V445 Pup between 2001 September
and 2006 April.

###  4.2 What powers the synchrotron-emitting shocks in V445 Pup?

The general consensus is that the source of synchrotron emission in novae is
due to acceleration of particles to relativistic speeds in shocks. Depending
on the nature of the companion star, these shocks can be either external with
pre-existing circumbinary material or internal within the ejecta. Which is it
for V445 Pup?

The clearest examples of synchrotron emission in hydrogen-rich classical novae
come from embedded novae with red giant companions, where external shocks are
produced in the interaction of the nova ejecta and the red giant wind.
Examples of this type of synchrotron-emitting shocks are RS Oph (O’Brien et
al., 2006; Rupen et al., 2008; Sokoloski et al., 2008; Eyres et al., 2009),
V745 Sco (Kantharia et al., 2016), and V1535 Sco (Linford et al., 2017). In
these cases, the radio light curve evolves relatively quickly (over
$\sim$weeks), and can be used to trace the radial density profile of the
circumbinary material. A late-time thermal radio component is not observed in
most cases, indicating that the ejecta are low mass (as expected for the
relatively high accretion rates driven by red giant companions; e.g., Yaron et
al. 2005).

Another way to produce synchrotron emission could be internal shocks within
the ejecta. These type of shocks likely dominate in a white dwarf system whose
companion is a main sequence star, and hence the binary system is surrounded
by less dense circumbinary material. Such shocks form at the interface of two
outflows moving at different speeds, following a nova eruption. For decades
there has been evidence of internal shocks in hydrogen-rich classical novae,
based on hard X-ray emission (O’Brien et al., 1994; Mukai & Ishida, 2001;
Mukai et al., 2008), and more recently, GeV $\gamma$-ray emission (Ackermann
et al., 2014; Franckowiak et al., 2018; Martin et al., 2018). It has also
recently been recognized that a significant fraction of these novae show
evidence of non-thermal radio emission, manifesting as early bright radio
flares. Novae showing evidence of synchrotron emission from internal shocks
include QU Vul (Taylor et al., 1987), V959 Mon (Chomiuk et al., 2014), V1723
Aql (Weston et al., 2016a), V5589 Sgr (Weston et al., 2016b), and V1324 Sco
(Finzell et al., 2018). These flares rise rapidly with time
($\sim$days–weeks), in contrast to expectations for expanding thermal ejecta
(rise time $\approx$ months), and have brightness temperatures $\gtrsim
10^{5}-10^{6}$ K. In most cases, a second radio maximum becomes visible at
late times which is well-described as expanding thermally emitting ejecta.

Is V445 Pup’s radio synchrotron emission driven by external or internal
shocks? We know little about the companion star due to dust obscuration (Ashok
& Banerjee, 2003; Woudt et al., 2009), so it is difficult to predict the
properties of the circumbinary material surrounding V445 Pup. We can rule out
external shocks with relatively spherically-distributed circumbinary material,
based on our radio imaging (§3.3). If the pre-existing material was
isotropically distributed, we would expect the synchrotron emission to be
brightest at the fastest shocks (see Equation 3), and so to be easily
resolvable (as, e.g., the near-IR high-velocity knots; Woudt et al. 2009).
Instead, the radio emission is confined to much nearer the binary.

Based on radio imaging of V959 Mon, Chomiuk et al. (2014) hypothesize that at
the beginning of a nova eruption, a slow outflow concentrated in the
equatorial plane of the binary system is generated. A more isotropic fast wind
then follows, primarily escaping in the polar directions. The collision
between the two distinct flows results in shocks and particle acceleration.
Based on near-infrared and radio imaging in the years following the 2000
eruption, V445 Pup exhibits a similar bipolar outflow and an equatorial disc
(Woudt et al., 2009). Our radio imaging reveals that the synchrotron emission
is concentrated near the equatorial plane, even 3–5 years after explosion
(§3.3, Figure 4). We also know that the equatorial disc maintains its
structure for years following the eruption (Woudt et al., 2009). Therefore,
interactions between a polar flow and equatorial disc, as proposed for V959
Mon, are the most likely source of the synchrotron emission.

The origin of the equatorial disc, however, is unclear. It may have pre-dated
the nova eruption, as mass lost in a previous nova eruption, or from the
binary during quiescence (perhaps from the outer Lagrange points during mass
transfer; e.g., Pejcha et al. 2016a). Indeed, from pre-eruption photometry,
Woudt et al. (2009) deduced substantial circumbinary dust around V445 Pup in
quiescence. The very strong IR signatures of dust early in the eruption led
Lynch et al. (2001) to surmise that the dust may have pre-dated the eruption,
a conclusion also reached by Shimamoto et al. (2017) when they measured very
large dust masses ($\sim 5\times 10^{-4}$ M⊙) around V445 Pup in 2006. On the
other hand, in at least the case of V959 Mon, an equatorial disc-like
structure was ejected during the nova eruption itself (Chomiuk et al., 2014;
Linford et al., 2015). It is hypothesized that the equatorial structure was
produced by the puffed-up nova envelope, marginally bound to the binary
shortly after thermonuclear runaway (Chomiuk et al., 2014). As the binary
orbited inside the envelope, it transferred energy to help the envelope
expand, preferentially in the equatorial direction (i.e., Pejcha et al.
2016b). It is worth noting that, unlike in V959 Mon, the equatorial disc is
not observed to expand or diffuse during the eruption of V445 Pup; it remains
present in imaging until at least 2015, and significant dust obscuration
persists around the binary up until the present day (Woudt et al. 2021, in
prep). This relative constancy of the equatorial disc over $\sim$ two decades
may suggest a pre-eruption origin.

###  4.3 Understanding the synchrotron-dominated light curve of V445 Pup

The radio synchrotron emission from V445 Pup persists for an unprecedentedly
long time ($\sim$7 years; Figure 1). Synchrotron emission in other novae lasts
for just a few weeks–months (Eyres et al., 2009; Weston et al., 2016a, b;
Kantharia et al., 2016; Linford et al., 2017). One relatively simple way to
explain the long synchrotron duration of V445 Pup would be if a wind was
launched from the binary and continued blowing for years after eruption, while
the equatorial disc retained its structure over this time. Then ongoing
interactions between the wind and the disc would continue to power synchrotron
luminosity. The standard mechanism for driving prolonged winds in novae is
radiation pressure from an $\sim$Eddington luminosity white dwarf, powered by
nuclear burning on the white dwarf’s surface (Kato & Hachisu, 1994). While
$\sim$7 years is relatively long for this sustained burning phase, it is not
unprecedented amongst hydrogen-rich classical novae (Henze et al., 2014). The
larger envelope masses in helium novae lead to expectations of longer
durations for the sustained burning phase in systems like V445 Pup ($\sim$few
yr – 10,000 yr; Kato & Hachisu 2004). Therefore, a wind prolonged over $\sim$7
years seems reasonable. Unfortunately, we are not able to directly test if a
wind in V445 Pup was powered by the nuclear-burning white dwarf, as no X-ray
observations of the eruption are available, and the dusty equatorial disc
would likely have absorbed the white dwarf supersoft X-ray emission.

To explain the synchrotron emission from V445 Pup, we consider a cartoon model
where the white dwarf wind impacts upon the equatorial disc (we assume the
disc is not expanding, as it has appeared largely unchanged in imaging over
$\sim$15 years post eruption; Woudt et al. 2009, Woudt et al. 2021, in prep.).
We approximate that the wind expands at 1600 $\rm km~{}s^{-1}$, based on our
radio imaging (§3.3), noting that this is the measured velocity in the polar
(NE-SW) direction. We take a scenario where a wind of this velocity emanates
from the white dwarf isotropically, but is decelerated in the equatorial
direction by the disc, creating shocks, accelerating particles, and producing
the observed synchrotron emission. We use a simple prescription for
synchrotron luminosity, as described in Appendix A and largely taken from
Chevalier (1982, 1998). We assume a fraction of the post-shock energy density
is transferred to energy density of the amplified magnetic field
($U_{B}=\epsilon_{B}\rho_{\rm disc}v_{\rm w}^{2}$) and of relativistic
electrons ($U_{e}=\epsilon_{e}\rho_{\rm disc}v_{\rm w}^{2}$). Here $\rho_{\rm
disc}$ is the density of the pre-shock material and $v_{\rm w}$ is the
velocity of the wind, $\epsilon_{B}$ and $\epsilon_{e}$ represent the fraction
of the post-shock energy due to amplified magnetic fields and the relativistic
electrons, respectively. We note that this is likely an oversimplification if
the wind significantly decelerates in the equatorial direction, implying that
a reverse shock contributes to the shock luminosity (Metzger et al., 2014). A
thorough treatment of V445 Pup’s shocks and resultant synchrotron luminosity
requires a multi-dimensional hydrodynamics simulation, so our goal here is
only to draw a simple cartoon. When the synchrotron emission is optically
thin, its luminosity ($L_{\nu}$) is proportional to the synchrotron-emitting
volume $V_{\rm synch}\times U_{e}\times U_{B}^{(p+1)/4}$. For V445 Pup, the
index of the relativistic electron energy spectrum is measured to be $p\approx
2$ (§4.1); therefore

$L_{\nu}\propto V_{\rm synch}\,\epsilon_{e}\,\epsilon_{B}^{3/4}\,\rho_{\rm
disc}^{7/4}\,v_{\rm w}^{7/2}$ (3)

As described in Appendix A, the synchrotron luminosity of V445 Pup can be
explained if $\rho_{\rm disc}\approx 10^{4}$ cm-3.

