Characterising the Extended Morphologies of BL Lacertae Objects at 144 MHz with LOFAR

Blazars, interpreted to be radio-loud active galactic nuclei (AGNs) with relativistic jets oriented at small angles along the line of sight, are the largest known population of sources in the extragalactic γ-ray sky. The small inclination angles result in strong Doppler beaming effects that significantly boost the observed flux of the jet moving toward the Earth and deboost the flux of the counterjet. The jets eventually dissipate either by decollimation or by depositing their kinetic energy in a terminal shock. These processes produce spatially extended diffuse unbeamed emission, which is potentially observable at low frequencies in addition to the beamed emission (as indicated by simulations in, e.g., Hardcastle & Krause 2014; Massaglia et al. 2016).

Blazars are classified as either BL Lac objects, which typically exhibit narrow emission or absorption lines in their optical spectra, or flat-spectrum radio quasars, which have broad emission lines typical of quasars (Landt et al. 2001). Hereinafter we adopt the nomenclature of the blazar catalog Roma-BZCAT (Massaro et al. 2015), labeling the former class of BL Lac objects as BZBs and the latter as BZQs. BZBs are the focus of this study. Their emission is more dominated by nonthermal components than that of BZQs, which can have features such as a dusty torus and a big blue bump in their broadband spectral energy distribution (Wilkes 2004).

According to the unification scheme of radio-loud AGNs (Urry & Padovani 1995), source orientation with respect to the line of sight is key to explaining observational differences between blazars and radio galaxies, with low-excitation and high-excitation radio galaxies (LERGs and HERGs; Hine & Longair 1979) believed to be the parent populations of BZBs and BZQs, respectively. A strong prediction of the unification theory is that at low frequencies the morphologies of BZBs should conform with LERGs viewed at small angles to the jet (see the review by Best & Heckman 2012). For highly aligned sources the low-frequency radio emission is expected to consist of an unresolved beamed core surrounded by extended diffuse emission related to the jet terminus, while for jets with nonzero inclination angles, in addition to the core, there may be emission associated with the large-scale jet and potentially the counterjet including both termination regions.

While there have been gigahertz studies that detected extended emission (e.g., Ulvestad et al. 1983; Antonucci & Ulvestad 1985; Laurent-Muehleisen et al. 1993), to date, the BZBs morphologies at ≤144 MHz have not been systematically explored because no wide-field survey has had the spatial resolution, dynamic range, and sensitivity required to resolve all the components of the sources. Information about the beamed and extended emission has been inferred from spectral studies, where the beamed emission is expected to follow a power law with a flat spectral index (i.e., −0.5 ≤ α ≤ 0.5, where S_ν ∝ ν^α throughout) and the diffuse emission is believed to have a power-law spectral index more typical of optically thin synchrotron emission (α ≈ −0.8). The flat-spectrum beamed component dominates the radio spectrum above ∼1 GHz (e.g., Healey et al. 2007), and in the last decade it has been shown that the spectral indices of blazars are generally flat below ∼1 GHz as well (Massaro et al. 2013b). Indeed, this characteristic flat spectrum at low frequencies has been successfully leveraged in identifying γ-ray sources (Massaro et al. 2014).

Blazars tend to be core-dominated in the gigahertz regime, where the core dominance is a proxy for the beaming factor and hence the inclination angle (Antonucci & Ulvestad 1985; Perlman & Stocke 1993). In the ∼100 MHz regime, it has been inferred that blazars are core-dominated, on the basis of the flat spectral indices (Massaro et al. 2014), but a direct measurement of the core dominances for a sample of blazars has yet to be made. Giroletti et al. (2016) and d'Antonio et al. (2019) estimated the low-frequency core dominances of blazars using a spectral decomposition technique, relying on assumptions about the spectral indices of the core and extended components respectively.

