Extragalactic background Light: a measurement at 400 nm using dark cloud shadow II. Spectroscopic separation of dark cloud's light, and results

TL;DR

This study measures the optical extragalactic background light at 400 nm using spectroscopic analysis of a dark cloud's shadow, separating scattered starlight from the EBL, and finds an excess over galaxy light.

Contribution

It introduces a spectroscopic method to distinguish EBL from scattered starlight using dark cloud shadows, providing new measurements at 400 nm.

Findings

EBL at 400 nm is approximately 2.9 x 10^{-9} erg/cm^2/s/sr/Å

Detected EBL exceeds the integrated galaxy light by a factor of two

Set an upper limit for EBL at 520 nm with no significant detection

Abstract

In a project aimed at measuring the optical Extragalactic Background Light (EBL) we are using the shadow of a dark cloud.We have performed, with the ESO VLT/FORS, spectrophotometry of the surface brightness towards the high-galactic-latitude dark cloud Lynds 1642. A spectrum representing the difference between the opaque core of the cloud and several unobscured positions around the cloud was presented in Paper I (Mattila et al. 2017a). The topic of the present paper is the separation of the scattered starlight from the dark cloud itself which is the only remaining foreground component in this difference. While the scattered starlight spectrum has the characteristic Fraunhofer lines and the discontinuity at 400 nm, typical of integrated light of galaxies, the EBL spectrum is a smooth one without these features. As template for the scattered starlight we make use of the spectra at two semi-transparent positions. The resulting EBL intensity at 400 nm is $I_{\rm EBL} = 2.9\pm1.1$ $10^{-9}$ erg cm$^{-2}$s$^{-1}$sr$^{-1}$\AA$^{-1}$, or $11.6\pm4.4$ nW m$^{-2}$sr$^{-1}$, which represents a 2.6$\sigma$ detection; the scaling uncertainty is +20%/-16%. At 520 nm we have set a 2$\sigma$ upper limit of $I_{\rm EBL} \le$4.5 $10^{-9}$ erg cm$^{-2}$s$^{-1}$sr$^{-1}$\AA$^{-1}$ or $\le$23.4 nW m$^{-2}$sr$^{-1}$ +20%/-16%. Our EBL value at 400 nm is $\ge 2$ times as high as the integrated light of galaxies. No known diffuse light sources, such as light from Milky Way halo, intra-cluster or intra-group stars appear capable of explaining the observed EBL excess over the integrated light of galaxies.

Tables

Table 1. Table 1: Calculated values of the effective blocking factor h = 1 − e − τ cl − f sca ​ ( τ cl ) ℎ 1 superscript 𝑒 subscript 𝜏 cl subscript 𝑓 sca subscript 𝜏 cl h=1-e^{-\tau_{\rm cl}}-f_{\rm sca}(\tau_{\rm cl}) for a spherical cloud of different optical thicknesses (diameters) τ cl subscript 𝜏 cl \tau_{\rm cl} and for isotropic incident radiation. The errors reflect the uncertainties of the scattering parameters a 𝑎 a and g 𝑔 g . Error estimates in parentheses are based on the values for τ cl = 2 − 16 subscript 𝜏 cl 2 16 \tau_{\rm cl}=2-16 .

${\tau }_{\mathrm{cl}}$	$h$
0.5	0.18($\pm$0.03)
1	0.32($\pm$0.06)
2	0.53$\pm$0.10
4	0.75$\pm$0.12
8	0.90$\pm$0.09
16	0.95$\pm$0.05
20	0.96($\pm$0.05)

Table 2. Table 2: Intensities of spectral lines in the differential spectrum Δ ​ I ​ ( λ ) ​ ( Pos9 / 42 − Pos8 ) Δ 𝐼 𝜆 Pos9 42 Pos8 \Delta I(\lambda){\rm(Pos9/42-Pos8)} , see Fig. 1. Unit for line areas is 10 − 9 superscript 10 9 10^{-9}  ergs cm -2 s -1 sr -1 and for peak intensities  10 − 9 superscript 10 9 10^{-9}  erg cm -2 s -1 sr -1 Å -1  . The model fit is given for line-of-sight optical depth of τ 1 subscript 𝜏 1 \tau_{1} (H  β 𝛽 {\beta} )= 0.90 for Pos9/42. In the last line is given the derived H  β 𝛽 \beta intensity for the background emission.

Line	Observed line		Model
	————————		——————-
	Area	Peak	${\tau }_1$	Area
H $\beta$	$112.8\pm 2.8$	9.8	0.90	112.8
H $\gamma$	$46.1\pm 2.8$	5.1	1.03	46.1
H $\delta$	$18.7\pm 3.2$	2.4	1.11	23.4
$[$O ii$]$ 372.8 nm	$135.0\pm 6.9$	13.2
$[$O iii$]$ 500.7 nm	$20.7\pm 2.3$	2.2
Derived background H $\beta$ intensity			227

Table 3. Table 3: EBL values from MPFITFUN fitting utilizing different spectral features of the scattered ISL. Statistical errors are given as resulting from the pixel-to-pixel noise of the spectra (see Section 3.1), the zero level uncertainty of the Δ ​ I ​ ( λ ) ​ ( Pos9 / 42 − Pos8 ) Δ 𝐼 𝜆 Pos9 42 Pos8 \Delta I(\lambda){\rm(Pos9/42-Pos8)} spectrum (Section 3.2), and the Balmer line correction (Section 3.3). Their quadratic sum is σ tot subscript 𝜎 tot \sigma_{\rm tot} . The upper limits given for cases 6 and 7 include also the systematic error caused by the zero level uncertainty of the Pos8-OFF spectrum (Section 3.2).

No.	Wavelength range [nm]	Spectral features	Remarks	$I_{EBL}$333 $I_{EBL}$ and errors are units of ${10}^{-9}$ erg cm-2s-1sr-1Å-1  except for ${\sigma }_{\mathrm{cal}}$ and ${\sigma }_{\mathrm{model}}$ which are in per cent of the $I_{EBL}$ value	Statistical errorsa	Systematic erra
		used for fit			${\sigma }_{\mathrm{fit}}$,${\sigma }_{\mathrm{zero}}$,${\sigma }_{\mathrm{Bal}}$, ${\sigma }_{\mathrm{tot}}$, ${\sigma }_{\mathrm{cal}}$	${\sigma }_{\mathrm{zero}}$, ${\sigma }_{\mathrm{model}}$
(1)	(2)	(3)	(4)	(5)	(6)	(7)
1	381-432.5	400 nm jump,	H $\delta$,H $ϵ$,H $\zeta$,H9	3.20	0.81 0.70  0.3   1.11   9%	0.13  ${}_{-13\%}{}^{}{}_{}{}^{+18\%}$
		G, Ca ii H+K	included
2	381-382.5,385-387.5,	400 nm jump,	Balmer lines &	2.54	0.94 0.70     -    1.17   9%	0.13  ${}_{-13\%}{}^{}{}_{}{}^{+18\%}$
	390-396,398-408,412-432.5	G, Ca ii K	Ca ii H excluded
3	381-382.5,385-387.5,	400 nm jump,	Balmer lines &	2.54	1.16 0.70    -    1.35    9%	0.13  ${}_{-13\%}{}^{}{}_{}{}^{+18\%}$
	390-392.5,398-408,412-432.5	G band	Ca ii H+K excl
4	390-399	Ca ii H+K	H $ϵ$ included	3.58	1.42  0.70  0.5  1.66   9%	0.13  ${}_{-13\%}{}^{}{}_{}{}^{+18\%}$
5	390-396	Ca ii K	Ca ii K only	1.76	1.86 0.70     -    1.99   9%	0.13  ${}_{-13\%}{}^{}{}_{}{}^{+18\%}$
6	425-432.5,436-445	G band	G band only	$\le 5.0\left(2\sigma \right)$
				0.84	1.91 0.70     -    2.03   9%	0.13  ${}_{-13\%}{}^{}{}_{}{}^{+18\%}$
7	510-519, 522-530	Mg517,Fe527	520 nm Airglow	$\le 4.5\left(2\sigma \right)$
			line excluded	-1.80	2.40  1.20    -    2.70   9%	0.84   ${}_{-13\%}{}^{}{}_{}{}^{+18\%}$

Table 4. Table 4: Contribution of resolved galaxies in the 2 arcsec slit at the OFF positions. The columns give position name (1) and indicate whether chip 1, 2 or both were used for the spectrum (2). Then follows the date of the spectrum (3). In columns (4) to (6) the date, integration time (in seconds) and filter are given for the images. Columns (7) and (8) give the magnitude range of galaxies and their contribution to the EBL in units of 10 − 9 superscript 10 9 10^{-9}  erg cm -2 s -1 sr -1 Å -1  .

Posit-	Chip	Date		Int.	Filter	Magnitude	EBL
ion		Spectrum	Deep image	time		range	contribution
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Master spectra
POS18	1	2003-10-20	2011-10-02	600	B_HIGH	24.0-26.8	0.50
POS20	1&2	2010-12-14	2010-12-14	600	B_HIGH	22.4-26.1	0.57
POS24	1	2003-10-20	2009-01-29	600	B_HIGH	23.3-26.3	0.40
POS24	1&2	2004-09-18	2009-01-29	600	B_HIGH	23.2-26.3	0.58
Mean							0.51
Secondary spectra
POS18	1&2	2011-10-02	2011-10-02	600	B_HIGH	24.0-26.8	0.42
POS24	1&2	2004-02-18	2009-01-29	600	B_HIGH	23.7-26.2	0.44
POS25	1&2	2004-01-25	2004-01-25	90	B_BESS	22.3-24.3	0.44
POS32	1&2	2004-01-25	2004-01-25	90	B_BESS	21.9-24.4	0.74
POS34a	2	2004-09-16	2009-01-30	600	B_HIGH	22.7-26.5	1.11
POS34b	1&2	2004-01-24	2009-01-30	600	B_HIGH	23.6-25.6	0.29
POS36	1&2	2003-11-24	2011-10-27	600	B_HIGH	23.0-26.0	0.36
Mean							0.54

Table 5. Table 5: Data for space distribution parameters of stars and spectral library (STELIB) stars used for the ISL synthetic spectrum. Column 3 gives the mean and columns 4-5 the range of absolute magnitude, M V subscript 𝑀 𝑉 M_{V} , of the spectral group; column 6 gives the number density, D ​ ( 0 ) 𝐷 0 D(0) and column 8 the stellar emission coefficient, j i ​ ( 0 ) subscript 𝑗 𝑖 0 j_{i}(0) , in units of M V = 0 subscript 𝑀 𝑉 0 M_{V}=0  mag stars pc -3 , in the Galactic plane, z = 0 𝑧 0 z=0 ,; the scale height h z subscript ℎ 𝑧 h_{z} for a distribution of the form D ​ ( z ) = D ​ ( 0 ) 𝐷 𝑧 𝐷 0 D(z)=D(0) sech ( z / h z ) 𝑧 subscript ℎ 𝑧 (z/h_{z}) is given in column 7; the last column gives the number in the STELIB library of the spectrum adopted as template for each spectral group. The full table is available in the online version .

