Properties of spectrally-defined red QSOs at z = 0.3-1.2

TL;DR

This study characterizes red QSOs at z=0.3-1.2 using optical, radio, and infrared data, revealing their stronger infrared emission and potential existence of two types based on redshift and luminosity differences.

Contribution

It introduces a spectral color criterion for selecting red QSOs and compares their properties to typical QSOs across redshifts using multi-wavelength data.

Findings

Red QSOs have stronger infrared emission than typical QSOs.

The ratio of red to typical QSOs decreases with increasing redshift.

Red QSO luminosities are lower at low redshift but similar at high redshift.

Abstract

We investigated the properties of a sample of red Quasi-stellar Objects (QSOs) using optical, radio, and infrared data. These QSOs were selected from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) quasar catalog. We only selected sources with sky coverage of the Very Large Array Faint Images of the Radio Sky at Twenty-centimeters (VLA FIRST) survey, and searched for sources with Wide-field Infrared Survey Explorer (WISE) counterparts. We defined the spectral color of the QSOs based on the flux ratio of the rest frame 4000$\AA$ to 3000$\AA$ continuum emission to select red QSOs and typical QSOs. In accordance with this criterion, only QSOs with redshifts between 0.3 and 1.2 could be selected. We found that the red QSOs have stronger infrared emission than the typical QSOs do. We noted that the number ratios of the red QSOs to the typical QSOs decrease with increasing redshifts, although the number of the typical QSOs increase with redshifts. Furthermore, at high redshifts, the luminosity distributions of the typical QSOs and the red QSOs seem to have similar luminosity distribution peaks; however, at low redshifts, the luminosities of the red QSOs seem to be lower than those of the typical QSOs. These findings suggest that there might be at least two types of red QSOs in our QSO samples.

Tables

Table 1. Table 1 Number and number fractions of tQSOs and rQSOs at different luminosities

Luminosity	$n_{\mathrm{QSO}}$	$n_{\mathrm{tQSO}}$	$\xi \left(\mathrm{tQSO}\right)$	$n_{\mathrm{rQSO}}$	$\xi \left(\mathrm{rQSO}\right)$
40 41	2265	218	9.62%	1009	44.55%
41 42	12749	3124	24.50%	1530	12.00%
42 43	7384	2236	30.28%	392	5.31%
43 44	31	7	22.58%	1	3.23%
40 44	22429	5585	24.90%	2932	13.07%
1. $n_{\mathrm{QSO}}$ is the number of the whole QSO sample.
2. $n_{\mathrm{tQSO}}$ is the number of the typical QSOs. $\xi \left(\mathrm{tQSO}\right)=n_{\mathrm{tQSO}}/n_{\mathrm{QSO}}$.
3. $n_{\mathrm{rQSO}}$ is the number of the red QSOs. $\xi \left(\mathrm{rQSO}\right)=n_{\mathrm{rQSO}}/n_{\mathrm{QSO}}$.

Table 2. Table 2 Number and number fractions of tQSOs and rQSOs at different redshifts

Redshift	$n_{\mathrm{QSO}}$	$n_{\mathrm{tQSO}}$	$\xi \left(\mathrm{tQSO}\right)$	$n_{\mathrm{rQSO}}$	$\xi \left(\mathrm{rQSO}\right)$
0.3 0.4	2446	365	14.92%	845	34.55%
0.4 0.5	2397	426	17.77%	622	25.95%
0.5 0.6	2389	479	20.05%	455	19.05%
0.6 0.7	2264	548	24.20%	282	12.46%
0.7 0.8	2143	594	27.72%	160	7.47%
0.8 0.9	2286	636	27.82%	158	6.91%
0.9 1.0	2502	700	27.98%	140	5.60%
1.0 1.1	2880	841	29.20%	144	5.00%
1.1 1.2	3122	996	31.90%	126	4.04%
0.3 1.2	22429	5585	24.90%	2932	13.07%
1. The symbols are the same with those in Table 1.

Table 3. Table 3 Number and number fractions of tRLQs and rRLQs at different luminosities

Luminosity	$n_{\mathrm{RLQ}}$	$n_{\mathrm{tRLQ}}$	${\xi }_{\mathrm{RLQ}}\left(\mathrm{tRLQ}\right)$	$n_{\mathrm{rRLQ}}$	${\xi }_{\mathrm{RLQ}}\left(\mathrm{rRLQ}\right)$
40 41	159	6	3.77%	103	64.78%
41 42	992	187	18.85%	285	28.73%
42 43	674	157	23.29%	102	15.13%
43 44	4	0	0.00%	1	25.00%
40 44	1829	350	19.14%	491	26.85%
1. $n_{\mathrm{RLQ}}$ is the number of the radio-loud QSOs.
2. $n_{\mathrm{tRLQ}}$ is the number of the radio-loud typical QSOs.    ${\xi }_{\mathrm{RLQ}}\left(\mathrm{tRLQ}\right)=n_{\mathrm{tRLQ}}/n_{\mathrm{RLQ}}$.
3. $n_{\mathrm{rRLQ}}$ is the number of the radio-loud red QSOs.    ${\xi }_{\mathrm{RLQ}}\left(\mathrm{rRLQ}\right)=n_{\mathrm{rRLQ}}/n_{\mathrm{RLQ}}$.

