UTILIZING SYNTHETIC VISIBLE SPECTRA TO EXPLORE THE PHYSICAL BASIS FOR THE CLASSIFICATION OF LAMBDA BOÖTIS STARS

The Lambda Boo class is a subgroup of late B- to early F-type stars that have an unusually low abundance of iron-peak elements in their surface layers. The prototype, Lambda Boötis (HD 125162; A3VakB9mB9 lambda Boo; see Gray et al. 2003), was first reported as peculiar by Morgan et al. (1943). Over the past 70+ years, more than 200 Lambda Boo candidates published in the literature have been selected using different criteria. The distinguishing characteristic in a Lambda Boo star's spectrum is the overall weakness of metallic lines, but their C, N, O, and S abundances are near solar. A good portion of these Lambda Boo candidates have been identified by visually examining the difference between their low-resolution spectra and spectra of standard stars. However, some ambiguity remains, especially for mild or borderline Lambda Boo stars.

Murphy et al. (2015) carried out a systematic review of published papers for all previously identified Lambda Boo candidates. Cheng et al. 2016 (hereafter Paper I) utilized synthetic ultraviolet spectra to explore the physical basis for the classification of Lambda Boo stars, demonstrating that the C i 1657 Å/Al ii 1671 Å equivalent width ratio is the best quantitative UV criterion to distinguish between Lambda Boo stars and other metal-weak stars hotter than 8000 K. Since cooler Lambda Boo stars (late A type and early F type) do not have enough flux shortward of 1700 Å, we sought similar diagnostic ratios in the visible wavelength range.

Lambda Boo-type stars are not overall metal-weak, because their C, N, O, and S abundances tend to be near solar. Since we seek to understand the cause of this distinctive abundance pattern, the diagnostic line ratios we are looking for should be based on the relative strength of light (e.g., C, O) and heavier elements (e.g., Mg, Al). We obtained high-resolution visible spectra for our program Lambda Boo stars, normal/reference stars, and non-Lambda Boo stars from the ELODIE and ESO archives.⁶ ${}^{,}$ ⁷

In this paper, our specific goals are to:

• 1.  
  establish a "quantitative" classification criterion using visible spectra that helps distinguish Lambda Boo stars from normal stars and other metal-weak stars with T_eff < 8000 K (see Section 4 for details), and
• 2.  
  demonstrate how synthetic spectra (models) can be used to study the characteristics of Lambda Boo stars.

2.1. Confirmed Lambda Boo Stars

As discussed in Paper I, Lambda Boo candidates have been selected using several different criteria, and sometimes the agreement among the published lists is quite poor. A common set of Lambda Boo-class characteristics is required to discriminate between theories explaining the origin of the Lambda Boo phenomenon. We started with a list of over 200 stars cited in the literature as Lambda Boo stars. This list led to the compilation of possible Lambda Boo stars presented in Murphy et al. (2015). In this paper we carry out a more detailed evaluation of the visible properties of the 64 "confirmed" Lambda Boo stars listed in Murphy et al. (2015). These "confirmed" members are not concentrated in any particular region in the sky (see Figure 1). Among them, 47 Lambda Boo stars have high-resolution archival visible spectra. Because we are exploring quantifiable classification criteria for the Lambda Boo class as a function of T_eff and [M/H], we searched for all of the published T_eff and [M/H] values for each program star in our study. We assigned a "mean" effective temperature to each star based on a range of temperatures found in the literature (excluding any outliers), and we did not include any duplicate temperatures. We also limited the number of sources included in this range to the five values that best represent the data set for each star. The mean effective temperature, a range of effective temperatures, and the observations (data sets) we used in this paper are listed in Table 1. We also list previously published metallicity values, which allow us to compare our program stars to models with different metallicities. The methods that have been used to determine metallicity differ from paper to paper, and sometimes [M/H] and [Fe/H] are used interchangeably. We cite them as [M/H] or [Fe/H] based on how they are labeled in their original publications. Of our 64 program Lambda Boo stars, 62 have literature log g values. The average log g value for those 62 program Lambda Boo stars is 4.01 (Figure 2(a)). Of our 64 program Lambda Boo-type stars, 48 have literature v sin i values. Because the median v sin i value of those 48 confirmed Lambda Boo stars with literature values is about 100 km s⁻¹ (Figure 2(b)), we explored how rotational broadening affects our equivalent width measurement (see Sections 4.4 and 5).

