Photometric scaling relations of antitruncated stellar discs
in S0-Scd galaxies

Erwin et al. (2005) introduced for the first time a definition of antitruncated or Type-III galaxies, as those in which the surface brightness of the disc does not follow the typical exponentially-decaying profile with the radius (Patterson, 1940; de Vaucouleurs, 1957, 1958; Freeman, 1970), but presents an up-bending profile, with the outer disc exhibiting a distinct shallower slope than the inner disc outside a given radius (known as the break radius, $R_{\mathrm{brkIII}}$). This nomenclature was an extension of the classification defined by Freeman (1970), who classified Type-I discs as those with single exponentially-decaying profiles and Type-II discs as those with down-bending profiles outside the break radius (see also van der Kruit, 1979, 1987).

In edge-on systems, antitruncations tend to coincide with the superposition of a thin disc and a thick disc (Comerón et al., 2012). However, while nearly all Type-II profiles are associated with galaxy subcomponents (such as rings, pseudorings, lenses, or strong star formation regions), only $\sim 1/3$ of Type-III profiles are related to distinct morphological substructures (see Laine et al., 2014, L14 henceforth). The structural properties and frequencies of antitruncations seem to differ in S0 and spiral types. The percentage of antitruncations rises from $\sim$10–20% in Sc–Sd galaxies to $\sim$20–50% in S0–Sa types (Erwin et al., 2008; Ilyina & Sil’chenko, 2012; Gutiérrez et al., 2011, G11 hereafter; L14; Maltby et al. 2015). In spirals, antitruncations are basically disc-related phenomena, with less than $\sim$15% of them associated with the contribution of central spheroidal components to the galaxy outskirts (Maltby et al., 2012b, 2015). However, this percentage rises to $\sim$25% in S0–Sb galaxies (Erwin et al., 2005) and up to $\sim$50% if only S0s are considered (Maltby et al., 2015).

Type-II profiles are known to be related to bars in most cases (see, e.g., Kim et al., 2014), but the origin of Type-III discs is still poorly constrained. Diverse mechanisms have been proposed to explain the formation of antitruncations. The majority of them are related to gravitational or tidal interactions, such as minor mergers (Laurikainen & Salo, 2001; Peñarrubia et al., 2006; Younger et al., 2007), major mergers (Borlaff et al., 2014), interactions of the disc with dark matter subhaloes (Kazantzidis et al., 2009), high-eccentricity fly-by encounters (Younger et al., 2008), or harassment (Roediger et al., 2012). Other formation scenarios include the existence of different star formation thresholds as a function of the radius in the galaxy (Elmegreen & Hunter, 2006), ram-pressure stripping (Roediger et al., 2012), ongoing gas accretion (Minchev et al., 2012), and simple fading of stellar discs (Maltby et al., 2015). Herpich et al. (2015) have also proposed that the disc profile type of a galaxy may basically depend on the initial spin of its host halo. It seems that bars are unrelated to antitruncations, as derived from the observational fact that the relative frequency of Type-III profiles found in samples of barred and unbarred galaxies is similar (Sil’chenko, 2009; Erwin et al., 2008, E08 hereafter; G11; L14). However, this needs to be confirmed by other means.

Recently, Borlaff et al. (2014) have found that the structures of the inner and outer discs and the location of the break in Type-III S0 galaxies are strongly coupled, and this coupling seems to be independent of the existence of bars in the galaxies. These authors have shown that the characteristic photometric parameters of the inner and outer discs and the breaks in S0s satisfy several scaling relations, tighter in many cases if the scalelengths are normalized to the optical size of the galaxy. The question is whether or not these scaling relations (or similar ones) are also obeyed by Type-III discs of other morphological types. If not this would imply that antitruncations do form through diverse and independent mechanisms in different Hubble types (which seems reasonable, accounting for the wide variety of possible formation processes). However, if the antitruncated discs of spiral galaxies satisfy scaling relations similar to those observed in S0s, it becomes challenging to understand the physical processes underlying this coupling in galaxies spanning the whole Hubble Sequence. Analogously, if bars are relevant in determining the structure of some antitruncated discs or have triggered their formation in some cases, we should expect to find significant differences between the photometric trends followed by Type-III discs of barred and unbarred galaxies, whereas negligible differences would be expected if both phenomena are structurally unrelated.

