VERITAS Prospects for Geminga Pulsar · 2018-08-14 · A.Positron Excess and Geminga One of the most interesting topics in astrophysics to-day is the study of the positron fraction

VERITAS Prospects for Geminga Pulsar

Emily HarrisUniversity of Pittsburgh, Department of Physics and Astronomy

Columbia University, Nevis Laboratories(Dated: August 7, 2018)

Recent observations of the positron excess in Earth’s atmosphere by PAMELA and Fermi-LAT suggest that particleacceleration in nearby pulsar wind nebulae play an important role in the local interstellar medium. Measurementsshow that lepton acceleration by the Geminga pulsar wind nebula reaches multi-TeV energies, which then leads togamma-ray emission detectable by Cherenkov telescopes such as VERITAS. The high energy emission, close proximity,and old age of Geminga indicates it may be the origin of the positron flux in local interstellar space. In this study,we aim to investigate the prospects for VERITAS detection of Geminga, which has an emission region greater thanthe field of view of the telescopes. We perform simulations of the gamma-ray emission region around Geminga usingthe 3-Dimensional Maximum Likelihood Method. We find that by simulating our pointing strategy along with ourmodel of the lepton diffusion around Geminga, VERITAS will be able to detect Geminga with a high significancegreater than 11σ. However, the skymaps produced by the tools currently available with the likelihood analysis do notaccurately represent the quality of the expected data, and are rather dominated by statistical fluctuations.

I. Introduction

High-energy gamma-ray astronomy is a relativelyyoung field when compared to the history of astronomyin other wavelengths [1]. This field has prospects of dis-covering the nature of high-energy particle accelerators inour universe and understanding their effects on our localinterstellar medium. Currently, there are over 200 de-tected sources of very high energy (VHE; E > 100 GeV)gamma rays that give valuable insight to these extremeastrophysical environments.

Gamma rays are undisturbed by the magnetic fieldsthat permeate our galaxy and travel nearly straight pathsfrom their source. As a result, they are an excellenttool for discovering the location of VHE emission. How-ever, gamma rays can’t penetrate Earth’s atmosphereand must be studied by space-based instruments in or-der to be detected directly. These telescopes are thuslimited in size and very costly. Moreover, the flux ofVHE gamma rays is so low that even the largest spacetelescopes would have trouble detecting their source. Amethod of indirect detection by ground-based telescopesis possible due to gamma-ray interactions in the Earth’satmosphere. As gamma rays come into contact with theatmosphere, they interact with nuclei and undergo pairproduction, producing a positron and an electron. Theseparticles then interact with more nuclei and undergo aprocess called Bremsstrahlung, in which they producesecondary gamma rays. This process of pair productionand Bremsstrahlung continues until there is a cascade ofparticles known as a particle shower. Since the secondaryparticles are moving faster than the speed of light in air,they emit Cherenkov radiation which peaks in blue to ul-traviolet wavelengths. This radiation is what allows forthe indirect detection by ground-based Cherenkov tele-scopes such as VERITAS.

A. VERITAS

VERITAS (Very Energetic Radiation Imaging Tele-scope Array System) is one of the major ground-based

gamma-ray observatories and is located at the FredLawrence Whipple Observatory in Tuscon, Arizona.It is an array of four 12-meter imaging atmosphericCherenkov telescopes (IACTs), with a field of view ofabout 3.5◦. Each telescope is equipped with 350 hexag-onal mirrors, which reflect and focus Cherenkov lightfrom the atmosphere onto cameras containing 499 photo-multiplier tubes [1]. The cameras operate by convertingthe Cherenkov photons into an electronic current that isthen digitized, recording an image of the particle shower.The array system allows for stereoscopic observation inwhich each telescope views the air shower from a differentperspective, giving different orientations to the resultingimages. This enables the reconstruction of the particleshower geometry. A majority of these images are dueto cosmic-ray initiated air showers. But the gamma-rayshowers can be discriminated from the cosmic-ray back-ground based on the shape and orientation of the showerfound through stereoscopic observations. The gamma-ray images appear as long, narrow ellipses, while thecosmic-ray showers appear wider and more irregular inshape. The long axis of the ellipse points back towardsthe direction of the source of the gamma rays and thesource position is simply the intersection point of the var-ious image axes [1]. VERITAS is most sensitive to VHEgamma rays ranging from 85 GeV to 30 TeV. These high-energy rays originate from extreme astrophysical phe-nomena such as pulsar wind nebulae which will be thefocus of this study.

