Progenitor constraint with circumstellar material for the magnetar-hosting supernova remnant RCW 103

While it is expected that CSM contains N-rich materials produced in stars (e.g., Maeder, 1983) and that the resultant N/O becomes higher than solar, it has been difficult to detect N lines in SNRs so far. Frank et al. (2015) found that the plasmas in the shell of RCW 103 have sub-solar ($\sim 0.5$) abundances of heavier elements (Ne, Mg, Si, S, and Fe) and presumed that the CSM is a largely dominant component across the remnant. Our result confirms their conclusion and shows robust evidence of the N-rich shell in RCW 103 for the first time. The averaged abundance ratio is $\rm{N/O}=3.8\pm 0.1$, which fits well into the picture that the N-rich materials yielded from a massive star are blown out at the RSG or WR stage (e.g., Owocki, 2004).

On the basis of the result, we constrain environments around the progenitor of RCW 103 in its pre-supernova phase, where stellar winds are blown out with various abundances in various conditions. As illustrated in Figure 5, we assume two cases with different CSM structures, in which we take into account CSM-hydrodynamic and stellar evolutions as described below. An outermost region from a central star is called a main sequence (MS) shell, which contains MS winds and swept-up ISM (Weaver et al., 1977). The region inside the MS shell is called a stellar wind bubble formed by shock waves through collision between the MS winds and the ISM (Castor et al., 1975).

When the wind bubble comes into pressure equilibrium with surroundings, its radius $r_{\rm{wb}}$ is described as

where $M_{\rm{w}}$ and $v_{\rm{w}}$ are total mass and velocity of the MS wind, respectively. The value $p_{\rm{i}}$ is the pressure of ISM, and $k$ is Boltzmann’s constant (Chevalier, 1999). In our Galaxy, $p_{\rm{i}}/k$ and $v_{\rm{w}}$ at MS are typically $\sim 10^{4}~{}\rm{cm^{-3}~{}K}$ (e.g., Berghöfer et al., 1998) and $\sim 10^{3}~{}\rm{km~{}s^{-1}}$, respectively (as summarized by Chen et al., 2013). Since the total wind mass $M_{\rm{w}}$ depends on a progenitor mass $M_{\rm{ZAMS}}$, we calculated a typical value using a stellar evolution code (HOngo Stellar Hydrodynamics Investigator; HOSHI) developed by Takahashi et al. (2013, 2014, 2016, 2018); Yoshida et al. (2019). As a result, if the progenitor has $M_{\rm{ZAMS}}$ of $10M_{\odot}$, obtained wind mass is $M_{\rm{w}}~{}=~{}9.5\times 10^{-1}~{}M_{\odot}$. In this condition, the wind bubble radius $r_{\rm{wb}}$ is calculated as

Since the size of the wind bubble has a positive liner relation with $M_{\rm{ZAMS}}$ (Chen et al., 2013), Eq.2 gives a minimum value of $r_{\rm{wb}}$ by assuming a lower limit $M_{\rm{ZAMS}}\sim 10M_{\odot}$ for CC-SN progenitors. On the other hand, RCW 103 has a radius of $4.5~{}\rm{pc}$ (see Figure 5), which confirms that the bright clumps observed in our study are within the MS wind shell; the low-$kT_{\rm{e}}$ component is not contaminated by ISM.

To investigate an abundance pattern of the swept-up CSM, a stellar wind blown out just before the SN explosion is the most important component. Relatively low $M_{\rm{ZAMS}}$ stars end up as RSG, surrounded by an RSG wind (panel (a) of Figure 5), whose radius $r_{\rm{RSG}}$ is described as

where ${\dot{M}}_{\rm{w}}$ and $v_{\rm{w}}$ are the mass-loss rate and velocity of the RSG wind, respectively. The value $p_{\rm{wb}}$ represents the pressure of stellar wind bubbles (Chevalier & Emmering, 1989; Chevalier, 2005). In Eq.3, we assume a typical pressure of bubbles $\sim 10^{4}~{}\rm{cm^{-3}~{}K}$ (Castor et al., 1975), wind velocity at the RSG phase $10\textrm{--}20~{}\rm{km~{}s^{-1}}$ (Goldman et al., 2017), and the mass-loss rate $\sim 10^{-5\textrm{--}7}~{}M_{\odot}~{}\rm{yr^{-1}}$ calculated with the HOSHI code. The result indicates that the swept-up CSM in RCW 103 contains all RSG-wind materials if the progenitor ended up as RSG.

