HD 137595 | $21.23^{+0.04}_{-0.05}$ | $-0.06\pm 0.06$ | $-0.34\pm 0.07$ | $20.85\pm 0.14$ | $20.59\pm 0.06$ | $21.17\pm 0.08$ | $-0.28\pm 0.10$
HD 147683 | $21.41^{+0.11}_{-0.14}$ | $-0.11\pm 0.08$ | $-0.42\pm 0.15$ | $21.00\pm 0.21$ | $20.68\pm 0.12$ | $21.29\pm 0.13$ | $-0.31\pm 0.17$
HD 147888 | $21.73^{+0.07}_{-0.09}$ | $-0.68\pm 0.11$ | $-0.98\pm 0.09$ | $20.74\pm 0.21$ | $20.45\pm 0.05$ | $21.05\pm 0.12$ | $-0.30\pm 0.13$
HD 147933 | $21.70^{+0.08}_{-0.10}$ | $-0.70\pm 0.11$ | $-0.83\pm 0.16$ | $20.42\pm 0.44$ | $20.57\pm 0.15$ | $21.00\pm 0.19$ | $-0.13\pm 0.23$
HD 152590 | $21.47^{+0.06}_{-0.07}$ | $-0.29\pm 0.08$ | $-0.70\pm 0.11$ | $20.96\pm 0.14$ | $20.47\pm 0.10$ | $21.18\pm 0.10$ | $-0.41\pm 0.14$
HD 156359 | $20.80^{+0.10}_{-0.13}$ | $-1.36\pm 0.13$ | $-2.43\pm 0.22$ | $19.40\pm 0.16$ | $18.07\pm 0.21$ | $19.44\pm 0.15$ | $-1.07\pm 0.24$
HD 157857 | $21.44^{+0.07}_{-0.08}$ | $-0.17\pm 0.09$ | $-0.46\pm 0.12$ | $20.96\pm 0.20$ | $20.68\pm 0.10$ | $21.27\pm 0.12$ | $-0.29\pm 0.15$
HD 165246 | $21.45^{+0.03}_{-0.03}$ | $-0.49\pm 0.07$ | $-1.01\pm 0.07$ | $20.80\pm 0.10$ | $20.14\pm 0.07$ | $20.96\pm 0.08$ | $-0.52\pm 0.10$
HD 165955 | $21.11^{+0.06}_{-0.07}$ | $-0.95\pm 0.07$ | $-1.72\pm 0.09$ | $20.08\pm 0.10$ | $19.09\pm 0.07$ | $20.16\pm 0.09$ | $-0.77\pm 0.11$
HD 167402 | $21.20^{+0.05}_{-0.05}$ | $-0.23\pm 0.10$ | $-0.84\pm 0.11$ | $20.84\pm 0.13$ | $20.06\pm 0.10$ | $20.97\pm 0.11$ | $-0.60\pm 0.14$
HD 168076 | $21.73^{+0.20}_{-0.37}$ | $-0.24\pm 0.08$ | $-0.75\pm 0.21$ | $21.33\pm 0.23$ | $20.68\pm 0.08$ | $21.49\pm 0.17$ | $-0.51\pm 0.19$
HD 168941 | $21.25^{+0.04}_{-0.05}$ | $-0.17\pm 0.07$ | $-0.84\pm 0.09$ | $20.97\pm 0.10$ | $20.11\pm 0.08$ | $21.08\pm 0.08$ | $-0.66\pm 0.11$
HD 177989 | $21.10^{+0.05}_{-0.05}$ | $-0.08\pm 0.07$ | $-0.64\pm 0.13$ | $20.88\pm 0.11$ | $20.16\pm 0.12$ | $21.02\pm 0.09$ | $-0.56\pm 0.14$
HD 190918 | $21.40^{+0.06}_{-0.07}$ | $-0.37\pm 0.05$ | $-1.26\pm 0.10$ | $20.97\pm 0.08$ | $19.84\pm 0.08$ | $21.03\pm 0.07$ | $-0.89\pm 0.10$
HD 191877 | $21.10^{+0.05}_{-0.06}$ | $-0.27\pm 0.05$ | $-0.80\pm 0.17$ | $20.69\pm 0.11$ | $20.00\pm 0.17$ | $20.84\pm 0.10$ | $-0.54\pm 0.19$
HD 192035 | $21.39^{+0.04}_{-0.05}$ | $-0.13\pm 0.08$ | $-0.46\pm 0.10$ | $20.98\pm 0.16$ | $20.63\pm 0.09$ | $21.26\pm 0.10$ | $-0.33\pm 0.13$
HD 192639 | $21.48^{+0.07}_{-0.08}$ | $-0.28\pm 0.06$ | $-0.45\pm 0.12$ | $20.72\pm 0.25$ | $20.73\pm 0.10$ | $21.20\pm 0.12$ | $-0.17\pm 0.15$
HD 195455 | $20.62^{+0.04}_{-0.04}$ | $-0.92\pm 0.24$ | $-1.89\pm 0.19$ | $19.64\pm 0.27$ | $18.42\pm 0.19$ | $19.69\pm 0.25$ | $-0.97\pm 0.29$
HD 195965 | $21.08^{+0.04}_{-0.05}$ | $-0.12\pm 0.07$ | $-0.50\pm 0.09$ | $20.73\pm 0.14$ | $20.28\pm 0.08$ | $20.96\pm 0.09$ | $-0.38\pm 0.12$
HD 201345 | $21.02^{+0.05}_{-0.05}$ | $-0.69\pm 0.04$ | $-1.36\pm 0.13$ | $20.23\pm 0.08$ | $19.36\pm 0.12$ | $20.33\pm 0.07$ | $-0.67\pm 0.13$
HD 203374 | $21.40^{+0.04}_{-0.05}$ | $-0.23\pm 0.06$ | $-0.43\pm 0.08$ | $20.73\pm 0.20$ | $20.67\pm 0.07$ | $21.17\pm 0.09$ | $-0.20\pm 0.11$
HD 206267 | $21.49^{+0.05}_{-0.06}$ | $-0.28\pm 0.06$ | $-0.34\pm 0.09$ | $20.31\pm 0.49$ | $20.85\pm 0.08$ | $21.21\pm 0.12$ | $-0.06\pm 0.14$
HD 206773 | $21.24^{+0.05}_{-0.06}$ | $-0.21\pm 0.05$ | $-0.53\pm 0.08$ | $20.76\pm 0.12$ | $20.41\pm 0.06$ | $21.04\pm 0.07$ | $-0.32\pm 0.09$
HD 207198 | $21.50^{+0.05}_{-0.05}$ | $-0.24\pm 0.10$ | $-0.41\pm 0.07$ | $20.75\pm 0.28$ | $20.79\pm 0.05$ | $21.26\pm 0.11$ | $-0.16\pm 0.12$
HD 207308 | $21.45^{+0.04}_{-0.05}$ | $-0.14\pm 0.06$ | $-0.35\pm 0.07$ | $20.90\pm 0.17$ | $20.80\pm 0.06$ | $21.31\pm 0.08$ | $-0.21\pm 0.10$
HD 207538 | $21.52^{+0.04}_{-0.05}$ | $-0.09\pm 0.05$ | $-0.36\pm 0.07$ | $21.09\pm 0.14$ | $20.85\pm 0.06$ | $21.42\pm 0.07$ | $-0.27\pm 0.09$
HD 208440 | $21.33^{+0.05}_{-0.06}$ | $-0.35\pm 0.05$ | $-0.75\pm 0.12$ | $20.75\pm 0.12$ | $20.28\pm 0.11$ | $20.97\pm 0.09$ | $-0.39\pm 0.14$
HD 209339 | $21.27^{+0.04}_{-0.04}$ | $-0.35\pm 0.04$ | $-0.84\pm 0.07$ | $20.75\pm 0.07$ | $20.13\pm 0.06$ | $20.92\pm 0.05$ | $-0.49\pm 0.08$
HD 210839 | $21.48^{+0.04}_{-0.04}$ | $-0.23\pm 0.07$ | $-0.38\pm 0.06$ | $20.69\pm 0.23$ | $20.80\pm 0.05$ | $21.24\pm 0.08$ | $-0.14\pm 0.10$
HD 212791 | $21.13^{+0.12}_{-0.16}$ | $-0.46\pm 0.12$ | $-1.41\pm 0.15$ | $20.62\pm 0.17$ | $19.42\pm 0.11$ | $20.67\pm 0.15$ | $-0.95\pm 0.18$
HD 219188 | $20.76^{+0.07}_{-0.08}$ | $-0.62\pm 0.07$ | $-1.08\pm 0.12$ | $19.96\pm 0.13$ | $19.38\pm 0.11$ | $20.14\pm 0.10$ | $-0.46\pm 0.14$
HD 220057 | $21.10^{+0.11}_{-0.14}$ | $-0.21\pm 0.09$ | $-0.53\pm 0.13$ | $20.61\pm 0.21$ | $20.27\pm 0.09$ | $20.89\pm 0.13$ | $-0.32\pm 0.15$
BD$+$35 4258 | $21.26^{+0.03}_{-0.03}$ | $-0.50\pm 0.08$ | $-1.35\pm 0.11$ | $20.69\pm 0.09$ | $19.61\pm 0.11$ | $20.76\pm 0.08$ | $-0.85\pm 0.13$
$\gamma$ Cas | $20.16^{+0.08}_{-0.10}$ | $-1.03\pm 0.10$ | $-3.33\pm 0.09$ | $19.13\pm 0.12$ | $16.53\pm 0.05$ | $19.13\pm 0.12$ | $-2.30\pm 0.13$
$\epsilon$ Per | $20.50^{+0.09}_{-0.12}$ | $-0.44\pm 0.08$ | $-0.68\pm 0.27$ | $19.70\pm 0.35$ | $19.52\pm 0.26$ | $20.07\pm 0.23$ | $-0.24\pm 0.32$
$\psi$ Ori | $20.49^{+0.15}_{-0.23}$ | $-1.65\pm 0.14$ | $-5.41\pm 0.20$ | $18.84\pm 0.19$ | $14.78\pm 0.15$ | $18.84\pm 0.19$ | $-3.76\pm 0.23$
$\lambda$ Ori | $20.80^{+0.10}_{-0.12}$ | $-0.54\pm 0.07$ | $-1.38\pm 0.21$ | $20.19\pm 0.13$ | $19.12\pm 0.20$ | $20.26\pm 0.12$ | $-0.84\pm 0.22$
$\epsilon$ Ori | $20.45^{+0.08}_{-0.10}$ | $-1.32\pm 0.03$ | $-3.58\pm 0.21$ | $19.12\pm 0.09$ | $16.57\pm 0.20$ | $19.13\pm 0.08$ | $-2.26\pm 0.21$
$\kappa$ Ori | $20.52^{+0.04}_{-0.04}$ | $-1.23\pm 0.04$ | $-4.54\pm 0.20$ | $19.29\pm 0.06$ | $15.68\pm 0.20$ | $19.29\pm 0.06$ | $-3.31\pm 0.20$
139 Tau | $20.96^{+0.08}_{-0.09}$ | $-0.77\pm 0.10$ | $-0.92\pm 0.21$ | $19.65\pm 0.43$ | $19.73\pm 0.20$ | $20.18\pm 0.22$ | $-0.15\pm 0.27$
1 Sco | $21.13^{+0.10}_{-0.13}$ | $-0.93\pm 0.16$ | $-1.60\pm 0.20$ | $20.10\pm 0.22$ | $19.23\pm 0.18$ | $20.20\pm 0.18$ | $-0.67\pm 0.24$
$\pi$ Sco | $20.69^{+0.06}_{-0.07}$ | $-0.90\pm 0.10$ | $-1.07\pm 0.20$ | $19.28\pm 0.41$ | $19.32\pm 0.20$ | $19.79\pm 0.21$ | $-0.16\pm 0.27$
$\delta$ Sco | $21.17^{+0.08}_{-0.09}$ | $-0.57\pm 0.02$ | $-1.45\pm 0.21$ | $20.54\pm 0.09$ | $19.41\pm 0.20$ | $20.60\pm 0.08$ | $-0.89\pm 0.21$
$\beta^{1}$ Sco | $21.14^{+0.04}_{-0.04}$ | $-0.36\pm 0.01$ | $-1.00\pm 0.07$ | $20.66\pm 0.04$ | $19.83\pm 0.06$ | $20.78\pm 0.04$ | $-0.64\pm 0.07$
$\omega^{1}$ Sco | $21.23^{+0.07}_{-0.09}$ | $-0.68\pm 0.08$ | $-0.88\pm 0.13$ | $20.11\pm 0.27$ | $20.05\pm 0.11$ | $20.55\pm 0.13$ | $-0.20\pm 0.16$
$\sigma$ Sco | $21.36^{+0.14}_{-0.22}$ | $-1.15\pm 0.08$ | $-1.27\pm 0.20$ | $19.60\pm 0.47$ | $19.79\pm 0.15$ | $20.21\pm 0.20$ | $-0.12\pm 0.23$
$\chi$ Oph | $21.31^{+0.10}_{-0.13}$ | $-0.09\pm 0.03$ | $-0.38\pm 0.20$ | $20.90\pm 0.23$ | $20.63\pm 0.18$ | $21.22\pm 0.15$ | $-0.28\pm 0.22$
$\mu$ Nor | $21.19^{+0.08}_{-0.10}$ | $-0.14\pm 0.05$ | $-0.44\pm 0.16$ | $20.77\pm 0.19$ | $20.45\pm 0.15$ | $21.06\pm 0.13$ | $-0.31\pm 0.19$
$\gamma$ Ara | $20.71^{+0.08}_{-0.09}$ | $-1.05\pm 0.04$ | $-1.18\pm 0.24$ | $19.07\pm 0.50$ | $19.23\pm 0.23$ | $19.66\pm 0.24$ | $-0.13\pm 0.31$

