A Principal component analysis of the diffuse interstellar bands

TL;DR

This study applies principal component analysis to 23 interstellar parameters, revealing that four main factors explain most variations, with implications for understanding the environment of diffuse interstellar bands.

Contribution

It introduces a PCA approach to analyze interstellar parameters, identifying key factors influencing diffuse interstellar bands and their environmental dependencies.

Findings

Four principal components explain 93% of the variation.

The first component correlates with DIB-producing material.

The second component relates to UV radiation levels.

Abstract

We present a principal component analysis of 23 line of sight parameters (including the strengths of 16 diffuse interstellar bands, DIBs) for a well-chosen sample of single-cloud sightlines representing a broad range of environmental conditions. Our analysis indicates that the majority ($\sim$93\%) of the variations in the measurements can be captured by only four parameters The main driver (i.e., the first principal component) is the amount of DIB-producing material in the line of sight, a quantity that is extremely well traced by the equivalent width of the $\lambda$5797 DIB. The second principal component is the amount of UV radiation, which correlates well with the $\lambda$5797/$\lambda$5780 DIB strength ratio. The remaining two principal components are more difficult to interpret, but are likely related to the properties of dust in the line of sight (e.g., the gas-to-dust ratio). With our PCA results, the DIBs can then be used to estimate these line of sight parameters.

Tables

Table 1. Table 1: Basic target data.

