Figure 4.4: Comparison of the final mass before the explosion between the new PARSEC and the old PADOVA evolutionary
tracks of massive stars (fromSlemer et al.(2017))
4.2.1
Which Supernovae Feed Non-Thermal Radio Emission ?
The final fate of stars primarily depends on their initial mass Mi and metallicity Zi. The conditions for a
star to proceed through all nuclear stages up to silicon burning with consequent formation of an iron core are that carbon burning in the centre is ignited in non-degenerate conditions, and that an oxygen-neon core is built up with a mass larger than ' 1.37 M (Nomoto 1984). We call the corresponding minimum
initial mass that fulfull these requirements Mmas. The detailed analysis ofSiess(2007) shows that Mmas
is related to a minimum mass of the He-exhausted (CO) core formed at the end of the He-burning phase, MHemas ' 1.246 ± 0.015 M for stellar models with convective overshoot, with a relatively small
dependence on the initial metallicity. Using this criterion for the PARSEC tracks,Slemer et al.(2017)) find that Mmasis an increasing function of the metallicity, ranging from Mmas' 6 M at Zi = 0.0001 to
Mmas' 8 M at Zi= 0.02. This is thus the initial mass of the least massive star that must be assumed
in the calculations.
Concerning the final fate of these massive stars, we first remind that not all these stars die with an exploding supernova. Detailed evolutionary calculations including the latest stages of massive stars show that, depending on the mass of H-exausted core at the end of pre-supernova phase, MHe, massive stars
can be divided in two main broad groups (Heger & Woosley 2002;Heger et al. 2003;Nomoto et al. 2013) Core Collapse Supernovae (CCSN): stars that develop MHe≤ 40 M . These objects form an iron core
before ending the evolution as supernova explosion or collapsing into a black hole. They have initial masses in the range from Mmas to 100 M , depending on the adopted mass loss rates. However the
occurrence or not of the explosion, and the corresponding kind of remnant (neutron star or black hole), crucially depend on the structure just prior to the core collapse.
42 Chapter 4: Radio Emission from Star Forming Regions
Very Massive Object (VMO): stars that have MHe≥ 40 M may explode before forming the iron
core. This class comprises three sub-groups. The pulsation pair instability supernovae (PPISN), with 40 M ≤ MHe ≤ 65 M , corresponding to initial masses in the interval 100 M ≤ Mi≤ 140 M . The
pair-instability supernovae (PISN), with 65 M ≤ MHe≤ 133 M and 140 M ≤ Mi≤ 260 M . The
stars with MHe≥ 65 M which proceed directly to a massive black hole, without producing ejecta.
In the following section I will analyze in detail the different final fates of massive stars belonging to the various groups, focusing on the nature (SN, BH) and mass of their remnants.
The link between the late evolutionary stages of massive stars and their final fates and remnants, neutron stars (NS) or black holes (BH), is still poorly constrained. The type of remnant finally produced is a critical parameter for estimating its contribution to non-thermal radio emission. If it is a BH, it is likely that the external envelope also collapses, thus leaving behind neither significant ashes for a typical SN light curve nor relativistic electrons. These events are termed Failed SN (O’Connor & Ott 2011) because they will likely remain undetected in optical-NIR surveys. Indeed the existence of a class of failed SN could solve the so called Red Supergiant (RSG) and SN rate problems at once. The first problem concerns the lack of SNII detections with RSG precursors more massive than about 20M (Smartt 2009). The second one concerns the mismatch between the observed cosmic SN rate and the rate expected from the cosmic star formation history, which is about a factor of two larger (Horiuchi et al. 2011).
The first important parameter that affects the final evolution of the massive stars is the mass-loss rate. To highlight this important point and to stress the need of a revision of the whole radio model by B02 we show in Figure4.4the differences between the final masses before the explosion predicted by the new PARSEC models and by the previous Padova models. We see from the figure that, e.g. at Z=0.02, due to the lower mass-loss rates adopted, the PARSEC final masses can be even a factor of three more massive than those predicted by the old Padova models. Thus the differences in the mass loss rates are the prime cause of the differences in the final phases.
Concerning the explosion phase, some recent works in the attempt to characterize the parameters of successful and failed supernovae have yielded some structural parameters of the pre-SN stars, such as the compactness parameter, that can be utilized in predicting the fate of SNe (eg.Ertl et al. 2015;Sukhbold & Woosley 2014;Ugliano et al. 2012;Janka 2012;O’Connor & Ott 2011). Using these parameters,Spera et al. (2015); Spera & Mapelli (2017); Slemer et al. (2017) were able to characterize the final fate of
PARSEC massive stars for the different criteria adopted for successful CCSN explosion.
The reader can refer to Figures 6 to 11 of Spera et al. (2015) for the mass spectrum the compact remanants obtained with PARSEC models as a function of MZAM S for different metallicities and SN
recipes. Here we limit the discussion to the range of exploding CCSNe and to failed SNe, as calculated by Spera et al. (2015). Figure 4.5 shows the results of adopting the so called compactness parameter (O’Connor & Ott 2011) while Figure4.6shows the results obtained with the M4 parameter ofErtl et al.
(2015). In both plots the horizontal axis is the initial mass while the vertical axis refers to the value of the adopted parameter. The white bars refer to models in which the explosion energy is enough to eject the external layers producing a visible SN. The filled bars refers to models where the explosion is not able to eject the external mantle and the stars thus collapses to a black hole. We remind here that in the SN