Phosphorus Enrichment by ONe Novae in the Galaxy

Recent observations have shown that [P/Fe] in the Galactic stars decreases with increasing [Fe/H] for [Fe/H] ≳ − 1 whereas it is almost subsolar for [Fe/H] ≲ −2. These [P/Fe] trends with [Fe/H] have not been well reproduced by previous theoretical models incorporating phosphorus (P) enrichment only by core collapse supernoave. We here show, for the first time, that the trends can be naturally explained by our new models incorporating P enrichment by oxygen–neon (ONe) novae, which occur at the surface of massive white dwarfs whose masses are larger than 1.25M ⊙ with a metallicity-dependence rate. We also show that the observations can be better reproduced by the models by assuming that (i) the total mass of gaseous ejecta per ONe nova (M ej) is as high as 4 × 10−5 M ⊙ and (ii) the number of such novae per unit mass (N ONe) is as large as 0.01 at [Fe/H] ≈ −3. The assumed M ej is consistent with observations, and the high N ONe is expected from recent theoretical models for ONe nova fractions. We predict that (i) [P/Fe] increases with increasing [Fe/H] for −2 ≲ [Fe/H] ≲ −1 and (ii) [P/Fe] and [Cl/Fe] trends with [Fe/H] are very similar to each other due to very large yields of P and Cl from ONe novae. It is thus worthwhile for future observations to assess the validity of the proposed P enrichment by ONe novae by confirming or ruling out these two predictions.


INTRODUCTION
Recent spectroscopic observations of the Galactic stars have revealed intriguing abundance patterns of phosphorus (P) depending on metallicities (e.g., Caffau et al. 2011;Roederer et al. 2014;Hinkel et al. 2020;Masseron et al. 2020, M20;Snedin et al. 2021;Maas et al. 2022;Nandakumar et al. 2022).For example, [P/Fe] is observed to decrease with increasing [Fe/H] at −1 [Fe/H] 0.3 (e.g., Caffau et al. 2011;Nandakumar et al. 2022), which is similar to [α/Fe] (e.g., [Mg/Fe]) trends with [Fe/H].Roederer et al. (2014) found that [P/Fe] at −4 [Fe/H] −2 is either slightly above solar or subsolar with no stars having higher (> 0.3) [P/Fe], which is in a striking contrast with the observed trend of [α/Fe] with [Fe/H].These characteristic trends of [P/Fe] with [Fe/H], which need to be reproduced by any theory of galaxy formation, are summarized in Figure 1.Cescutti et al. (2012, C12) first tried to reproduce the observed trend of [P/Fe] with [Fe/H] from Caffau et al. (2011).They demonstrated that their models with the adopted P yields of core collapse supernovae (CCSNe) being by a factor of 3 higher than those from Kobayashi et al. (2006, K06) can reproduce well the decreasing [P/Fe] with increasing [Fe/H] at [Fe/H] −1.However, it is unclear whether such an ad hoc yield increase is really reasonable and realistic in the nucleosynthesis of CCSNe.Furthermore the observed sub-solar [P/Fe] at [Fe/H] −2 (e.g., Roederer et al. 2014Roederer et al. , 2016) ) is inconsis-tent with the models by C12 which predicted high [P/Fe] ( 0.3) at [Fe/H] −2.Other chemical evolution models with P enrichment by CCSNe and rotating massive stars by Prantzos et al. (2018) predicted an almost constant [P/Fe] (∼ solar value) and accordingly cannot reproduce the observed [P/Fe] trend with [Fe/H] either.Therefore, polluter other than CCSNe (e.g., AGB stars and novae) are required to reproduce the [P/Fe] evolution of the Galaxy.As shown in M20, the P yields of AGB stars are significantly lower than those of novae, which suggests that P-enrichment by novae would need to be first considered in the Galactic chemical evolution models.
Previous and recent nucleosynthesis models for novae formed from oxygen-neon-magnesium (ONe) white dwarfs (WDs) have shown that the mass fractions of P in ONe novae with WD masses (M WD ) being 1.25 and 1.35M ⊙ (referred to as "P-rich" ONe nova just for convenience) are as high as 0.01 corresponding to the mass fractions by a factor of ≈ 1000 larger than those of CCSNe in some of the models (e.g., José & Hernanz 1998, JH98;Starrfield et al. 1998, S98).This suggests that P enrichment by these ONe novae can be crucial in [P/Fe] evolution even if the total ejecta mass is relatively small compared to those from CCSNe: chemical enrichment by P-rich ONe nova should be more seriously considered in chemical evolution models of the Galaxy.However, no chemical evolution models have ever investigated whether P enrichment by ONe novae can explain )*+,-.