No.	Sp class	$M_V$	$M_V$ range		$D_0$	$h_z$	$j_0$	STELIB
								star No.
		mag	mag		stars pc-3	pc	$M_V=0$ mag
							stars pc-3
Main sequence, thin disk
1	B0 V	-4.0	-4.20	-3.25	0.46E-06	56.	0.13E-04	23
2	B2 V	-2.45	-3.20	-1.85	0.34E-05	56.	0.32E-04	21
3	B5 V	-1.2	-1.80	-0.75	0.13E-04	56.	0.38E-04	94
4	B8 V	-0.25	-0.70	0.20	0.44E-04	57.	0.53E-04	124
5	A0 V	0.65	0.25	0.95	0.92E-04	68.	0.52E-04	163
6	A2 V	1.3	1.00	1.60	0.15E-03	82.	0.44E-04	152
7	A3-5 V	1.8	1.65	1.95	0.11E-03	92.	0.21E-04	149
…	…	…	…	…	…	…	…	…
72	M3-4 I-II	-5.79	-5.8	-5.8	0.13E-07	56.	0.27E-05	7

Equations

$$\Delta I_{\mathrm{obs}}(\lambda )=\Delta I_{\mathrm{EBL}}^{\prime }(\lambda )+\Delta I_{\mathrm{SCA}}(\lambda )+\Delta I_{\mathrm{BAL}}(\lambda )$$

$$\Delta I_{\mathrm{EBL}}^{\prime }(\lambda )=I_{\mathrm{EBL}}(\lambda )[e^{-{\tau }_{\mathrm{cl}}}+f_{\mathrm{sca}}({\tau }_{\mathrm{cl}})]-I_{\mathrm{EBL}}(\lambda )=$$

$$h=1-e^{-{\tau }_{\mathrm{cl}}}-f_{\mathrm{sca}}({\tau }_{\mathrm{cl}}).$$

$$I_{\mathrm{SCA}}^{\mathrm{on}}(\lambda )=⟨i_{\mathrm{GAL}}(\lambda )⟩G_{\mathrm{SCA}}(\lambda )$$

$$⟨i_{\mathrm{GAL}}(\lambda )⟩=⟨I_{\mathrm{GAL}}(\lambda )⟩/⟨I_{\mathrm{GAL}}({\lambda }_0)⟩$$

$$G_{\mathrm{SCA}}(\lambda )=G_{\mathrm{SCA}}({\lambda }_0)[1+grad\times (\lambda -{\lambda }_0)].$$

$$I_{\mathrm{SCA}}^{\mathrm{off}}(\lambda )=C_{\mathrm{N}}\times {\tau }_{\mathrm{off}}(\lambda )\times ⟨i_{\mathrm{GAL}}(\lambda )⟩$$

$$I_{\mathrm{SCA}}(\lambda )(Pos9/42)=\Delta I(\lambda )(Pos9/42-\mathrm{OFF})+I_{\mathrm{SCA}}^{\mathrm{off}}(\lambda )+$$

$$I_{\mathrm{SCA}}^{\mathrm{off}}(\lambda )=C_{\mathrm{N}}\times {\tau }_{\mathrm{off}}(\lambda )\frac{I_{\mathrm{SCA}}(\lambda )(Pos9/42)}{1-\exp (-{\tau }_1(\lambda ))}$$

$$\mathtt{MYFUNCT}=[p_0+p_1(\lambda -{\lambda }_0)]I_{\mathrm{SCA}}(\lambda )(Pos9/42)-I_{\mathrm{SCA}}^{\mathrm{off}}(\lambda )$$

$$\mathtt{MYFUNCT}=$$

Full text

††pagerange: Extragalactic Background Light: a measurement at 400 nm using dark cloud shadow ††thanks: K.M., P.V., K.L. and Ch.L. dedicate this paper to the memory of Gerhard von Appen-Schnur, friend and colleague, who deceased on 13 February 2013 ††thanks: Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, under ESO programmes 072.A-0208(A), 082.A-0421(A), and 086.A-0201(A) II. Spectroscopic separation of the dark cloud’s light, and results–LABEL:lastpage††pubyear: 2002

1 Introduction

Besides the Cosmic Microwave Background (CMB) also ’the other’ extragalactic background radiations from $\gamma$– and X–rays over ultraviolet (UV), optical, near–infrared (NIR) to far–infrared (FIR) radiation and long radio waves have been recognized as an important source of information for cosmology and galaxy formation studies and have been intensively studied both by ground-based and space-borne telescopes; for a review see e.g. Longair (1995). Energetically, the optical–NIR and the FIR components are (after the CMB) the most important ones. The source of energy for both of them is mainly the starlight, the direct one in optical/NIR and the dust–processed one in the mid– and far–IR. While already Loys de Chéseaux (1744) and Olbers (1823) recognized the relevance of the night sky darkness for cosmology the optical EBL has remained, paradoxically, the observationally least well determined component so far. This is the consequence of the smallness of the Extragalactic Background Light (EBL) as compared to the much brighter sky foreground components.

The conventional approach for EBL measurement has been to observe the total sky brightness and try to measure or model all the foreground components. Then, after subtraction, what is left over is the EBL. In this method, because of smallness of the EBL, the two large surface brightness components, $I_{\rm total}$ and $I_{\rm foreground}$, must be very accurately known and, if measured by different telescopes or methods, absolutely calibrated at $<0.5$% accuracy which for surface brightness measurements is hardly possible (Bernstein, 2007).

When all or part of the observations are done from ground the first hindrance is the atmospheric diffuse light, ADL, consisting of the Airglow, AGL, and the tropospheric scattered light. The second large foreground is the Zodiacal Light, ZL, which remains a problem with full weight even if the observations are carried out outside the atmosphere. A very promising approach is to make the measurements beyond the interplanetary dust cloud. However, unless a small and accurately positioned aperture can be used, the light from stars in the measuring aperture enters with full weight and overwhelms the EBL (Matsuoka et al., 2011). Even if all these nearby foregrounds had been successfully determined there remains, for an observer within the Galactic dust layer, the emission by interstellar gas and the Diffuse Galactic Light, DGL, the starlight scattered by interstellar dust. No perfect cosmological windows, completely free of gas and dust, are known to exist. Besides the acronyms EBL, ADL, AGL, DGL and ZL we will in the following use also ISRF for Interstellar Radiation Field, ISL for Integrated Starlight and IGL for the integrated light of galaxies.

In the present paper, based on the results of Mattila et al. (2017a), hereafter Paper I, we present a (spectro)photometric determination of the EBL using the dark cloud shadow method (Mattila, 1976; Mattila & Schnur, 1990). The method utilizes the screening effect of a dark cloud on the background light. In this method no absolute measurements or modelling of $I_{\rm total}$ and $I_{\rm foreground}$ are required. The difference of the night sky brightness in the direction of an opaque high galactic latitude dark cloud and a surrounding transparent area is due to two components only: (i) the EBL, and (ii) the starlight that has been diffusely scattered by interstellar dust in the cloud. The three large foreground components, i.e. the ZL, the AGL, and the tropospheric scattered light, are eliminated. Also any emission by interstellar gas or dust that is homogeneously distributed in front of the cloud is eliminated. A sketch shown as Fig. 1 of Paper I illustrates the principle of the method. The method utilizes one and the same instrument for all sky components and, therefore, does not require any higher-than-usual calibration accuracy.

The main task in the method is to account for the surface brightness of the dark cloud. For the cloud, and even for its dark core, we have to take into account a substantial scattered light component. Such a component, although maybe smaller, is present in any direct photometric EBL measurement and is not an extra annoyance specific to the dark cloud method only. For efficient detection of the EBL with the dark cloud method it is essential that the dark cloud has an opaque core, $\tau>10$, and that there are areas with good transparency in its immediate neighbourhood on sky.

The rest of this paper is organized as follows. In Section 2 the method of spectroscopic separation of the EBL from the scattered light is described. In Section 3 we present our observational results and error estimates for the EBL intensity in the blue band, $\lambda\sim 400$ nm, and at 520 nm. In Section 4 we discuss our EBL result in comparison with the integrated light of galaxies (as derived from deep galaxy counts) and with the $\gamma$-ray attenuation measurements of blazars. In the final Section 5 we present our summary and conclusions.

The Paper has two appendices containing supporting data. Appendix A describes synthetic spectrum modelling of the the Solar neighbourhood ISL; it is used for comparision with the empirically determined scattered light spectrun in the cloud. Appendix B presents a survey of possible sources of diffuse light from outskirts of galaxies, low surface brightness galaxies and intergalactic stars that could contribute substantially to the EBL

2 Separation of the EBL and scattered light

The observational result of Paper I consists of the surface brightness spectra at the opaque central position, Pos 8, and the semi-transparent positions 9, and 42 in L 1642 relative to the OFF positions: $\Delta I^{0}(\lambda)$(Pos8 – OFF), $\Delta I^{0}(\lambda)$(Pos9 – OFF), and $\Delta I^{0}(\lambda)$(Pos42 – OFF). These spectra represent the surface brightness difference relative to the mean sky brightness in the transparent surroundings of the cloud, represented by the OFF-positions 18, 20, 24, 25, 32, 34, and 36 (see Table 1 of Paper I). The results refer to the corrected spectra, i.e. outside-the-atmosphere. In the following they will be referred to, for simplicity, without the superscript ’0’. The mean values for Pos9 and Pos42 will be designated by $\Delta I(\lambda)$(Pos9/42 – OFF) and $\Delta I(\lambda)$(Pos9/42 – Pos8).

2.1 The components of the cloud spectrum

The following components contribute to the surface brightness difference ’dark cloud minus surrounding sky’.

(A) We designate the isotropic EBL as seen by an observer outside the Galaxy $I_{\rm EBL}(\lambda)$. It is attenuated by the intervening dust along the line-of-sight (LOS) and there is additional light scattered from the all-sky isotropic EBL into the LOS; (a) toward the comparison (OFF) fields we see almost unattenuated LOS EBL; (b) toward the opaque cloud position, Pos8, we see almost completely attenuated LOS EBL plus a weak scattered EBL signal; and (c) toward the translucent cloud positions, Pos9 and Pos42, we see moderately attenuated LOS EBL and a moderate scattered EBL signal. We designate the modified EBL signal $I^{\prime}_{\rm EBL}(\lambda)$. It is discussed in Section 2.1.1.

(B) Light scattered by dust with all-sky ISL plus DGL as source of illumination; (a) in the cloud; and (b) in the comparison (OFF) fields; the spectrum is a modified copy of the ISL spectrum, i.e. a continuum with Fraunhofer lines and the 400 nm discontinuity;

(C) Light scattered by dust into the LOS with diffuse all-sky ionized-gas emission as source of illumination; (a) toward the cloud positions; and (b) toward the comparison (OFF) fields. The spectrum is dominated by the Balmer lines. The Galactic scattered light, including the components under (B) and (C), is designated $I_{\rm SCA}(\lambda)$ and will be discussed in Sections 2.1.2 and 2.1.3.

(D) Direct line-of-sight diffuse emission by ionized gas; (a) toward the dark cloud positions Pos8, Pos9 and Pos42; and (b) toward the comparison (OFF) positions; the spectrum is an emission line spectrum dominated by strong Balmer lines plus a weak continuum. This component is designated $I_{\rm BAL}(\lambda)$ and will be discussed in Section 2.1.3.

Components (C) and (D) contribute substantially only to the wavelength slots where the stronger Balmer lines are present. The observed differential spectrum ’dark cloud (ON) minus surrounding sky (OFF)’ can be represented as follows:

[TABLE]

Notice that while ${\Delta I_{\rm SCA}(\lambda)}>0$ the differences $\Delta I^{\prime}_{\rm EBL}(\lambda)$ and $\Delta I_{\rm BAL}(\lambda)$ are negative since the EBL and the Balmer line contribution are larger at the OFF than at the ON positions.

2.1.1 The EBL signal

We consider first the idealized case with an EBL signal only and fully tranparent OFF areas. Then, for an optical depth of $\tau_{\rm cl}$ through the cloud, we can write the difference $\Delta I^{\prime}_{\rm EBL}(\lambda)=I^{\prime\rm~{}on}_{\rm EBL}(\lambda)-I^{\prime\rm~{}off}_{\rm EBL}(\lambda)$ in the form

[TABLE]

where $f_{\rm sca}(\tau_{\rm cl})$ is the fraction of scattered EBL from the dark cloud and

[TABLE]

For a completely opaque cloud, $\tau_{\rm cl}>>1$, with non-scattering dust grains (i.e. albedo $a=0$) $f_{\rm sca}(\tau_{\rm cl})=0$ and the correction factor is $h=1$. For a finite optical depth and the presence of scattered light its value is reduced below unity.

