Phosphorus Abundances of B-Type Stars in the Solar Neighborhood
Yoichi Takeda





Phosphorus Abundances of B-Type Stars in the Solar Neighborhood
Yoichi  T a k e d a11-2 Enomachi, Naka-ku, Hiroshima-shi, Japan 730-0851

e-mail: ytakeda@js2.so-net.ne.jp

Month Day, Year



Phosphorus abundances of ∼ 80 apparently bright sharp-lined early-to-late B-type 
stars on the upper main sequence are determined by applying the non-LTE analysis 
to the P ii line at 6043.084 Å, with an aim of getting information on the P 
abundance of the galactic gas (from which these young stars were formed) in 
comparison with the reference solar abundance (A_⊙≃ 5.45).
These sample stars turned out to be divided into two distinct groups with respect 
to their P abundances: (1) chemically peculiar late B-type stars of HgMn group show 
considerable overabundances of P (supersolar by ∼ 0.5–1.5 dex), the extent of which
progressively increases with T_ eff. (2) In contrast, the P abundances of 
normal B-type stars are comparatively homogeneous, though a notable difference is 
observed between the LTE and non-LTE cases. Although their LTE abundances are near-solar,
a slight gradual trend with T_ eff is observed. However, after applying the negative 
non-LTE corrections (amounting ∼ 0.1–0.5 dex), this T_ eff-dependence is 
successfully removed, but the resulting non-LTE abundances (their mean is ≃ 5.20) 
are appreciably underabundant relative to the Sun by ∼ 0.2–0.3 dex. 
The cause of this systematic discrepancy (contradicting
the galactic chemical evolution) is yet to be investigated.

Galaxy: solar neighborhood – stars: abundances – stars: chemically peculiar – 
stars: early-type – stars: population I



§ INTRODUCTION


Astrophysical interest in the cosmic abundance of phosphorus (P; Z = 15) is rapidly 
growing these days. While one reason is that the mechanism of how this element is synthesized
in the chemical evolution of the Galaxy is not yet well understood, another intriguing    
motivation lies in its astrobiological context.
That is, P is (along with H, C, N, O) an indispensable key element 
for life, which is the backbone of nuclear acids (RNA, DNA) or cell 
membranes, and plays a significant role in producing/reserving 
the vital energy via ATP (Adenosine TriPhosphate). 
Especially, the original P abundance of protoplanetary material (or star-forming gas)  
in comparison with that of the Sun (comparatively P-rich) is an important factor, 
because substantially subsolar case would make it difficult to leave sufficient amount P 
for life on the surface of planets due to its strongly partitioning nature in the planetary 
core (Hinkel et al. 2020).

Accordingly, not a few stellar spectroscopists devoted their energies to P abundance determinations
since 2010s, and more than a dozen papers have been published during the short period of 
the past decade (see, e.g., Table 1 of  Sadakane & Nishimura 2022, Sect. 1 of Maas et al. 2022, 
and the references therein). These authors established the phosphorus abundances of
various late-type (FGK-type) stars by using neutral P i lines in the near-infrared 
region (Y-band or H-band) or in the ultraviolet region (∼ 2135Å). 

It has thus revealed that [P/Fe] (logarithmic P-to-Fe ratio) tends 
to progressively increase with a decrease in the metallicity ([Fe/H]) 
like α-elements for stars of disk population (from [P/Fe] ∼ 0 
at [Fe/H] ∼ 0 to [P/Fe] ∼ +0.5 at [Fe/H]∼ -1)  
whereas it turns to drop again in the metallicity regime of halo 
population ([P/Fe] ∼ 0 at [Fe/H] ≲ -2), as shown 
in Fig. 1 of  Bekki & Tsujimoto (2024).
While several theoreticians tried to explain this trend of [P/Fe] 
mainly in terms of the P production by core-collapse supernovae,
Bekki & Tsujimoto (2024) recently argued that oxygen–neon (ONe) 
novae (triggered in close binary systems including heavier white 
dwarfs) should play a significant role in the galactic nucleosynthesis 
of P. 

However, these studies are directed only to comparatively cool stars of lower mass (typically 
around ∼ 1 M_⊙) which have ages on the order of ∼ 10^9–10^10 yr.
Meanwhile, much less efforts have been made to young hotter stars, such as B-type stars 
of ∼ 3–10 M_⊙ (reflecting the gas composition of the Galaxy in the more 
recent past; i.e. several times ∼ 10^7–10^8 yr ago). Actually, phosphorus 
abundance determinations of B stars are generally scarce, excepting HgMn stars (chemically 
peculiar late B-type stars showing considerable overabundance of P by up to ∼ 1–2 dex),
for which P abundances have been reported for quite a number of stars as compiled by 
Ghazaryan & Alecian (2016).  

This is presumably due to the difficulty in finding useful P lines of sufficient
strengths. In the atmosphere of B-type stars, P atoms are mainly in the ionization stages 
of P ii (late–mid B) or P iii (early B), as illustrated in Fig. 1. 
Since available P ii or P iii lines in the optical wavelength 
regions are all of high-excitations (χ_ low > 10 eV), they are
fairly weak in strength for the case of usual (near-solar) P abundances and thus 
not easy to detect.[Although strong low-excitation P ii or 
P iii lines do exist in the ultraviolet region, they are not suitable for 
reliable abundance determinations (i.e., too strong and apt to suffer blending).]
 