Therefore, we have investigated whether the Type-III discs of spirals obey scaling relations as tight as those observed in antitruncated S0s and, in this case, whether the scaling relations can be considered similar or both galaxy types exhibit significant differences between them. The same analysis has been performed for barred and unbarred galaxies, to find out whether bars and antitruncations are structurally related or not.

For this purpose, we have used the data published by E08 and G11 in the $R$ band, and by L14 in the 3.6 $\mu$m Spitzer band. In Section 2, we briefly comment on the galaxy samples of these authors, their data, and the procedures they followed to obtain and characterize the surface brightness profiles. Section 3 describes our fitting technique to the trends found in the studied photometric planes, as well as the tests performed to identify the correlations that were statistically significant. In Section 4 we show the main trends and scaling relations that we have found involving the characteristic scalelengths of the inner and outer discs ($h_{\mathrm{i}}$ and $h_{\mathrm{o}}$, respectively), $R_{\mathrm{brkIII}}$, and $R_{\mathrm{25}}$. There we also statistically analyse the differences and similarities of the trends followed by S0 vs. spiral galaxies, by barred vs. unbarred galaxies, and of $R$ vs. 3.6 $\mu$m data. Finally, the discussion and main conclusions are provided in Sections 5 and 6.

We have analysed the possible correlations between the characteristic parameters of the breaks and the inner and outer discs of two samples of local galaxies with Type-III stellar discs, in the $R$ and 3.6 $\mu$m bands. The $R$-band dataset contains the photometric parameters derived for 16 Type-III barred nearby galaxies by E08 and for 24 Type-III unbarred ones by G11 (40, in total), with S0-Sbc types. The 3.6 $\mu$m dataset comprises the 62 Type-III (barred and unbarred) galaxies from the sample analysed by L14, with types spanning from S0 to Scd. Our study is exclusively centered on galaxies with pure Type-III profiles, i.e., the galaxies with hybrid profiles from the original samples (Type II$+$III) have been excluded in our subsamples to avoid a possible additional dispersion in the trends we were looking for (they were 4 galaxies in the E08 sample, 5 from G11, and 7 from L14). The E08 sample overlaps with the L14 sample in 4 galaxies, while G11 sample has 7 galaxies in common with L14.

Table 1 summarizes the statistics of the samples in terms of morphological types and barred/unbarred nature in both bands. The statistics of the two subsamples is not very high (40 S0–Sbc galaxies in $R$ and 62 S0–Scd’s in 3.6 $\mu$m), but the numbers are sufficiently large to allow us to look for photometric scaling relations in S0s and spirals separately, because the galaxies distribute nearly equally among the two types in both bands. A similar argument holds for barred and unbarred galaxies. The original data, reduction, and methodology to characterize the surface brightness profiles are extensively described in the original papers, so we provide just a brief description here.

The original samples were defined using different selection criteria for the radial velocities, angular sizes, galactic latitudes, and morphologies of the galaxies. The galaxies in the $R$-band sample have distances $<$ 30 Mpc, while those of the L14 sample lie at $<$ 80 Mpc, but both datasets present -18 $<$ $M_{B}$ $<$ -22 magnitudes. E08 and G11 used data in the $r$ and $R$ bands taken with different telescopes, with PSF FWHM$\sim$0.7” and limiting surface brightness $\mu_{\mathrm{lim}}$ $\sim$ 26–27 mag arcsec^-2 in $R$ (Vega system). L14 combined data obtained in the 3.6 $\mu$m IRAC band for Sa-Sd galaxies of the S⁴G survey (FWHM$\sim$1.7”, see Sheth et al., 2010) with $K_{s}$-band images for S0-S0/a galaxies from the NIRS0S survey (FWHM$\sim$0.7”, see Laurikainen et al., 2011). In L14, the distances of the galaxies coming from the S⁴G sample are $<$ 40 Mpc, and $<$ 80 Mpc for those coming from NIRS0S.