From the results presented in Table 9, we find that, to varying degrees, the
molecular hydrogen fraction in the optically-thick H2 region is always larger
than the line-of-sight integrated value. This is illustrated in Figure 17,
where the derived values of $f_{1}({\rm H}_{2})$ are plotted against the
observed line-of-sight values $f({\rm H}_{2})$. All of the data points lie
above the line of equality represented by the diagonal dashed line in the
figure. For the median sight line in our sample, the molecular fraction in the
optically-thick H2 region is a factor of 2.8 larger than the line-of-sight
value. Note that, according to Equation (4), the ratio $f_{1}({\rm
H}_{2})/f({\rm H}_{2})=1/f({\rm Cl~{}\textsc{i}})$. Thus, the larger the
neutral chlorine fraction, the smaller the contrast between $f_{1}({\rm
H}_{2})$ and $f({\rm H}_{2})$. Another way to state this is that the neutral
chlorine fraction is equivalent to the fraction of total hydrogen associated
with the optically-thick H2 region: $f({\rm Cl~{}\textsc{i}})=N({\rm
Cl~{}\textsc{i}})/N({\rm Cl}_{\rm tot})=N_{1}({\rm H}_{\rm tot})/N({\rm
H}_{\rm tot})$.

The largest neutral chlorine fractions (i.e., $f({\rm Cl~{}\textsc{i}})\gtrsim
0.8$) are seen toward HD 24534 (X Per), HD 137595, HD 177989, HD 207538, and
$\chi$ Oph. For these sight lines, more than 80% of the interstellar material
is associated with the H2-bearing gas. The smallest fractions ($f({\rm
Cl~{}\textsc{i}})\lesssim 0.05$) are found toward HD 121968, HD 156359, $\psi$
Ori, and $\epsilon$ Ori. The sight line to HD 121968 is interesting because,
while the molecular material constitutes only $\sim$4% of the total hydrogen
column, the molecular fraction in that material is high (i.e., $f_{1}({\rm
H}_{2})\approx 0.65$). Similar results are found toward $\sigma$ Sco and
$\gamma$ Ara, where $f({\rm Cl~{}\textsc{i}})\approx 0.07$ and 0.09,
respectively, but $f_{1}({\rm H}_{2})\approx 0.76$ and 0.74. (The
uncertainties associated with these values are relatively large, however; see
Table 9) For the median sight line in our sample, $\sim$36% of the total
hydrogen column is associated with the optically-thick H2 region.