The calculation of $h$ for the isotropic incident EBL and for a homogeneous spherical cloud has been presented in Appendix 1 of Mattila (1976). Monte Carlo method was used to solve the radiative transfer problem for different values of $\tau_{\rm cl}$ (=cloud diameter) and the scattering parameters of the grains, i.e. the albedo $a$ and asymmetry parameter $g$. Using the values $a=0.6\pm 0.1$ and $g=0.7$ to 0.8 (Mattila, 1971) the values as given in Table 1 were found for $h$. They refer to the central part of the cloud disk, with an area of 1/10th of the disk area. Towards the opaque ’standard position’, Pos8, with $A_{\rm V}$(Pos8)$\ga 15$ mag (see Section 3 and Table 1 of Paper I) the directly transmitted EBL through the cloud is $<10^{-5}$, and the scattered EBL does not influence the ON – OFF difference $\Delta I_{\rm EBL}(\lambda)$ by more than 5%, i.e. the cloud’s blocking efficiency is $\sim 95$%. Towards the two intermediate opacity positions, Pos9 and Pos42, with $A_{\rm V}\approx 1$ mag (see Section 3 and Table 1 of Paper I), the cloud blocks $\sim 30$% of the EBL. Towards the OFF positions with a mean extinction of $A_{\rm V}$(OFF)$\approx 0.15$ mag the EBL blocking factor is $\sim 5$%, i.e. $\sim 95$% of the EBL signal is transmitted.

2.1.2 Scattered Galactic light

The spectrum of the scattered Galactic light from the cloud can be represented as the product of two factors

[TABLE]

where $\langle i_{\rm GAL}(\lambda)\rangle$ stands for the normalized spectrum of the impinging Galactic light; it is normalized to = 1 at a reference wavelength $\lambda_{0}$, i.e.

[TABLE]

and $G_{\rm SCA}(\lambda)$ accounts for the intensity of the scattered light as well as for the reddening (or bluening) caused by the wavelength–dependent scattering and extinction in the cloud. $G_{\rm SCA}(\lambda)$ is assumed to be, over a limited wavelength range, a linear function of $\lambda$

[TABLE]

The intensity and spectrum of the Galactic light, as seen by a virtual observer at the cloud’s location, is a function of the galactic coordinates, $I_{\rm GAL}(\lambda)=I_{\rm GAL}(\lambda,l,b)$. The radiation impinging at the cloud’s surface from different directions $l,b$ is multiply scattered by the dust grains in the cloud, and $\langle I_{\rm GAL}(\lambda)\rangle$ is the weighted mean of $I_{\rm GAL}(\lambda,l,b)$ over the sky, with the direction-dependent weighting function being determined by the scattering properties of dust and the cloud’s optical thickness.

In Appendix A a synthetic spectrum of the Galactic starlightlight has been calculated by using spectra of representative stars of different spectral classes. The mean ISL spectrum over sky as seen by a cloud at the $|z|$-distance of 85 pc, representative of L 1642, is shown in Fig. A1 in Appendix A. The normalized Galactic spectrum, $\langle i_{\rm GAL}(\lambda)\rangle$, can be assumed to be closely the same for all positions in the cloud (i.e. Pos8, 9, 42) as well as for the OFF positions as far as the strengths of the Fraunhofer lines and 400 nm discontinuity are concerned. The absolute level and the wavelength dependence of $G_{\rm SCA}(\lambda)$ will be different and this is accounted for by different values of $G_{\rm SCA}(\lambda_{0})$ and $grad$.

For the OFF positions, with $A_{V}\approx 0.15$ mag (see Section 3 and Table 1 of Paper I), the scattered Galactic light can be calculated using the optically thin approximation:

[TABLE]

The absolute level is normalized using the factor $C_{\rm N}$ so that at 555 nm $I_{\rm SCA}^{\rm off}(\lambda)$ = 3.34 $10^{-9}$ erg cm*-2s-1sr-1Å-1* . This value has been determined using the intermediate band photometry at 555 nm combined with ISOPHOT 200 $\mu$m absolute surface photometry (see Appendix C of Paper I). The wavelength dependence of extinction has been adopted from Cardelli, Clayton, & Mathis (1989). The albedo of the dust has been taken to be constant over the wavelength range considered in this paper; this is justified by the results of Laureijs, Mattila, & Schnur (1987). Because $\tau_{\rm off}(\lambda)$ increases toward shorter wavelengths, $I_{\rm SCA}^{\rm off}(\lambda)$ is bluer than the integrated Galactic light represented by $\langle i_{\rm GAL}(\lambda)\rangle$.

2.1.3 Direct line-of-sight emission by ionized gas

There is an all-sky diffuse light component caused by the widely distributed ionized gas. The strongest features in the optical spectrum are the Balmer emission lines; in addition, a weak Balmer continuum emission and other emission lines are present, such as [O ii] 372.8 nm, [O iii] 500.7 nm, [N ii] 654.8 and 658.3 nm, and [S ii] 671.6 and 673.1 nm (Brandt & Draine, 2012; Lehtinen & Mattila, 2013). The Balmer lines are present as strong absorption lines in the ISL spectrum (see Fig. A1 of Appendix A). They could, in principle, serve as good measures of the dark cloud’s scattered ISL if there were not the emission lines from the ionized gas. The corrections for H ${\beta}$ and H ${\gamma}$ are so large that these lines have to be excluded from the scattered light separation analysis. However, the Balmer emission lines at $\lambda<400$ nm, H ${\epsilon}$, H8, H9 and H10 are much weaker and cause only small corrections to the ISL spectrum; their contributions can be estimated from H $\beta$, H $\gamma$ and H $\delta$ lines using the Balmer decrement valid for diffuse interstellar gas.

The relative Balmer line intensities have been adopted according to Table 4.2 of Osterbrock & Ferland (2006) for Case B, low-density limit, $T_{e}$ = 10,000 K. The lines are broadened to fit the observed, instrumentally broadened line profiles. The continuum has been adopted according to Aller (1984), Table 4.9, $T_{e}$= 10,000 K.

When using the observed spectrum at Pos9/42 as proxy for the impinging Galactic light spectrum $\langle i_{\rm GAL}(\lambda)\rangle$ (see Section 2.2.3 below) the scattered light from not only the ISL and DGL but also from the all-sky Balmer line (and continuum) emission is included in it.

Emission by the gas layer in front of the cloud cancels out, on average, in the differential spectra $\Delta I(\lambda){\rm(Pos8-OFF)}$ and $\Delta I(\lambda){\rm(Pos9/42-OFF)}$. The intensity of the direct line-of-sight Balmer line emission from the background gas, $I_{\rm BAL}^{\rm bg}(\lambda)$ can be estimated as follows: Because of the large extinction, $I_{\rm BAL}^{\rm bg}(\lambda)$ is negligible toward Pos8 and only its contribution at OFF and at positions 9 and 42 has to be considered. Because of the transmitted background light the differential spectrum $\Delta I(\lambda)$(Pos9/42 – Pos8) shows the Balmer lines in emission, see Fig. 1. In Table 2 the line areas and peak values, as obtained from this spectrum, are given for the H $\beta$, H $\gamma$, H $\delta$, [O ii] 372.8 nm and [O iii] 500.7 nm lines. The peak values were derived from the line areas using the line width of 10.5 Å  as determined by the spectral resolution. We designate the optical depth through the cloud at Pos9/42 $\tau_{1}(\lambda)$. Then, the background H $\beta$ intensity, $I_{\rm BAL}^{\rm bg}$(H$\beta$), can be calculated from

$\Delta I({\rm H}\beta)({\rm Pos9/42-Pos8})=I_{\rm BAL}^{\rm bg}({\rm H}\beta){\rm e}^{-\tau_{1}({\rm H}\beta)}$.

The omission of the scattered H $\beta$ line contribution is justified because the scattered light intensity at the wavelength of H $\beta$ is closely the same for Pos8 and Pos9/42 and thus cancels out in their difference (see Fig. 6 of Paper I).

We have adopted for the optical depth the value $\tau_{1}({\rm H}\beta)$ = 0.90 which correctly reproduces the observed line ratio H $\beta$/H $\gamma$. It is somewhat smaller than the unweighted mean value for Pos9 and 42, $\tau_{1}({\rm H}\beta)$ = $1.1\pm 0.1$, but close to $\tau_{1}({\rm H}\beta)=0.94\pm 0.1$ for Pos42 which dominates by its higher weight in the spectrum $\Delta I{\rm(Pos9/42-Pos8)}$. (For the extinction values towards Pos9 and 42 see Section 3 and Table 1 of Paper I.)

In the model fitting procedure the intensities of the Balmer lines and Balmer continuum relative to H $\beta$ intensity are kept fixed and the whole spectrum is scaled by one and the same factor. At $\lambda>380$ nm the level of Balmer continuum correction is always $\la 0.25$ $10^{-9}$ erg cm*-2s-1sr-1Å-1* . Its uncertainty is $\la 10$% which means that the correction introduces no significant uncertainty to the EBL determination.

2.2 Model fitting of the observed spectrum of the opaque position

2.2.1 Cloud geometry

The high opacity position Pos8 towards the centre of the cloud is bracketed by the intermediate opacity positions 9 and 42 on its northern and southern side, separated from it by $\sim$ 10 and 7 arcmin, respectively. It is plausible that the dense core is located at about half way inside the lower opacity halo which has an extinction of $A_{V}\approx 1$ mag. Then, a layer with $A_{V}\approx 0.5$ mag would be located in front and a layer with $A_{V}\approx 0.5$ mag behind of it. Scattered light intensity from the layer in front of the core amounts to $\sim$half of the intensity at the positions 9 and 42. The model is schematically shown in Fig. 2. Variations on the model will be considered by placing the core at different fractional depths of $d$ = 0, 0.3, 0.5 and 0.7 from the surface of the cloud.

2.2.2 Model fit using the synthetic ISL spectrum

Synthetic models of the ISL spectrum have been calculated as described in Appendix A. In order to test and validate such a spectrum we have compared it with the observed mean spectrum for positions 9 and 42, $\Delta I(\lambda){\rm(Pos9/42-OFF)}$ (see Appendix A, Fig. A1). At these positions the obscuration of the EBL is small and the spectral shape is only weakly influenced by dust. The comparison shows that while the overall fit is good for $\lambda>400$ nm there is a substantial discrepancy with the 400 nm step size: the ’observed minus model’ values deviate systematically upwards at $\lambda<400$ nm, i.e. the ISL model predicts a larger step at 400 nm than the observed one. Such a behaviour can not be explained by an EBL contribution. A residual EBL contribution would have an effect in the opposite direction.

Rather than trying to adjust the model parameters of the synthetic ISL spectrum we will in the following use the observed Pos9/42 spectrum to derive a proxy for the impinging Galactic spectrum.

2.2.3 Model fit using the observed scattered light spectrum

We use the observed ON–OFF spectrum $\Delta I(\lambda){\rm(Pos9/42-OFF)}$ to derive an expression for the ’total power’ scattered light spectrum, $I_{\rm SCA}(\lambda)({\rm Pos9/42})$, which will be used as a proxy for the impinging all-sky Galactic light spectrum, $\langle i_{\rm GAL}(\lambda)\rangle$.

[TABLE]

The term for the scattered Galactic light at the OFF positions, $I_{\rm SCA}^{\rm off}(\lambda)$, will be estimated below. The moderate contribution by the EBL signal is corrected for by the term $h_{1}I_{\rm EBL}(\lambda)$, where $h_{1}\approx 0.32$ corresponding to $\tau_{1}\approx 1$ (see Table 1). This correction term will be included into the final component separation procedure to be applied to the opaque position, Pos8, spectrum.