),-+/.001234567 839:;-3<73 3333=2-354>8 !"#$%&'$()*( ((((+(,"#($"-+(.'/0&/$1*234/(5+((( Fig. 1.-Distribution of the Galactic P-normal stars with [P/Fe]< 1 on the [Fe/H]−[P/Fe] plane and illustration of the predicted evolutionary path of the "ONe nova" scenario (wide gray line).Observational results for P-normal stars ([P/Fe]< 1) from (i) Roederer et al. (2014Roederer et al. ( , 2016)), (ii) Maas et al. (2022), and (iii) Caffau et al. (2016Caffau et al. ( , 2019)) The purpose of this Letter is thus to demonstrate, for the first time, that P enrichment by ONe nova is responsible for the observed unique [P/Fe] trend with [Fe/H] in the Galactic stars.In this investigation, we particularly consider a recent theoretical prediction from Kemp et al. (2022, K22) that nova rates strongly depend on metallicities (Z) such that they are significantly lower at higher Z.As illustrated in Figure 1, the combination of high P yields from P-rich ONe novae and Z-dependent nova rates can reproduce the observed unique [P/Fe]−[Fe/H] relation of the Galactic stars in the present study.Using one-zone chemical evolution models incorporating P enrichment by ONe novae and the above theoretical prediction of P yields from ONe novae, we investigate how [P/Fe] evolution with [Fe/H] depends on the model parameters such as the total ejecta mass per ONe nova (M ej ) and the number fraction of P-rich ONe novae among all nova populations.Our future chemodynamical models of the Galaxy incorporating P enrichment will predict how the [P/Fe]−[Fe/H] relation is different in different regions of the Galaxy.

THE MODEL
We use our original code for one-zone chemical evolution of galaxies developed in our previous studies (Bekki & Tsujimoto 2012, 2023) to investigate the time evolution of [P/Fe] and [Cl/Fe] of the Galaxy.In the presentstudy, we newly incorporate (i) P enrichment by ONe novae (JH98) and (ii) P yields of CCSNe that can depend on metallicities in the code (K06).In investigating P enrichment by novae, we consider contributions only from P-rich ONe novae with their accreting white dwarf masses (M WD ) being as large as or larger than 1.25M ⊙ , because the mass fraction of P in the ejecta (f P ) can be ≈ 0.01: Other novae from CO WDs and ONe novae with M WD < 1.25M ⊙ have very low f P (≪ 0.01).We consider that (i) the number of novae per unit (starforming) mass (N N ), (ii) the number of outbursts per nova (N burst ), (iii) the number fraction of P-rich ONe novae among all nova populations (f ONe ), and (iv) the total mass of ejecta per nova (M ej ) are key parameters in P evolution of the Galaxy.
We adopt N burst = 10 4 that was adopted by chemical evolution models of the Galaxy (e.g., Matteucci et al. 2003;Romano et al. 2003;C12) and is consistent with observations (e.g., Della Valle and Izzo 2020 for a recent review).Since previous models adopted N N = 0.03 to explain the observed lithium (Li) abundance patterns of the Galactic stars and the present-day total nova rate (e.g., Cescutti et al. 2019), we consider the same value too: it should be noted here, however, that N N ≈ 0.014 at Z = 0.0001 is predicted by K22.The number of P-rich ONe novae per unit mass (N ONe ) is the most important parameter of the present study and denoted as follows; (1) K22 predicted that (i) the number fraction of ONe novae among all (CO and ONe) novae is about 70% in the Galaxy (see their Fig.12) and (ii) the number fraction of P-rich ONe novae with M WD > 1.25M ⊙ among ONe novae is also high (roughly 0.6 in their Fig.13).We therefore consider that f ONe (the above (i) multiplied by (ii)) can be as high as ≈ 0.4 corresponding to N ONe = 0.012 for N N = 0.03.K22 calculated the time delay between star formation and the onset of the nova outburst for each binary star system and thereby derived the delay time (t delay ) distribution for ONe novae.K22 showed that a very strong peak is at t delay = 500 Myr both for Z = 0.0001 and 0.03 and the majority of the novae have t delay < 2 Gyr (see their Fig.11).Given that the novae recurrence time for M WD > 1.2M ⊙ is shorter than 2.8 × 10 4 yr (Truran & Livio 1986), N burst = 10 4 means that all outbursts for Prich ONe nova can occur within a timescale of less than 10 9 yr after star formation.Considering these previous results, we assume that the first and last outbursts occur 10 8 and 10 9 yr after star formation, respectively, for P-rich ONe novae.