Figure 17: Molecular fraction associated with the optically-thick H2 region,
denoted $f_{1}$(H2), plotted against the line-of-sight molecular fraction,
$f$(H2). The plotting symbols have the same meaning as in Figure 11. The
diagonal dashed line indicates the line of equality between $f_{1}$(H2) and
$f$(H2). Four sight lines with very low values of $f$(H2) (i.e., $\gamma$ Cas,
$\psi$ Ori, $\epsilon$ Ori, and $\kappa$ Ori) are not shown in this plot.

An interesting pattern emerges from the data plotted in Figure 17. For sight
lines with $\log f({\rm H}_{2})\gtrsim-0.85$, the $f_{1}({\rm H}_{2})$ values
adhere more closely to the line of equality (the diagonal dashed line in
Figure 17). If a data point lies along this line of equality, then all of the
hydrogen along the line of sight is associated with the H2-bearing gas. (Note
this does not mean that all of the hydrogen is in the form of H2.) Values of
$\log f({\rm H}_{2})\gtrsim-0.85$ roughly correspond to molecular hydrogen
column densities of $\log N({\rm H}_{2})\gtrsim 20.0$. This threshold value in
$f({\rm H}_{2})$ also approximately corresponds to the point at which the gas-
phase abundances (of P and other depleted elements, such as Mg, Ti, and Fe)
begin to fall sharply with increasing $f({\rm H}_{2})$ (Figure 16; see also
Figure 21 in Welty et al., 2020).

One of the motivations for the analysis of neutral chlorine fractions
described here is to determine whether any of the sight lines in our sample
contain “translucent” interstellar material. A translucent cloud is generally
defined as having a total visual extinction $A_{V}\gtrsim 1$ mag, a molecular
hydrogen fraction $f({\rm H}_{2})\gtrsim 0.9$, and a kinetic temperature
$T_{k}\lesssim 40$ K (van Dishoeck & Black, 1988; Rachford et al., 2002).
Previous H2 surveys with FUSE (e.g., Rachford et al., 2002, 2009) have
generally failed to detect true translucent clouds along any of the sight
lines surveyed. This failure may (at least partly) be due to the fact that the
line-of-sight molecular fractions that are examined are lower limits to the
true molecular fractions in the portions of the clouds where the H2 molecules
reside (Figure 17). Sonnentrucker et al. (2002) recognized that an analysis of
neutral chlorine fractions could help to identify any translucent material
along an otherwise complex line of sight.

There are several sight lines in Table 9 where the results for $f_{1}({\rm
H}_{2})$ indicate that the molecular fraction in the H2-bearing gas could be
as high as $\sim$1\. Two intriguing cases are presented by the sight lines to
HD 94493 and HD 97175. In both cases, the outcome for $N_{1}({\rm
H~{}\textsc{i}})$ is negative because $f({\rm Cl~{}\textsc{i}})$ is slightly
smaller than $f({\rm H}_{2})$. (This is an unphysical result, based on our
simple model, because there cannot be more molecular hydrogen than total
hydrogen in the H2-bearing gas.) Nevertheless, within the uncertainties, both
sight lines could have a value of $f_{1}({\rm H}_{2})\approx 1$. Neither of
these sight lines would traditionally be characterized as a translucent sight
line, however. The total visual extinction toward HD 94493 is $A_{V}=0.82\pm
0.18$ (Valencic et al., 2004). The extinction may be somewhat less toward HD
97175 based on a comparison of the $E(\bv)$ values (Table 1). The H2
rotational temperatures in the two directions are $T_{01}=79$ K and 74 K,
respectively (Jenkins, 2019), consistent with the average interstellar value
of $\sim$80 K.

The outcome for $N_{1}({\rm H~{}\textsc{i}})$ toward HD 37903 is also
negative. However, again, the result for $f_{1}({\rm H}_{2})$ is consistent
with 1 (within the uncertainties). This is an interesting sight line, which
has been included in many previous surveys of “translucent clouds” (e.g.,
Cartledge et al., 2001; Rachford et al., 2009). The total visual extinction in
this direction is $A_{V}=1.28\pm 0.15$ and the H2 rotational temperature is
$T_{01}=68\pm 7$ K (Rachford et al., 2009). However, this sight line shows
enhanced depletion of Cl, which tends to complicate the analysis of the
neutral chlorine fraction (see below). Nevertheless, the “true” molecular
fraction seems to be quite high in this direction, despite the fact that only
$\sim$36% of the total H is associated with the H2-bearing gas.

Three other sight lines are worth mentioning in this context. The derived
values of $f_{1}({\rm H}_{2})$ toward HD 24534 (X Per), HD 73882, and HD
206267 are consistent (within the quoted 1$\sigma$ uncertainties) with
$f_{1}({\rm H}_{2})\approx 1$. The values are $f_{1}({\rm H}_{2})=0.84\pm
0.15$ toward X Per, $0.93\pm 0.46$ toward HD 73882, and $0.88\pm 0.33$ toward
HD 206267. In all three cases, the $f_{1}({\rm H}_{2})$ values are larger than
the line-of-sight molecular fractions, which are $f({\rm H}_{2})=0.76\pm 0.10$
toward X Per, $0.65\pm 0.21$ toward HD 73882, and $0.46\pm 0.11$ toward HD
206267. The values of total visual extinction are also fairly high in these
directions: $A_{V}=2.05\pm 0.18$ (X Per), $2.36\pm 0.23$ (HD 73882), and
$1.41\pm 0.18$ (HD 206267) (Rachford et al., 2009). The H2 rotational
temperatures, however, are somewhat larger than the values expected for
translucent clouds: $T_{01}=57\pm 4$ K (X Per), $51\pm 6$ K (HD 73882), and
$65\pm 5$ K (HD 206267) (Rachford et al., 2002). There may be stratification
in the molecular gas, however, since the kinetic temperatures derived from C2
excitation are lower than the H2 rotational temperatures: $T_{k}=45\pm 10$ K
toward X Per, $20\pm 5$ K toward HD 73882, and $35\pm 5$ K toward HD 206267
(Sonnentrucker et al., 2007).

Figure 18: Total gas-phase Cl abundance plotted as a function of the fraction
of neutral chlorine along the line of sight. Plotting symbols have the same
meaning as in Figure 16. (Note the differences in the scales of the axes
between this figure and Figure 16.)

An explicit assumption in the derivation of Equation (4) is that the depletion
of Cl does not vary between the zone where the H2 is optically thick and the
zone where the hydrogen is predominantly atomic (Jura & York, 1978).
Justification for this assumption is provided by Figure 16, where it is shown
that the gas-phase Cl abundance does not vary significantly as a function of
the line-of-sight molecular hydrogen fraction. As demonstrated in Figure 18,
the gas-phase Cl abundance also does not vary as a function of the neutral
chlorine fraction. (Recall that the neutral chlorine fraction is equivalent to
the fraction of the total hydrogen column associated with the optically-thick
H2 region.) To illustrate this point, consider the line of sight toward X Per,
where $\sim$90% of the interstellar material is associated with the H2-bearing
gas. This sight line has a total gas-phase Cl abundance of $\log({\rm Cl}/{\rm
H})=-6.79^{+0.04}_{-0.05}$, indicating a logarithmic depletion of $[{\rm
Cl}/{\rm H}]=-0.12$. In contrast, $\sim$2% of the interstellar material toward
$\psi$ Ori is associated with the H2 component. However, the total gas-phase
Cl abundance is identical to that toward X Per: $\log({\rm Cl}/{\rm
H})=-6.79^{+0.16}_{-0.27}$.

