WHAT IS THE PHYSICAL ORIGIN OF STRONG Lyα EMISSION? I. DEMOGRAPHICS OF Lyα EMITTER STRUCTURES^*

In order to search for UV and optical counterparts of our LAEs, we first extract 3'' × 3'' cutout images from the I₈₁₄ and H₁₆₀ data at the position of each LAE in a manner similar to previous morphological studies (Bond et al. 2009, 2010, 2012; Gronwall et al. 2011). The size of the cutouts is exactly the same as in Bond et al. (2012), who have studied the morphology of z = 2.1 LAEs. In total, we obtain 942 and 297 cutout images of the I₈₁₄ and H₁₆₀ bands, respectively.

Next, we detect sources in the HST cutout images and perform photometry for all of the sources having an area larger than five contiguous pixels (DETECT_MINAREA =5) with a flux greater than 2.5σ over the sky surface brightness (DETECT_THRESH =2.5) using SExtractor version 2.8.6 (Bertin & Arnouts 1996). Our DETECT_THRESH value is higher than that in Bond et al. (2012,  ; DETECT_THRESH =1.65). Because one of our aims is to estimate the merger fraction from the number of close galaxy pairs (Section 3.2.1), a reliable detection of objects is required even for very faint sources. If a low DETECT_THRESH value is chosen, then false detections increase, leading to an overestimate of the merger fraction. Here, we tune a DETECT_THRESH parameter to identify real galaxy pairs by visual inspection. Meanwhile, DETECT_THRESH is set to 1.65 instead of 2.5 when we derive the morphological indices for counterparts of LAEs in Section 3.2.2.

Finally, we define the I₈₁₄ and H₁₆₀ counterparts of LAEs as objects within a radius of 065 (∼5.4 kpc at z = 2.2) from an NB source center, following the definition of Bond et al. (2012). According to the assessment by Bond et al. (2012), this selection radius can effectively exclude field sources. Figure 1 shows the Lyα EW and I₈₁₄/H₁₆₀ magnitudes of the counterparts. Figure 1 reproduces the Ando effect (Ando et al. 2006) that Lyα EW anti-correlates with continuum magnitudes. We adopt a continuum magnitude cut of 26.5 mag, and derive the average I₈₁₄/H₁₆₀ magnitudes in each Lyα EW bin of 20–50, 50–100, and >100 Å. These average values are almost constant within a 1σ error bar between the EW bins. In our analyses, we only use objects with a continuum brighter than 26.5 mag.

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We estimate the merger fraction of our LAE sample using two methods, the close-pair method (Section 3.2.1) and the morphological index method (Section 3.2.2). The former is used to count the number of resolved sources falling within a specific selection radius. The latter is used to classify mergers with the non-parametric morphological indices, CAS (Conselice et al. 2000; Conselice 2003), for the sources that are unresolved in the close-pair method. In a merger process, galaxies first approach each other, and then undergo coalescence(s). The close-pair method selects merger objects in the approaching phase, and the index method identifies the final coalescence phase. In calculations of morphological indices, all of the sources in a selection radius are usually considered to be a galaxy system, even if they are clearly isolated. Using the morphological indices, we aim to examine whether unresolved single sources are interacting (correspondingly morphologically disturbed) galaxies or intrinsically isolated components. The classification with the morphological indices is complementary to the close-pair method which identifies mergers with discrete components.

3.2.1. Close-pair Method

The close-pair method has been used to identify mergers at low- (e.g., Ellison et al. 2013; Le Fèvre et al. 2000) and high-z (e.g., Law et al. 2012b). It is extremely difficult to detect the faint components of minor mergers at high-z. In our analysis, we consider only major mergers with multiple components of comparable flux (a flux ratio of 0.3–1). By counting the number of sources within the selection radius, r_sel = 065 (Section 3.1), we simply define (major) mergers as counterparts with multiple sources. Figure 2 shows representative examples of a merger and a non-merger classified with the close-pair method.