Higher synchrotron luminosities imply faster shocks and/or higher densities
for interaction. Therefore, the variations in synchrotron luminosity observed
in V445 Pup’s light curve imply variations in the wind velocity or density of
the equatorial disc—or in the optical depth. Synchrotron-dominated light
curves of radio transients often show an optically-thick rise, where the flux
increases as $\tau$ drops, and an optically-thin decline, usually interpreted
as a decline in the density of material being shocked and/or a decline in the
shock velocity (e.g., Weiler et al., 2002). V445 Pup is unusual in showing
multiple peaks in its light curve (although see the embedded nova V1535 Sco
for a similar albeit less dramatic case; Linford et al. 2017).

These flares are accompanied by changes in the optical depth. While most of
the time the synchrotron emission appears optically thin (flux density
monotonically rising toward lower frequency or $\alpha<0$), on the rise to
radio peaks, the radio spectrum flips to be brighter at higher frequencies
(Figures 1 and 3). Between days 429 and 447 (on the rise to the brightest
flare observed, peaking on day $\sim$460), the flux density increases with
frequency all the way up to 22.5 GHz, implying $\alpha=0.2$ to 0.4. On days
337–341 (rising to a slightly fainter peak on day $\sim$340), the 1.4 GHz
point falls substantially below the power law fit to higher-frequencies,
implying that absorption is present but milder than on day 429. In both cases,
the radio spectrum returns to optically thin at the peak of the radio flare,
and thereafter. The observed cyclic change in the radio spectrum of V445
Pup—starting with optically thin emission, then becoming optically-thick, then
thin, and then thick and thin again—is unusual and challenging to explain
(although again, similar sudden, cyclic changes of $\alpha$ are seen in V1535
Sco; Linford et al. 2017). With a few rough calculations, we can exclude the
possibility that the optical depth is due to synchrotron self-absorption
(Appendix B). The optical depth is therefore due to free-free absorption, and
changes in opacity mean that the ionization state of the absorbing material
must be changing. The spectrum never reaches the canonical $\alpha=2$ for
free-free absorption, implying that the emission is only partially optically
thick—perhaps because the $\tau\approx 1$ photospheres shrink with frequency
as expected in a stellar wind (Panagia & Felli, 1975; Wright & Barlow, 1975)
or because the covering factor of the absorbing screen is substantially
smaller than unity (e.g., Diaz et al., 2018).

So, what might explain the observed radio flares, and attending changes in
free-free opacity? One possibility is that the white dwarf wind is sweeping
through the inner parts of the equatorial disc, and encountering density
enhancements within it. This would imply that there are at least four regions
of enhanced density in the disc, to explain the flares on day $<$300 (we only
captured its decline), day 340, day 460, and day $\sim$1300 (Figure 1).
Simulations of equatorial discs produced by mass loss from the outer
Lagrangian points of a mass-transferring binary often find structured discs
with spiral-like density enhancements (Pejcha et al., 2016a, b). The flux of
V445 Pup rose by a factor of $\sim$10 (from 2 mJy to 22 mJy at 4.9 GHz)
between day 430 and 460. According to Equation 3, this would imply an increase
in density of a factor of $\sim$4 to explain this flare.

This interpretation is supported by the rapid declines of the radio flares,
which we parameterize as $S_{\nu}~{}\propto~{}t^{\beta}$; the value of $\beta$
can give hints on the source of the synchrotron emission. Harris et al. (2016)
performed hydrodynamic simulations of a shock interacting with “shells" of
enhanced density. During impact with a shell, the energy densities in
relativistic electrons and magnetic fields increase dramatically, and
therefore the radio light curve will peak. However, as the shock propagates to
the outer side of the shell, there is no more material to sweep up, particle
acceleration ceases, and the energy densities in relativistic electrons and
magnetic fields rapidly drop as expected for adiabatic expansion. At this
point the radio light curves decline rapidly as
$L_{\nu}~{}\propto~{}t^{-11.5~{}\rm to~{}-9}$ based on their simulations and
analytical relations. Considering the declines from the radio flares on days
337 and 462 (see Figure 2), $\beta$ is in the range
$-10\lessapprox\beta\lessapprox-9$, consistent with the shell-interaction
simulations.

The other possibility is that the velocity of the wind is variable with time,
and synchrotron flares are produced when it is faster. To produce a factor of
ten increase in synchrotron luminosity requires a factor of $\sim$2 increase
in the wind velocity, according to Equation 3. Other nova eruptions have been
observed to host multiple outflows with a range of velocities, seen in optical
spectra as new absorption features and broadening emission lines (e.g., Jack
et al., 2017; Aydi et al., 2019). Aydi et al. (2020) observed rapid changes in
$\gamma$-ray flux and shock luminosity over the first $\sim$40 days of V906
Car’s 2018 nova eruption, and attributed this to changes in outflow velocity
with support from optical spectroscopy. However, the flares observed in V906
Car, and indeed most hydrogen-rich novae, occur over substantially shorter
periods than the $\sim$few years covered by our V445 Pup radio light curve.
Perhaps helium nova eruptions evolve more slowly due to their likely larger
envelope masses. However, this is difficult to test, as there was essentially
no spectroscopic monitoring of V445 Pup during the time window 1–3 years after
explosion, due to very heavy dust obscuration (Ashok & Banerjee, 2003; Lynch
et al., 2004; Iijima & Nakanishi, 2008), and so it is difficult to constrain
if or how the wind velocity changed during this time.

In either case—whether it is variations in density or velocity that produce
the radio flares—the likely cause of the changes in optical depth is changes
in shock luminosity. If much of this shock luminosity is radiated in the
ultraviolet band, it can ionize portions of the equatorial disc ahead of it.
The higher the shock luminosity, the more ionized material there will be, and
the stronger the free-free absorption. The free-free absorption later
dissipates, either because this material recombines or because it is swept up
by the shock. We prefer the latter explanation, because if the disc material
has a density $\sim 10^{4}$ cm-3 (Appendix A), the recombination time should
be of order a century (Ferland, 2003): much longer than the $\sim$200 day
duration of the radio flare.

###  4.4 Is V445 Pup a SN Ia progenitor system?

As the only helium nova known, V445 Pup is often singled out as an intriguing
candidate for a progenitor system to SNe Ia (e.g., Li et al. 2011; McCully et
al. 2014; Kelly et al. 2014). The progenitors of SNe Ia have been constrained
with radio continuum observations, where the synchrotron-emitting blast wave
formalism of Chevalier and collaborators (i.e., Appendix A) is used to place
limits on the density and distribution of circumstellar material near the SN
site (e.g., Panagia et al., 2006; Chomiuk et al., 2016; Lundqvist et al.,
2020). Tested configurations of circumstellar material are usually over-
simplistic, with smooth density profiles and spherical symmetry. Therefore
interpretations of radio limits for SNe Ia have substantial associated
uncertainty.

The fact that V445 Pup’s radio light curve is synchrotron dominated and
powered by interaction with an equatorial disc that likely pre-dated the nova
eruption presents a unique opportunity to predict what a radio light curve of
a realistic SN Ia might look like. We had originally hoped that we could
simply “scale up" from nova ejecta energetics to SN ejecta energetics to
predict how a SN exploding in a V445 Pup-like progenitor system would appear
at radio wavelengths. However, there are two problems with this strategy.
First, the synchrotron emission in V445 Pup was likely produced by a prolonged
wind that continued to blow and interact with the disc for years—very
different from the impulsive yet homologous explosions of SNe. Second, while
the equatorial disc apparently withstood the nova eruption of V445 Pup, it is
not clear if it would be destroyed by SN Ia ejecta—and on what timescale.

In the future, hydrodynamic simulations should model the V445 Pup wind/disc
system and work to constrain the mass loss rate of the white dwarf wind and
the density profile of the equatorial disc, using our radio light curve as a
critical constraint on the dynamics. This would inform the ejecta mass and
energetics of the only helium nova known, and also recreate the circumstellar
environment of one of the most promising SN Ia progenitor systems. Once the
mass, extent, and morphology of the equatorial disc are better constrained,
another hydrodynamic simulation could model the interaction of a SN Ia-like
explosion with the disc, and make real predictions for observable signatures
at radio, optical, and X-ray wavelengths that might indicate a V445 Pup-like
progenitor (see Booth et al. 2016 for a similar strategy implemented on
another SN Ia progenitor candidate, RS Oph).

##  5 Conclusions

The helium nova V445 Pup is observed at radio frequencies for years following
its eruption in late 2000 (Figure 1). Steep spectral indices and high
brightness temperatures imply that the radio light curve is powered by
synchrotron emission through 2008; we see no evidence of thermal emission from
an expanding ionized nova remnant, as seen in many other novae at radio
wavelengths. The radio light curve is characterised by at least four re-
brightening events, which sometimes are subject to free-free absorption on the
rise but revert back to optically-thin synchrotron emission as they fade.
Spatially-resolved radio images show that the synchrotron emission is more
compact than the thermal ejecta and is confined near the equatorial disc
imaged at near IR wavelengths (Figure 4).