A key element of the present model is that N ONe depends on metallicities ([Fe/H]) as follows: where N ONe,0 is N ONe at the adopted initial [Fe/H] (i.e., [Fe/H] 0 = −3) and α Z determines the slope of the N ONe − [Fe/H] relation.Since K22 predicts that N N is significantly higher for lower Z (thus lower [Fe/H]), α Z should be negative: N ONe should be larger for lower [Fe/H] too.We mainly show the results of the models with N ONe,0 = 0.01 and α Z = −3.0× 10 −3 , because they can better reproduce observations.We investigate the models with M ej ranging from 10 −5 M ⊙ to 6 × 10 −5 M ⊙ , which is consistent with observations (e.g., Dell Valle & Izzo 2020).Since the mass fractions of Cl (f Cl ) in gaseous ejecta of P-rich ONe novae are very high too (> 10 −3 ; JH98), it is expected that [P/Fe] and [Cl/Fe] evolutionary trends with [Fe/H] are very similar with each other.We adopt f P = 0.01 and f cl = 0.004 from JH98 for all models, though these values can be even higher (e.g., S98).We consider that the mass fraction of P in the ejecta of CCSNe (f P,CCSN , calculated from tables in K06) for a given initial mass function of stars (IMF) is also fundamentally important for [P/Fe] evolution.Given that P yields of CCSNe depend on metallicities (K06), we assume that f P,CCSN can depend on metallicities (Z) as follows: f P,CCSN = 1.1 × 10 −5 + β Z × Z, where β Z determines the slope of the metallicity-dependence.We use this simplified model for f P,CCSN , because P yields are given only for four different Z in K06.Given a possible uncertainty in the metallicity-dependence, we investigate the models with β Z = 0 (no metallicity-dependence), 0.001, 0.002, and 0.004.We choose 1.1 × 10 −5 at Z = 0, because the present models can reproduce the observed We adopt the Salpeter IMF of stars with the slope (α) of −2.35, the lower and upper mass cut-off being 0.1M ⊙ and 50M ⊙ , respectively.The gas infall timescale and the the number of SNe Ia per unit mass are set to be 3 Gyr and 0.085, respectively.The star formation rate (SFR) at each time step is assumed to be proportional to the gas mass (M g ), i.e., SFR= C sf M g , where C sf is chosen such that the final [Fe/H] is close to the solar value.We investigate 13 Gyr chemical evolution of the Galaxy for the initial gaseous [Fe/H] of −3.The model with N ONe,0 = 0.01, α Z = −3 × 10 −3 , f P =0.01, f P,CCSN = 1.1 × 10 −5 at [Fe/H]= −3, β Z = 0, and M ej = 4 × 10 −5 M ⊙ is selected and referred to as the "fiducial" model, because it can best explain both the observed peak [P/Fe] at [Fe/H]≈ −0.8 and [P/Fe]−[Fe/H] relation among all models investigated.ent metallicity-dependent P yields of CCSNe and without ONe novae all fail to explain the observed characteristic [Fe/H]−[P/Fe] relation.This demonstrates that chemical enrichment by P-rich ONe novae is essential to reproduce the characteristic relation.In order to reproduce the observed [P/Fe] decrease with increasing [Fe/H] at [Fe/H] −0.8 the models without ONe novae need to assume that f P,CCSN is smaller for higher [Fe/H] at [Fe/H] −0.8.Such a contrived metallicity-dependent f P,CCSN appears to be unphysical, given that P yields are larger for higher metallicities in CCSNe with different initial stellar masses (K06).We therefore conclude that CCSNe alone cannot be responsible for the observed unique [Fe/H]−[P/Fe] relation in the Galaxy.
