THE NEW DETECTIONS OF ⁷Li/⁶Li ISOTOPIC RATIO IN THE INTERSTELLAR MEDIA^*

As discussed below, the distances of background continuum sources are key issues for the secondary purpose of this study. The HIPPARCOS catalog (Perryman et al. 1997) provides the most reliable parallax measurements for nearby objects (<1 kpc), however, as we wished to identify more distant candidates for background continuum sources we needed to use distance indicators other than parallax. We selected our candidates from the brightest stars in the galaxy tabulated by Humphreys (1978) although spectroscopic distance estimates involve several uncertainties to be discussed below.

The lithium ⁷Li/⁶Li ratios reported in the previous observations are summarized in Table 5. It is notable that the background stars are all within 0.5 kpc of the Sun. We observed one of these nearby stars ζ Oph as a reference because it was most frequently studied by several groups and because it satisfied the necessary criteria for successfully observing the Li i absorption lines in the ISM being bright and having a featureless spectrum and a fair color excess. In our present work, we chose from Humphreys (1978) two further stars HD169454 and HD250290 as background continuum sources that also satisfied the above criteria.

In this section, we discuss how to estimate the distances of these stars together with other useful properties and observational information to be summarized in Tables 1 and 2.

2.2.1. ζ Oph

2.2.2. HD169454

2.2.3. HD250290

Although the background sources may be located far from the solar system, there are not definite evidences which indicate large distance of absorbing clouds. Furthermore, the fact that observed radial velocities of the clouds are near zero in the local standard of rest (LSR) indicates these gas clouds are likely to be near the Sun. So we adopted zero as the distance of the absorbing clouds toward HD169454 and HD250290.

In order to resolve the weak ⁷Li i doublet lines at 6707.76 Å and 6707.91 Å with isotopic shifts of 0.16 Å for the ⁶Li i, the relative spectral resolution should be at least (6708/0.16) × 2 ∼ 84000. Since the expected strength of the interstellar Li absorption is a few milliangstroms, the required S/N to detect small fraction of ⁶Li is higher than 1000 pixel⁻¹ element. In order to resolve the velocity structure of the absorber, according to the method presented by Knauth et al. (2000), we chose the weak K i lines at 4044 Å and 4047 Å for reference. These lines have similar strength to the Li lines, so they are suitable to resolve the velocity components.

All observations were taken with the HDS on the optical-Nasmyth platform of the 8.2 m Subaru Telescope of National Astronomical Observatory of Japan at the summit of Mauna Kea. The observational data were collected in two spectral regions: one a blue region including K i 4045 Å for resolving the velocity structure of the absorbing cloud, the other a red region including the Li i 6708 Å for investigating the isotopic ratio of Li. The blue and red setting covered 3400–5200 Å and 5100–7800 Å, respectively. For ζ Oph, only a red spectrum was obtained. We adopted the velocity component estimated by previous work (Ferlet & Dennefeld 1984; Meyer et al. 1993; Lemoine et al. 1995; Howarth et al. 2002). The slit width was set to 0.180 mm (0.36 arcsec on the sky) and the spectral resolution measured using the Th–Ar emission line width was 95,000 at 6700 Å. For the red setting, an SC-46 order cut filter was placed after the entrance slit in order to block the second-order light of the cross disperser. For the blue setting, a quartz plate was inserted after the slit so as not to shift the focal position of the spectrograph. Our objects were sufficiently bright on the Subaru Telescope that all exposures were limited to 10 minutes at most to avoid saturation. We took tens of exposures for each object to attain the required S/N.