We hypothesise that a wind from the white dwarf interacts with the equatorial
disc, giving rise to shocks, particle acceleration, and synchrotron emission.
This model is very similar to the scenario proposed to explain radio
synchrotron and GeV $\gamma$-ray emission in hydrogen-rich classical nova V959
Mon, also based on radio imaging (Chomiuk et al., 2014). However, the data
presented here on V445 Pup present the clearest case to date of synchrotron
emission being associated with a dense equatorial disc in a nova. We note
that, based on its high synchrotron luminosity and detection of $\gamma$-rays
in other novae (Ackermann et al., 2014; Franckowiak et al., 2018), V445 Pup
was likely a source of substantial GeV $\gamma$-rays, but unfortunately its
eruption occurred between the _Compton Gamma-Ray Observatory_ and _Fermi
Gamma-Ray Space Telescope_ missions.

The duration of bright synchrotron emission from V445 Pup ($\sim$7 years) is
unprecedented amongst novae. In our model, this implies that the equatorial
disc must have maintained its structure throughout these years (a hypothesis
directly supported by near IR imaging of V445 Pup; Woudt et al. 2009). In
addition, the wind from the white dwarf must have persisted over these years,
which is not surprising if the wind is powered by radiation pressure from
sustained burning of helium on the white dwarf’s surface (Kato & Hachisu,
2004). The re-brightening events in the radio light curve could be produced by
changes in wind velocity or density enhancements encountered in the disc, as
it is swept up by the wind. Similar fluctuations in shock luminosity have been
seen in GeV $\gamma$-rays—albeit over shorter timescales—in the 2018 nova V906
Car (Aydi et al., 2020).

## Acknowledgements

The authors are grateful to Dr. Chelsea E. Harris and Dr. Ken J. Shen for
useful discussions. They also thank Prof. Michael Rupen, Dr. Amy Mioduszewski
and Dr. Vivek Dhawan for their work in obtaining the VLA observations
presented here. The National Radio Astronomy Observatory is a facility of the
National Science Foundation operated under cooperative agreement by Associated
Universities, Inc.

This research was supported by the South African Radio Astronomy Observatory,
which is a facility of the National Research Foundation (NRF), an agency of
the Department of Science and Innovation. MMN and PAW kindly acknowledge
financial support from the University of Cape Town and the NRF. V.A.R.M.R.
acknowledges financial support from the Fundação para a Ciência e a Tecnologia
(FCT) in the form of an exploratory project of reference
IF/00498/2015/CP1302/CT0001, FCT and the Ministério da Ciência, Tecnologia e
Ensino Superior (MCTES) through national funds and when applicable co-funded
EU funds under the project UIDB/EEA/50008/2020, and supported by Enabling
Green E-science for the Square Kilometre Array Research Infrastructure
(ENGAGE-SKA), POCI-01-0145-FEDER-022217, and PHOBOS,
POCI-01-0145-FEDER-029932, funded by Programa Operacional Competitividade e
Internacionalização (COMPETE 2020) and FCT, Portugal. L.C. and K.V.S.
acknowledge financial support of NSF awards NSF AST-1751874 & AST-1907790,
NASA grants _Fermi_ /80NSSC18K1746 & _NuSTAR_ /80NSSC19K0522, and a Cottrell
fellowship of the Research Corporation. J.S. acknowledges support from the
Packard Foundation.

Software: CASA (McMullin et al., 2007), AIPS (Greisen, 2003b), difmap
(Shepherd, 1997b), SciPy (Oliphant, 2007), Numpy (van der Walt et al., 2011),
matplotlib (Hunter, 2007).

## DATA AVAILABILITY

The data presented in this work are available through the VLA archive which
can be accessed via https://archive.nrao.edu/archive/advquery.jsp.

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##  Appendix A Simple Model for Synchrotron Emission from Novae

Chevalier (1982) developed a simple formalism for interpreting synchrotron
emission from stellar explosions. The model was developed for application to
SNe, where the ejecta blast wave crashes into pre-existing circumstellar
material. The shock between the ejecta and the circumstellar material
accelerates particles to relativistic speeds (through diffusive shock
acceleration; e.g., Blandford & Ostriker 1978; Bell 1978) and amplifies the
magnetic field (through the streaming instability; e.g., Bell 2004). The
relativistic electrons gyrate along the magnetic field lines to give rise to
synchrotron emission. Here we give a few more details of how this model might
be applied to V445 Pup.

The magnetic field strength in the synchrotron-emitting region is simply
$B=\sqrt{8\pi U_{B}}$. The energy density of relativistic electrons is spread
between electrons with a power-law distribution of energies,
$dN(E)=N_{0}E^{-p}dE$ where $N_{0}$ is a constant, and we assume a minimum
energy of relativistic electrons equivalent to the rest mass energy of the
electron (Chevalier, 1998). We take $p=2.1$, as measured from the spectrum of
V445 Pup (§4.1), noting that some of the equations in Chevalier (1998) are not
defined for $p=2.0$.

To convert from a magnetic field strength to physical parameters of the
system, we assume a fraction of the post-shock energy density ($\rho_{\rm
disc}v_{\rm w}^{2}$) is converted into amplified magnetic fields and
relativistic electrons (as described in §4.3). In supernova synchrotron
models, conversion factors of $\epsilon_{e}=\epsilon_{B}=0.1$ are often
assumed (e.g. Chevalier & Fransson, 2006; Chomiuk et al., 2012; Cendes et al.,
2020). However, recent considerations imply that $\epsilon_{B}$ could be much
lower ($\lesssim$0.01, Kundu et al. 2017; Lundqvist et al. 2020), and
$\epsilon_{e}$ may also be lower at slower shock velocities (e.g.,
Sarbadhicary et al., 2017). To roughly estimate the density of material
surrounding V445 Pup, we take $\epsilon_{e}=\epsilon_{B}=0.01$.

We estimate $V_{\rm synch}\approx 10^{47}$ cm-3, as for a shell that has been
expanding for 460 days at 1600 km s-1, with a thickness of 10%. If we take a
relatively modest flux density for V445 Pup around this time of 3 mJy at an
intermediate frequency of 8.4 GHz (consistent with measurements both before
and after the day 460 radio flare), this implies that the shock is interacting
with material of density, $\sim$3000 cm-3. Given that this interaction is
probably with the equatorial disc, our estimate of a spherical $V_{\rm synch}$
is over-simplistic. The implied density will increase as the volume filling
factor of the synchrotron-emitting material decreases.

##  Appendix B Synchrotron Self Absorption in V445 Pup?

Could synchrotron self-absorption be the cause of the opacity on the rise to
the radio peaks? We can use the flux density at radio peak on day $\sim$460,
combined with a few other rough estimates of system parameters, to estimate
the opacity due to synchrotron self-absorption ($\tau_{\rm SSA}$). If
synchrotron self-absorption is the dominant source of opacity, we would expect
$\tau_{\rm SSA}\approx 1$ at radio peak.

Using the same assumptions described in Appendix A, but instead taking a flux
of 12 mJy, we estimate $B=0.01$ G. We can then plug these quantities into the
equation for synchrotron self-absorption optical depth (Equation 1 of
Chevalier 1998), and find that $\tau_{\rm SSA}\approx 10^{-8}$ at the peak of
the day 460 radio flare. As $\tau_{\rm SSA}$ is eight orders of magnitude
smaller than unity, we conclude synchrotron self-absorption is not the
dominant source of opacity. We note that for $\tau_{\rm SSA}\approx 1$, the
emitting volume would need to be $V_{\rm synch}\approx 10^{38}$ cm-3, a factor
of a billion smaller than our estimate in Appendix A—but the emitting region
is directly constrained by our radio imaging (§3.3), and exclude this
possibility.

##  Appendix C VLA observations of V445 Pup, measured flux densities and
spectral indices

Table 5: Log of VLA observations of V445 Pup.