B. Pulsars

One of the important sources of VHE emission are pul-sars, first discovered in 1968 by observation of a rapidlypulsating source of radio emission [1]. Although notknown at the time, it is now understood that a pul-sar is a compact, rapidly rotating neutron star whichemits a beam of radiation that is observable from Earth.These rotating neutron stars are formed when a massivestar reaches the end of its life and all of the fuel is ex-hausted in its core, resulting in a violent explosion known

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as a supernova. This supernova may then leave behinda remnant such as a neutron star. If the core of the pre-supernova star were rotating even slowly, the decreasein radius as it collapses and the conservation of angularmomentum gives the resulting neutron star a rapid ro-tation [2]. With rotation periods of a few millisecondsup to a few seconds, the neutron star produces intensemagnetic fields of the order of 1012 G [2]. These magneticfields accelerate particles which then emit a beam of ra-diation along the magnetic poles. Often, the magneticaxis is misaligned with the rotational axis of the neutronstar, causing the beam of radiation to sweep around asthe star rotates. If Earth falls within the path of thisbeam, the observed signal will seem to pulse at regularintervals [1]. Although the first pulsars discovered hadonly been observed in radio wavelengths, pulsars havesubsequently been found to emit in visible, X-ray, andgamma-ray wavelengths [2].

C. Pulsar Wind Nebulae

Pulsar wind nebulae (PWN) make up a large class ofidentified VHE gamma-ray sources. PWN are formedwhen the central pulsar produces a high energy parti-cle wind, driven by the spin-down power of the star asit loses rotational energy. Since a pulsar is formed in asupernova explosion, the star and its PWN are initiallysurrounded by an expanding supernova remnant. Thesupernova remnant first creates a forward shock wavethat moves freely outward into the interstellar medium(ISM) [3]. A reverse shock wave is then formed, causedby the rebounding material from the forward shock waveinteracting with the ISM [1]. This reverse shock travelsback into the freely expanding supernova ejecta and de-celerates it (Fig. 1). The pulsar wind nebula continuesto gain energy and expand, but is eventually deceleratedto match the boundary conditions of the more slowly ex-panding shell of supernova ejecta which creates a windtermination shock [3]. As the positrons and electronscross the termination shock, they are accelerated to rel-ativistic energies, which then leads to synchrotron andinverse Compton emission.

FIG. 1: A diagram of a supernova remnant’s forward andreverse shock waves with pulsar and PWN in the center[1].

1. Synchrotron and Inverse Compton Emission

As high energy leptons in the PWN move through theintense magnetic field lines produced by the pulsar, theylose energy through synchrotron radiation. Synchrotronemission occurs when a relativistic charged particle isaccelerated in a spiral path around magnetic field lines.The subsequent radiation is emitted in a narrow beampointing in the direction of the motion of the particle.However, the random distribution of magnetic fields inPWN causes the particles to randomly scatter; thus thesynchrotron radiation is emitted in all directions [1]. Thisradiation spans from radio wavelengths to beyond the X-ray band, with most high-energy electrons emitting inX-rays [1].

High-energy leptons can also upscatter photonsthrough a process called inverse Compton scattering.These photons may come from the cosmic microwavebackground, nearby light from stars, or synchrotron pho-tons emitted by the surrounding electrons [1]. This radi-ation can reach energies greater than 100 GeV, which iswithin the VHE range detectable by VERITAS.