In case that the progenitor of RCW 103 was a high-$M_{\rm{ZAMS}}$ star, we additionally need to consider an effect of the WR wind, which may sweep up the ambient RSG wind material before the SN explosion. The WR wind expands into the RSG-wind materials with a velocity of 100–200 km s^-1 (Chevalier & Imamura, 1983; Chevalier, 2005) during a WR phase duration of $\sim 10^{3\textrm{--}4}$ year for $M_{\rm{ZAMS}}$ $\leq 60~{}M_{\odot}$ (from a calculation using a stellar evolution model Geneva Code Ekström et al., 2012). From these estimations, the radius of the shell of the RSG wind swept up by the WR wind is calculated to be $\leq 2.5~{}\rm{pc}$. The bright clumps therefore contain all the RSG and WR materials if the progenitor of RCW 103 ended up as a WR star (panel (b) of Figure 5).

For constraining progenitors, we need to know a relationship between CSM abundances and conditions of stars. The N/O ratio measured in CSM is related to the progenitor $M_{\rm{ZAMS}}$, rotation velocity (Maeder et al., 2014), and convective overshoot (the extrusion of convective motion due to non-zero velocities of material on a boundary between the convection zone and the radiative zone in stars). We, therefore, investigate trends between N/O and progenitor parameters by using the HOSHI code. The results are summarized in Figure 6. Note that in our calculation, the metallicity, which may also affects our study (Maeder et al., 2014), is assumed to be a solar since RCW 103 is one of young Galactic SNRs. As shown in Figure 6, N/O increases in the stellar surface during the evolution, but its timescale highly depends on the assumed stellar properties.

$M_{\rm{ZAMS}}$ is generally thought to have a positive relationship with N/O since the mass-loss rate is positively related to $M_{\rm{ZAMS}}$ (e.g., Mauron & Josselin, 2011). Figures 6 (b1) and (c1) indicate that a more rapid increase of N/O is expected in case of higher $M_{\rm{ZAMS}}$. This is because a sub-solar outer layer ($\rm{N/O}\sim 1$) is blown out in early stage of evolution due to the higher mass loss rate caused by stronger radiative force (e.g., Mauron & Josselin, 2011). In contrast, lower mass progenitors ($M_{\rm{ZAMS}}$$\leq 12M_{\odot}$) result in a rapid increase of N/O at an earlier stage of stellar evolution. This is possibly because N-rich materials in the H-burning layer of stars with $M_{\rm{ZAMS}}$$=10\textrm{--}12~{}M_{\odot}$ are carried to the stellar surface by convection at earlier evolution stage than those of more massive stars: for instance, in case of $M_{\rm{ZAMS}}$$\sim 15~{}M_{\odot}$, the He burning occurs before the RSG phase, which prevents the star’s expansion resulting in an inefficient transfer of N to the stellar surface.

As claimed by previous studies (Owocki, 2004; Heger et al., 2000), rotation velocities of stars also affect the final yield of the CNO elements. This is, for instance, clearly seen in Figures 6 (b1) and (b2), where N/O increases more rapidly by a faster rotation ($v_{\rm{init}}/v_{\rm{K}}=0.1$, where $v_{\rm{init}}$ is the initial surface rotation velocity and $v_{\rm{K}}$ is the Kepler velocity at the surface). The trend is interpreted as an effect of the centrifugal force, which enhances the mass-loss rate at the stage of OB stars (Owocki, 2004) and carries materials from the He-burning layer to the H-burning layer such as C and O causing an additional N production by CNO-cycle (Heger et al., 2000).