Observation | $t$ | $t-t_{0}$ | Configuration | Observation time on target (min)
---|---|---|---|---
Date | (MJD) | (Days) |  | 1.43 GHz | 4.86 GHz | 8.46 GHz | 14.94 GHz | 22.46 GHz | 43.34 GHz
2001 Oct 04 | 52187 | 337 | C&D | 8.9 | 6.7 | 6.7 | 6.7 | 6.7 | 6.2
2001 Oct 08 | 52191 | 341 | C&D | 3.1 | 4.7 | 4.7 | 3.7 | 5.2 | 5.4
2001 Oct 10 | 52193 | 343 | C&D | 3.6 | 4.2 | 4.2 | 5.1 | 5.2 | 5.6
2001 Oct 12 | 52195 | 345 | D | 2.6 | 4.1 | 4.2 | 5.1 | 5.2 | 5.6
2001 Oct 14 | 52197 | 347 | D | 4.4 | 4.2 | 4.2 | 5.7 | 6.9 | 6.4
2001 Oct 17 | 52200 | 350 | D | 10.2 | 4.2 | 4.2 | 6.2 | 7.6 | …
2001 Oct 22 | 52204 | 354 | D | 2.9 | 2.7 | 2.4 | 5.2 | … | 4.7
2001 Oct 24 | 52207 | 357 | D | 4.9 | 2.7 | 2.8 | 6.9 | 7.6 | …
2001 Oct 26 | 52209 | 359 | D | 5.4 | 5.7 | 7.4 | 7.7 | 7.6 | …
2001 Oct 27 | 52210 | 360 | D | 7.3 | 5.6 | 7.4 | 7.7 | 7.7 | …
2001 Oct 29 | 52212 | 362 | D | 4.4 | 4.7 | 4.7 | 6.9 | 7.4 | …
2001 Nov 02 | 52216 | 366 | D | 7.6 | 8.4 | 8.6 | 7.6 | 7.7 | …
2001 Nov 04 | 52218 | 368 | D | 7.8 | 8.4 | 24.6 | 9.2 | … | …
2001 Nov 06 | 52220 | 370 | D | 5.9 | 5.3 | 5.2 | 6.2 | … | …
2001 Nov 07 | 52221 | 371 | D | 5.9 | 4.7 | 4.2 | 5.8 | 6.6 | …
2001 Nov 11 | 52224 | 374 | D | 6.1 | … | 4.2 | 5.3 | 6.2 | 5.7
2001 Nov 14 | 52227 | 377 | D | … | 3.9 | 3.7 | … | … | …
2001 Nov 15 | 52229 | 379 | D | 4.1 | 4.2 | 2.2 | 5.1 | … | …
2001 Nov 16 | 52230 | 380 | D | … | 5.2 | 4.9 | 6.2 | 6.9 | …
2001 Nov 18 | 52231 | 381 | D | 4.2 | 5.1 | 3.1 | 6.2 | 6.9 | …
2001 Nov 20 | 52233 | 383 | D | 4.6 | 4.2 | 4.2 | 6.0 | 6.9 | 6.2
2001 Nov 23 | 52236 | 386 | D | … | 4.9 | … | … | … | …
2001 Nov 24 | 52237 | 387 | D | … | 4.4 | 5.1 | 5.7 | 7.1 | …
2001 Nov 26 | 52240 | 390 | D | 8.1 | 4.2 | … | 6.4 | … | …
2001 Nov 29 | 52242 | 392 | D | 5.1 | 5.1 | 5.4 | 6.1 | 7.1 | …
2001 Dec 07 | 52250 | 400 | D | 8.2 | 4.2 | 4.2 | 6.2 | … | …
2001 Dec 09 | 52252 | 402 | D | … | … | 5.2 | 6.2 | … | …
2001 Dec 31 | 52274 | 424 | D | 5.3 | 4.2 | 4.1 | 6.2 | … | …
2002 Jan 05 | 52279 | 429 | D | 7.6 | 4.2 | 4.1 | 6.1 | 6.7 | 6.2
2002 Jan 12 | 52286 | 436 | D | … | 4.1 | 4.2 | 4.7 | … | …
2002 Jan 13 | 52287 | 437 | D | … | 4.1 | … | 5.6 | … | …
2002 Jan 23 | 52297 | 447 | A | 6.4 | 5.9 | 7.6 | 10.6 | … | …
2002 Feb 07 | 52312 | 462 | A | 4.2 | 3.2 | 9.1 | 4.7 | … | …
2002 Feb 14 | 52319 | 469 | A | 1.9 | 4.6 | 10.9 | 4.7 | … | …
2002 Feb 21 | 52326 | 476 | A | 4.1 | 2.3 | 6.2 | 4.7 | … | …
2002 Mar 01 | 52334 | 484 | A | 3.9 | 3.1 | 7.6 | 3.7 | … | …
2002 Mar 06 | 52339 | 489 | A | … | … | 4.7 | … | … | …
2002 Mar 10 | 52343 | 493 | A | 4.6 | 4.6 | 9.1 | 3.7 | 4.2 | …
2002 Mar 18 | 52351 | 501 | A | 2.6 | 3.2 | 4.6 | 3.2 | 3.2 | …
2002 Apr 03 | 52367 | 517 | A | 3.2 | 5.2 | 6.1 | 3.6 | 3.2 | …
2002 Apr 21 | 52385 | 535 | A | 3.2 | 5.2 | 6.1 | … | … | …
2002 Apr 29 | 52393 | 543 | A | 6.6 | 5.2 | 15.3 | 5.9 | … | …
2002 May 04 | 52398 | 548 | A | 6.1 | 5.2 | … | 6.1 | … | …
2002 May 17 | 52412 | 562 | A&B | 3.3 | 4.2 | … | … | … | …
2002 May 26 | 52421 | 571 | A&B | 3.2 | 3.1 | … | … | … | …
2002 Jun 07 | 52433 | 583 | A&B | 4.0 | 3.2 | … | … | … | …
2002 Jun 17 | 52443 | 593 | B | 3.6 | 3.2 | … | … | … | …
2002 Jun 25 | 52451 | 601 | B | 3.4 | 3.2 | 3.1 | .. | … | …
2002 Jul 05 | 52461 | 611 | B | 3.4 | 3.2 | 3.1 | … | … | …
2002 Jul 19 | 52475 | 625 | B | … | … | 16.3 | … | … | …
2002 Jul 27 | 52483 | 633 | B | 4.1 | 3.2 | 4.7 | … | … | …
2002 Aug 17 | 52504 | 654 | B | 4.72 | 6.2 | 10.6 | … | … | …
2002 Aug 30 | 52517 | 667 | B | 10.6 | 14.0 | 13.6 | … | … | …
2002 Sep 01 | 52519 | 669 | B | 6.6 | 8.1 | 7.9 | … | … | …
2002 Oct 04 | 52552 | 702 | B | … | 7.1 | 7.6 | … | … | …
2002 Oct 28 | 52575 | 725 | B | 4.9 | 4.1 | 4.2 | … | … | …
2002 Oct 31 | 52579 | 729 | B | … | … | 4.1 | … | … | 4.7
2002 Dec 09 | 52617 | 767 | C | … | 8.2 | 8.4 | … | … | …
2002 Dec 21 | 52629 | 779 | C | … | 6.2 | 6.1 | … | … | …
2002 Dec 29 | 52637 | 787 | C | … | 6.1 | 6.1 | … | … | …
2003 Jan 03 | 52642 | 792 | C | … | 8.1 | 8.1 | … | … | …
2003 Jan 06 | 52645 | 795 | C | … | 8.1 | 8.2 | … | … | …
2003 Jan 08 | 52647 | 797 | C | … | 8.1 | 8.2 | … | … | …

  * •

‘…’ indicates no observations for this epoch at that frequency

Table 6: continued

Log of VLA observations of V445 Pup.  Observation $t$ $t-t_{0}$ Configuration
Observation time on target (min) Date (MJD) (Days) 1.43 GHz 4.86 GHz 8.46 GHz
14.94 GHz 22.46 GHz 43.34 GHz 2003 Jan 14 52653 803 C … 9.2 9.2 … … … 2003 Jan
20 52659 809 C … 9.1 9.1 … … … 2003 Jan 29 52668 818 C … 9.7 9.0 … … … 2003
Feb 06 52676 826 D 8.6 9.7 9.1 … … … 2003 Feb 23 52693 843 D … 9.7 9.1 … … …
2003 Mar 04 52702 852 D … 10.4 9.9 … … … 2003 Mar 11 52709 859 D … 10.3 12.2 …
… … 2003 Mar 13 52711 861 D … 16.4 22.1 … … … 2003 Mar 19 52717 867 D … 10.4
9.2 … … … 2003 Mar 26 52724 874 D … 10.6 9.2 … … … 2003 Apr 18 52748 898 D …
15.9 12.2 … … … 2003 May 30 52790 940 A 8.8 6.9 6.2 … … … 2003 Jun 04 52795
945 A 8.6 7.0 … … … … 2003 Jun 16 52807 957 A 8.8 7.7 … … … … 2003 Jun 30
52821 971 A 8.9 7.7 … … … … 2003 Jul 18 52839 989 A … … 15.2 … … … 2003 Jul 21
52842 992 A … 15.2 … … … … 2003 Jul 25 52846 996 A … 16.2 … … … … 2003 Jul 31
52856 1002 A … … 9.6 … … … 2003 Aug 11 52863 1013 A 8.6 9.2 11.1 … … … 2003
Aug 25 52877 1027 A 6.9 9.1 10.7 … … … 2003 Sep 03 52886 1036 A 7.3 9.1 18.2 …
… … 2003 Sep 11 52894 1044 A 10.9 10.1 22.4 … … … 2003 Sep 19 52902 1052 A
10.9 … 24.4 … … … 2003 Sep 52905 1055 A 8.6 8.1 10.7 … … … 2003 Sep 27 52910
1060 A&B 10.8 10.1 … … … … 2003 Sep 29 52912 1062 A&B … 10.6 11.6 … … … 2003
Oct 08 52921 1071 A& B … 12.2 … … … … 2003 Oct 21 52934 1084 B … 10.2 14.2 … …
… 2003 Nov 02 52946 1096 B … 8.2 8.3 … 003 Nov 09 52953 1103 B … 8.7 18.4 … …
… 2003 Nov 18 52962 1112 B … … 14.4 … … … 2003 Nov 24 52967 1117 B … 8.7 10.2
… … … 2003 Dec 15 52988 1138 B 5.9 9.1 12.2 … … … 2003 Dec 28 53001 1151 B 5.9
9.1 12.2 … … … 2004 Jan 03 53007 1157 B 5.1 9.1 12.2 … … … 2004 Jan 08 53012
1162 B 5.7 9.2 11.7 … … … 2004 Jan 14 53018 1168 B … 9.2 11.5 … … … 2004 Jan
23 53027 1177 B&C … 6.2 6.4 … … … 2004 Feb 01 53036 1186 B&C 5.9 6.2 6.2 2004
Feb 02 53037 1187 B&C … … 4.1 10.3 10.2 10.7 2004 Feb 12 53047 1197 B&C … 4.2
4.1 … 9.0 10.7 2004 Feb 24 53059 1209 B&C … 4.2 4.1 … 11.9 … 2004 Mar 02 53066
1216 B&C … 4.2 4.1 … 12.3 … 2004 Mar 10 53074 1224 C … 57.4 … … … … 2004 Mar
20 53084 1234 C … 4.2 8.1 … … … 2004 Mar 22 53086 1236 C … … 6.2 … … … 2004
Apr 01 53096 1246 C … … 8.2 … … … 2004 Apr 07 53102 1252 C … 4.2 8.1 … 13.6 …
2004 Apr 15 53111 1261 C … 4.2 4.8 … … … 2004 May 03 53129 1279 C … 5.2 8.1 …
… … 2004 May 10 53136 1286 C 10.6 10.6 9.9 … … … 2004 May 17 53143 1293 C& D
10.6 8.9 10.1 … … … 2004 May 22 53147 1297 C& D 7.4 … … … … … 2004 May 30
53156 1306 C& D 6.8 5.2 5.1 … … … 2004 Jun 12 53169 1319 C& D 6.0 8.9 10.1 … …
… 2004 Jun 25 53182 1332 D … 8.9 10.1 … … … 2004 Jul 01 53188 1338 D … 8.6
10.1 … … … 2004 Jul 10 53197 1347 D … … 10.1 20.4 … … 2004 Jul 17 53204 1354 D
… 8.9 10.1 19.2 … … 2004 Jul 23 53210 1360 D … 8.6 6.9 …. … … 2004 Aug 07
53225 1375 D … 8.9 10.1 12.7 … … 2004 Aug 21 53239 1389 D … 9.2 10.2 10.2 … …