As such, published studies of P abundances for “normal” B-type stars are quite limited:


  * Phosphorus abundances are reported for the well-studied benchmark sharp-lined star 
ι Her (B3 IV), as summarized in Table 1 of Golriz & Landstreet 
(2017). However, the results by three studies (Pintado & Adelman 1993; Peters & Polidan 
1985; Peters & Aller 1970; based either on P ii or P iii lines) show 
rather large diversities in A[A is the logarithmic number abundance 
of the element (P) relative to that of hydrogen with the usual normalization of 
A_ H = 12 for H.] from ∼ 5.8 to ∼ 6.4; i.e., apparently P-rich
if simply compared with the solar abundance (A_⊙ = 5.45).[
In this article, Anders & Grevesse's (1989) solar photospheric P abundance of 
A_⊙ = 5.45 is adopted as the reference, in order to keep consistency with 
Kurucz's (1993) ATLAS9/WIDTH9 program. See Appendix A for a more detailed discussion
on this subject.]

  * Pintado & Adelman (1993) also determined the P abundance of γ Peg 
(B2 IV) from P iii lines to be A ∼ 5.4 (i.e., almost solar). 

  * In Allen's (1998) abundance studies on early A and late B stars, attempts 
of P abundance determinations for 7 normal stars based on P ii lines in 
the optical region turned out to be unsuccessful, though 5 HgMn stars 
were confirmed to be significantly P-rich (A ∼ 5.9–7.8). 

  * Fossati et al.'s (2009) analysis on 2 normal late B-type stars (21 Peg and 
π Cet) based on P ii lines yielded [P/H][As usual, [X/H] 
is the differential abundance of element X relative to the Sun; 
i.e., [X/H] ≡ A_ star( X)- A_⊙( X).] ∼ +0.3 dex 
(moderately overabundant) for both.

  * In Niemczura et al.'s (2009) abundance study on late B-type stars (including HgMn 
stars), the P abundances of 3 normal stars were determined as A = 6.01 (HD 49481), 
5.60 (HD 50251), and 5.28 (HD 182198); i.e., nearly solar or moderately supersolar.

  * Przybilla et al. (2006) derived a near-solar P abundance of A = 5.53 (± 0.06) 
for the B-type supergiant β Ori (B8 Iae) based on 4 P ii lines.


Therefore, phosphorus abundance problem of normal B-type stars is far from being 
settled (near-solar? or somewhat supersolar?), given such insufficient data 
by different investigators for only a small number of stars. What we require 
is a comprehensive study based on a large sample of stars, by which wealthy 
and homogeneous data of P abundances would be accomplished.  

Motivated by this consideration, I decided to conduct an extensive analysis of 
P abundances for ∼ 80 young B-type stars (including HgMn stars) by using 
the P ii line at 6043.08 Å (hereinafter often 
referred to as P ii 6043; it is the strongest P ii line in 
the optical region and almost free from any appreciable blending), 
in order to estimate the P composition of the galactic gas 
at the time of their formation.

Besides, an emphasis was placed on incorporating the non-LTE affect in 
P abundance determinations based on statistical equilibrium calculations. 
Since non-LTE calculation for P has never been carried out 
so far (to the author's knowledge) and all the past investigations mentioned
above were done based on the assumption of LTE, it would be interesting   
to see how the new non-LTE results compare with the previous ones.

In addition, the significance of the non-LTE effect in the determination of 
phosphorus abundance in the Sun (and FGK-type stars) based on P i lines
in the near-infrared region was also examined as a related topic.
This supplementary analysis is separately presented in Appendix A. 



§ OBSERVATIONAL DATA


The observational materials used in this study are the high-dispersion 
(R ∼ 70000) and high-S/N (∼ 200–700) spectra obtained by HIgh Dispersion 
Echelle Spectrograph (HIDES) placed at the coudé focus of the 188 cm reflector 
at Okayama Astrophysical Observatory, which are the same as already employed in the 
previous two papers of the author. (i) 64 early-to-late B-type stars (mostly normal stars
but some are late-B chemically peculiar stars) observed in 2006 October, which were 
studied by Takeda et al. (2010; hereinafter referred to as Paper I) for their O and 
Ne abundance determinations by using O i 6156–8 and Ne i 6143 lines. 
(ii) 21 late B-type stars (HgMn-type peculiar stars and normal stars) observed
in 2012 May, which were analyzed by Takeda et al. (2014; hereinafter Paper II)
for their Na abundance determinations based on Na i 5890/5896 lines.
See these original papers for more details about the adopted spectra.
The program stars (85 in total) are all sufficiently sharp-lined (projected 
rotational velocities are v_ esin i ≲ 60 km s^-1) and are located  
in the solar neighborhood (within ≲ 1 kpc). Their fundamental stellar data 
are listed in Table 1, where two groups (i) and (ii) are presented separately.  

These 85 targets are plotted on the log L vs. log T_ eff diagram in Fig. 2, 
where Lejeune & Schaerer's (2001) standard theoretical evolutionary tracks 
(solar metallicity, non-rotating models with mass loss; see Sect. 2 therein 
for the details of the input physics they adopted) 
corresponding to different stellar masses are also depicted. 
This figure indicates that the sample stars are in 
the mass range of 2.5 M_⊙≲ M ≲ 9 M_⊙.

















§ ATMOSPHERIC PARAMETERS


Regarding the effective temperature (T_ eff) and the surface gravity (log g)
of each star, the same values as adopted in Papers I and II are used unchanged (cf. Table 1),
which were determined from colors (b-y, c_1, m_1, and β) 
of Strömgren's uvbyβ photometric system. 