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Table 1.  Lambda Boo Stars

Identificationa	Mean Teff	Teff Differenceb	[Fe/H]	[M/H]	v sin ic	Data Set	S/Nd
	(K)	(K)			bin
HD 141569	10260 (2), (3), (4), (5)	−260/+240	−0.5 (47)	...	f	ELODIE 19970703/0014	158
HD 294253	10103 (1), (9)	−798/+798	−0.54 (1)	...	b	FEROS 2009-12-02T07:52:58.138	164
HD 170680	9774 (7), (8), (9)	−151/+226	−0.4 (7)	...	f	FEROS 2009-06-05T04:42:29.580	313
HD 23392	9759 (2), (9), (10)	−494/+741	...	...	d	FEROS 2010-07-22T09:18:51.642	208
HD 36726	9542 (1), (9), (11), (27)	−222/+258	−0.58 (1)	...	c	FEROS 2009-12-04T06:34:07.441	231
HD 130767	9209 (9), (11), (12)	−14/+18	...	...	d	ELODIE 20020331/0010	140
HD 37411	9100 (13)	−0/+0	...	−1.5 (48)	e	FEROS 2010-01-28T04:11:12.612	107
HD 183324	9050 (8), (12), (14), (15)	−350/+250	−1.24 (54)	−1.80 (49)	c	FEROS 2010-07-22T05:02:20.981	352
HD 110411	8976 (7), (11), (16), (17)	−176/+224	−1.0 (7)	−1.10 (40)	d	ELODIE 20040519/0017	209
HD 31295	8871 (8), (12), (15), (16), (18)	−96/+119	−0.89 (15)	−1.24 (40)	c	ELODIE 20031105/0069	225
HD 74873	8815 (12), (19), (20), (21)	−225/+435	−0.01 (50)	...	c	HARPS 2014-09-16T11:04:01.560	193
HD 221756	8733 (8), (12), (16), (17), (18)	−223/+287	−0.64 (18)	−0.75 (49)	c	ELODIE 20011127/0012	107
HD 125162	8700 (12), (17), (22), (23)	−50/+29	−2.05 (22)	−2.00 (49)	c	ELODIE 19960522/0014	303
HD 101412	8500 (6), (59), (60)	−200/+300	−1.0 (4)	...	a	HARPS 2014-09-23T11:03:07.090	80
HD 120500	8394 (1), (9)	−7/+7	−0.67 (51)	...	d	FEROS 2009-06-06T00:49:43.346	357
HD 319	8348 (12), (14), (15), (18)	−328/+294	−0.35 (18)	...	b	HARPS 2014-10-02T10:00:01.553	213
HD 35242	8327 (9), (10), (12), (27)	−190/+184	...	...	c	ELODIE 20030122/0007	168
HD 153747	8256 (11), (12), (28)	−52/+104	0.00 (50)	...	c	HARPS 2014-09-26T16:53:39.050	134
HD 204041	8239 (14), (15), (29)	−239/+378	−0.44 (18)	−0.83 (19)	b	FEROS 2009-06-05T06:59:05.057	229
HD 91130	8159 (1), (9), (10), (11), (30)	−159/+199	−1.69 (1)	...	d	ELODIE 19970322/0015	124
HD 105759	8157 (2), (9)	−443/+443	...	...	c	FEROS 2009-06-04T02:41:19.045	382
HD 192640	7988 (11), (15), (31)	−45/+42	−2.0 (31)	...	c	ELODIE 19990604/0032	324
HD 30422	7977 (9), (10), (11), (32)	−107/+210	−0.02 (50)	−0.52 (19)	c	FEROS 2009-12-05T06:35:55.983	371