  * •

‘…’ indicates no observations for this epoch at that frequency

Table 7: continued

Log of VLA observations of V445 Pup.  Observation $t$ $t-t_{0}$ Configuration
Observation time on target (min) Date (MJD) (Days) 1.43 GHz 4.86 GHz 8.46 GHz
14.94 GHz 22.46 GHz 43.34 GHz 2004 Sep 09 53258 1408 A … 9.2 10.2 10.2 … …
2004 Sep 23 53272 1422 A … 8.6 12.2 … … … 2004 Oct 01 53280 1430 A … … 18.2 …
… … 2004 Oct 08 53287 1437 A … … 17.4 … … … 2004 Oct 16 53295 1445 A … … 15.2
… … … 2004 Oct 31 53310 1460 A … 9.1 9.2 … … … 2004 Nov 03 53312 1462 A … 8.2
18.2 … … … 2004 Nov 07 53317 1467 A … … 14.1 … … … 2004 Nov 12 53321 1471 A …
… 21.1 … … … 2004 Nov 20 53329 1479 A … … 20.8 … … … 2004 Nov 29 53338 1488 A
… … 21.2 … … … 2004 Dec 22 53361 1511 A … … 14.6 … … … 2004 Dec 31 53370 1520
A … … 15.2 … … … 2005 Jan 06 53376 1526 A … … 13.6 … … … 2005 Jan 16 53386
1536 A& B … … 10.2 … … … 2005 Jan 24 53394 1544 A& B … … 8.6 … … … 2005 Jan 29
53399 1549 A& B … 12.1 11.8 … … … 2005 Feb 03 53404 1554 A& B … … 7.1 … … …
2005 Feb 26 53427 1577 B … 8.6 9.2 … … … 2005 Mar 13 53442 1592 B 8.9 8.1 10.3
… … … 2005 Mar 20 53449 1599 B 8.8 8.1 10.4 … … … 2005 Mar 25 53454 1604 B 8.9
8.1 10.2 … … … 2005 Apr 04 53464 1614 B … 37.7 … … … … 2005 Apr 14 53475 1625
B … 6.6 8.2 … … … 2005 Apr 26 53486 1636 B … 6.4 9.1 … … … 2005 May 06 53497
1647 B … 5.2 9.0 … … … 2005 May 14 53504 1654 B … 5.1 10.2 … … … 2005 May 29
53520 1670 B … 22.4 … … … … 2005 Jun 03 53525 1675 B … 19.9 … … … … 2005 Jun
12 53534 1684 B&C … … 10.7 … … … 2005 Jun 18 53540 1690 B&C … … 15.4 … … …
2005 Jun 23 53545 1695 B&C … 13.1 12.2 … … … 2005 Jul 02 53554 1704 B&C 11.4
13.1 12.2 … … … 2005 Jul 09 53561 1711 C … … 4.2 … … … 2005 Jul 14 53566 1716
C … 10.9 … … … … 2005 Jul 23 53575 1725 C … 10.1 14.2 … … … 2005 Aug 02 53585
1735 C … … 17.2 … … … 2005 Aug 06 53589 1739 C … … 6.2 … … … 2005 Aug 27 53610
1760 C … 20.2 12.2 … … … 2005 Sep 05 53619 1769 C … 20.4 16.7 … … … 2005 Sep
25 53639 1789 C … 22.2 … … … … 2005 Sep 27 53641 1791 C … 12.2 18.2 … … … 2005
Oct 01 53645 1795 C … 20.4 16.7 … … … 2005 Oct 05 53649 1799 C&D … … 14.4 … …
… 2005 Oct 16 53660 1810 C&D … … 10.4 … 18.7 … 2005 Oct 23 53666 1816 C&D …
61.6 14.2 … … … 2005 Oct 31 53675 1825 C&D … … 18.4 … … … 2005 Nov 08 53683
1833 D … 9.1 9.2 … … … 2005 Nov 15 53690 1840 D … … 9.2 … … … 2005 Nov 21
53696 1846 D … … 21.2 … … … 2005 Nov 29 53703 1853 D … … 17.4 … … … 2005 Dec
01 53705 1855 D … 13.2 15.6 … … … 2005 Dec 11 53715 1865 D … 13.1 15.6 … … …
2005 Dec 20 53724 1874 D … 13.1 15.2 … … … 2006 Jan 13 53748 1898 D … … 14.9 …
… … 2006 Jan 15 53750 1900 D … … 18.2 … … … 2006 Jan 22 53757 1907 D … 9.2 … …
… … 2006 Feb 09 53775 1925 A … … 16.2 … … … 2006 Mar 15 53809 1959 A 9.6 …
12.2 … … … 2006 Mar 22 53816 1966 A 9.5 … … … … … 2006 April 07 53832 1982 A
8.9 … … … … … 2006 May 08 53863 2013 A … … 20.2 … … … 2006 May 10 53865 2015 A
… … 14.2 … … …

  * •

‘…’ indicates no observations for this epoch at that frequency

Table 8: continued

Log of VLA observations of V445 Pup.  Observation $t$ $t-t_{0}$ Configuration
Observation time on target (min) Date (MJD) (Days) 1.43 GHz 4.86 GHz 8.46 GHz
14.94 GHz 22.46 GHz 43.34 GHz 2006 Aug 05 53953 2103 B … … 24.6 … … … 2006 Aug
09 53957 2107 B … 24.4 … … … … 2006 Aug 31 53979 2129 B … 20.6 … … … … 2006
Sep 11 53990 2140 B … 38.3 … … … … 2007 Jan 23 54123 2273 C&D … … 29.3 … … …
2007 Sep 30 54374 2524 A&B … … 36.0 … … … 2008 Jan 17 54482 2632 B … … 28.0 …
… … 2008 Mar 28 54554 2704 C … … 10.4 … … …