Spectral images directly obtained with the CCD were reduced in a standard way using the Image Reduction and Analysis Facility (IRAF)¹¹ version 2.11.3. Ten bias images were taken each night to remove any instrumental effects due to the CCD electronics. Wavelength calibration spectra of Th–Ar lamp were taken every 2 hr during observations. The average value of the overscan region in each image was subtracted from the respective images. The median image of bias images was subtracted from all stellar, Th–Ar and flat images. The scattered light was fitted by a two-dimensional low-order polynomial and subtracted from all stellar, Th–Ar and flat images. The pixel-to-pixel sensitivity variations and interference fringes were taken into account in making the normalized flat image. The flat image was the median of 30 flat lamp images and the total flux for the flat image was 100 times greater than a single stellar image. All stellar and Th–Ar images were divided by the normalized flat image. The pixels across the dispersion axis at each wavelength were summed in each spectral order for stellar and Th–Ar images. The extracted one-dimensional spectra were wavelength calibrated by using the pre- and post-Th–Ar images and were Doppler-corrected to convert to the LSR wavelengths. The stellar spectra were then co-added and normalized to unity with a polynomial or cubic spline function. Since the rms noise in a featureless wavelength region is equivalent to the expected noise derived from the photon number, it appears unlikely that the final spectrum is affected by non-statistical errors.

Figures 1–5 show normalized spectra in order to display the area around the Li i and K i absorption lines.

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There are several DIB features observed around the Li i absorption lines at 6699.28, 6701.87, and 6709.65 Å, whose source species are not identified (Herbig 1995; Tuairisg et al. 2000). Their equivalent widths were shown to be 60, 27, and 10 mÅ by Herbig (1995) for HD183143. Tuairisg et al. (2000) reported equivalent widths for these DIB features of 41, 15, 16 mÅ and 48, 20, 13 mÅ for BD+63°1964 and HD183143, respectively. We also found these three DIB features clearly in the spectra for HD169454 and HD250290 at the expected positions with equivalent widths of 20, 10, 6 mÅ and 25, 15, 6 mÅ, respectively. Although no positive detection of the 6709.65 Å DIB feature has been reported for ζ Oph in the literature, we found the 6709.65 Å DIB feature as well as the other two DIB features at 6699.28 Å and 6701.87 Å as shown in Figure 1. Our measured equivalent widths were 3, 5, and 4 mÅ for ζ Oph. The relative strength of the 6699.28 Å DIB was exceptionally weak for ζ Oph compared with the other stars BD+63°1964, HD183143, HD169454, and HD250290. It should be noted that the broad wings of the DIB features do not affect the analysis of the Li i absorption line at all.

We found an unknown feature at 6706.1 Å in the spectrum of ζ Oph (see Figure 1), although Lemoine et al. (1995) reported no corresponding feature in their higher resolution and higher S/N spectrum. We carefully inspected our flat-field images in detail and found a weak gray patch at the corresponding position ∼6706.1 Å. It is therefore likely that the flat fielding was not perfect or there is some non-linear response of pixels in the gray patch. We regard this weak absorption feature as artificial. We, however, confirmed that there is no CCD defect at the wavelength of the Li i absorption line.

3.1.1. ζ Oph

Although we do not have spectral data for K i, ζ Oph is well investigated as a background source of interstellar absorption and the velocity structure of the absorbing cloud toward ζ Oph was reported by several groups. Although the reported velocity structure toward ζ Oph shows some diversity, there are at least two velocity components of absorbing clouds in the line of sight toward ζ Oph. However, as the spectral resolving power of our observations cannot distinguish velocity components clearly, we assume a single velocity component absorber in the first analysis (model 1: Figure 6). Under this assumption, we find in model 1 the ⁷Li/⁶Li ratio of 7.1^+2.9_−1.6 (1σ).

