Table 1
Number statistics of the matched Herschel-LOFAR samples.
| Field | Area (deg2) |  (mJy) |
 |
 |
 |
Fmul | NHLIRG | DHLIRG (deg−2) |
|---|---|---|---|---|---|---|---|---|
| Boötes | 8.63 | 45 | 982 (974) | 178 | 330 (326) | 15% | 44 | 5.1 |
| Lockman Hole (LH) | 10.28 | 40 | 1750 (1742) | 269 | 509 (507) | 13% | 164 | 16.0 |
| Elais-N1 (ELAIS-N1) | 6.74 | 35 | 1484 (1470) | 654 | 1266 (1255) | 30% | 125 | 18.5 |
Notes. 
is the adopted 250 μm flux density limit. 
is the number of Herschel sources with a unique LOFAR counterpart, and the number within the brackets is the number of these LOFAR counterparts with redshift estimates (including both spectroscopic and photometric redshifts).
is the number of Herschel sources that are matched to multiple LOFAR sources.
is the number of LOFAR sources in these multiple matches, and the number inside the brackets indicates the number of these LOFAR sources with redshift estimate. Fmul is the fraction of Herschel sources that are matched to multiple LOFAR counterparts. NHLIRG is the total number of HLIRGs, and DHLIRG is the observed surface density of the HLIRGs.
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