2. Crab and Geminga

The Crab PWN is a remnant of a historical supernovaobserved in 1054 A.D., located about 2000 pc away. It isone of the most energetic pulsars discovered in our galaxy,with a rotation period of about 33 ms, a spin-down powerof 4.6 × 1038 erg/s, and a surface magnetic field strengthof 3.78 × 1012 G [4]. It is among the brightest and reason-ably steady point sources of gamma-ray emission abovea few hundred GeV, with VHE emission detected fromboth the Crab pulsar and its PWN independently [5]. Asa result, the Crab is considered by many to be the stan-dard candle of gamma-ray astronomy and is often usedfor validating new analysis techniques for IACTs such asVERITAS.

The Geminga PWN is located nearby at a distanceof 250 pc, and is the second brightest VHE gamma-raysource observed in our galaxy behind the Crab Nebula.It is about 300,000 years old, with a rotation period of240 ms and a spin-down power of 3.2 × 1034 erg/s. Ini-tially discovered by its gamma-ray emission, it was thefirst VHE emission pulsar detected with no known radiocounterpart [6]. Since Geminga’s discovery, it has beenan interesting area of study considering its close proxim-ity and possible role in the observed characteristics of thelocal interstellar medium, which will be discussed in thenext section.

II. Scientific Motivation

A. Positron Excess and Geminga

One of the most interesting topics in astrophysics to-day is the study of the positron fraction in Earth’s at-mosphere, which is the ratio of the total number ofpositrons to the combined number of positron and elec-trons (e+/(e+ + e−)) at a given energy range [1]. The

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observed positron fraction was thought to be dominatedby secondary particles that originate from hadronic in-teractions between cosmic rays and nuclei as they prop-agate through the ISM. If secondary particles dominate,the positron fraction is expected to decrease smoothly asa function of increasing energy [5]. However, recent mea-surements by the PAMELA satellite show an unexpectedexcess of positrons at energies greater than 10 GeV, com-pared to the predicted flux that originates from cosmic-ray interactions. Precise follow-up measurements by theFermi-LAT telescope confirm these results and show thatthe positron excess extends up to hundreds of GeV [7].These measurements suggest that there is an unknownsource of positrons contributing to the local interstellarflux.

One possible explanation for the origin of this positronexcess is the annihilation of dark matter particles intohigh energy electrons and positrons. Another potentialsolution could come from the enhanced contribution ofnearby pulsars and PWN, such as Geminga. This the-ory provides that as a pulsar ages, its surrounding neb-ula will dissipate slowly. Once the nebula has dissipatedsubstantially, the particles are no longer confined in thePWN, allowing them to diffuse freely away from the pul-sar [1]. The close proximity and relatively old age ofGeminga make it a great candidate for this theory, as itsnebula has had sufficient time to dissipate, thus allow-ing leptons from its more energetic past to make it toEarth by the present day. Studying the gamma-ray fluxsurrounding nearby pulsars with IACTs could provide asubstantial constraint on the flux of leptonic emissionsfrom these sources [1]. Observations of Geminga specifi-cally will provide evidence to prove or disprove that it isthe primary source of the positron excess.

B. HAWC Observations of Geminga

The High-Altitude Water Cherenkov (HAWC) Obser-vatory is a VHE gamma-ray observatory located on theflanks of the Sierra Negra volcano in Mexico. HAWCconsists of a large array of 300 water Cherenkov detec-tors designed to detect Cherenkov radiation from parti-cle showers at ground-level. With a much larger area,wider field of view, and higher elevation than its prede-cessor Milagro, the sensitivity of HAWC is increased byan order of magnitude [8]. It is well suited for observingnearby sources that have a larger angular extent, makingit an ideal instrument to study VHE gamma-ray emis-sion from sources proposed to produce the local positronexcess [8].