As to the microturbulence (ξ), the values assumed in Paper I 
[3 (± 2) km s^-1 for early-to-late B-type stars] and Paper II 
[1 (± 1) km s^-1 for late B-type stars] were not consistent.
In this paper, T_ eff-dependent values are assigned as 
ξ = 1 (± 1) km s^-1 (10000 K < T_ eff < 16500 K) and
ξ = 2 (± 1) km s^-1 (16500 K < T_ eff < 23000 K).

This is due to the fact that ξ plays a significant role only for the case of
P-rich chemically peculiar stars (HgMn stars) found only among late B-type stars, 
while the P-line strengths of normal stars (existing over the entire T_ eff 
range) are so weak that their P abundances are practically ξ-independent. 
Therefore, the same value as in Paper II (ξ = 1 km s^-1; specific 
to late B-type stars) is adopted for T_ eff < 16500 K. while a tentative 
value of 2 km s^-1 is roughly assumed at T_ eff > 16500 K 
(all are normal stars with weak lines of phosphorus). 

The model atmospheres adopted for each of the targets are the same as in Papers I 
and II, which are the solar-metallicity models constructed by two-dimensionally 
interpolating Kurucz's (1993) ATLAS9 model grid in terms of T_ eff and log g.



§ SPECTRUM FITTING ANALYSIS AND EVALUATION OF EQUIVALENT WIDTHS


As already mentioned in Sect. 1, it is important to employ a spectral line 
of as large transition probability (log gf) as possible for successful 
P abundance determinations of B-type stars, because lines tend to be 
considerably weak and hard to detect for near-normal P abundances.
In this respect, the suitable candidate lines in the optical region 
are the P ii lines of 4s ^3P^∘ – 4p ^3D transition 
(lower excitation potentials of χ_ low∼ 10.8 eV, multiplet 5). 
They are at 6024.13, 6034.34, 6043.08, 6087.84, and 6165.60 Å  
and have log gf values of +0.20, -0.15, +0.44, -0.38, and -0.41,
respectively, according to the VALD database (Ryabchikova et al. 2015). 
Therefore, we invoke the P ii line at 6043.08 Å, which is the strongest 
one among these and also free from any appreciable blending. Besides, 
this line has another advantage that it lies almost in the middle part of 
the relevant Echelle order (covering 5990–6100 Å) where the S/N ratio 
is comparatively higher. 

The procedures of analysis (spectrum fitting, equivalent width derivation, 
estimating abundance errors due to parameter uncertainties) are essentially the same 
as adopted in Papers I and II (cf. Sect. 4 therein). Note that all the calculations 
in this section are done with the assumption of LTE at this stage. 



 §.§ Synthetic Spectrum Fitting


First, a spectrum-fitting technique was applied to the 6040–6050 Å region
(comprising the P ii 6043 line), by which the best-fit between theoretical and 
observed spectra is accomplished. Here, the parameters varied are the abundances of 
P, O, and Ne (+ Mn if necessary), rotational broadening velocity (v_ esin i), 
and radial velocity (V_ rad). The data of all atomic lines included in this
wavelength region were taken from the VALD database (Ryabchikova et al. 2015).  
Specifically, the data for the relevant P ii line at 6043.084 Å are 
χ_ low = 10.802 eV (lower excitation potential), log gf = +0.442
(logarithmic gf value), Gammar = 9.22 (radiation damping parameter), 
Gammas = -5.76 (Stark effect damping parameter), and Gammaw = -7.73 (van der Waals 
effect damping parameter).[
Gammar is the radiation damping width (s^-1), logγ_ rad.
Gammas is the Stark damping width (s^-1) per electron density (cm^-3) 
at 10^4 K, log(γ_ e/N_ e). 
Gammaw is the van der Waals damping width (s^-1) per hydrogen density 
(cm^-3) at 10^4 K, log(γ_ w/N_ H).]
The phosphorus abundances could be successfully established for 83 stars 
(out of 85 program stars), except for HD 029248 and HR 3652, for which 
the P abundance was tentatively fixed at an arbitrary value in the fitting.
The agreement between the theoretical spectrum (for the solutions 
with converged parameters) with the observed spectrum for each star 
is shown in Fig. 3.







 §.§ Equivalent Widths and Their Errors


Next, the equivalent width of the P ii 6043 line W_6043 was inversely 
evaluated from the abundance solution resulting from the fitting analysis. 
The W_6043 values derived in this manner are given in Table 1. While 
this line is generally weak for ordinary B stars (1 mÅ≲ W_6043≲ 10 mÅ), 
it can be stronger (up to W_6043∼ 100 mÅ) for P-rich peculiar stars (cf. Fig. 4a). 

The error involved with W_6043 was estimated as

    δ W ∼ϵ W_6043(1 - R_0)/R_0

according to Takeda (2023; cf. Sect. 6.2 therein) 
where ϵ (≡ ( S/N)^-1) is the random fluctuation of the 
continuum level and R_0 (≡ 1 - F_0/F_ c) is the line depth 
at the line center. 
By inserting the S/N ratios (measured around the P ii 6043 line; see column 12 
in Table 1) into Eq. (1), typical values of δ W were found to be 
∼ 1–3 mÅ in most cases[
Errors of W_6043 evaluated by Cayrel's (1988) formula (depending on S/N, pixel 
size, and line widths) were found to be smaller (typically by several times) than 
δ W defined by Eq. (1), and thus not taken into account.] (or up to 
∼ 10 mÅ in the exceptional case of low S/N and very shallow R_0), 
as depicted by error bars attached to the symbols in Fig. 4a.
The impact of δ W on the P abundance (denoted as δ_W) can be significant 
(e.g., a few tenths dex or even more) for the very weak line case where W_6043 
and δ W are on the similar size.