Target	Alt.	RA	DEC	V	E(B-V)	N(H I)	N(H2)	f(H2)	F⋆	$\frac{W\left(\lambda 5797\right)}{W\left(\lambda 5780\right)}$	$v_{\mathrm{ISM}}$aaValue and reference refer to the velocity of the dominant interstellar component.	RefaaValue and reference refer to the velocity of the dominant interstellar component.	Data
	Name	[J2000]	[J2000]			[1021cm-2]	[1020cm-2]				[km s-1]		Source
HD 15137 (catalog )		02 27 59.81	+52 32 57.6	7.86	0.24	1.29${}_{}{}^{+0.57}{}_{-0.40}{}^{}$	1.86${}_{}{}^{+0.26}{}_{-0.12}{}^{}$	0.22${}_{}{}^{+0.09}{}_{-0.06}{}^{}$	0.37$\pm$0.09	0.30$\pm$0.02	-9.58	1	ELODIE
HD 22951 (catalog )	40 Per	03 42 22.65	+33 57 54.1	4.98	0.19	1.10${}_{}{}^{+0.35}{}_{-0.32}{}^{}$	2.88${}_{}{}^{+1.48}{}_{-0.98}{}^{}$	0.35${}_{}{}^{+0.27}{}_{-0.18}{}^{}$	0.73$\pm$0.05	0.35$\pm$0.02	12.47	1	ELODIE
HD 23180 (catalog )	o Per	03 44 19.13	+32 17 17.7	3.86	0.22	0.76${}_{}{}^{+0.26}{}_{-0.23}{}^{}$	3.98${}_{}{}^{+1.64}{}_{-1.16}{}^{}$	0.51${}_{}{}^{+0.33}{}_{-0.24}{}^{}$	0.84$\pm$0.06	0.65$\pm$0.04	13.45	2	ELODIE
HD 23630 (catalog )	$\eta$ Tau	03 47 29.08	+24 06 18.5	2.87	0.05	0.22${}_{}{}^{+0.10}{}_{-0.07}{}^{}$	0.35${}_{}{}^{+0.18}{}_{-0.12}{}^{}$	0.28${}_{}{}^{+0.23}{}_{-0.15}{}^{}$	0.89$\pm$0.10	0.16$\pm$0.04	16.76	2	ELODIE
HD 24398 (catalog )	$\zeta$ Per	03 54 07.92	+31 53 01.1	2.88	0.27	0.63${}_{}{}^{+0.06}{}_{-0.07}{}^{}$	4.68${}_{}{}^{+2.40}{}_{-1.59}{}^{}$	0.59${}_{}{}^{+0.46}{}_{-0.31}{}^{}$	0.88$\pm$0.05	0.55$\pm$0.02	14.54	2	ELODIE
HD 24534 (catalog )	X Per	03 55 23.08	+31 02 45.0	6.10	0.31	0.54${}_{}{}^{+0.08}{}_{-0.07}{}^{}$	8.32${}_{}{}^{+0.80}{}_{-0.73}{}^{}$	0.76${}_{}{}^{+0.13}{}_{-0.11}{}^{}$	0.90$\pm$0.06	0.62$\pm$0.04	14.5	5	ELODIE
HD 24760 (catalog )	$ϵ$ Per	03 57 51.23	+40 00 36.8	2.90	0.07	0.25${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	0.33${}_{}{}^{+0.27}{}_{-0.15}{}^{}$	0.21${}_{}{}^{+0.25}{}_{-0.14}{}^{}$	0.68$\pm$0.04	0.18$\pm$0.02	7.06	2	ELODIE
HD 24912 (catalog )	$\xi$ Per	03 58 57.90	+35 47 27.7	4.04	0.26	1.29${}_{}{}^{+0.26}{}_{-0.24}{}^{}$	3.39${}_{}{}^{+1.40}{}_{-0.99}{}^{}$	0.35${}_{}{}^{+0.21}{}_{-0.15}{}^{}$	0.83$\pm$0.02	0.26$\pm$0.01	11.2	1	ELODIE
HD 27778 (catalog )	62 Tau	04 23 59.76	+24 18 03.6	6.33	0.34	0.22${}_{}{}^{+0.55}{}_{-0.22}{}^{}$	5.25${}_{}{}^{+1.06}{}_{-0.88}{}^{}$	0.82${}_{}{}^{+0.45}{}_{-0.27}{}^{}$	1.19$\pm$0.07	0.43$\pm$0.03	15.22	2	ELODIE
HD 35149 (catalog )	23 Ori	05 22 50.00	+03 32 40.0	5.00	0.08	0.43${}_{}{}^{+0.12}{}_{-0.13}{}^{}$	0.03${}_{}{}^{+0.00}{}_{-0.03}{}^{}$	0.02${}_{}{}^{+0.00}{}_{-0.02}{}^{}$	0.54$\pm$0.11	0.20$\pm$0.04	24.09	2	UVES
HD 35715 (catalog )	$\Psi$ Ori	05 26 50.23	+03 05 44.4	4.60	0.03	0.31${}_{}{}^{+0.13}{}_{-0.13}{}^{}$	6$\pm 2\times {10}^{-6}$	4$\pm 2\times {10}^{-6}$	0.66$\pm$0.11	0.10$\pm$0.04	25.2	1	ELODIE
HD 36822 (catalog )	${\phi }^1$ Ori	05 34 49.24	+09 29 22.5	4.40	0.07	0.65${}_{}{}^{+0.13}{}_{-0.12}{}^{}$	0.21${}_{}{}^{+0.09}{}_{-0.06}{}^{}$	0.06${}_{}{}^{+0.04}{}_{-0.03}{}^{}$	0.74$\pm$0.08	0.19$\pm$0.04	25.53	1	ELODIE
HD 36861 (catalog )	$\lambda$ Ori A	05 35 08.28	+09 56 03.0	3.30	0.10	0.60${}_{}{}^{+0.16}{}_{-0.16}{}^{}$	0.13${}_{}{}^{+0.08}{}_{-0.05}{}^{}$	0.04${}_{}{}^{+0.04}{}_{-0.02}{}^{}$	0.57$\pm$0.04	0.48$\pm$0.04	25.2	3	ELODIE
HD 40111 (catalog )	139 Tau	05 57 59.66	+25 57 14.1	4.82	0.10	0.79${}_{}{}^{+0.16}{}_{-0.15}{}^{}$	0.54${}_{}{}^{+0.31}{}_{-0.20}{}^{}$	0.12${}_{}{}^{+0.10}{}_{-0.07}{}^{}$	0.49$\pm$0.04	0.20$\pm$0.04	15.29	2	ELODIE
HD 110432 (catalog )	BZ Cru	12 42 50.27	$-$63 03 31.0	5.32	0.39	0.71${}_{}{}^{+0.29}{}_{-0.21}{}^{}$	4.37${}_{}{}^{+0.42}{}_{-0.38}{}^{}$	0.55${}_{}{}^{+0.13}{}_{-0.11}{}^{}$	1.17$\pm$0.11	0.25$\pm$0.01	6.8	3	UVES
HD 143275 (catalog )	$\delta$ Sco	16 00 20.01	$-$22 37 18.1	2.29	0.00	1.41${}_{}{}^{+0.29}{}_{-0.29}{}^{}$	0.26${}_{}{}^{+0.15}{}_{-0.09}{}^{}$	0.03${}_{}{}^{+0.03}{}_{-0.02}{}^{}$	0.90$\pm$0.03	0.19$\pm$0.02	-10.90	2	UVES
HD 144217 (catalog )	${\beta }^1$ Sco	16 05 26.23	$-$19 48 19.6	2.62	0.18	1.23${}_{}{}^{+0.12}{}_{-0.11}{}^{}$	0.68${}_{}{}^{+0.10}{}_{-0.09}{}^{}$	0.10${}_{}{}^{+0.02}{}_{-0.02}{}^{}$	0.81$\pm$0.02	0.11$\pm$0.01	-8.95	2	UVES
HD 145502 (catalog )	$\nu$ Sco	16 11 59.74	$-$19 27 38.5	4.13	0.20	1.17${}_{}{}^{+0.56}{}_{-0.59}{}^{}$	0.78${}_{}{}^{+0.32}{}_{-0.23}{}^{}$	0.12${}_{}{}^{+0.08}{}_{-0.07}{}^{}$	0.80$\pm$0.11	0.18$\pm$0.01	-8.49	2	ELODIE
HD 147165 (catalog )	$\sigma$ Sco	16 21 11.32	$-$25 35 34.0	2.91	0.31	2.19${}_{}{}^{+0.90}{}_{-0.87}{}^{}$	0.62${}_{}{}^{+0.25}{}_{-0.18}{}^{}$	0.05${}_{}{}^{+0.04}{}_{-0.03}{}^{}$	0.76$\pm$0.06	0.13$\pm$0.01	-6.26	2	UVES
HD 147933 (catalog )	$\rho$ Oph A	16 25 35.10	$-$23 26 48.7	5.02	0.37	4.27${}_{}{}^{+0.98}{}_{-0.80}{}^{}$	3.72${}_{}{}^{+1.53}{}_{-1.09}{}^{}$	0.15${}_{}{}^{+0.09}{}_{-0.07}{}^{}$	1.09$\pm$0.08	0.27$\pm$0.03	-8.02	2	UVES
HD 149757 (catalog )	$\zeta$ Oph	16 37 09.54	$-$10 34 01.5	2.58	0.29	0.52${}_{}{}^{+0.02}{}_{-0.04}{}^{}$	4.47${}_{}{}^{+0.90}{}_{-0.75}{}^{}$	0.63${}_{}{}^{+0.20}{}_{-0.17}{}^{}$	1.05$\pm$0.02	0.50$\pm$0.04	-14.98	2	UVES
HD 164284 (catalog )	66 Oph	18 00 15.80	+04 22 07.0	4.78	0.11	0.42${}_{}{}^{+0.23}{}_{-0.39}{}^{}$	0.71${}_{}{}^{+0.29}{}_{-0.21}{}^{}$	0.25${}_{}{}^{+0.18}{}_{-0.20}{}^{}$	0.89$\pm$0.18	0.15$\pm$0.02	-15.32	1	ELODIE
HD 170740 (catalog )		18 31 25.69	$-$10 47 45.0	5.76	0.38	1.07${}_{}{}^{+0.59}{}_{-0.47}{}^{}$	7.24${}_{}{}^{+1.47}{}_{-1.22}{}^{}$	0.58${}_{}{}^{+0.22}{}_{-0.18}{}^{}$	1.02$\pm$0.11	0.26$\pm$0.01	-12.9	6	UVES
HD 198478 (catalog )	55 Cyg	20 48 56.29	+46 06 50.9	4.86	0.43	2.04${}_{}{}^{+0.84}{}_{-0.63}{}^{}$	7.41${}_{}{}^{+3.06}{}_{-2.17}{}^{}$	0.42${}_{}{}^{+0.27}{}_{-0.20}{}^{}$	0.81$\pm$0.05	0.24$\pm$0.01	-10.04	2	ELODIE
HD 202904 (catalog )	$\upsilon$ Cyg	21 17 55.08	+34 53 48.8	4.43	0.09	0.23${}_{}{}^{+0.21}{}_{-0.23}{}^{}$	0.14${}_{}{}^{+0.07}{}_{-0.05}{}^{}$	0.11${}_{}{}^{+0.12}{}_{-0.10}{}^{}$	0.39$\pm$0.11	0.13$\pm$0.05	-12.90	4	ELODIE
HD 207198 (catalog )		21 44 53.28	+62 27 38.0	5.96	0.47	3.39${}_{}{}^{+0.59}{}_{-0.50}{}^{}$	6.76${}_{}{}^{+0.65}{}_{-0.59}{}^{}$	0.28${}_{}{}^{+0.05}{}_{-0.05}{}^{}$	0.90$\pm$0.03	0.53$\pm$0.01	-15.28	2	ELODIE
HD 209975 (catalog )	19 Cep	22 05 08.79	+62 16 47.3	5.11	0.27	1.29${}_{}{}^{+0.41}{}_{-0.38}{}^{}$	1.20${}_{}{}^{+0.62}{}_{-0.41}{}^{}$	0.16${}_{}{}^{+0.12}{}_{-0.09}{}^{}$	0.57$\pm$0.26	0.31$\pm$0.01	-11.39	2	ELODIE
HD 214680 (catalog )	10 Lac	22 39 15.68	+39 03 01.0	4.88	0.08	0.50${}_{}{}^{+0.14}{}_{-0.15}{}^{}$	0.17${}_{}{}^{+0.05}{}_{-0.04}{}^{}$	0.06${}_{}{}^{+0.03}{}_{-0.03}{}^{}$	0.50$\pm$0.06	0.34$\pm$0.02	-9.2	1	ELODIE
HD 214993 (catalog )	12 Lac	22 41 28.65	+40 13 31.6	5.23	0.06	0.58${}_{}{}^{+0.20}{}_{-0.18}{}^{}$	0.43${}_{}{}^{+0.22}{}_{-0.14}{}^{}$	0.13${}_{}{}^{+0.10}{}_{-0.07}{}^{}$	0.68$\pm$0.10	0.17$\pm$0.02	-9.44	1	ELODIE
HD 218376 (catalog )	1 Cas	23 06 36.82	+59 25 11.1	4.84	0.16	0.89${}_{}{}^{+0.28}{}_{-0.26}{}^{}$	1.41${}_{}{}^{+0.73}{}_{-0.48}{}^{}$	0.24${}_{}{}^{+0.19}{}_{-0.13}{}^{}$	0.60$\pm$0.06	0.28$\pm$0.01	-12.65	1	ELODIE

Table 2. Table 2: Input variables used in the PCA, and their mean values and standard deviations.

