Heavy element contributions of rotating massive stars to Interstellar Medium
aa r X i v : . [ a s t r o - ph . GA ] F e b Research in Astron. Astrophys.
Vol. X No. XX , 000–000 (L A TEX: 2020-0450.tex; printed on February 3, 2021; 1:40) R esearchin A stronomyand A strophysics Heavy element contributions of rotating massive stars toInterstellar Medium ∗ Ruiqing Wu , Chunhua Zhu , Guoliang L ¨u , Zhaojun Wang , Helei Liu School of Physical Science and Technology, Xinjiang University, Urumqi 830046, China; [email protected], [email protected]
Received 2020 December 9; accepted 2021 January 12
Abstract
Employing the the stellar evolution code (Modules for Experiments in StellarAstrophysics), we calculate yields of heavy elements from massive stars via stellar windand core − collapse supernovae (CCSN) ejecta to interstellar medium (ISM). In our mod-els, the initial masses ( M ini ) of massive stars are taken from 13 to 80 M ⊙ , their initialrotational velocities (V) are 0, 300 and 500 km s − , and their metallicities are [ F e/H ] = -3, -2, -1, and 0. The yields of heavy elements coming from stellar winds are mainlyaffected by the stellar rotation which changes the chemical abundances of stellar surfacesvia chemically homogeneous evolution, and enhances mass-loss rate. We estimate that thestellar wind can produce heavy element yields of about − (for low metallicity models)to several M ⊙ (for low metallicity and rapid rotation models) mass. The yields of heavyelement produced by CCSN ejecta also depend on the remnant mass of massive masswhich is mainly determined by the mass of CO-core. Our models calculate that the yieldsof heavy elements produced by CCSN ejecta can get up to several M ⊙ . Compared withstellar wind, CCSN ejecta has a greater contribution to the heavy elements in ISM. Wealso compare the Ni yields by calculated in this work with observational estimate. Ourmodels only explain the Ni masses produced by faint SNe or normal SNe with progen-itor mass lower than about 25 M ⊙ , and greatly underestimate the Ni masses producedby stars with masses higher than about 30 M ⊙ . Key words:
Stars: massive—rotation—ISM: abundances
Interstellar medium (ISM) is defined as follows: atomic, gas ions, dust grains, cosmic rays, and alsoincludes many molecules. Heavy elements are fundamental components to ISM and play a critical rolein the stellar evolution of astrophysics and the chemical evolution in the ISM. It is well known thatmassive stars with a initial mass larger than ∼ M ⊙ play the most important role for producing theheavy elements in ISM (e. g., Dunne et al. 2003; Ablimit & Maeda 2018; Du 2020). These massivestars contribute to heavy elements via stellar wind and the ejecta of core − collapse supernovae (CCSN).Although the heavy elements may originate from other sources including the stellar wind of asymp-totic giant branch stars, ejecta of classical novae, binary merger et al, their contribution is very low(Groenewegen & de Jong 1993; Marigo 2007; Hix 2001; L¨u et al. 2013; Zhu et al. 2013; Jos´e et al.2006; Li et al. 2016; Rukeya et al. 2017; Zhu et al. 2019; Duolikun et al. 2019; Shi et al. 2020; Guoet al. 2020). ∗ Supported by the National Natural Science Foundation of China. R.-Q. Wu et al.