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We carry out Monte Carlo simulations with artificial galaxy pairs to estimate the detection completeness of major mergers. We consider two cases of flux ratios in major merger components, 0.3–1 and 0.5–1. We create 100 galaxy pairs with GALLIST and MKOBJECTS in the IRAF package in bins of I₈₁₄/ H₁₆₀ magnitudes. In this procedure, we make these artificial galaxies at a redshift and do not take into account the distance along the line of sight between components. This is because we aim to simply estimate the detection completeness of the fainter component as a function of HST-band magnitudes. On the other hand, our selection radius efficiently finds intrinsically interacting objects, minimizing the chance projection rate of ∼10% (see Bond et al. 2012). The created galaxy pairs are embedded into cutout images of randomly selected blank fields. We detect these pairs in the same manner as for LAEs.

The estimated completeness is shown in Figure 3. The artificial merger events with a flux ratio of 0.5–1 are reproduced well for pairs brighter than 26.5 mag in I₈₁₄ (>50%). The completeness in H₁₆₀ is approximately half of that in I₈₁₄ at 26.0–26.5 mag. This leads to the difference of derived merger fractions in I₈₁₄ and H₁₆₀ in Section 4.1. In the case of the mergers with a flux ratio of 0.3–1, the completeness is only ∼50% even at <24 mag in I₈₁₄/H₁₆₀. This is because the magnitudes are severely underestimated for fainter components in the 0.3:1 merger.

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As a result, we use 426 and 237 LAEs brighter than 26.5 mag in I₈₁₄ and H₁₆₀, respectively, in the close-pair method. Table 2 summarizes the numbers of the LAEs used, including those in the following analyses. We provide the derived merger fraction and its dependence on Lyα EW in Section 4.1.

Table 2. Number of Our Lyα Emitters for Each Analysis

Quantity	Criteria	Number of LAEs
(1)	(2)	(3)
Merger fraction	(I814 < 26.5)	426
	(H160 < 26.5)	237
Lyα spatial offset	(NB387 <24.5 & I814 < 26.5)	106
	(NB387 <24.5 & H160 < 26.5)	40
Ellipticity	(I814 < 25.0 & Re > 009)	41
	(H160 < 25.0 & Re > 018)	35

Notes. Columns: (1) Quantity. (2) Magnitude and size cuts applied in each investigation. (3) Number of LAEs.

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3.2.2. Morphological Index Method

The non-parametric morphological indices have been widely utilized to characterize the structure and morphology of nearby and high-z galaxies (e.g., Cassata et al. 2007; Zamojski et al. 2007; Scarlata et al. 2007).

The CAS system consists of the concentration (C), asymmetry (A), and smoothness (S) proposed by Abraham et al. (1996), Conselice et al. (2000), and Conselice (2003). Concentration C is an index representing how much the flux concentrates in the galaxy's center. We calculate C using the definition of Conselice (2003), C = 5log (r₈₀/r₂₀), where r₈₀ and r₂₀ are the radii which contain 80% and 20% of the total flux of the galaxy, respectively. Asymmetry A quantifies the degree of the rotational symmetry of the galaxy's light profile. It is calculated by

$$\begin{equation} A \equiv A_{\rm obj} - A_{\rm sky} = \frac{\Sigma | F - F_{180}|}{\Sigma |F|} - \frac{\Sigma | B - B_{180}|}{\Sigma |B|}, \end{equation} \tag{ 1 }$$

where F and F₁₈₀ (B and B₁₈₀) are the original image of the galaxy (sky background) and its image rotated by 180° around the galaxy's center, respectively. The value of A ranges from zero to one. Asymmetry becomes zero for a galaxy with a completely rotationally symmetric light profile. The first term in the definition of A is the asymmetry of a galaxy. The second term is the apparent asymmetry caused by the sky background. We use average values of A_sky as representative of A_sky in each field (e.g., Scarlata et al. 2007). Both A_obj and A_sky are computed by using all pixels contained within a 1.5 Petrosian radius of a targeted galaxy (Petrosian 1976). The rotational center is defined as the position minimizing A in the 3 × 3 grid searching method (Conselice et al. 2000). The determined rotational center is also applied to the calculation of C. Since smoothness S cannot be correctly calculated for high-z galaxies (Lotz et al. 2004; Conselice & Arnold 2009), we do not use S in our analysis.