Variable	Mean		Standard
Name			Deviation
($x_i$)	(${\overline{x}}_i$)		($s_{x_i}$)
$x_1=W\left(\lambda 4428\right)$	645\@alignment@align.9	350.9
$x_2=W\left(\lambda 4964\right)$	6\@alignment@align.8	5.7
$x_3=W\left(\lambda 5494\right)$	5\@alignment@align.6	4.1
$x_4=W\left(\lambda 5513\right)$	3\@alignment@align.9	3.9
$x_5=W\left(\lambda 5545\right)$	5\@alignment@align.9	4.3
$x_6=W\left(\lambda 5546\right)$	2\@alignment@align.8	2.2
$x_7=W\left(\lambda 5769\right)$	2\@alignment@align.6	2.2
$x_8=W\left(\lambda 5780\right)$	131\@alignment@align.5	77.0
$x_9=W\left(\lambda 5797\right)$	37\@alignment@align.7	27.8
$x_{10}=W\left(\lambda 5850\right)$	15\@alignment@align.6	13.6
$x_{11}=W\left(\lambda 6196\right)$	13\@alignment@align.5	8.3
$x_{12}=W\left(\lambda 6270\right)$	20\@alignment@align.7	13.9
$x_{13}=W\left(\lambda 6284\right)$	149\@alignment@align.4	84.1
$x_{14}=W\left(\lambda 6376\right)$	9\@alignment@align.3	7.4
$x_{15}=W\left(\lambda 6379\right)$	24\@alignment@align.7	18.0
$x_{16}=W\left(\lambda 6614\right)$	52\@alignment@align.5	35.2
$x_{17}$ = E(B-V)	0\@alignment@align.20	0.13
$x_{18}$ = N(H I)	1\@alignment@align.0$\times {10}^{21}$	9.2$\times {10}^{20}$
$x_{19}$ = N(H2)	2\@alignment@align.4$\times {10}^{21}$	2.6$\times {10}^{20}$
$x_{20}$ = N(H)	1\@alignment@align.5$\times {10}^{21}$	1.2$\times {10}^{21}$
$x_{21}$ = f(H2)	0\@alignment@align.27	0.23
$x_{22}$ = F⋆	0\@alignment@align.75	0.21
$x_{23}$ = $\frac{\text{W}\left(\lambda 5797\right)}{\text{W}\left(\lambda 5780\right)}$	0\@alignment@align.2907	0.1567

Table 3. Table 3: Principal components, eigenvalues and relative importance of each PC for a 2D example involving E(B-V) and N(H).

PC	Eigen-	%	Cumulative	Eigenvector
	value	Variation	%
1	1.813	90.63	90.63	(0.707, 0.707)
2	0.187	9.37	100.00	(0.707, -0.707)

Table 4. Table 4: Principal components, eigenvalues and relative importance of each PC.

PC	Eigenvalue	% Variation	Cumulative %
1	15.248	66.30	66.30
2	3.158	13.73	80.03
3	1.801	7.83	87.86
4	1.139	4.95	92.81
5	0.355	1.54	94.35
6	0.262	1.14	95.49
7	0.192	0.84	96.33
8	0.186	0.81	97.14
9	0.157	0.68	97.82
10	0.117	0.51	98.33
11	0.096	0.42	98.75
12	0.074	0.32	99.07
13	0.066	0.29	99.35
14	0.055	0.24	99.60
15	0.032	0.14	99.74
16	0.025	0.11	99.85
17	0.012	0.05	99.90
18	0.008	0.03	99.93
19	0.006	0.03	99.96
20	0.005	0.02	99.98
21	0.003	0.01	99.99
22	0.002	0.01	100.00
23	0.000	0.00	100.00

Table 5. Table 5: Equivalent widths and uncertainties of the λ ​ λ 𝜆 𝜆 \lambda\lambda 4428, 4964, 5494, 5513, 5545, 5546, 5769 and 5780 DIBs.