If the depletion of Cl does vary between the two zones, then the analysis of
the neutral chlorine fractions becomes more complicated. In general, if the
depletion level is higher in the zone where Cl is predominantly neutral, then
the derived values of $f_{1}({\rm H}_{2})$ will be lower (see the discussion
in Sonnentrucker et al., 2002). However, while there are a handful of sight
lines that exhibit enhanced Cl depletion (see Section 4.3), these appear to be
special cases. Depletion results for the vast majority of sight lines in our
Cl sample indicate that Equation (4) should be generally valid.

##  5 DISCUSSION

###  5.1 Implications for Dust Formation and Evolution

The primary purpose of our reexamination of phosphorus and chlorine abundances
in the diffuse ISM is to clarify the depletion behaviors of these elements. In
his landmark study of gas-phase element depletions, Jenkins (2009) found that
the depletion trends for P and Cl indicated that the abundances of these
elements were supersolar at $F_{*}=0$. With our new evaluation of the
depletion properties of P and Cl (Figure 14 and Table 8), we have demonstrated
that this is not the case. We find values of $[{\rm P}/{\rm H}]_{0}$ and
$[{\rm Cl}/{\rm H}]_{0}$ that are slightly less than zero (but consistent with
zero within the uncertainties), indicating very little (if any) depletion of P
or Cl in the low-density diffuse ISM.

With our improved constraints on P and Cl depletions, it is worthwhile
reexamining the depletion results for all of the elements that have been
analyzed via the Jenkins (2009) formalism. In Figure 19, we plot the
depletions at $F_{*}=0$ and $F_{*}=1$ for 24 different elements as a function
of the 50% condensation temperatures ($T_{C}$) calculated by Lodders (2003).
(This is an updated version of a similar figure presented in Ritchey et al.
(2018). New results obtained in this investigation are indicated by orange
symbols in Figure 19.) Note that, in addition to the new depletion parameters
obtained for P and Cl, we also include in Figure 19 depletion results for the
element F. These values are obtained from an analysis of F depletions reported
in the literature (Federman et al., 2005; Snow et al., 2007, see Appendix B).

Figure 19: Element depletions (at $F_{*}=0$ and $F_{*}=1$) as a function of
the condensation temperature ($T_{C}$) from Lodders (2003). Orange symbols are
used for results obtained in this work; black symbols show results for
additional elements examined in previous investigations (Jenkins, 2009;
Ritchey et al., 2018). Note the depletions for Mn and Cu (from Jenkins, 2009)
have been adjusted here by +0.165 dex and $-$0.016 dex, respectively, to
account for updated $f$-values (Toner & Hibbert, 2005; Brown et al., 2009).

Our new results on P, Cl, and F depletions help to clarify the situation
regarding gas-phase element depletions at $F_{*}=0$. A fairly coherent trend
now emerges, where the depletions at $F_{*}=0$ are consistent with zero for
elements with $T_{C}\lesssim 800$ K. For $T_{C}\gtrsim 800$ K, the elements
Ge, Ga, Cu, Mn, Cr, Fe, Ni, and Ti exhibit a clear trend of increasing
depletion with increasing $T_{C}$, although the trend appears to flatten for
$T_{C}\gtrsim 1200$ K. The elements P, Si, and Mg do not participate in this
trend, however, as they exhibit very little depletion at $F_{*}=0$ despite
having large condensation temperatures. (Note that the initial depletions for
the elements As and Pb are highly uncertain because these elements are
detected only along sight lines with relatively high values of $F_{*}$; see
Ritchey et al., 2018).

At $F_{*}=1$, another fairly regular pattern emerges. The volatile elements
(i.e., C, N, O, and Kr) exhibit somewhat more depletion at $F_{*}=1$ than at
$F_{*}=0$ (except for N, which has a depletion slope of $A_{\rm N}=0$).
Meanwhile, a nearly linear trend of increasing depletion with increasing
$T_{C}$ is seen for most of the more refractory elements from Cd at
$T_{C}=650$ K to Ti at $T_{C}=1580$ K. (Note that the depletion results for S
are also uncertain; see Jenkins, 2009). The elements Cl, As, P, Si, and Mg,
however, do not follow this linear trend. These elements seem to form a second
branch of the trend displaced toward higher gas-phase abundance.101010Recent
work by Lodders & Fegley (2023) indicates that the 50% condensation
temperature for Cl may be significantly lower than that adopted here. Lodders
& Fegley (2023) find a value of $T_{C}=427$ K for Cl, which would place it
among the low-depletion elements with $T_{C}\lesssim 800$ K.

In the context of dust grain formation, the depletions at $F_{*}=0$ are
probably a good representation of the dust-phase abundances that pertain to
the cores of the grains that emerge from stellar outflows and supernova
ejecta. After being released into the ISM, the grains produced by stellar
sources are subject to interstellar shocks, which may strip the outer portions
of the grains leaving only the resilient cores. There are therefore two
possibilities that might explain the elevated gas-phase abundances of P, Si,
and Mg at $F_{*}=0$. Either these elements are inhibited from condensing into
the grains produced in some stellar sources, or these elements are primarily
incorporated into grain mantles that are more easily disrupted or destroyed
through sputtering in interstellar shocks.

Observations of dust shells around O-rich AGB stars (e.g., Karovicova et al.,
2013) are consistent with two distinct populations of dust grains condensing
at different distances from the stellar photosphere. Alumina grains (Al2O3)
condense close to the stellar surface (at $\sim$2 $R_{*}$), while silicate
grains condense at larger distances ($\sim$4–5 $R_{*}$) where the gas
temperature is lower. Karovicova et al. (2013) find that some O-rich AGB stars
have both an alumina shell and a silicate shell, while others have only an
alumina dust shell. Furthermore, the stars with silicate shells tend to have
much higher mass-loss rates. For the less-evolved stars with low mass-loss
rates, the density in the cooler regions of the outflow (farther from the
stellar surface) may be too low for significant SiO condensation. (SiO is
thought to be the seed particle for silicate nucleation; e.g., Paquette et
al., 2011; Gail et al., 2013). Since the condensation temperature for Al2O3 is
significantly larger than that for SiO, alumina condensation takes place
closer to the stellar photosphere where the gas density is higher.

The fact that some AGB stars do not form silicate dust shells may help to
explain why the gas-phase abundances of Si and Mg are significantly larger
than those of other refractory elements (e.g., Fe) at $F_{*}=0$ (Figure 19).
Karovicova et al. (2013) argue that, owing to the relatively low cosmic
abundance of Al, alumina grains alone cannot account for the observed dust-to-
gas ratios in the outflows of AGB stars lacking silicate dust shells. The
alumina grains that condense near the stellar surface may become seeds for
further dust growth at larger radii and lower dust temperatures. Metallic Fe
grains are good candidates for a dust growth species that would contribute
mass but would not alter the spectral signature of Al2O3. It is interesting to
note that many of the elements that exhibit a clear dust condensation sequence
at $F_{*}=0$ (Ge, Ga, Cu, Cr, Fe, and Ni) condense into a host phase of Fe
alloy (Lodders, 2003).

Gobrecht et al. (2016) model dust and molecule formation in the inner wind of
the O-rich AGB star IK Tau. These authors consider the effects of periodic
shocks on the gas induced by stellar pulsation and follow the resulting non-
equilibrium chemistry in the shocked gas layers. They find that some molecules
(e.g., CO, PN, and HCl) form in the post-shock gas of the shocked photosphere
and maintain almost constant abundances in the inner wind. The near constant
abundances indicate that these molecules do not participate in complex
chemistries or in the formation of dust clusters in the post-shock gas. The
modelled abundances of PN and HCl are comparable to (and even somewhat larger
than) the cosmic abundances of P and Cl, indicating that all of the P and Cl
atoms are locked up in these species. The predictions of the Gobrecht et al.
(2016) model are in agreement with our interstellar measurements, which show
that there is essentially no depletion of P and very little (if any) depletion
of Cl at $F_{*}=0$.