The yields of heavy elements from massive stars have been investigated by many literatures (e.g., Woosley & Weaver 1995; Chieffi & Limongi 2004; Nomoto et al. 2006; Heger & Woosley 2010;Nomoto et al. 2013). However, these works do not consider mass loss which is very important forthe massive star evolution (A recent review can be seen in Smith 2014). Usually, the mass loss wasthought to be caused by stellar wind driven by drastic radiation (Castor et al. 1975; Puls et al. 2008).Simultaneously, it is also affected by metallicity and rotation (Vink 2000; Vink et al. 2001; Meynet 2000;Maeder & Meynet 2012). Because the efficiency of radiation pressure removing the stellar envelopedepends on metallicity, it has an effect on the mass-loss rates ( ˙ M ) of massive stars by ˙ M ∝ Z m , wherethe index range of m is from 0.5 to 0.94 (Vink 2000; Vink et al. 2001; Mokiem et al. 2007). Rotationcan enhance the mass-loss rate (Langer et al. 1998; Heger 1998). More importantly, rapidly rotationcan result in quasi chemically homogeneous evolution (CHE) induced by various instability, such asdynamical shear instability, the Solberg-Hiøland instability, the secular shear instability, the Eddington-Sweet circulation, and the Goldreich Schubert-Fricke instability (e. g., Pinsonneault et al. 1989; Heger& Langer 2000). CHE can carry the heavy elements produced by nuclear burning in the core to thestellar surface, thus these heavy elements enter ISM via stellar wind (e. g., Brott et al. 2011; Song et al.2016; Cui et al. 2018). The role of heavy elements mixing is critical, it will affect the opacity of theenvelope and increase the luminosity and effective temperature of the star (Glebbeek et al. 2009).The standard non-rotating single-star model is strongly opposed as a possible progenitor of theSupernovae (SNe) (Fremling et al. 2014; Bersten & Nomoto 2014a). But Prantzos et al. (2018) recentlygave the heavy element yields of rotating massive stars. They considered effects of three initial rotationalvelocities, namely, 0, 150 and 300 km s − . Initial velocity above ∼ km s − more likely attain tothe critical velocity (Meynet & Maeder 2006). Furthermore, in the VLT-FLAMES Tarantula Survey,Dufton et al. (2013) found that the projected rotational velocities of single early B-type stars can reachapproximately 450 km s − . In binary systems, owing to mass transfer rotation velocity will reach to theKepler velocity (de Mink et al. 2013).Meanwhile, rapidly rotation result in a more massive helium core via CHE (Belczynski et al. 2016;Eldridge & Maund 2016; Mandel & De Mink 2016; Marchant et al. 2016; Wang et al. 2018). On accountof the helium-core masses have greatly effects on the remnant masses of neutron stars and black holes (e.g., Hurley et al. 2000; Belczynski et al. 2008). At the pre-supernova (pre-SN) stage, a larger helium-coreburning produces a bigger CO-core (Meynet & Maeder 2006; K¨ohler et al. 2015; Marassi et al. 2019).Hence, rotation as well as affects the heavy elements of CCSN ejecta. Very recently, in order to studydust formation in CCSN ejecta, Marassi et al. (2019) considered the effects of rotation, metallicity, andfallback, they computed the heavy element yields of massive stars. However, they did not still consideredthe yields via stellar wind.Therefore, it is necessary to study the heavy element yields coming from stellar wind and CCSNejeca for massive stars. Even the research on the relevant factors of elemental abundance is very urgent.In this paper, we study the effects of metallicity, rotation and fallback on the contribution of heavyelements produced by massive stars. In Section 2, the input physical parameters in models are described.The detailed results are discussed in Section 3. The main conclusions appear in Section 4. We use