As shown in Figure 5, irrespectively of f Cl,CCSN , the present models can reproduce the observed [Cl/Fe] at [Fe/H] −0.5 pretty well.As P-rich ONe novae start to enrich the ISM around [Fe/H]= −2, [Cl/Fe] increases rapidly with increasing [Fe/H] to reach its peak at [Fe/H]≈ −0.8.[Cl/Fe] subsequently decreases with increasing [Fe/H] due to the chemical enrichment by SNe Ia and the lower rates of P-rich and Cl-rich ONe novae at higher metallicities.The derived [Cl/Fe] evolution at [Fe/H] −0.5 is qualitatively similar to the observed one, though the observed dispersion of [Cl/Fe] at a given [Fe/H] appears to be large.These behaviors of [Cl/Fe] are very similar to those of [P/Fe], which is a unique prediction of the ONe nova scenario to be tested against future observations.Since there is no observational data point at [Fe/H] −0.5, it is not clear whether the characteristic evolutionary path of the ONe nova scenario on the [Fe/H]−[Cl/Fe] plane can be consistent with the corresponding observation.observational studies of WDs by the Gaia space mission have found that the masses of progenitor stars that lead to WDs with M WD 1.2M ⊙ is around 7M ⊙ (Tremblay et al. 2024).Accordingly, the number of stars with their initial masses (M ) ranging from 7M ⊙ to 10M ⊙ (corresponding to M WD = 1.35M ⊙ ; Truran and Livio 1986) per unit mass is 3.6 × 10 −3 for α = 2.35 (the Salpeter IMF) and 9.1 × 10 −3 for α = 1.5 (top-heavy).Therefore, if only these massive stars become P-rich ONe novae during their binary evolution, the required N ONe,0 ≈ 0.01 at [Fe/H]= −3 for M ej = 4 × 10 −5 can be marginally consistent with top-heavy IMFs.This required top-heavy IMFs is consistent with observational evidence of more topheavy IMFs for lower metallicities discovered by Marks et al. (2012).
ONe nova models with higher P yields (f P > 10 −3 ) show lower M ej (< 10 −5 M ⊙ ) in previous studies (e.g., JH98; S98; Starrfield et al. 2024): M ej is only 5.2 × 10 −6 M ⊙ for the model 8 with f p = 0.02 in S98.José et al. (2007) showed that novae with initial metallicities (Z) of 10 −7 and 2 × 10 −6 have M ej = 1.33 × 10 −5 M ⊙ and 1.01 × 10 −5 M ⊙ , respectively, yet very high P yields corresponding roughly to ≈ 500 times the solar abundance.Although this implies that there are no previous novae models that reproduce both f P ≈ 0.01 and high M ej ≈ 4 × 10 −5 M ⊙ , low-metallicity nova models with 10 −6 < Z < 10 −2 have not been explored yet.The validity of the ONe nova scenario therefore depends crucially on whether these low-metallicity nova models can predict both high f P and high M ej .
The observed ejecta mass from V1974 Cyg 1992 that is a candidate of ONe nova with M WD = 1.25M ⊙ ranges from 5 × 10 −5 M ⊙ to 5 × 10 −4 M ⊙ (e.g., Shore et al. 1993;Austin et al. 1996), which is [10-100] times larger than the predicted values by S98.If most P-rich ONe novae can eject a larger amount (≈ 10 −4 M ⊙ ) of gas like V1974 Cygni, the required N ONe,0 can be significantly lower for a reasonable range of IMFs.The observed large M ej in V1974 Cygni, which is yet to be reproduced by existing nova models, would demand the update of the ONe nova models too.
The present study has provided the following two key predictions that can be tested against observations: (i) [P/Fe] increases with increasing [Fe/H] for −2 [Fe/H] −1 and (ii) the evolutionary path of the Galaxy on the [Fe/H]−[Cl/Fe] plane is very similar to that on the [Fe/H]−[P/Fe] plane.It is therefore doubtlessly worthwhile for future observations to investigate [P/Fe] of the Galactic halo and thick disk stars with for −2 [Fe/H] −1.Such observations will also be able to distinguish between chemical enrichment by ONe novae and by massive stars with O-C shell merging (Ritter et al. 2018).Likewise, spectroscopic studies of [Cl/Fe] of stars with [Fe/H]< −0.5 are crucial to assess the validity of the ONe nova scenario, though such observations could be challenging for existing telescopes.