 §.§ Impact of Parameter Uncertainties


How the ambiguities in atmospheric parameters (T_ eff, log g, 
and ξ) affect the P abundances was estimated by repeating the analysis on 
the W_6043 values while perturbing these standard parameters interchangeably 
by ± 3%, ± 0.2 dex, and ± 1 km s^-1, which are the typical 
uncertainties for T_ eff and log g (cf. Sect. 3 in Paper I) and 
for ξ (cf. Sect. 3 of this paper).

The resulting A^ L (P abundances in LTE), 
δ_T± (abundance changes by perturbations of T_ eff), 
δ_g± (abundance changes by perturbations of log g), and
δ_ξ± (abundance changes by perturbations of ξ)
are plotted against T_ eff in Figs. 4b, 4c, 4d, and 4e,
respectively. 

As seen from Figs. 4c and 4d, both |δ_T| and |δ_g| 
are ≲ 0.1 dex and thus not very significant.
According to Fig. 4e, |δ_ξ| is negligibly small for normal stars,
while |δ_ξ| amounts up to ∼ 0.1 dex for P-rich late B-type 
peculiar stars. The error bars attached to the symbols in Fig. 4b
are the root-sum-squares of δ_W, δ_T, δ_g,
and δ_ξ.



§ STATISTICAL EQUILIBRIUM CALCULATIONS FOR P II




 §.§ Atomic Model


The non-LTE calculations for P ii were carried out based on the P ii model 
atom comprising 83 terms (up to 3s^2 3p 9g at 154582 cm^-1) and 1206 radiative 
transitions, which was constructed by consulting the updated atomic line data 
(filename: “gfall21oct16.dat”)[http://kurucz.harvard.edu/linelists/gfnew/]
 compiled by Dr. R. L. Kurucz. Though the contribution of P i was neglected,
P iii was taken into account in the number conservation of total P atoms. 

Regarding the photoionization cross section, the data calculated by Nahar et al. 
(2017)[The cross-section profiles (as functions of ionizing photon energy)
were roughly digitized from their Fig. 1, where attention was paid to reproduce 
only the global trend, because many sharp resonance peaks included in the 
original data are very difficult to read out.]
were used for the lowest 4 terms (^3P, ^1D, ^1S, and ^5S^∘), 
while the hydrogenic approximation was assumed for the remaining terms.  
Otherwise (such as the treatment of collisional rates), the recipe described in Sect. 3.1.3 
of Takeda (1991) was followed (inelastic collisions due to neutral hydrogen 
atoms were formally included as described therein, though insignificant 
in the atmosphere of early-type stars considered here).   



 §.§ Grid of Models


The calculations were done on a grid of 36 (= 9 × 4) 
solar-metallicity model atmospheres 
resulting from combinations of nine T_ eff values 
(9000, 10000, 12000, 14000, 16000, 18000, 20000, 22000, and 24000 K) 
and four  log g values (3.0, 3.5, 4.0, and 4.5).
while assuming ξ = 2 km s^-1.
Regarding the input P abundance, three values of A(P) = 4.45,
5.45, and 6.45 (corresponding to [P/H] = -1, 0, and +1) were assumed, 
resulting in three kinds of non-LTE grids.  
The depth-dependent non-LTE departure coefficients to be used for each star were 
then evaluated by interpolating the grid (for each [P/H]) 
in terms of T_ eff and log g.



§ NON-LTE EFFECT ON P ABUNDANCE DETERMINATIONS




 §.§ Characteristic Trends








Fig. 5 displays the l_0^ NLTE(τ)/l_0^ LTE(τ) (the 
non-LTE-to-LTE line-center opacity ratio; almost equal to ≃ b_ l) and 
S_ L(τ)/B(τ) (the ratio of the line source function to the Planck 
function; nearly equal to ≃ b_ u/b_ l) for the transition 
relevant to the P ii 6043 line (b_ l and b_ u are the non-LTE 
departure coefficients for the lower and upper levels) as functions of optical depth 
at 5000Å for selected representative cases. 
Likewise, Fig. 6 illustrates how the theoretical equivalent widths calculated in LTE 
(W^ L) as well as in non-LTE (W^ L) and the corresponding non-LTE 
corrections (Δ≡ A^ N - A^ L, where A^ L and A^ N are 
the abundances derived from W^ N with LTE and non-LTE) depend upon T_ eff.
The following characteristic trends are read from these figures.


  * As seen from Fig. 6, the inequality W^ N > W^ L (and Δ < 0) holds 
in most cases (except for the high T_ eff end at ≳ 20000 K where the trend
is inverse), which means that the non-LTE effect tends to strengthen the 
P ii 6043 line. 

  * For a given [P/H], |Δ| almost correlates with W as well as T_ eff 
in the sense that |Δ| takes the largest value around T_ eff∼ 15000 K 
where W reaches a maximum, as recognized from each panel of Fig. 6. 
This is understandable because an increase of W makes the line formation zone shallower 
where the departure from LTE is larger. 

  * As to g-dependence of the non-LTE effect, |Δ| tends to be larger for lower 
log g (i.e., lower density atmosphere) as seen at T_ eff≲ 15000 K, 
though the situation is not so simple at the higher T_ eff regime
where Δ gradually shifts in the direction of changing its sign. 

  * A more important factor significantly affecting the degree of departure from LTE is 
the P abundance ([P/H]) assumed in the calculations. That is, the non-LTE effect 
(|Δ|) tends to be progressively less significant with an increase in [P/H] 
(Fig. 6d → Fig. 6e → Fig. 6f) if compared at the same 
T_ eff and log g, despite that the line strength (W) is enhanced 
with increasing [P/H] (Fig. 6a → Fig. 6b → Fig. 6c).