HD 11413	7956 (5), (9), (16), (33)	−31/+42	−1.5 (16)	−2.03 (52)	d	FEROS 2010-07-22T10:39:57.651	366
HD 198160	7912 (10), (16), (34), (35)	−316/+169	−0.850 (16)	−1.00 (34)	e	FEROS 2010-08-31T01:06:00.125	261
HD 290799	7864 (5), (9), (12), (36)	−151/+136	−0.97 (1)	...	b	FEROS 2009-12-05T07:17:58.019	97
HD 111604	7798 (1), (9), (17)	−198/+202	−1.08 (1)	−0.75 (49)	e	ELODIE 19960502/0029	157
HD 193256	7739 (9), (10), (16)	−653/+531	−0.95 (63)	...	f	FEROS 2009-06-09T10:14:21.058	243
HD 168740	7582 (9), (10), (37)	−182/+292	...	0.0 (43)	d	FEROS 2009-06-02T07:05:57.888	453
HD 210111	7521 (5), (9), (10), (16), (23)	−71/+72	−1.1 (16)	−1.0 (53)	b	FEROS 2009-11-29T02:01:05.469	359
HD 111786	7500 (8), (14), (15)	−50/+49	−1.45 (54)	−0.58 (55)	d	FEROS 2009-06-07T23:34:24.541	160
HD 139614	7500 (4), (38)	−100/+100	−0.5 (4)	...	a	FEROS 2009-06-10T03:49:51.778	226
HD 218396	7465 (9), (27), (39), (40)	−110/+121	−0.7 (62)	−0.47 (25)	b	ELODIE 20030730/0010	336
HD 87271	7434 (9), (10), (11)	−233/+151	...	...	c	ELODIE 20030121/0011	104
HD 174005	7412 (9), (10), (41)	−292/+325	−0.20 (56)	−0.77 (61)	c	FEROS 2009-06-03T07:28:27.034	333
HD 75654	7341 (9), (10), (11), (19)	−81/+90	−0.02 (50)	−0.95 (19)	b	FEROS 2010-01-27T06:04:24.542	386
HD 7908	7340 (2), (9), (34), (42)	−337/+510	−0.03 (50)	...	c	FEROS 2010-01-29T01:15:24.839	291
HD 6870	7337 (9), (11), (19)	−97/+107	...	−1.08 (19)	d	FEROS 2009-12-05T00:54:59.865	235
HD 107233	7274 (9), (10), (32)	−74/+96	...	...	c	FEROS 2010-03-08T06:07:26.136	283
HD 142703	7231 (8), (11), (14), (15), (43)	−31/+30	−1.10 (18)	...	c	FEROS 2010-03-05T09:36:21.595	360
HD 120896	7213 (9), (10), (37)	−194/+171	−0.074 (57)	−0.5 (58)	c	FEROS 2009-06-06T00:59:59.932	266
HD 13755	7195 (2), (9), (10), (42)	−119/+105	0.15 (34)	−0.18 (34)	c	FEROS 2009-12-08T03:07:21.235	121
HD 15165	7157 (11), (44)	−143/+143	−0.46 (44)	...	c	ELODIE 20020813/0028	246
HD 64491	7055 (5), (9), (30), (45), (46)	−147/+104	...	...	a	ELODIE 20020328/0022	138
HD 142994	7016 (9), (29)	−66/+66	−0.56 (29)	−0.88 (19)	e	HARPS 2014-09-26T16:52:50.327	176
HD 106223	6769 (1), (7), (9), (37)	−269/+231	−1.44 (7)	...	c	ELODIE 20030121/0012	135
HD 4158	6483 (19), (30), (32)	−83/+67	−0.17 (9)	−1.59 (19)	c	FEROS 2009-12-14T00:48:21.918	135