Target	$\lambda$4428	$\lambda$4964	$\lambda$5494	$\lambda$5513	$\lambda$5545	$\lambda$5546	$\lambda$5769	$\lambda$5780
HD 15137	1163 $\pm$ ${}_{115}{}^{}{}_{}{}^{106}$	7.9 $\pm$ 2.5	11.1 $\pm$ 2.2	2.1 $\pm$ 3.0	6.9 $\pm$ 1.9	0.0 $\pm$ 1.9	3.9 $\pm$ 1.7	230.1 $\pm$ 9.1
HD 22951	471 $\pm$ ${}_{76}{}^{}{}_{}{}^{68}$	6.4 $\pm$ 1.1	2.0 $\pm$ 1.1	1.3 $\pm$ 1.5	6.2 $\pm$ 0.7	3.6 $\pm$ 1.0	0.7 $\pm$ 0.8	102.8 $\pm$ 3.6
HD 23180	403 $\pm$ ${}_{47}{}^{}{}_{}{}^{45}$	12.3 $\pm$ 1.4	6.4 $\pm$ 0.2	10.7 $\pm$ 1.7	10.3 $\pm$ 1.5	5.4 $\pm$ 1.5	7.2 $\pm$ 1.3	88.1 $\pm$ 5.0
HD 23630	325 $\pm$ ${}_{39}{}^{}{}_{}{}^{48}$	1.2 $\pm$ 1.0	2.4 $\pm$ 0.9	0.2 $\pm$ 1.5	0.8 $\pm$ 1.1	1.5 $\pm$ 1.0	2.3 $\pm$ 0.9	40.7 $\pm$ 4.8
HD 24398	450 $\pm$ ${}_{70}{}^{}{}_{}{}^{61}$	8.8 $\pm$ 0.9	5.4 $\pm$ 1.0	5.8 $\pm$ 1.1	6.1 $\pm$ 0.6	3.3 $\pm$ 1.0	2.5 $\pm$ 0.7	100.4 $\pm$ 2.7
HD 24534	402 $\pm$ ${}_{55}{}^{}{}_{}{}^{49}$	13.4 $\pm$ 1.6	7.6 $\pm$ 1.2	5.3 $\pm$ 1.9	9.4 $\pm$ 1.2	4.8 $\pm$ 1.6	7.1 $\pm$ 1.1	95.1 $\pm$ 5.0
HD 24760	322 $\pm$ ${}_{30}{}^{}{}_{}{}^{41}$	1.5 $\pm$ 0.8	3.3 $\pm$ 0.8	1.1 $\pm$ 1.0	1.5 $\pm$ 0.9	0.2 $\pm$ 0.8	1.6 $\pm$ 0.6	77.0 $\pm$ 3.4
HD 24912	949 $\pm$ ${}_{65}{}^{}{}_{}{}^{89}$	9.7 $\pm$ 1.3	7.0 $\pm$ 1.0	2.7 $\pm$ 1.2	8.9 $\pm$ 1.0	2.4 $\pm$ 1.2	2.4 $\pm$ 0.8	198.3 $\pm$ 3.1
HD 27778	490 $\pm$ ${}_{58}{}^{}{}_{}{}^{74}$	8.3 $\pm$ 1.4	4.6 $\pm$ 1.6	3.6 $\pm$ 1.4	8.0 $\pm$ 1.1	4.5 $\pm$ 1.0	2.2 $\pm$ 1.0	86.6 $\pm$ 4.6
HD 35149	254 $\pm$ ${}_{38}{}^{}{}_{}{}^{43}$	2.8 $\pm$ 1.3	2.8 $\pm$ 1.7	1.0 $\pm$ 1.9	2.6 $\pm$ 1.3	0.0 $\pm$ 1.4	1.7 $\pm$ 1.5	58.0 $\pm$ 5.5
HD 35715	221 $\pm$ ${}_{23}{}^{}{}_{}{}^{47}$	1.3 $\pm$ 0.8	1.1 $\pm$ 0.8	1.2 $\pm$ 0.9	1.1 $\pm$ 0.8	0.7 $\pm$ 0.9	0.7 $\pm$ 0.7	34.6 $\pm$ 3.6
HD 36822	483 $\pm$ ${}_{69}{}^{}{}_{}{}^{78}$	1.6 $\pm$ 2.4	1.4 $\pm$ 2.8	2.9 $\pm$ 3.0	2.0 $\pm$ 2.4	2.9 $\pm$ 2.4	1.0 $\pm$ 2.0	84.5 $\pm$ 9.6
HD 36861	402 $\pm$ ${}_{86}{}^{}{}_{}{}^{49}$	4.6 $\pm$ 1.0	3.2 $\pm$ 1.0	4.4 $\pm$ 1.1	3.2 $\pm$ 0.9	3.2 $\pm$ 0.9	1.5 $\pm$ 0.7	49.0 $\pm$ 3.5
HD 40111	739 $\pm$ ${}_{81}{}^{}{}_{}{}^{109}$	2.2 $\pm$ 4.7	2.7 $\pm$ 4.9	0.0 $\pm$ 7.2	3.6 $\pm$ 4.4	3.2 $\pm$ 4.9	3.3 $\pm$ 3.7	157.7 $\pm$ 19.5
HD 110432	880 $\pm$ ${}_{45}{}^{}{}_{}{}^{64}$	8.3 $\pm$ 1.0	4.1 $\pm$ 1.0	3.8 $\pm$ 1.4	5.2 $\pm$ 1.0	1.8 $\pm$ 0.8	0.3 $\pm$ 0.8	137.3 $\pm$ 3.7
HD 143275	383 $\pm$ ${}_{12}{}^{}{}_{}{}^{21}$	2.1 $\pm$ 1.0	5.1 $\pm$ 0.1	2.1 $\pm$ 1.5	5.2 $\pm$ 1.1	1.4 $\pm$ 1.2	1.9 $\pm$ 1.1	92.7 $\pm$ 4.2
HD 144217	430 $\pm$ ${}_{38}{}^{}{}_{}{}^{54}$	3.5 $\pm$ 0.8	2.6 $\pm$ 1.0	1.1 $\pm$ 1.6	4.1 $\pm$ 1.1	1.0 $\pm$ 1.0	0.7 $\pm$ 1.1	156.0 $\pm$ 4.9
HD 145502	583 $\pm$ ${}_{48}{}^{}{}_{}{}^{50}$	3.3 $\pm$ 1.2	6.3 $\pm$ 2.0	2.8 $\pm$ 2.5	4.4 $\pm$ 1.0	2.0 $\pm$ 1.2	3.0 $\pm$ 0.9	186.9 $\pm$ 5.2
HD 147165	872 $\pm$ ${}_{53}{}^{}{}_{}{}^{50}$	6.1 $\pm$ 1.0	8.2 $\pm$ 1.5	5.1 $\pm$ 1.6	4.5 $\pm$ 1.0	1.9 $\pm$ 1.2	0.8 $\pm$ 1.1	240.0 $\pm$ 4.2
HD 147933	1254 $\pm$ ${}_{77}{}^{}{}_{}{}^{121}$	20.0 $\pm$ 0.8	7.6 $\pm$ 0.5	13.8 $\pm$ 0.7	8.3 $\pm$ 0.5	6.9 $\pm$ 0.6	11.7 $\pm$ 2.8	209.8 $\pm$ 16.1
HD 149757	576 $\pm$ ${}_{47}{}^{}{}_{}{}^{52}$	6.6 $\pm$ 0.9	5.3 $\pm$ 1.1	3.0 $\pm$ 1.3	5.7 $\pm$ 0.9	2.5 $\pm$ 0.8	2.8 $\pm$ 1.1	65.1 $\pm$ 3.8
HD 164284	686 $\pm$ ${}_{53}{}^{}{}_{}{}^{73}$	2.5 $\pm$ 1.3	1.8 $\pm$ 1.4	2.3 $\pm$ 1.8	3.4 $\pm$ 1.1	1.5 $\pm$ 1.4	0.7 $\pm$ 1.0	94.4 $\pm$ 4.4
HD 170740	834 $\pm$ ${}_{91}{}^{}{}_{}{}^{107}$	10.5 $\pm$ 1.0	10.6 $\pm$ 1.0	8.6 $\pm$ 1.5	11.3 $\pm$ 1.0	4.6 $\pm$ 1.0	2.4 $\pm$ 0.8	240.3 $\pm$ 4.0
HD 198478	1592 $\pm$ ${}_{108}{}^{}{}_{}{}^{191}$	14.2 $\pm$ 2.0	10.5 $\pm$ 1.8	5.8 $\pm$ 2.1	11.8 $\pm$ 1.4	5.0 $\pm$ 1.5	1.5 $\pm$ 1.3	315.6 $\pm$ 5.8
HD 202904	541 $\pm$ ${}_{67}{}^{}{}_{}{}^{92}$	2.5 $\pm$ 1.5	2.6 $\pm$ 1.5	1.8 $\pm$ 1.6	1.0 $\pm$ 1.0	1.1 $\pm$ 1.2	1.0 $\pm$ 1.1	44.5 $\pm$ 4.6
HD 207198	1282 $\pm$ ${}_{89}{}^{}{}_{}{}^{67}$	24.6 $\pm$ 1.0	19.3 $\pm$ 0.9	16.6 $\pm$ 1.1	20.5 $\pm$ 0.9	9.9 $\pm$ 0.9	9.8 $\pm$ 0.7	249.0 $\pm$ 2.8
HD 209975	1032 $\pm$ ${}_{74}{}^{}{}_{}{}^{182}$	8.8 $\pm$ 1.4	13.0 $\pm$ 1.5	1.9 $\pm$ 1.9	11.2 $\pm$ 0.7	4.6 $\pm$ 1.6	0.4 $\pm$ 1.3	234.2 $\pm$ 4.7
HD 214680	361 $\pm$ ${}_{64}{}^{}{}_{}{}^{55}$	0.9 $\pm$ 1.0	4.4 $\pm$ 0.8	1.8 $\pm$ 1.4	1.7 $\pm$ 1.0	2.0 $\pm$ 0.9	0.6 $\pm$ 0.5	58.8 $\pm$ 2.8
HD 214993	232 $\pm$ ${}_{47}{}^{}{}_{}{}^{63}$	4.0 $\pm$ 0.7	0.2 $\pm$ 1.2	1.6 $\pm$ 1.3	1.4 $\pm$ 1.0	1.2 $\pm$ 0.9	0.6 $\pm$ 0.8	78.6 $\pm$ 4.8
HD 218376	766 $\pm$ ${}_{108}{}^{}{}_{}{}^{64}$	5.1 $\pm$ 1.0	5.9 $\pm$ 1.1	3.9 $\pm$ 1.2	6.2 $\pm$ 0.8	1.1 $\pm$ 1.1	1.1 $\pm$ 0.8	138.7 $\pm$ 4.4

Table 6. Table 6: Equivalent widths and uncertainties of the λ ​ λ 𝜆 𝜆 \lambda\lambda 5797, 5850, 6196, 6270, 6284, 6376, 6379 and 6614 DIBs.