L14 converted the $K$-band surface brightness profiles of the galaxies from the NIRS0S sample to AB magnitudes in the 3.6 $\mu$m band accounting for the color differences and magnitude offsets derived for the 93 galaxies that the two surveys have in common. These authors computed total magnitudes in elliptical apertures tracing the $\mu=22.5$ mag arcsec^-2 isophote in 3.6 $\mu$m in each galaxy. The median difference between the magnitudes obtained in the two surveys was derived, including a linear term to describe the dependence on colour. This conversion factor was then applied to the surface brightness profiles and total magnitudes of the NIRS0S data to transform them into 3.6 $\mu$m. L14 data finally presented $\mu_{\mathrm{lim}}\sim$ 26.4 mag arcsec^-2 for the Sa-Scd’s and $\mu_{\mathrm{lim}}\sim$ 24.7 mag arcsec^-2 for the S0-S0/a’s in 3.6 $\mu$m (AB magnitudes).

Both data samples are analogous in terms of depth for the spiral types, but the $R$-band sample is at least $\sim 1$ mag deeper than the 3.6 $\mu$m sample for the S0 galaxies. L14 compared the limiting surface brightness of their sample with that of the $V$-band sample by Maltby et al. (2012a), finding that $V-[3.6]\sim 1.5$ mag (AB system, see their Section 6). Considering that $V-R$ ranges $\sim 0.2$–0.5 in the discs of Sa–Sd galaxies (Möllenhoff, 2004) and $(V-R)=0.5$– 0.65 in those of S0s (Gregg, 1989), we find that the limiting magnitudes of the 3.6 $\mu$m sample by L14 roughly correspond in the $R$ band to $\mu_{\mathrm{lim}}\sim 27.5$ for the spirals and $\mu_{\mathrm{lim}}\sim 25.5$ for the S0s (Vega system). Here, we have considered that $V(\mathrm{AB})-V(\mathrm{Vega})=0.02$ (Blanton & Roweis, 2007). Assuming that $\mu_{\mathrm{lim}}\sim 26.5$ mag arcsec^-2 on average in the E08 and G11 samples, this means that the 3.6 $\mu$m data sample is $\sim 1$ mag arcsec^-2 deeper than the $R$-band sample for the spirals. On the other hand, the E08 and G11 samples are $\sim 1$ mag arcsec^-2 deeper than the L14 sample for the S0s. However, some profiles in E08 and G11 achieve $\mu_{\mathrm{lim}}\sim 28$ mag arcsec^-2. So, the $R$-band sample may be reaching similar depths to the L14 sample in some specific cases.

E08 and G11 used the morphological types available in the RC3 catalog (de Vaucouleurs et al., 1991), based on the optical morphology of the galaxies, whereas the types in L14 were assigned according to the morphology in their $K$ or 3.6 $\mu$m images (Laurikainen et al., 2011; Buta et al., 2015). E08 considered as barred galaxies those exhibiting strong (SB) or weak (SAB) bars according to the RC3 classification, but revised the classes according to their deep $R$ band images and rejected the galaxies without clear bars in them or involved in strong interactions. The barred/unbarred classification in L14 was, however, made on the basis of their deep $K$ and 3.6 $\mu$m images from the NIRS0S and S⁴G surveys.

The surface brightness profiles were obtained by azimuthally averaging the light within ellipses fitted to the isophotes of the galaxies. The three studies (E08, G11, and L14) held the values of the centre, ellipticity, and position angle of isophotes fixed to the values of the outer discs in the fits.

E08 and L14 fitted the disc profiles using ”broken-exponential” functions, which describe the inner and outer discs through two exponentially-decaying profiles joined by a transition region, according to the following expression:

Consequently, we have used the characteristic parameters of the breaks and the inner and outer discs of Type-III galaxies derived by E08, G11, and L14 to compare the trends of S0 and spiral types in several photometric planes, in the $R$ and 3.6 $\mu$m bands. We remark that the magnitudes of the $R$-band data are the Vega system and in AB for the 3.6 $\mu$m dataset.

We performed linear fits ($y=m\,x+C_{0}$) to the trends followed in each photometric plane by all galaxies, by spirals and S0s independently, by types of spirals (Sa–Sab, Sb–Sbc, Sc–Scd), as well as by barred and unbarred galaxies. The trends of the types in each sample have been fitted using ordinary least squares. The photometric parameters of the inner and outer discs characterized by E08, G11, and L14 had no errors assigned in their original papers, so no error weighting could be considered in the fits. In order to estimate realistic confidence intervals to the fitted regression coefficients, we adopted a bootstrapping method. We generated $n=10^{5}$ artificial data samples with the same size as the original one in each diagram with replacement. The final regression coefficients of each fit correspond to the median values of the probability distributions of each coefficient obtained with the $10^{5}$ results, in order to reduce the systematic bias introduced by outliers. The upper and lower errors considered for each coefficient are those enclosing 2.5% and 97.5% of the values in the corresponding probability distribution. The bootstrap distribution is closer to the real probability distribution of the coefficients than a simple Gaussian in general, so this method derives robust and conservative (asymmetric) confidence intervals for the regression coefficients, reducing the effects of possible outliers or high leverage points at the same time.