Notes.

^aNote that these stars are listed in descending T_eff order to assist with locating each star in Figure 10. ^bThe difference between the mean effective temperature and the lowest/highest effective temperature. ^cThe v sin i bin indicates the wavelength ranges listed in Table 4 that we used to measure this star's equivalent width values. Each star's v sin i bin was determined by comparing their observed spectra to models with similar stellar parameters. ^dSignal-to-noise ratios are provided for ELODIE, HARPS, and X-SHOOTER data by the ELODIE and ESO archives, respectively. We estimated signal-to-noise ratios for the FEROS data near 5500 Å.

References. (1) Andrievsky et al. (2002), (2) Wright et al. (2003), (3) Wyatt et al. (2007), (4) Guimarães et al. (2006), (5) Soubiran et al. (2010), (6) Cowley et al. (2010), (7) Heiter (2002), (8) Solano & Paunzen (1999), (9) Ammons et al. (2006), (10) McDonald et al. (2012), (11) Paunzen et al. (2002a), (12) Paunzen et al. (2002b), (13) Maaskant et al. (2014), (14) Koleva & Vazdekis (2012), (15) Cenarro et al. (2007), (16) Sturenburg (1993), (17) Hauck et al. (1998), (18) Prugniel et al. (2011), (19) Gerbaldi et al. (2003), (20) Paunzen et al. (1998), (21) Mittal et al. (2015), (22) Venn & Lambert (1990), (23) Paunzen et al. (2003), (24) Koleva & Vazdekis (2012), (25) Gray & Kaye (1999), (26) Zorec & Royer (2012), (27) Allende Prieto & Lambert (1999), (28) Xu et al. (2002), (29) Solano et al. (2001), (30) Kamp et al. (2001), (31) Heiter et al. (1998), (32) Solano & Paunzen (1998), (33) Koen et al. (2003), (34) Kordopatis et al. (2013), (35) David & Hillenbrand (2015), (36) Faraggiana et al. (1997), (37) Masana et al. (2006), (38) Labadie et al. (2014), (39) Cuypers et al. (2009), (40) Gray et al. (2003), (41) Ammler-von Eiff & Reiners (2012), (42) Lafrasse et al. (2010), (43) North et al. (1994), (44) Andrievsky et al. (1995), (45) Muñoz Bermejo et al. (2013), (46) Kamp et al. (2002), (47) Merín et al. (2004), (48) Gray & Corbally (1998), (49) Griffin et al. (2012), (50) Gontcharov (2012), (51) Anderson & Francis (2012), (52) Faraggiana et al. (2004), (53) Paunzen et al. (2012), (54) Saffe et al. (2008), (55) Ohanesyan (2008), (56) Marsakov & Shevelev (1995), (57) Luo et al. (2015), (58) Paunzen (2015), (59) Folsom et al. (2012), (60) Hubrig et al. (2010), (61) Faraggiana et al. (2001), (62) Gebran et al. (2016), (63) Paunzen et al. (2001).

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2.2. Normal Reference Stars

2.3. Non-Lambda Boo Stars Used to Test Our Visible Classification Criterion

We examined archival visible spectra of our program stars from four different sources: ELODIE, HARPS, FEROS, and X-SHOOTER. These four sources provide data for 73% of our program "confirmed" Lambda Boo stars, and both northern and southern sky coverage (see Figure 1). For "northern" program stars we obtained data from the ELODIE archive. For "southern" program stars we obtained archival data from three European Southern Observatory (ESO) sources: HARPS, FEROS, and X-SHOOTER (in descending order of resolving power). Details on each of these archival data sources can be found below.

3.1. ELODIE Archival Spectra

3.2. HARPS Archival Spectra

3.3. FEROS Archival Spectra

3.4. X-SHOOTER Archival Spectra

4.1. Generating Visible Synthetic Spectra of Lambda Boo-type Stars

We used Gray's stellar spectral synthesis program SPECTRUM (Gray & Corbally 1994) to compute synthetic spectra covering the wavelength range of ELODIE and ESO data. We generated synthetic spectra for three "bona fide" Lambda Boo stars that have a thorough abundance analysis published in the literature (Venn & Lambert 1990). In Figure 3, we show that the observed spectra of Lambda Boo (HD 125162), 29 Cyg (HD 192640), and Pi¹ Ori (HD 31295) are well represented by synthetic spectra.

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Heiter (2002) used abundances of 34 Lambda Boo stars to construct a "mean" Lambda Boo abundance pattern. She concluded that the iron-peak elements from Sc to Fe as well as Mg, Si, Ca, Sr, and Ba are depleted by about 1.00 dex relative to the solar chemical composition (Al is 0.50 dex more depleted than Fe). The abundances of the light elements C, N, O, and S are around the solar values. In this study we use Heiter's "mean" Lambda Boo abundance pattern to create visible synthetic spectra of "average" Lambda Boo-type stars. The details of our modeling procedures can be found in Paper I (Cheng et al. 2016; Section 3).

4.2. Generating Synthetic "Model" Spectra

4.3. Absorption Line Selection

In Paper I, we demonstrated that the C i 1657 Å/Al ii 1671 Å equivalent width ratio can be used to distinguish between Lambda Boo stars and other metal-weak stars. However, it only works well for stars hotter than ∼8000 K, because cooler stars do not have much flux shortward of 1700 Å. It also requires the acquisition of ultraviolet spectra from a space-based telescope. Since more than half of all known Lambda Boo stars have ${T}_{\mathrm{eff}}\lt 8000$ K (see Figure 4 and Table 1), we have searched for other equivalent width ratios in the visible wavelength range that can be used to classify cooler Lambda Boo stars.