Target	$\lambda$5797	$\lambda$5850	$\lambda$6196	$\lambda$6270	$\lambda$6284	$\lambda$6376	$\lambda$6379	$\lambda$6614
HD 15137	68.1 $\pm$ 3.1	20.8 $\pm$ 2.8	19.9 $\pm$ 2.7	33.4 $\pm$ 4.6	298.6 $\pm$ 19.4	12.7 $\pm$ 3.4	36.2 $\pm$ 4.2	80.6 $\pm$ 4.1
HD 22951	35.9 $\pm$ 1.3	18.8 $\pm$ 1.2	10.5 $\pm$ 2.2	9.0 $\pm$ 2.9	130.8 $\pm$ 8.5	5.1 $\pm$ 1.3	23.8 $\pm$ 1.5	41.0 $\pm$ 2.1
HD 23180	57.7 $\pm$ 2.0	27.8 $\pm$ 1.3	12.8 $\pm$ 1.9	18.0 $\pm$ 3.3	95.4 $\pm$ 9.4	10.5 $\pm$ 2.1	41.3 $\pm$ 3.0	53.7 $\pm$ 3.4
HD 23630	6.7 $\pm$ 1.3	1.5 $\pm$ 1.0	1.9 $\pm$ 1.3	3.8 $\pm$ 3.3	21.0 $\pm$ 7.7	2.0 $\pm$ 2.0	3.0 $\pm$ 2.1	8.9 $\pm$ 2.8
HD 24398	55.5 $\pm$ 1.3	27.3 $\pm$ 1.1	15.2 $\pm$ 1.2	11.0 $\pm$ 2.5	94.1 $\pm$ 6.7	12.2 $\pm$ 1.8	46.3 $\pm$ 2.5	59.3 $\pm$ 1.9
HD 24534	58.9 $\pm$ 1.3	29.0 $\pm$ 1.4	15.2 $\pm$ 1.4	18.8 $\pm$ 3.5	78.2 $\pm$ 8.2	10.5 $\pm$ 3.7	40.3 $\pm$ 2.3	66.1 $\pm$ 2.4
HD 24760	13.5 $\pm$ 1.0	2.9 $\pm$ 0.8	6.0 $\pm$ 1.2	11.6 $\pm$ 2.0	105.9 $\pm$ 5.5	0.3 $\pm$ 1.3	8.2 $\pm$ 1.5	23.3 $\pm$ 2.1
HD 24912	51.4 $\pm$ 1.2	22.3 $\pm$ 1.7	21.7 $\pm$ 1.0	33.0 $\pm$ 1.7	272.4 $\pm$ 9.6	13.0 $\pm$ 1.9	30.1 $\pm$ 2.3	79.7 $\pm$ 1.8
HD 27778	37.4 $\pm$ 2.0	12.7 $\pm$ 1.3	10.8 $\pm$ 1.5	6.9 $\pm$ 3.2	117.8 $\pm$ 10.2	8.0 $\pm$ 1.8	17.4 $\pm$ 2.1	45.7 $\pm$ 2.7
HD 35149	11.8 $\pm$ 2.1	6.8 $\pm$ 1.3	7.1 $\pm$ 1.9	12.4 $\pm$ 3.7	78.0 $\pm$ 14.4	0.9 $\pm$ 2.4	6.0 $\pm$ 3.3	21.9 $\pm$ 4.6
HD 35715	3.3 $\pm$ 1.2	0.5 $\pm$ 0.7	2.4 $\pm$ 1.1	4.0 $\pm$ 2.0	55.4 $\pm$ 8.4	0.7 $\pm$ 2.0	2.8 $\pm$ 1.9	9.5 $\pm$ 1.9
HD 36822	16.4 $\pm$ 3.1	3.7 $\pm$ 2.2	8.1 $\pm$ 3.1	9.5 $\pm$ 8.8	106.6 $\pm$ 15.9	3.5 $\pm$ 3.3	10.1 $\pm$ 5.4	18.0 $\pm$ 6.2
HD 36861	23.3 $\pm$ 1.2	12.3 $\pm$ 0.8	4.9 $\pm$ 1.0	4.8 $\pm$ 2.1	51.6 $\pm$ 10.8	4.7 $\pm$ 1.8	6.2 $\pm$ 1.4	14.9 $\pm$ 1.8
HD 40111	32.3 $\pm$ 5.3	3.6 $\pm$ 3.1	13.0 $\pm$ 5.6	17.1 $\pm$ 1..0	211.1 $\pm$ 22.5	8.0 $\pm$ 7.6	12.9 $\pm$ 9.5	41.1 $\pm$ 9.6
HD 110432	35.0 $\pm$ 1.7	19.4 $\pm$ 1.0	18.0 $\pm$ 1.0	29.6 $\pm$ 2.0	185.1 $\pm$ 5.1	7.0 $\pm$ 1.8	32.4 $\pm$ 1.8	74.3 $\pm$ 2.1
HD 143275	17.4 $\pm$ 1.3	6.3 $\pm$ 1.1	7.6 $\pm$ 0.9	10.0 $\pm$ 3.8	118.9 $\pm$ 13.1	4.3 $\pm$ 1.8	10.1 $\pm$ 3.0	23.9 $\pm$ 1.6
HD 144217	17.3 $\pm$ 1.6	6.5 $\pm$ 1.1	13.5 $\pm$ 1.5	25.0 $\pm$ 2.3	159.3 $\pm$ 9.1	5.0 $\pm$ 2.4	14.0 $\pm$ 3.6	50.9 $\pm$ 1.7
HD 145502	33.7 $\pm$ 1.7	12.2 $\pm$ 1.2	14.1 $\pm$ 2.6	20.5 $\pm$ 2.5	199.6 $\pm$ 8.8	7.8 $\pm$ 2.0	30.0 $\pm$ 2.0	58.8 $\pm$ 2.5
HD 147165	31.3 $\pm$ 1.6	16.7 $\pm$ 1.1	17.5 $\pm$ 1.1	26.4 $\pm$ 2.7	214.2 $\pm$ 7.7	10.9 $\pm$ 2.0	21.1 $\pm$ 2.0	61.3 $\pm$ 2.3
HD 147933	57.2 $\pm$ 5.3	30.6 $\pm$ 2.6	17.0 $\pm$ 2.7	24.9 $\pm$ 5.0	173.8 $\pm$ 16.9	15.5 $\pm$ 2.8	28.0 $\pm$ 3.7	62.5 $\pm$ 3.6
HD 149757	32.6 $\pm$ 1.6	14.2 $\pm$ 1.1	10.3 $\pm$ 1.2	16.8 $\pm$ 2.9	72.0 $\pm$ 6.9	10.9 $\pm$ 2.0	16.7 $\pm$ 1.9	46.4 $\pm$ 2.0
HD 164284	13.8 $\pm$ 1.7	0.4 $\pm$ 1.3	6.8 $\pm$ 1.5	15.7 $\pm$ 3.0	111.3 $\pm$ 9.2	1.8 $\pm$ 2.0	11.3 $\pm$ 2.2	26.9 $\pm$ 2.7
HD 170740	63.3 $\pm$ 1.8	24.6 $\pm$ 1.1	26.3 $\pm$ 1.2	52.7 $\pm$ 2.6	249.6 $\pm$ 9.9	20.9 $\pm$ 1.6	60.7 $\pm$ 1.7	122.4 $\pm$ 2.2
HD 198478	75.0 $\pm$ 2.2	34.6 $\pm$ 1.6	33.1 $\pm$ 1.5	53.3 $\pm$ 4.2	379.5 $\pm$ 11.6	21.2 $\pm$ 3.5	46.7 $\pm$ 4.1	130.6 $\pm$ 3.4
HD 202904	5.7 $\pm$ 2.3	1.9 $\pm$ 1.7	3.6 $\pm$ 1.8	15.2 $\pm$ 3.1	82.2 $\pm$ 10.6	3.0 $\pm$ 2.6	11.7 $\pm$ 3.5	18.4 $\pm$ 2.7
HD 207198	132.6 $\pm$ 1.1	61.1 $\pm$ 0.7	32.3 $\pm$ 1.0	43.2 $\pm$ 1.7	227.2 $\pm$ 9.6	30.0 $\pm$ 1.8	71.8 $\pm$ 2.1	121.8 $\pm$ 1.9
HD 209975	71.5 $\pm$ 1.4	26.5 $\pm$ 1.6	26.9 $\pm$ 4.5	43.1 $\pm$ 3.1	240.2 $\pm$ 10.0	25.5 $\pm$ 2.7	45.5 $\pm$ 2.6	114.1 $\pm$ 3.1
HD 214680	20.1 $\pm$ 0.9	3.9 $\pm$ 0.9	5.4 $\pm$ 1.0	9.2 $\pm$ 1.6	68.7 $\pm$ 7.9	6.4 $\pm$ 1.5	4.5 $\pm$ 1.4	16.1 $\pm$ 2.0
HD 214993	13.6 $\pm$ 1.3	0.9 $\pm$ 0.7	7.6 $\pm$ 1.4	10.0 $\pm$ 2.2	107.1 $\pm$ 10.0	4.4 $\pm$ 1.7	13.9 $\pm$ 1.7	18.0 $\pm$ 2.3
HD 218376	38.7 $\pm$ 1.3	17.2 $\pm$ 1.0	14.2 $\pm$ 1.2	31.6 $\pm$ 2.3	175.7 $\pm$ 10.0	11.2 $\pm$ 2.0	37.0 $\pm$ 2.2	66.0 $\pm$ 2.2