  * •

‘…’ indicates no observations for this epoch at that frequency

Table 9: Flux densities and spectral indices of V445 Pup

$t$ | $t-t_{0}$ | Radio flux densities (mJy) | $\alpha$
---|---|---|---
(MJD) | (Days) | 1.43 GHz | 4.86 GHz | 8.46 GHz | 14.94 GHz | 22.46 GHz | 43.34 GHz |
52187 | 337 | 12.62 $\pm$ 0.67 | 13.85 $\pm$ 0.71 | 12.01 $\pm$ 0.62 | 8.69 $\pm$ 0.91 | 5.98 $\pm$ 0.88 | 5.10 $\pm$ 1.21 | $-0.46~{}\pm~{}0.08$
52191 | 341 | 14.26 $\pm$ 0.76 | 14.01 $\pm$ 0.73 | 11.33 $\pm$ 0.60 | 7.54 $\pm$ 1.17 | 8.61 $\pm$ 1.26 | 4.30 $\pm$ 1.18 | $-0.43~{}\pm~{}0.07$
52193 | 343 | 13.54 $\pm$ 0.80 | 12.48 $\pm$ 0.66 | 9.29 $\pm$ 0.52 | 7.27 $\pm$ 0.88 | 5.13 $\pm$ 1.05 | 2.49 $\pm$ 0.78 | $-0.58~{}\pm~{}0.06$
52195 | 345 | 12.15 $\pm$ 0.85 | 11.46 $\pm$ 0.63 | 8.67 $\pm$ 0.49 | 5.83 $\pm$ 0.71 | 5.66 $\pm$ 0.75 | 7.00 $\pm$ 1.22 | $-0.24~{}\pm~{}0.07$
52197 | 347 | 14.75 $\pm$ 1.21 | 10.4 $\pm$ 0.57 | 7.64 $\pm$ 0.42 | 7.93 $\pm$ 0.87 | 7.79 $\pm$ 0.92 | 7.21 $\pm$ 1.16 | $-0.25~{}\pm~{}0.06$
52200 | 350 | 13.96 $\pm$ 1.18 | 8.81 $\pm$ 0.50 | 8.45 $\pm$ 0.46 | 8.31 $\pm$ 0.91 | 7.36 $\pm$ 1.0 | … | $-0.23~{}\pm~{}0.06$
52204 | 354 | 10.30 $\pm$ 1.31 | 8.83 $\pm$ 0.79 | 7.56 $\pm$ 0.46 | 5.82 $\pm$ 0.66 | … | 3.14 $\pm$ 0.86 | $-0.27~{}\pm~{}0.07$
52207 | 357 | 10.20 $\pm$ 0.93 | 7.37 $\pm$ 0.41 | 7.30 $\pm$ 0.44 | 6.18 $\pm$ 0.68 | 4.2 $\pm$ 0.57 | … | $-0.24~{}\pm~{}0.02$
52209 | 359 | 12.5 $\pm$ 1.18 | 8.2 $\pm$ 0.44 | 7.17 $\pm$ 0.37 | 5.69 $\pm$ 0.60 | 5.64 $\pm$ 0.72 | … | $-0.30~{}\pm~{}0.02$
52210 | 360 | 9.42 $\pm$ 0.84 | 7.23 $\pm$ 0.40 | 6.72 $\pm$ 0.36 | 4.52 $\pm$ 0.58 | 3.71 $\pm$ 0.69 | … | $-0.26~{}\pm~{}0.07$
52212 | 362 | 8.42 $\pm$ 0.45 | 7.52 $\pm$ 0.41 | 6.62 $\pm$ 0.38 | 4.30 $\pm$ 0.51 | 3.94 $\pm$ 0.72 | … | $-0.20~{}\pm~{}0.07$
52216 | 366 | 8.14 $\pm$ 0.44 | 6.99 $\pm$ 0.37 | 5.29 $\pm$ 0.30 | 3.62 $\pm$ 0.50 | 1.89 $\pm$ 0.41 | … | $-0.65~{}\pm~{}0.13$
52218 | 368 | 8.29 $\pm$ 0.42 | 6.33 $\pm$ 0.35 | 4.75 $\pm$ 0.25 | 3.95 $\pm$ 0.52 | … | … | $-0.30~{}\pm~{}0.05$
52220 | 370 | 10.26 $\pm$ 0.61 | 5.66 $\pm$ 0.35 | 4.28 $\pm$ 0.26 | 3.16 $\pm$ 0.49 | … | … | $-0.49~{}\pm~{}0.01$
52221 | 371 | 8.56 $\pm$ 0.45 | 5.52 $\pm$ 0.33 | 4.28 $\pm$ 0.26 | 3.51 $\pm$ 0.40 | 2.53 $\pm$ 0.54 | … | $-0.39~{}\pm~{}0.02$
52224 | 374 | 8.39 $\pm$ 0.42 | … | 4.48 $\pm$ 0.28 | 4.57 $\pm$ 0.65 | 2.96 $\pm$ 0.77 | 2.89 $\pm$ 0.477 | $-0.32~{}\pm~{}0.03$
52227 | 377 |  | … | 4.81 $\pm$ 0.037 | 4.29 $\pm$ 0.29 | … | … | …
52229 | 379 | 6.79 $\pm$ 0.93 | 4.68 $\pm$ 0.29 | 4.71 $\pm$ 0.35 | 4.89 $\pm$ 0.83 | … | … | $-0.15~{}\pm~{}0.09$
52230 | 380 | … | 4.5 $\pm$ 0.28 | 5.01 $\pm$ 0.29 | 4.80 $\pm$ 0.60 | 3.72 $\pm$ 0.64 | … | $-0.22~{}\pm~{}0.13$
52231 | 381 | 5.61 $\pm$ 0.81 | 4.81 $\pm$ 0.30 | 5.25 $\pm$ 0.29 | 4.38 $\pm$ 0.54 | 3.88 $\pm$ 0.59 | … | $-0.10~{}\pm~{}0.06$
52233 | 383 | 9.99 $\pm$ 0.58 | 5.10 $\pm$ 0.33 | 4.66 $\pm$ 0.26 | 3.65 $\pm$ 0.47 | 3.15 $\pm$ 0.48 | 2.14 $\pm$ 0.63 | $-0.43~{}\pm~{}0.04$
52236 | 386 | … | 4.95 $\pm$ 0.41 | … | … | … | … | …
52237 | 387 | … | 4.49 $\pm$ 0.33 | 4.01 $\pm$ 0.26 | 3.15 $\pm$ 0.44 | 2.39 $\pm$ 0.52 | … | $-0.34~{}\pm~{}0.08$
52240 | 390 | 6.39 $\pm$ 0.37 | 4.51 $\pm$ 0.32 | … | 2.35 $\pm$ 0.51 | … | … | $-0.33~{}\pm~{}0.08$
52242 | 392 | 12.38 $\pm$ 1.08 | 4.10 $\pm$ 0.29 | 3.46 $\pm$ 0.20 | 2.30 $\pm$ 0.33 | 2.59 $\pm$ 0.72 | … | $-0.43~{}\pm~{}0.03$
52250 | 400 | 4.91 $\pm$ 0.47 | 3.30 $\pm$ 0.30 | 2.49 $\pm$ 0.26 | 1.97 $\pm$ 0.47 | … | … | $-0.38~{}\pm~{}0.03$
52252 | 402 | … | … | 2.16 $\pm$ 0.22 | 2 .30 $\pm$ 0.40 | … | … | …
52274 | 424 | 5.03 $\pm$ 0.27 | 2.02 $\pm$ 0.23 | 1.71 $\pm$ 0.18 | 3.09 $\pm$ 0.71 | … | … | $-0.54~{}\pm~{}0.16$
52279 | 429 | 6.31 $\pm$ 0.57 | 2.02 $\pm$ 0.17 | 2.65 $\pm$ 0.19 | 3.12 $\pm$ 0.42 | 3.77 $\pm$ 0.57 | 3.20 $\pm$ 1.15 | 0.36 $\pm$ 0.06
52286 | 436 | … | 3.91 $\pm$ 0.33 | 4.67 $\pm$ 0.33 | 4.36 $\pm$ 0.78 | … | … | 0.19 $\pm$ 0.15
52287 | 437 | … | 3.61 $\pm$ 0.30 | … | 2.80 $\pm$ 0.62 | … | … | …
52297 | 447 | 4.46 $\pm$ 0.29 | 4.93 $\pm$ 0.31 | 9.38 $\pm$ 0.52 | 14.01 $\pm$ 1.52 | … | … | 0.44 $\pm$ 0.18
52312 | 462 | 6.91 $\pm$ 0.36 | 21.92 $\pm$ 1.12 | 17.68 $\pm$ 0.89 | 11.39 $\pm$ 1.30 | … | … | $-0.51~{}\pm~{}0.13$
52319 | 469 | 11.49 $\pm$ 0.63 | 15.53 $\pm$ 0.83 | 13.02 $\pm$ 0.67 | 4.35 $\pm$ 0.95 | … | … | $-0.54~{}\pm~{}0.44$
52326 | 476 | 16.27 $\pm$ 0.83 | 14.09 $\pm$ 0.74 | 10.38 $\pm$ 0.54 | 6.46 $\pm$ 1.04 | … | … | $-0.26~{}\pm~{}0.09$
52334 | 484 | 17.91 $\pm$ 1.12 | 13.34 $\pm$ 0.82 | 9.23 $\pm$ 0.50 | 6.02 $\pm$ 0.91 | … | … | $-0.39~{}\pm~{}0.08$
52339 | 489 | … | … | 8.53 $\pm$ 0.57 | … | … | … | …
52343 | 493 | 18.65 $\pm$ 0.95 | 11.48 $\pm$ 0.63 | 8.44 $\pm$ 0.45 | 4.73 $\pm$ 0.60 | 3.39 $\pm$ 0.42 | … | $-0.53~{}\pm~{}0.08$
52351 | 501 | 16.44 $\pm$ 0.84 | 9.03 $\pm$ 0.86 | 6.72 $\pm$ 0.43 | 4.22 $\pm$ 1.00 | 2.93 $\pm$ 0.57 | … | $-0.53~{}\pm~{}0.04$
52367 | 517 | 12.30 $\pm$ 0.68 | 7.31 $\pm$ 0.40 | 6.15 $\pm$ 0.34 | 4.66 $\pm$ 0.55 | 3.12 $\pm$ 0.96 | … | $-0.41~{}\pm~{}0.02$
52385 | 535 | 9.30 $\pm$ 0.49 | 5.25 $\pm$ 0.41 | 3.66 $\pm$ 0.28 | … | … | … | $-0.51~{}\pm~{}0.04$
52393 | 543 | 7.91 $\pm$ 0.41 | 4.53 $\pm$ 0.30 | 2.88 $\pm$ 0.18 | 2.01 $\pm$ 0.35 | … | … | $-0.55~{}\pm~{}0.05$
52398 | 548 | 6.52 $\pm$ 0.35 | 3.69 $\pm$ 0.29 | … | 1.70 $\pm$ 0.32 | … | … | $-0.51~{}\pm~{}0.06$
52412 | 562 | 7.66 $\pm$ 0.59 | 1.97 $\pm$ 0.13 | … | … | … | … | …
52421 | 571 | 4.84 $\pm$ 0.31 | 1.95 $\pm$ 0.16 | … | … | … | … | …
52433 | 583 | 2.32 $\pm$ 0.13 | 1.43 $\pm$ 0.09 | … | … | … | … | …
52443 | 593 | 2.79 $\pm$ 0.16 | 1.10 $\pm$ 0.13 | … | … | … | … | …
52451 | 601 | 2.10 $\pm$ 0.11 | 1.40 $\pm$ 0.14 | 1.07 $\pm$ 0.26 | … | … | … | $-0.35~{}\pm~{}0.02$
52461 | 611 | 3.35 $\pm$ 0.21 | 1.01 $\pm$ 0.12 | 0.94 $\pm$ 0.20 | … | … | … | $-0.87~{}\pm~{}0.15$
52475 | 625 | … | … | 0.68 $\pm$ 0.08 | … | … | … | …
52483 | 633 | 1.89 $\pm$ 0.11 | 1.02 $\pm$ 0.11 | 0.88 $\pm$ 0.14 | … | … | … | $-0.46~{}\pm~{}0.04$
52504 | 654 | 1.73 $\pm$ 0.15 | 0.99 $\pm$ 0.15 | 0.75 $\pm$ 0.10 | … | … | … | $-0.47~{}\pm~{}0.01$
52517 | 667 | 1.06 $\pm$ 0.08 | 0.61 $\pm$ 0.06 | 0.49 $\pm$ 0.05 | … | … | … | $-0.44~{}\pm~{}0.01$
52519 | 669 | 2.09 $\pm$ 0.11 | 1.20 $\pm$ 0.15 | 0.92 $\pm$ 0.17 | … | … | … | $-0.46~{}\pm~{}0.00$
52552 | 702 | … | 0.78 $\pm$ 0.12 | 0.61 $\pm$ 0.11 | … | … | … | …
52575 | 725 | 1.46 $\pm$ 0.19 | 0.89 $\pm$ 0.07 | 0.49 $\pm$ 0.11 | … | … | … | $-0.47~{}\pm~{}0.07$
52579 | 729 | … | … | 0.52 $\pm$ 0.12 | … | … | 1.50 $\pm$ 0.31 | …
52617 | 767 | … | 1.15 $\pm$ 0.08 | 0.98 $\pm$ 0.14 | … | … | … | …
52629 | 779 | … | 0.80 $\pm$ 0.06 | 0.86 $\pm$ 0.12 | … | … | … | …
52637 | 787 | … | 0.99 $\pm$ 0.11 | 0.88 $\pm$ 0.14 | … | … | … | …
52642 | 792 | … | 0.85 $\pm$ 0.11 | 0.71 $\pm$ 0.10 | … | … | … | …
52645 | 795 | … | 1.08 $\pm$ 0.12 | 0.84 $\pm$ 0.10 | … | … | … | …
52647 | 797 | … | 0.77 $\pm$ 0.11 | 0.66 $\pm$ 0.16 | … | … | … | …

