Towards a Luminosity Function of TeV Gamma-ray Blazars
TTowards a Luminosity Function of TeV Gamma-rayBlazars
Aryeh Brill ∗ , for the VERITAS Collaboration †‡ Columbia University, Department of Physics, New York, NY, USAE-mail: [email protected]
Over seventy blazars identified as sources of TeV gamma ray emission have been detected, includ-ing approximately sixty BL Lac objects and seven flat spectrum radio quasars. The distributionin space of these objects can be described by a luminosity function, which gives their comovingspace density as a function of their luminosity. We investigate a source selection method to beused for determining the luminosity function of TeV gamma-ray blazars using observations fromVERITAS, a ground-based gamma-ray observatory consisting of an array of four atmosphericCherenkov telescopes located in southern Arizona. ∗ Speaker. † https://veritas.sao.arizona.edu/ ‡ for collaboration list see PoS(ICRC2019)1177 c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/ a r X i v : . [ a s t r o - ph . H E ] A ug owards a Luminosity Function of TeV Gamma-ray Blazars Aryeh Brill
1. Introduction
Imaging atmospheric Cherenkov telescopes (IACTs) have detected over seventy TeV gamma-ray blazars, including about sixty BL Lac objects and seven flat spectrum radio quasars (FSRQs;Figure 1). These detections come from over a decade of observations by both current-generationIACTs and the
Fermi gamma-ray space telescope. With this rich dataset, we can study TeV blazarsnot just as individual sources but as a population. A key to understanding TeV blazars as a popula-tion is deriving their luminosity function (LF). The LF gives the comoving space density of thesesources as a function of their luminosity, describing how they are distributed in space.Estimating the LF of TeV blazars has numerous scientific motivations. To start, integrating theLF and subtracting the contribution from resolved sources provides an estimate of the contributionof blazars to the diffuse extragalactic gamma-ray background (EGRB) at ∼
100 GeV and above.Blazar jets may produce neutrinos as well as gamma rays via pion production if they contain rel-ativistic protons. Extrapolating the energy density of the gamma-ray blazar EGRB contributionto that of the isotropic high-energy neutrino flux using a power-law emission model provides asource-independent way to estimate the extent to which blazars produce high-energy neutrinos [1].In addition, emission above ∼ Fermi -LAT at 100 MeV - 100GeV [2] [3], as well as earlier using the smaller sample of blazars detected by EGRET between20 MeV and 30 GeV [9]. Here, a preliminary investigation is conducted to study the requirementsfor deriving the luminosity function of TeV blazars using archival data from VERITAS, whichintroduces several complications not present with data from all-sky blazar surveys conducted atlower energies. VERITAS is an array of four IACTs sensitive to gamma rays with energies between100 GeV and >30 TeV, located in southern Arizona. It has a 3.5 ◦ field of view and observes onlyunder clear, dark skies. VERITAS regularly monitors known and candidate TeV blazars and followsup flaring events seen in its own and multiwavelength observations [5].
2. Challenges for Creating a TeV Blazar Luminosity Function
A common approach for determining the LF and evolution of a population of sources givena flux-limited survey is to use a maximum likelihood (ML) estimator to fit a parameterized modelusing each source’s luminosity, redshift, and any other source properties to be modeled. Thismethod avoids binning the data, thereby reducing information loss and preventing potential biases1 owards a Luminosity Function of TeV Gamma-ray Blazars
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Figure 1: Left: The extragalactic TeV sky in Galactic coordinates [16]. Right: Redshift distributionof the 60 TeV blazars with known redshifts.caused by evolution within the bins, at the cost of introducing the assumption that the LF take aparticular functional form.However, performing a population study with a pointed instrument like VERITAS is morecomplicated than with all-sky instruments. The short, targeted observations performed by IACTsare highly sensitive to blazars’ significant flux variability. Observations may be taken dispropor-tionately during flaring states, biasing estimates of average flux. The effects of absorption on theextragalactic background light (EBL), too, become important at very high energies. IACTs havean overall low integration time and their sky coverage depends strongly on observation strategy,which is generally not geared toward conducting a uniform survey. Among other biases, IACTobservations are not randomly distributed on the sky, but concentrated on known sources (either ingamma rays or other wave bands). Given this bias, it is not valid to consider IACT observations asa uniform survey limited by the sensitivity of TeV observations alone. The remainder of this articleconsiders a method to counteract source selection bias, leaving other challenges for future work.