Equations

$$y_i{\hat{\mathbf{n}}}_i^{\prime }=a_{i,1}{x}_1{\hat{\mathbf{n}}}_1+a_{i,2}{x}_2{\hat{\mathbf{n}}}_2+...+a_{i,n}{x}_n{\hat{\mathbf{n}}}_n$$

$$a_{i,1}^2+a_{i,2}^2+...+a_{i,n}^2=1$$

$$Y=AX$$

$$z_{i,j}=\frac{x_{i,j}-{\bar{x}}_i}{s_{x_i}}$$

$$\begin{gathered} X=\left[\begin{array}{c}{z}_{17}\\ z_{20}\end{array}\right] \\ =\left[\begin{array}{cccc}0.273& -0.106& \dots & -0.333\\ 0.121& 0.121& \dots & -0.285\end{array}\right] \end{gathered}$$

$$A=\left[\begin{array}{cc}{a}_{1,1}& a_{1,2}\\ a_{2,1}& a_{2,2}\end{array}\right]=\left[\begin{array}{cc}0.707& 0.707\\ 0.707& -0.707\end{array}\right]$$

$$Y=\left[\begin{array}{c}P{C}_1\\ P{C}_2\end{array}\right]=\left[\begin{array}{cccc}0.279& 0.011& \dots & -0.437\\ 0.107& -0.161& \dots & -0.034\end{array}\right]$$

$$P{C}_1=$$

$$=$$

$$P{C}_2=$$

$$=$$

$$N(H)=$$

$$N(H)=10.0\times 10^{21}E(B-V)-0.50\times 10^{21}$$

$$N(H)=5.8\times 10^{21}E(B-V)$$

$$C_1=\sum _i\frac{a_{i,1}(\overline{x_i})}{s_{x_i}}$$

$$P{C}_{1,uncentered}$$

$$=P{C}_1+6.616$$

$$N_{DIB}$$

$$=0.136(P{C}_1)+0.900$$

$$N_{DIB}\approx 0.0185W(\lambda 5797)+0.19$$

$$G_{DIB}=P{C}_2$$

$$G_{DIB}\approx -9.07[W(\lambda 5797)/W(\lambda 5780)]+2.55$$

$$G_{DIB}=-9.98[W(\lambda 5797)/W(\lambda 5780)]+2.67$$

$$G_{DIB}\approx \{\begin{array}{ll}\text{undefined},& \text{if }\frac{W(\lambda 5797)}{W(\lambda 5780)}\lesssim 0.3\\ -8.44(\frac{W(\lambda 5797)}{W(\lambda 5780)})+1.94,& \text{if }\frac{W(\lambda 5797)}{W(\lambda 5780)}\gtrsim 0.3\end{array}$$

$$\frac{\mathrm{N}(\mathrm{H})\times 10^{-21}}{E(B-V)}=(7.29\pm 0.23)+P{C}_3\times (1.63\pm 0.26)$$

$$\frac{\mathrm{N}(\mathrm{H})\times 10^{-21}}{E(B-V)}=(7.31\pm 0.27)+P{C}_3\times (1.89\pm 0.26)$$

$$GTD=0.318(P{C}_3)+1.29$$

$$P{C}_1=$$

$$+0.207(z_8)+0.245(z_9)+0.244(z_{10})+0.238(z_{11})+0.208(z_{12})+0.177(z_{13})0.240(z_{14})$$

$$+0.234(z_{15})+0.236(z_{16})+0.232(z_{17})+0.186(z_{18})+0.203(z_{19})+0.232(z_{20})+0.110(z_{21})$$

$$+0.096(z_{22})+0.118(z_{23})$$

$$=$$

$$+(5.63\times 10^{-2})W(\lambda 5545)+(9.36\times 10^{-2})W(\lambda 5546)+(5.62\times 10^{-2})W(\lambda 5769)+(2.69\times 10^{-3})W(\lambda 5780)$$

$$+(8.83\times 10^{-3})W(\lambda 5797)+(1.80\times 10^{-2})W(\lambda 5850)+(2.85\times 10^{-2})W(\lambda 6196)+(1.49\times 10^{-2})W(\lambda 6270)$$

$$+(2.10\times 10^{-3})W(\lambda 6284)+(3.24\times 10^{-2})W(\lambda 6376)+(1.30\times 10^{-2})W(\lambda 6379)+(6.70\times 10^{-3})W(\lambda 6614)$$

$$+(1.75)E(B-V)+(2.03\times 10^{-22})N(H\text{textsc}i)+(7.80\times 10^{-22})N(H_2)+(1.95\times 10^{-22})N(H)$$

Full text

ISM:lines and bands — ISM:molecules — methods:data analysis — methods:statistical

††software: IDL; molecfit (Smette et al., 2015; Kausch et al., 2015); MPFITEXY (Williams et al., 2010); MPFIT package (Markwardt, 2009)

1 Introduction

One of the greatest outstanding astronomical challenges is the identification of the diffuse interstellar bands (DIBs): a series of $\sim$500 absorption features detected in optical and infrared spectra toward reddened stars (see Herbig 1995; Sarre 2006; Snow 2014 for reviews and Hobbs et al. 2008, 2009 for recent surveys). It has been clear that the DIBs arise from material in interstellar clouds since they were first detected (Heger, 1922); but despite nearly 100 years of research, most of the DIB carriers remain unidentified. The only notable exception is the recent identification of four DIBs as due to C${}_{60}^{+}$ (Campbell et al., 2015; Walker et al., 2015). This identification is in line with the general consensus that the DIB carriers are highly stable, carbonaceous, gas-phase molecules.