Table 4. Table 4 Number and number fractions of tRLQs and rRLQs at different redshifts

Redshift	$n_{\mathrm{RLQ}}$	$n_{\mathrm{tRLQ}}$	${\xi }_{\mathrm{RLQ}}\left(\mathrm{tRLQ}\right)$	$n_{\mathrm{rRLQ}}$	${\xi }_{\mathrm{RLQ}}\left(\mathrm{rRLQ}\right)$
0.3 0.4	191	17	8.90%	100	52.36%
0.4 0.5	183	23	12.57%	83	45.36%
0.5 0.6	211	34	16.11%	78	36.97%
0.6 0.7	175	31	17.71%	57	32.57%
0.7 0.8	197	41	20.81%	41	20.81%
0.8 0.9	192	50	26.04%	40	20.83%
0.9 1.0	203	47	23.15%	35	17.24%
1.0 1.1	251	60	23.90%	35	13.94%
1.1 1.2	226	47	20.80%	22	9.73%
0.3 1.2	1829	350	19.14%	491	26.85%
1. The symbols are the same with those in Table 3.

Table 5. Table 5 Radio-loud fractions of tQSOs and rQSOs at different luminosities

Luminosity	$\xi \left(\mathrm{RLQ}\right)$	${\xi }_{\mathrm{tQSO}}\left(\mathrm{tRLQ}\right)$	${\xi }_{\mathrm{rQSO}}\left(\mathrm{rRLQ}\right)$
40 41	7.02%	2.75%	10.21%
41 42	7.78%	5.99%	18.63%
42 43	9.13%	7.02%	26.02%
43 44	12.90%	0.00%	100.00%
40 44	8.15%	6.27%	16.75%
1. $\xi \left(\mathrm{RLQ}\right)=n_{\mathrm{RLQ}}/n_{\mathrm{QSO}}$.
2. ${\xi }_{\mathrm{tQSO}}\left(\mathrm{tRLQ}\right)=n_{\mathrm{tRLQ}}/n_{\mathrm{tQSO}}$.
3. ${\xi }_{\mathrm{rQSO}}\left(\mathrm{rRLQ}\right)=n_{\mathrm{rRLQ}}/n_{\mathrm{rQSO}}$.

Table 6. Table 6 Radio-loud fraction of tQSOs and rQSOs at different redshifts

Redshift	$\xi \left(\mathrm{RLQ}\right)$	${\xi }_{\mathrm{tQSO}}\left(\mathrm{tRLQ}\right)$	${\xi }_{\mathrm{rQSO}}\left(\mathrm{rRLQ}\right)$
0.3 0.4	7.81%	4.66%	11.83%
0.4 0.5	7.63%	5.40%	13.34%
0.5 0.6	8.83%	7.10%	17.14%
0.6 0.7	7.73%	5.66%	20.21%
0.7 0.8	9.19%	6.90%	25.62%
0.8 0.9	8.40%	7.86%	25.32%
0.9 1.0	8.11%	6.71%	25.00%
1.0 1.1	8.72%	7.13%	24.31%
1.1 1.2	7.24%	4.72%	17.46%
0.3 1.2	8.15%	6.27%	16.75%
1. The symbols are the same with those in Table 5.

Table 7. Table 7 Number, median, and standard deviation for the luminosity of the QSOs

	4000Å			6000Å			[OIII]5007Å
Redshift	rQSO	tQSO		rQSO	tQSO		rQSO	tQSO
0.3 0.4	845 (40.73$\pm$0.23)	365 (41.03$\pm$0.28)		844 (40.69$\pm$0.18)	365 (40.80$\pm$0.25)		832 (42.02$\pm$0.39)	348 (42.21$\pm$0.44)
0.4 0.5	621 (41.04$\pm$0.20)	426 (41.23$\pm$0.26)		621 (40.90$\pm$0.18)	425 (40.97$\pm$0.23)		612 (42.38$\pm$0.38)	421 (42.39$\pm$0.32)
0.5 0.6	455 (41.26$\pm$0.22)	476 (41.42$\pm$0.26)		113 (41.00$\pm$0.17)	83 (41.07$\pm$0.26)		447 (42.63$\pm$0.40)	466 (42.61$\pm$0.32)
0.6 0.7	282 (41.48$\pm$0.21)	548 (41.59$\pm$0.24)		3 (41.39$\pm$0.29)	1 (41.61$\pm$0.00)		280 (42.79$\pm$0.40)	532 (42.78$\pm$0.33)
0.7 0.8	160 (41.71$\pm$0.23)	594 (41.78$\pm$0.24)		1 (41.81$\pm$0.00)	-		156 (43.04$\pm$0.36)	585 (43.00$\pm$0.35)
0.8 0.9	158 (41.85$\pm$0.20)	636 (41.89$\pm$0.22)		-	-		51 (43.27$\pm$0.40)	161 (43.20$\pm$0.31)
0.9 1.0	140 (42.02$\pm$0.20)	700 (42.00$\pm$0.23)		-	-		-	-
1.0 1.1	144 (42.14$\pm$0.19)	841 (42.09$\pm$0.22)		-	-		-	1 (43.43$\pm$0.00)
1.1 1.2	126 (42.25$\pm$0.20)	996 (42.18$\pm$0.21)		-	-		-	-
1. The integer value is the number of different types of QSOs within the corresponding redshift range. 2. The values inside the parenthesis are the median and the standard deviation of logarithmic scale luminosity in different types of QSOs within the corresponding redshift range. 3. The unit of luminosity for both 4000Å and 6000Å is erg s-1Å-1, and that for [OIII]5007Å is erg s-1. 4. The symbol “-” means there is no QSO found. 5. The standard deviation of $\pm$0.00 means there is only one QSO found.

