CATALOG OF NARROW Mg II ABSORPTION LINES IN THE BARYON OSCILLATION SPECTROSCOPIC SURVEY

The BOSS project (Dawson et al. 2013) of SDSS-III (Eisenstein et al. 2011) contains 87,822 unique quasar spectra in its ninth data release (DR9Q; Pâris et al. 2012), which does not contain quasars from previous SDSS quasar catalog. The project uses upgraded versions of the SDSS spectrographs (Smee et al. 2012) mounted on the Sloan 2.5 m telescope (Gunn et al. 2006) at Apache Point, New Mexico. The spectra are taken through 2'' diameter fibers and cover a wavelength range from 3600 to 10400 Å with a resolution of R ∼ 2000 and a dispersion of 69 km s⁻¹ pixel⁻¹. The green histogram in Figure 1 shows the distribution of the emission line redshifts of the DR9Q sample. BOSS is designed to target z > 2.15 quasars, as shown in Figure 1. The two peaks at z ∼ 0.8 and z ∼ 2.2 are due to known degeneracies in the SDSS color space. The DR9Q catalog contains about 2.6 times more high-redshift quasars than the whole SDSS-I/II survey (seventh data release, DR7; Schneider et al. 2010), which provides us an excellent data set for searching Mg ii absorption doublets in the redshift range 0.3 ≲ z ≲ 2.6.

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The criteria used to select the quasar sample and the surveyed spectral region used in our analysis are the following.

• 1.  
  Surveyed spectral region. The spectral region shortwards of the Lyα emission line is dominated by Lyα forest absorption. Thus, in order to avoid the influence of Lyα absorption, we conservatively give up the spectral data shortwards of 1250 Å at quasar rest frame. This leads to quasars with z_em > 0.2. The Mg ii absorbers with z_abs ∼ z_em are likely physically related to the background quasars and can be blueshifted or redshifted by the motion of the absorbing gas clouds within the quasar system (Lü et al. 2007; Vanden Berk et al. 2008; Pan & Chen 2013). The gas clouds must be located in the foreground of the quasar to produce the absorption signature in the quasar spectra. To accommodate the redshift errors and the redshifted absorbers, we restrict ourselves to the spectral data corresponding to a velocity of less than 20,000 km s⁻¹ redward of the quasar Mg ii emission line. Therefore, our spectral region used to search for Mg ii absorption doublets is defined as 1250 × (1 + z_em) Å < λ < 2800 × (1 + z_em + δz) Å, where δz = z_abs − z_em = 20,000 km s⁻¹ ×(1 + z_em)/c.
• 2.  
  Median signal-to-noise ratio ($\langle {\rm{S}}/{\rm{N}}\rangle$) per pixel larger than 4. The median value of the $\langle {\rm{S}}/{\rm{N}}\rangle$ of quasar spectra in the surveyed spectral region is ∼4 pixel⁻¹. The $\langle {\rm{S}}/{\rm{N}}\rangle$ cut is set to guarantee robust absorption line measurements.

After taking into account the above limits, we select 43,260 quasars to detect Mg ii absorption doublets. The quasar spectra of the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) have an $\langle {\rm{S}}/{\rm{N}}\rangle$ of about 8 pixel⁻¹ in the same spectral region as ours, which is higher than our median value of 4 pixel⁻¹. Seyffert et al. (2013) surveyed Mg ii absorption doublets in the SDSS DR7 quasar spectra with an $\langle {\rm{S}}/{\rm{N}}\rangle$ of no less than 4 pixel⁻¹, which includes a total of 79,294 quasar spectra. Using the SDSS DR7 quasar spectra, Zhu & Ménard (2013) also completed a systematic survey of Mg ii absorption doublets. The number of quasar spectra used by both Seyffert et al. (2013) and Zhu & Ménard (2013) is about two times the number we use.