Given the broadband nature of blazar spectral energy distributions, a comprehensive understanding of their low-frequency spectra is paramount to obtain a complete view of blazars. This is highlighted by the radio-to-γ-ray connection, where there is a well-established link between the ≳1 GHz flux and the γ-ray flux, spanning ∼17 decades of energy (e.g., Ackermann et al. 2011). From this, it is inferred that the radio and γ-ray emissions are produced by the same population of relativistic electrons. The relationship between the flux density at hundreds of megahertz and the γ-ray flux is less clear, however (Giroletti et al. 2016; Mooney et al. 2019), possibly because the γ-ray-emitting particles are distinct from the electrons that give rise to the large-scale diffuse emission that is expected to be prevalent at low frequencies.

The Low Frequency Array (LOFAR) is conducting a high-angular-resolution, highly sensitive survey of the Northern Hemisphere sky at 144 MHz (LoTSS; the LOFAR Two-Metre Sky Survey; Shimwell et al. 2017), with more than 21% of the sky observed to date. The LoTSS Second Data Release (LDR2) presents a unique opportunity to make improved low-frequency radio measurements of blazars and, for the first time, investigate the morphology of blazars at 144 MHz. We present LDR2 data for a sample of BZBs and measure the spatial extents, core dominances, and spectral indices to characterize the diffuse emission. The radio-to-γ-ray connection is investigated for the low-frequency core and extended components separately in order to understand why this trend, which is clear at gigahertz frequencies, tends not to be significant at 144 MHz.

This paper is organized as follows: the sample selection is outlined in Section 2, the analysis is detailed in Section 3, the results are presented in Section 4, the findings are discussed in Section 5, and a summary is provided in Section 6. A ΛCDM cosmological model is used in this paper with h = 0.70 (The LIGO Scientific Collaboration et al. 2017), Ω_m = 0.26, and Ω_Λ = 0.74, where H₀ = 100h km s⁻¹ Mpc⁻¹ is the Hubble constant.

2.1. LOFAR Data Set

LOFAR (van Haarlem et al. 2013) is a radio interferometer with stations located throughout Europe. One goal of the LOFAR Surveys Key Science Project (SKSP) is to map the Northern Hemisphere sky at 120–168 MHz; this is known as the LOFAR Two-Metre Sky Survey (LoTSS; Shimwell et al. 2017). In this paper we use data from a subset of the LoTSS Second Data Release (LDR2).

LDR2 data were processed with the SKSP pipeline ¹⁷ version 2.2 as described by Shimwell et al. (2019). In the pipeline, direction-dependent calibration was carried out using killMS (Tasse 2014; Smirnov & Tasse 2015) and imaging was done using DDFacet (Tasse et al. 2018), where a novel self-calibration strategy was employed (Section 5 of Shimwell et al. 2019; Tasse et al. 2021). With this strategy, extended emission that is undetected in early cycles of self-calibration is less likely to be modeled out, and more attention is paid to properly deconvolving that emission. This more complex self-calibration process improved the sensitivity to extended emission with respect to LoTSS DR1 (Tasse et al. 2021). Source catalogs were extracted by the pipeline using PyBDSF (Mohan & Rafferty 2015).

LDR2 observations are in progress. We use the LDR2 data that were available as of 2020 February 1, amounting to 4240 deg² of sky coverage, which is 21% of the Northern Hemisphere sky (Figure 1). This LDR2 subset encompasses the publicly-available LDR1 and the catalog contains 3.6 million sources. The resolution is 6'' with a pixel size of 15 and the median rms noise level is ∼70 μJy beam⁻¹.

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2.2. Ancillary Data Sets

The Faint Images of the Radio Sky at Twenty Centimeters (FIRST; Becker et al. 1995) ¹⁸ survey was used, where available, to visually check for the presence of extended emission at 1.4 GHz. FIRST data were only unavailable for BL Lac objects lying outside its footprint. These data have a comparable resolution to LDR2 (∼5'').