Table 8. Table 8 The t 𝑡 t -test of L [ OIII ] ​ 5007 subscript 𝐿 delimited-[] OIII 5007 L_{\rm[OIII]5007} between the rQSOs and the tQSOs

Redshift		$t$	$s$
0.3 0.4		-7.9907	0.0000
0.4 0.5		0.5531	0.5803
0.5 0.6		0.9368	0.3491
1. $t$ is the $t$-test statistic. 2. $s$ is the significance. The significance is a value in the interval [0.0, 1.0]. A small value () indicates that two samples have significantly different means.

Table 9. Table 9 Number and fractions of QSOs with the H β 𝛽 \beta FWHM < < 1000 km s -1

Redshift	QSOs	rQSOs	tQSOs
0.3 0.4	77 (3.15%)	50 (5.92%)	3 (0.82%)
0.4 0.5	24 (1.00%)	22 (3.54%)	0 (0.00%)
0.5 0.6	14 (0.59%)	11 (2.43%)	1 (0.21%)
0.6 0.7	5 (0.22%)	3 (1.07%)	0 (0.00%)
0.7 0.8	3 (0.14%)	2 (1.25%)	0 (0.00%)
0.8 0.9	2 (0.11%)	2 (1.64%)	0 (0.00%)
0.9 1.0	0 (0.00%)	0 (0.00%)	0 (0.00%)
1.0 1.1	0 (0.00%)	0 (0.00%)	0 (0.00%)
1.1 1.2	0 (0.00%)	0 (0.00%)	0 (0.00%)
0.3 1.2	125 (0.93%)	90 (3.63%)	4 (0.14%)
1. The integer value is the number of different types of QSOs within the corresponding redshift range. 2. The value inside the parenthesis is the number fraction of different types of QSOs within the corresponding redshift range.

Equations

$$\begin{gathered} r=\frac{{\bar{f}}_{4000}}{{\bar{f}}_{3000}} \\ =\frac{{\int }_{3950\mathring{\mathrm{A}}}^{4050\mathring{\mathrm{A}}}{f}_{\lambda }d\lambda }{{\int }_{2950\mathring{\mathrm{A}}}^{3050\mathring{\mathrm{A}}}{f}_{\lambda }d\lambda }, \end{gathered}$$

$$R_{\mathrm{g}}=\log (\frac{f_{\mathrm{radio}}}{f_{\mathrm{optical}}})=0.4(g-t),$$

$$t=-2.5\log (\frac{f_{\mathrm{FIRST}}}{3631\mathrm{Jy}}),$$

$$f_{\lambda }=\frac{1}{1+z}\frac{L_{\lambda /(1+z)}}{L_{\lambda }}\frac{L_{\lambda }}{4\pi D_L^2},$$

$$L_{4000}=(1+z)4\pi (D_L(z){)}^2{\bar{f}}_{4000(1+z)},$$

$$M_{10\text{micron}}=m_{10\text{micron}}-(5\log (D_{\mathrm{L}})-5),$$

Full text

1. Introduction

Quasi-Stellar Objects (QSOs) are one type of active galactic nuclei (AGNs), and are among the most luminous objects in the universe. The energy of AGNs is believed to be powered by surrounding accretion disks feeding matter into a supermassive black hole (SMBH) at the center of the host galaxy. The accretion disk and SMBH are surrounded by a dusty torus that can obscure the line of sight in certain directions. Some AGNs also have strong radio emission with relativistic jets perpendicular to the accretion disk (Urry & Padovani, 1995).

A typical QSO spectrum shows a non-stellar continuum with strong broad line emission and narrow line emission. In the rest frame, the continuum spectrum usually peaks at ultraviolet (UV) to soft X-ray wavebands. However, recent observations have discovered a new population of QSOs, which show redder optical or infrared (IR) colors than typical QSOs do (Webster et al., 1995; Richards et al., 2003; Glikman et al., 2007). No standard definition for these red QSOs currently exists.

The nature of these red QSOs is still unclear. The redness could be attributed to several different effects, such as dust-reddening (Glikman et al., 2004; Urrutia et al., 2009), an intrinsic red continuum of these QSOs (Richards et al., 2003), contamination from stars in host elliptical galaxies (Masci et al., 1998), or additional red synchrotron emission (Whiting et al., 2001). The majority of the red QSOs discovered are considered to be reddened by dust (Cutri et al., 2002; Glikman et al., 2004; Canalizo et al., 2006). The origins of the red color could be explained by one of the following two scenarios: (1) the lines of sight to the dust-reddened QSOs pass through the AGN torus; or (2) the dust is produced during starburst activities which follow the galaxy mergers that trigger QSOs. The second scenario is likely related to an early evolutionary stage of QSOs. However, although dust might be a crucial effect of reddening, we do not know whether the reddening is caused entirely by dust. Therefore, using various methods to test the potential effects involved in reddening is essential.