We also investigate an effect of the convective overshoots, which may also enhance the abundance ratio of N/O because convective layers contain large amount of N-rich materials (e.g., Luo et al., 2022). In the HOSHI code, convective overshoot is treated as a diffusion approximation with the diffusion coefficient $D=D_{0}\exp(-2{\Delta}r/f_{\rm{ov}}H_{\rm{p}}$), where $D_{0}$ is the diffusion constant at the boundary, ${\Delta}r$ is the distance from the boundary, $f_{\rm{ov}}$ is the overshoot parameter variable, and $H_{\rm{p}}$ is the pressure scale hight. We tried two overshoot models with different variables ($f_{\rm{ov}}=0.01$ and 0.03, namely model $M_{A}$ and $L_{A}$, respectively, given in § 2 of Luo et al., 2022) and found that a higher overshoot parameter results in a higher N/O on the stellar surface as seen in panels (b1) and (b3) of Figures 6. This is because N-rich materials in the H-burning layer are carried to the region closer to the surface by convection.

In accordance with the calculations demonstrated in § 4.2, we compared the measured abundance ratio of N/O$=3.8\pm 0.1$ in the CSM of RCW 103 with several models having different $M_{\rm{ZAMS}}$, rotation velocity, and overshoot parameters. In this analysis, we calculated the abundance ratio of N/O by summing up a total amount of N and O contained in post-main sequence winds. The abundance evolution of WR stars and RSGs was obtained from the results in Ekström et al. (2012) and the model calculations using Hoshi code, respectively. The results are displayed in Figure 7 (WR) and Figure 8 (RSG), from which we can constrain the progenitor properties and origin of RCW 103.

If we assume the WR models, the progenitor of RCW 103 is likely to be a 25–32$M_{\odot}$ star with a very rapid initial rotation velocity ($v_{\rm{init}}/v_{\rm{crit}}=0.4$, where $v_{\rm{crit}}$ is the critical velocity reached when the gravitational acceleration is equal to the centrifugal force in the Roche model) or a 40–50$M_{\odot}$ star with no rotation. Here, it is noted that $v_{\rm{crit}}$ is slightly different to $v_{\rm{K}}$ by a factor of $\sqrt{2/3}$. These results are, however, inconsistent with recent theoretical expectations that stars over $20M_{\odot}$ are hard to explode and that those over $35M_{\odot}$ mostly become black holes (Sukhbold et al., 2016). Although the explodability of such massive stars is under debate, we conclude that it is less likely that the progenitor of RCW 103 was a WR star.

In the case of RSG (Figure 8), the progenitor of RCW 103 is likely to be a low-mass ($\leq 12M_{\odot}$) or medium-mass $\geq 15M_{\odot}$) star with normal rotation velocities ($v_{init}/v_{K}\leq 0.2$). The latter result is consistent with a previous estimation based on the ejecta abundances ($\sim 18M_{\odot}$; Frank et al., 2015). It is, however, somewhat unlikely in the context of birth conditions of compact objects (Higgins & Vink, 2019). They present a relation between the progenitor properties and a compactness parameter $\zeta_{M}$, which is defined as

where $M$ is the relevant mass scale for black hole formation and $R(M_{\rm{bary}}=M)$ is the radial coordinate that encloses $M$ at the time of core bounce (O’Connor & Ott, 2011). Higgins & Vink (2019) claimed that $\zeta_{M}$ is related to how easily a pre-supernova stellar core explodes. As they suggest, it is difficult for medium $M_{\rm{ZAMS}}$ (15–40$M_{\odot}$) stars to explode except stars having very rapid rotation velocities ($v_{init}/v_{K}\geq 0.4$), which can be ruled out by our estimation (the black lines in Figure 8).