To check the adequacy of our calculation, we compute CA for other galaxies whose morphological indices have already been derived in previous studies. Cassata et al. (2007) calculated the indices for ∼23, 000 galaxies at low-z in the COSMOS-Wide field. From their sample, we extract 300 galaxies whose I₈₁₄ magnitudes are comparable to those of our LAEs and calculate their CA. Our calculation reproduces well the results of Cassata et al. (2007). We apply the 1σ standard deviation from the CA values obtained in Cassata et al. (2007) to the errors of the derived indices for our LAE sample.

The morphological indices cannot be robustly calculated for objects with a low signal-to-noise ratio (e.g., Cassata et al. 2007). To obtain reliable values of the indices, we use LAEs with I₈₁₄ and H₁₆₀ magnitudes brighter than 25.0 mag in our CA calculation. The magnitude cut of 25.0 mag has usually been applied in previous morphological studies with HST data (e.g., Cassata et al. 2007). We also exclude objects whose half light radii in I₈₁₄ and H₁₆₀ are smaller than 009 and 018, which are unresolved with ACS and WFC3, respectively. We use 41 in I₈₁₄ and 35 LAEs in H₁₆₀, respectively, that meet all of these selection criteria. Representative examples of objects with high and low A values are shown in Figure 2. The calculated morphological indices of our LAE sample are shown in Figure 4. The distributions of indices in these parameter spaces are quite similar to the results of Lyman break galaxies (LBGs) at z ∼ 2–3 (e.g., Law et al. 2012b).

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In order to classify mergers, we adopt the following criterion,

$$\begin{equation} A > 0.30, \end{equation} \tag{ 2 }$$

which is defined by Lotz et al. (2008) for high-z galaxies. We do not use the C parameter for the merger classification, but we make the C–A diagram simply for the sake of clarity (Figure 4).

In the A classification, we identify mergers that are brighter than a specific MAG_APER magnitude (MAG_APER cut) in addition to the MAG_AUTO cut. The MAG_AUTO cut mistakenly selects objects with extremely low surface brightness. The asymmetry parameter might be overestimated for these objects due to their diffuse structure. We also derive the merger fraction for the sample selected in the MAG_APER cut to eliminate the diffuse objects. We use a 03 aperture to calculate MAG_APER. The number of selected counterparts significantly decreases, especially in the H₁₆₀ data. Even in this case, we find a similar trend of Lyα EW dependence as in the MAG_AUTO cut.

We discuss the merger fraction based on the index classification in Section 4.1.

We calculate the projected distance between the rest-frame UV/optical continuum positions and the centroids of Lyα emission. In this calculation, we consider two types of components in stellar-continuum emission. One type is the brightest components in all of the sources within the selection radius, and the other type is the nearest ones from Lyα centroids among objects identified in our detection criteria of SExtractor (the top panel of Figure 5). The central position of each HST cutout image corresponds to Lyα centroids. We calculate δ_Lyα from the coordinates of sources in the cutout images.

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We find that the Lyα centroids are slightly shifted in toward the extended and diffuse light structure in several NB images, as shown in the top panel of Figure 5. The central position of LAEs has been determined by performing source detection with SExtractor in whole ∼30' × 30' Suprime-Cam images (Nakajima et al. 2012; the magenta cross). The small positional offsets of Lyα are certainly caused by setting DETECT_THRESH to a relatively low value (2.0σ) for the LAE selection in the wide images. They have used a typical value of DETECT_THRESH in selections for high-z galaxies. That value is too low to estimate the peak position of Lyα.

In order to estimate the peak position of Lyα, we carry out the source detection with a higher DETECT_THRESH value (2.5σ) in each NB cutout image than the value used in the NB selection. This procedure is very efficient for calculating the Lyα spatial offset from the position where Lyα is emitted most efficiently. This position corresponds to the location where the galaxy is brightest in Lyα. In the re-detection process, NB centroids are slightly shifted for several objects and we obtain redefined values of δ_Lyα. We adopt the original centroids for objects with a Lyα positional difference smaller than 01 corresponding to ∼0.5 pixel in NB images.