The 144–1400 MHz spectral indices are computed using the NRAO Very Large Array Sky Survey (NVSS; Condon et al. 1998) ¹⁹ with LDR2. NVSS is preferred to FIRST because for extended sources there can be a deficit in the FIRST total flux densities compared to NVSS, particularly for sources with total fluxes in the 2–20 mJy range. This is due to extended flux being undetectable given the lack of short baselines in the FIRST UV coverage (Helfand et al. 2015). However, the FIRST resolution is more favourable than the 45'' resolution offered by NVSS, so FIRST was used over NVSS to look for large-scale jets at 1.4 GHz.

The difference between the spatial resolutions of NVSS and LoTSS is not likely to be problematic (de Gasperin et al. 2018). All BL Lac objects are mainly pointlike in FIRST and NVSS (i.e., consistent with the beam size), and flux densities were computed by integrating over the beam. We also checked the flux densities against those reported in Giroletti et al. (2016) and Massaro et al. (2013a) to verify that no flux was missing (where NVSS had similar beam sizes to these surveys).

We used i-band data from the Panoramic Survey Telescope and Rapid Response System Data Release 1 (Pan-STARRS1; Chambers et al. 2016) ²⁰ to check that, for each BZB, the emission at detected megahertz frequencies is likely associated with its optical counterpart corresponding to the coordinates reported in Roma-BZCAT. Both FIRST and Pan-STARRS1 images for the sample can be seen in Figure 2 online.

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2.3. BZB Sample Selection

The images and the catalog we constructed based on LDR2 were the starting point of this analysis. The extents, core dominances, and spectral indices of the BZBs were calculated as follows.

3.1. Angular and Spatial Extents at 144 MHz

We used the empirically derived equation in Section 3.1 of Shimwell et al. (2019) to determine which BZBs in the sample are resolved (rBZBs) and which are unresolved (uBZBs). This equation defines an envelope separating resolved and unresolved sources,

where S_total is the total flux density of a source, S_peak is the peak flux, and σ is the rms noise as per the LDR2 catalog. If , then the source is classified as an rBZB, otherwise it is a uBZB. In total, there are 66/99 rBZBs and 33/99 uBZBs in the sample.

The intrinsic angular extent, Φ, of each BZB was taken to be the FWHM of the major axis of the source after Gaussian deconvolution of the point-spread function (PSF). For BZBs that consist of multiple Gaussians grouped, the FWHM in the catalog refers to the combination of the major axes of the individual components combined using moment analysis. The median intrinsic angular extent for the rBZBs is (13 ± 2)'' and the median upper limit on the intrinsic angular extents for the uBZBs is (4 ± 1)''.

We computed the spatial extent, D, of each BZB using the intrinsic angular extent and the redshifts, assuming the flat cosmology described in Section 1 of this paper (Wright 2006). For uBZBs, the angular and spatial extents are reported as upper limits.

3.2. Core Dominances at 144 MHz

The core dominance is the ratio of fluxes from the core and extended regions (Giovannini et al. 1990), and the distribution of relative intensities of the core to the extended emission should reflect the distribution of Doppler factors (Antonucci & Ulvestad 1985; Perlman & Stocke 1993). Following on from studies such as that of Morganti et al. (1997), we define the core dominance at 144 MHz, ρ₁₄₄, as

where S_core and S_ext are the core and extended flux densities respectively and the core is defined to be coincident with the AGN central engine. The core dominances are calculated for the rBZBs only.

To calculate ρ₁₄₄ for each rBZB, first the core and extended flux components were separated. We simulated a point source that, when convolved with the LDR2 PSF, had the same peak flux as the core in the LDR2 image. The integration of this Gaussian component represents the core flux density, S_core. We then computed the extended flux density as . Finally, S_core and S_ext were used with Equation (2) to yield ρ₁₄₄.

3.3. Spectral Properties at 144 MHz

4.1. Overview

The median properties of the sample are provided in Table 2, with uncertainties derived from bootstrapping. Values for each BL Lac are reported in this section, with the full table accessible in a machine-readable format.