Jones et al. (2017) offer an alternative explanation for why the depletions of
Si and Mg are different from those of the iron group elements. They postulate
that the differences in depletion are a natural consequence of the composition
and structure of interstellar silicate grains. In the Jones et al. (2017)
model, the silicate group elements (O, Si, and Mg) form Mg-rich olivine and
pyroxene-type amorphous silicate structures, while the iron group elements
(Fe, Cr, Ni, Ti, and Mn) are present as Fe-rich nano-inclusions within the
amorphous silicate matrix. Jones et al. (2017) argue that the iron group
elements show less variation in depletion because, as nano-inclusions, they
are better protected by the surrounding silicate matrix and thereby better
able to withstand the effects of sputtering in interstellar shocks.

Dwek (2016) argues that most of the Fe missing from the gas phase in
interstellar clouds must have precipitated from the ISM gas by a cold
accretion onto preexisting silicate or carbon grains. He bases this conclusion
on the fact that most Fe is produced in Type Ia SNe yet observational evidence
suggests that these objects do not produce significant quantities of dust
(e.g., Blair et al., 2007). While some thermally-condensed Fe dust may be
contributed by core-collapse SNe and AGB star winds, Dwek (2016) estimates
that less than 35% of the Fe that is injected into the ISM is in solid form.
The observed fraction of Fe in interstellar dust ranges from 89% at $F_{*}=0$
to 99% at $F_{*}=1$ (Jenkins, 2009). Thus, if the argument advanced by Dwek
(2016) is correct, there must be a very efficient cycling of material between
the cold and warm phases of the diffuse ISM.

In a series of dust evolution models based on a hydrodynamic simulation of the
ISM, Zhukovska et al. (2016, 2018) are able to reproduce the observed trends
of increasing Si and Fe depletion with gas density by adopting a grain size
distribution that includes a population of very small negatively-charged dust
grains. Coulomb interactions between negatively-charged grains and ionized gas
species enhance collision rates and lead to an increase in grain growth in the
cold neutral medium (CNM). The rates of dust growth in the ISM in the
Zhukovska et al. (2016, 2018) models far exceed the rates of dust production
by stellar sources.

Priestley et al. (2021), however, question the efficiency of grain growth in
the diffuse ISM. They argue that if accretion were as efficient as in the
Zhukovska et al. (2016, 2018) models, the small grains would grow to the point
where they become positively charged, thereby halting any further accretion.
Priestley et al. (2021) suggest that the strong depletions seen in the CNM
(i.e., at $F_{*}=1$) represent the dust-phase abundances of grains produced by
evolved stars and supernovae. The variation in depletions (e.g., between
$F_{*}=1$ and $F_{*}=0$) would then mostly be due to the destruction of dust
grains in supernova shocks, although the dust destruction efficiency would
need to be reduced.

Our results on interstellar P and Cl depletions provide evidence that grain
growth in fact does occur in the diffuse ISM and that the depletion rates are
enhanced by ion-grain reactions (Section 4.3). We find enhanced Cl depletions
along sight lines with higher than expected levels of Cl ionization (e.g.,
along sight lines probing PDRs, such as HD 37903, HD 147933, and HD 147888).
Moreover, if we examine the P and Cl depletion trends for just those sight
lines exhibiting elevated levels of ionization, we find much steeper depletion
slopes (i.e., rates of depletion) than for the general samples. Clearly, these
increased depletion rates are related to the environmental conditions in the
interstellar clouds and not to the injection of depleted gas from stellar
sources. The elevated levels of ionization strongly suggest that efficient
ion-grain reactions are the source of the enhanced depletions.

###  5.2 The Molecular Content of Diffuse Clouds

It is commonly assumed that the molecular hydrogen fraction in the H2-bearing
portion of a diffuse cloud is larger than the value derived from the
integrated column densities of H i and H2 along a line of sight. However, it
is not often possible to directly assess the true local value of the molecular
hydrogen fraction. The analysis described in Section 4.4 involving neutral
chlorine fractions allows us to obtain estimates for the molecular fractions
in the H2-bearing gas, provided that our simple two-zone model for Cl
chemistry is reasonably correct. We find that all sight lines with $\log
N({\rm H}_{2})\gtrsim 18$ have molecular fractions in the optically-thick H2
region of $f_{1}({\rm H}_{2})\gtrsim 0.1$ (Figure 20). The only sight lines
with $f_{1}({\rm H}_{2})$ values significantly less than 0.1 are those that
probe molecular gas in the transition region where H2 is not yet fully self-
shielded (i.e., $\gamma$ Cas, $\psi$ Ori, $\epsilon$ Ori, and $\kappa$ Ori).
For $\log N({\rm H}_{2})\gtrsim 18$, the $f_{1}({\rm H}_{2})$ values increase
only gradually until the molecular hydrogen column reaches a value of $\log
N({\rm H}_{2})\approx 20$, after which there is a much steeper rise. The
H2-bearing gas is essentially fully molecular at $\log N({\rm H}_{2})\approx
21$.

Figure 20: Molecular fraction associated with the optically-thick H2 region,
$f_{1}$(H2), plotted against the column density of molecular hydrogen,
$N$(H2). The plotting symbols have the same meaning as in Figure 11. Four
sight lines with very low values of $N$(H2) (i.e., $\gamma$ Cas, $\psi$ Ori,
$\epsilon$ Ori, and $\kappa$ Ori) are not shown in this plot.

There are some exceptions to this general trend. For example, there is a group
of sight lines (that includes HD 121968, $\gamma$ Ara, $\pi$ Sco, $\epsilon$
Per, 139 Tau, and $\sigma$ Sco) with $\log N({\rm H}_{2})\lesssim 20$ and
$f_{1}({\rm H}_{2})\gtrsim 0.5$. The most prominent outlier among these is HD
121968, which has $\log N({\rm H}_{2})\approx 18.7$ and $f_{1}({\rm
H}_{2})\approx 0.65$. This sight line probes gas in the lower halo at a
distance of $\sim$3.3 kpc above the Galactic plane. While much of that
pathlength is evidently filled with low-density neutral, atomic gas, the sight
line also apparently crosses a small, moderately-dense diffuse molecular
cloud. Kinematic evidence suggests that this small cloud is located close to
the Galactic disk rather than near the position of the background star. The
other outliers mentioned above (which are from the Copernicus sample; see
Moomey et al., 2012) have rather large errors associated with their derived
values of $f_{1}({\rm H}_{2})$.

The median value of $f_{1}({\rm H}_{2})$ for our sample of 78 sight lines with
determinations of $f({\rm Cl~{}\textsc{i}})$ is 0.40, which may be compared to
the median value of $f({\rm H}_{2})$ for the same sight lines, which is 0.15.
A value of $f({\rm H}_{2})\approx 0.4$ might then be adopted as a typical
molecular hydrogen fraction for the H2-bearing portions of diffuse clouds.
This value is somewhat lower than the values that have been adopted in
previous efforts to analyze the physical conditions in diffuse molecular gas.
Jenkins & Tripp (2011), for example, adopt a value of $f({\rm H}_{2})=0.6$ for
the CNM in their analysis of thermal pressures from C i fine-structure
excitation. (Many of the same sight lines studied in that paper are included
in our analysis.) From Figure 20, we find that values of $f_{1}({\rm H}_{2})$
as high as 0.6 are generally only seen along sight lines with relatively high
molecular hydrogen column densities (i.e., $\log N({\rm H}_{2})\gtrsim 20.5$),
and these sight lines represent only $\sim$13% of the sample.

##  6 SUMMARY AND CONCLUSIONS

We have presented a comprehensive examination of interstellar P and Cl
abundances based on an analysis of archival HST/STIS and FUSE spectra. Column
densities of P ii, Cl i, and Cl ii were derived through detailed profile
synthesis fits for a combined sample of over 100 sight lines. P ii column
densities were obtained from the weak P ii $\lambda 1532$ line wherever
possible. Measurements of P ii $\lambda 1301$ were included only in cases
where there was no significant blending with O i $\lambda 1302$. Cl i column
densities were derived through simultaneous fits to the Cl i $\lambda 1347$
line (from STIS spectra) and either the $\lambda 1379$ line or the $\lambda
1097$, $\lambda 1094$, or $\lambda 1004$ transition (from FUSE data). Cl ii
column densities were obtained from the Cl ii $\lambda 1071$ transition, after
fitting and removing absorption from a nearby H2 feature.