We create artificial galaxies to estimate positional errors using the same method as described in Section 3.2.1. Figures 6 and 7 show the estimated positional errors of the I₈₁₄/H₁₆₀ and NB387 images, respectively. These figures indicate that the positional uncertainties tend to be larger for fainter objects. In the HST images, the positional error is less than ∼ ± 002 at I₈₁₄/H₁₆₀ magnitudes brighter than 26.5. In contrast, the NB387 images have a large positional error of ∼03 (at 1σ) even at NB387 =24.5. This large uncertainty is due to the relatively large seeing sizes (∼08) in the NB data obtained by ground-based observations.

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To obtain reliable Lyα spatial offsets, we use objects with I₈₁₄/H₁₆₀ < 26.5 and NB387 <24.5 in this analysis. In this case, 106 and 40 LAEs are selected in I₈₁₄ and H₁₆₀, respectively. Moreover, no systematic error in the simulation ensures a statistical investigation of the Lyα spatial offset. NB387 and I₈₁₄ images of example galaxies are shown in Figure 5. We provide the dependence of δ_Lyα on Lyα EW in Section 4.2.

We measure the ellipticity of the counterparts in I₈₁₄/H₁₆₀ using the GALFIT software (Peng et al. 2002, 2010). The ellipticity is defined as = 1 − b/a, where a and b are the major and minor axes, respectively. The ellipticity is calculated for both the brightest and nearest components in the same manner as in Section 3.3. In this calculation, we use objects whose I₈₁₄/H₁₆₀ magnitudes are brighter than 25.0 and whose half light radii are larger than the typical PSF sizes of each band.

The profile fittings are performed in a manner similar to Gronwall et al. (2011). The counterparts are fitted to a Sérsic profile. Some initial parameters are needed in the GALFIT fitting. The coordinates (x_c, y_c), total magnitude m, axis ratio q(= b/a), position angle, and half light radius r_e of each counterpart are input into the GALFIT configuration file as initial parameters. These initial parameters are estimated with SExtractor prior to the GALFIT fitting. The Sérsic index is set to n = 4 (i.e., de Vaucouleurs profile) as an initial value, while the initial Sérsic index does not affect the fitting results (Yuma et al. 2011, 2012). In the fitting procedure, we also allow the following parameters to move in ranges: 24 < m < 29, 0.1 < r_e < 15 pixels, 0.1 < n < 15, 0.1 < q < 1, Δx < 2, and Δy < 2. We create PSF images for I₈₁₄ and H₁₆₀ data by stacking 100 bright isolated point sources. GALFIT outputs best-fit parameters corrected for PSF broadening. Figure 8 shows examples of original I₈₁₄ images, the best-fit Sérsic profiles, and their residual images. As shown in Figure 8, the GALFIT fits the stellar-continuum emission to Sérsic profiles well.

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We provide the dependence of ellipticity on Lyα EW in Section 4.3.

We first compare the merger fractions of the entire sample with results from previous studies for LAEs at z ∼ 2–6. The merger fractions in I₈₁₄ and H₁₆₀ are 0.23 ± 0.02 and 0.14 ± 0.02, respectively, in the close-pair method. These values are broadly consistent with other studies using similar methods (e.g., Taniguchi et al. 2009; Pirzkal et al. 2007; Cowie et al. 2010; Bond et al. 2009). Pirzkal et al. (2007) investigated the rest-frame UV morphologies of nine LAEs at 4 ≲ z ≲ 5.7 based on the C–A classification. They find that ∼30%–40% of the sample show clumpy, complex, or morphologically disturbed structures. Taniguchi et al. (2009) determine that only two out of ∼50 LAEs at z = 5.7 have double-component structures, and ∼50% of the sample are spatially extended in the rest-frame UV. Bond et al. (2009) determine that at least ∼17% of their 120 LAEs at z = 3.1 have multiple components. Cowie et al. (2010) claim that >30% of z ∼ 0.3 LAEs show merger features. Theoretically, the dark matter simulation combined with the physical model of Tilvi et al. (2011) predicts that the merger fraction of z ∼ 3 LAEs is ∼0.20 after matching the merger mass ratio with that of observational studies. Our merger fractions are also nearly the same as those of LBGs at 1.5 ≲ z ≲ 3 estimated with the close-pair method (∼0.05–0.2; Law et al. 2012b). Our merger fractions in the A classification are also similar to those of their LBG sample estimated with the same method.

