The use of color selection to identify high-z objects was first proposed more than four decades ago (e.g., Meier, 1976a,b). Since then this approach has been applied successfully to select quasars up to z ≳ 6 (Fan et al., 2001; Willott et al., 2007). The multi-color selection for finding high-z quasars usually employs at least 3 bands: one containing the Lyα emission line, one blueward (the dropout band), and one redward. This translates into a set of colors that can be to used to locate the Lyα emission line.

Although, quasars are starlike in appearance their radiation mechanisms are different to those of stellar sources. Stars have approximately single-temperature black-body spectral energy distributions (SEDs) (Bisnovatyi-Kogan, 2001), whereas energetic processes sculpt the distinctive power-law SEDs of quasars (Davidson and Netzer, 1979). These differences in the SEDs imply that stars and quasars occupy different regions in colorspace (Fan, 1999). Thus, in principle, optical color cuts can be chosen to reject the majority of stars.

The 9.2 deg² region in Boötes covered by the NOAO Deep Wide Field Survey (NDWFS, Jannuzi and Dey 1999) has optical data available on the U_spec, B_w, R, I, and Z bands. All these filters are standard except the U_spec and B_w, which have better efficiency and a more uniform wavelength coverage than the U-Bessel and B-Johnson filters, respectively. Additionally, the Boötes field has multi-wavelength coverage spanning from X-rays to radio wavelengths. In the X-rays and UV regimes, it has been observed with the Chandra (Kenter et al., 2005) and GALEX (Martin et al., 2003) satellites. At infrared wavelengths, it was part of the NEWFIRM survey (J,H,K bands; Autry et al., 2003) and Spitzer Deep, Wide-Field Survey (SDWFS) with IRAC (Ashby et al., 2009). Finally, in the radio regime, the Boötes region has been observed at 1.4 GHz with the VLA (Becker et al., 1995) and WSRT (de Vries et al., 2002), and at 150MHz with GMRT (Williams et al., 2013) and LOFAR (Williams et al., 2016). In this work, we use the deep 150 MHz LOFAR imaging presented by Retana-Montenegro and Röttgering (in preparation), with a noise level of 1σ~50μJy with a spatial resolution of 5″. We use AB magnitudes for all bands in our analysis. We assume the convention Sν∝ν-α, where ν is the frequency, α is the spectral index, and S_ν is the flux density as function of frequency.

To test our quasar selection method, we utilize spectroscopy data from the AGES survey (Kochanek et al., 2012). While the spectroscopic sample spans the range 0 < z < 5.8, we limit our selection to the intervals 1.0 ≤ z ≤ 2.0 and 2.0 ≤ z ≤ 3.0. The reason for using these two redshift intervals is twofold. First, quasars in these intervals provide a good test for our selection method. Secondly, there are more spectroscopically confirmed quasars for the redshift intervals considered as compared to those available at z > 3.0.

Quasars at 1.0 ≤ z ≤ 2.0 are frequently selected using the excess of ultra-violet flux in the u-band, which results in a bluer u-g color as compared to that of stars with the same visual color (e.g., the g-r color) (Richards et al., 2002). However, the NDWFS-Boötes bandpass system (U_spec,B_w,R,I,Z) does not include a g filter found in other photometric systems such as the SDSS filter set (u,g,r,i,z) (Fukugita et al., 1996). But instead the non-standard U_spec (λ_c = 3590, FWHM=540) and B_w (λ_c = 4111, FWHM=1275) filters had been used. The main disadvantage of the U_spec and B_w filter combination is the significant wavelength overlap between the two filters. This implies that quasars at 1.0 ≤ z ≤ 2.0 can not be efficiently selected using their U_spec − B_w colors.

To optimally define the color cuts for candidate quasars at 1.0 < z < 2.0, we generate a library of synthetic quasar spectra following the procedure described in detail by Retana-Montenegro et al. (in preparation). These spectra are convolved with the NDWFS-Boötes filter curves to calculate the colors for the selection of 1.0 < z < 2.0 quasars. Based on the colors derived, we adopt the color cuts shown by magenta lines in the first panel of Figure 1. These color cuts are:

where y = B_w − R and x = U_spec − Z.

Based on the colors obtained from simulated quasar spectra, we derive the color cuts to select 2.0 ≤ z ≤ 3.0 quasars. The color cuts adopted for the selection are the following:

To reduce contamination from low-z star-forming galaxies in our quasar samples we adopt in both redshift bins the color cuts proposed by Donley et al. (2012):

and Lacy et al. (2007):

where w=log10(S5.8μmS3.6μm) and z=log10(S8.0μmS4.5μm).

Having defined the color cuts, the next task is to crossmatch the catalogs to find radio counterparts of the optical sources. We initially search for radio sources that lie within a radius of 2″ from the optical source that fulfill our color cuts with a 5σ detection in our LOFAR catalog. For each one of these objects, we inspect its images in at least 4 bands. During this examination, we require that our candidate quasars are unresolved, not close to a bright neighbor and not blended. Additionally, we examine the morphology of the radio counterparts to prevent imaging artifacts or radio-lobes being incorrectly matched to optical sources. This examination of the radio maps ensures that only robust radio counterparts are matched to optical sources. Finally, we performed SED fitting to these sources with the photometric redshift code EAZY (Brammer et al., 2008). This allow us to assess the overall quality of the quasars photometry and to filter out contaminants from our sample. Figure 2 shows two candidate quasars SEDs from our sample.