We tested the significance of each photometric trend using the Spearman rank correlation test, which measures whether two variables are monotonically related and the level of correlation between them, and it has the advantage of being non parametric. Only those trends with an associated probability of random correlation below 5% according to the test ($p_{S}<0.05$) are considered as statistically significant. The 3.6 $\mu$m dataset presents higher statistics than the $R$-band sample, but the Spearman rank correlation test accounts for the number of data pairs yielding the trend to derive $p_{S}$. Additionally, the Pearson coefficient ($\rho$) has been used to determine the level of linear correlation of each trend.

The slope ($m$) and $Y$-intercept ($C_{0}$) of the linear fits performed to the different trends analysed in each photometric plane, their asymmetric error intervals, as well as the values of $p_{S}$, $\rho$, and the number of available data pairs ($N_{\mathrm{pairs}}$) for each trend, are listed in Tables 2-7.

Figures 2-9 show the trends followed by Type-III galaxies in these photometric planes. We have overplotted the obtained linear fits only when they fulfill the Spearman rank correlation test at 95% of significance level, i.e., only if there is a significant correlation in the diagram. Note that, although there may be a significant correlation between two parameters according to the Spearman test, it does not have to be significantly linear. In fact, some trends are significant according to it ($p_{S}<0.05$), but they exhibit low values of the Pearson coefficient $\rho$ (e.g., the $\mu_{\mathrm{brkIII}}$ – $R_{\mathrm{brkIII}}$ trend in 3.6 $\mu$m in Fig. 2). In these figures, we have written the results of the most relevant fits which are being compared at the top of each panel even when the correlations are not significant. For simplicity, we have symmetrized the error interval of $m$ and $C_{0}$ in the figures, but the asymmetrical upper and lower errors really obtained for the coefficients of the fits are available in Tables 2-7.

The characteristic scalelengths are plotted in logarithmic scales in all figures, because the correlations exhibit more defined linear trends in this way than using linear scales. In many photometric planes, we have normalized the characteristic scalelengths ($h_{\mathrm{i}}$, $h_{\mathrm{o}}$, $R_{\mathrm{brkIII}}$) to the optical radius of each galaxy. We have defined this following E08 and G11, i.e., as the radius of the isophote with $\mu=25$ mag arcsec^-2 in the $B$ band ($R_{\mathrm{25}}$). These authors provide $R_{\mathrm{25}}$ for each galaxy in their samples, so we have used their tabulated values directly. The values of $R_{\mathrm{25}}$ for the galaxies in the L14 sample have been obtained from HyperLeda¹¹1HyperLeda database is available at: http://leda.univ-lyon1.fr/, and include a correction for Galactic extinction and inclination effects.

In Section 4.1, we discuss the trends and correlations found in several photometric planes for the different morphological types and for barred and unbarred galaxies in the two datasets ($R$ and 3.6 $\mu$m). In Section 4.2, we compare the slopes and $Y$-intercepts of the linear trends fitted in each photometric plane for S0s and spirals, as well as for barred and unbarred. The fits obtained for the $R$-band and 3.6 $\mu$m data are only compared in the photometric relations exclusively relating characteristic scalelengths.

In Section 4, we have shown that Type-III discs obey tight photometric scaling relations for galaxy types spanning the whole Hubble Sequence. We have found no statistical evidence of noticeable differences between the relations followed by S0s and spirals and barred and unbarred galaxies, a fact that suggests that the structure of antitruncated discs may be independent of the galaxy type and the existence, or not, of bars in the galaxy. Although the statistical evidence is not strong, considering the low numbers and the uncertainties of the available data samples, the structural independence of bars and antitruncations agrees pretty well with the similar relative frequency of Type-III profiles found in samples of barred and unbarred galaxies (E08; Sil’chenko, 2009, G11; L14). Our results thus support the idea that bars and antitruncations are decoupled structures in all morphological types. This does not imply that the two structures have formed independently, as some mechanisms are known to trigger the formation of both kind of features, such as mergers or flybys (Walker et al., 1996; Lang et al., 2014). However, this is indicative for that bars cannot have induced the formation of Type-III discs, as opposed to their tight structural link with Type-II discs (see, e.g., Kim et al., 2014).