Next, we examine the dependence of the merger fraction on Lyα EW. Figure 9 shows the derived merger fractions in each EW(Lyα) bin. The error bars in each plot include the Poisson statistical errors. We find that the merger fraction does not significantly increase with Lyα EW in all cases. Instead, merger fractions decrease from the lowest to the highest EW bin over the 1σ error bars in several cases. The merger fractions in H₁₆₀ are a factor of ∼2–3 lower than those in I₈₁₄ in the corresponding methods. This is likely to be caused by the difference in completeness (Section 3.2.1). In addition to the completeness effect, the difference of the merger fractions could be explained by the shapes of the SEDs, since the I₈₁₄- and H₁₆₀-band data trace the rest-frame UV and optical stellar continuum emission, respectively. We also examine the total merger fraction derived in combination with the close-pair and morphological index methods. We define the total merger fraction as the logical sum of mergers identified by the close-pair method and A classification. However, we do not find the increase of the merger fraction with EW(Lyα), similar to Figure 9. We additionally calculate the Lyα EW from the total magnitudes in the NB data, and evaluate the effect of the Lyα flux loss in the aperture photometry on the Lyα dependence. We compute the total magnitudes with MAG_AUTO of SExtractor. Even in this test, we still do not find the trend that the merger fraction increases with Lyα EW.

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We change the selection radius to r_sel = 15 (∼13 kpc at z = 2.2) in order to check possible differences in the merger fraction between the searching radii. The 15 radius is the same as that used in Law et al. (2012b). However, we do not find a significant rise of merger fraction even in the larger radius. The merger fractions with r_sel = 15 are a factor of ∼2 higher than those with r_sel = 065. Adopting the 15 aperture, the merger fractions increase to 0.35 ± 0.03 in I₈₁₄ and 0.30  ±  0.03 in H₁₆₀. We confirm that the trend of Figure 9 is also found in the results of the r_sel = 15 aperture.

The dependence of the merger fraction on the Lyα EW is also clearly shown in Figure 10. The figure illustrates a trend where objects with a larger Lyα EW have a smaller half light radius, as claimed by, e.g., Law et al. (2012a) and Pentericci et al. (2010), which is also justified by our statistical tests. The individual LAEs identified in the close-pair method are marked by the black circles. Figure 10 clearly exhibits the small number of mergers at EW(Lyα) > 100 Å. Note that the decline in the merger fraction in high EW(Lyα) bins is caused by many incomplete detections of fainter merger components in LAEs with a high EW. Our magnitude cut of 26.5 mag ensures that there is no bias in the I₈₁₄/H₁₆₀ magnitudes between EW bins (Figure 1). The merger completeness is considered to be almost constant in all of the EW bins.

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We investigate the δ_Lyα of the Lyα spatial offset and examine whether δ_Lyα is produced by measurement errors or a real signal. Figure 11 shows δ_Lyα as a function of NB387 magnitude. We include statistical errors estimated from the Monte Carlo simulation (Section 3.3) in δ_Lyα. We find a tendency that the error in δ_Lyα becomes larger for the objects with a fainter NB387 magnitude, but successfully identify that several LAEs have an offset beyond our statistical errors for relatively bright objects. The identification of the large δ_Lyα objects could not be due to large scatters in δ_Lyα, which is justified by our non-parametric Kolmogorov–Smirnov (K-S) tests between the LAEs and artificial galaxies in each NB387 magnitude bin. The K-S probabilities are calculated to be P_KS ≲ 0.05.

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Next, we investigate the dependence of δ_Lyα on Lyα EW for the brightest continuum sources in Figure 12 and the nearest ones in Figure 13. We find that there are few LAEs with a high EW and a large δ_Lyα. LAEs with a high Lyα EW tend to have a single continuum counterpart, as described in Section 4.1. The distribution of δ_Lyα for high EW objects does not depend strongly on whether we use the brightest or the nearest continuum counterparts.