An identification of DIBs with specific carriers requires a perfect match between laboratory spectra and astronomical observations; however, given the countless numbers of possible carrier candidates, this is not an easy task. To guide these laboratory efforts, observational studies aim to learn about the nature of the carriers and constrain the set of possible species. Two types of such studies that are particularly relevant for this paper are correlation studies – either mutual DIB correlations, or correlations between the DIBs and line of sight properties (see e.g. Seab & Snow, 1984; Herbig, 1993; Cami et al., 1997; McCall et al., 2010; Friedman et al., 2011) – and research into the environmental behavior of the DIBs (e.g. Jenniskens et al., 1994; Cami et al., 1997; Sonnentrucker et al., 1997; Cox et al., 2006).

The basic idea behind pairwise correlations is simple: If two DIBs arise from the same state in the same carrier, they should have the same strength ratio in all lines of sight and thus, their equivalent widths (EWs) should exhibit a perfect correlation. Observational studies have not found two DIBs that show such a perfect correlation. The best case is the $\lambda$6196 and $\lambda$6614 DIBs which correlate well in a large sample of sightlines (correlation coefficient $r$ of 0.986; see McCall et al., 2010). However, even these two DIBs show quite different behavior in the remarkable sightline towards Herschel 36 implying that they are most likely originating from different carriers (Dahlstrom et al., 2013; Oka et al., 2013). This has led to the “one DIB, one carrier” paradigm (Herbig, 1995; Cami et al., 1997; Snow, 2014). At the same time, the notion of DIB “families” can be established: sets of DIBs that correlate fairly well with one another and that might have similar or chemically related carriers (Krelowski & Walker, 1987; Cami et al., 1997). There are two important caveats though in correlation studies. First, correlation studies generally include only a small number of DIBs, typically fairly strong and narrow DIBs. Second, while the role of measurement uncertainties on the correlation coefficient is well established (see e.g. discussions in Herbig, 1975; Cami et al., 1997), they are often not taken into account in correlation studies.

Correlations between the DIB strengths and line of sight parameters can reveal additional properties about the DIB carriers. DIB strengths often show some correlation ($r$ typically 0.7) with various other line of sight parameters, albeit typically with a large scatter around the mean relation; examples are the correlation with $E(B-V)$, or the $\lambda$5780 DIB strength with N(H I) or the column densities of other interstellar species (see e.g. Herbig, 1975, 1993, 1995; Krełowski et al., 1999; Welty et al., 2006; Friedman et al., 2011; Lan et al., 2015; Baron et al., 2015). A particularly intriguing finding is a subset of DIBs (the so-called “C2-DIBs”) that roughly correlate with N(C2) and are thought to be chemically related to C2 or else form under similar conditions (Thorburn et al., 2003). Modern surveys have confirmed such relations for averaged DIB strengths on large scales, and have furthermore also shown that much of the scatter can be traced back to differences in the amounts of H2 relative to H I in the line of sight (Herbig, 1993; Lan et al., 2015).

Part of the scatter in these correlations must thus be due to changes in the physical environment that drive the carrier abundances. Indeed, the DIBs exhibit clear environmental behavior, and show intensity variations that could be explained for instance by ionization or (de-)hydrogenation (Jenniskens et al., 1994; Cami et al., 1997; Sonnentrucker et al., 1997). Interestingly, various parameters have been shown to be indicative of these environmental conditions. The strength ratio between two strong DIBs, $\lambda$5797 and $\lambda$5780, is highly variable and a good indicator of local conditions (Krelowski et al., 1997). Using this ratio, diffuse clouds can typically be subcategorized into two groups – $\sigma$ and $\zeta$ type clouds, named after their prototypes $\sigma$ Sco (HD 147165) and $\zeta$ Oph (HD 149757). $\sigma$ clouds have lower W($\lambda$5797)/W($\lambda$5780) ratios and are characterized by stronger UV exposure; $\zeta$ clouds, on the other hand, probe deeper layers of diffuse clouds where material is sheltered from UV radiation, and this causes a much larger W($\lambda$5797)/W($\lambda$5780) ratio while simultaneously affecting the dust properties (Cami et al., 1997).

The large number of DIBs coupled with the lack of strong correlations suggest that the DIBs carry an enormous diagnostic potential to study the environments in which they reside. At the same time, it raises the question of what factors drive these variations in the DIB strengths, and how it is possible that there is such a lack of correlations in such a large collection of spectral lines. Here, we address these questions, and in particular the key question: how many parameters do we need to explain the variations in the DIB spectrum and what are those parameters?

To this end, we present a multivariate analysis of a set of strong and clean DIBs with several line of sight parameters. In a proof-of-concept study, we first perform a principal component analysis (PCA) on the data to find out how many parameters are required to describe the observed variations among the DIBs. We physically interpret these new parameters and find convenient quantitative alternatives to represent these parameters. From this work, the huge diagnostic potential of the DIBs becomes clear: since DIBs are products of their environments, we can use DIBs to determine physical parameters of their environment – even without identifying the carriers.

This paper is organized as follows. In Section 2, we describe our sample selection and how we acquired our data. We then describe PCA in Section 3, followed by our results in Section 4. We interpret the results in Section 5 and present our conclusions in Section 6.

2 Data, Observations & Methods

2.1 Target Selection

Our goal in this paper is to determine the parameters that drive the variations in the DIB spectrum. Thus, we need to select a sample of sightlines where physical conditions are reasonably well determined, and that represent the overall observed variations of the DIB spectrum. The first requirement implies that we should restrict ourselves as much as possible to single-cloud lines of sight to avoid having to deal with ill-defined averages throughout multiple intervening clouds. The second requirement stresses the importance of including lines of sight that are as observationally different as possible. Finally, in order to be able to relate any changes to known observables, we need to pick lines of sight for which auxiliary data (e.g. hydrogen column densities, $E(B-V)$, extinction properties, …) are known and available. In this pilot study, we chose to restrict ourselves to include only a limited number of DIBs, and to lines of sight for which we can find high-resolution spectra that allow us to exclude possible blends with stellar lines.

We started our selection of targets from the thorough and detailed study of elemental depletion in the lines of sight towards 243 stars published by Jenkins (2009). This study critically reviews available literature data for E(B-V), N(H I), N(H2), N(H), and introduces a depletion strength factor, F⋆, describing the collective level of elemental depletion in a line of sight. Starting from this sample thus ensures a consistent treatment of the required auxiliary line-of-sight data and allows us to ensure a wide coverage of environmental conditions (to the extent that they can be traced by any of these parameters).