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There are many literatures on the velocity components of ISMs in the line of sight toward ζ Oph. We chose recent papers to determine the velocity structure. Crawford (1997) reported two velocity components with separation of 1.1 km s⁻¹ by using C₂ molecular lines. Welty & Hobbs (2001) performed a survey for interstellar K i absorption and revealed that there are two strong components (comp. 3 and 4 in Table 2 of the reference) and three weak components (comp. 1, 2, and 5) in the line of sight, and, the reported value of the separation between the two strong components is 1.02 km s⁻¹. Howarth et al. (2002) reported two velocity components in the line of sight toward ζ Oph with the separation of ∼1.0 km s⁻¹. Knauth et al. (2003) showed that there are two velocity components in the line of sight and their separation is 1.04 km s⁻¹. We therefore tried to introduce the second velocity component in second case (model 2: Figure 7) by adopting the following four constraints; a fixed velocity difference of 1.0 km s⁻¹, a common b parameter, a fixed equivalent width ratio of 2.0 between the two velocity components and a common ⁷Li/⁶Li ratio. These constraints are introduced because the velocity resolution of our data is not sufficient to resolve this small velocity separation, 1.0 km s⁻¹, and therefore, we cannot treat these all parameters independently. In this second model, we derived the isotopic ratio 6.6^+2.5_−1.5 (1σ), consistent with the value obtained in the first model assuming a single line component.

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To check the precision of our results, we compared our results with the previous works, Howarth et al. (2002) and Knauth et al. (2003). Since the velocity separation in our models was cited from previous works, we narrowed the comparison down to the column density and the b parameter. Howarth et al. (2002) and Knauth et al. (2003) estimate the total column density for Li i of 3.48 ± 0.09 × 10⁹ cm⁻² and 3.24 ± 0.14 × 10⁹ cm⁻², respectively. Our result, 3.56 ± 0.14 × 10⁹ cm⁻² for one component model, is similar to previous values. For the b parameter, there is some discrepancy between Howarth et al. (2002) and Knauth et al. (2003). The unconstrained fits in Howarth et al. (2002) show 1.1–1.2 km s⁻¹ and the constrained fits for smaller b-value resulted in poorer matches to the data. Knauth et al. (2003) present the b-value of 0.65 and 0.57 km s⁻¹ for two velocity components. Our b parameter 1.03 ± 0.23 is close to the value of Howarth et al. (2002). However, we cannot resolve this contradiction because the resolving power of our data is not sufficiently high. We tried to fit our data under the constraint of fixed b parameters derived by Knauth et al. (2003) as model 3 (Figure 8). The result is very similar to the case of model 2. So we conclude that the effect of small-scale velocity structure upon the isotopic ratio of Li is very small.

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The results of the profile fitting in models 1–3 are shown in Table 4.