Table 2. Median Properties of the Resolved and Unresolved BL Lac Objects

	Resolved	Unresolved	Total
N	68	31	99
z	0.38 ± 0.02	0.37 ± 0.04	0.38 ± 0.02
	25.6 ± 0.1	24.8 ± 0.2	25.3 ± 0.2
	−0.37 ± 0.06	−0.12 ± 0.05	−0.30 ± 0.03
ρ144	0.74 ± 0.06	⋯	⋯
D (kpc)	69 ± 4	⋯	⋯
Φ (arcsec)	13 ± 2	⋯	⋯

Note. Number of sources is N, redshift is z, 144 MHz luminosity is L₁₄₄, 144–1400 MHz spectral index is , 144 MHz core dominance is ρ₁₄₄, spatial extent is D, and angular extent is Φ.

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4.2. Visual Inspection of the BZB Images

4.3. Angular and Spatial Extents at 144 MHz

The distribution of angular extents is shown in Figure 3 (bottom) and redshift as a function of angular extent is shown in Figure 3 (top). The BZBs with the most extended emission tends to be at lower redshifts, but generally there is no trend. The median angular extent of the rBZBs is (13 ± 2)''. Note that we classify the sources as rBZBs or uBZBs only to aid the analysis. That is, the uBZBs and rBZBs likely form a continuous distribution rather than representing distinct BZB subclasses.

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Figure 4 shows the distribution of the spatial extents for the rBZBs, where the median value is (69 ± 4) kpc. There is a large spread in the extents, ranging up to 410 kpc, and two sources—J1231+3711 (z = 0.219) and J1340+4410 (z = 0.546)—are more than 300 kpc. While this implies large deprojected (although not necessarily unphysical) sizes, it is possible that these jets are bent to some degree (as is typical for astrophysical jets), which could have the effect of reducing the deprojected sizes.

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4.4. Core Dominances at 144 MHz

We find 19/66 of the rBZBs are core-dominated (i.e., ρ₁₄₄ ≥ 1). The median core dominance of the rBZBs is 0.74 ± 0.06. Figure 5 (bottom) shows the distribution of ρ₁₄₄ for the rBZBs, which spans two orders of magnitude, reflecting the sensitivity of the beaming factor with respect to the inclination angle and the Lorentz factor. There is a trend ²¹ (r = 0.63, N = 64, and p = 3 × 10⁻⁸) between ρ₁₄₄ and (Figure 5; top), where the least core-dominated BZBs tend to have steeper .

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4.5. Spectral Properties at 144 MHz

Of the 99 sources, 22 BZBs have steep spectra (), 74 are flat (), and three are inverted (). The median 144–1400 MHz spectral index for the sample is also flat (−0.30 ± 0.03). A permutation test (Good 2013) was used to show that the median spectral index of the well-resolved sources () is steeper than that of the unresolved sources () at a significance level of p < 3 × 10⁻⁴. The median spectral indices can be classed as flat for both subsamples. Figure 6 shows the distribution of for the uBZBs (top) and rBZBs (bottom).

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4.6. Radio Luminosities and Redshifts

The integrated specific luminosities (W Hz⁻¹) of the sources were taken into account using . Figure 7 (top) shows the luminosity at 144 MHz, L₁₄₄, as a function of redshift, z. While L₁₄₄ loosely increases with z, this could be attributed to Malmquist bias (Malmquist 1925). The redshift distributions for the uBZBs and rBZBs are shown in Figure 7 (middle; bottom). All BZBs in the sample are at z ≤ 0.761, and the median redshifts of the uBZBs and rBZBs are 0.38 ± 0.02 and 0.37 ± 0.04 respectively.

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The distribution of luminosities for the uBZBs and the rBZBs is shown in Figure 8 (top two panels respectively). There is a clear distinction between these distributions, where rBZBs tend to be more luminous. The rBZBs have higher total luminosities due to the presence of more extended radio emission. The luminosities of the core and extended components were then calculated for the rBZBs, where the core and extended spectral indices were assumed to be 0 and −0.8 respectively. This assumption is relatively uncontroversial because the cores of blazars are known to have flat spectral indices, whereas optically thin synchrotron emission has a spectral index close to −0.8. The distributions for the core and extended luminosities are shown in Figure 8 (bottom two panels respectively). While the rBZBs tend to be more luminous than the uBZBs, the distributions of the core luminosities of the rBZBs and the total luminosities of the uBZBs are similar. The total and core luminosities are shown as a function of redshift in Table 3.