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We first explored the Mg ii 4481 Å/Fe i 4383.5 Å equivalent width ratio because this ratio has been used extensively in the literature to classify Lambda Boo stars (cf. Gray & Corbally 2009, ch. 5). After carefully analyzing the observed spectra of all of our program stars and synthetic spectra, however, we conclude that the Mg ii 4481 Å/Fe i 4383.5 Å equivalent width ratio does not discriminate Lambda Boo stars from normal stars with temperatures cooler than 9500 K when applied "quantitatively" (see Figure 5). Nevertheless, the Mg ii 4481 Å/Fe i 4383.5 Å ratio plays an important role in the discovery of Lambda Boo stars via visual classification techniques (see Section 5), as it was used to successfully discover and classify the "confirmed" Lambda Boo stars discussed in Murphy et al. (2015).

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Lambda Boo stars have subsolar abundances of heavier elements but near-solar abundances of the lighter C, N, O, and S elements, so a diagnostic line ratio should be based on the relative strength of light and heavy elements. We explored various measurable lines in the wavelength range of 4000–6800 Å. Although this visible wavelength range is rich in absorption lines from the chemical elements we are interested in, weak lines and some blended features cannot be used because they cannot be accurately measured. Since more than 50% of our program Lambda Boo-type stars have projected rotational velocities over 100 km s⁻¹ (Figure 2(b)), nearly all absorption features are blended to some extent. Our absorption line selection was done by examining both observed and synthetic spectra.

We found that the C i 5052.17 Å/Mg ii 4481 Å equivalent width ratio is the most useful line ratio for separating cooler Lambda Boo stars from normal stars and other metal-poor stars. It also helps to separate "strong" Lambda Boo-type stars from "mild" Lambda Boo-type stars. Both the C i and Mg ii lines are, of course, blended features (see Figures 6 and 7). There is some contamination in both features from nearby Fe i lines, and the amount of Fe i contamination varies with temperature (see Figure 8). We therefore carefully selected our equivalent width measurement wavelength ranges (see Table 4) to cover the primary line of interest with minimal and consistent amounts of contamination.

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Table 4.  Selected Features

Blended Feature	Component	Observed Wavelength1
(Equivalent Width Measurement Range)		(Å)
C i 5052.17 Å (Air)	Co ii	5050.7096
([a] 5050.5–5053.7 Å for 0 km s−1≤v sin i < 25 km s−1;	Ni i	5051.5065
[b] 5050.5–5053.7 Å for 25 km s−1≤v sin i < 75 km s−1;	Fe i	5051.6342
[c] 5050.2–5053.7 Å for 75 km s−1 ≤v sin i < 125 km s−1;	C i	5052.1673
[d] 5049.9–5054.0 Å for 125 km s−1 ≤v sin i < 175 km s−1;	Fe i	5052.9812
[e] 5049.9–5054.3 Å for 175 km s−1 ≤v sin i < 225 km s−1;	C i	5053.5153
[f] 5049.7–5055.0 Å for v sin i ≥225 km s−1)	Fe i	5054.6422
Mg ii 4481 Å (Air)	Fe i	4479.6032
([a] 4479.0–4483.5 Å for 0 km s−1≤v sin i < 25 km s−1;	Fe i	4479.9622
[b] 4478.6–4483.5 Å for 25 km s−1≤v sin i< 75 km s−1;	Fe i	4480.1362
[c] 4478.1–4483.9 Å for 75 km s−1≤v sin i < 125 km s−1;	Mg ii	4481.1304
[d] 4478.0–4485.1 Å for 125 km s−1≤v sin i < 175 km s−1;	Mg ii	4481.3274
[e] 4477.5–4485.2 Å for 175 km s−1≤v sin i < 225 km s−1;	Fe i	4481.6092
[f] 4476.5–4485.6 Å for v sin i ≥225 km s−1)	Fe I	4482.1702
	Fe i	4482.2522
	Fe i	4482.7392
	Fe i	4484.2202

References. Kramida et al. (2014), (2) Nave et al. (1994), (3) Moore (1970), (4) Risberg (1955), (5) Kurucz & Bell (1995), (6) Pickering et al. (1998).