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We carry out the K-S test in order to evaluate whether δ_Lyα is statistically related to Lyα EW. We calculate the K-S probability that LAEs with Lyα EW >100 Å and <100 Å are drawn from the statistically same distribution of the Lyα spatial offset. We summarize the K-S probabilities, P_KS, in Table 3. The P_KS values are 0.05–0.1 in the case of the original Lyα centroid. In the I₈₁₄ data, the low P_KS values indicate that the two groups of δ_Lyα are drawn from statistically different distribution. Even in the case of the redefined values of δ_Lyα, the probabilities are not significantly changed (P_KS ∼ 0.1–0.3).

We show the ellipticities of the brightest and nearest continuum objects in Figures 14 and 15, respectively. The average ellipticity of LAEs with EW(Lyα) > 100 Å is smaller than that of objects with EW(Lyα) < 100 Å. There is a possible trend that the LAEs with a large Lyα EW have a small ellipticity for both the brightest and nearest components. The right panel of each figure displays histograms of the ellipticity. The ellipticity distribution is quite similar to that estimated by Gronwall et al. (2011), who have studied the morphologies of LAEs at similar redshift.

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We calculate the K-S probability for the ellipticity in a similar manner as for the Lyα spatial offset in Section 4.2. The probabilities are listed in Table 3. The probabilities are calculated to be 0.5–0.6 in the I₈₁₄ data. The high values indicate that LAEs with Lyα EW >100 Å and <100 Å have statistically indistinguishable distributions. These probabilities suggest that the dependence of ellipticity on Lyα EW cannot be concluded in a statistical sense. The small sample size of LAEs with EW(Lyα) > 100 Å may not allow us to obtain accurate K-S probabilities.

In Section 4.1, we find that the merger fraction of LAEs does not significantly increase with their Lyα EW. Instead, Figure 9 shows the merger fraction decreases from EW(Lyα) = 20–100 to >100 Å. However, our statistical analysis indicates that mergers are rare in the subsample of LAEs with a Lyα EW larger than 100 Å. Our result would suggest that the galaxy merger does not heavily affect the distribution of H i gas and dust. On the contrary, the H i clouds disturbed by a merger would envelop a central ionizing source instead of making holes in the gas shell. The nearly uniform clouds might prevent Lyα photons from easily escaping from a galaxy.

This is opposite to the trend where Lyα emission is enhanced by a galaxy merger. Several observational studies have examined a relationship between Lyα EW and galaxy merger in the LAE population. For example, Cooke et al. (2010) and Chonis et al. (2013) claim that Lyα emission is enhanced by galaxy mergers. This trend is commonly based on the idea that a galaxy interaction triggers star formation, and disperses obscuring gas and dust in the system (e.g., Chonis et al. 2013).

Cooke et al. (2010) carry out spectroscopic observations for 140 LBGs at z ∼ 3 and find serendipitously five LBG pairs with projected proper separations of less than 15 kpc. They additionally discover two LAEs with a close LBG in their MOS slitlets. One of these LAEs has a Lyα EW of 48 Å. The separation between the LAE and its LBG companion is 22.7 kpc. Another LAE has a Lyα EW of 140 Å, but its LBG companion is not definitively confirmed by spectroscopy. This merger candidate has a relatively large projected separation of 40.1 kpc between its components. In this survey, only one object with such a high EW has been found in the seven serendipitously discovered close pairs (∼14%) if the LAE with EW(Lyα) = 140 Å is a genuine merger.