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Table 3. Median Total and Core Luminosities of Resolved and Unresolved BL Lac Objects

z	Resolved				Unresolved
	N	Ltotal	Lcore		N	Ltotal
0.0–0.2	8	3.7 × 1024	1.4 × 1024		5	2.0 × 1024
0.2–0.4	29	3.2 × 1025	9.2 × 1024		14	4.9 × 1024
0.4–0.6	18	8.4 × 1025	1.9 × 1025		12	1.0 × 1025
0.6–0.8	11	5.5 × 1025	2.3 × 1025		2	1.5 × 1026
All	66	3.5 × 1025	1.2 × 1025		33	6.2 × 1024

Note. Redshift bin is z, number of sources is N, total luminosity is L_total, and core luminosity is L_core (both in W Hz⁻¹).

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4.7. The Radio-to-γ-ray Connection

In total, 53/99 BZBs had γ-ray detections; properties of the γ-ray BZBs are given in Table 4. The medians of the logarithms of the integrated photon fluxes at 1–100 GeV for the rBZBs (−9.61 ± 0.08) and uBZBs (−9.61 ± 0.13) are the same within uncertainty. The γ-ray-detected and non-γ-ray-detected BZBs are similar in terms of spatial extents, angular extents, luminosities, and core dominances. However, the γ-ray BZBs tend to have smaller redshifts. The median radio spectral index of the γ-ray BZBs is also slightly flatter than that of the BZBs without a detection.

Table 4. Median Properties of the γ-ray- and Non-γ-ray-detected BL Lac Objects

	γ-ray	Non-γ-ray
N	53	46
z	0.29 ± 0.04	0.46 ± 0.02
	25.3 ± 0.3	25.3 ± 0.1
	−0.26 ± 0.05	−0.38 ± 0.06
	−9.6 ± 0.1	⋯
Next	36	30
ρ144	0.83 ± 0.17	0.72 ± 0.05
D (kpc)	70 ± 15	69 ± 6
Φ (arcsec)	15 ± 3	12 ± 1

Note. Reported uncertainties are the standard error. Number of sources is N, redshift is z, 144 MHz luminosity is L₁₄₄, 144–1400 MHz spectral index is , γ-ray flux is S_GeV, number of extended BL Lac objects is N_ext, 144 MHz core dominance of extended BL Lac objects is ρ₁₄₄, spatial extent of extended BL Lac objects is D, and angular extent of extended BL Lac objects is Φ.

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Table 5. Details of the BZB Sample

Name	R.A.	Decl.	z	Resolved?	Stotal	SGeV		ρ144	D	Φ	L144
	(deg)	(deg)			(mJy)	(ph cm−2 s−1)			(kpc)	(arcsec)	(W Hz−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
J0047+3948	11.9801	39.8160	0.252	T	264 ± 53	(7.4 ± 0.5) × 10−10	−0.46 ± 0.09	0.36 ± 0.07	68.1 ± 0.4	17.1 ± 0.1	(4.6 ± 0.9) × 1025
J0112+2244	18.0243	22.7441	0.265	T	233 ± 47	(8.0 ± 0.2) × 10−9	0.22 ± 0.04	1.21 ± 0.25	38.3 ± 0.1	9.3 ± 0.1	(3.9 ± 0.8) × 1025
J0123+3420	20.7860	34.3468	0.272	T	169 ± 34	(2.4 ± 0.4) × 10−10	−0.60 ± 0.12	0.20 ± 0.04	95.9 ± 0.4	22.9 ± 0.1	(3.6 ± 0.7) × 1025
J0203+3042	30.9345	30.7105	0.761	T	345 ± 69	(2.24 ± 0.09) × 10−9	−0.30 ± 0.06	0.84 ± 0.17	130.7 ± 0.3	17.4 ± 0.1	(6.4 ± 1.3) × 1026
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
J1808+3520 a	272.2071	35.3452	0.141	T	94 ± 19	(2.2 ± 0.4) × 10−10	−0.50 ± 0.10	0.19 ± 0.04	72.7 ± 0.8	29.1 ± 0.3	(4.7 ± 0.9) × 1024
J2229+2255 a	337.2966	22.9166	0.440	T	18 ± 4	⋯	0.35 ± 0.07	0.31 ± 0.06	58.3 ± 1.7	10.1 ± 0.3	(8.9 ± 1.8) × 1024
J2237+1840 a	339.2701	18.6822	0.722	F	7 ± 1	⋯	−0.08 ± 0.02	⋯	≤28.1 ± 0.7	≤3.8 ± 0.1	(9.9 ± 2.0) × 1024
J2343+3439	355.8899	34.6641	0.366	T	203 ± 41	(3.9 ± 0.5) × 10−10	−0.79 ± 0.16	0.11 ± 0.02	151.9 ± 1.7	29.6 ± 0.3	(8.9 ± 1.8) × 1025