  * This [P/H]-dependence may be understood by considering the mechanism controlling 
the level populations for the relevant P ii 6043 line.
The lower level (4s ^3P^∘; χ_ low≃ 10.8 eV) 
of this transition is radiatively connected to the ground level (3p^2 ^3P; 
χ_ low≃ 0 eV) by lines of large transition probabilities at 
∼ 1150–1160 Å. Then, this strong UV transition is almost in the condition 
of radiative detailed balance (if it is sufficiently optically thick), which 
makes the 4s ^3P^∘ level as if “meta-stable”.
In this case, if the subordinate lines originating from 4s ^3P^∘ 
become optically thin, this level would be overpopulated (b > 1) by cascading 
from the upper levels. Here, the P abundance would play a significant role 
in the sense that lower [P/H] (thinner optical thickness of subordinate lines) 
leads to more enhanced cascades and larger overpopulation. Actually, the extent 
of overpopulation systematically increases with a decrease in [P/H] if compared
at the same depth (dotted lines → solid lines → 
dashed lines in Fig. 5a–5c).

  * Note, however, that this argument is based on the presumption that
the 3p^2 ^3P – 4s ^3P^∘ UV transition is so optically 
thick to be in detailed balancing. This condition is destined to break down 
when double ionization proceeds and P ii is replaced by P iii 
(T_ eff≳ 16000 K; cf. Fig. 1d), because the population of 
P ii ground level comes short due to ionization. In this case,
the 4s ^3P^∘ level can not be meta-stable any more, and 
eventually becomes underpopulated (b < 1). Figs. 5a–5c illustrate this 
situation of how the overpopulation progressively turns into underpopulation 
in the optically-thin layer as T_ eff increases from late B to early B. 
This also explains the reason why Δ becomes positive (i.e., non-LTE
line weakening) at T_ eff≳ 20000 K (cf. Figs. 6d–6f). 
 



 §.§ Non-LTE Corrected Abundances


Since non-LTE corrections are appreciably dependent upon [P/H], it is necessary 
to adopt a correction corresponding to an adequate [P/H] consistent with 
the final non-LTE abundance. Therefore, we proceed as follows.

First, three kinds of non-LTE abundances are derived from W_6043 
(A_-1^ N, A_0^ N, and A_+1^ N, corresponding to
[P/H] = -1, 0, and +1, respectively) by using three sets of departure 
coefficients prepared for each star (cf. Sect. 5.2).
These three non-LTE abundances are sufficient to express A^ N
by a second-order polynomial in terms of x (≡ [P/H]) as 

    A^ N = a x^2 + b x + c,
 
where a, b, and c are known coefficients.
Meanwhile, according to the definition,

    A^ N = x + 5.45.

Combining Eqs. (2) and (3), we have 

    a x^2 + b x + c = x+ 5.45.
 
Let us denote the solution of Eq. (4) as x_* (which of two solutions  
should be adopted is self-evident), from which we obtain 
A_*^ N (= x_* + 5.45) and 
Δ_* (= A_*^ N - A^ L)   
as the final non-LTE abundance and non-LTE correction.

Such derived Δ_* values are plotted against T_ eff in Fig. 7b 
(black filled circles), where Δ_-1 (blue), Δ_0 (green), 
and Δ_+1 (red) are also overplotted by open symbols for comparison.
Likewise, the final non-LTE abundances (A_*^ N) are shown 
against T_ eff in Fig. 7c.
 





§ PHOSPHORUS ABUNDANCES OF B-TYPE STARS


It is apparent from Fig. 7c that the P abundances of the program stars are divided into two 
groups: (i) late B-type chemically peculiar stars which exhibit conspicuous overabundances 
systematically increasing from A^ N∼ 6 (T_ eff∼ 10000 K) to 
A^ N∼ 7 (T_ eff∼ 16000 K), and (ii) normal early-to-late B-type
stars (10000 ≲ T_ eff≲ 22000 K) which show rather
similar P abundances irrespective of T_ eff. These two groups of stars are 
separately discussed below. 



 §.§ P-rich Peculiar Stars


The former P-enhanced group mostly consists of non-magnetic late B-type 
chemically peculiar stars (HgMn stars), which are known to show considerable
overabundance of P.  Nevertheless, P-rich stars and those classified as 
HgMn peculiar stars are not strictly equivalent but some exceptions do exist
(P-strong stars classified as normal or P-weak HgMn stars).

The tendency observed in Fig. 7c (P is overabundant in HgMn stars and its anomaly
increases with T_ eff) is actually a reconfirmation of the trend shown 
in Fig. 4 of Ghazaryan & Alecian (2016), though the extent of overabundance
seen in their figure ([P/H] ∼ +2 at T_ eff∼ 14000 K) appears to 
be somewhat overestimated by ∼ +0.5 dex in comparison with Fig. 7c,
which is presumably due to their neglect of non-LTE corrections.

It should be noted, however, that P abundances derived by using the conventional 
model atmosphere (1D plane-parallel model with vertically changing physical variables 
but homogeneous abundances) are of limited significance in the present case 
of HgMn stars, because the chemical composition of P is likely to be stratified in their 
atmospheres (i.e., increasing with height) due to the element segregation process 
as indicated by recent studies (see, e.g., Catanzaro et al. 2016, Ndiaye et al. 2018, 
Alecian & Stift 2019).