Recently, Chonis et al. (2013) investigated three LAEs in the HETDEX sample. The Lyα EW of all the three LAEs exceeds 100 Å (114 ± 13, 140  ±  43, and 206 ± 65 Å) due to a unique LAE selection method of the HETDEX survey (Adams et al. 2011). In the HST images, two LAEs with EW(Lyα) = 114 and 140 Å show close components with projected separations of ∼5 and 8 kpc, respectively. One of these close components has also been spectroscopically confirmed to be at the same redshift as its central LAE. The LAE with the highest EW of 206 Å does not have a companion within 1'' (∼8.2 kpc).⁷ Thus, the merger fraction at EW(Lyα) > 100 Å is $0.67^{+0.33}_{-0.43}$ in their HETDEX sample. The error is due to the small number statistics (Gehrels 1986). Our merger fraction at EW(Lyα) > 100 is 0.23 ± 0.08 in I₈₁₄ in a searching radius of 15 (∼13 kpc) similar to that of Chonis et al. (2013). The merger fractions are consistent within 1σ uncertainties. In the study of Chonis et al. (2013), the merger fraction at EW(Lyα) > 100 Å probably becomes higher due to the small number of sample objects.

In contrast to these suggestions, some morphological studies provide results that are consistent with our Lyα dependence. Law et al. (2007) have investigated the morphologies of 216 z ∼ 2–3 LBGs with spectroscopic redshifts using the HST data. They quantify a multiplicity of a galaxy with the multiplicity parameter Ψ. The value of Ψ is zero for a galaxy with a single component and becomes positive for a galaxy with multiple components. This parameter is used to find multiple components, which is similar to our close-pair method. They reveal that the Lyα EW monotonically increases from 0 to 15 Å with decreasing Ψ. This trend is consistent with the behavior of our merger fractions in the EW range of 20–200 Å, which is larger than the EW range of Law et al. (2007). Pentericci et al. (2010) have measured the asymmetry parameter for z ∼ 3 LBGs with and without Lyα emission. They find no difference of A between LBGs with a high and a low EW. The decrease in the merger fraction for our LAEs might be found in the wider dynamic range in EW(Lyα) than that of their LBG sample.

Another explanation is that dust created by past star-formation in individual pre-mergers produces the anti-correlation between Lyα EW and merger fraction. The star formation triggered by a major merger would enhance Lyα emission, but Lyα photons could be absorbed by the dust already existing in individual evolved galaxies. For this reason, Lyα EW would be less enhanced in a system consisting of evolved major merger components, which would yield the anti-correlation.

In addition to observational studies, Yajima et al. (2013) have investigated the physical properties of interacting Lyα Blob (LAB) pairs by combining hydrodynamical simulations with three-dimensional radiative transfer calculations. The star formation rate (SFR) of LABs is boosted during each galaxy-coalescence phase. In contrast to SFR, Lyα EW fluctuates in the range of 20–100 Å, and is not enhanced to >100 Å even at the time of coalescences. Note that the simulated LABs have a larger size and slightly brighter Lyα luminosity than those of our normal LAEs.

There is a possibility that the anti-correlation between the merger fraction and Lyα EW could be produced by a difference of viewing angle. In this study, we have defined mergers as objects with multi-components or interacting features shown in the plane of the sky. However, mergers along the line of sight would boost the radial velocity of the surrounding gas clouds, and consequently enhance the Lyα escape in the direction of the observer. The detection of the line-of-sight mergers could be more challenging than the identification of interacting events shown in the plane of the sky.

We find that there are few LAEs with a high Lyα EW and a large δ_Lyα. The dependence of δ_Lyα on Lyα EW would suggest that Lyα photons could be heavily attenuated by dust on the long path lengths prior to escaping an H i cloud. This might yield a δ_Lyα difference in objects with a high and a low Lyα EW.

Prior to our statistical study, several NB imaging studies have also estimated δ_Lyα for high-z LAEs. Jiang et al. (2013) have studied rest-frame UV morphologies of 51 LAEs at z ∼ 5.7, 6.5, and 7.0 using the HST data. The Lyα positions of these LAEs have been estimated in NB images taken with Subaru/Suprime-Cam. They find that several LAEs show evidence of positional offset between UV and Lyα emission. In these z ∼ 6–7 LAE samples, LAEs with a spatially symmetric light profile tend to have a small δ_Lyα. The offset is also shown in an extended Lyα emission, Himiko, at z = 6.595 (Ouchi et al. 2013). Rauch et al. (2011) find a large positional offset in a galaxy at z = 3.334 based on a deep spectroscopic survey. For the z = 3.334 galaxy, the Lyα and UV structure is highly peculiar and is likely to be affected by several physical processes, such as cold gas inflow.