  * •

‘…’ indicates no measurements for flux density for this epoch at that
frequency

Table 10: continued

Flux densities and spectral indices of V445 Pup  $t$ $t-t_{0}$ Radio flux
densities (mJy) $\alpha$ (MJD) (Days) 1.43 GHz 4.86 GHz 8.46 GHz 14.94 GHz
22.46 GHz 43.34 GHz 52653 803 … 0.84 $\pm$ 0.10 0.61 $\pm$ 0.10 … … … … 52659
809 … 0.77 $\pm$ 0.07 0.65 $\pm$ 0.10 … … … … 52668 818 … 1.22 $\pm$ 0.09 0.60
$\pm$ 0.07 … … … … 52676 826 2.85 $\pm$ 0.59 0.78 $\pm$ 0.09 0.77 $\pm$ 0.07 …
… … $-0.79~{}\pm~{}0.08$ 52693 843 … 0.86 $\pm$ 0.11 0.63 $\pm$ 0.09 … … … …
52702 852 … 0.90 $\pm$ 0.11 0.724 $\pm$ 0.13 … … … … 52709 859 … 0.93 $\pm$
0.10 0.80 $\pm$ 0.12 … … … … 52711 861 … 0.94 $\pm$ 0.09 0.74 $\pm$ 0.09 … … …
… 52717 867 … 0.84 $\pm$ 0.09 0.83 $\pm$ 0.10 … … … … 52724 874 … 1.42 $\pm$
0.18 1.15 $\pm$ 0.13 … … … … 52748 898 … 1.17 $\pm$ 0.11 0.66 $\pm$ 0.09 … … …
… 52790 940 2.21 $\pm$ 0.19 0.91 $\pm$ 0.09 0.24 $\pm$ 0.04 … … …
$-0.93~{}\pm~{}0.47$ 52795 945 2.53 $\pm$ 0.27 0.78 $\pm$ 0.08 … … … … … 52807
957 2.55 $\pm$ 0.24 0.90 $\pm$ 0.10 … … … … … 52821 971 2.49 $\pm$ 0.22 1.76
$\pm$ 0.22 … … … … … 52839 989 … … 1.14 $\pm$ 0.10 … … … … 52842 992 … 1.7
$\pm$ 0.15 … … … … … 52846 996 … 1.56 $\pm$ 0.15 … … … … … 52852 1002 … … 0.65
$\pm$ 0.08 … … … .. 52863 1013 1.69 $\pm$ 0.16 1.37 $\pm$ 0.10 1.07 $\pm$ 0.08
… … … $-0.25~{}\pm~{}0.08$ 52877 1027 2.22 $\pm$ 0.32 1.59 $\pm$ 0.23 1.49
$\pm$ 0.20 … … … … 52886 1036 2.67 $\pm$ 0.24 1.89 $\pm$ 0.31 1.01 $\pm$ 0.08
… … … … 52894 1044 1.49 $\pm$ 0.17 1.43 $\pm$ 0.16 0.87 $\pm$ 0.08 … … … …
52902 1052 1.02 $\pm$ 0.16 … 1.10 $\pm$ 0.07 … … … … 52905 1055 1.49 $\pm$
0.16 1.51 $\pm$ 0.16 1.00 $\pm$ 0.14 … … … … 52910 1060 2.05 $\pm$ 0.18 1.44
$\pm$ 0.12 … … … … … 52912 1062 … 1.58 $\pm$ 0.20 0.87 $\pm$ 0.08 … … … …
52921 1071 … 1.09 $\pm$ 0.21 … … … … … 52934 1084 … 1.38 $\pm$ 0.11 1.28 $\pm$
0.13 … … … … 52946 1096 … 1.32 $\pm$ 0.16 1.28 $\pm$ 0.17 … … … … 52953 1103 …
1.34 $\pm$ 0.16 1.28 $\pm$ 0.12 … … … … 52962 1112 … … 1.44 $\pm$ 0.15 … … … …
52967 1117 … 1.59 $\pm$ 0.15 1.30 $\pm$ 0.15 … … … … 52988 1138 1.41 $\pm$
0.25 1.82 $\pm$ 0.11 1.46 $\pm$ 0.08 … … … $-0.10~{}\pm~{}0.24$ 53001 1151
2.06 $\pm$ 0.10 1.72 $\pm$ 0.12 1.60 $\pm$ 0.15 … … … … 53007 1157 3.06 $\pm$
0.22 1.80 $\pm$ 0.18 1.71 $\pm$ 0.18 … … … … 53012 1162 2.01 $\pm$ 0.11 1.90
$\pm$ 0.20 1.62 $\pm$ 0.16 … … … … 53018 1168 … 1.76 $\pm$ 0.13 1.56 $\pm$
0.14 … … … … 53027 1177 … 1.74 $\pm$ 0.14 1.67 $\pm$ 0.15 … … … … 53036 1186
2.17 $\pm$ 0.19 2.10 $\pm$ 0.21 1.50 $\pm$ 0.16 … … … … 53037 1187 … … 1.54
$\pm$ 0.15 1.33 $\pm$ 0.38 1.05 $\pm$ 0.22 0.78 $\pm$ 0.18
$-0.42~{}\pm~{}0.08$ 53047 1197 … 2.09 $\pm$ 0.30 1.85 $\pm$ 0.19 … 0.84 $\pm$
0.17 1.29 $\pm$ 0.37 … 53059 1209 … 1.53 $\pm$ 0.13 1.35 $\pm$ 0.12 … 1.14
$\pm$ 0.27 … $-0.20~{}\pm~{}0.02$ 53066 1216 … 1.33 $\pm$ 0.12 1.30 $\pm$ 0.10
… 0.84 $\pm$ 0.18 … … 53074 1224 … 1.72 $\pm$ 0.10 … … … …. … 53084 1234 …
1.54 $\pm$ 0.17 1.34 $\pm$ 0.13 … … … … 53086 1236 … … 1.29 $\pm$ 0.15 … … … …
53096 1246 … … 1.10 $\pm$ 0.12 … … … … 53102 1252 … 1.15 $\pm$ 0.12 1.27 $\pm$
0.12 … 0.73 $\pm$ 0.14 … $-0.24~{}\pm~{}0.28$ 53111 1261 … 1.37 $\pm$ 0.20
1.04 $\pm$ 0.12 … … … … 53129 1279 … 1.61 $\pm$ 0.20 1.14 $\pm$ 0.15 … … … …
53136 1286 2.27 $\pm$ 0.28 1.48 $\pm$ 0.10 1.18 $\pm$ 0.08 …. … …
$-0.37~{}\pm~{}0.02$ 53143 1293 0.94 $\pm$ 0.17 1.63 $\pm$ 0.20 1.13 $\pm$
0.16 … … … … 53147 1297 3.45 $\pm$ 0.50 … … … … … … 53156 1306 1.49 $\pm$ 0.18
1.79 $\pm$ 0.22 1.52 $\pm$ 0.18 … … … … 53169 1319 2.51 $\pm$ 0.24 1.50 $\pm$
0.16 1.23 $\pm$ 0.12 … … … … 53182 1332 … 1.01 $\pm$ 0.10 0.72 $\pm$ 0.08 … …
… … 53188 1338 … 1.29 $\pm$ 0.18 0.96 $\pm$ 0.13 … … … … 53197 1347 … … 0.89
$\pm$ 0.12 0.59 $\pm$ 0.11 … … … 53204 1354 … 1.46 $\pm$ 0.12 1.17 $\pm$ 0.09
0.91 $\pm$ 0.19 … … $-0.42~{}\pm~{}0.01$ 53210 1360 … 1.42 $\pm$ 0.18 1.25
$\pm$ 0.17 … … … … 53225 1375 … 1.21 $\pm$ 0.16 1.07 $\pm$ 0.12 0.98 $\pm$
0.21 … … …