The existence of dust in QSOs can significantly affect the observational properties of the QSOs and their host galaxies (Rudy, 1984). In optical observations, a population of dust-obscured QSOs would be missed by magnitude-limited surveys. The percentage of the missing QSOs might be from a few percent to $\sim 30\%$ (Whiting et al., 2001). However, the optically obscured photons re-emerge as emission at the infrared band. Therefore, the infrared emission might reveal properties of dust-obscured QSOs. In addition, we noted that radio emission is barely affected by dust absorption, and that radio emission of the QSOs should be independent of the amount of dust in the sources. To investigate the origins of the red color of QSOs, we used optical, infrared, and radio data to study the properties of selected QSO samples.

Most selection methods for finding red QSOs rely on photometric selection. For example, the parent QSO samples were selected from either optical (Richards et al., 2003), infrared–infrared matching (Banerji et al., 2013), optical–infrared matching (Cutri et al., 2001; Georgakakis et al., 2009; Fynbo et al., 2013; Ross et al., 2015), or optical–infrared–radio matching sources (Glikman et al., 2007; Urrutia et al., 2009; Glikman et al., 2012). The criteria for selecting red QSOs were mainly based on their photometric colors such as optical–optical (e.g., $r-i$, $g-r$; Fynbo et al. 2013), optical–infrared (e.g., $R-K$, $g-J$, $i-K$, $r-$W4; Cutri et al. 2001; Glikman et al. 2007; Georgakakis et al. 2009; Urrutia et al. 2009; Glikman et al. 2012; Fynbo et al. 2013; Ross et al. 2015), and infrared–infrared colors (e.g., $J-K_{\rm s}$, $J-K$, W1–W2; Cutri et al. 2001; Glikman et al. 2007; Georgakakis et al. 2009; Urrutia et al. 2009; Glikman et al. 2012; Banerji et al. 2013; Fynbo et al. 2013). However, even for the same photometric colors, the red QSOs could be defined by different color criteria in different surveys; for example, the red QSOs were selected with $J-K>2$ and $R-K>5$ from 2MASS-SDSS samples by Georgakakis et al. (2009), $J-K>1.7$ and $R-K>4$ from FIRST-2MASS samples by Glikman et al. (2007, 2012), and $J-K>1.3$ and $R-K>5$ from FIRST-2MASS samples by Urrutia et al. (2009). This implies that the red QSOs discussed in various studies might not be uniform. Furthermore, other concerns of photometric selection include: redshifted strong emission lines that could contaminate the photometric colors, and photometric data of the same filter representing different waveband properties at different redshifts. To avoid these problems of photometric selection for red QSOs, Richards et al. (2003) defined red QSOs based on “relative photometric colors”, which are the differences between the measured photometric colors and the median colors of QSOs at the redshift of the QSO. In this study, we developed a new method for classifying red QSOs with a statistical definition based on “relative spectral flux” to not only facilitate avoidance of the inconsistency caused by photometric cut-offs, but also enable selection of statistically-defined red QSOs to study the origins of their redness. Since the redness of our QSOs was uniformly defined at the same rest-frame wavelengths over the whole redshift range we considered, conducting follow-up confirmations for the reality of the redness is not necessary.

In this study, we selected the parent QSOs from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) Quasar Catalog based on their spectra at the rest frame. The SDSS DR7 QSOs included both photometrically selected and FIRST-matched QSO samples (Richards et al., 2002). We chose QSOs with radio counterparts from the Very Large Array Faint Images of the Radio Sky at Twenty-centimeters (VLA FIRST) radio survey, as well as infrared counterparts from the Wide-field Infrared Survey Explorer (WISE). We defined QSO colors based on the relative flux ratio from the spectrum. Through this method, we could select red QSOs without the contamination of strong emission lines, thereby enabling us to include a wide range of red QSOs to study their general properties. The detail of the data selection is described in Section 2. We present our results in Section 3 and discuss the implication of our results in Section 4. The cosmology parameters we are using in this paper are $H_{0}=70$ km s*-1* Mpc*-1*, $\Omega_{\rm m}=0.30$, and $\Omega_{\Lambda}=0.70$.

2. Sample Selection

2.1. Optical Data and Definition of QSO Color

Our QSOs were selected from the SDSS DR7 Quasar Catalog (Schneider et al., 2010). We limited our sample to $i$-band magnitudes brighter than the PSF magnitude of 19.1 111http://www.sdss2.org/dr7/ PSF mag. $i<19.1$ for $z<2.3$. We downloaded the spectra222 The spectra were downloaded using the interface of the Tenth SDSS Data Release. We note that the spectra are actually from DR7, which mainly includes QSOs at $z<2.3$. For DR10, the QSOs are at $z>2.2$.

of these QSOs and defined the QSO color with the flux ratio of the two continuum bands at the rest frame $\lambda=4000\pm 50$Å to $\lambda=3000\pm 50$Å (see Figure 1). The flux ratio $r$ is defined as,

[TABLE]

where $\bar{f}_{\lambda}$ is the mean flux density within a range of wavelengths, $f_{\lambda}$ is the flux density per unit wavelength, and $\lambda$ is in units of Å. These two bands were selected to avoid strong narrow lines (e.g., Mg II, O II, and H$\gamma$) and broad emission lines (e.g., Fe II). Because of the wavelength range of SDSS spectra, only QSOs with redshifts from 0.3 to 1.2 could be selected.