Note. (1) Source name. (2, 3) Coordinates in the J2000 frame. (4) Redshift. (5) A flag stating whether the source is resolved ("T") or not ("F"). (6) Integrated flux density at 144 MHz from LDR2. (7) γ-ray flux from 4LAC. (8) 144–1400 MHz spectral index with LDR2 and NVSS. (9) Core dominance. (10) Spatial extent. (11) Angular extent. (12) Radio luminosity.

^a BZBs not in Roma-BZCAT v5.0.

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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Figure 9 shows the total (top), core (middle), and extended (bottom) 144 MHz flux density against S_GeV for the rBZBs. The Pearson correlation coefficient between S_total and S_GeV is 0.52 (N = 36 and p = 1 × 10⁻³). For S_core and S_GeV, r increases to 0.69 (N = 36 and p = 3 × 10⁻⁶), while for S_ext and S_GeV, r = 0.42 (N = 35 and p = 1 × 10⁻²).

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Previous studies identified extended emission at gigahertz frequencies around BZBs (e.g., Ulvestad et al. 1983), but the preliminary LoTSS Second Data Release has made it possible to systematically study the morphology of BZBs at 144 MHz for the first time, where we expect to find a larger fraction of diffuse emission due to the steeper spectra of the extended structures. We identified extended emission around 66/99 BZBs at 144 MHz. We compare BZBs and LERGs because unification theories for radio-loud AGNs predict that these observational source classifications are the same source type intrinsically (Capetti et al. 2020; Massaro et al. 2020a, 2020b). The spatial extents spanned a wide range (up to 410 kpc), and this is in line with predictions of the AGN unification scenario, where BZBs are LERGs viewed end-on, because LERGs range from several kiloparsecs to several megaparsecs in the plane of the sky. For the BZBs that were not found to be extended, it is possible that the resolution is insufficient to spatially resolve these sources, or that extended low-surface-brightness radio emission exists below the LDR2 sensitivity. Particularly for the BZBs with S_total ≲ 40 mJy, the extended emission may be below the detection threshold of LDR2.

The core luminosities per redshift bin of the rBZBs are comparable to the total luminosities of the uBZBs, suggesting no major difference in intrinsic core power between the two sources. That is, at a given core power we find large ranges of D and L_ext. A similar effect has also been seen in Faranoff–Riley class 0 sources (FR-0s; Baldi et al. 2015) and FR-Is, where Capetti et al. (2020) found that for a given core power, FR-0s tend to have fainter diffuse emission than FR-Is. The key variables controlling whether a BZB is extended or not is unclear, and could relate to the initial conditions or the environment. It is possible that either the uBZBs have only switched on recently, where the AGN activity is too recent to have produced plumes, or perhaps that they have been switched off for ≳10⁸ yr, as suggested by Punsly et al. (2015), where this timescale is an upper limit based on the fact that the synchrotron break frequency drops to ≲100 MHz, assuming , a ∼1 μG magnetic field, and no new injections of energetic particles (Cordey 1986; Jamrozy et al. 2007).