The red histogram of Figure 1 shows the emission redshifts of the quasars used to survey the Mg iiabsorption doublets in this work. It is clear that most quasars are located in redshift ranges of 0.4 ≲ z_em ≲ 1 and z_em > 2. The gas clouds producing Mg ii absorption features in the quasar spectra should be located in the foreground of the quasars, and absorbers might cluster around quasars (e.g., Nestor et al. 2008; Wild et al. 2008; Chen et al. 2015). The wavelength coverage of the Sloan spectrograph is from 3600 to 10400 Å, which defines a redshift range for Mg ii absorption doublets detected from the BOSS quasar spectra from ∼0.27 to ∼2.7 as long as the quasars have higher redshifts. Thus, the distribution of quasar redshifts might affect the distribution of absorber redshifts.

We closely follow the method described in Chen et al. (2014a, 2014b) to search for Mg ii absorption doublets. Here, we briefly summarize the main steps involved in the detection of absorption lines. We refer readers to Chen et al. (2014a, 2014b) for more details on the method.

In the first step, we fit the underlying continuum plus broad emission lines by invoking a combination of cubic spline and Gaussian functions in an iterative fashion (e.g., pseudo-continuum; Nestor et al. 2005; Quider et al. 2011), which is utilized to normalize the spectral fluxes and flux uncertainties. The upper panel of Figure 2 shows the spectrum of quasar SDSS J121628.03+035031.8 with z_em = 0.9966 (black line), overplotted in green is the pseudo-continuum fitting. In the bottom panel, we show the spectrum normalized by the pseudo-continuum fitting in black. The ±1σ and −2σ flux uncertainty levels, which have been normalized by the pseudo-continuum fitting, are also shown with red and blue lines in Figure 2. We eliminate the absorption troughs within the 2σ flux uncertainty level. We disregard the continual absorption features (broad absorption lines; BALs) with widths greater than 2000 km s⁻¹ at depths larger than 10% under the pseudo-continuum.

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For the second step, we survey Mg ii doublet candidates with FWHM smaller than 600 km s⁻¹ in the normalized spectra. This routine is mainly dominated by the separations of the Mg iidoublets, which vary with redshift or observed wavelength. We neglect broad or mini-broad absorption features with FWHM > 600 km s⁻¹ as well as weak absorptions within the 2σ flux uncertainty region. We fit a pair of Gaussian functions to model each Mg ii doublet candidate and visually inspect all of the Gaussian fittings one by one. Some strong Mg ii absorption systems might tend toward saturated or self-blended systems. Figure 3 shows an example of strong Mg ii absorption at z_abs = 0.4937 imprinted on the quasar spectrum of SDSS J121816.58+364517.4 with a pair of Gaussian function fits, which suggests that a pair of Gaussian functions can also well model the saturated or self-blended Mg ii absorption system.

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The C iv absorption doublets are often detected in the BOSS quasar spectra as well (e.g., Chen et al. 2014a, 2014b). The C iv doublets with high redshifts have velocity separations similar to those of Mg ii doublets with low redshifts. In addition, the absorption strengths and profiles of C iv doublets are parallel to those of Mg ii doublets. These might contaminate the true Mg ii doublets. In order to reduce the confusions of C iv doublets with true Mg ii doublets, we use our previous results for C iv absorption catalogs (Chen et al. 2014a, 2014b) during the individual inspection of the Mg iidoublet candidates.

In the third step, we measure the equivalent widths at the absorber rest frame (W_r) for candidate absorption features by integrating the Gaussian model. The uncertainties on the rest equivalent widths are estimated by

$$\begin{eqnarray}&&(1+z){\sigma }_{w}=\displaystyle \frac{\sqrt{\displaystyle \sum _{i=1}^{N}{P}^{2}({\lambda }_{i}-{\lambda }_{0}){\sigma }_{{f}_{i}}^{2}}}{\displaystyle \sum _{i=1}^{N}{P}^{2}({\lambda }_{i}-{\lambda }_{0})}{\rm{\Delta }}\lambda ,\end{eqnarray} \tag{ 1 }$$

where P(λ_i − λ₀), λ_i, ${\sigma }_{{f}_{i}}$, and N are the line profile centered at λ₀, the wavelength, the normalized flux uncertainty, and the number of pixels over ±3σ, where σ is given by the best Gaussian fit of the given absorption line candidate. The uncertainty in the pseudo-continuum fitting is not factored into the estimation of the uncertainty of W_r. We estimate the S/N^λ of candidate absorption features (see Qin et al. 2013 for more detail) via