3. Source Selection Study
Constructing a valid TeV blazar LF requires emulating a uniform, flux-limited survey. Onemethod to do this is to consider subsets of targets in a multiwavelength catalog that fulfill physicallymotivated selection criteria. For example, a
Fermi -LAT blazar catalog could be used, or an X-ray one motivated by the production of TeV emission by X-rays undergoing inverse Comptonscattering. This procedure matches how VERITAS chooses bright sources from catalogs of blazarsof various source classes for blazar discovery observations [5], e.g. 2WHSP, an infrared catalogof high synchrotron peaked blazars [8], for HBLs. The selection criteria and catalog sensitivityare then used to derive an approximate TeV flux limit. Assuming all TeV emitters of the givensource class are in the underlying catalog, and that the catalog itself provides an unbiased, completesample, this process results in a complete, uniform survey up to the TeV flux limit. The chosencatalog and selection criteria must maximize completeness while minimizing false positives. Ofcourse, in order to use archival data, the selected sources that are visible must already have beenobserved. Multiple catalogs may be combined to obtain sources of different classes.2 owards a Luminosity Function of TeV Gamma-ray Blazars
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The above method can be illustrated using the objects selected by Costamante & Ghisellini(2002; CG02) [11], who produced a list of 33 candidate (and 5 already-known) TeV BL Lac objectsusing selection limits on the X-ray and radio energy flux. Their sources were selected from a set ofBL Lac samples for which radio, optical and X-ray observations were all available, including somesurveys with coverage of the entire Northern sky, with others looking at bright sources only. Of the38 candidate and known sources, 30 now have TeV detections [16] and all have 4FGL associations[12]. 31 are visible to VERITAS (declination between − ◦ and + ◦ ), which has detected 20 andpublished upper limits on 8 of them [4].The CG02 TeV candidate BL Lac objects can be used to explore the potential, and possiblepitfalls, of this source selection approach for emulating a TeV blazar survey. To be useful, a sourceselection method based on an external catalog must both allow for the establishment of an effectiveTeV flux limit and provide a reasonably complete sample. The results of a preliminary investigationusing these sources as the selected sample are shown in Figures 2, 3, and 4.Figure 2: Distribution of the predicted TeV fluxes above 0.3 TeV from Costamante & Ghisellini(2002; CG02) [11] from EBL absorption applied using Model C of [13]. EBL absorption wasapplied using the redshift of each source from TeVCat [16] or SIMBAD [18], or z = . E th = . Γ = . F X = . µ Jy at ν X =
4. Discussion
One way to obtain a predicted TeV flux given the observed fluxes at other wavelengths is toderive it from a model of the spectral energy distribution (SED) fitted to the multiwavelength data.3 owards a Luminosity Function of TeV Gamma-ray Blazars
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Figure 3: Distribution of the fluxes of VERITAS detected blazars and upper limits, overlaid onthe CG02 flux predictions shown in Figure 2. The solid dark blue histogram shows the energyfluxes of the 33 BL Lac objects detected by VERITAS, using fluxes in Crab Units and spectralindices from TeVCat [16], assuming F Mrk 501 = .
85 Crab and Γ = . . × − cm − s − TeV − . The photon flux was converted into energy flux above 0.3 TeV using thespectral index, assuming a power law spectrum. No attempt was made to distinguish average fluxesor spectra from those in flaring or other states. The dashed-dotted light blue histogram shows thedistribution of VERITAS blazar upper limits from [4], with differential flux limits converted energyflux assuming E th = . Γ = . . × − erg cm − s − [7].Fortunately, this is exactly what CG02 have already done. They apply two models, a one-zoneSynchrotron Self-Compton (SSC) model and the parameterization of [14], built to describe sourceswith synchrotron and self-Compton peaks of equal power, and use both to predict the energy fluxesabove 40 GeV, 0.3 TeV and 1 TeV without incorporating absorption by the EBL. Figure 2 showsthe distributions of the flux predictions above 0.3 TeV for the two models, with EBL absorptionusing the Model C from Finke et al. (2010) [13] additionally applied.A second way to obtain a TeV flux limit is to use a simple physically motivated relationshipbetween luminosities at different wavelengths, such as that of Stecker et al. (1996), ν TeV F TeV ∼ ν X F X for X-ray selected BL Lac objects [15]. An extrapolation using this relationship of the X-rayselection flux limit of CG02, F X = . µ Jy, with the same EBL absorption correction applied,is also shown in Figure 2. The predicted fluxes span over three orders of magnitude, with theextrapolated X-ray limit over an order of magnitude higher in flux than the lowest TeV predictionof each of the two models. For these predictions and luminosity relation to provide a useful fluxlimit, the predicted fluxes should cut off sharply at the low-flux end at a level consistent with the4 owards a Luminosity Function of TeV Gamma-ray Blazars