The direct line-of-sight gas emission from the layer behind the cloud introduces two terms: (1) the transmitted light at Pos9/42, exp$(-\tau_{1})I^{\rm bg}_{\rm BAL}(\lambda)$(Pos9/42), and (2) the emission toward the OFF positions, $I^{\rm bg}_{\rm BAL}(\lambda)$(OFF). While the former term is known from the analysis of the spectrum $\Delta I(\lambda){\rm(Pos9/42-Pos8)}$ (see Section 2.1.3 and Fig. 1) the latter term is not. In equation (8) we have assumed that $I^{\rm bg}_{\rm BAL}(\lambda)$ is equal for Pos9/42 and the OFF positions. Above, we have also assumed that the foreground Balmer emission is the same towards the cloud and the OFF positions, $I^{\rm fg}_{\rm BAL}(\lambda)({\rm Pos8})$= $I^{\rm fg}_{\rm BAL}(\lambda)({\rm Pos9/42})$= $I^{\rm fg}_{\rm BAL}(\lambda)({\rm OFF})$, and has thus cancelled out in the differential spectra. While fitting the spectrum $\Delta I(\lambda)({\rm Pos8-OFF})$ these approximations can be accounted for by adjusting the scaling of the Balmer line spectrum; it will be slightly different from the value found for Pos9/42, $I^{\rm bg}_{\rm BAL}(H\beta)$ = 26 $10^{-9}$ erg cm*-2s-1sr-1Å-1* . We notice that the terms $I^{\rm bg}_{\rm BAL}$ and $I^{\rm fg}_{\rm BAL}$ are important only for the wavelengths of Balmer lines.

For the OFF positions, with $A_{V}\approx 0.15$ mag, the scattered Galactic light can be represented using the optically thin approximation and the spectrum for positions 9 and 42, modified by a correction for the optical depth effect, $[1-\exp({-\tau_{1}(\lambda))}]^{-1}$:

[TABLE]

Concerning the normalization factor $C_{\rm N}$ and the wavelength dependence of the optical depth, $\tau(\lambda)$, we refer to to equation (7) above. Because $I_{\rm SCA}^{\rm off}(\lambda)$ and $I_{\rm SCA}(\lambda)({\rm Pos9/42})$ depend on each other according to equations (8) and (9) their values have to be determined iteratively. In practice, two iterations were found to be enough.

The observed spectrum $\Delta I(\lambda){\rm(Pos8-OFF)}$ to be fitted in accordance with equations (1), (2) and (6) is the mean of the ’Master A&B Mean’ and ’Secondary Mean’ spectra (see Section 8 and Fig. 6 of Paper I). The spectrum is re-binned with 5-pixel boxcar function resulting in 0.7 nm bins, closely corresponding to the physical resolution.

For the fitting procedure we used the idl111http://www.exelisvis.com/ProductsServices/IDL.aspx programme MPFITFUN222www.physics.wisc.edu/ graigm/idl/fitting.html. The function MYFUNCT used for the fitting of $\Delta I(\lambda){\rm(Pos8-OFF)}$ is formulated as follows:

[TABLE]

The parameters $p_{0}$ and $p_{1}$ correspond to $G_{\rm SCA}(\lambda_{0})$ and $grad$ in equation (6); for $\lambda_{0}$ we use 400.0 nm. For $I_{\rm SCA}(\lambda)$(Pos9/42) and $I_{\rm SCA}^{\rm off}(\lambda)$ we use the spectra derived according to equations (8) and (9) from the spectrum $\Delta I(\lambda){\rm(Pos9/42-OFF)}$. The EBL intensity, $I_{\rm EBL}(\lambda)$ is assumed to be constant over each of the limited wavelength intervals used for the fitting procedure. For the parameter $h_{0}$ corresponding to $\tau\ga 15$ for Pos8 we adopt according to Table 1 the value $h_{0}=0.95$. The direct line-of-sight Balmer emission will be scaled using the parameter $p_{2}$.

Equation (10) corresponds to the geometric model where the opaque core is located on the near side of the cloud envelope, i.e. $d=0$. As discussed in Subsection 2.2.1 above, in a more likely geometric configuration the core is at an intermediate depth, say $d\sim 0.5$, within the cloud. We have run alternative model fits with this geometry in mind. Model-wise, we can peel off the the foreground dust layer by modifying the observed spectrum for Pos8. In the case that the core is located at a depth $d$ within the cloud the observed spectrum for Pos8 is replaced by

$\Delta I(\lambda){\rm(Pos8-OFF)}-d\times\Delta I(\lambda){\rm(Pos9/42-OFF)}$

and MYFUNCT is modified as follows:

[TABLE]

In the MPFITFUN fitting run $p_{0}$, $p_{1}$ and $I_{\rm EBL}$ are free parameters which are simultaneously determined by least squares fitting. The scaling factor $p_{2}$ for the Balmer emission is determined in a separate fitting procedure applied to the Balmer lines only, and its value is kept fixed in the main fitting procedure. The quality of the fit is judged by the $\chi^{2}$ value that results from the fit.

3 Results from MPFITFUN fitting

Promising spectral features for the separation of the scattered light are the 400 nm discontinuity, the strong Fraunhofer lines H and K of Ca ii at 397 and 393 nm, and the G band at 430 nm. To a lesser extent the Mgi+MgH band at 517 nm and the Fe line at 527 nm can be useful for setting at least an upper limit to $I_{\rm EBL}$. Balmer lines H $\beta$, H $\gamma$ and H $\delta$ would appear as good candidates because they are strong in the ISL spectrum (see Fig. A1 of Appendix A). However, because they are present in the direct line-of-sight ionized gas emission as well, they do not enable an estimation of the scattered light. Nevertheless, one can use them to estimate the contamination effect which H $\epsilon$ has on the Ca ii H line, and H8, H9 and H10 on the overall mean intensity level at 380–390 nm.

3.1 Results from different wavelength slots

We first demonstrate qualitatively that the spectroscopic separation method is capable of reaching the required sensitivity level of $\la 1$ $10^{-9}$ erg cm*-2s-1sr-1Å-1* . In Fig. 3 we demonstrate the use of the 400 nm discontinuity to the determination of the EBL. The 380–440 nm spectrum of the opaque central position 8 (black dots) is shown together with the Pos9/42 spectrum according to equation (8). The lower blue curve at $\sim 4$ $10^{-9}$ erg cm*-2s-1sr-1Å-1* is the scattered light spectrum for the OFF positions (equation (9)). The red line shows the correction for the direct line-of-sight Balmer emission lines.

Model fits are shown superimposed on the observed spectrum for $I_{\rm EBL}$ = 0 (blue), 3 $10^{-9}$ erg cm*-2s-1sr-1Å-1*  (red), and 8 $10^{-9}$ erg cm*-2s-1sr-1Å-1* (green), respectively. The residuals, observation minus fit, are shown as the bottom-most three curves. Their deviations from zero level at $\lambda<400$ nm reflect the influence of the 400 nm step size. For $I_{\rm EBL}$ = 0 the step size of the model fit is smaller while for $I_{\rm EBL}$ = 8 $10^{-9}$ erg cm*-2s-1sr-1Å-1*  it is larger than the observed one. For an intermediate value of $I_{\rm EBL}$ = 3 $10^{-9}$ erg cm*-2s-1sr-1Å-1*  a good agreement is reached.

In Fig. 4 we demonstrate the use of the H and K lines to the determination of the EBL. The 390–400 nm spectrum of the opaque position 8 (black dots) is again fitted with the Pos9/42 spectrum (blue line) for three values of the EBL. The fitted spectra are deciphered in the same way as in Fig. 3. Comparison of the fitted line depths with the observed ones indicates that for $I_{\rm EBL}$ = 0 the model predicts too shallow lines while for $I_{\rm EBL}$ = 8 $10^{-9}$ erg cm*-2s-1sr-1Å-1*  they are deeper than the observed ones. Again, the intermediate value of $I_{\rm EBL}$ = 3 $10^{-9}$ erg cm*-2s-1sr-1Å-1*  gives the best fit.

In Table 3 we give $I_{\rm EBL}$ values and their statistical errors, $\sigma_{\rm fit}$, obtained from MPFITFUN fitting for seven cases. The wavelength slots used are given in the second column. The third column gives the relevant spectral features that are facilitating the separation of the scattered light from the EBL. The EBL values and their $1\sigma$ statistical errors or $2\sigma$ upper limits are given in the fifth and sixth column. Systematic errors follow in column 7.

The most sensitive probe is provided by the case where both the H and K lines and the 400 nm discontinuity are included in the fit. The first result is for the 50 nm wide range, $\lambda$ = 381–432.5 nm, which includes also the Balmer lines H $\delta$ to H9. The Balmer line scaling factor is included as a free parameter in the fitting. Its value is thereby well determined mainly by the H $\delta$ line which is not blended with other spectral features.

Although all the Balmer lines at $\lambda<400$ nm are substantially weaker than H $\delta$ there may still be a residual effect, especially because of the H $\epsilon$ line at 397 nm that is blended with the Ca ii H line. As the second case we have, therefore, made a fit to the same wavelength range, $\lambda$=381–432.5 nm, but excluding all Balmer lines and thereby also the H line of Ca ii.

In the third case even the K line has been excluded and the result is thus based mainly on the 400 nm jump only. In the fourth case we use a narrow window including the H and K lines only, while in the fifth case only the K line is included.

The error estimates, $\sigma_{\rm fit}$, as given by MPFITFUN, are seen to increase while the wavelength window is narrowed down. The first four cases provide significant $I_{\rm EBL}$ values ($\ga 2\sigma$ detections) in agreement with each other. In the fifth case the error is too large to allow an EBL detection.

A fit to the G band alone (Case 6) can be used to set an upper limit of $I_{\rm EBL}\leq 5.0$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*  $(2\sigma)$. The region 510-530 nm includes two relatively strong Fraunhofer lines, MgH+Mgi at 517 and Fe at 527 nm. The fitting allows an upper limit to be set to the EBL at 520 nm, $I_{\rm EBL}\leq 4.5$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*  ($2\sigma$) (Case 7).

3.2 Errors caused by zero level uncertainties of the observed spectra

The observational errors of the spectra $\Delta I(\lambda){\rm(Pos8-OFF)}$, $\Delta I(\lambda){\rm(Pos9/42-Pos8)}$ and $\Delta I(\lambda){\rm(Pos9/42-OFF)}$ can be separated into three categories: (1) the pixel-to-pixel statistical errors; (2) the error of the zero level, which for $\Delta I(\lambda){\rm(Pos8-OFF)}$ is partly statistical and partly caused by the uncertainties of the differential ADL and ZL corrections; and (3) the calibration errors.

The effect of the pixel-to-pixel statistical errors is taken into account by the MPFIFUN fitting procedure.The effect of calibration errors is straight forward and will be added to the errors resulting from the modelling (see Section 3.4 below).

It has been found in Section 8.1 of Paper I that the zero point error of $\Delta I(\lambda){\rm(Pos8-OFF)}$ is $\pm$0.5 $10^{-9}$ erg cm*-2s-1sr-1Å-1* . Because the spectrum $\Delta I(\lambda){\rm(Pos9/42-OFF)}$ was calculated as the sum of $\Delta I(\lambda){\rm(Pos9/42-Pos8)}$ and $\Delta I(\lambda){\rm(Pos8-OFF)}$ it is subject to the same zero level error as $\Delta I(\lambda){\rm(Pos8-OFF)}$. In addition, it has the zero point error inherent in the spectrum $\Delta I(\lambda){\rm(Pos9/42-Pos8)}$. This error was found to be $\sim\pm 0.47$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*  at $\lambda\approx 400$ nm; and $\sim\pm 0.63$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*  at $\lambda\approx 520$ nm (see Section 8.1 and Table 3 of Paper I). For the spectrum $\Delta I(\lambda){\rm(Pos9/42-Pos8)}$, because the positions 8, 9 and 42 have small angular separations, the ADL and ZL corrections are unimportant and the error is purely statistical.