the open-source stellar evolution code Modules Experiments in Stellar Astrophysics (MESA,version 10108, model core-collapsed supernova) to simulate massive star evolutions (Paxton et al. 2011,2013, 2015). In these simulations, we select 67 − isotope network. The mixing-length parameter ( α mlt )is taken as 1.5 (Brott et al. 2011; Moravveji 2016; Ma et al. 2020; Shi et al. 2020). In addition, theLedoux criterion connects with boundaries of convection, semi-convection ( α sc ) is selected as 0.02.Most of all, MESA has the Ledoux criterion ∇ = ∇ rad in the overshoot area, which is different withdeep overshoot method (Maeder 1975; Viallet et al. 2015). Overshooting between convective core andradiative of interior diffusion parameter is expressed by ( f ov = 0 . ). Another effective parameter( f o = 0 . ) is from the surface down to overshoot layer, (Paxton et al. 2011; Moravveji 2016; Higgins& Vink 2019), they are considered at all stages of evolution, they also can affect the total mass of stellar eavy elements contribution of massive stars 3 loss. Thermohaline mixing parameter ( α th ) is equal to . (Kippenhahn et al. 1980; Paxton et al. 2013).In this work, we use the formulae of Vink et al. (2001) to calculate the mass-loss rates. In addition,rotation can enhance mass-loss rate by ˙ M (Ω) = ( 11 − Ω / Ω crit ) γ ˙ M (0) , (1)where ˙ M (0) is the mass − loss rate without rotation, Ω and Ω crit represent the angular velocity andcritical Keplerian angular velocity, respectively, and parameter γ equals . (Langer et al. 1998). ˙ M (0) is calculated by the formulae in Vink et al. (2001). But when the angular velocity reaches the criticalangular velocity, there will be a singularity. We limit the mass loss rate so that the mass loss time scaleis longer than the thermal time scale of the star, see (1)-(3) equations in Yoon et al. (2012).In order to discuss the effects of metallicity, the 4 initial metallicities are taken in different mod-els as follows: [ F e/H ] = 0 , [ F e/H ] = − , [ F e/H ] = − and [ F e/H ] = − . Here, [ F e/H ] =log[(
F e/H ) / ( F e/H ) ⊙ ] where [ F e/H ] ⊙ = 0 . is the solar metallicity (Thielemann et al. 2010;Chiaki et al. 2015).Considering that rotational velocity of massive stars may get up to the critical velocity (de Minket al. 2013) at the stellar surface, we take the initial rotational velocities in different simulations as 0,300 and 500 km s − , respectively. Rotation triggers some instabilities, then lead to angular momentumtransport and chemical mixing (e. g., Meynet 2012). Based on the research of Pinsonneault et al. (1989),Heger & Langer (2000) and Yoon & Langer (2006), MESA uses the ratio of the turbulent viscosity tothe diffusion coefficient ( f c ) and the ratio of sensitivity to chemical gradients ( f µ ) to calculate angularmomentum transport and chemical mixing induced by rotation. Zhu et al. (2017) and Cui et al. (2018)employed MESA to investigate rotating massive stars. Following them, we choose f c = f µ = > . M ⊙ , and we do not considerthe nuclear reaction in this stage. The explosion mechanism of CCSNe is a complex process which isstill has not been well explained. In our model the explosion energy (E) is × ergs (Nomoto et al.2007; Paxton et al. 2013; Hirschi et al. 2017; Curtis et al. 2019).Simultaneously, a supernova explosion occurs when stellar central density gets to . × g/cm and central temperature is ∼ . × k .Fig. 1: The evolutions of massive stars with different masses and rotation velocities for Z = 0 . .The solid lines represent a non-rotating star, while the dash-dotted lines represent a star with a rotationvelocity of 550 km s − . Green and blue lines are the evolutional tracks calculated by Brott et al. (2011),and black and red lines are simulated in our models. R.-Q. Wu et al.