Experimentally determined oscillator strengths were used for most of the P ii,
Cl i, and Cl ii lines included in our analysis (Table 2.1). However, since no
recent experimental $f$-value is available for the P ii $\lambda 1532$
transition, an empirical $f$-value was determined from the data for thirteen
sight lines that have high-resolution STIS spectra covering both P ii $\lambda
1301$ and P ii $\lambda 1532$. Our empirical $f$-value for the $\lambda 1532$
transition, $f(1532)=0.00737$, is very similar to the results of recent
theoretical calculations (Tayal, 2003; Froese Fischer et al., 2006). These
theoretical results and our empirical determination indicate that a downward
revision of $\sim$0.4 dex is required for P ii column densities obtained using
the $f$-value for P ii $\lambda 1532$ reported in Morton (2003).

We reexamined the relationships between various Cl and H species, finding
significant correlations between $N$(Cl i) and $N$(H2) and between $N$(Cltot)
and $N$(Htot). The generally good correlation between Cl i and H2 results from
the neutralization of chlorine ions in regions where H2 is abundant. The tight
linear relationship between the total column densities of Cl and H indicates
that the abundance and/or depletion of Cl does not vary appreciably with
$N$(Htot). While the relationships we find are similar to those presented in
previous investigations (e.g., Harris & Bromage, 1984; Moomey et al., 2012),
our results apply to a much larger, more representative sample of interstellar
sight lines.

We derived depletion parameters for P and Cl in accordance with the
methodology of Jenkins (2009). For P, we find that the depletion slope is
somewhat shallower than that reported in Jenkins (2009). This difference may
be a result of our much larger sample or it may be related to our use of weak,
unblended P ii transitions (from high quality STIS observations). For Cl, we
find that the depletion slope is much shallower compared to the slope obtained
by Jenkins (2009). In this case, the difference in slope is almost entirely
due to our inclusion of Cl i column densities in determinations of total Cl
abundances. A major improvement over the Jenkins (2009) results is that the
initial depletions of P and Cl no longer indicate that the abundances of these
elements are supersolar at $F_{*}=0$. In large part, this is due to improved
oscillator strengths for the relevant P ii (and Cl i) transitions.

In general, we find that Cl is only lightly depleted along most interstellar
sight lines, regardless of the fraction of hydrogen in molecular form (or the
fraction of Cl in neutral form). Indeed, the existence of a _negative_
depletion slope for Cl appears to be dependent on an enhanced rate of
depletion for a subset of sight lines with anomalously low Cl i abundances and
higher-than expected Cl ii abundances. Many of these sight lines probe PDR-
like regions where the flux of UV radiation is likely to be enhanced. The
implication is that an elevated level of ionization in relatively dense gas
leads to an enhanced rate of accretion of the ions onto grain surfaces. This,
in turn, implies the existence of a population of small, negatively-charged
grains, which accrete ionized species more efficiently through Coulomb
interactions. We take this as concrete evidence of the growth of dust grains
in diffuse interstellar clouds.

From an analysis of neutral chlorine fractions, we obtained estimates for the
molecular hydrogen fractions that pertain to the H2-bearing gas along the
lines of sight in our survey. We find that for all sight lines with $\log
N({\rm H}_{2})\gtrsim 18$ (where H2 transitions to being fully self shielded),
the H2-bearing gas has a molecular fraction of at least 10% and that the gas
becomes essentially fully molecular at $\log N({\rm H}_{2})\approx 21$. A
typical value of the molecular fraction in the H2-bearing portion of a diffuse
cloud is 0.4. This might then be adopted as a representative value for the CNM
in general for studies seeking to analyze the chemistry and physical
conditions in diffuse molecular clouds.

We acknowledge the efforts of undergraduate students Jennifer Hobbs and Luke
Russell, who performed a preliminary analysis of Cl abundances as part of the
Pre-Major in Astronomy Program (Pre-MAP) at the University of Washington. The
profile fitting routine used in this work (ISMOD), which was originally
created by Yaron Sheffer, was updated by Johnathan Rice to accommodate
simultaneous fits to multiple absorption features. We thank Dan Welty for
providing us with the H2GUI package. Our research has made use of the SIMBAD
database operated at CDS, Strasbourg, France. Support for this work was
provided by the Space Telescope Science Institute through grants HST-
AR-15807.001-A to Eureka Scientific and HST-AR-15807.002-A to the University
of Toledo. Observations were obtained from the MAST data archive at the Space
Telescope Science Institute. STScI is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.

##  Appendix A Chlorine Measurements from Copernicus Observations

To supplement our sample of Cl measurements from STIS and FUSE observations,
we have included in our analysis additional Cl abundance determinations based
on observations made with the Copernicus satellite. The Copernicus sample
consists of the results presented in Moomey et al. (2012), who studied sight
lines probing the transition from atomic to molecular gas, and the results
obtained by Brown (2015), who focused on sight lines with very low H2 column
densities as part of a Masters Thesis at the University of Toledo. Brown
(2015) derived Cl i and Cl ii column densities via ISMOD fits to the Cl i
$\lambda 1088$, Cl i $\lambda 1347$, and Cl ii $\lambda 1071$ lines, adopting
component structures from high-resolution ground-based observations of K i, Ca
ii K, and Na i D. For convenience, the results on $N$(Cl i) and $N$(Cl ii)
from Brown (2015) are provided in Table 10. Upper limits were determined for
$N$(Cl i) in cases where the Cl i $\lambda 1347$ feature is not detected in
the Copernicus spectra. Column densities of H i and H2 for these sight lines,
along with the sight line depletion factors, are obtained from Jenkins (2009).
Values of $N$(Cltot) are listed in Table 10 even in cases where Cl i is not
detected, provided that the upper limit on $N$(Cl i) is low enough that Cl i
will not contribute meaningfully to the total Cl column density. The same is
true for values of $N$(Htot) in cases where H2 is not detected. A detailed
comparison between the Cl i and Cl ii column densities shown in Table 10 and
those obtained in previous Copernicus studies of the same sight lines (Jura &
York, 1978; Harris & Bromage, 1984; Jenkins et al., 1986) is presented in
Brown (2015). In general, the Brown (2015) results agree with those of the
previous studies within the mutual uncertainties, although the uncertainties
in Brown (2015) tend to be smaller.111111For further details, see Brown
(2015), available at the following URL:
http://rave.ohiolink.edu/etdc/view?acc_num=toledo1431040914.