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Figure 4: Distribution of energy fluxes of BL Lac objects detected by VERITAS from Figure 3,split into those included in the candidates or known sources of Costamante & Ghisellini (2002;CG02) [11] (solid green), and those that are not (dotted red).extrapolated flux limit. However, this behavior is not evident.In addition, to take the selected sources as the basis for a flux-limited sample, the sensitivityof actual observations must match the supposed flux limit. Figure 3 shows the predicted fluxesof CG02 overlaid with the fluxes of the BL Lac objects actually detected by VERITAS, as wellas upper limits of blazar discovery targets observed but not detected. The reported blazar fluxesplotted in Figure 3 do not necessarily come from similar emission states, limiting the physical in-terpretation of this distribution, but are here intended for characterizing the sensitivity of VERITASto these sources. A rough drop-off in both the detected and constrained fluxes is apparent around1 × − erg cm − s − . This value approximately matches the extrapolated X-ray flux limit, butis significantly higher than the lowest fluxes predicted by CG02 using spectral modeling.Also shown is the empirical flux limit of Broderick, Chang, & Pfrommer (2012) at 4 . × − erg cm − s − , which was derived from a sample of 28 objects with publicly available well-defined SEDs observed by H.E.S.S., MAGIC, and VERITAS [7]. This limit appears too high todescribe well the flux distributions from VERITAS or the predictions of CG02, indicating that acareful consideration of the sample being used is necessary when defining a TeV flux limit.Finally, for the source selection method to be useful, not only should VERITAS have observedall of the selected sources, but the converse must also be true: the source selection must be completein the sense that all of the sources detected by VERITAS above the effective TeV flux limit areincluded. In fact, this is not the case. Of the 33 BL Lac objects detected by VERITAS, only 20 areCG02 known sources or candidates, and the other 13 are not in the catalog, a ∼
40% incompletenessrate. Figure 4 shows the distributions of these two subpopulations. Visually, the distributions donot differ substantially, particularly at the critical low-flux end, showing that this incompletenesscannot be captured by a simple difference in flux levels (such as excluded sources being dimmer).5 owards a Luminosity Function of TeV Gamma-ray Blazars
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Although the study performed here does not allow a definite conclusion to be drawn, a possibleexplanation for both the lack of a clear limiting flux and the sample incompleteness is suggested.Blazars, including BL Lac objects, are highly variable across the electromagnetic spectrum. Thisvariability matters in the context of source selection in several ways.First, sources in a low state when measured by multiwavelength surveys could fall below theselection criteria flux level but still be TeV emitters. The X-ray, optical, and radio data avail-able in the literature to CG02 to set selection cutoffs and assemble SEDs were not necessarilysimultaneous, which, in addition to uncertainties from their model choices and parameters, likelyplayed a role in incomplete source selection. For example, one VERITAS source missed by CG02,W Comae, was identified as a promising candidate for TeV emission by a study that performeddetailed modeling of its simultaneous broadband SED and X-ray variability [6]. Since simultane-ous multiwavelength measurements are not guaranteed to exist in the literature for every blazar,large uncertainties in predicted fluxes and selection thresholds are to some extent inherent in anyselection method for TeV blazar candidates relying on archival data.In addition, the difficulty of predicting TeV fluxes reflects not only uncertainties in extrapolat-ing from lower wavelengths, reducible with simultaneous measurements and detailed modeling, butalso actual variability in the TeV emission. TeV blazar detectability thus depends both on the lim-iting flux and the flux state when observed. A source might only be detected if it by chance flaredwhile being observed. While over many sources this effect would average out without changingpopulation characteristics, for smaller samples it may present a source of systematic uncertainty.
5. Conclusion
Determining the luminosity function of TeV-emitting blazars is an important step for under-standing these sources as a population. Over a decade of gamma-ray data on these sources nowexists. Over 70 TeV blazars have now been detected, and the upcoming Cherenkov Telescope Ar-ray (CTA), with an order of magnitude increase in sensitivity, should detect many more. Althoughthe LF of gamma-ray blazars has been determined using data from all-sky high-energy surveys,extending these methods for a population of very-high-energy TeV blazars poses new challenges:correcting for selection effects, incorporating variability, and accounting for EBL absorption.This work presents a preliminary study of a method to use targeted observations to emulate auniform survey by restricting the sources considered to those satisfying multiwavelength selectioncriteria. Setting an effective flux limit and obtaining a complete sample are both found to bechallenging. The variability of blazars at all wavelengths can explain these difficulties.
6. Acknowledgements
This research is supported by grants from the U.S. Department of Energy Office of Science, theU.S. National Science Foundation and the Smithsonian Institution, and by NSERC in Canada. Thisresearch used resources provided by the Open Science Grid, which is supported by the NationalScience Foundation and the U.S. Department of Energy’s Office of Science, and resources of theNational Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy6 owards a Luminosity Function of TeV Gamma-ray Blazars
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Office of Science User Facility operated under Contract No. DE-AC02-05CH11231. We acknowl-edge the excellent work of the technical support staff at the Fred Lawrence Whipple Observatoryand at the collaborating institutions in the construction and operation of the instrument.
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