Recent measurements by the HAWC observatory re-port the detection of TeV gamma rays in the vicinity oftwo close pulsars, Geminga and PSR B0656+14 [7]. TheTeV emission region is several degrees across due to lep-tons diffusing away from the central pulsar and inverseCompton scattering low energy photons to high energygamma-rays. Both pulsar sources were detected withstatistical significances of 13.1 and 8.1 standard devia-tions, respectively. The energy range and angular ex-

tent measured by HAWC are consistent with previousresults reported by Milagro, although the statistical sig-nificance is much higher than Milagro’s detection [7]. Byfitting the TeV gamma-ray emission profile with modelsderived from calculations of how fast leptons are diffusingaway from the pulsar, the diffusion constant in the envi-ronment surrounding the pulsar was measured. HAWCfinds this diffusion constant value to be nearly 100 timessmaller than the typical diffusion constant measured ininterstellar space. [7]. This suggests that leptons arediffusing much too slowly in the vicinity of Geminga tobe able to reach Earth. Therefore, they concluded thatthese pulsars, Geminga and PSR B0656+14, are unlikelyto be the origin of the excess positrons, which may havea more exotic origin.

C. VERITAS Prospects for Geminga

A detailed spatial morphology of Geminga is still notprecisely measured. Therefore, VERITAS wants to ex-tend HAWC’s measurements to lower energies to searchfor substructure or anisotropy in the gamma-ray emissionthat HAWC would not have been able to detect. Detect-ing the spatial morphology of this source would providea valuable constraint on the positron fraction in Earth’satmosphere.

However, the gamma-ray emission region seen byHAWC spans roughly 5◦ in the sky, which is wider thanthe 3.5◦ field of view of VERITAS telescopes. The typ-ical analysis techniques of VERITAS first rejects eventsthat look like particle showers from cosmic rays based onthe shape of the Cherekov light images. They then esti-mate the remaining background from parts of the field ofview that are located away from the source. This analy-sis method works well for point sources which have a welldetermined background region, such as the Crab. But itfails for sources with very extended emission regions thatspan roughly 0.5◦ or more, like Geminga. VERITAS cur-rently has around 50 hours of on-source data on Geminga;however no detection has been seen yet. Thus, in orderto study such highly extended emission from Geminga, anew analysis technique is necessary. One such techniquefor VERITAS will be presented in the next section.

III. 3D Maximum Likelihood Analysis

Created by a group at Iowa State University, the 3-Dimensional Maximum Likelihood Method (3D MLM) isa new technique implemented in order to study extendedemission in VERITAS data [9]. This section provides anoverview of this technique and describes the method ofanalysis used to study Geminga.

A. 3D Maximum Likelihood Models

In general, the method of maximum likelihood is anapproach to model the expected distribution of events indata. The 3D MLM models data in 2 spatial dimensionsas well as mean scaled width dimension for both sourceand background components.

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1. Spatial Models

The source spatial model is the expected spatial dis-tribution of the source’s gamma-ray emission. In or-der to accurately model this source data, instrument re-sponse functions (IRFs) are incorporated into the code[1]. These IRFs are functions of the observing positionson the sky known as zenith and azimuth angles, atmo-spheric conditions, configuration of the telescope array,and number of telescopes participating in gamma-rayevent reconstruction. Simulations based on these param-eters are then made through a Monte Carlo technique.

The background spatial model is the expected distri-bution of gamma-ray-like background events in the tele-scope’s field of view. The distribution of these events isbased on data taken from sources that have weak or nodetectable gamma-ray emission such as weak blazars ordwarf spheroidal galaxies [9].

2. Mean Scaled Width Model

The mean scaled width (MSW) is the third dimensionof computed models incorporated into the 3D MLM. Thisparameter is used to discriminate against backgrounddata and improve sensitivity to sources greater than 0.5◦

in diameter [9]. It is based on the width of shower imagesreconstructed in the telescope’s field of view. The widthof each image is divided by the expected width derivedfrom simulated particle showers which are based on size,impact distance, and zenith angle of the shower. Afterscaling, gamma-ray events should be peaked at 1.0, whilebackground cosmic-ray events peak at higher values dueto their wider and more irregular shower shapes. Theweighted average is then taken for all telescope images.Like the spatial models, the source MSW model is de-rived from simulations of gamma-ray showers, while thebackground MSW model is derived from actual observa-tions [9].