Table 10: Chlorine Column Densities from Copernicus Observations Star | Name | log $N$(Cl i) | log $N$(Cl ii) | log $N$(Cltot) | log $N$(H i)aaAtomic and molecular hydrogen column densities and sight line depletion factors are obtained from Jenkins (2009). | log $N$(H2)aaAtomic and molecular hydrogen column densities and sight line depletion factors are obtained from Jenkins (2009). | log $N$(Htot) |  $F_{*}$aaAtomic and molecular hydrogen column densities and sight line depletion factors are obtained from Jenkins (2009).
---|---|---|---|---|---|---|---|---
HD 5394 |  $\gamma$ Cas | $12.20\pm 0.06$ | $13.19\pm 0.09$ | $13.24\pm 0.08$ | $20.16\pm 0.08$ | $16.53\pm 0.05$ | $20.16^{+0.08}_{-0.10}$ | $0.52\pm 0.04$
HD 35715 |  $\psi$ Ori | $12.05\pm 0.12$ | $13.69\pm 0.08$ | $13.70\pm 0.08$ | $20.49\pm 0.15$ | $14.78\pm 0.15$ | $20.49^{+0.15}_{-0.23}$ | $0.66\pm 0.11$
HD 36486 |  $\delta$ Ori | $<11.41$ | $13.31\pm 0.01$ | $13.31\pm 0.01$ | $20.19\pm 0.04$ | $14.68\pm 0.26$ | $20.19^{+0.04}_{-0.04}$ | $0.54\pm 0.02$
HD 37043 |  $\iota$ Ori | $<11.40$ | $13.16\pm 0.04$ | $13.16\pm 0.04$ | $20.15\pm 0.06$ | $14.69\pm 0.20$ | $20.15^{+0.06}_{-0.07}$ | $0.41\pm 0.03$
HD 37128 |  $\epsilon$ Ori | $12.09\pm 0.01$ | $13.39\pm 0.03$ | $13.41\pm 0.03$ | $20.45\pm 0.08$ | $16.57\pm 0.20$ | $20.45^{+0.08}_{-0.10}$ | $0.54\pm 0.03$
HD 37468 |  $\sigma$ Ori | $12.60\pm 0.06$ | $13.67\pm 0.05$ | $13.71\pm 0.05$ | $20.52\pm 0.08$ | $<18.30$ | $20.52^{+0.08}_{-0.10}$ | $0.58\pm 0.04$
HD 38771 |  $\kappa$ Ori | $12.29\pm 0.04$ | $13.49\pm 0.01$ | $13.52\pm 0.01$ | $20.52\pm 0.04$ | $15.68\pm 0.20$ | $20.52^{+0.04}_{-0.04}$ | $0.67\pm 0.03$
HD 57060 | 29 CMa | $<13.00$ | $13.22\pm 0.09$ | … | $20.70\pm 0.08$ | $15.78\pm 0.18$ | $20.70^{+0.08}_{-0.10}$ | $0.50\pm 0.05$
HD 57061 |  $\tau$ CMa | $<12.00$ | $13.91\pm 0.06$ | $13.91\pm 0.06$ | $20.70\pm 0.04$ | $15.48\pm 0.18$ | $20.70^{+0.04}_{-0.04}$ | $0.39\pm 0.04$
HD 64740 | … | $<12.30$ | $13.93\pm 0.07$ | $13.93\pm 0.07$ | $20.05\pm 0.18$ | $<14.95$ | $20.05^{+0.18}_{-0.31}$ | $0.27\pm 0.30$
HD 64760 | … | $<11.89$ | $13.57\pm 0.04$ | $13.57\pm 0.04$ | $20.26\pm 0.09$ | $<14.60$ | $20.26^{+0.09}_{-0.11}$ | $0.35\pm 0.06$
HD 65575 |  $\chi$ Car | $<12.28$ | $13.52\pm 0.05$ | $13.52\pm 0.05$ | $<20.74$ | $<14.78$ | … | …
HD 65818 |  $\nu$ Pup | $<12.54$ | $13.92\pm 0.09$ | $13.92\pm 0.09$ | $20.52\pm 0.13$ | $15.08\pm 0.30$ | $20.52^{+0.13}_{-0.19}$ | $0.36\pm 0.09$
HD 106490 |  $\delta$ Cru | $<11.95$ | $13.31\pm 0.07$ | $13.31\pm 0.07$ | $<19.69$ | $<14.08$ | … | …
HD 108248 |  $\alpha^{1}$ Cru | $<11.38$ | $12.94\pm 0.03$ | $12.94\pm 0.03$ | $19.60\pm 0.10$ | $<14.18$ | $19.60^{+0.10}_{-0.13}$ | $0.15\pm 0.05$
HD 118716 |  $\epsilon$ Cen | $<11.54$ | $12.95\pm 0.03$ | $12.95\pm 0.03$ | $19.60\pm 0.19$ | $<14.08$ | $19.60^{+0.19}_{-0.35}$ | $0.15\pm 0.16$
HD 127972 |  $\eta$ Cen | $<11.67$ | $13.21\pm 0.20$ | $13.21\pm 0.20$ | $<19.48$ | $<14.18$ | … | …
HD 136298 |  $\delta$ Lup | $<11.81$ | $13.11\pm 0.07$ | $13.11\pm 0.07$ | $<19.76$ | $<14.26$ | … | …
HD 143118 |  $\eta$ Lup | $12.03\pm 0.10$ | $12.85\pm 0.14$ | $12.91\pm 0.13$ | $<20.12$ | $<14.23$ | … | …
HD 151890 |  $\mu^{1}$ Sco | $<11.78$ | $13.20\pm 0.06$ | $13.20\pm 0.06$ | $<20.12$ | $<14.26$ | … | …
HD 160578 |  $\kappa$ Sco | $<11.53$ | $13.05\pm 0.05$ | $13.05\pm 0.05$ | $20.22\pm 0.12$ | $<14.23$ | $20.22^{+0.12}_{-0.17}$ | $0.50\pm 0.07$

##  Appendix B Fluorine Depletions from the Literature

Fluorine abundances were reported by Federman et al. (2005) and Snow et al.
(2007) from analyses of the F i lines at 951 and 954 Å in FUSE spectra.
However, fluorine was not included in the depletion study of Jenkins (2009)
(presumably because there are relatively few published detections). From a
thermochemical perspective, fluorine is very similar to chlorine. (For
example, like Cl+, F reacts exothermically with H2; Neufeld & Wolfire, 2009).
Moreover, the depletions of F and Cl are often assumed to be similar (e.g.,
Federman et al., 2005). Thus, in order to compare the depletion behaviors of F
and Cl in a more quantitative way, we derived depletion parameters for F using
the Jenkins (2009) methodology. In Figure 21, we plot the gas-phase F
abundances from Federman et al. (2005) and Snow et al. (2007) as a function of
the sight depletion factors from Jenkins (2009). (Note that Federman et al.
(2005) incorporate a measurement of F i absorption toward $\delta$ Sco into
their analysis. This measurement was originally obtained by Snow & York (1981)
based on Copernicus observations.) A least-squares linear fit yields the
following parameters: $A_{\rm F}=-0.304\pm 0.288$, $B_{\rm F}=-0.213\pm
0.077$, $z_{\rm F}=0.483$, $[{\rm F}/{\rm H}]_{0}=-0.066\pm 0.159$, and $[{\rm
F}/{\rm H}]_{1}=-0.370\pm 0.167$. The $\chi^{2}$ statistic is 13.6 with 7
degrees of freedom, yielding a reduced chi-squared value of 1.9. From these
results, we find that the initial depletion of F is consistent with zero (as
expected), and the depletion slope for F is very similar to that for Cl. The
depletion results for F derived here are compared to those for many other
elements in Figure 19.

Figure 21: Gas-phase F abundances from the literature (Federman et al., 2005;
Snow et al., 2007) as a function of the sight line depletion factor ($F_{*}$).
Solid squares represent abundances derived from FUSE observations; the open
diamond represents the F abundance toward $\delta$ Sco, which is based on
Copernicus observations (Snow & York, 1981; Federman et al., 2005). The solid
orange line represents a linear fit to the data derived according to the
methodology of Jenkins (2009). The horizontal dotted line gives the adopted
solar system abundance from Lodders (2003).