Using MESA code, we simulate the evolutions from main sequence (MS) to CCSN for 8 massive starswith masses of 13, 15, 20, 25, 30, 40, 60 and 80 M ⊙ . In order to discuss the effects of rotation, theinitial rotational velocities are taken 0, 300 and 500 km s − in different simulations, respectively. Inorder to check our model, we compare the evolutions of several stars with these in Brott et al. (2011)under similar input parameters. Figure 1 shows the evolutional tracks in two works are similar. All heavyelements originating from star are produced by nucleosynthesis. They are ejected into ISM via stellarwind and CCSN ejecta. Before massive stars occur CCSN, their heavy elements enter ISM via stellar winds. These heavy ele-ments locate in stellar envelope. In this work, we estimate the yields of i-th heavy element by M i = Z t pre ˙ M ( t ) X i ( t )d t, (2)where t pre is the time from zero-age MS to pre-CCSN, ˙ M ( t ) and X i ( t ) are the mass-loss rate and themass fraction of i-th heavy element on the surface of massive star, respectively. Therefore, the heavyelements coming from stellar wind mainly depend on the mass-loss rates and the chemical abundanceson the stellar surface.In our model, the mass-loss rates are affected by metallicity and rotational velocity. Figure 2 showsthe evolutions of mass-loss rates for different initial mass stars with different metallicities and rotationalvelocities.Fig. 2: The evolutions of mass-loss rates for models with different masses (20 and 60 M ⊙ ), metallicities( [ F e/H ] = 0 , − ) and rotational velocities (0 and 500 km s − ).Compared the two metallicities models, a high metallicity can result in a high mass-loss rate because ˙ M ∝ Z m , where parameter m ranges from 0.64 to 0.85 (Vink et al. 2001). Simultaneously, the mass-loss rates depends on the rotational velocities by Eq. 1 mainly for MS stage, we also consider the redsupergiant (RSG) or Wolf-Rayet (WR) stage (Nugis & Lamers 2000). Therefore, the higher the initialrotational velocity is, the higher the mass-loss rates is. The mass-loss rate can be enhanced about 1-4magnitude when the initial rotational velocity increases from 0 to 500 km s − . The chemical abundanceson stellar surfaces are determined by CHE. During MS late phase, the star begins to rapidly expand, therotational velocity sharply decrease. Therefore, CHE mainly works in MS phase. The heavy elementsaffected by nucleosynthesis during MS phase are C, N and O (key elements of the evolution ofmassive stars). eavy elements contribution of massive stars 5
Fig. 3: The evolutions of heavy-element abundances [ C (black), N (red), O (green), and Fe(blue)] on the stellar surfaces for massive stars. The two panels in the top region represent the modelswith 20 M ⊙ , while the two panels in the bottom region is for 60 M ⊙ . The solid and dash-dotted linesrepresent models with V = 0 and 500 km s − , respectively. The different metallicities are given in theleft-top region of every panel.Figure 3 gives the evolutions of heavy-element ( C, N and O) abundances on the stellar sur-faces. Obviously, if there is no CHE in models without rotation, the heavy-element abundances on thestellar surface are constant during its life. However, in rotational models, the abundances of C, N and O elements on the stellar surfaces change. C and O abundance decreases, while N abundancesincreases. In particular, the lower metallicity is, the stronger CHE is. Therefore, for lower metallicitymodels, the range of increase and decrease in abundance is more obvious. In addition, for 60 M ⊙ panel,because the H-rich shell are stripped out before the RSG phase, and the star come in a WR stage. AsFigure 3 shows, C and O elements under stellar surface deeply increase while N elements de-creases. Similar results have been discussed in Maeder & Meynet (2001), Hirschi et al. (2005), Chieffi& Limongi (2013), Groh et al. (2014), and Meyer et al. (2020).Figure 4 gives the yields of heavy elements ( C, N, O, and Fe) produced via stellar winds.Hirschi et al. (2005b) also calculated the yields of heavy elements produced by stellar winds. In the Table3 for a model with M ini = 20 M ⊙ , [ F e/H ] = 0 and V = 300 km s − , Hirschi et al. (2005b) gave theyields of C, N, O elements are . × − , . × − and . × − M ⊙ , respectively. Undersimilar input parameters, the yields in our models are . × − , . × − , and . × − M ⊙ ,respectively. For a model with M ini = 40 M ⊙ , they in Hirschi et al. (2005b) are . , . × − and . × − M ⊙ , respectively. They in our work are . , . × − and . × − M ⊙ , respectively.The results in both works are consistent.In short, the yields of heavy elements coming from stellar winds can get to several M ⊙ for highrotation and high metallicity, while they may only be − M ⊙ for low rotation and low metallicity. The heavy elements locating in stellar interiors are ejected into ISM via CCSN. They are mainly de-termined by mass fractions before CCSN occurs. Figure 5 and Figure 6 show the fractions of differentelements in the models. For models with a mass of 20 M ⊙ , rapid rotation can enhance mass-loss rates.The star with V = 500 km s − have lost whole hydrogen envelope. Simultaneously, it can trigger CHE,produce a larger CO-core. Therefore, compared with the star without rotation, it has more massive core R.-Q. Wu et al.