The scaling relations of Type-III discs found in the present study impose strong constraints on any formation scenarios proposed to explain the formation of antitruncations, independently of whether the relations really depend (or not) on the morphological type or the hosting of a bar. Accounting for the wide diversity of mechanisms proposed to explain the formation of antitruncations (see Section 1), it is challenging to understand the physics underlying the scaling relations that we have found between Type-III discs across the whole Hubble Sequence.

The dependence of these features on the environment becomes a key to discriminate between these mechanisms. Many studies have reported traces of recent or ongoing interactions in the outskirts of many Type-III discs, supporting a merging- or interaction-related nature (Erwin et al., 2005). L14 found a positive correlation between the scalelengths of Type-III discs and the tidal interaction strength, also pointing to external mechanisms. Coherently, flat and/or positive age gradients prevail in galaxies of the three profile types (in particular, of Type-III) in the Virgo cluster, contrary to the expectations of scenarios in which the formation of these discs were mostly driven by secular inside-out disc growth and/or stellar migrations (Roediger et al., 2012). So, all these results suggest external processes as the main drivers of the formation of antitruncations, probably as a result of the gravitational response of the disc to a tidal interaction.

However, in this case we should also expect to find some dependence of the structural properties of Type-III discs on the local galaxy density. But, on the contrary, the inner and outer disc scalelengths and the break strength²²2The break strength of Type-II and Type-III profiles is defined as the logarithm of the outer-to-inner scalelengths ratio. of Type-III discs show no trends with the environment, either in spiral or S0 galaxies (Maltby et al., 2012a, 2015). Additionally, similar fractions of Type-III S0 galaxies are found in both cluster and field environments, suggesting that the environment hardly affects the outer structure of these galaxies (Erwin et al., 2012; Roediger et al., 2012). How can all these results be reconciled?

External processes may induce the formation of antitruncations as the result of gravitational-driven instabilities in the disc or through gas/stars accretion in the galaxy outskirts. The tight scaling relations found here strongly support mechanisms related to the dynamical response of discs to tidal forces rather than other scenarios. In fact, a gravitational-driven mechanism would have three advantages. The first is that this can be induced through a wide diversity of processes (such as those commented in Section 1). Secondly, it could provide a feasible explanation for the independence of these scaling relations of the Hubble type of the galaxy (although it must be confirmed more robustly, as explained above), since just a stellar disc and gravity are required to give rise to them. And finally, a gravitationally-induced mechanism could also explain some of the apparently contradictory results with the environment discussed previously. If the processes triggering antitruncations are mostly related to gravitational interactions, we expect to find them present in both groups and clusters and in similar fractions, because mergers and interactions can be equally relevant in both environments (Moran et al., 2007; Wilman et al., 2009; Plauchu-Frayn & Coziol, 2010a, b; Bekki & Couch, 2011; Vijayaraghavan & Ricker, 2013). Therefore, it is reasonable to find a weak dependence of their properties on the tidal interaction field (as reported by L14), but we do not expect to find significant trends of the break properties with the local density at the same time, because the antitruncation can have formed through an interaction not related with the current environment of the galaxy.

In any case, these speculative suggestions need to be confirmed through numerical simulations. At the moment, only Borlaff et al. (2014) have shown that major mergers are capable of producing antitruncated S0 galaxies that obey these scaling relations using N-body simulations. Nevertheless, it is obvious that the role of major mergers in the formation of late-type spirals must have been quite limited, so at least the Type-III discs in Sbc-Sd galaxies require different mechanisms, which also have to predict these scaling relations. In particular, satellite accretions are known to produce antitruncations (Laurikainen & Salo, 2001; Peñarrubia et al., 2006; Younger et al., 2007), inducing secular evolution in the disc that can couple the inner and outer galaxy structure at the same time (Eliche-Moral et al., 2006, 2011, 2012, 2013). This makes them good candidates to form antitruncated stellar discs. However, additional studies demonstrating the feasibility of this and other mechanisms in reproducing the scaling relations found here are required.