$$\begin{eqnarray}&&{\rm{S}}/{{\rm{N}}}^{\lambda }=\displaystyle \frac{1-{S}_{\mathrm{abs}}}{{\sigma }_{S}},\end{eqnarray} \tag{ 2 }$$

where S_abs is the largest depth within ±3 characteristic Gaussian widths (±3σ) around an absorption feature relative to unity in the normalized spectrum, and σ_S is calculated by

$$\begin{eqnarray}&&{\sigma }_{S}=\sqrt{\displaystyle \frac{\displaystyle \sum _{i=1}^{N}{[\displaystyle \frac{{F}_{\mathrm{noise}}^{i}}{{F}_{\mathrm{cont}}^{i}}]}^{2}}{N}},\end{eqnarray} \tag{ 3 }$$

where F_noise, F_cont, and N are the flux uncertainty, the flux of the pseudo-continuum, and the number of pixels over ±3 characteristic Gaussian widths (±3σ) around an absorption feature.

Finally, only the absorption doublets with W_r ≥ 0.2 Å and S/N^λ ≥ 2.0 for both the λ2796 and λ2803 lines are retained in our Mg ii absorption doublet catalog.

Among the 43,260 quasars, there are 12,958 with at least one detected Mg ii absorption doublet, whose emission redshifts are shown with the blue solid line in Figure 1. We detect a total of 18,598 Mg ii absorption doublets with 0.2933 ≤ z_abs ≤ 2.6529. The distribution of absorption redshifts is shown as the black solid line in Figure 1. We also provide the absorption system properties in Table 1. Previous works (e.g., Nestor et al. 2008; Wild et al. 2008; Chen et al. 2015) noted that absorbers might cluster around quasars. We would like to suggest that the sharp decrease in detected Mg ii doublets at z_abs > 2 is due to the poor SDSS spectral quality at λ > 8000 Å since contamination by strong sky spectra.

Table 1.  Catalog of Mg ii Absorption Systems

SDSS NAME	PLATEID	MJD	FIBERID	zem	zabs	${W}_{r}^{\lambda 2796}$	${N}_{\sigma }^{\lambda 2796}$	${W}_{r}^{\lambda 2803}$	${N}_{\sigma }^{\lambda 2803}$	S/Nλ2796	S/Nλ2803	β
						(Å)		(Å)
000009.27 + 020622.0	4296	55499	0616	1.4354	0.9521	1.14	8.14	0.45	3.46	7.4	3.2	0.21767
000014.07 + 012951.5	4296	55499	0370	3.2284	1.0077	1.52	6.91	1.27	5.52	6.4	5.2	0.63206
000015.17 + 004833.2	4216	55477	0718	3.0277	1.5452	1.21	10.08	1.43	7.94	9.5	7.4	0.42926
000016.49 + 022715.1	4296	55499	0642	0.8820	0.8703	1.02	6.38	0.69	4.60	5.9	4.2	0.00624
000042.90 + 005539.5	4216	55477	0758	0.9517	0.4965	0.52	7.43	0.46	4.60	7.1	4.4	0.25950
000050.59 + 010959.1	4216	55477	0746	2.3678	1.9181	1.08	7.20	0.52	5.20	6.6	5.0	0.14235
000050.59 + 010959.1	4216	55477	0746	2.3678	0.7809	0.40	5.00	0.55	4.23	4.9	4.0	0.56295
000057.58 + 010658.6	4216	55477	0750	2.5493	0.8182	0.78	3.12	0.92	2.56	3.0	2.4	0.58426
000057.58 + 010658.6	4216	55477	0750	2.5493	1.0589	1.25	7.35	1.57	4.62	7.0	4.4	0.49645
000104.13 + 010541.6	4216	55477	0788	1.9141	1.0585	1.48	5.92	1.03	6.44	5.5	5.9	0.33423

Note. N_σ = W_r/σ_W represents the significant level of the detection. $\beta =v/c=({(1+{z}_{\mathrm{em}})}^{2}-{(1+{z}_{\mathrm{abs}})}^{2})/({(1+{z}_{\mathrm{em}})}^{2}+{(1+{z}_{\mathrm{abs}})}^{2})$.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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From the SDSS DR7 quasar spectra, Seyffert et al. (2013) found that 26,167 quasars have at least one detected Mg ii absorption doublet, and identified a total number of 35,629 Mg ii absorption doublets. Using about 100,000 quasar spectra from the SDSS DR7 data set, Zhu & Ménard (2013) detected 40,429 Mg ii absorption doublets. These previous two works are larger than ours both in the number of quasars used to survey the Mg ii absorption doublet and the number of resulting doublets.