In order to investigate the effects of these zero point errors we have run the MPFITFUN fitting procedure

(1) for the three cases where a zero point correction of -0.5, 0.0, and +0.5 $10^{-9}$ erg cm*-2s-1sr-1Å-1*  was applied to both $I(\lambda){\rm(Pos8-OFF)}$ and $I(\lambda){\rm(Pos9/42-OFF)}$; and (2) for each of these three cases we have applied, in addition, a correction to the spectrum $I(\lambda){\rm(Pos9/42-OFF)}$ of -0.47, 0.0, and +0.47 $10^{-9}$ erg cm*-2s-1sr-1Å-1*  for $\lambda$ = 381–433 nm, or -0.63, 0.0, and +0.63 $10^{-9}$ erg cm*-2s-1sr-1Å-1*  for $\lambda\approx 520$ nm.

The former zero point corrections change the EBL value by $\pm 0.13$ $10^{-9}$ erg cm*-2s-1sr-1Å-1* . Because this error is partly caused by uncertainties in the differential ADL and ZL corrections we conservatively assign it as systematic error. It is given as the first item ($\sigma_{\rm zero}$) in column (7). The latter zero level uncertainty causes a statistical error. It amounts to $\sigma_{\rm zero}=\pm 0.70$ and $\pm 1.20$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*  at $\lambda$ = 381–433 nm and 520 nm, respectively. It is given as the second item in the sixth column of Table 3.

3.3 Errors caused by modelling uncertainties

In addition to the observationally based errors there are errors caused by uncertainties in the modelling. These are the uncertainties of $I^{\rm off}_{\rm SCA}(\lambda)$, the scattered light intensity at the OFF positions; the scaling of $I_{\rm BAL}(\lambda)$, the direct line-of-sight Balmer line intensity; the uncertainties of the effective blocking factors $h_{0}$ and $h_{1}$; and the influence of the wavelength-dependence of $I_{\rm EBL}$.

3.3.1 OFF-position scattered light intensity

We have varied $I^{\rm off}_{\rm SCA}(\lambda)$, given by equation (9), by scaling it up and down by 30%. This corresponds to the extinction uncertainty of $\pm 0.05$mag at the OFF positions. This scaling had no effect on the derived EBL value. This, at first sight, surprising result can be understood because the spectral features in the OFF spectrum are the same as in the Pos9/42 spectrum used for the fitting. Thus, the scaling of the OFF spectrum does not change the strengths (equivalent widths) of the spectral features in the Pos9/42 spectrum. The spectral separation method is sensitive to the different absorption feature strengths of the Pos8 and Pos9/42 spectra, and not to their overall scaling difference.

3.3.2 Balmer line intensities

The Balmer line scaling factor $p_{2}$ (see equations (10) and (11)) was determined using the H $\delta$ line. While H $\delta$ itself was included only in the first EBL fit as given in Table 3 it was used to give the scaling for H $\epsilon$ included in the EBL determination for the wavelength slot 390–399 nm (fourth case in Table 3). The statistical uncertainty of $p_{2}$, as determined from the fitting of H $\delta$ line was found to be $\pm 10$%. This causes to the EBL estimate an error of $\pm 0.5$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*  as given as the fourth value in column (6) of Table 3.

3.3.3 Case of the embedded dense core

Fig. 5 illustrates the case where an envelope layer has been ’peeled off’ in front of the opaque core (see model in Section 2.2.1 and Fig. 2). The core has been assumed to be half way between the front and back surface of the envelope, i.e. $d=0.5$. The spectrum to be fitted in this case is

$\Delta I(\lambda){\rm(Pos8-OFF)}-0.5\times\Delta I(\lambda){\rm(Pos9/42-OFF)}$,

and equation (11) with $d=0.5$ will be used in MPFITFUN instead of equation (10). A fit to the spectrum in the interval 380–432.5 nm with $I_{\rm EBL}=3$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*  is shown as red line superimposed on the ’peeled off’ spectrum shown as black dots.

Somewhat surprisingly, the result for $I_{\rm EBL}$ is the same as for the case $d=0$. Also for the other values, $d=0.3$ and 0.7, the same is true. This result can be understood because the spectrum of the surface layer, removed in front of the core, has the same Pos9/42 spectrum that is used in the fitting procedure. This outcome demonstrates that our fitting results for the EBL do not depend on the geometrical model, i.e. on the assumed location of the opaque core within the cloud envelope.

3.3.4 Effect of the cloud’s blocking factor

We have varied the the effective blocking factors from their adopted values of $h_{0}=0.95$ and $h_{1}=0.32$ by $\pm 0.05$ and $\pm 0.06$, i.e. by their uncertainties as listed in Table 1 for $\tau_{cl}\geq 16$ and $\tau_{cl}=1$. The maximum deviations of the $I_{\rm EBL}$ value of +18% and -13% resulted for the parameter pairs $h_{0}=1.0$, $h_{1}=0.26$ and $h_{0}=0.90$, $h_{1}=0.38$, respectively.

3.3.5 Effect of the EBL spectral shape

We have finally tested the effect of a non-constant $I_{\rm EBL}(\lambda)$ spectrum. We assume a linear dependence with wavelength of the form $I_{\rm EBL}(\lambda)=I_{\rm EBL}({\rm 400~{}nm})[1+C(\lambda-{\rm 400~{}nm})]$ and with a large gradient, $C=+0.5$ and -0.5 per 100 nm, respectively. For these two extreme gradients the resulting $I_{\rm EBL}$ values for the second case in Table 3 differed by $\leq\pm 3\%$. The effect on the other $I_{\rm EBL}(\lambda)$ values in Table 3, covering the same or smaller wavelength range, is equal or smaller than this.

3.4 The EBL results at 400 and 520 nm

In Table 3 the first two EBL estimates are based on the same wavelength slot, $\lambda$ = 381–432.5 nm, one with and the other without the Balmer lines. The two $I_{\rm EBL}$ values are not independent. The good agreement between them demonstrates, however, that our correction for the Balmer line contamination is reasonably good. The two strongest spectral features of the scattered Galactic light spectrum in this wavelength range are the 400 nm jump and the H and K lines of Ca ii. The third case in Table 3 excludes, besides all Balmer lines and H, also the K line. The result is thus based essentially on the 400 nm jump only.

In the fourth case we have limited the wavelength range to a narrow window covering the H and K lines only. The result is thus independent of the 400 nm discontinuity. Using a window that includes the K line only (Case 5) the fitting error becomes too large to allow a useful $I_{\rm EBL}$ estimate.

All $I_{\rm EBL}$ values as derived for cases 1–4 agree within a fraction of their $1\sigma_{\rm tot}$ statistical errors. The first two values, based on the largest number of spectral elements, have the smallest statistical errors. Their unweighted mean value can thus be considered a good choice in this wavelength range: $I_{\rm EBL}=2.87\pm 1.1$ $10^{-9}$ erg cm*-2s-1sr-1Å-1* . Because the two values are not independent the error of their mean is not reduced below the individual errors. Another estimate with comparable precision is the mean of the third and fourth $I_{\rm EBL}$ values which are independent. Their weighted mean and its standard error is $I_{\rm EBL}=2.95\pm 1.0$ $10^{-9}$ erg cm*-2s-1sr-1Å-1* . As weights we have used the $\sigma_{\rm tot}^{-2}$ values.

The two mean values (1 & 2) and (3 & 4) are, somewhat fortuitously, almost equal and have almost the same standard error. We adopt their mean value as our final choice in the wavelength region $\lambda$ = 380–432.5 nm: $I_{\rm EBL}=2.9\pm 1.0$ $10^{-9}$ erg cm*-2s-1sr-1Å-1* .

In Section 3.2 we saw that an error of $\pm$0.13 $10^{-9}$ erg cm*-2s-1sr-1Å-1*  was caused by the zero level uncertainty of $\Delta I(\lambda){\rm(Pos8-OFF)}$. If we conservatively assume that most of it is systematic it has to be added linearly to the statistical error resulting in: $I_{\rm EBL}=2.9\pm 1.1$ $10^{-9}$ erg cm*-2s-1sr-1Å-1* .

The multiplicative error consists of the spectrophotometric calibration error of $\pm 9\%$ (see Section 8.2 of Paper I), the uncertainty caused by the blocking factor of +18%/-13%, and an error of maximally $\pm 3\%$ caused by possible wavelength dependence of $I_{\rm EBL}(\lambda)$. Quadratic addition results in the total multiplicative error of +20%/-16%. It increases or decreases the $I_{\rm EBL}$ value and its statistical error limits in the same way and, therefore, does not influence the statistical significance level ($2.6\sigma$) of our EBL detection.

Our result for the wavelength range $\lambda=381-432.5$ nm can thus be written in the form:

$I_{\rm EBL}=2.9\pm 1.1$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*  +20%/-16%, or

$11.6\pm 4.4$ nW m*-2sr-1* +20%/-16%.

The two upper limits for $I_{\rm EBL}$, at $\lambda\sim 430$ nm and at $\lambda\sim 520$ nm, given in Table 3 as cases 6 and 7, are based on their statistical error estimates, $\sigma_{\rm tot}$, complemented by the partly systematic error caused by the zero level uncertainty of $\Delta I(\lambda){\rm(Pos8-OFF)}$. In Case 6 ($\lambda\sim 430$ nm) the error caused by the zero uncertainty is again $\pm 0.13$ $10^{-9}$ erg cm*-2s-1sr-1Å-1* . In Case 7 ($\lambda\sim 520$ nm) it is $\pm 0.84$ $10^{-9}$ erg cm*-2s-1sr-1Å-1* . The multiplicative error is the same as above.

We thus end up with the following final $2\sigma$ upper limits:

$I_{\rm EBL}\leq$ $5.0$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*  +20%/-16%, or

$\leq 20.0$  nW m*-2sr-1* +20%/-16% at 430 nm, and

$I_{\rm EBL}\leq$ $(4.5$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*  +20%/-16%, or

$\leq 23.4$  nW m*-2sr-1* +20%/-16% at 520 nm.

4 Discussion

4.1 Contribution by resolved galaxies

Part of our measured EBL signal is caused by resolved galaxies in the slit area. The slit positions were chosen to avoid stars and galaxies visible on the DSS2 blue plates. This corresponds to $B\approx 22$ mag. In order to measure the contribution of galaxies fainter than this limit we have secured for each one of our fields as listed in Table 2 of Paper I a direct $\sim$ 6.8 x 6.8 arcmin $B$ band image using VLT with FORS1 or FORS2, see Table 4. For Positions 18, 20, 24, 34 and 36, with integration time of $t_{\rm int}$ = 600 s, the limiting magnitude was $\sim$26.5 mag, and for Pos 25 and 32 with $t_{\rm int}$ = 90 s it was $\sim$25.5 mag. Accurate positioning of the slit relative to the direct image was secured by taking immediately before each spectrum exposure a 10 s acquisition image after which the telescope pointing was kept fixed.

The images were bias-subtracted and flat-fielded and zero point and extinction corrections were applied using the ESO Quality Control nightly zero points and extinction coefficients for FORS1444http://www.eso.org/observing/dfo/quality/FORS1/qc/

/̃zeropoints/zeropoints.html and FORS2555http://www.eso.org/observing/dfo/quality/FORS2/qc/

/̃zeropoints/zeropoints.html. Kron magnitudes of all objects were determined using the SExtractor software (Bertin & Arnouts, 1996) from within the Starlink gaia v4.4.6 package.