Table 4. Result of Profile Fitting

Star	Model	Species	VLSR (km s−1)	b (km s−1)	EW (mÅ)	N (109 cm−2)	7Li/6Li	Reduced χ2	Note
ζ Oph	1	7Li i	−0.47 ± 0.08	1.26 ± 0.19	1.06 ± 0.04	3.56 ± 0.14		31.7/31
		6Li i	−0.47 ± 0.08	1.26 ± 0.19	0.15 ± 0.04	0.50 ± 0.14	7.1+2.9−1.6
	2	7Li i	−0.81 ± 0.08	1.03 ± 0.23	0.70 ± 0.03	2.35 ± 0.10		31.7/31
		6Li i	−0.81 ± 0.08	1.03 ± 0.23	0.11 ± 0.03	0.37 ± 0.10	6.6+2.5−1.5
		7Li i	+0.19 ± 0.08	1.03 ± 0.23	0.35 ± 0.01	1.18 ± 0.04
		6Li i	+0.19 ± 0.08	1.03 ± 0.23	0.06 ± 0.01	0.20 ± 0.04
	3	7Li i	−0.85 ± 0.08	0.65	0.78 ± 0.03	2.62 ± 0.10		36.9/32
		6Li i	−0.85 ± 0.08	0.65	0.12 ± 0.03	0.40 ± 0.10	6.5+2.5−1.5
		7Li i	+0.15 ± 0.08	0.57	0.39 ± 0.01	1.31 ± 0.04
		6Li i	+0.15 ± 0.08	0.57	0.06 ± 0.01	0.20 ± 0.04
HD169454	1	K i	+4.92 ± 0.06	1.97 ± 0.12	2.53 ± 0.07	4.63 ± 0.13 × 104		93.4/76
		7Li i	+4.76 ± 0.14	3.15 ± 0.16	1.81 ± 0.06	6.08 ± 0.20		66.2/46
		6Li i	+4.76 ± 0.14	3.15 ± 0.16	0.22 ± 0.06	0.74 ± 0.20	8.1+3.6−1.8
	2	K i	+4.52 ± 0.06	0.44	1.29 ± 0.07	2.36 ± 0.13 × 104		93.7/76
			+5.22 ± 0.06	0.36	1.29 ± 0.07	2.36 ± 0.13 × 104
		7Li i	+4.41 ± 0.14	0.44	0.90 ± 0.06	3.02 ± 0.20		66.3/46
		6Li i	+4.41 ± 0.14	0.44	0.11 ± 0.06	0.37 ± 0.20	8.1+3.6−1.8
		7Li i	+5.11 ± 0.14	0.36	0.90 ± 0.06	3.02 ± 0.20
		6Li i	+5.11 ± 0.14	0.36	0.11 ± 0.06	0.37 ± 0.20
HD250290	1	K i	+0.90 ± 0.11	3.52 ± 0.14	4.80 ± 0.14	8.78 ± 0.26 × 104		53.1/76
			+6.75 ± 0.35	1.42 ± 0.70	0.50 ± 0.14	0.92 ± 0.26 × 104
		7Li i	+0.64 ± 0.09	3.35 ± 0.11	4.21 ± 0.10	14.15 ± 0.33		21.4/28
			+6.50 ± 0.09	2.55 ± 1.02	0.20 ± 0.20	0.67 ± 0.67
		6Li i	+0.64 ± 0.09	3.35 ± 0.11	0.69 ± 0.23	2.32 ± 0.77	6.3+3.0−1.7		Main comp.
			+6.50 ± 0.09	2.55 ± 1.02	0.43 ± 0.08	1.45 ± 0.26	0.5+0.6−0.5		Sub comp.
	2	K i	+0.61 ± 0.13	3.28 ± 0.15	4.33 ± 0.16	7.92 ± 0.29 × 104		60.1/77
			+5.61 ± 0.44	3.28 ± 0.15	0.98 ± 0.14	1.79 ± 0.26 × 104
		7Li i	+0.52 ± 0.10	3.28 ± 0.13	3.92 ± 0.12	13.17 ± 0.40		54.6/30
			+5.52 ± 0.10	3.28 ± 0.13	0.51 ± 0.20	1.71 ± 0.67
		6Li i	+0.52 ± 0.10	3.28 ± 0.13	0.78 ± 0.16	2.62 ± 0.54	5.0+1.5−1.0		Main comp.
			+5.52 ± 0.10	3.28 ± 0.13	0.10 ± 0.02	0.34 ± 0.07			Sub comp.

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3.1.2. HD169454

In analyzing HD169454, K i lines at 4044 Å and 4047 Å were used to determine the velocity components. These lines are a doublet pair and the intensity ratio of these lines is about 2:1. Although a weak absorbing structure may be claimed to be seen in the blue wing of the main velocity component at 4044 Å, we consider that there is only one absorbing cloud because there is no feature observed in the blue wing of 4047 Å line (see Figure 9). The residual of the profile fitting is comparable with the S/N of these data. The result of the profile fitting (model 1) is shown in Table 4. We find the ⁷Li/⁶Li ratio of 8.1^+3.6_−1.8(1σ).

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According to Crawford (1997), there are two components of absorber separated by 0.7 km s⁻¹ with b-values 0.36 ± 0.03 km s⁻¹ and 0.44 ± 0.07 km s⁻¹ along the line of sight toward HD169454. We tried to introduce these parameters in our analysis. Because there is no information about strength of metallic line absorption of each velocity components, we used the velocity separation and b parameters derived from molecular absorption for K i and Li i lines and assumed that strength of two velocity components is the same. In this case (model 2), we obtained about the same values as that of model 1. The result of the profile fitting (model 2) is also shown in Figure 10 and Table 4.