We searched the VLT/UVES and ELODIE archives to find good-quality, high-resolution spectra of these targets. UVES (the Ultraviolet and Visual Echelle Spectrograph) is a high-resolution instrument on the VLT covering wavelength ranges from 3000 - 4000Å and 4200 - 11,000Å, with maximum resolutions of 80,000 and 110,000, respectively (Dekker et al., 2000). ELODIE is an echelle spectrograph on the 1.93m telescope at the Observatoire de Haute-Provence in France. ELODIE has a resolution of 42,000 and covers the wavelength range from 3906 - 6801Å (Moultaka et al., 2004). We found appropriate data for 91 of the Jenkins targets: 43 targets in the UVES database; the remaining 48 from the ELODIE database. In a few rare cases, parts of the spectrum would be of too low quality, or simply missing from the data, and in those cases we supplemented our data with archival spectra from the ESPaDOns (Echelle spectropolarimetric device for the observation of stars) instrument on the Canada-France-Hawaii Telescope (CFHT) – a bimodal instrument with maximum resolutions of 68,000 and 81,000 for its spectropolarimetric and non-polarimetric modes, respectively, covering a wavelength range of 3700 - 10,000Å (Donati, 2003).

To further select only single-cloud lines of sight, we examined the interstellar Na I D lines at 5890 and 5895Å and the K I lines at 7665 and 7699Å (see e.g., Bhatt & Cami (2015), illustrated in Figure 1). For our current study, we consider a sightline to be a single cloud if these interstellar lines show only one dominant component at the spectral resolution of UVES or ELODIE. Thus, a target was still considered to be a single cloud if there were multiple radial velocity components, but one component had significantly stronger features than the others. For example, HD 149757 is known to have two strong radial velocity components at approximately $-27$ and $-15$ km s*-1*, but the one at $-15$ km s*-1* has much larger column densities (Herbig, 1968, see also Fig. 1). For the targets with only ELODIE spectra, the K I lines are outside the available wavelength range, and thus we could only use the Na I D lines to inspect the number of radial velocity components. An obvious and inherent drawback of using these lines is that they are easily saturated. We searched for Ca I and CH lines too, but in most cases, these were too weak to be seen.

With this exercise, we established that 33 of our targets can be identified as single-cloud lines of sight. However, for three of them, the UVES archival spectra have a gap in the wavelength coverage from approximately 5760-5830Å and thus two important DIBs, $\lambda$5780 and $\lambda$5797 are missing. We therefore excluded these targets from our data set. After these considerations, we were left with a sample of 30 single-cloud lines of sight. These targets are listed in Table 2.2 along with their line of sight parameters we will use in this paper (see below).

It should be noted that six of the targets in our sample – HD 23630, HD 24534, HD 110432, HD 149757, HD 164284, and HD 202904 – are Be stars. Such objects have an intrinsic E(B-V) value relative to non-Be stars of the same spectral type (Schild, 1978; Sigut & Patel, 2013); the hot, circumstellar gas produces excess emission in the V filter and therefore, their E(B-V) values are over-estimated. Furthermore, any dust existing in the circumstellar shell (CS) can contribute to E(B-V), while there is no evidence to suggest that DIBs exist in CS environments (Krełowski & Sneden, 1995; Snow & Wallerstein, 1972; Snow, 1973). Hence, we expect weaker-than-normal DIB strengths relative to E(B-V) for these six targets.

We applied a heliocentric correction to all targets, and then shifted all spectra to their interstellar rest frames. Interstellar velocity components were obtained from the literature, or measured from a known interstellar feature, if not available. These velocities are listed in column 14 of Table 2.2.

2.2 DIB Measurements

For our purposes, we only wanted to include those DIBs whose equivalent widths can be confidently measured, i.e., with small relative errors. This limits our selection to fairly strong and often narrow DIBs that are as much as possible free of contamination from stellar lines. The only exceptions we made was to include four of the C2 DIBs – $\lambda\lambda$4964, 5513, 5546, and 5769 – despite the latter three being quite weak. We thus include a sample of 16 DIBs in our analysis: $\lambda\lambda$4428, 4964, 5494, 5513, 5545, 5546, 5769, 5780, 5797, 5850, 6196, 6270, 6284, 6376, 6379, and 6614.

We measured the equivalent widths for these 16 DIBs in all lines of sight. Most of these were straightforward to measure, as they are not heavily contaminated by stellar and/or telluric features. The largest uncertainty on these measurement stems from establishing the continuum. To obtain a good estimate of these uncertainties, we used the following Monte Carlo approach to vary the continuum level and perform direct integration of the spectra (similar to that in Bhatt & Cami (2015); see Figure 2 for illustration). First, we measured the standard deviation of the flux values over a specified, featureless range of data in the vicinity of the feature to estimate the uncertainty on the flux values – i.e. we measured the signal-to-noise ratio (S/N). Next, we selected a point on each side of the feature and defined a continuum baseline by adopting a linear continuum between those two points. We also selected points as our integration limits; note that for consistency, we used the same integration limits for the same feature in all lines of sight. To simulate the process of determining the continuum, we varied the two selected continuum points 1,000 times by adding a random number to the flux values selected from a normal distribution with a mean of zero and standard deviation equal to $\frac{1}{3}$ the measured standard deviation in the featureless continuum; we believe that this represents well how accurately one can position the continuum (which corresponds to determining the mean flux in the adjacent continuum), and we found that this produces reasonable continuum estimates (see Figure 2). Using one full standard deviation produces many continuum points which are clearly too high or too low and thus result in unrealistic continuum levels. In essence, we thus simulated the entire process of determining a continuum line 1,000 times. For each continuum, we then measured the equivalent width. The equivalent width we use in this paper is then the mean of these 1,000 measurements, and the standard deviation of these measurements provides the uncertainty.

We kept a few precautions in mind when using this method. For instance, the sharp and narrow $\lambda$5797 is known to be blended with the broader and shallower $\lambda$5795. To avoid measuring a contribution from $\lambda$5795, we measured the $\lambda$5797 while treating the $\lambda$5795 as continuum (see Figure 2). If bad pixels were found within the integration range, that data point was replaced with the average of the neighboring points. For HD 23180, the $\lambda$5494 feature was strongly contaminated by a stellar line. We could not resolve the two features to obtain a proper measurement, so instead we adopted the value obtained from higher resolution observations by Bondar (2012).

The two broad DIBs in our sample – $\lambda$4428 and $\lambda$6284 – cannot be measured using the methods described above, because they are heavily contaminated by stellar and telluric features, respectively. For the $\lambda$6284 DIB, we first applied a telluric correction using molecfit (version 1.1.0) (Smette et al., 2015; Kausch et al., 2015) and then proceeded as for the other DIBs.

The $\lambda$4428 DIB is extremely broad, and the region spanned by this DIB is plagued by stellar features. Snow et al. (2002) showed that the intrinsic profile of the band is Lorentzian, and thus, rather than numerically integrating the DIB profile, we preferred to fit a Lorentzian profile to the observations and determine the equivalent widths from the fitted parameters. In addition to our best fit, we also determined Lorentzians that represent the upper and lower envelope of the observed profiles; these then have a different full-width-at-half-max (FWHM) and central depth (CD) value (while we kept the same continuum). We found the difference between the best-fit values and upper or lower envelope values and determined the uncertainties on EW through error propagation.

We compared our measurements to values found in the literature whenever possible and found a generally good agreement. For instance, 23 out of our 30 lines of sight were also studied by Friedman et al. (2011) and we found a very good correlation between their reported EW values and ours (see e.g. Figure 3).

All of our equivalent width measurements are shown in Table 5 in the appendix to this paper.

\floattable