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4.4. Equivalent Width Measurements

We measured the equivalent widths of the C i 5052.17 Å and Mg ii 4481 Å absorption features (Table 4) of all our observed visible spectra and each of the model spectra. Each observed spectrum was individually wavelength-shifted to align with models of similar parameters (T_eff, log g, [M/H], etc.). We performed the equivalent width measurements using autocfeature, which is a heavily modified version of the program feature in the IUEDAC IDL library.¹² The details of our autocfeature program can be found in Paper I. Because the projected rotational velocity (v sin i) of the confirmed Lambda Boo stars ranges from 3 km s⁻¹ to 267 km s⁻¹, we also explored the effects of stellar rotation on the line profiles and our equivalent width measurements. Spectral lines that are broadened and blended due to rotation cannot be clearly separated (see Figures 6 and 7) using the standard equivalent width measurement method.

Because the equivalent width of the line is conserved under rotational broadening, we first adopted fixed wavelength ranges for measuring C i and Mg ii equivalent widths. We then utilized synthetic spectra to determine the optimal wavelength range for various v sin i values (see Table 4). This allowed us to balance the equivalent width lost from our lines of interest with the equivalent width gained from other nearby features. The temperature dependence of the blends (see Figure 8) makes this procedure unreliable for v sin i > 200 km s⁻¹.

Figure 9 illustrates the use of our program autocfeature to measure the equivalent widths of a standard star's (HD 113139; v sin i ∼100 km s⁻¹) C i 5052.17 Å and Mg ii 4481 Å absorption features. The equivalent width is defined as the area enclosed by the feature and a "pseudo-continuum" drawn through its highest points, therefore the "pseudo-equivalent width" heavily depends on how one chose the continuum. These "pseudo-equivalent widths" are useful only for an empirical classification but not for a detailed abundance analysis. We used the same procedure and a v sin i-dependent equivalent width measurement range to measure the equivalent widths of these two lines in every observed and synthetic spectrum. For each model and observed spectrum, several members of our team independently measured the equivalent widths of selected lines used in this study. From these measurements we determined internal error bars in order to quantify measurement repeatability. The equivalent width measurements of the model spectra were internally consistent to better than 2% (without noise or rotational broadening) and 7% (with S/N = 200 and various amounts of rotational broadening) for all selected features.

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The primary goal of this paper is to establish a "quantitative" classification criterion that uses visible spectra to distinguish Lambda Boo stars from other stars with temperatures less than 8000 K. We measured the C i 5052.17 Å/Mg ii 4481 Å equivalent width ratios of all the "confirmed" Lambda Boo stars and "nonmember" stars listed in Murphy et al. (2015) that have archival ELODIE/ESO spectra.

Initially, we selected fixed wavelength ranges to measure the equivalent width of the absorption features (5050.0–5054.4 Å for C i and 4479.0–4483.5 Å for Mg ii). Our results using these fixed wavelength ranges to measure the C i and Mg ii equivalent widths in both observed spectra and noise-free comparison models without rotational broadening are illustrated in Figure 10. This equivalent width ratio has the highly desirable property that overall metal-weak stars have a smaller ratio than normal stars, and Lambda Boo stars have higher ratios. Equivalent width ratios of the observed spectra generally match the model predictions (see Figure 10). At temperatures cooler than 9500 K the differences among the normal star, average Lambda Boo-type star, and metal-weak star models are significant. At temperatures hotter than 9500 K, these models converge. For program stars with T_eff values >10,000 K, the C i 5052.17 Å feature is too weak to perform an accurate measurement of its equivalent width (see Figure 8), so we exclude program stars with T_eff > 10,000 K from Figure 10. Stars hotter than 8000 K can be discriminated by the C i 1657 Å/Al ii 1671 Å equivalent width ratio we presented in Paper I if UV spectra are available. For stars with effective temperatures between 8000 K and 9500 K, both the C i 1657 Å/Al ii 1671 Å and C i 5052.17 Å/Mg ii 4481 Å equivalent width ratios can be used together. The error bars shown in Figure 10 represent multiple independent measurements by various co-authors but do not compensate for effects such as inaccurate continuum placement due to random noise or for uncorrected telluric contributions to the ratio.