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For this star, there are few previous observational works on Li i absorption. Only White (1986) reported the upper limit of equivalent width of Li i interstellar absorption. The value of the upper limit is <4.5 mÅ and is consistent with our result of 2.0 mÅ for ⁷Li i + ⁶Li i.

3.1.3. HD250290

The K i lines at 4044 Å and 4047 Å are used in a similar way to those of HD169454. Since a weak component is detected at the red wing of the main component, we assumed two velocity components for HD250290 (model 1). The model is compared with the observed data in Figure 11. Two velocity components are assumed for the Li i lines, too. We find the ⁷Li/⁶Li ratio of the main component ⁷Li/⁶Li = 6.3^+3.0_−1.7(1σ). The isotopic ratio derived by using the secondary velocity component is excluded from our final results, because of its extremely large error caused by the weakness of the line.

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Although the values from the secondary component are not adopted in the final results, the effects on the analysis of the first component should be taken into consideration. The resultant isotopic ratio ⁷Li/⁶Li = 0.5^+0.6_−0.5 for the secondary weak component is unexpectedly small. Theoretically, it should be ∼2 larger in the extreme case that only the GCR–ISM interactions contribute to both ⁶Li and ⁷Li. Such a small ratio for the secondary weak component was reported by Lemoine et al. (1995) for ζ Oph, too, as summarized in Table 5. We therefore made another model analysis (model 2) that assumes the same isotopic ratio for both main and secondary components. In this analysis, we also adopted the following reasonable assumptions as we did for ζ Oph; a fixed velocity difference of 5.0 km s⁻¹ and a common b parameter. The model is compared with the observed data in Figure 12. The inferred ratio turns out to be ⁷Li/⁶Li = 5.0^+1.5_−1.0 with a larger reduced χ² of 54.6/30. Similarly to the first model analysis, the b parameter for ⁶Li and ⁷Li is almost the same as that for K i, which suggests that the bulk motion dominates over the thermal motion in the clouds or the clouds have more unresolved velocity components. Higher resolution and higher S/N data are required for resolving this unexpected result.

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Table 5. Compiled Observational Data

Star	7Li/6Li	7Li/6Li Error	(l, b)	d (kpc)	RG (kpc)a	Refs.b
ζ Oph	38.5c	(+141.5, − 13.5)	(6.3, + 23.6)	0.14	8.37	(1)
	13.8c	(+∞, − 4.8)				(1)
	6.8d	(+1.4, − 1.7)				(3)
	8.6e	(+2.2, − 2.2)				(4)
	1.4f	(+1.8, − 1.1)				(4)
	13.2d	(+7.7, − 4.9)				(6)
	⩾12.0e					(7)
	⩾11.7f					(7)
	7.1d	(+2.9, − 1.6)				This work
ρ Oph	12.5	(+4.3, − 3.4)g	(353.7, + 17.7)	0.12	8.39	(2)
ζ Per	5.5	(+1.3, − 1.1)	(162.3, − 16.7)	0.30	8.77	(3)
	10.6	(+2.9, − 2.9)				(5)
o Per	3.6e,h	(+0.6, − 0.6)	(160.4, − 17.7)	0.45	8.91	(5)
	1.7f,h	(+0.3, − 0.3)				(5)
	8.1e	(+2.1, − 2.1)				(7)
	2.1f	(+1.1, − 1.1)				(7)
χ Oph	7.6	(+4.8, − 4.8)	(357.9, + 20.7)	0.15	8.36	(7)
20 Aql	⩾9.4e		(28.2, − 8.3)	0.37	8.17	(7)
	⩾5.6f					(7)
HD169454	8.1	(+3.6, − 1.8)	(17.5, − 0.7)	1.7i	6.8	This work
HD250290	6.3e	(+3.0, − 1.7)	(186.6, + 0.1)	2.2, 0.44i	10.7, 8.94	This work