The total redshift path covered by our sample as a function of signal-to-noise ratio per pixel (S/N^λ2796) in our surveyed spectral regions is given by

$$\begin{eqnarray}&&{\rm{\Delta }}Z({\rm{S}}/{{\rm{N}}}^{\lambda 2796})=\displaystyle \sum _{i=1}^{{N}_{\mathrm{spec}}}{\displaystyle \int }_{{z}_{i}^{\mathrm{min}}}^{{z}_{i}^{\mathrm{max}}}{g}_{i}({\rm{S}}/{{\rm{N}}}^{\lambda 2796},z){dz},\end{eqnarray} \tag{ 7 }$$

where ${g}_{i}({\rm{S}}/{{\rm{N}}}^{\lambda 2796},z)=1$ if the detection threshold S/N^lim  ≤ S/N^λ2796, otherwise g_i(S/N^λ2796, z) = 0; ${z}_{i}^{\mathrm{max}}$ and ${z}_{i}^{\mathrm{min}}$ are the redshifts corresponding to the maximum and minimum wavelengths in the survey spectral region of quasar i; and the sum is over all of the quasar spectra used to search for Mg ii absorption doublets. Figure 6 shows the total redshift path as a function of S/N^λ2796 or redshift. The conspicuous features of the redshift path at z > 1.5 are probably due to the poor sky-line substraction in the SDSS spectra.

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The incident rate of absorbers is defined as the number of absorbers within an interval of S/N^λ2796 and normalized by the total redshift path, which can be calculated by

$$\begin{eqnarray}&&\displaystyle \frac{\partial N}{\partial z}=\displaystyle \sum _{i}^{{N}_{\mathrm{abs}}}\displaystyle \frac{1}{{\rm{\Delta }}Z({\rm{S}}/{{\rm{N}}}_{i}^{\lambda 2796})},\end{eqnarray} \tag{ 8 }$$

where, in the specified redshift bin, N_abs is the number of detected Mg ii absorbers in the given interval of S/N^λ2796 and ${\rm{\Delta }}Z({\rm{S}}/{{\rm{N}}}_{i}^{\lambda 2796})$ is the redshift path of the Mg ii absorber determined by Equation (7). Note that ΔZ(S/N^λ2796) is a function of the S/N of the absorption line, which differs from ${\rm{\Delta }}Z({W}_{r}^{\lambda 2796})$ which is a function of the equivalent width of the absorption line (e.g., Seyffert et al. 2013; Zhu & Ménard 2013). Thus, we note the caveat for the incident rate of absorbers that the $\partial N/\partial {\text{}}z$ of the current work cannot be compared directly to the same values whose redshift path is determined by the equivalent width of the absorption line (e.g., Seyffert et al. 2013; Zhu & Ménard 2013). We straightforwardly resample the flux of each quasar spectra used to survey the Mg iiabsorption doublets with Monte Carlo simulation from its flux uncertainty constrained by the SDSS to constrain the uncertainty on ${\rm{\Delta }}{\rm{Z}}({\rm{S}}/{{\rm{N}}}_{i}^{\lambda 2796})$, and then estimate the uncertainty on $\partial N/\partial z$. The $\partial N/\partial z$, ${\rm{\Delta }}Z({\rm{S}}/{{\rm{N}}}_{i}^{\lambda 2796})$, and their uncertainties in different redshift bins are listed in Table 3.