Figure 2 shows the flux ratios at different redshifts. We found that the mode values of flux ratios at different redshifts are all located within 0.5 – 0.6 bin and were independent of redshift. Notably, the flux ratios at low redshifts more scattered than those at high redshifts. The number distribution of the flux ratios look like a Gaussian distribution with an extended right tail (Figure 3). Therefore, we fitted the left wing of the distribution with a Gaussian function and folded the result to the right wing. The distribution peaked at $r_{\rm peak}=0.52$ with $\sigma\approx 0.042$. The 3$\sigma$ at the right wing was at $r\approx 0.65$. Therefore, for comparison, we defined our QSO samples with $r\geqslant 0.66$ as red QSOs (hereafter, rQSOs), and the QSOs with $0.50\leqslant r\leqslant 0.54$ ($r_{\rm peak}\pm\frac{1}{2}\sigma$) as typical QSOs (hereafter, tQSOs). Notably, the tQSOs only represented the sources with the most likely color in the SDSS QSO samples. Section 4 offers further discussion regarding the distribution of the QSO samples. We noted that the color ratio difference between the the rQSOs and the tQSOs roughly corresponded to absorption of 0.26 magnitude at 4000Å when the colors were caused by dust absorption, assuming that the SMC dust extinction law (Pei, 1992) was in effect. Notably, the effective E(B–V) of 0.26 was similar to the definition of red QSOs in Lacy et al. (2013, 2015).

2.2. Radio Data and Definition of Radio-loud QSOs and Radio-quiet QSOs

We looked for the radio counterparts of the QSOs in the sky coverage of the VLA FIRST radio survey (Becker et al., 1997) within a 2$\arcsec$ radius, which can match 98% of sources with real association (e.g., McMahon et al. 2002.) For the QSOs with radio detection, we used their radio-to-optical ratios to classify a group of radio-loud QSOs (RLQs) (Kellermann et al., 1989; Ivezić et al., 2002). The radio-to-optical ratio $R_{\rm g}$ is defined as

[TABLE]

where $f_{\rm radio}$ is the radio flux, $f_{\rm optical}$ is the optical flux, $g$ is the SDSS $g$-band magnitude, and $t$ is the radio magnitude defined as

[TABLE]

where $f_{\rm FIRST}$ is the integrated flux density of FIRST (Ivezić et al., 2002; Oke & Gunn, 1983). We defined QSOs with $R_{\rm g}>1$ as RLQs (Kellermann et al., 1989; Ivezić et al., 2002). The QSOs without radio detection and those with radio detection but with $R_{\rm g}\leqslant 1$ were both classified as radio-quiet QSOs (RQQs).

2.3. Infrared Data

In order to investigate the dust properties at the infrared band, we searched for the infrared counterpart of the QSOs within the FIRST sky coverage using the data of WISE, which performed an all sky survey at four different wavebands, W1 (3.4 µm), W2 (4.6 µm), W3 (12 µm), and W4 (22 µm), where W1 and W2 are narrow bands, and W3 and W4 are broad bands (Wright et al., 2010). The infrared counterparts were identified by matching the All-Sky WISE Source Catalog objects within a 2$\farcs$75 radius, which is the pixel scale of the WISE detectors. We found a counterpart in WISE within a 2$\farcs$75 radius search for all SDSS QSOs, except for 22 sources. For the following analysis, we considered only these WISE-detected sources.

3. Results

3.1. Distributions of the rQSOs

Our sample included 22,429 QSOs, of which 5,585 were tQSOs with $0.50\leqslant r\leqslant 0.54$ ($\approx 25\%$ of the total QSOs) and 2,932 were rQSOs with $r\geqslant 0.66$ ($\approx 13\%$ of the total QSOs). In order to compare the luminosities of different types of QSOs, we chose the luminosity at the rest frame 4000Å to represent the luminosity of each source. The luminosity per unit wavelength can be derived from the flux density per unit wavelength (Hogg, 1999),

[TABLE]

where $z$ is the redshift, $L_{\lambda/(1+z)}$ is the luminosity per unit wavelength at rest frame, $L_{\lambda}$ is the luminosity per unit wavelength in the observed frame, and $D_{L}$ is the luminosity distance. Therefore, we defined the luminosity $L_{4000}$ at rest frame as,

[TABLE]

where $z$ is the SDSS redshift, ${\bar{f}_{4000(1+z)}}$ is the mean flux at $4000(1+z)\AA$ in the observer frame, $D_{L}(z)$ is the luminosity distance. The $L_{4000}$ luminosity distribution of these QSOs is shown in Figure 4a. The luminosity distribution of the tQSOs is similar to that of the whole QSO sample: both peaks at log($L_{4000})\approx 42.1$. However, the distribution of the rQSOs peaks at log$(L_{4000})\approx 41.1$. Notably, dust absorption might have led to an underestimation of the luminosity; therefore, if the redness of these QSOs was caused by dust, the QSOs might have lower luminosities.