Notes. ^aRadius of the solar circle assumed to be 8.5 kpc. ^bReferences. (1) Ferlet & Dennefeld 1984, (2) Lemoine et al. 1993, (3) Meyer et al. 1993, (4) Lemoine et al. 1995, (5) Knauth et al. 2000, (6) Howarth et al. 2002, and (7) Knauth et al. 2003. ^cOmitted from discussions because of their extremely large errors. See the text for details. ^dSingle component fitting is used. ^eThe main velocity component. ^fThe secondary weaker velocity component. Omitted from discussions because of weakness of absorption. ^gErrors at 95% CL. ^hOmitted from discussions because same authors (7) published the revised value of ⁷Li/⁶Li. ⁱSee Table 1.

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All results of the profile fitting are summarized in Table 4.

We mention an uncertainty in the isotopic ratio for this star. Since there is no higher resolution data for HD250290, the isotopic ratio may contain larger uncertainty than those for ζ Oph and HD169454. Assuming that the difference between observed isotopic ratios toward ζ Oph and HD169454 represents the systematic uncertainty of the ratio, the value 1.0 should be added in quadrature with the uncertainties from the fitting procedure. In this case, the confidence interval of the isotopic ratio becomes ⁷Li/⁶Li = 6.3^+3.2_−2.0.

We summarize the previous observations of the ⁷Li/⁶Li isotopic abundance ratio in Table 5 together with the present results for ζ Oph, HD169454, and HD250290. The distances shown in Table 5 for the previous data are based on HIPPARCOS parallaxes (Perryman et al. 1997) of background stars and the Galactocentric distance refers to the radius of the solar circle of 8.5 kpc. For our data, the distance of background stars are discussed in Sections 2.2.2 and 2.2.3. However, we adopted 0 kpc as the distance for all absorbing clouds for safety.

We use only data that have both upper and lower detection limits for the ⁷Li/⁶Li abundance ratio in the following discussions. In the cases where the observed spectrum exhibits more than one velocity component, we use the dominant component, because the dominant component can be treated as a representative in each direction by their strong absorption. Other components have such weak absorption lines superimposed upon the main strongest component that the identification of the abundance ratio becomes less reliable. We thus do not use the isotopic abundance ratios in discussion if they are derived from the secondary velocity component, as for o Per (Knauth et al. 2003) and ζ Oph (Lemoine et al. 1995) because they are the results from subtle analysis of very weak component with extremely low column density in overlapping main component. We also do not use the data of Ferlet & Dennefeld (1984) because their result has extremely large error bars as indicated in Table 5.

Our new data are in reasonable agreement with the mean value of those observed previously in the solar neighborhood within ±2σ error bars. This agreement is robust evidence for homogeneous mixing and instantaneous recycling of the gas component in the Galactic disk.

Many theoretical and observational studies of the GCE indicate that the ⁶Li abundance in the ISM gas clouds near the solar neighborhood is entirely synthesized by GCR interactions with the ISMs. However, ⁷Li has three different production sources: (1) similarly to ⁶Li, GCR spallation and α + α fusion (Ramaty et al. 1997, 2000; Yoshii et al. 1997; Suzuki et al. 1999; Fields et al. 2000); (2) stellar nucleosyntheses in Type II SNe (Woosley et al. 1990; Woosley & Weaver 1995), in novae (José et al. 2003) and in AGB stars (Forestini & Charbonnel 1997); and (3) BBN (Wagoner 1973; Yang et al. 1984). The observed ⁷Li/⁶Li ratio can thus be written as

$$\begin{equation} \left(\frac{^7 {\rm Li}}{^6 {\rm Li}}\right)_{\rm obs} = \frac{^7 {\rm Li_{GCR}}}{^6 {\rm Li_{GCR}}}+ \frac{^7 {\rm Li_{STAR}}}{^6 {\rm Li_{GCR}}}+ \frac{^7 {\rm Li_{BBN}}}{^6 {\rm Li_{GCR}}}. \end{equation} \tag{ 1 }$$

Since we do not have definite evidences to argue about distance of absorbing clouds, we assume that the (⁷Li/⁶Li)_obs is independent of R_G in this subsection. The mean-weighted average of all observed data in Table 5 including ours is (⁷Li/⁶Li)_obs = 7.6 ± 2.3(1σ). Let us try to decompose this into several production sources of ⁷Li.