## References

  * Alkhayat et al. (2019) Alkhayat, R. B., Irving, R. E., Federman, S. R., Ellis, D. G., & Cheng, S. 2019, ApJ, 887, 14
  * Bailer-Jones et al. (2021) Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Demleitner, M., & Andrae, R. 2021, AJ, 161, 147
  * Balashev et al. (2015) Balashev, S. A., Noterdaeme, P., Klimenko, V. V., et al. 2015, A&A, 575, L8
  * Blair et al. (2007) Blair, W. P., Ghavamian, P., Long, K. S., et al. 2007, ApJ, 662, 998
  * Bohlin et al. (1983) Bohlin, R. C., Hill, J. K., Jenkins, E. B., et al. 1983, ApJS, 51, 277
  * Brown (2015) Brown, J. M. 2015, M.S. Thesis, Univ. Toledo
  * Brown et al. (2018) Brown, M. S., Alkhayat, R. B., Irving, R. E., et al. 2018, ApJ, 868, 42
  * Brown et al. (2009) Brown, M. S., Federman, S. R., Irving, R. E., Cheng, S., & Curtis, L. J. 2009, ApJ, 702, 880
  * Cartledge et al. (2004) Cartledge, S. I. B., Lauroesch, J. T., Meyer, D. M., & Sofia, U. J. 2004, ApJ, 613, 1037
  * Cartledge et al. (2006) Cartledge, S. I. B., Lauroesch, J. T., Meyer, D. M., & Sofia, U. J. 2006, ApJ, 641, 327
  * Cartledge et al. (2001) Cartledge, S. I. B., Meyer, D. M., Lauroesch, J. T., & Sofia, U. J. 2001, ApJ, 562, 394
  * Dwek (2016) Dwek, E. 2016, ApJ, 825, 136
  * Dwek & Scalo (1980) Dwek, E., & Scalo, J. M. 1980, ApJ, 239, 193
  * Federman et al. (2007) Federman, S. R., Brown, M., Torok, S., et al. 2007, ApJ, 660, 919
  * Federman et al. (2005) Federman, S. R., Sheffer, Y., Lambert, D. L., & Smith, V. V. 2005, ApJ, 619, 884
  * Froese Fischer et al. (2006) Froese Fischer, C., Tachiev, G., & Irimia, A. 2006, ADNDT, 92, 607
  * Gail et al. (2013) Gail, H.-P., Wetzel, S., Pucci, A., & Tamanai, A. 2013, A&A, 555, A119
  * Gobrecht et al. (2016) Gobrecht, D., Cherchneff, I., Sarangi, A., Plane, J. M. C., & Bromley, S. T. 2016, A&A, 585, A6
  * Harris & Bromage (1984) Harris, A. W., & Bromage, G. E. 1984, MNRAS, 208, 941
  * Hibbert (1988) Hibbert, A. 1988, PhyS, 38, 37
  * Hobbs (1974) Hobbs, L. M. 1974, ApJ, 188, L107
  * Jenkins (2009) Jenkins, E. B. 2009, ApJ, 700, 1299
  * Jenkins (2019) Jenkins, E. B. 2019, ApJ, 872, 55
  * Jenkins et al. (1986) Jenkins, E. B., Savage, B. D., & Spitzer, L. 1986, ApJ, 301, 355
  * Jenkins & Tripp (2011) Jenkins, E. B., & Tripp, T. M. 2011, ApJ, 734, 65
  * Jensen & Snow (2007a) Jensen, A. G., & Snow, T. P. 2007a, ApJ, 669, 378
  * Jensen & Snow (2007b) Jensen, A. G., & Snow, T. P. 2007b, ApJ, 669, 401
  * Jones et al. (2017) Jones, A. P., Kohler, M., Ysard, N., Bocchio, M., & Verstraete, L. 2017, A&A, 602, A46
  * Jones et al. (1994) Jones, A. P., Tielens, A. G. G. M., Hollenbach, D. J., & McKee, C. F. 1994, ApJ, 433, 797
  * Jura (1974) Jura, M. 1974, ApJ, 190, L33
  * Jura & York (1978) Jura, M., & York, D. G. 1978, ApJ, 219, 861
  * Karovicova et al. (2013) Karovicova, I., Wittkowski, M., Ohnaka, K., et al. 2013, A&A, 560, A75
  * Lebouteiller et al. (2005) Lebouteiller, V., Kuassivi, & Ferlet, R. 2005, A&A, 443, 509
  * Lodders (2003) Lodders, K. 2003, ApJ, 591, 1220
  * Lodders & Fegley (2023) Lodders, K., & Fegley, Jr., B. 2023, submitted to Geochemistry [arXiv:2301.03674]
  * Moomey et al. (2012) Moomey, D., Federman, S. R., & Sheffer, Y. 2012, ApJ, 744, 174
  * Morton (2003) Morton, D. C. 2003, ApJS, 149, 205
  * Neufeld & Wolfire (2009) Neufeld, D. A., & Wolfire, M. G. 2009, ApJ, 706, 1594
  * Oliver & Hibbert (2013) Oliver, P., & Hibbert, A. 2013, ADNDT, 99, 459
  * Paquette et al. (2011) Paquette, J. A., Ferguson, F. T., & Nuth, J. A. 2011, ApJ, 732, 62
  * Press et al. (2007) Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 2007, Numerical Recipes, The Art of Scientific Computing (3rd ed.; Cambridge: Cambridge Univ. Press)
  * Priestley et al. (2021) Priestley, F. D., De Looze, I., & Barlow, M. J. 2021, MNRAS, 502, 2438
  * Rachford et al. (2009) Rachford, B. L., Snow, T. P., Destree, J. D., et al. 2009, ApJS, 180, 125
  * Rachford et al. (2002) Rachford, B. L., Snow, T. P., Tumlinson, J., et al. 2002, ApJ, 577, 221
  * Ritchey et al. (2018) Ritchey, A. M., Federman, S. R., & Lambert, D. L. 2018, ApJS, 236, 36
  * Ritchey et al. (2011) Ritchey, A. M., Federman, S. R., Sheffer, Y., & Lambert, D. L. 2011, ApJ, 728, 70
  * Ritchey et al. (2023) Ritchey, A. M., Jenkins, E. B., Shull, J. M., et al. 2023, submitted to ApJ
  * Sarangi & Cherchneff (2015) Sarangi, A., & Cherchneff, I. 2015, A&A, 575, A95
  * Savage & Sembach (1991) Savage, B. D., & Sembach, K. R. 1991, ApJ, 379, 245
  * Schectman et al. (1993) Schectman, R. M., Federman, S. R., Beideck, D. J., & Ellis, D. J. 1993, ApJ, 406, 735
  * Schectman et al. (2005) Schectman, R. M., Federman, S. R., Brown, M., et al. 2005, ApJ, 621, 1159
  * Sheffer et al. (2008) Sheffer, Y., Rogers, M., Federman, S. R., et al. 2008, ApJ, 687, 1075
  * Slavin et al. (2015) Slavin, J. D., Dwek, E., & Jones, A. P. 2015, ApJ, 803, 7
  * Snow et al. (2007) Snow, T. P., Destree, J. D., & Jensen, A. G. 2007, ApJ, 655, 285
  * Snow et al. (2008) Snow, T. P., Destree, J. D., & Welty, D. E. 2008, ApJ, 679, 512
  * Snow & York (1981) Snow, T. P., & York, D. G. 1981, ApJ, 247, L39
  * Sonnentrucker et al. (2002) Sonnentrucker, P., Friedman, S. D., Welty, D. E., York, D. G., & Snow, T. P. 2002, ApJ, 576, 241
  * Sonnentrucker et al. (2006) Sonnentrucker, P., Friedman, S. D., & York, D. G. 2006, ApJ, 650, L115
  * Sonnentrucker et al. (2007) Sonnentrucker, P., Welty, D. E., Thorburn, J. A., & York, D. G. 2007, ApJS, 168, 58
  * Tayal (2003) Tayal, S. S. 2003, ApJS, 146, 459
  * Toner & Hibbert (2005) Toner, A., & Hibbert, A. 2005, MNRAS, 361, 673
  * Tumlinson et al. (2002) Tumlinson, J., Shull, J. M., Rachford, B. L., et al. 2002, ApJ, 566, 857
  * Valencic et al. (2004) Valencic, L. A., Clayton, G. C., & Gordon, K. D. 2004, ApJ, 616, 912
  * van Dishoeck & Black (1988) van Dishoeck, E. F., & Black, J. H. 1988, ApJ, 334, 771
  * Weingartner & Draine (1999) Weingartner, J. C., & Draine, B. T. 1999, ApJ, 517, 292
  * Welty & Crowther (2010) Welty, D. E., & Crowther, P. A. 2010, MNRAS, 404, 1321
  * Welty & Hobbs (2001) Welty, D. E., & Hobbs, L. M. 2001, ApJS, 133, 345
  * Welty et al. (2020) Welty, D. E., Sonnentrucker, P., Snow, T. P., & York, D. G. 2020, ApJ, 897, 36
  * Zhukovska et al. (2016) Zhukovska, S., Dobbs, C., Jenkins, E. B., & Klessen, R. S. 2016, ApJ, 831, 147
  * Zhukovska et al. (2018) Zhukovska, S., Henning, T., & Dobbs, C. 2018, ApJ, 857, 94