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As shown in Figure 10, the C i 5052.17 Å/Mg ii 4481 Å equivalent width ratio is an excellent quantitative diagnostic for cooler (<9500 K), unambiguous Lambda Boo stars. Of the 47 confirmed Lambda Boo stars listed in Table 1, seven stars cooler than 9500 K fall below the normal star models (see Table 5). Among them, four have been previously classified as mild Lambda Boo stars. Of the 43 nonmember stars listed in Table 3, five stars cooler than 9500 K fall above the normal star models (with [M/H] = 0 and solar abundances; see Table 5). We exclude one of those five nonmember stars (HD 89353, a post-AGB star; Kohoutek 2001) from Figure 10 because its ratio is much higher than the y-axis range due to its hyper-metal depletion ([Fe/H] = −4.7; Venn et al. 2014) but near-solar C, N, O, and S abundances (Mathis & Lamers 1992).

Having demonstrated that the C i 5052.17 Å/Mg ii 4481 Å equivalent width ratio can be used to clearly separate our three groups of program stars ("confirmed" Lambda Boo stars, normal/reference stars, and nonmember stars), we then performed an in-depth study to explore how v sin i, log g, and finite S/N affect our equivalent width measurements. Instead of using a fixed wavelength range to measure our program stars' equivalent width, we adopted v sin i-dependent wavelength ranges (see Table 4) and used the procedure described in Section 4.4. We also generated synthetic models with v sin i ranging from 0 to 250 km s⁻¹ in increments of 50 km s⁻¹. Each set of models has three subsets generated with log g = 3.50, 4.00, and 4.50, respectively (as shown in Figure 2(a), the average log g for our confirmed Lambda stars is ∼4.01). We also explored a range of S/N and found that random noise has little effect on the C i/Mg ii equivalent width ratio if S/N > 200. Because most of our program stars' observed spectra have S/N > 200, we added random noise corresponding to an S/N of 200 to all of our synthetic spectra and measured them using the same equivalent width measuring procedure we used to measure the equivalent widths of the C i 5052.17 Å and Mg ii 4481 Å absorption features in observed spectra.

The results of this in-depth analysis are illustrated in Figure 11. The shaded bands represent the overall envelope within which all of our models fall. While a Lambda Boo star may fall within the green band among models with abundances scaled uniformly from the solar abundances, this alone is not indicative that the star is not a Lambda Boo-type star. These bands illustrate the range of uncertainty when this diagnostic is applied to a sample of stars with undetermined stellar parameters. If v sin i has been determined for a particular sample star, this range of uncertainty can be reduced by using the revised wavelength ranges shown in Table 4. Ideally, each star should be compared to specific models with comparable stellar parameters. Figure 11 illustrates that our program Lambda Boo stars are still separated from normal and nonmember stars in a similar manner as illustrated in Figure 10, so our initial, simpler procedure provides a valid empirical diagnostic to separate most Lambda Boo stars from other metal-weak stars. For stars with v sin i > 200 km s⁻¹, this ratio becomes highly uncertain, but most of our program stars are well below this threshold.

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A long-standing problem in the classification of Lambda Boo stars is the status of apparent Lambda Boo stars with spectral types of F1 and later. Figure 4 shows the dramatic decrease in Lambda Boo frequency for spectral types later than F1 (T_eff < 7000 K); this is presumably due to the mixing brought about by the development of a deep surface convection zone, which would erase the peculiar surface abundances of the Lambda Boo stars. Nonetheless, a number of potential Lambda Boo stars have been identified in the literature with spectral types (hydrogen-line types) as late as F3. A case in point is HD 106223, which has been classified as a field horizontal-branch star (Oke et al. 1966), a Lambda Boo star (Slettebak 1968), and a field blue straggler (Bond & MacConnell 1971). Gray (1988) classified this star as "F3 V kA1mA0 λ Boo?" but left the Lambda Boo status uncertain. More recent abundance determinations (Andrievsky et al. 2002; Heiter 2002) have shown an unambiguous Lambda Boo abundance pattern, with the carbon abundance near or even exceeding solar ($+0.3;$ Heiter 2002), whereas the metals in general are about 1.5 dex below solar. Paunzen et al. (2014) also studied HD 106223 in their investigation of the possibility of an intrinsic chemical peculiarity in the Lambda Boo stars. It is thus of considerable interest that the C i 5052.17 Å/Mg ii 4481 Å classification criterion established in this paper clearly supports the Lambda Boo status of both HD 106223 and a similar star HD 4158 (see Table 1 and Figures 10 and 11). This illustrates the use of this criterion for separating late-type (F1 and later) Lambda Boo stars from metal-weak thick-disk early F-type stars.