Table 3.  The Redshift Number Density

z bin	Nabs	$\partial N/\partial z$	ΔZ
[0.2933, 0.3933)	116	${1.676}_{-0.223}^{+0.198}$	${69.2}_{-8.2}^{+9.2}$
[0.3933, 0.4933)	350	${3.382}_{-0.296}^{+0.443}$	${103.5}_{-13.6}^{+9.1}$
[0.4933, 0.5933)	611	${4.234}_{-0.367}^{+0.593}$	${144.3}_{-20.2}^{+12.5}$
[0.5933, 0.6933)	990	${5.950}_{-0.435}^{+0.879}$	${166.4}_{-24.6}^{+12.2}$
[0.6933, 0.7933)	1204	${6.936}_{-0.487}^{+0.954}$	${173.6}_{-23.9}^{+12.2}$
[0.7933, 0.8933)	1337	${7.778}_{-0.582}^{+1.026}$	${171.9}_{-22.7}^{+12.9}$
[0.8933, 1.0433)	1675	${7.014}_{-3.324}^{+0.711}$	${238.8}_{-24.2}^{+113.2}$
[1.0433, 1.1933)	1602	${8.678}_{-1.306}^{+0.835}$	${184.6}_{-17.8}^{+27.8}$
[1.1933, 1.3433)	1744	${8.694}_{-1.569}^{+0.732}$	${200.6}_{-16.9}^{+36.2}$
[1.3433, 1.4933)	1889	${10.606}_{-1.930}^{+0.782}$	${178.1}_{-13.1}^{+32.4}$
[1.4933, 1.6933)	2310	${10.248}_{-0.616}^{+0.913}$	${225.4}_{-20.1}^{+13.5}$
[1.6933, 1.9433)	2266	${8.331}_{-2.239}^{+1.056}$	${272.0}_{-34.5}^{+73.1}$
[1.9433, 2.6529]	2503	${4.073}_{-1.808}^{+0.565}$	${614.6}_{-85.3}^{+272.8}$

Note. N_abs represents the number of the detected Mg ii absorption doublets in corresponding redshift intervals.

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In Figure 7, we show the incidence rate of all of the detected Mg ii absorbers as a function of redshift, which increases by about a factor of 6 from z ≈ 0.4 to z ≈ 1.5 and tends to decrease toward higher redshift. Both Seyffert et al. (2013) and Zhu & Ménard (2013) searched for Mg ii absorption doublets in the quasar spectra of the SDSS-I/II, and also found similar redshift evolutions for the incidence rate of Mg ii absorbers with ${W}_{r}^{\lambda 2796}\gt 1\;\mathring{\rm A}$.

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In their recent work, Madau & Dickinson (2014) found that the evolution of the star formation rate density follows the parametrization of

$$\begin{eqnarray}&&{\dot{\rho }}_{*}={{dM}}_{*}/({dtdAdX})=\displaystyle \frac{{p}_{1}{(1+z)}^{{p}_{2}}}{1+{(\frac{1+z}{{p}_{3}})}^{{p}_{4}}}{M}_{\odot }\;{\mathrm{yr}}^{-1}\;{\mathrm{Mpc}}^{-3},\end{eqnarray} \tag{ 9 }$$

where X is the comoving distance, A is the comoving area, and [p₁, p₂, p₃, p₄] are fitting parameters. The shape of this evolution scaled by dX/dz can be expressed as

$$\begin{eqnarray}f(z) & = & {\dot{\rho }}_{*}\displaystyle \frac{{dX}}{{dz}}=\displaystyle \frac{{p}_{1}{(1+z)}^{{p}_{2}}}{1+{(\frac{1+z}{{p}_{3}})}^{{p}_{4}}}\displaystyle \frac{{dX}}{{dz}}\\ & = & \displaystyle \frac{{p}_{1}{(1+z)}^{{p}_{2}}}{1+{(\frac{1+z}{{p}_{3}})}^{{p}_{4}}}\displaystyle \frac{c}{{H}_{0}}\displaystyle \frac{{(1+z)}^{2}}{\sqrt{{{\rm{\Omega }}}_{M}{(1+z)}^{3}+{{\rm{\Omega }}}_{{\rm{\Lambda }}}}}\\ & & \times {M}_{\odot }\;{\mathrm{yr}}^{-1}\;{\mathrm{Mpc}}^{-2}.\end{eqnarray} \tag{ 10 }$$