Fig. 4: The yields of the heavy elements, C (black), N (red), O (green), and Fe (blue), pro-duced via stellar winds from massive stars with different initial masses, metallicities ( [ F e/H ] =0 , − , − , − ), and V =
0, 500 km s − . The multiplication and addition symbols represent calculatedmodels with V = 0 and 500 km s − , respectively.Fig. 5: The mass fractions of chemical elements in stellar interiors [M(r)] at pre-CCSN for models withinitial mass of 20 M ⊙ . The left two panels (the initial rotational velocities are 0 and 500 km s − ,respectively) represent the models with [ F e/H ] = − , and the right two panels for the models with [ F e/H ] = 0 . The abundance of various chemical elements is represented by colorful lines, for example, H (yellow), C (red), N (green) etc.before CCSN. The stars with low metallicity can undergoes efficient CHE and have low mass-loss rate.Their CO-core at pre-CCSN are larger than those for the stars with high metallicity. Similar resultsappear in models with 60 M ⊙ star. These results are consistent with these in van Marle et al. (2007);Tominaga (2008); Limongi & Chieffi (2018). During CCSN, massive stars eject a portion of their massesand leave compact objects (neutron stars or black holes). Generally, the remnant mass ( M rem ) is calcu-lated by CO-core mass ( M CO ) (e. g., Belczynski et al. 2008). In this work, we use the Equations (1) to(4) in Belczynski et al. (2008) to calculate M rem .Figure 7 (Left) gives M CO and M rem calculated by different models. M CO and M rem are mainlydetermined by mass-loss rates. The stars with high metallicity and high rotational velocity have highmass-loss rates, their M CO and M rem hardly exceed 10 M ⊙ . CHE triggered by rapid rotation can onlyincrease the M CO and M rem of models with initial masses lower than about 30 M ⊙ . We compare theCO-core with the work of Belczynski et al. (2008) model with a rotation of 300 km s − , obviously thesize of the CO-core of the two models are consistent. eavy elements contribution of massive stars 7 Fig. 6: Similar with Figure 5 but for models with initial mass of 60 M ⊙ .Fig. 7: Left: the CO-core ( M CO ) and remnant ( M rem ) masses vs. The initial masses in different models.The black and the red lines represent M CO and M rem , respectively (Our work). The solid blue linerepresents the CO-core size of the Belczynski et al. (2008) model with a rotation of 300 km s − . Right:comparison of the remnant masses in our work with those in Marassi et al. (2019). Black and red linesrepresent Marassi et al. (2019) results and ones in our.Figure 7 (Right) compares M rem calculated by this work with those in Marassi et al. (2019).Obviously, M rem of stars with initial masses lower than about 30 M ⊙ in our work is higher than thatin Marassi et al. (2019), while others in our work are lower. The main reasons are mass-loss rates andthe method for calculating remnant mass. For the former, as Figure 2 in Marassi et al. (2019) showed,the hydrogen envelope with a mass of about 3 M ⊙ in the model with 60 M ⊙ initial mass and [Fe/H]=-1is left before CCSN. However, under the model with [Fe/H]=-1, there is no hydrogen envelope for 60 M ⊙ initial mass at pre-CCSN. For the latter, the remnant mass in Marassi et al. (2019) is determined bythe initial mass and the metellicity, while this work calculates M rem via M CO . Observation show thatthe CO nucleus will only appear when the gas density of the star reaches the standard value Chen et al.(2006). The yield of the i-th element produced by CCSN ejecta can be calculated by explosion.Figure 8 shows the yields of heavy elements produced by CCSN ejecta in this work. M i = Z M fin M rem [ X i ( m ) − X ]d m (3)where X i ( m ) is the i-th element mass fraction before the SN with Lagrangian coordinate m, X is theinitial abundance, the X of these elements are 0. M fin is the final mass of the star Ekstr¨om et al. (2008).However, compared with stellar winds (see Figure 4), CCSN ejecta can produce more heavy elements,especially the elements heavier than O element. Compared with Marassi et al. (2019), our work giveslower yields of heavy elements. The main reason is that our models have higher mass-loss rates. BeforeCCSN occurs, the stars in our models have lost more mass than those in Marassi et al. (2019).