Knauth et al. (2003) adopted an approach to seek for constraints on the stellar source for ⁷Li by adopting a primordial abundance of ⁷Li/H = 1.23 × 10⁻¹⁰ in addition to the GCR term unambiguously known. Cosmological observations of the CMB anisotropies (Spergel et al. 2003, 2007), however, invoked a potential difficulty that their assumption of the primordial ⁷Li abundance may not be a unique one, as discussed in Section 1. We therefore adopt another approach here that is to estimate by all means the first GCR term and the second stellar term in order to infer the third BBN term.

The first term on the right-hand side of Equation (1) takes a constant value of ⁷Li_GCR/⁶Li_GCR = 1.5 ± 0.3 almost independent of the GCE model (Ramaty et al. 2000; Austin 1981). This is because the ratio is determined by the observed GCR energy spectrum and the measured spallation and α + α fusion cross sections.

The second term is calculated theoretically in our GCE model by using stellar nucleosynthesis yields of ⁷Li from several different sources divided by the ISM ⁶Li abundance of ⁶Li/H = 3.4 × 10⁻¹⁰ (Suzuki et al. 1999; Kawanomoto 2002). The stellar term is estimated to be ⁷Li_STAR/⁶Li_GCR = 5.4 ± 1.6.

The estimated error bars Δ⁷Li_STAR/⁶Li_GCR = ±1.6 are inferred from the following comparison among different GCE model calculations. In our GCE model, the calculated stellar lithium abundance in the current ISM gas clouds at time t = 13.5 Gy is ⁷Li/H = 2.6 × 10⁻⁹, which is slightly larger than the solar abundance of ⁷Li/H = 1.9 × 10⁻⁹ at time t = 9 Gy for solar system formation because of extensive gas-phase evolution during the last 4.5 Gy. Note that the meteoritic lithium abundance is known to be (⁶Li/H + ⁷Li/H)_☉ = 2.04 × 10⁻⁹ (Anders & Grevesse 1989), leading to (⁷Li/H)_☉ = 1.89 × 10⁻⁹ and (⁶Li/H)_☉ = 1.53 × 10⁻¹⁰ by taking account of meteoritic (⁷Li/⁶Li)_☉ = 12.3 ± 0.2. Our stellar ⁷Li/H abundance value is ∼15% smaller than that predicted by Romano et al. (2003) and their value is ∼30% different from their previous theoretical estimate (Romano et al. 2001) in similar GCE modeling which assumed a different BBN ⁷Li abundance predicted in the standard BBN theory for the Ω_B-value taken from the CMB–WMAP data. Our GCE model (Suzuki et al. 1999; Kawanomoto 2002) is different from Romano et al. (2001, 2003) in that the latter model included a contribution from low-mass red giants in addition to our production sources of Type II SNe, novae and AGB stars. It is also to be noted that the referred stellar nucleosynthesis yields and each contribution are different from each other. Nevertheless, the difference between the resultant stellar ⁷Li abundance is no more than ∼30%. This is because both the measured meteoritic lithium abundance (⁶Li/H + ⁷Li/H)_☉ = 2.04 × 10⁻⁹ (Anders & Grevesse 1989) and the uppermost envelope of the stellar lithium abundances of population I stars (e.g., Ryan et al. 2001) impose strong constraints on the GCE of lithium in the ISM gas clouds. This fact applies to many other GCE models too. We can therefore estimate systematic theoretical error bars of ±30% for the second stellar ⁷Li production term in Equation (1). Since the ISM ⁶Li abundance, ⁶Li/H = 3.4 × 10⁻¹⁰, is thought to be produced entirely from GCR spallation and α + α fusion and its associated error bars are small, we finally end up with ⁷Li_STAR/⁶Li_GCR = 5.4 ± 1.6(sys), where we take the theoretical uncertainties Δ⁷Li_STAR/⁶Li_GCR = ±1.6 as the systematic error bars.