 §.§ Superficially Normal B-type Stars


We are now to discuss the photospheric P abundances of normal B-type stars, 
which should retain the composition of galactic gas from which they were formed.

As long as LTE abundances are concerned, their A^ L values almost
distribute around the solar abundance (A_⊙ = 5.45) but exhibit a
T_ eff-dependent trend at T_ eff≲ 16000 K 
(dA^ L/dT_ eff∼ 0.1 dex/1000 K) as shown in Fig. 4c.

However, since the non-LTE corrections (Δ) also have a systematic gradient with 
T_ eff just in the inverse sense (Fig. 7b), the non-LTE abundances (A^ N) 
turn out to be almost independent upon T_ eff (Fig. 7c), accomplishing a reasonable
homogeneity. An inspection of Fig. 7c suggests that the demarcation line dividing
the two groups may be set at ∼ 5.7. Then, those 61 stars satisfying the criterion 
A^ N < 5.7 are regarded as normal B stars, for which the mean abundance is 
calculated as ⟨ A^ N⟩ = 5.20 (standard deviation is σ =  0.18).
   
Here, we are confronted with a somewhat puzzling problem if this result is compared 
with the reference solar abundance of A_⊙ = 5.45. That is, P abundances 
of young B-type stars (representing the gas composition at the time of 
some ∼ 10^7–10^8 yr ago) are by ∼ 0.2–0.3 dex “lower”
than that of the Sun (formed ∼ 4.6 × 10^9 yr ago).
This may suggests that P abundance of galactic gas has “decreased” with time, 
which apparently contradicts the standard concept of chemical evolution in the Galaxy
(elements are synthesized and expelled by stars, by which gas is chemically 
enriched with the lapse of time).  

Given that P abundances were determined based only on one line (P ii 6043), 
whether its transition probability is credible or not may be worth checking, 
because it directly affects the result. The adopted log gf  = +0.442 for 
this line (taken from VALD) was obtained by Dr. Kurucz in 2012 based on 
the new observed data of P ii levels, by which the previous Kurucz & Bell's 
(1995) value of +0.384 was somewhat revised. 
This VALD value is also quite consistent with the data (+0.42) of Wiese et al. (1969),
which is also included in the database of NIST (National Institute of Standards 
and Technology). 
Therefore, it is unlikely that our A^ N results are significantly
underestimated due to the use of an erroneous gf value.

Another possibility is that the actual solar P abundance might be lower 
than the currently believed value (A_⊙∼ 5.4–5.5).
This problem is separately focused upon in Appendix A.
As discussed therein (cf. Sect. A5), although a possibility can not be ruled 
out that A_⊙ could be somewhat reduced by ≲ 0.1–0.2 dex 
(i.e., down to ∼ 5.3), since uncertainties are still involved with 
P i line formation calculations (e.g., H i collision rates, 
treatment of 3D effect), there is no convincing reason for such a downward 
revision of A_⊙.
Moreover, if the solar photospheric P abundance were to be appreciably changed,
another problem of discrepant A_⊙ from A_ meteorite would 
newly emerge, because a good agreement has already been accomplished between 
these two (Asplund et al. 2009).

Therefore, frankly accepting the result of the analysis, we conclude that 
the phosphorus abundances of B-type stars (⟨ A^ N⟩) are 
systematically lower than that of the Sun (A_⊙) by ∼ 0.2–0.3 dex.
The cause for such a puzzling discrepancy (apparently contradicting 
the scenario of galactic chemical evolution) would be worth further earnest 
investigation. Meanwhile, follow-up studies by other researchers are also 
desirably awaited for an independent check of this observational finding.
 


§ SUMMARY AND CONCLUSION


Recently, special attention is being focused on the abundance of phosphorus
in the universe, mainly because of its astrobiological importance as a key 
element for life. For example, whether or not a sufficient amount of P 
(required for the rise of life) remains on the surface of a planet depends 
critically upon the primordial P abundance of the material, from which a star 
and the associated planetary system were formed.

Stimulated by such increasing interest, a number of spectroscopic studies 
intending to establish stellar P abundances have been published lately.
These P-specific investigations are directed to late-type (FGK-type) stars of 
lower mass (around ∼ 1 M_⊙), which are generally long-lived and 
thus retain the information of P composition in comparatively earlier time 
of the Galaxy (∼ 10^9–10^10 yr ago) when they were formed.

However, little efforts have been made so far to comprehensive P abundance
determinations of young hotter stars, such as B-type stars of 
∼ 3–10 M_⊙,  which reflect the gas composition of the Galaxy 
in the more recent past (several times ∼ 10^7–10^8 yr ago). 
This is presumably because P lines of sufficient strength usable as abundance
indicators are scarce. Actually, many of those B-type stars for which 
such determinations were done are P-rich chemically peculiar stars (HgMn 
stars), while the number of normal B-type stars with known P abundances   
is quite limited. 

Thus, motivated by the necessity of clarifying the behavior of phosphorus 
in hotter stars of higher mass, P abundances of ∼ 80 apparently 
bright sharp-lined early-to-late B-type stars on the upper main sequence 
were determined from the P ii 6043.084 Å line (the strongest 
P ii line in the optical region), with an aim of getting information
on the composition of this element in the young galactic gas in comparison 
with the abundance of the older Sun (age of 4.6× 10^9 yr).

A special emphasis was placed upon taking into account the non-LTE effect
based on extensive statistical-equilibrium calculations on P ii atoms, 
since the assumption of LTE was assumed in all the previous P abundance 
determinations.