An important aspect to consider is the accuracy of the photometric redshifts. An inaccurate photometric redshift may cause the rejection of a quasar candidate. In Figure 3, we compare the EAZY z_photo and z_spec in the range 1.0 < z < 3.0 for Boötes spectroscopic quasars with a signal-to-noise greater than 5σ. The objects that are catastrophic outliers (i.e., objects with a difference between the photometric and spectroscopic redshift larger than the 3σ uncertainty for the photometric redshift) based on the one-to-one relation are found using an iterative 3σ-clipped standard deviation. The fraction of catastrophic outliers is around 3.1%. After catastrophic outliers are eliminated, we compute the standard dispersion δz = (z_photo − z_spec)/(1 + z_spec) (Ilbert et al., 2006), and the normalized median absolute deviation (NMAD), defined as NMAD(δz) = 1.48×Median(δz) (Hoaglin et al., 1983). We find δz = 0.15 and NMAD = 0.12. For comparison, Salvato et al. (2011) obtained more accurate photometric redshifts for COSMOS quasars with NMAD = 0.015 using 30 bands, while Assef et al. (2010) found δz = 0.18 for point-source AGNs in Boötes. Therefore, we conclude that fraction of candidates quasars rejected with inaccurate z_photo is small in comparison with the total number of candidates in the final sample.

The optical and MIR colors of the spectroscopic quasars detected by LOFAR in the Boötes field are shown in Figure 1. The colors of the spectroscopic quasars are generally consistent with the proposed color cuts. Figure 4 shows the colors for the 154 candidate quasars selected using our method.

In order to assess the performance of our selection method, we calculate the completeness and efficiency for our samples.

We define the completeness C as the number of spectroscopic quasars selected as candidates compared to the total number of spectroscopic quasars (Hatziminaoglou et al., 2000; MacLeod et al., 2010a):

Similarly, the efficiency E, i.e., the number of spectroscopic quasars selected as candidates compared to the number of objects selected as candidate quasars, is defined as:

At 1.0 < z < 2.0, our selection method identifies 59 of the 116 radio quasars with spectroscopic confirmation, resulting in a completeness of 51%. In the range 2.0 < z < 3.0, 25 of 40 quasars pass our selection, which results in a completeness of 62%. For the entire redshift interval considered, we obtain a completeness of 54%.

With our method, we find 74 quasars candidates at 1.0 < z < 2.0 , which corresponds to an efficiency of 80%. In the range 2.0 < z < 3.0, 84 candidate quasars are identified, which gives E = 30%. For the full range, we find an efficiency equal to E = 53%.

In this section, we investigate the effect of the radio spectral index distribution on our selection of candidate quasars. We therefore combine our LOFAR data with the deep 1.4 GHz radio survey of the Boötes field obtained using the Westerbork Synthesis Radio Telescope (WSRT) telescope (de Vries et al., 2002). The WSRT-Boötes observations reach a rms noise of 1σ ~ 28μJy, with an angular resolution of 13″ × 27″. To compare the LOFAR and WSRT maps, we must take into account that there are incompleteness effects due to the different noise levels between the two observations. Therefore, we compare the LOFAR and WSRT observations using a flux density threshold of S_150MHz = 1.5mJy. For a spectral index of −0.7 (Smolčić et al., 2017), this threshold is approximately equivalent to a noise level of 11σ in the WSRT-Boötes map, and ensures all the α > −1.0 sources with a signal-to-noise > 5σ will be detected in the WSRT-Boötes map. The spectral index distribution for the 1998 sources in the LOFAR-WSRT sample has a median of α = −0.65 ± 0.016.

Using these cuts, in the overlapping area between the LOFAR and WSRT maps, we find that 42 of 154 candidate quasars are detected at 1,400 MHz. The detected objects have a spectral index distribution with a median value of α = −0.73 ± 0.07 (see Figure 5). Using the flux density threshold of S_150MHz ≥ 1.50 mJy, we find that the spectral index distribution of the 21 candidate quasars in this sample is steeper than the general LOFAR-WSRT spectral index distribution with a median of α = −0.80 ± 0.06. The 21 candidate quasars detected at 1, 400MHz with S_150MHz < 1.5 mJy are characterized by a steeper spectral index distribution compared to the LOFAR full sample with a median value of α = −0.71 ± 0.05. For the remaining 112 candidates undetected by WSRT, we derive an upper limit for their spectral indices assuming a 5σ WSRT detection (S_1.4GHz = 0.140 mJy). The median upper limit of the distribution of spectral indexes for these objects is α_upp < −0.75. In the WSRT footprint, there are 70 of 139 spectroscopic quasars detected by WSRT. These detected quasars have a steeper distribution of spectral indices compared to the LOFAR-WSRT full sample with a median of α = −0.70 ± 0.06.