By contrast, low-mass (10–12$M_{\odot}$) progenitor models are acceptable from the point of view of the explodability and also well fit with previous estimations derived from a comparison of metal compositions of ejecta with a core-collapse nucleosynthesis model; 12–13 $M_{\odot}$ (Braun et al., 2019) and $<$ 13 $M_{\odot}$ (Zhou et al., 2019). We also point out that according to a relation between Fe/Si and $M_{\rm{ZAMS}}$  given by Katsuda et al. (2018) the obtained ejecta abundance ratio ($\rm{Fe/Si}>0.6$ from Table 2) prefers a lower-mass star as well. From these results, we conclude that the progenitor of RCW 103 was most likely a star with $M_{\rm{ZAMS}}$ of 10–12$M_{\odot}$. We also presume that its rotation velocity was relatively normal; $v_{init}/v_{K}\leq 0.2$.

RCW 103 has a magnetar candidate 1E 161348$-$5055. Our result may also hint at physical conditions that lead to form magnetars after SN explosions. One of the well-established hypotheses is a ”dynamo effect” model (Thompson & Duncan, 1993). In this scenario, magnetars are born with rapidly rotating (on the order of millisecond) proto-neutron stars (PNSs), which can power energetic SNe (or release most of the energy through gravitational waves).

Since the rotation velocity of PNSs shows a positive correlation with $M_{\rm{ZAMS}}$, Gaensler et al. (2005) and Heger et al. (2005) indicate that fairly high $M_{\rm{ZAMS}}$ ($\geq~{}35~{}M_{\odot}$) is required to produce a magnetar with this effect in the case of the progenitors with $v_{init}=200~{}\rm{km~{}s^{-1}}$. On the other hand, White et al. (2022) suggests that low mass progenitors ($M_{\rm{ZAMS}}$ =9–25 $M_{\odot}$) with no initial rotation can also make the strong magnetic fields by the dynamo effect considering sufficiently low Rossby number. Masada et al. (2022) also suggests that the strong magnetic fields can be generated in the relatively slowly ($\sim 100~{}\rm{ms}$) rotating PNSs considering different internal structures of the convection. From Figure 7, there is no possible solution for $\geq$ 35 $M_{\odot}$ with a rapid rotation ($v_{init}>300~{}\rm{km~{}s^{-1}}$) and the progenitor parameters given by White et al. (2022) are consistent with our estimation. An alternative scenario to account for the formation of the magnetars is the fossil field hypothesis, which requires a progenitor star with strong magnetic fields (Ferrario & Wickramasinghe, 2006; Vink & Kuiper, 2006; Hu & Lou, 2009) originating from massive ($>20M_{\odot}$; Ferrario & Wickramasinghe, 2006, 2008) or less massive progenitors (Hu & Lou, 2009). This case is also in good agreement with our estimation and it is consistent with the previous study (Zhou et al., 2019).

Note that 1E 161348$-$5055 has an extremely long periodicity ($6.67$h; De Luca et al., 2006) unlike most magnetars ($\sim 1\textrm{--}10$s; Olausen & Kaspi, 2014). Some magnetars with short periodicity are thought to have low-mass progenitors (Zhou et al., 2019) and many OB stars in our Galaxy have the same velocities as the progenitor of RCW 103 (Daflon et al., 2007). Therefore, the progenitor of RCW 103 is thought to have similar physical characteristics to majority of OB stars in our Galaxy except an extremely long periodicity of 1E 161348$-$5055.

A measurement of N/O in CSM established in our study is a good method to constrain progenitors of SNRs; e.g., stellar properties such as $M_{\rm{ZAMS}}$, initial rotation velocities, and convective overshoots. The microcalorimeter Resolve onboard the XRISM satellite (Tashiro et al., 2018) will be able to detect the C, N and O lines in many diffuse sources in our Galaxy. Athena (Barret et al., 2018) and Lynx (Gaskin et al., 2019) will be able to expand the targets to Large and Small Magellanic Clouds SNRs. With these future observatories, to measure the CNO abundances will become a key method to probe the relationship between the stellar evolution and the final fate of stars, such as supernovae and compact objects, and formation probability of magnetars, neutron stars, and black holes.