3. Spectral Models

Another important component in accurately modelingthe spatial distribution is the spectral energy distributionof the source. For this analysis, a power-law function wasused to model the energy spectrum:

dN

dE= N0

( EE0

)α(1)

Where N0 is the flux normalization, E0 is the energyat which the normalization is calculated, and α is thespectral index. For all Geminga simulations in this anal-ysis, the following spectral parameters were used: N0 =8 × 10−9 photons/m2/s/TeV, E0 = 2 TeV, α = −2.23.These parameters are a factor of 3 lower than those usedby HAWC, which our simulations are based on. As aresult, our likelihood analysis underestimates the signifi-cance values of the source detection (see Section 4).

B. Crab Consistency Check

As an initial test to validate the accuracy of the 3DMLM source model generation, a consistency check forthe Crab Nebula was performed. As mentioned previ-ously, the Crab Nebula is the brightest detected sourceof VHE gamma-ray emission and is used to validatenew analysis techniques. Using the coordinates of Crab,83.63◦ declination and 22.01◦ right ascension, along withits spectral model, Monte Carlo simulations were createdwith the 3D MLM. The resulting skymaps are shown inFig. 2. The first map (a) shows the the Monte Carlodata, while maps (b) and (c) are the model maps createdby the Monte Carlo code. The next two (d and e) areresidual maps created to show how well the model fitsthe data. If our model is a good fit for the data, thenthe statistical fluctuations in skymap (d) should roughlyfollow a Gaussian distribution, as shown in map (f).

(a) MC Event Counts (b) Source+BG Model

(c) Background (BG) Model (d) Residual: Data-BG Model

(e) Residual: Data-Full Model (f) Residual Significance Dist.

FIG. 2: Spatial model maps created by the 3D MLMfor Crab. The color bar shows counts for maps a-c, andsignificance values for d-e. Y-axis is declination in de-grees, X-axis is right ascension in time. Due to an errorin the 3D MLM code, the residual maps (d and e) showincorrect right ascension.

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The Mean Scaled Width model for Crab (Fig. 3a)shows a strong source of gamma rays with the Sourcemodel and Full model peaking at one. The backgroundcomponent is dominated by cosmic rays and thus thecontribution stays small and peaks out near two. TheSpectral model for Crab follows the power-law functiondescribed in the previous section.

(a) Mean Scaled Width Plot

(b) Spectrum Plot

FIG. 3: (a) The number of gamma-ray events as a func-tion of Mean Scaled Width, showing the source compo-nent (red dashed), background component (blue dashed),and full model (solid purple). (b) The number of photonsas a function of energy.

In order to check the effect of 3D MLM simulationson Crab, this data was converted into files that are com-patible with VEGAS, which is one of the official analysispackages used for VERITAS data [10]. These new fileswere then run through the VEGAS analysis and the re-sults are shown in Fig. 4. The Acceptance plot (Fig.

4a) falls off due to geometrical effects that reduce theefficiency of the array towards the edge of the field ofview, making it less likely for events to be detected. TheTheta Squared Wobble plot (Fig. 4b) is the distributionof events as a function of the square of their angular dis-tance from the source, so it should peak in the directionof the source of gamma-ray emission. Finally, the Signif-icance map (Fig. 4c) shows the same 40σ detection ofCrab as the 3D MLM map.

(a) Acceptance curve

(b) Theta Square Wobble Plot

(c) Significance Map

FIG. 4: (a) The probability of accepting a gamma-raylike event constructed at a position in the telescopesFOV. (b) The number of gamma-ray like events as a func-tion of angular distance squared from the center of: thesource (red), background region (blue). (c) A significancemap of the Crab source showing a firm detection of 40σ.