R.-Q. Wu et al.
Fig. 8: Yields of heavy elements produced by CCSN ejecta. The left panel represents the results in thiswork. The right panel gives the comparison of our results with ones in Marassi et al. (2019).Fig. 9: The Ni masses produced by CCSN ejecta and their progenitor masses at MS phase. These datacome from Nomoto et al. (2013). The red, black and purple cycles represent faint SNe, normal SNeand hypernovae, respectively. The yields of Ni calculated by our models are given by dotted lines( [ F e/H ] = 0 ) and dashed lines ( [ F e/H ] = − ). For example, the green and blue colors representmodels with V = 0 and 500 km s − , respectively.Via the comparison of observed light curves and the theoretical models, Nomoto et al. (2013) esti-mated the Ni masses produced by some CCSN ejecta and their progenitor masses, which are showedin Figure 9. Here, Ni is caused by the decay of Ni → Co → Fe (Argast et al. 2002; Hamuy2003). We calculate the yields of Ni in the different initial mass models. Similar with the fixed energymodels in Marassi et al. (2019), our results only explain the Ni masses produced by faint SNe ornormal SNe with progenitor mass lower than 25 M ⊙ . Clearly, our understanding for the massive starevolution and CCSN is still poor. In this work, we calculate the contribution of heavy elements from massive stars via stellar wind andCCSN ejecta to ISM.In our models, the evolutions of massive stars are affected by rotation, mass-loss rate and metallicity.The rotation via CHE changes the chemical abundances of stellar surfaces, and enhances mass-loss rate. eavy elements contribution of massive stars 9
It can increase N abundance by 10 times while decrease C and O abundances by similar times.It can enhance the mass-loss rates by about 1-4 magnitude when the initial rotational velocity increasesfrom 0 to 500 km s − . Therefore, the yields of heavy elements coming from stellar winds are mainlyaffected by the stellar rotation. We estimate that the stellar wind can produce heavy element yields ofabout − (for low metallicity models) to several M ⊙ mass (for low metallicity and rapid rotaionmodels), which depends on stellar rotation and metallicity.The yields of heavy element produced by CCSN ejecta depend on not only rotation, mass-loss rateand metallicity, but also the remnant mass of massive mass. Here, the latter mainly depends on the massof CO-core which is greatly affected by the above three parameters. Our models calculate that the yieldsof heavy elements produced by CCSN ejecta can get up to several M ⊙ mass. Compared with stellarwind, CCSN ejecta have a greater contribution to the heavy elements in ISM.We also compare the Ni yields by calculated in this work with observational estimate. Our modelsonly explain the Ni masses produced by faint SNe or normal SNe with progenitor mass lower thanabout 25 M ⊙ , and greatly underestimate the Ni masses produced by stars with initial masses higherthan about 30 M ⊙ . It means that there is still a long way to understand the massive star and CCSNevolution. Acknowledgements
This work received the generous support of the National Natural ScienceFoundation of China, projects No, 11763007, 11863005, 11803026, and U2031204. We would alsolike to express our gratitude to the Tianshan Youth Project of Xinjiang No. 2017Q014.
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