The objects in the slit areas were visually inspected and most appeared to be galaxies although at $m>23$ mag the star/galaxy separation remains uncertain. According to Windhorst et al. (2011) the fraction of stars is $\la 10\%$ and $\la 1\%$ at $g\approx 23$ and 26 mag, respectively (see Appendix B1). In column 8 of Table 4 we give the contribution by all objects in the slit area in units of $10^{-9}$ erg cm*-2s-1sr-1Å-1* . Only a few per cent of this will be due to stars and we interpret it as the EBL contribution by the galaxies in the covered magnitude interval, given in column 7. The magnitude range varies from field to field with the bright and faint end values between 21.9–24.0 and 24.3–26.8 mag, respectively. The galaxy contributions for the ’Master’ spectra areas vary from 0.40 to 0.58 $10^{-9}$ erg cm*-2s-1sr-1Å-1* , with a mean of 0.51 $10^{-9}$ erg cm*-2s-1sr-1Å-1* . For the ’Secondary’ spectra fields the corresponding numbers are 0.29 to 1.11, with a mean of 0.54 $10^{-9}$ erg cm*-2s-1sr-1Å-1* .

These numbers agree closely with the EBL contribution of 0.49 $10^{-9}$ erg cm*-2s-1sr-1Å-1*  for the magnitude interval of 22 to 27 mag, as estimated from galaxy count data in the HST F435W band by Driver et al. (2016) (their Table 3). We conclude that our total EBL intensity of $I_{EBL}=2.9\pm 1.1$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*  includes a contribution of $\sim$0.5 $10^{-9}$ erg cm*-2s-1sr-1Å-1*  by galaxies in the magnitude interval of $\sim$22–26.5 mag.

4.2 Comparison with the integrated light of galaxies (IGL)

We show in Fig. 6 a selection from UV to NIR (0.1 - 5 $\mu$m) of direct EBL measurements and upper and lower limits (colour symbols and lines), as well as lower limits set by the integrated galaxy light (IGL) from galaxy counts as derived by Driver et al. (2016) (black symbols). The EBL values from the present paper are shown as the red solid square with $1\sigma$ error bars at 400 nm and as $2\sigma$ upper limits at 430 and 520 nm. For references see the figure legend.

When comparing our total EBL value at 400 nm with the IGL from galaxy counts one should take into account the magnitude limits of galaxies included in each case. As stated above, our EBL values exclude galaxies brighter than $B\approx 22$ mag whereas the extrapolated eIGL values of Driver et al. (2016) cover the the whole magnitude range, including extrapolations below $m\approx 10$ and above $m\approx$28–30 mag in optical bands from $u$ to $h$. Using their Table 3 one can estimate that galaxies with $g\leq$22 mag contribute $\sim$0.52 $10^{-9}$ erg cm*-2s-1sr-1Å-1*  of the total IGL of $1.14\pm 0.2$ $10^{-9}$ erg cm*-2s-1sr-1Å-1* . Thus the IGL contribution to be compared with our EBL measurement is $I_{\rm IGL}(g\geq 22^{\rm m})=0.62\pm 0.2$ $10^{-9}$ erg cm*-2s-1sr-1Å-1* . On the other hand, if we include the bright-galaxy contribution for $g\leq 22$ mag, to our measured EBL value it will be increased to $I_{\rm EBL}$ = 3.5 $10^{-9}$ erg cm*-2s-1sr-1Å-1* .

4.2.1 Cosmic variance and galaxy counts

We are able to check directly whether the L 1642 EBL fields are abnormal in terms of IGL using the direct imaging of the OFF fields described in Section 4.1. The photometric catalogues of the fields were cleaned of stars with the help of the SExtractor CLASS parameter (though the star contribution is significant only at $B<22$, see Windhorst et al. 2011) and also of obvious artifacts and edge effects. The resulting $B$-band galaxy counts per deg2 and 0.5 mag bin, averaged over the 7 fields, are shown in Fig. 7. The counts from the shallower images, the Pos25 and Pos32 fields, are included only for $B\leq 24$ mag. The counts are not completeness corrected. For comparison we also show recent wide-field galaxy counts adopted from a large compilation of multi-wavelength data by Driver et al. (2016). The points shown are $g$-band counts from GAMA and COSMOS/G10 surveys as described therein, we have merely shifted them using an average $B-g$ = 0.6 mag conversion (Fukugita et al., 1996). The galaxy counts in our fields down to $B\sim 26$ mag thus appear totally normal and consistent with wide field galaxy counts.

The error bars in Fig. 7 are the standard deviations of counts between the fields, the nominal Poissonian errors within a field are in fact much smaller. The scatter reflects the cosmic variance. For the size (0.0126 deg2) of our OFF fields we expect the cosmic variance to be of the order of 15-20% (Driver & Robotham, 2010), consistently with our results.

Finally, we note that there is a galaxy cluster, Abell 496, just north of the L 1642 area. One of our OFF positions, Pos18, is at the projected distance of 36.5 arcmin from the cD galaxy at the cluster centre. This corresponds to 1.63 Mpc at the cluster distance of 153.5 Mpc. While Pos18 shows one of the two highest galaxy counts of the 7 fields examined, the difference is well within the scatter, the cosmic variance. An upper limit to the the diffuse intra-cluster light contribution from Abell 496 can be estimated from the survey by Gonzalez, Zabludoff, & Zaritsky (2005) of 24 clusters having a bright central galaxy with diffuse cD envelope. In this sample the highest diffuse light signal at large radii (up to $\sim 400$ kpc) was for Abell 2984. Extrapolated to the projected distance of 1.63 Mpc and assuming a $B-I$ colour index of $\geq 2$ mag it gives a $B$ band upper limit of $\leq 0.01$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*. Photoelectric photometry of intra-cluster light in Abell 496 by Schnur & Mattila (1979) gave an upper limit of $\la 2$ $10^{-9}$ erg cm*-2s-1sr-1Å-1at the projected radial distance of 270-600 kpc. Adopting the radial gradient of Abell 2984 this extrapolates for 1.63 Mpc to $\la$0.2 $10^{-9}$ erg cm-2s-1sr-1Å-1*. We conclude that Abell 496 does not have a measurable effect on our analysis. The contribution by Abell 496 can also be considered as a natural ingredient in the cosmic variance; in an area of $\sim 4\degr\times 4\degr$ as covered by our OFF positions there normally exists, by chance, one major Abell cluster.

4.3 Comparison with EBL from gamma–ray attenuation measurements

The intergalactic radiation density has been derived from gamma-ray attenuation measurements of blazars by ground based Cerenkov telescopes, e.g. H.E.S.S., MAGIC and VERITAS, sensitive in the 0.2–20 TeV (VHE) range, as well as by the Large Area Telescope (LAT), aboard the Fermi satellite, sensitive in the 1–500 GeV (HE) range. Results based on extensive data sets from Fermi-LAT (Ackermann et. al., 2012) and H.E.S.S. (H.E.S.S. Collaboration, 2013) are shown in Fig. 6 as upper and lower boundaries to the allowed range of EBL values. Similar results have been published by the MAGIC collaboration (Ahnen et al., 2016). Fermi-LAT probes with high sensitivity the EBL photon energy range from UV to optical ($\lambda\approx$ 200–600 nm) while the ground-based VHE telescopes cover the wider range from optical to FIR, $\lambda\approx$ 0.3–100 $\mu$m.

As can be seen from Fig. 6 the above mentioned gamma-ray attenuation results agree with the IGL values from galaxy counts but they do allow a modestly higher (by up to $\la 70\%$) EBL intensity as well. The good agreement of spectral shapes is, however, a direct result of the underlying assumption of an IGL–like template spectrum: the EBL spectrum template comes from a model that is obtained by summing up empirically–constrained galaxy populations spectra, see e.g. Franceschini, Rodighiero, & Vaccari (2008) and Domínguez et al. (2013). The observed gamma-ray optical depths are fit to optical depths predicted by EBL spectral models, with a normalisation factor as the only free parameter. Thus, the derived EBL spectrum will closely follow the spectrum of the IGL.

The interaction of gamma-rays vs. optical and infrared EBL photons has a very broad wavelength response function, with the kernel covering roughly a decade of the EBL spectrum (Biteau & Williams, 2015). Therefore, the intensity maximum at $\sim 1$ $\mu$m dominates the normalisation factor over the whole UV–NIR range 0.2–5 $\mu$m and it will be difficult, if not impossible, to detect deviations from the IGL-like spectral shape using the ’model template approach’.

Recently, Biteau & Williams (2015) have taken a more general approach. They abstain from an a priory assumption on constraining the EBL spectrum with the IGL–like spectrum shape. Using gamma-ray observations only they were able to derive a ’free-standing’ EBL spectrum which covered the 0.2–100 $\mu$m range by coarse binning, with four spectral elements with widths of $\sim$  half a decade. Two of these spectral elements fall into the wavelength range displayed in Fig. 6 and they are shown as light blue crosses. The horizontal bars indicate the wavelength coverages of the bins, 0.26–1.2 $\mu$m and 1.2–5.2 $\mu$m, respectively.

Biteau & Williams (2015) have compared their EBL values with appropriately weighted IGL mean values in the four bins. While a good individual and overall agreement was found for the three bins at 1.2–5.2 $\mu$m, 5.2–23 $\mu$m, and 23–103 $\mu$m, the bin at 0.26–1.2 $\mu$m showed an excess of $4.7\pm 2.2$ nW m*-2sr-1*. This excess over the IGL value, as well as over the Fermi–LAT and H.E.S.S. EBL values, is also well demonstrated by Fig. 6.

To compare with our EBL measurement we note that while the gamma-ray based EBL value of $15.9\pm 2.2$ nW m*-2sr-1* for the bin 0.26–1.2 $\mu$m corresponds to the total EBL, our EBL measurement at 0.4 $\mu$m does not include the contribution of the bright galaxies with $g\leq$22 mag. Including that contribution, our EBL value increases from $11.6\pm 4.4$ nW m*-2sr-1*, as shown in Fig. 6, to $13.6\pm 4.5$ nW m*-2sr-1* which is in good agreement with the gamma–ray value of Biteau & Williams (2015). Furthermore, our total EBL value is in excess over the IGL value of Driver et al. (2016) at 0.4 $\mu$m by $9.0\pm 4.5$ nW m*-2sr-1*.

We show in Fig. 8, in accordance to Fig. 4 of Biteau & Williams (2015), our EBL excess value together with their four gamma-ray based residual values. It can be seen that our excess value, while agreeing within the error limits with the 0.26–1.2 $\mu$m gamma–ray–based value, suggests an even larger excess at 0.4 $\mu$m.

In conclusion, our result that the EBL intensity at 400 nm exceeds the IGL from galaxy counts is supported by the Biteau & Williams (2015) EBL value, determined by the independent method of gamma–ray absorption.

4.4 Optical EBL in context of other wavelengths

The galaxies, intergalactic stars or any other light sources that give rise to the optical EBL will contribute to the background light also in the adjacent UV and NIR wavelength bands. We will briefly review the recent results in these bands and their relevance for the optical EBL.

In the near ($\lambda\approx 150$ nm) and far ultraviolet ($\lambda\approx 230$ nm) some of the large foreground sky components, e.g. the ZL, that plague optical EBL measurements are absent or much reduced. However, other difficulties appear, see e.g. Murthy (2009, 2014a, 2014b) for a review. The Galaxy Evolution Explorer (GALEX) (Martin et al., 2005) has recently provided a comprehensive survey of the near (NUV) and far ultraviolet (FUV) background, covering $\sim 75$ per cent of the sky. Among the other surveys, Schiminovich et al. (2001) have covered a large fraction of sky at 174 nm in the NUVIEWS rocket experiment. The minimum sky brightness seen by GALEX toward the North and South Galactic Poles was $\sim 300-400$ (FUV) and $\sim 600$ photons cm*-2s-1sr-1Å-1* (NUV) (see Hamden, Schiminovich, & Seibert 2013 and Murthy et al. 2017). While these values still contain airglow as ’likely the dominant contributor’ (Hamden, Schiminovich, & Seibert, 2013) they can be used as upper limits to the EBL: $I_{\rm EBL}(\lambda)\la 6-8$ and $\la$12 nW m*-2sr-1* in the FUV and NUV band, respectively. These values are by a factor of $\sim 4$ higher than the corresponding IGL values as displayed in Fig. 6.