M20 have discovered P-rich stars with unusually high [P/Fe] (> 1) and suggested that super-AGB stars and novae can produce a large amount of P required to explain [P/Fe] of the P-rich stars.Although the present study has so far focused on the [P/Fe]−[Fe/H] relation of P-normal stars in the Galaxy, it can provide a possible solution to the origin of P-rich stars discovered by M20.If P-rich ejecta from P-rich ONe novae is mixed with a smaller amount of ISM without being much polluted by CCSNe and SNe Ia, new stars formed from the mixed gas can have rather high [P/Fe].A key question of this scenario is whether the observed abundances of elements other than P such as [O/Fe], [Mg/Fe], [Al/Fe], and [Si/Fe] can be self-consistently explained by the scenario.Since JH98 predicted higher levels of enhancement in the above elements, it is our future study to investigate whether the observed chemical abundance patters of these elements in P-rich stars can be reproduced well by our future models.The observed higher [Ce/Fe] of P-rich stars also needs to be investigated by our future models incorporating chemical enrichment by super-AGB stars that are progenitor of WDs for ONe novae and can eject Ce-rich winds (e.g., Doherty et al. 2014).

ACKNOWLEDGMENT
We are grateful to the referee for constructive and useful comments that improved this paper.TT was supported by JSPS KAKENHI Grant Numbers 18H01258, 19H05811, and 23H00132.

Figure 2 Fig. 4 .
Figure 2 describes how the evolutionary path of the Galaxy on the [Fe/H]-[P/Fe] plane depends on M ej in four models with the same α Z (= 3 × 10 −3 ) yet different M ej .Clearly, all models show (i) constantly low [P/Fe] at [Fe/H] −2, (ii) increasing [P/Fe] with increasing [Fe/H] at −2 [Fe/H] −0.8, and (iii) decreasing [P/Fe] with increasing [Fe/H] at [Fe/H] −0.8, though the peak [P/Fe] at [Fe/H]≈ −0.8 strongly depends on M ej .The above result (ii) is due to the earlier enrichment by P-rich ONe novae that can occur only 10 8 yr after star formation.The result (iii) is caused by a significant decrease of [P/Fe] due to the combination effect of lower ONe nova rates at higher [Fe/H] and efficient iron production by SNe Ia.This result implies that the observed [Fe/H]−[P/Fe] relation can constrain M ej : If N ONe,0 ≤ 0.01, then M ej ≤ 10 −5 M ⊙ can be ruled out in the ONe nova scenario.Given that different M ej is expected among ONe novae with different WD masses (JH98), Figure 2 also suggests that the observed [P/Fe] dispersion at a given [Fe/H] could be due to the different degrees of P enrichment in ISM polluted by different ONe novae.Figure 3 shows that the models with no or weaker dependence of N ONe on [Fe/H] (−2.7 ≤ α Z ≤ 0) cannot reproduce the observed [Fe/H]−[P/Fe] relation at [Fe/H] −1 so well compared with the fiducial model with α Z = −3 × 10 −3 .These results clearly demonstrate that steep metallicity-dependent nova rates are essential to explain the observed characteristic [Fe/H]−[P/Fe] relation.Although the model with a lower initial number of P-rich ONe novae (N ONe,0 = 5×10 −3 ) and a shallower metallicity-dependent nova rate (α Z = −1.3× 10 −3 ) can reproduce [Fe/H]−[P/Fe] relation at [Fe/H] −0.6 , the peak [P/Fe] at [Fe/H]≈ −0.8 is significantly lower than the observed [P/Fe].This result suggests that N ONe,0 needs to be higher (> 5 × 10 −3 ) for M ej ≈ 4 × 10 −5 M ⊙ to explain the observed high [P/Fe] around [Fe/H]=−0.8,It is clear from Figure 4 that four models with differ- Figure 5 also demonstrates that peak [Cl/Fe] at [Fe/H]≈ −0.8 can be only slightly different between models with different f Cl,CCSN , even if the adopted initial [Cl/Fe] values are quite different.