The third primordial term can be determined by subtracting the first and second terms from the observed value (⁷Li/⁶Li)_obs = 7.6 ± 2.3(1σ): ⁷Li_BBN/⁶Li_GCR = 0.7^+2.3_−0.7(1σ) ± 1.6(sys). Multiplying by the ISM ⁶Li abundance, we can estimate the corresponding primordial abundance of ⁷Li to be ⁷Li/H = 2.4^+7.8_−2.4(1σ) ± 5(sys) × 10⁻¹⁰.

Although we assumed a "flat" distribution of the ⁷Li/⁶Li ratio in the Galactic disk in the last section, there is a clear observational evidence that indicates radial variation of other elemental abundances over 6 kpc ⩽ R_G ⩽ 18 kpc (Rolleston et al. 2000). Concerning isotopic ratios, Penzias (1979) reported that the D/H abundance ratio shows an appreciable gradient with respect to R_G from the Galactic center to outside the solar orbit, i.e., 0 kpc ⩽R_G⩽12 kpc, with an anomaly in D/H near the Galactic center (Wannier 1980; Lubowich et al. 2000). Recent observational studies of D/H in the local ISM reported a uniform single value D/H ∼ 1.5 × 10⁻⁵ within the Local Bubble (Moos et al. 2002; Oliveira et al. 2003), although variations of factors of 2 or so is also observed in the distant ISM beyond the Local Bubble (Hébrard & Moos 2003; Wood et al. 2004; Hébrard et al. 2005; Friedman et al. 2006). From a theoretical viewpoint, Prantzos (1996) proposed a chemical evolution model of the Galactic disk with each ring of appropriate width at different Galactocentric distance R_G evolving independently under an assumption of homogeneous mixing and instantaneous recycling of the ISM. His model predicted D/H ≃ 1.5 × 10⁻⁵ at 13.5 Gy in the solar neighborhood which is in reasonable agreement with the average of observed D/H. The GCE models (Prantzos 1996; Romano et al. 2003) indicate a rather steep gradient of the abundance ratios D/H and ³He/H at 5 kpc ⩽ R_G ⩽ 15 kpc and satisfy an extremely depleted D/H ratio as observed in the Galactic center (Lubowich et al. 2000).

Prantzos' GCE model applies also to the chemical evolution of metals over a wide range of R_G so that it describes the observed isotopic abundance ratios such as ¹²C/¹³C, ¹⁴N/¹⁵N, ¹⁶O/¹⁸O, etc. Remarkable gradients of the carbon isotopic ratios are reported by Savage et al. (2002) and Milam et al. (2005). A comprehensive review on isotopes in the ISM presented by Wilson (1999) concluded that there is a gradient in the isotopic ratio of carbon, nitrogen, and oxygen. Tosi (1982) tried to reproduce the observed radial distribution of the metal abundances in a GCE model with minimum assumptions on theoretical parameters. She suggested steeper gradients of metal abundance ratios in the outer parts of the Galaxy. We cannot expect a steep gradient in ⁷Li/⁶Li because the second stellar term and the third BBN term offset their R_G dependence made by the star-formation efficiency and the GCR intensity in each term.

If we obtain ⁷Li/⁶Li data in wide range of R_G similar to other elements, we can discuss the gradient of ⁷Li/⁶Li ratio and proportions of the second stellar term and the third BBN term in the isotopic ratio in detail.