Using a model for the distribution of dust and stellar light sources and adopting likely scattering parameters for the grains Murthy et al. (2017) estimated the scattered light from dust to be $\sim$1.2 - 1.8 (FUV) and $\sim$1 nW m*-2sr-1* (NUV). Schiminovich et al. (2001) estimated from their NUVIEWS data an EBL intensity of $4\pm 2$ nW m*-2sr-1* at 174 nm. We conclude that the EBL estimates at FUV and NUV do allow an EBL contribution by at least 2 times as large as the IGL derived from galaxy counts, and are in this respect compatible with the EBL excess at 400 nm found in the present paper.

Henry et al. (2015) have presented a different interpretation for the $\sim 300$ photons cm*-2s-1sr-1Å-1* isotropic component of the GALEX FUV sky: they argue that most of it is not due to EBL but is ’of unknown (but Galactic) origin’.

The diffuse near infrared (NIR) background sky brightness has been studied by several groups using the COBE Diffuse Infrared Background Experiment (DIRBE) data in combination with the 2MASS star catalogue (see Dwek, Arendt, & Krennrich 2005; Levenson, Wright, & Johnson 2007; Sano et al. 2015 for reviews), the AKARI InfraRed Camera (Tsumura et al., 2013), and the IRTS Near Infrared Spectrometer (Matsumoto et al., 2005, 2015). Most of these results are consistent, within their large error bars, with the values as shown in Fig. 6 at 1.25, 2.2 and 3.6 $\mu$m according to the DIRBE - 2MASS analysis of Levenson, Wright, & Johnson (2007). The consensus, shared also by the TeV gamma-ray absorption results (Section 4.4 and Figs.6 and 8), appears to be that the NIR EBL does not exceed the IGL by more than a factor of 2.

Matsumoto et al. (2005), however, using their IRTS data have announced and Matsumoto et al. (2015) repeated the claim for detection of an excess emission of up to  6 times as large as the IGL at $\lambda=1-2~{}\mu$m. A large excess has also been found by Sano et al. (2015) at $1.25~{}\mu$m and by Matsuura et al. (2017) at $1-1.7~{}\mu$m. It has been poined out by e.g. Dwek, Arendt, & Krennrich (2005) and Mattila (2006) that a likely explanation for the excess found in Matsumoto et al. (2005) is the insufficient subtraction of Zodiacal Light. Besides the ZL also the DGL introduces substantial uncertainty, especially at the shorter NIR wavelengths, into all these results.

Because of the persistent problems caused by the ZL the attention has turned towards the NIR sky fluctuatuations (see e.g. Kashlinsky et al. 2005, 2012, Matsumoto et al. 2011, Cooray et al. 2012). Recently Zemcov et al. (2014), using the Imager instrument of the Cosmic Infrared Background Experiment (CIBER), found in the auto-correlation spectra of the fluctuations at 1.1 and 1.6 $\mu$m evidence for an excess power at angular scales $l=\pi/\theta<5000$ (angular separations $\theta>4.3$ arcmin). When interpreted as diffuse light from galaxy clusters and groups (jointly called intra-halo light, IHL), the modeling (Cooray et al., 2012) of this fluctuation excess lead them to conclude that the IHL contributes to the mean EBL (i.e. the ’dc component’) at 1.1 and 1.6 $\mu$m 0.7 and 1.3 times as much light as the IGL from the galaxy counts. The interpretation has been challenged, however, by Yue, Ferrara, & Salvaterra (2016) and Mitchell-Wynne et al. (2016) who suggest that most of these observed large-angular-scale fluctuations are due to the foreground DGL.

We conclude that direct photometric measures, both in the UV (100 – 300 nm) and NIR ($1-5~{}\mu$m), are compatible with an extra EBL component beyond the IGL from the galaxy counts of roughly the same amount as the IGL itself. However, the the TeV gamma-ray absorption measurements, especially according to Biteau & Williams (2015), seem to exclude any substantial NIR excess (see Section 4.3 and Figs. 6 and 8) while they support an optical excess, such as found in the present paper.

4.5 Possible sources of background light from Milky Way halo and outside of galaxies

A survey for light sources that could explain the observed EBL excess over the integrated light of galaxies is presented in Appenxix B. Possible light sources that are known to exist include light from Milky Way halo, from the outskirts of galaxies, or from intergalactic stars in galaxy clusters and groups. The contribution of such light sources may in certain objects or environments be very substantial, e.g. the intergalactic stars contribute up to 40% of the luminosity of some clusters or groups. However, none of these sources are capable of explaining a substantial increase of the overall mean EBL beyond the IGL as derived from galaxy counts. Because of Lyman line and continuum absorption the redshift range of light sources contributing to sky brightness at $\lambda\la 450$ mm is limited to redshifts $z\la 3.5$. Contributions by primordial objects such as population III stars or direct–collapse black holes are thus excluded. Light from hypothetical decaying dark matter particles, such as axions, remains an open field.

5 Summary and conclusions

This paper is based on the results of Paper I (Mattila et al., 2017a) where we have presented in the area the high galactic latitude dark cloud L 1642 spectrophotometric surface brightness observations performed with VLT/FORS at ESO/Paranal. Spectra for several transparent sight-lines were observed differentially relative to the opaque core of the cloud. Because the transparent and opaque positions have been observed with exactly the same instrumental setup and in rapid time sequence no special requirements arised for absolute calibration accuracy. This is a decisive advantage as compared with those projects which derive the EBL as a (small) difference between two, $\sim$20 to 100 times larger, surface brightness signals measured by different telescopes and different techniques, requiring an extremely high absolute calibration accuracy, separately for each.

The dark cloud offers an opaque screen toward which the EBL is close to zero. However, it produces also a foreground component, the scattered light from the dust. This, the only, foreground contaminant is an order of magnitude weaker than Zodiacal Light and Integrated Starlight, the main contaminants in the EBL measurement methods of Bernstein et al. (2002a) and Matsuoka et al. (2011). We have accomplished the separation of the scattered light at the opaque position using the different spectral characteristics of the scattered Galactic starlight and the EBL spectrum. As template for the scattered starlight we have made use of the observed spectrum at semitransparent positions in the cloud.

The main results and conclusions of this paper can be summarized as follows:

(1) The EBL has been detected at 400 nm at 2.6$\sigma$ level. At 520 nm we have set a significant upper limit.

(2) The EBL value at 400 nm is

$2.9\pm 1.1$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*  +20%/-16%, or

$11.6\pm 4.4$ nW m*-2sr-1* +20%/-16% which is $\ga 2$ times as high as the IGL, even if possible contributions by galaxy halos to the IGL are included.

(3) The 2$\sigma$ upper limit to EBL at 520 nm is

$\leq 4.5$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*  +20%/-16%, or

$\leq$ 23.4 nW m*-2sr-1* +20%/-16%.

(4) Our EBL value at 400 nm is in good agreement with the indirect measurement via gamma-ray attenuation of blazars, presuming that the attenuation analysis has been performed, like in Biteau & Williams (2015), without a restrictive presupposed EBL spectral template form.

(5) No diffuse light sources, such as light from Milky Way halo, intra-cluster or intra-group stars, or from decaying elementary particles appear capable of explaining the observed EBL excess over the IGL.

Acknowledgements

This research has made use of the USNOFS Image and Catalogue Archive operated by the United States Naval Observatory, Flagstaff Station (http://www.nofs.navy.mil/data/fchpix/).

The Digitized Sky Surveys were produced at the Space Telescope Science Institute under U.S. Government grant NAG W-2166. The images of these surveys are based on photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope. The plates were processed into the present compressed digital form with the permission of these institutions. We thank Dr. Simon Driver for valuable comments concerning galaxy counts and photometry and the anonymous referee for useful comments of general nature. KM and KL acnowledge the support from the Research Council for Natural Sciences and Engineering (Finland); PV acnowledges the support from the National Research Foundation of South Africa.

Appendix A Synthetic model of the Integrated Starlight

Spectral synthesis is a common method in studies of stellar populations in external galaxies that are too distant to be resolved into individual stars (see e.g. Bruzual & Charlot 2003). We address the opposite problem: given the number densities and spatial distribution of the different types of stars and dust in the Solar neighbourhood what is the spectrum of the Integrated Starlight (ISL) in different directions of sky and for different vantage points of an observer off the Galactic plane. In addition to the ISL the Galactic surface brightness contains also the diffusely scattered starlight, the Diffuse Galactic Light (DGL). Since its spectrum is a copy of the ISL spectrum it does not influence the strengths of the spectral features (absorption lines, bands, discontinuities). Our calculation of the ISL spectrum between 370 and 600 nm follows the methods as presented in Mattila (1980a, b) with an update in Lehtinen & Mattila (2013).

A.1 Galaxy model and stellar distribution parameters

A simple model of the the Galactic structure is adopted in which stars and dust are distributed in plane parallel layers. The effect of clumpy dust distribution is taken into account. Stars have been divided into 72 spectral groups covering the different parts of the HR-diagram. The division has been made according to the approach of Flynn et al. (2006) based on their analysis of the Hipparcos data base666Drs. Flynn and Portinari kindly provided us with their results in detailed tabular form. The spectral groups are combined under the following seven categories (see Table A1): (i, ii) Main Sequence (thin and thick disk), (iii, iv) Clump Stars (thin and thick disk), (v, vi) Old Giants (thin and thick disk), (vii) Young Giants. For each group Table A1 gives the mean absolute magnitude, $M_{V}$, the number density, $D(0)$, and stellar emission coefficient, $j_{i}(0)$, in the Galactic plane, $z=0$, and the scale height $h_{z}$ for a distribution of the form $D(z)=D(0)$sech$(z/h_{z})$. Because of the limited distance range of Hipparcos its coverage for the supergiants was sparse. We complemented this part by using the compilation of Wainscoat et al. (1992).

A.2 Stellar spectral library

For the synthetic model of the 370 - 600 nm ISL spectrum we need a spectral library with good spectral type and wavelength coverage and a sufficient spectral resolution, corresponding to our observed spectra. The STELIB library (Le Borgne et al., 2003)777http://www.ast.obs-mip.fr/article181.html matches well these conditions. In order to choose the best template stars from the library for each of our stellar groups as given in Table A1 we have used besides the spectral classes and absolute magnitudes $M_{V}$ also the colour indices $B-V$ and $V-I_{c}$ as selection criteria. In most cases a satisfactory match was possible. The STELIB catalogue numbers are given in column 9 of Table A1.

A.3 Results

We have shown in Fig. 2 of Paper I the resulting ISL spectrum, mean over the sky, for an observer located at 85 pc off the Galactic plane, corresponding to the estimated $z$-distance of the L 1642 cloud. In Fig. A1 we compare this ISL spectrum with the observed mean spectrum for positions 9 and 42, $\Delta I(\lambda){\rm(Pos9/42-OFF)}$. At these positions the obscuration of the EBL is small and the spectral shape is only weakly influenced by dust. The observed spectrum is shown as black dots and the ISL model spectrum as the uppermost blue curve. It has been scaled by the factor $G_{\rm sca}(\lambda)=0.225[1-1.0\cdot 10^{-4}{\rm~{}nm^{-1}}(\lambda-500{\rm~{}nm})]$ (see equation (6)) to account for a slight bluening of the Pos9/42 spectrum w.r.t. the ISL spectrum. The OFF spectrum, calculated according to equation (7), is shown as the lower blue curve. The ON – OFF model fit, shown as the red curve, has been optimised for $\lambda>400$ nm. The Balmer line emission in the OFF areas is shown in red with baseline at zero. It can be seen that while the overall fit is good for $\lambda>400$ nm there is a substantial discrepancy with the 400 nm step size: this results in observed minus model values, shown as black line, deviating systematically upwards at $\lambda<400$ nm, i.e. the ISL model predicts a larger step at 400 nm than the observed one. Such a behaviour cannot be explained by an EBL contribution either: a residual EBL contribution would have an effect in the opposite direction.