Using FUV and IR data, Madau & Dickinson (2014) found that ${\dot{\rho }}_{*}$ increases with redshifts until z ≈ 2 before declining again toward higher redshifts, which is also shown by the unfilled diamonds in Figure 7 after being scaled by dX/dz. Figure 7 shows that both $\partial N/\partial z$ and ${\dot{\rho }}_{*}$ share a parallel evolution at z < 1.7. Therefore, the parametric equation of ${\dot{\rho }}_{*}$ scaled by dX/dz would likely well characterize the incidence rate of Mg ii absorbers. The quickly declining $\partial N/\partial z$ at z > 1.7 might be due to an underestimate of the true number of Mg ii absorbers considering the poor sky-line substraction redward of the SDSS spectra. The reduced χ² fitting of Equation (10) to the incidence rate of Mg ii absorbers at z_abs < 1.7 gives [p₁, p₂, p₃, p₄] = [0.046 ± 0.053, 12.146 ± 3.974, 12.125 ± 3.642, 1.436 ± 0.061]. The best fit is shown with the red solid line in Figure 7.

[O ii] λ3727 is a good indicator of the star formation rate (Gallagher et al. 1989; Kewley et al. 2004). Thus, the study of [O ii] emission and Mg ii absorption might provide a clue toward the relationship between star formation within galaxies and the properties of Mg ii absorbers. In fact, a number of previous studies have suggested a relationship between strong (W_r ≳ 1 Å) absorbers and star formation. Using more than 8500 strong (W_r > 0.7 Å) Mg ii absorbers measured from the SDSS quasar spectra, Ménard et al. (2011) detected a tight correlation between ${W}_{r}^{\lambda 2796}$ and mean [O ii] luminosity density, which can be reproduced by a Monte Carlo simulation (López & Chen 2012). Based on a sample of intermediate-redshift star-forming galaxies, Noterdaeme et al. (2010) found that the stronger (W_r > 1 Å) Mg ii absorbers, which were detected from the quasar spectra, match the higher average luminosities of the [O ii] emission measured from the foreground galaxy spectra. No matter what the absorption strengths are, Shen & Ménard (2012) found that the composite quasar spectra with Mg ii associated absorption doublets (z_em ≈ z_abs) exhibit a significant excess in [O ii] emission when compared to the unabsorbed quasars. The dependence of strong Mg ii absorbers on [O ii] emission implies that the Mg ii absorbers can trace the cosmic star formation history. In our catalog, about 75% of Mg iiabsorbers have ${W}_{r}^{\lambda 2796}\geqslant 1\;\mathring{\rm A}$. The parallel redshift evolutions of the star formation rate density and the incidence rate of Mg ii absorbers (see also Matejek & Simcoe 2012; Seyffert et al. 2013; Zhu & Ménard 2013) suggest a valuable clue to investigate the cosmic star formation history through strong absorbers.

We note a caveat in the connection between the absorber and the star formation history. Not all Mg ii absorbers form within star-forming galaxies (e.g., Zibetti et al. 2007; Gauthier & Chen 2011). For weak absorbers (W_r < 1 Å), the colors of galaxies do not obviously correlate with the absorption strength (e.g., Chen et al. 2010a; Kacprzak et al. 2011b), which implies the lack of a strong relationship between the absorption strength and the recent star formation rate within the galaxies. The redshift number density evolution of the weak absorbers shows no or only weak evolution (e.g., Nestor et al. 2005; Matejek & Simcoe 2012). The difference in redshift number density evolution between weak absorbers and strong absorbers suggests that there may be different origins for weak and strong absorbers.

Using large quasar absorber samples, several previous studies (e.g., Nestor et al. 2008; Wild et al. 2008; Chen et al. 2015) suggest that absorbers with z_abs ≈ z_em would likely cluster around quasars. However, there is a common feature in their studies that β shows an asymmetrical distribution around β ≈ 0, which might be caused by outflows; β is defined as follows:

$$\begin{eqnarray}&&\beta \equiv \displaystyle \frac{\upsilon }{c}=\displaystyle \frac{{(1+{z}_{\mathrm{em}})}^{2}-{(1+{z}_{\mathrm{abs}})}^{2}}{{(1+{z}_{\mathrm{em}})}^{2}+{(1+{z}_{\mathrm{abs}})}^{2}}.\end{eqnarray} \tag{ 11 }$$

The derivation of β is given in the Appendix. The difference between emission redshift and absorption redshift, measured from the same quasar spectra, mainly originates from the cosmological distance between the quasar and absorber and the relative motion of the absorber with respect to the quasar. Also, this difference is dominated by the cosmological distance for the intervening absorber, and by the relative motion for the intrinsic or associated absorber. Figure 8 shows the β distribution of all of the Mg iiabsorbers in our absorber catalog, which is similar to that reached by previous studies (e.g., Nestor et al. 2008; Wild et al. 2008; Chen et al. 2015). Note that a distinct excess of Mg ii absorbers at β ≈ 0 ∼ 0.02 is remarkable.