We directly measured the core dominances of the extended BZBs by separating the core and extended flux components. Our results are broadly in line with Giroletti et al. (2016) and Fan & Wu (2018), where the core dominances of blazars were calculated by decomposing S_total using estimates of the core and extended spectral indices. While the core component contributes more than half of the total flux for 19/66 of the rBZBs, the majority of these extended BZBs were not core-dominated. This finding is in agreement with d'Antonio et al. (2019), where they state that deeper low-frequency surveys should result in lower core dominances because more radio lobe emission can be detected. Thus, the core dominance may not be a reliable parameter for selecting new blazar candidates in future low-frequency surveys.

The median radio spectral index for the sample is flat, which confirms several recent studies that have found that BZBs, and blazars generally, have flat spectral indices down to ∼100 MHz at least (Giroletti et al. 2016; d'Antonio et al. 2019; Mooney et al. 2019). However, the most extended BZBs tended to have spectral indices closer to −0.8, similar to classic radio galaxies, likely due to the presence of diffuse emission.

The population of relativistic electrons that give rise to the beamed radio emission are thought to be responsible for producing the γ-ray emission, by upscattering seed photons from external radiation fields to γ-ray energies. This is believed to be also the mechanism behind the radio-to-γ-ray connection at gigahertz frequencies. Previous studies have shown that this correlation weakens with decreasing radio frequency (e.g., Giroletti et al. 2016; Mooney et al. 2019). By calculating the radio-to-γ-ray correlation using the core and extended flux densities at 144 MHz separately, we have shown that this connection weakens at low radio frequencies because there is an increase in diffuse emission. The diffuse megahertz emission is not expected to correlate strongly with the γ-ray emission because the former is unbeamed, and the electron population producing it is likely to be distinct from the electrons that give rise to the γ-rays, reflecting the time-integrated history of jet activity rather than the instantaneous view given by the core emission. In contrast, the beamed core emission at low frequencies still correlates reasonably well with the γ-ray photon flux. Finally, we highlight that all data collected and analyzed for our BL Lac sample are reported in Table 5, which is accessible in machine-readable format.

We have presented the first morphological study of a sample of BZBs at 144 MHz. Our findings are as follows.

• 1.  
  Extended emission was revealed around 66/99 BZBs. The distributions of spatial extents and the extended component luminosities at 144 MHz are consistent with expectations based on the AGN unification paradigm, where BZBs are the aligned counterparts of LERGs. For a given core luminosity and redshift, a range of spatial extents were found.
• 2.  
  The median integrated 144–1400 MHz spectral index for the BZBs was −0.30 ± 0.03, confirming that the low-frequency spectra of BZBs are still dominated by the beamed core component, but this depends on the spatial extent, with the spectral index being steeper for more extended BZBs.
• 3.  
  Of the 66 rBZBs, 19 were core-dominated at 144 MHz, and the most core-dominated sources tended to have smaller spatial extents and flatter spectral indices.
• 4.  
  Positive correlations were identified between the 1–100 GeV flux and both the 144 MHz total (r = 0.52) and core (r = 0.69) flux densities for the rBZBs. The correlation between the γ-ray flux and the extended emission was weaker (r = 0.42). This suggests that the 144 MHz emission from the core is more likely to be directly related to the present nuclear activity than the large-scale extended emission.