Regarding the procedures of analysis, a spectrum-fitting was first applied 
to the wavelength region comprising the P ii 6043 line, and its 
equivalent width (W_6043) was then derived from the fitting-based 
abundance solution for each star. Finally, non-LTE abundance/correction 
as well as possible error were evaluated from such established W_6043.
An inspection of the resulting P abundances revealed that the program stars 
are divided into two groups.

The first group is those showing a considerable overabundance of P 
(supersolar by ∼ 0.5–1.5 dex), the extent of which progressively 
increases with T_ eff. These P-rich stars are observed 
at T_ eff≲ 16000 K (late B-type) and mostly belong to 
chemically peculiar stars of HgMn-type.

The second group consists of normal B-type stars, whose P abundances are 
comparatively homogeneous without such a prominent P anomaly as in the first 
group. However, different trends are observed between the LTE and non-LTE cases. 
(i) Though the LTE abundances tend to distribute around the solar value, 
they show a slight gradient (i.e., increasing with a decrease in T_ eff 
at T_ eff≳ 16000 K). 
(ii) Meanwhile, this systematic trend disappears in the non-LTE 
abundances which are satisfactorily uniform, because of the cancellation 
due to the T_ eff-dependent negative non-LTE corrections (amounting 
to ∼ 0.1–0.5 dex). 

This T_ eff-independent nature seen in the non-LTE abundances 
of normal B stars suggests that they represent the P composition of 
the galactic gas at the time when these young stars were born (some 
∼ 10^7–10^8 yr ago).
One puzzling problem is, however, that these non-LTE abundances (around ∼ 5.2) 
are appreciably lower than the P abundance of the Sun (formed ∼ 4.6 × 10^9 yr 
ago) by ∼ 0.2–0.3 dex, which means that the galactic gas composition of P  
has decreased with time in contradiction to the concept of chemical evolution.

Although other possibilities (e.g., error in the adopted gf value of 
P ii 6043 line?, inadequacy in the current solar P abundance?) 
were also examined, they do not seem to be so likely.
It may thus be concluded that the discrepancy of P abundance between the Sun 
and B-type stars really exists, the cause of which should be further investigated. 

This investigation has made use of the SIMBAD database, operated by CDS, 
Strasbourg, France, and the VALD database operated at Uppsala University,
the Institute of Astronomy RAS in Moscow, and the University of Vienna.





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Appendix A: On the Solar Photospheric Abundance of Phosphorus




 §.§ A1. Literature Values of Solar P Abundance


Regarding the phosphorus abundance in the solar photosphere (usually
derived from P i lines in the Y- or H-band of the near-IR region),
not a few spectroscopic studies have been published over the past half century, 
in which rather similar A_⊙ values of ≃ 5.4–5.5 are reported.
See Table 2 of Caffau et al. (2007) for a summary of 8 values (5.43, 5.45, 5.45,
5.45, 5.49, 5.45, 5.36, and 5.46) published before 2007. Thereafter, 
Asplund et al. (2009) presented a revised value of A_⊙ = 5.41.
The Anders & Grevesse's (1989) value of A_⊙ = 5.45 adopted in 
this paper (cf. footnote 3) is almost the same as the mean of these values.

However, all these determinations were done with the assumption of LTE, 
given the lack of information regarding the non-LTE effect on the P i 
lines  so far. Therefore, non-LTE calculations for neutral phosphorus 
were newly carried out in order to elucidate how and whether the non-LTE
corrections are important in P abundance determinations for the Sun.
In addition, how this effect would depend upon the atmospheric parameters
is also briefly examined in scope of application to late-type stars in general. 



 §.§ A2. Atomic Model


The adopted model atom of P i comprises 56 terms (up to 3s^2 3p^2 5d ^4D
at 79864 cm^-1) and 761 radiative transitions, which was constructed in a similar 
manner to the case of P ii described in Sect. 5. The contribution of P ii 
was taken into account in the number conservation of total P atoms. 

Regarding the photoionization cross section, Tayal's (2004) theoretically calculated 
data were adopted for the lowest three terms (^4S^∘, ^2D^∘, 
^2P^∘; read from Fig. 1–3, Fig. 9, and Fig. 10 of his paper), while the 
hydrogenic approximation was assumed for the other terms.

As to the collisional rates, the recipe described in Sect. 3.1.3 of Takeda (1991)
was basically followed. The collision rates due to neutral hydrogen atoms 
(which are important in late-type stars but subject to large uncertainties) were 
computed by Steenbock & Holweger's (1984) formula (based on the classical Drawin's 
cross section), which can be further multiplied by a correction factor (k) 
if necessary. Although we adopt k=1 (use of classical formula unchanged)
as the standard choice, a special case of k=10^-3 (considerably reduced 
to a negligible level) was also tried in order to see its importance.



 §.§ A3. Non-LTE Effect on P I 10581 Line in FGK-type Stars


First, the calculations were done for 10 solar-metallicity models (ATLAS9 models 
by Kurucz 1993) resulting from combinations of (T_ eff =  4500, 5000, 5500, 
6000, 6500 K) and (log g = 2.0, 4.0), while assuming ξ = 2 km s^-1
and [P/H] = 0 (A = 5.45).
The runs of l_0^ NLTE/l_0^ LTE and S_ L/B with depth
for the transition corresponding to P i 10581.58 line (representative 
P i line in the near-IR region) are shown in Fig. 8, while Fig. 9 displays 
how W_10581 (equivalent widths calculated in LTE and non-LTE; upper panel (a)) 
as well as Δ_10581 (non-LTE correction; lower panel (b))
depend upon T_ eff and log g.
The following characteristics are read from these figures.