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Accurate emission redshifts of quasars are crucial for the shape of the β distribution, especially for those absorbers with z_abs ≈ z_em. Large errors will be introduced to redshifts estimated from broad emission lines compared to those estimated from host galaxy absorption lines or narrow emission lines (e.g., [O iii] λ5007; Hewett & Wild 2010). We construct a lower-redshift quasar sample by cutting our Mg ii absorption catalog to those quasars with z_em ≤ 1.0770, for which the emission line redshift can be determined from the narrow emission lines.

The quasar subsample with z_em ≤ 1.0770 contains a total number of 1677 Mg ii absorption doublets, whose β distribution is shown in Figure 9. Note that distinct excess of Mg ii absorbers at β ≈ 0 ∼ 0.02 and the approximately flat distribution in β ≳ 0.03. Our Mg ii absorption catalog probably includes all three kinds of absorbers: (1) cosmologically intervening absorbers; (2) environmental absorbers (associated absorbers) that reside within quasar host galaxies or galaxy clusters/groups; and (3) intrinsic absorbers that are physically related to the quasar central region. We statistically identify the three kinds of absorbers as follows.

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(1) Cosmologically intervening absorbers. The smooth tail of the β distribution suggests that the Mg ii absorption doublets with β ≳ 0.03 would probably be dominated by cosmologically intervening absorption. We adopt a linear function to fit the data with 0.05 < β < 0.15, which gives Number = (1.876 ± 0.896) + (8.812 ± 8.710) × β. We extrapolate the linear-fit to all of the data with β > 0 to characterize the contribution of the cosmologically intervening absorbers, which is shown with the red solid line in Figure 9. This linear fit accounts for a total of 1100 Mg ii absorbers with β > 0, namely, 1100 cosmologically intervening Mg ii absorbers.

(2) Environmental absorbers. The β distribution of Mg ii absorbers subtracted off the extrapolated linear-fit is shown in the top panel of Figure 10. We assume a Gaussian component centered at β = 0 to fit the data with β < 0, which gives σ = 0.0012. The Gaussian fit is extrapolated to the data with β > 0, which is shown with the blue solid line in the top panel of Figure 10. We adopt the extrapolated Gaussian fit to trace the environmental absorbers, which accounts for a total of 500 Mg ii absorbers, namely, 500 environmental absorbers.

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(3) Intrinsic absorbers. The β distribution of the Mg iiabsorbers subtracted from the combination of the extrapolated linear-fit and the extrapolated Gaussian fit is shown in the bottom panel of Figure 10, which contains 77 Mg ii absorbers. The significant excess of the β distribution in 0.00 ≲ β ≲ 0.02 is very interesting because it likely represents the contribution from quasar outflows. This excess peaks at υ ≈ 1500 km s⁻¹ and shows an asymmetric distribution. Here, some caveats cannot be ignored. The extrapolated Gaussian fit might overestimate environmental absorbers with low-relative velocities. In addition, the extrapolated linear fit might overestimate cosmologically intervening absorbers with low relative velocities. These overestimates may partly contribute to the rapid decrease of the quasar outflow component at low velocities. Nestor et al. (2008) and Chen et al. (2015) found that the similarly asymmetric distribution of β also exists for C iv absorbers, which peaks at v ≈ 2000 km s⁻¹. The ionization potentials are 15.035 eV for Mg ii and 64.49 eV for C iv. These different peak velocities imply that higher ionization intrinsic absorbers might be formed in higher velocity outflows. However, we note that the quasar emission redshifts where the C ivabsorber is detected are mainly estimated from broad emission lines, which might introduce large errors to the β of the C iv absorbers.