All of the skymaps and graphs created by the 3D MLMare comparable to the expected data from the standardVEGAS analysis. Thus, we concluded that the sourcemodel generation of the 3D MLM is working properly.

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C. Point Source vs. Extended Source

After showing that the 3D MLM works well for pointsources, we began to test the effects of an arbitrary ex-tended source on the analysis. We implemented a Gaus-sian source model, starting with a small width to simulatea point-source, and gradually increased the width to an-alyze changes in the skymaps. All sources in Fig. 5 aresimulated with a Crab strength energy spectrum and 30minutes of observation time.

(a) 0.05◦ width

(b) 0.2◦ width

(c) 0.4◦ width

(d) 0.8◦ width

FIG. 5: Left Column: Model map of the source, RightColumn: Residual Map: Data-Background Model cre-ated with a 0.1◦ integration radius.

The values seen in these significance maps are diag-

nostic and naturally less sensitive than significance fromthe likelihood analysis. The likelihood significance is thebest-fit of the full source model (spatial + MSW) to thedata, and is only done for one location on the sky, takinginto account all photons from the source. The diagnos-tic significance maps are generated by counting up all ofthe simulated event counts inside the integration radiusat each bin, and designating these as “on counts.” Thebackground part of the best-fit model is then used to es-timate the “off counts.” Each of these values are thenplugged into the “Li & Ma” equation to calculate thesignificance at each bin [11]. Therefore, the backgroundis overestimated and the significance value is lower thanthat of the likelihood analysis.

The left column of maps are the source models, show-ing the extensions of the source on the sky. The rightcolumn shows the residual maps, Data − BackgroundModel, where the source should again be seen. Theseskymaps show that as you increase the width of thesource, the analysis has trouble distinguishing the sourcefrom the background, and thus these maps become dom-inated by statistical fluctuations. This artifact of the 3DMLM plots will be discussed again in Section 4.

D. Diffusion Model

Now that we know the effects of a strong extendedsource on the 3D MLM code, we created a new model tosimulate a more diffuse, extended source like Geminga.Using equations borrowed from HAWC [7], a new elec-tron diffusion model was implemented into the MonteCarlo code with prospects to simulate detailed skymapsof Geminga’s emission region. The gamma-ray spectrumand morphology are determined from a model of positronand electron pairs diffusing into the interstellar mediumaround the pulsar [7]. The diffusion coefficient D(Ee),and the diffusion radius rd for Geminga are defined as:

D(Ee) = D100(Ee/10GeV )δ (2)

rd = 2√D(Ee)tE (3)

where δ = 1/3 is the spectral index of the diffu-sion coefficient, Ee is the energy of the electrons andpositrons, D100 = 3.2 × 1027 cm2/s is the diffusion coef-ficient for electrons at 100 TeV, and tE is the smaller oftwo timescales: the age of the pulsar, and the lifetime ofelectrons after synchrotron and inverse Compton emis-sion known as the cooling time [7]:

tcool =mec

2

4/3σT γ· 1

µB + µph/(4γε0)3/2(4)

where me is the mass of the electron, c is the speedof light, σT is the Thompson cross-section, γ is the bulkLorentz factor of the electron, µB = B2/8π is the mag-netic density, µph is the cosmic microwave background

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(CMB) energy density, and ε0 is the normalized CMBphoton energy. When the cooling time of electrons is lessthan the age of the pulsar, the diffusion radius of the elec-trons increases with energy. But when it becomes longerthan the age of the pulsar, the diffusion radius decreaseswith energy [7].

The diffusion angle of the pulsar as a function of thediffusion radius is given by:

θd =180◦

π· rddsource

(5)

where dsource = 250 pc is the distance from Earth toGeminga. The gamma-ray flux as a function of the dif-fusion angle θd from the pulsar is given by:

fθ =1.22

π3/2θd(θ + 0.06θd)

exp(− θ2/θ2d) (6)

Using this final equation for the gamma-ray flux of thepulsar, a new diffusion model was created for Gemingawhich was implemented into the 3D MLM code. The in-put value for the energy of gamma rays was chosen tobe 707 GeV and corresponds to an electron energy ofEe = 14 TeV, which is representative of typical VERI-TAS observations.