We also investigated why the Mg ii 4481 Å/Fe i 4383.5 Å equivalent width ratio is useful in "visual" classification, but cannot be used as a "quantitative" diagnostic ratio (see Figure 5) in the same way that the C i 5052.17 Å/Mg ii 4481 Å ratio can be used. The Mg ii 4481 Å doublet goes through a maximum in strength in the late-B, early A-type stars (T_eff ∼ 10,000 K), and declines in strength with decreasing temperature (see Figure 8). On the other hand, Fe i 4383.5 Å is a low-excitation line (∼1.5 eV), and thus grows in strength with declining temperature. This means that the Mg ii/Fe i ratio decreases with decreasing T_eff in both normal and metal-weak stars. This is why, at a given temperature, the Mg ii 4481 Å/Fe i 4383.5 Å ratio has no power to discriminate between metal-poor and metal-rich stars (see Figure 5). It is important to note that in spectral classification, we often compare spectra of stars with quite different effective temperatures. This is the case with the Lambda Boo stars. A classifier confronted with the blue-violet spectrum of a "strong," cool Lambda Boo star will first consider the strength of the metallic-line spectrum and the Ca ii K-line, and note their similarity to the spectrum of an early A-type star, except for one inconsistency—the "peculiar" weakness of the Mg ii 4481 Å line (yielding a small Mg ii/Fe i ratio). Further investigation will show that the hydrogen lines have profiles more consistent with a late-A or even early F-type star, revealing the true T_eff of the star and its general metal-weak nature. Once the T_eff is known, it is clear that the Mg ii/Fe i ratio for the Lambda Boo star is not in fact unusual, but is nearly equal to that of a solar-metallicity standard star of the same effective temperature. Therefore the Mg ii/Fe i ratio plays an important role in the discovery of Lambda Boo stars via "visual" classification techniques, although it has little or no power in "quantitative" analysis to distinguish members of the class.

We studied 47 Lambda Boo stars with existing ELODIE and/or ESO visible spectra. We also analyzed model spectra of normal/reference stars, metal-poor stars, and "mean" Lambda Boo stars. We conclude that:

• 1.  
  the visible spectra of Lambda Boo stars can be reproduced well with LTE synthetic spectra. These synthetic spectra can then be used to predict and explain the behavior of observed spectra as a function of stellar properties;
• 2.  
  the C i 5052.17 Å/Mg ii 4481 Å equivalent width ratio can be used as a visible criterion to distinguish between Lambda Boo stars and other metal-weak stars. This ratio is a function of the individual star's effective temperature and [M/H]. Between 6000 K and 9500 K, the C i/Mg ii equivalent width ratios of Lambda Boo stars are very different from the C i/Mg ii ratios of normal star models and from other metal-poor stars;
• 3.  
  this ratio can be used as an empirical diagnostic, even for a sample with unknown stellar parameters, by using "fixed" equivalent width measurement wavelength ranges (5050–5054.4 A for C i and 4479–4483.5 Å for Mg ii). If the star's v sin i is known, the power to discriminate Lambda Boo from normal stars and other metal-weak stars can be improved by using "v sin i-dependent" equivalent width measurement ranges;
• 4.  
  we cannot use the C i 5052.17 Å/Mg ii 4481 Å equivalent width ratio as a classification criterion for stars hotter than 9500 K because their C i 5052.17 Å absorption features are too weak to be measured accurately;
• 5.  
  we caution against using this equivalent width ratio as a classification criterion for stars with v sin i > 200 km s⁻¹; and
• 6.  
  one of the major advantages of establishing a visible Lambda Boo classification criterion is that archival visible data are widely available, and new visible observations are easier to obtain than UV observations.

Our future work will include:

• 1.  
  performing an abundance analysis for program Lambda Boo stars without an abundance analysis present in the literature;
• 2.  
  compiling an updated list of "bona fide" Lambda Boo stars that meet our quantitative visible and/or UV classification criteria, which can be used to investigate group properties in order to explain the origin of the Lambda Boo phenomenon.

This program is supported by grants from the National Science Foundation to California State University Fullerton (AST-1211213), the College of Charleston (AST-1211221, AST-1109695), and Appalachian State University (AST-1211215). Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX13AC07G and by other grants and contracts. Based on data obtained from the ESO Science Archive Facility under request numbers: djohnson 227337 and 240569. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This research has also made use of the VizieR catalogue access tool, CDS, Strasbourg, France.