Many of the ISL spectral structures, even at low levels, are recognized also in the scattered light spectrum. Notice, however, the emission line at 500.7 nm in the scattered light spectrum which is not present in the ISL; it originates from the all-sky ionized gas emission of [Oiii].

.

Appendix B Possible sources of EBL beyond galaxy counts: Milky Way halo, outskirts of galaxies,

low surface brightness galaxies, intergalactic stars, and decaying dark matter particles

B.1 Unresolved starlight and light from the Milky Way halo

Sky background light as seen by an observer inside the Galaxy contains contributions from unresolved stars, diffuse emission from gas, and scattered light from dust.

The light from unresolved stars in the $B$ band can be estimated by using the deep Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) starcounts in the F435W filter band ($\lambda_{c}=429.7$ nm) as presented by Windhorst et al. (2011) for the GOODS S field. At $m$(F435W) = 20 mag the number of stars is $\sim$equal to the galaxy numbers but, because of the shallow slope of the star counts $d(\log N(m))/dm\approx 0.065$, it drops at $m$(F435W)= 27 mag to $\sim$1% of the galaxy counts. Using this slope to extrapolate the star counts beyond 27 mag we find that the integrated starlight for $m$(F435W)$\geq 25$ mag amounts to $I_{\rm ISL}\approx 0.0034$ $10^{-9}$ erg cm*-2s-1sr-1Å-1* . The GOODS S field at $(l,b)$ = 224°, -54°is relatively close to the L 1642 field at $(l,b)$ = 210°, -37°. Taking into account the different line-of-sight lengths through the Galactic (roughly plane parallel) star layer we estimate that $I_{\rm ISL}$($B\geq$25 mag) $\approx 0.0045$ $10^{-9}$ erg cm*-2s-1sr-1Å-1*  towards L 1642 and can be neglected in the further discussion.

Extended far ultraviolet ($\lambda\approx 150-250$ nm) halos have been observed around several edge-on late-type galaxies out to 5–10 kpc from the mid-plane (e.g. NGC 891, NGC 5907; see Seon et al. 2014; Hodges-Kluck & Bregman 2014). They have been ascribed to thick dust disks that scatter light from stellar disks of the galaxies. The existence of substantial amounts of dust in the Milky Way halo at, say $|z|>2$ kpc, is not known. However, any such dust would be illuminated by an ISRF that has closely the same absorption line spectrum as the scattered light of the L 1642 cloud. Therefore, it will be largely eliminated by our spectral separation method as described in Section 2.

Gas emission from Milky Way halo is expected to be almost entirely in the form of line emission, mostly the hydrogen Balmer lines, plus a very weak continuum. They have been taken into account in the analysis as described in Section 2.1.3.

B.2 Light from the outskirts of galaxies

Not all light of a galaxy is captured by fixed aperture or Kron standard photometry. The light loss from the outskirts of galaxies, i.e. galaxy wings, may be only partially compensated for by corrections towards ’total’ magnitudes and this may lead to underestimates of the IGL. Totani et al. (2001) studied its influence via photometric modelling with reasonable assumptions on galaxy wings and other correction factors. They found that their ’best guess’ IGL from all galaxies in the Universe was up to 80% higher than the IGL from a simple integration of observed galaxy counts.

In a detailed analysis of the Hubble Space Telescope (HST) Deep Field (HDF) and their own EBL field Bernstein et al. (2002a, b) derived galaxy magnitudes using SExtractor Kron-type photometry with different Kron parameters $k=r/r_{iso}$ (their isophotal magnitudes varied from 24.7 to 25.8 ST mag arcsec*-2*.) They found that at least 20% of the flux of the faintest galaxies (i.e. within 4.5 mag of the detection limit) was contributed by galaxy wings at $r>1.4r_{iso}$. Furthermore, using a method called “ensemble photometry” they estimated that the true flux from $V>23$ AB mag galaxies in the HDF can be almost twice as much as that recovered by standard photometric methods. Benítez et al. (2004) analysed the faint galaxy population in two Early Release Science (ERS) fields of the HST ACS. They confirmed the claim of Bernstein et al. (2002a, b) of an up to 50% loss of light of the faintest galaxies.

The galaxy photometry used by Driver et al. (2016) for their IGL values in the optical bands is, at the faint end, based on the HST/ACS ERS and the Hubble Ultra Deep Field (HUDF) observations which are deeper than the HDF data used by Bernstein et al. (2002a, b) and are, therefore, less vulnerable to effects of galaxy wings. While both the ACS ERS (Windhorst et al., 2011) and the HUDF photometry made use of a larger Kron factor, $k=2.5$, than Bernstein et al. (2002a, b) the HUDF photometry was also otherwise designed to take better care of the galaxy-wing contribution. The galaxy counts from the two sets of data were in good agreement and agreed with the GAMA G10 data as well. This suggested that the galaxy wings do not have an effect of more than 20% on the faint galaxy fluxes used in Driver et al. (2016), and the effect is rather likely at $<10$% level (Driver 2016, private communication).

As a simple test of consistency and as test of aperture size effects regarding faint galaxy photometry, we downloaded the HUDF frames888https://archive.stsci.edu/prepds/udf/ and ran our SExtractor photometry mentioned in Section 4.1 over the $B$–band image. We did this in two ways, first with a standard setup using 2.5 for the Kron papameter, and then doubling it to 5.0, essentially doubling most elliptical aperture sizes. Other parameters were fixed, the background being estimated in a 24 pixel thick annulus outside the apertures. We do find, as e.g. Benítez et al. (2004) indicate, that many galaxies close to the detection limit become significantly brighter when using the larger apertures. However, the systematic effect in our simple test is not nearly as large as 50% for the light missed, but rather closer to 20%. Moreover, when summing up all the sources in the field over the whole detected magnitude range, the missing light fraction is only 6%.

Thus, while it well may be that significant amounts of light are missed in ’typical’ galaxy photometric techniques, it might be difficult to imagine that those surveys where specific care is taken against such effects could still miss more than, say, 20% of the the total light because of the galaxy outskirts. Moreover, an obvious counter-argument for large fractions of missing light at the outskirts of galaxies is the absence of large SN populations in these areas. From the results of Bartunov, Tsvetkov, & Pavlyuk (2007) one finds that only $\sim$5–7% of the total number of SN events occur at radii $r=(1.4-4)r_{25}$.

B.3 Low surface brightness galaxies

Galaxies with very low surface brightness (LSBG) could escape detection altogether in galaxy counts, or their total brightness be significantly underestimated even if detected, due to various selection effects (e.g. McGaugh 1994). Hence it is in principle possible that these galaxies could contribute significantly to EBL while not adding to the integrated galaxy counts, even by a factor of two or more if suitable populations are constructed (e.g. Väisänen 1996). However, though such galaxies exist (e.g. Malin 1, the most famous case, Impey & Bothun 1989), deep optical surveys (e.g. Driver et al. 2005) or using radio/21–cm HI surveys as pin-pointers (e.g. Doyle et al. 2005; Haynes et al. 2011) over the past two decades have failed to detect significant populations of field LSBGs. In rich clusters numerous LSBGs or ultra diffuse galaxies have recently been detected (e.g. Davies et al. 2015; van Dokkum et al. 2015; Koda et al. 2015) but their total contribution to the IGL remains small. The consensus appears to be that less than 20% of additional light is contributed by the LSBGs to the IGL (e.g. Driver 1999; Driver et al. 2005).

Note however that Disney et al. (2016) have recently argued that dim and/or dark galaxies might still be evading surveys if such galaxies were strongly clustered.

B.4 Intra-cluster and intra–group light

Intra–cluster (ICL) and intra–group light, sometimes collectively also referred to as Intra–Halo Light (IHL, Cooray et al. 2012), is a well established component among cosmic light sources. It originates from stars stripped off from galaxies in the cluster formation phase or in later interactions between galaxies or, perhaps, also from stars formed in situ in the intra-cluster gas (see e.g. Kapferer et al. 2010).

Diffuse light between the galaxies was first noted by Zwicky (1951) in deep photographs of the Coma Cluster. Wide-field CCD cameras have enabled deep surface brightness imaging of the intergalactic light in Coma (e.g. Adami et al. 2005), Virgo (e.g. Mihos et al. 2005; Rudick et al. 2010) and several other nearby and more distant clusters and galaxy groups (for a review see Mihos 2015).

The fraction of intra-cluster light of the total cluster luminosity varies between  15–40% for the nearby big clusters (Ciardullo et al., 2004). For clusters in the redshift range $z\sim$0.2–0.4 some studies (Burke, Hilton, & Collins, 2015) find that the ICL fractions are decreasing with redshift from $\sim$25 to $\la$5% while in others (Guennou et al., 2012; Presotto et al., 2014) the values are still high, $\sim$ 25%, or even higher (Adami et al., 2016). From six clusters at redshifts of $z\sim$0.8–1.2 Burke et al. (2012) find ICL fractions of $\sim$1–5%.

In galaxy groups the fraction of diffuse light varies even more strongly from undetectable in loose groups to $\sim$30–40% in many compact groups (see e.g. Da Rocha & Mendes de Oliveira 2005; White et al. 2003).

The intra-cluster SN events account for $\la 20\%$ of the SN rate for the clusters, in agreement with the estimates of the diffuse light fraction (Gal-Yam et al., 2003; Graham et al., 2015). For the intergalactic SN events in groups an upper limit of $\la 32$% has been set by the fraction of apparently hostless Type Ia SNe (McGee & Balogh, 2010).

Although the diffuse light fraction in individual clusters and dense groups may be high, up to 40%, it is important to remember that rich clusters contribute only a few percent of the total cosmic starlight while  80% of the light comes from individual field galaxies or loose groups, like the Local Group, with luminosities $<10^{11}L_{\sun}$ (Eke et al., 2005). Therefore, hardly more than 10% is added to the integrated galaxy light by the contributions from ICL and intra-group starlight.

B.5 Other sources of diffuse light

Because of Lyman line and continuum absorption the redshift range of light sources contributing to sky brightness at $\lambda\la 450$ mm is limited to $z\la 3.5$. Contributions by primordial objects such as population III stars or direct collapse black holes are thus excluded.

Decaying or annihilating dark matter candidate particles, such as neutrinos, WIMPs and axions, have been proposed as possible sources of diffuse background radiation fields. On the other side, the EBL might qualify as an important discovery channel for the elusive dark matter particles; for a review see Overduin & Wesson (2004, 2008) and the update in Henry et al. (2015). Recently, Gong et al. (2016) have discussed the possibility that the NIR background fluctuations could partly originate from decaying axions with mass around 4 eV, located mainly in the halos of clusters and groups. None of the three particle species have been found to produce enough radiation to qualify as serious contributor to the mean intensity of the EBL in UV (Henry et al., 2015), optical or NIR (Gong et al., 2016) domain. Furthermore, axions and WIMPS should be strongly concentrated to the dark matter halos of clusters, groups and individual galaxies. Even if some part of the diffuse intra-cluster, intra-group or galaxy halo diffuse light were caused by decaying particles, instead of stars, this would not change the amount of diffuse light as determined by the observations. Only a smoothly distributed diffuse light component, present also in the general field outside the clusters, could have escaped the observations.