FIG. 6: The diffusion template for a 707 GeV gamma-ray/14 TeV electron. Each bin corresponds to 0.1◦ andthe entire region shown in the graph is 5◦ by 5◦. Theradius that contains 68% of the gamma-ray flux is ap-proximately 5.8◦.

E. Pointing Strategy

Because Geminga is an extended source, we must finda way for the VERITAS telescopes to observe all of itsgamma-ray emission region. Using a feature of the tele-scopes known as the wobble offset, the telescopes can bepointed in different directions allowing for observation ofthe entire emission region. Exposure maps of the point-ing configurations can then be created by the 3D MLM.

We began this study by testing a simple pointing strat-egy in which the telescope was wobbled one degree ineach direction from the center of the source position at97.17◦ declination and 17◦ right ascension (Fig. 7). Eachpointing is 3◦ in diameter. The resulting exposure maphad one hot spot in the center and no smooth transi-tion between different exposure regions. The number ofpointings was then increased to 9 pointings, each spaced1◦ apart. This offered a slightly smoother exposure, butstill had a large central hot spot. We increased againto 16 pointings and then to 25 pointings, each spaced 1◦

apart. The 25-pointing strategy was found to be the bestconfiguration because it had a relatively smooth transi-tion in exposure, and the central region with the high-est exposure spans 3◦, which is ideal for detecting thehighest flux of gamma rays surrounding the center of thepulsar.

(a) 4 pointings (b) 9 pointings

(c) 16 pointings (d) 25 pointings

FIG. 7: Exposure maps created by the 3D MLM for dif-ferent pointing configurations of the telescopes.

IV. Results

A. Geminga Analysis with 1 Pointing

Using the diffusion model described in Section 3D, aset of Monte Carlo simulations were run with a 15-hourobservation in a single pointing on Geminga. This sim-ulation was chosen in order to model existing VERITASdata and to see how well the 3D MLM compared to actualdata. Former University of Utah PhD student, AndrewFlinders, analyzed this VERITAS data in his thesis titled,“A Detection of Significant Gamma-ray Emission fromthe Pulsar Wind Nebulae Geminga with VERITAS.” Heimplemented a unique analysis technique in order to ob-

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tain these results, which are not attainable by standardVERITAS analysis. A comparison of our 3D MLM re-sults and Andrew’s analysis results are shown in Fig. 8.

For our 3D MLM map, an integration radius of 1◦ wasused as opposed to the standard radius of 0.1◦ (used inFig. 5). This means that a larger sample of bins areintegrated over in the map, smearing out the gamma-rayevent counts making it easier to distinguish the source.We find that our 3D MLM analysis has a weaker signif-icance of 4σ compared to Andrews significance of 6σ.This weak signal indicates a problem with our 3D MLManalysis, most likely attributed to the use of a weakerspectrum.

Noticing that the shape of the telescopes’ acceptance(Fig. 4a) is similar to the diffusion profile for an on-axispointing (Fig. 6), we thought that this problem may alsooccur due to the 3D MLM having trouble distinguishingthe source events from background events. This couldresult in a weaker detection than expected.

(a) 3D MLM Residual Map: Data - Background Model

(b) VERITAS Significance Map

FIG. 8: A comparison of (a) The 3D MLM simulatedskymap of Geminga using the HAWC diffusion model and(b) the VERITAS significance map of Geminga using apoint-source analysis by Andrew Flinders.