  * •

‘…’ indicates no measurements for flux density for this epoch at that
frequency

Table 11: continued

Flux densities and spectral indices of V445 Pup  $t$ $t-t_{0}$ Radio flux
densities (mJy) $\alpha$ (MJD) (Days) 1.43 GHz 4.86 GHz 8.46 GHz 14.94 GHz
22.46 GHz 43.34 GHz 53239 1389 … 1.61 $\pm$ 0.18 1.37 $\pm$ 0.15 1.46 $\pm$
0.28 … … … 53258 1408 … 1.26 $\pm$ 0.19 1.45 $\pm$ 0.31 1.16 $\pm$ 0.28 … …
$-0.03~{}\pm~{}0.17$ 53272 1422 … 1.07 $\pm$ 0.11 1.43 $\pm$ 0.19 … … … …
53280 1430 … … 1.51 $\pm$ 0.19 … … … … 53287 1437 … … 1.56 $\pm$ 0.14 … … … …
53295 1445 … … 1.71 $\pm$ 0.15 … … … … 53310 1460 … 1.61 $\pm$ 0.14 1.09 $\pm$
0.16 … … … … 53312 1462 … 1.12 $\pm$ 0.12 1.38 $\pm$ 0.14 … … … … 53317 1467 …
… 1.39 $\pm$ 0.13 … … … … 53321 1471 … … 1.54 $\pm$ 0.13 … … … … 53329 1479 …
… 1.21 $\pm$ 0.15 … … … … 53338 1488 … … 1.26 $\pm$ 0.17 … … … … 53361 1511 …
… 1.27 $\pm$ 0.19 … … … … 53370 1520 … … 1.46 $\pm$ 0.19 … … … … 53376 1526 …
… 1.27 $\pm$ 0.11 … … … .. 53386 1536 … … 1.21 $\pm$ 0.17 … … … … 53394 1544 …
… 1.38 $\pm$ 0.15 … … … … 53399 1549 … 1.36 $\pm$ 0.15 1.23 $\pm$ 0.14 … … … …
53404 1554 … … 1.41 $\pm$ 0.16 … … … … 53427 1577 … 1.28 $\pm$ 0.14 1.20 $\pm$
0.13 … … … … 53442 1592 1.15 $\pm$ 0.12 0.94 $\pm$ 0.07 0.87 $\pm$ 0.08 … … …
$-0.16~{}\pm~{}0.01$ 53449 1599 0.89 $\pm$ 0.08 1.05 $\pm$ 0.08 1.06 $\pm$
0.12 … … … … 53454 1604 1.10 $\pm$ 0.11 1.32 $\pm$ 0.18 1.02 $\pm$ 0.16 … … …
… 53464 1614 … 1.17 $\pm$ 0.09 … … … … … 53475 1625 … 0.96 $\pm$ 0.12 0.86
$\pm$ 0.12 … … … … 53486 1636 … 1.21 $\pm$ 0.15 0.93 $\pm$ 0.11 … … … … 53497
1647 … 1.13 $\pm$ 0.14 0.72 $\pm$ 0.10 … … … … 53504 1654 … 0.90 $\pm$ 0.16
0.80 $\pm$ 0.12 … … … … 53520 1670 … 0.94 $\pm$ 0.12 … … … … … 53525 1675 …
0.99 $\pm$ 0.12 … … … … … 53534 1684 … … 0.62 $\pm$ 0.074 … … … … 53540 1690 …
… 0.83 $\pm$ 0.09 … … … … 53545 1695 … 1.01 $\pm$ 0.13 0.76 $\pm$ 0.13 … … … …
53554 1704 1.42 $\pm$ 0.10 0.73 $\pm$ 0.07 0.81 $\pm$ 0.11 … … … … 53561 1711
… … 0.64 $\pm$ 0.08 … … … … 53566 1716 … 0.77 $\pm$ 0.08 … … … … … 53575 1725
… 0.68 $\pm$ 0.08 0.51 $\pm$ 0.06 … … … … 53585 1735 … … 0.47 $\pm$ 0.08 … … …
… 53589 1739 … … 0.78 $\pm$ 0.09 … … … … 53610 1760 … 0.86 $\pm$ 0.09 0.53
$\pm$ 0.07 … … … … 53619 1769 … 1.12 $\pm$ 0.14 0.53 $\pm$ 0.05 … … … … 53639
1789 … 0.73 $\pm$ 0.08 … … … … … 53641 1791 … 0.58 $\pm$ 0.05 0.68 $\pm$ 0.04
… … … … 53645 1795 … 0.65 $\pm$ 0.05 0.54 $\pm$ 0.05 … … … … 53649 1799 … …
0.61 $\pm$ 0.09 … … … … 53660 1810 … … 0.75 $\pm$ 0.07 … 1.10 $\pm$ 0.30 … …
53666 1816 … … 0.66 $\pm$ 0.06 … … … … 53675 1825 … … 0.64 $\pm$ 0.07 … … … …
53683 1833 … 0.62 $\pm$ 0.11 0.58 $\pm$ 0.09 … … … … 53689 1840 … … 0.57 $\pm$
0.08 … … … … 53696 1846 … … 0.54 $\pm$ 0.07 … … … … 53703 1853 … … 0.74 $\pm$
0.09 … … … … 53705 1855 … 0.51 $\pm$ 0.05 0.55 $\pm$ 0.05 … … … … 53715 1865 …
0.82 $\pm$ 0.18 0.64 $\pm$ 0.08 … … … … 53724 1874 … 0.60 $\pm$ 0.12 0.53
$\pm$ 0.08 … … … … 53748 1898 … … 0.59 $\pm$ 0.08 … … … … 53750 1900 … … 0.48
$\pm$ 0.08 … … … … 53757 1907 … 0.47 $\pm$ 0.09 … … … … … 53775 1925 … … 0.43
$\pm$ 0.09 … … … … 53809 1959 0.54 $\pm$0.18 … 0.40 $\pm$ 0.09 … … … … 53816
1966 0.51 $\pm$0.12 … … … … … … 53832 1982 0.61 $\pm$0.22 … … … … … … 53863
2013 … … 0.66 $\pm$ 0.09 … … … …

  * •

‘…’ indicates no measurements for flux density for this epoch at that
frequency

Table 12: continued

Flux densities and spectral indices of V445 Pup  $t$ $t-t_{0}$ Radio flux
densities (mJy) $\alpha$ (MJD) (Days) 1.43 GHz 4.86 GHz 8.46 GHz 14.94 GHz
22.46 GHz 43.34 GHz 53865 2015 … … 0.37 $\pm$ 0.05 … … … … 53953 2103 … … 0.21
$\pm$ 0.03 … …. … … 53957 2107 … 0.42 $\pm$ 0.08 … … … … … 53979 2129 … 0.30
$\pm$ 0.06 … … … … … 54123 2273 … … 0.29 $\pm$ 0.06 … … … … 54374 2524 … …
0.22 $\pm$ 0.06 … … … … 54482 2632 … … 0.26 $\pm$ 0.09 … … … … 54554 2704 … …
0.19 $\pm$ 0.04 … … … …

  * •

‘…’ indicates no measurements for flux density for this epoch at that
frequency