  * The line is generally intensified by the non-LTE effect (W^ N > W^ L 
and Δ < 0; cf. Fig. 9), because both l_0^ NLTE/l_0^ LTE > 1 
and S_ L/B < 1 (cf. Fig. 8) act in the direction of line strengthening. 

  * This non-LTE effect becomes progressively larger with an increase in T_ eff 
and with a decrease in log g (Fig. 9b).

  * How the neutral hydrogen collision is treated has an appreciable impact on the non-LTE 
correction. If the standard value of H i collision is practically neglected by 
a drastic reduction (k=10^-3), |Δ| increases by ∼ 0.1–0.2 dex (Fig. 9b). 

  * In summary, non-LTE corrections had better be taken into account in P abundance 
determinations from P i lines for FGK stars, especially for those of 
comparatively higher T_ eff or lower log g, for which significant 
negative corrections amounting to several tenths dex may be expected. 











 §.§ A4. Reanalysis of Solar P I Lines


Then, statistical equilibrium calculation was done for Kurucz's (1993) ATLAS9 solar 
model atmosphere (T_ eff = 5780 K, log g = 4.44, solar metallicity) with [P/H] = 0.0,
in order to reanalyze the solar P i lines by taking into account the non-LTE effect. 
The basic data for the solar equivalent widths and log gf values of 15 P i
lines were taken from Table 3 of Biémont et al. (1994), which are the disk-center
values measured from Jungfraujoch Atlas (W_λ^ d.c.) and transition 
probabilities based on their refined calculations. Regarding the solar microturbulence,
a reasonable value of ξ_⊙ = 1 km s^-1 was adopted as often assumed.
The resulting P abundances and non-LTE corrections are summarized in Table 2,
from which the following conclusions can be drawn.




The extents of (negative) non-LTE corrections are only a few hundredths dex (k=1 case) 
and thus not particularly important, though |Δ| may somewhat increase further by 
∼ 0.1 if H i collision is neglected (k = 10^-3). This is mainly due to the 
high-gravity nature of the Sun (log g = 4.44) as a dwarf, since |Δ| appreciably 
decreases with an increase in log g (cf. Fig. 9b).[Actually, |Δ|  
in this case (disk-center intensity spectrum) is somewhat smaller than that obtained 
by an interpolation/extrapolation of Fig. 9b (calculated for the flux spectrum),
because the non-LTE effect becomes less significant for the former case of 
deeper-forming lines than the latter.] 
Therefore, the speculation addressed by Asplund et al. (2009) “departures from LTE 
are not expected to be significant for P” (based on an analogy with the S i 
case) may be regarded as reasonable.  

The mean P abundances averaged over 15 lines are ⟨ A^ L⟩ = 5.43 
(LTE abundance), ⟨ A^ N_k=1⟩ = 5.40 (non-LTE abundance for k=1),
and  ⟨ A^ N_k=10^-3⟩ = 5.31 (non-LTE abundance for k=10^-3),
where the standard deviation is σ = 0.11 for all the three cases.
This ⟨ A^ L⟩ (5.43) is reasonably consistent with Biémont et al.'s 
(1994) result of 5.45 (obtained by using the same lines with the same W_λ^ d.c. 
and log gf). According to the standard non-LTE abundance of 5.40 
(⟨ A^ N_k=1⟩) obtained here, we may state that the previously
reported results of solar P abundance (cf. Sect. A1) can not be significantly 
revised even when the non-LTE correction (a few hundredths dex) is taken into account.



 §.§ A5. Is Downward Revision of A_⊙ Possible?


In view of discrepancy between the P abundances of normal B-type stars and that of 
the Sun (the former being systematically lower than the latter by ∼ 0.2–0.3 dex) 
discussed in Sect. 7.2, some discussion about whether the actual A_⊙ 
could be lower than the currently accepted value may be in order. 
  
Neglecting the H i collision would further reduce A^ N by ∼ 0.1 dex 
down to ∼ 5.3. However, there is no justification for such 
a drastic reduction of the classical rates for rather high-excitation P i lines
under question.[Admittedly, such a situation does exist for the case of other lines. 
For example, it is known that neutral-hydrogen collision rates calculated by using the 
classical cross section are considerably overestimated for the resonance lines of 
alkali elements (e.g., Li i 6708 or K i 7699).] Therefore, much can not be
said about this possibility until more information of H i collision 
rates for P i is obtained (preferably based on up-to-date quantum-mechanical 
calculations).

Alternatively, it was once considered that inclusion of the 3D effect 
might reduce A_⊙ by ≲ 0.1 dex, since Asplund et al. (2005) derived an 
appreciably lower value of A_⊙ = 5.36 by including the 3D-effect. 
However, such a low-scale result was not confirmed by Caffau et al.'s (2007) 
new 3D analysis which resulted in A_⊙ = 5.46 (± 0.04), showing that 
the 3D correction is insignificant (only a few hundredths dex) for the solar 
P abundance determination. Thus, this possibility is not very prospective, either.

In any case, although a possibility of solar P abundance being reduced by 
≲ 0.1–0.2 (i.e., down to ∼ 5.3) can not be excluded, 
the solar P abundance would then be discrepant from that of meteorite.
That is, since the old A_ meteorite(P) value of 5.57 ± 0.04 derived by 
Anders & Grevesse (1989) was revised by Asplund et al. (2009) as 
5.43 ± 0.04 (based on the data of CI carbonaceous chondrites taken from 
Lodders et al. 2009), a good agreement between A_ meteorite and 
A_⊙ is now accomplished. This consistency would break down
if A_⊙ were appreciably changed.  