The luminosity distributions of the radio-loud and the radio-quiet sources within the rQSOs and the tQSOs are shown in Figure 4b and Figure 4c, respectively. For the tQSOs (Figure 4b), the overall luminosity distribution was dominated by the radio-quiet tQSOs (hereafter, tRQQs). The luminosity distributions of the tRQQs and the radio-loud tQSOs (hereafter, tRLQs) were similar; the distribution peaks of both were at log$(L_{4000})\approx 42.1$ and 41.9, respectively. For the rQSOs (Figure 4c), the overall luminosity distribution was also dominated by the radio-quiet rQSOs (hereafter, rRQQs). The distribution peaks for the radio-loud rQSOs (hereafter, rRLQs) and rRQQs were both at log($L_{4000})\approx 41.1$. However, the rRLQs showed a flat distribution, which was different from that of the rRQQs.

We showed the number fractions of the rQSOs and the tQSOs at different luminosities (Figure 5a and Table 1) and at different redshifts (Figure 5b and Table 2). We found that the rQSOs and the tQSOs had different trends along redshifts and luminosities. The number fractions of the rQSOs decreased with increasing redshifts and luminosities, whereas the number fractions of the tQSOs increased with redshifts and luminosities. We also listed the number fractions of the tRLQs and the rRLQs at different luminosities (Table 3) and at different redshifts (Table 4). The results shows that at all ranges of luminosities and redshifts, the RLQs had a higher number fraction to be red than the whole QSO sample did; the overall fraction of the rRLQs in the RLQ group ($\xi_{\rm RLQ}(\rm rRLQ)=26.85\%$) was approximately twice that of the rQSOs in the whole QSO sample ($\xi(\rm rQSO)=13.07\%$). We noted that the overall fraction of the tRLQs in the RLQ group ($\xi_{\rm RLQ}(\rm tRLQ)=19.14\%$) was smaller than the fraction of the tQSOs in the whole QSO sample ($\xi(\rm tQSO)=24.90\%$). These results suggest that the rQSOs are more likely to be radio-loud than the tQSOs.

We also presented the radio-loud fractions of the QSOs at different luminosities (Figure 6a and Table 5) and at different redshifts (Figure 6b and Table 6). Figure 6a shows that the radio-loud fractions of the rQSOs and the tQSOs increased with luminosities. Furthermore, the rQSOs showed higher radio-loud fractions than the tQSOs did at all luminosities. Moreover, the radio-loud fractions of the rQSOs increased with luminosities faster than those of the tQSOs. However, Figure 6b shows that the radio-loud fractions of the tQSOs did not change with redshift. Nevertheless, the radio-loud fractions of the rQSOs were higher than those of the tQSOs at all redshifts. The radio-loud fractions increased with redshifts at low redshifts ($z=0.3-0.7$), but maintained almost no change (or slightly decreased) at high redshifts ($z=0.8-1.1$). The overall radio-loud fraction of the rQSOs ($\xi_{\rm rQSO}(\rm rRLQ)=16.75\%$) was approximately three times that of the tQSOs ($\xi_{\rm tQSO}(\rm rRLQ)=6.27\%$).

Figure 7 shows the number distribution of the rQSOs and tQSOs at different redshifts. We found that the number ratios of the rQSOs to the tQSOs decreased with increasing redshifts, although the number of the tQSOs increased with redshifts. In addition, at high redshifts, the rQSOs and the tQSOs seemed to have similar luminosity distribution peaks, yet at the lowest redshifts ($z=0.3-0.4$), the rQSOs had a lower luminosity distribution peak than the tQSOs did. To investigate whether the red color was due to dust obscuration, we separated the rQSOs into two different color ranges with $0.66\leqslant r<0.80$ and $r\geqslant 0.80$. We found that at all redshifts, the distributions of these two rQSO groups were not significantly different from each other, indicating that the rQSO luminosity is independent of color.

3.2. Dust – Luminosity Relation

To investigate the differences of dust properties between the rQSOs and the tQSOs, we compared the dust continuum emission at the rest frame of 10µm between these two groups. Since our QSO samples were at redshifts between 0.3 and 1.2, the 10µm continuum emission was redshifted to 13µm – 22µm. Therefore, we used the $M_{10\micron}$ vs. log$(L_{4000})$ diagram (Figure 8a) to present the dust – luminosity relation for the QSOs, where $M_{10\micron}$ is the absolute magnitude at the rest frame 10µm derived from the WISE magnitudes and the SDSS redshifts:

[TABLE]

where $m_{10\micron}$ is the apparent magnitude of the source at $10(1+z)\micron$ in the observer frame, which can be derived from the interpolation from W3 and W4 magnitude.

Figure 8a shows that the $M_{10\micron}$ is proportional to the log($L_{4000}$). The fitted lines for the rQSOs and the tQSOs shows a small separation. The confidence intervals in Figure 8a and Figure 8b are too small to be easily visible, but they are still visible in Figure 8c. Since the confidence intervals did not overlap between the rQSO and the tQSO fittings, the small separation was highly significant.