We have investigated whether the tight scaling relations recently observed by Borlaff et al. (2014) in Type-III S0s are satisfied by antitruncated galaxies of other Hubble types. We have used the samples of Type-III galaxies published by E08 and G11 in the $R$ band and by L14 in Spitzer 3.6 $\mu$m band, as well as the characterizations performed by these authors to the surface brightness profiles of these galaxies. The $R$-band dataset consists of 40 antitruncated galaxies with types spanning from S0 to Sbc, while the 3.6 $\mu$m sample has 62 galaxies of S0–Scd types. Nearly half of the galaxies in each sample are barred.

We have analysed the trends followed by S0s and spirals (all, Sa–Sab, Sb–Sbc, and Sc–Scd), as well as for barred and unbarred galaxies, in several planes relating the characteristic photometric parameters of the breaks ($\mu_{\mathrm{brkIII}}$, $R_{\mathrm{brkIII}}$) and of the inner and outer discs of these antitruncated galaxies ($\mu_{0,\mathrm{i}}$, $h_{\mathrm{i}}$, $\mu_{0,\mathrm{o}}$, $h_{\mathrm{o}}$), for the $R$ and 3.6 $\mu$m datasets separately. We have used the Spearman rank correlation test to select the correlations which are significant at 95% of confidence level. Linear fits have been performed to the trends followed by each galaxy type in each photometric plane and the Pearson’s coefficient has been used to measure the level of linear correlation.

We have obtained the following results:

1. 1.

   The antitruncated discs of spirals (taking them all together, or dividing them into Hubble classes) obey tight photometric relations, like those observed in S0 galaxies, both in the $R$ and 3.6 $\mu$m bands.

2. 2.

   The antitruncated discs of barred and unbarred galaxies also follow tight photometric relations, again both in $R$ and 3.6 $\mu$m.

3. 3.

   The majority of these correlations have high statistical significance despite the relatively low numbers of the available datasets, showing clear linear trends when $h_{\mathrm{i}}$, $h_{\mathrm{o}}$, $R_{\mathrm{brkIII}}$, and $R_{\mathrm{25}}$ are plotted on a logarithmic scale. This implies the existence of strong scaling relations in the Type-III discs of all Hubble types between their characteristic parameters ($h_{\mathrm{i}}$, $h_{\mathrm{o}}$, $\mu_{0,\mathrm{i}}$, $\mu_{0,\mathrm{o}}$, $\mu_{\mathrm{brkIII}}$) and $R_{\mathrm{brkIII}}$, as well as between the parameters of the inner and outer discs ($\mu_{0,\mathrm{i}}$ – $h_{\mathrm{i}}$, $\mu_{0,\mathrm{o}}$ – $h_{\mathrm{o}}$, and $h_{\mathrm{i}}$ – $h_{\mathrm{o}}$).

4. 4.

   The correlations between $\mu_{0,\mathrm{i}}$, $\mu_{0,\mathrm{o}}$, or $\mu_{\mathrm{brkIII}}$ with the logarithm of the characteristic scalelengths ($h_{\mathrm{i}}$, $h_{\mathrm{o}}$, or $R_{\mathrm{brkIII}}$) improve significantly when the scalelengths are normalized to $R_{\mathrm{25}}$.

5. 5.

   The logarithm of the characteristic scalelengths of antitruncated discs ($h_{\mathrm{i}}$, $h_{\mathrm{o}}$, and $R_{\mathrm{brkIII}}$) scale with $\log(R_{\mathrm{25}})$ for all galaxy types in 3.6 $\mu$m. In $R$, the linear trends are less tight and lose significance in spiral types.

6. 6.

   The observational uncertainties of the data samples are too high to discern robustly whether the analysed scaling relations are similar (or not) in S0s and spirals, barred and unbarred galaxies, and in the $R$ and 3.6 $\mu$m bands. However, no statistical evidence is either found of significant differences between the relations followed by S0s and spirals and by barred and unbarred galaxies within errors. This result suggests that the scaling relations of antitruncated discs are independent of the morphological type and the presence or absence of bars. Deeper data and larger samples are required to confirm these results robustly.

In conclusion, the tight scaling relations found in the present study for Type-III discs impose strong constraints on any formation scenarios proposed to explain the formation of antitruncations in stellar discs across the Hubble Sequence, independently of whether the relations really depend (or not) on the morphological type or the hosting of a bar.