To break the degeneracy of the acceptance and dif-fusion model falling off at a similar rate, we offset thesource from the center of the skymap. This was done in

anticipation of a higher significance and stronger detec-tion of the source. The same 15-hour on-source pointingof Geminga was simulated, this time with a 0.5◦ and 1◦

north offset of the telescope. The source now appearslower in the skymap which is expected, however the like-lihood significance remained around 4σ. Thus, it is likelythat the weak detection is due to our spectral model.

(a) 0.5◦ north offset

(b) 1◦ north offset

FIG. 9: 3D MLM Residual Maps: Data - BackgroundModels for two offset pointings of Geminga.

As mentioned in Section 3A, the spectral model thatshould have been used for this Geminga analysis isstronger than the one used to create these results. Ad-ditional simulations were done using the correct spec-tral parameters to match our diffusion model: N0 =1.36 × 10−10 photons/m2/s/TeV, E0 = 20 TeV, α =−2.34. With the new spectral model, the likelihood sig-nificance increased from 4σ to 11σ, and the skymapsignificance increased from 3σ to 6σ, which are compa-rable to Andrew’s results.

B. Geminga Analysis with 25 Pointings

Using the diffusion model along with the 25-pointingstrategy described in Section 3E, we ran a set of fourMonte Carlo simulations for Geminga. Each simulationhad 7.5 hours per pointing, corresponding to a total of187 hours of observation time. The first run of this con-

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figuration seemed promising with a likelihood significanceof 11σ, and the skymap appeared to have a strong cen-tral source detection (Fig 10a). To test if this result wasvalid, three more simulations of the same configurationwere run (Fig 10 b, c, d). The likelihood significancestayed roughly the same for all four simulations witha value of 11σ. Any signal above 5σ is considered afirm detection of a source. Therefore, the 3D MLM isstrongly detecting Geminga. However, all of the result-ing skymaps look very different, suggesting that they aredominated by statistical fluctuations as predicted by ourextended source test described in Section 3C.

(a) Run 1 (b) Run 2

(c) Run 3 (d) Run 4

FIG. 10: 3D MLM Residual Maps: Data - BackgroundModels for all 4 simulations using the diffusion model and25-pointing strategy.

FIG. 11: Spectral Model for Geminga using a diffusionmodel, 25-pointing strategy and 1◦ integration radius.

Additional simulations of this configurations were run,this time with one third of the exposure totaling 62.5hours of observation and with the correct spectral modelfor Geminga. Using the stronger spectral parametersstated in the previous section, along with a decreasein exposure time, it was expected that the significanceshould increase from 11σ to 18σ. However, the like-lihood significance for this configuration increased tonearly 24σ, meaning a very strong detection.

V. Conclusion

In this paper, we have examined the prospects forVERITAS to detect the Geminga PWN through differ-ent 3D MLM simulations. We have shown that a goodobservation strategy is a 25-pointing configuration, with7.5 hours at each pointing, totaling 187 hours of obser-vation time on Geminga. Using this strategy, VERITASwill be able to detect Geminga with a high significance,greater than 11σ. With a very strong detection, we cansearch for substructure that might indicate alternativeemission mechanisms in the PWN, or elongation thatmight indicate the diffusion is not isotropic but has apreferred direction. Any detection by VERITAS in thefuture will provide a valuable constraint on Geminga’spotential contribution to the local cosmic-ray positronand electron fluxes.

To better examine the detections of Geminga in thefuture, improvements can be made to the 3D MLM whichwould still allow for a strong detection of the source butalso allow us to incorporate models with substructure.A more in-depth analysis may then be done to see theeffects of substructure in VERITAS data.

Acknowledgments

I would like to thank the National Science Founda-tion for funding this REU program. Many thanks tothe administrative staff who put together an incredibleprogram here at Nevis Laboratories, including John Par-sons, Georgia Karagiorgi, and Amy Garwood. Thankyou to the entire VERITAS/CTA group at Columbia aswell as my fellow REU students for their encouragementand helpful insight. Finally, I would like to extend mysincerest gratitude to Brian Humensky and Qi Feng formaking this such a valuable research experience, and fortheir continued support throughout this summer.

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