To determine whether radio activity is related to dust properties, we also present the relation for the RQQs and the RLQs in Figure 8b and Figure 8c, respectively. The results shows that the red samples were more luminous at 10µm than the typical samples for both the RQQs and the RLQs. Notably, the infrared magnitude difference between the rRLQs and the tRLQs was substantially larger than the difference between the rRQQs and the tRQQs.

4. Discussion and Conclusions

Notably, the red QSOs we selected might be different from the red QSOs selected for previous studies. Most red QSOs in previous studies have been selected by photometric color cuts with spectroscopic follow-ups (Cutri et al., 2001; Glikman et al., 2007; Georgakakis et al., 2009; Urrutia et al., 2009; Glikman et al., 2012; Fynbo et al., 2013; Ross et al., 2015). Such selections might include different red QSOs depending on different selection cut-offs. Since our red QSOs were selected based on the flux ratio of the rest frame 4000Å to 3000Å continuum emission, our data excluded sources affected by strong emission lines. In addition, we selected the red QSOs based on the statistical definition. Therefore, we could also include slightly-red QSOs, which can not be found through photometric selection.

Since the SDSS QSOs contained both UVX-pre-selected and FIRST-pre-selected samples (Richards et al., 2002), the color distributions of these two groups of QSOs were expected to be different. The FIRST-pre-selected QSOs were expected to have a wider color distribution than the UVX-pre-selected QSOs, which were expected to be bluer than the FIRST-pre-selected QSOs. To know whether the properties of our selected red QSOs were affected by the selection bias of their FIRST counterparts, we plotted the number distribution for the radio-detected and the radio-non-detected QSOs within the FIRST sky coverage (see Figure 9). Both distributions had the appearance of a Gaussian with an extended right tail. We fitted the left wing of the distributions with a Gaussian and folded the result to the right wing. Both distributions had peaks at $r_{\rm peak}=0.52$ and $\sigma\approx 0.041$, suggesting that the blue wings were similar for both distributions, indicating that our red QSO criterion was not affected by the FIRST-pre-selection. We could find red QSOs from the extended red tails whether the QSOs had FIRST detection or not.

However, the red wings were different; the red wing for the FIRST-detected QSOs extended further than that for the FIRST-non-detected QSOs did. This result might have been caused by the FIRST-pre-selected QSOs having a wider color distribution and more red QSOs. Notably, the FIRST QSOs were not UVX-pre-selected. In other words, a significant amount of red QSOs might have been missing in the UVX-pre-selected process. These red QSOs were not included in the SDSS catalog because of its photometric pre-selection. Comparing Figure 9a and 9b, the results suggest that there should be many more red QSOs, which were not found by SDSS because of the photometric pre-selection used in SDSS. In addition, Figure 6b shows that the radio-loud fractions of the tQSOs did not change with different redshifts, but that the radio-loud fractions of the rQSOs at low redshifts ($z=0.3-0.7$) increased with redshifts and became almost constant at high redshifts ($z=0.8-1.1$). Therefore, explaining the trends of the radio-loud fractions at different redshifts with radio selection bias is difficult. The red QSOs at low and at high redshift might have been caused by different types of reddening, or may be the result of selection effects.

Figure 5 and Figure 7 also support this argument. Both figures show that the rQSOs with low luminosities were mainly present at low redshifts, but the rQSOs with high luminosities were mainly present at high redshifts. This could be explained that at low redshifts, most rQSOs are dust-obscured tQSOs. They become faint at high redshifts and are not detectable. However, the rQSOs at high redshifts with high luminosities might not be dust-obscured tQSOs, but instead might belong to another type of QSOs.

To investigate whether the red color can be explained solely through dust obscuration (Cutri et al., 2002; Glikman et al., 2004; Canalizo et al., 2006), we created number distributions at different wavelength (Figure 10), including the luminosity distribution at 6000Å continuum emission (Figure 10a), and the luminosity distribution of [OIII] 5007Å (Figure 10b). We compared these two distributions with that in Figure 7. If dust obscuration was the main cause for the red color of the QSOs, then absorption would be different at different wavelengths following the dust-extinction curve.

Figure 10a shows the $L_{6000}$ luminosity distributions at low redshifts ($z=0.3-0.6$) because of the limit of the spectrum coverage for high-redshift sources. In Figure 7 and Table 7, the 4000Å luminosity distribution at $z=0.3-0.4$ shows that the median for the rQSOs is log$(L_{4000})=40.73$, and that for the tQSOs is log$(L_{4000})=41.03$. The luminosity difference at 4000Å is $\Delta$log$(L_{4000})=0.3$, which would cause a luminosity difference at 6000Å of $\Delta$log$(L_{6000})\approx 0.2$ if the difference was caused by the dust absorption assuming an SMC dust extinction law (Pei, 1992). Figure 10a and Table 7 show that the rQSOs and the tQSOs at $z=0.3-0.4$ had a luminosity difference at 6000Å of $\Delta$log$(L_{6000})\approx 0.1$. Furthermore, the rQSOs and the tQSOs at $z=0.4-0.6$ had a luminosity difference at 6000Å of $\Delta$log$(L_{6000})<0.1$, indicating that dust absorption was not the only cause of redness.