Characterising the diffuse emission around BZBs can help to explain some of the outstanding questions regarding blazars. For example, measurements of the diffuse flux allow for estimates of the jet power via scaling relations (Meyer et al. 2011). Calculating the jet power can shed light on the relationship between the jet power and the AGN accretion rate, while estimates of the diffuse flux and the spatial extent can also be used to characterize the environments. We focused on BZBs using LoTSS, the most sensitive low-frequency survey in existence. In future, LoTSS in-band spectral index maps will make it possible to distinguish between the beamed jet flux and the unbeamed diffuse flux that contribute to the extended emission. Other forthcoming surveys will help further constrain the 144 MHz morphology of BZBs. The LOFAR LBA Sky Survey (LoLSS; de Gasperin et al. 2021) will eventually cover the Northern Hemisphere sky at 42–66 MHz at a sensitivity of 1 mJy beam⁻¹ and 15'' resolution. With LoLSS, we will be able to identify possible ultrasteep-spectrum radio halos around the unresolved BZBs that are undetectable in LDR2. The future sky survey with the LOFAR international stations (Morabito et al. 2021) will image the 122–168 MHz sky at 03 resolution, potentially spatially resolving some of the unresolved BZBs. In addition, optical spectra provided by the WEAVE-LOFAR survey (Smith et al. 2016) will be beneficial in identifying LDR2 counterparts to unidentified γ-ray sources. In the long term, surveys with the Square Kilometre Array will also be key in studying this population (Kharb et al. 2016).

S.M. acknowledges support from the Irish Research Council Postgraduate Scholarship and UCD U21 funding. B.M. acknowledges support from the UK Science and Technology Facilities Council (STFC) under grants ST/R00109X/1 and ST/R000794/1. M.J.H. acknowledges support from STFC [ST/R000905/1]. F.M. acknowledges financial contribution from the agreement ASI-INAF n.2017-14-H.0. This work is supported by the "Departments of Excellence 2018–2022" grant awarded by the Italian Ministry of Education, University and Research (MIUR) (L. 232/2016). This research has made use of resources provided by the Compagnia di San Paolo for the grant awarded on the BLENV project (S1618_L1_MASF_01) and by the Ministry of Education, Universities and Research for the grant MASF_FFABR_17_01. This investigation is supported by the National Aeronautics and Space Administration (NASA) grants GO4-15096X, AR6-17012X, GO6-17081X, GO9-20083X, and GO0-21110X.

LOFAR is the Low Frequency Array designed and constructed by ASTRON. It has observing, data processing, and data storage facilities in several countries, which are owned by various parties (each with their own funding sources), and which are collectively operated by the ILT foundation under a joint scientific policy. The ILT resources have benefited from the following recent major funding sources: CNRS-INSU, Observatoire de Paris, and Université d'Orléans, France; BMBF, MIWF-NRW, MPG, Germany; Science Foundation Ireland (SFI), Department of Business, Enterprise and Innovation (DBEI), Ireland; NWO, The Netherlands; The Science and Technology Facilities Council, UK; Ministry of Science and Higher Education, Poland; The Istituto Nazionale di Astrofisica (INAF), Italy.

This research made use of the Dutch national e-infrastructure with support of the SURF Cooperative (e-infra 180169) and the LOFAR e-infra group. The Jülich LOFAR Long Term Archive and the German LOFAR network are both coordinated and operated by the Jülich Supercomputing Centre (JSC), and computing resources on the supercomputer JUWELS at JSC were provided by the Gauss Centre for Supercomputing e.V. (grant CHTB00) through the John von Neumann Institute for Computing (NIC).

This research made use of the University of Hertfordshire high-performance computing facility and the LOFAR-UK computing facility located at the University of Hertfordshire and supported by STFC [ST/P000096/1], and of the Italian LOFAR IT computing infrastructure supported and operated by INAF, and by the Physics Department of Turin university (under an agreement with Consorzio Interuniversitario per la Fisica Spaziale) at the C3S Supercomputing Centre, Italy.

The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, the Queen's University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation grant No. AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.

The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

Facilities: LOFAR - , Haleakala Observatory (Pan-STARRS) - , and VLA. -

Software: DDFacet (Tasse et al. 2018), KillMS (Tasse 2014; Smirnov & Tasse 2015), Python (van Rossum 1995), NDPPP (van Diepen et al. 2018), NumPy (van der Walt et al. 2011), Astropy (Astropy Collaboration et al. 2013), TOPCAT (Taylor 2005), PyBDSF (Mohan & Rafferty 2015), and Matplotlib (Hunter 2007).