In contrast, most of these LAEs with a large δ_Lyα show merger and/or interacting features. Finkelstein et al. (2011) have performed high resolution imaging observations with an NB filter on HST for three LAEs at z = 4.4. They do not find positional offsets between resolved Lyα and UV continuum emission. All three LAEs observed with HST also show no evidence of major merger/galaxy interactions.

These results would indicate that the relatively small δ_Lyα in high EW objects originates from physically stable and spatially symmetric H i gas clouds around a central ionizing source(s). On the contrary, the large δ_Lyα could result from inhomogeneous H i gas clouds disturbed by a merger. The disturbed clouds prevent Lyα radiation from escaping directly along the line of sight, making a large δ_Lyα from an original position of the stellar component. A large number for resonant scattering would suppress Lyα EW on the long path lengths in the disturbed clouds.

We find that there is a trend where the LAEs with a large Lyα EW have a small ellipticity. Figures 14 and 15 show a possible absence of objects at a high ellipticity and Lyα EW region (in the upper right corner in the figures). This trend is consistent with the recent theoretical claims that Lyα photons can more easily escape from face-on disks having a small ellipticity due to a low H i column density (e.g., Verhamme et al. 2012; Yajima et al. 2012b).

The ellipticity is a useful indicator of the galactic disk inclination. Verhamme et al. (2012) have investigated quantitatively the effect using their Lyα radiative transfer code combined with hydrodynamics simulations. They find that the Lyα EW strongly depends on the inclination for a simulated galaxy with thick star-forming clouds. From edge-on to face-on, the Lyα EW increases from −5 to 90 Å. Yajima et al. (2012b) have predicted that the Lyα flux is 100 times brighter in the face-on direction than the edge-on.

However, our K-S test does not definitively indicate that there is an anti-correlation between Lyα EW and the ellipticity (Section 4.3). The sample size of our high EW LAEs may be too small to obtain conclusive evidence of the anti-correlation. We require a larger LAE sample containing many high EW (>100 Å) objects bright (m_cont < 25) enough to measure robustly their morphologies.

Our results for Lyα EW dependence generally support the idea that an H i column density is a key quantity determining Lyα emissivity. We find that LAEs with EW(Lyα) > 100 Å tend to be a non-merger (Section 4.1) and compact (Figure 10), and to have a small ellipticity (Section 4.3) in our structure analyses. Our magnitude cut allows us to fairly compare structural properties between each EW(Lyα) bin under the same ranges of galaxy-luminosity-correlating mass (Figure 1). We also verify the above trends by using objects with a similar size, but we do not find any significant changes. These results could attribute the EW(Lyα) dependences on the LAE structures to predominantly Lyα emissivity rather than the galaxy mass. These trends do not depend strongly on whether we use the brightest or nearest counterparts.

Recent spectroscopic studies measure the Lyα velocity offset, Δv_Lyα, from the systemic redshift estimated from nebular lines for a number of LAEs (Hashimoto et al. 2013; Shibuya et al. 2014). Their kinematic analyses have suggested that LAEs typically have a smaller Δv_Lyα than that of LBGs with a lower Lyα EW, while their outflowing velocities are similar in the two populations. This indicates that the small Δv_Lyα of LAEs is caused by a low H i column density. On the other hand, NIR spectroscopy by Nakajima et al. (2013) has suggested that LAEs have a large [O iii]/[O ii] ratio, indicating that these systems are highly ionized with density-bounded H ii regions. This tendency has been confirmed by a subsequent systematic study in Nakajima & Ouchi (2013). The large [O iii]/[O ii] ratio also indicates a low column density of H i gas. Based on these results for the gas distribution and abundances, the difference in H i column density simply explains the Lyα-EW dependences of the merger fraction, the Lyα spatial offset, and the galaxy inclination. For objects with density-bounded H ii regions, Lyα photons would directly escape from central ionizing sources which produce a small δ_Lyα. The low H i abundance along the line of sight also induces the preferential escape of Lyα to the face-on direction. For these reasons, ionized regions with small amounts of H i gas would dominate in the subsample of our LAEs with EW > 100 Å.