Figure 10b shows the luminosity distribution of the collisionally excited lines [OIII] 5007Å at redshifts of $z=0.3-0.6$. The [OIII] 5007Å is the strongest and least blended narrow emission line in the AGN (Baskin & Laor, 2005). The luminosity distribution of [OIII] 5007Å depends on AGN activity. Table 8 shows the $t$-test results between the rQSOs and the tQSOs at $z=0.4-0.6$. It shows that the significance values are $0.3-0.6$ (i.e., the mean values of these two groups are indistinguishable), indicating that both groups of QSO at $z=0.4-0.6$ might show similar AGN activity. However, the $t$-test results at $z=0.3-0.4$ indicate that the rQSOs and the tQSOs have different AGN activities. The relatively faint luminosity of rQSOs at $z=0.3-0.4$ (Figure 10a) might have been related to absorption, indicating that the redness of the rQSOs can not be explained solely in terms of dust absorption. Therefore, dust obscuration is not the only cause of the red color for QSOs.

Figure 8 also supports this argument. From the dust – luminosity relation, we found that the rQSOs had a stronger 10µm emission than the tQSOs did, implying that the rQSOs might have had more hot dust than the tQSOs had. Furthermore, the infrared magnitude differences in the RLQs were substantially larger than those in the RQQs. Figure 8c shows that for a given absolute magnitude at 10µm, the magnitude difference between the rRLQs and the tRLQs was approximately 0.5 magnitude, which was larger than the magnitude difference subject to by dust obscuration of $<0.26$ magnitude (see Section 2.1). In other words, the influence of the assumed dust extinction is not as major a cause as the results suggest.

Moreover, Figure 7 shows that the luminosity peaks between the rQSOs and the tQSOs showed no difference in most redshifts ($z=0.4-1.1$) except for the lowest redshifts ($z=0.3-0.4$) where they were significantly different. If the rQSOs were tQSOs with dust obscuration, then the rQSOs should have had a lower luminosity than the tQSOs had at all redshifts. However, the luminosity distributions do not support the dust obscuration scenario. Furthermore, if a redder color represented more dust absorption, then the two groups of rQSOs (less red color with $0.66\leqslant r<0.80$ and much red color with $r\geqslant 0.80$) in Figure 7 should show different luminosity peaks. However, the result does not show a significant difference between these two red groups: the luminosities of the rQSOs were independent of their colors, which also reveals that most rQSOs in this study were not from dust-obscured sources.

On the other hand, the luminosity distributions of the rQSOs at low redshifts were different from those at high redshifts. At high redshifts ($z=0.6-1.2$), the number ratios of the rQSOs to the tQSOs were small, whereas at low redshifts ($z=0.3-0.6$), the number ratios of the rQSOs to the tQSOs were large. In addition, most rQSOs at low redshifts had relatively lower luminosities than the tQSOs had. In other words, the observed red QSOs showed extremely different luminosity distributions at different redshifts, and might have had different origins.

We also investigated whether the redness of the QSOs were caused by type II QSOs in the SDSS QSO samples. Some QSOs in the SDSS QSO catalog might have been from narrow-line sources (Schneider et al., 2010). We plotted the FWHM distribution of the H$\beta$ 4863Å emission for the rQSOs and the tQSOs (Figure 11), and found that most QSOs were broad-line sources; only a few were narrow-line sources, especially among the rQSOs at low redshifts with low luminosities. Approximately 3.6% of the rQSOs were narrow-line sources, and 0.14% of the tQSOs were narrow-line sources (see Table 9). These sources might have belonged to type II QSOs and been caused by dust absorption, or might be contaminated by the red light of stars in their host galaxies. However, the redness of the broad-line rQSOs might have different origins. These results support that there were at least two types of red QSOs in our red sample.

Notably, the colors of our rQSOs were independent of redshifts (Figure 2). Since our rQSOs were selected from the QSO samples with color deviation $>3\sigma$, the number of rQSOs were $<0.3\%$ of the QSO samples when the rQSOs followed a normal distribution. However, the fractions of the rQSOs in the whole QSO sample at low redshifts (e.g., $\xi({\rm rQSO)}=25.95-34.55\%$ at $z=0.3-0.5$ as shown in Table 2) was approximately $2-3$ times larger than the overall fraction of the rQSOs in the whole QSO sample ($\xi({\rm rQSO})=13.07\%$). The fractions of the rQSOs in the whole QSO sample at high redshifts could be much higher than we originally expected.

In conclusion, we suggest that at least two types of red QSOs are present in our red sample. One group are the bright red QSOs, which have a luminosity distribution similar to that of the typical QSOs at the same redshifts. The number of bright red QSOs is substantially lower than that of typical QSOs. The red color is not due dust-obscured sources from typical QSOs. The other group is the faint red QSOs, which have lower luminosities than those of the typical QSOs at the same redshifts. Here the red color could be related to dust obscuration. Notably, these faint red QSOs can easily be detected at low redshifts, whereas at high redshifts, they cannot be detected because of the detection limit.

We are appreciative of Anthony Moraghan for English correction. We also thank the anonymous referee for very useful comments. This work is supported by the Ministry of Science and Technology (MOST) of Taiwan, MOST 103-2119-M-008-017-MY3. This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.