Blazars as sources of astrophysical neutrino flux

Neutrino emission from the direction of the blazar TXS 0506+056 prior to the IceCube-170922A alert

Fabio Cufino

TU Dortmund University

June 14, 2024

Introduction

High-Energy Cosmic Rays and Neutrinos

• Extragalactic Origin: Highest-energy cosmic rays come from outside our galaxy.
• Acceleration Sites: the exact acceleration locations are unidentified.
• Neutrinos: Produced near acceleration sites when cosmic rays interact with matter and light.

Neutrinos as Probes

• Unlike cosmic rays, neutrinos can travel unimpeded through the Universe.
• Nearly massless, electrically neutral particles: not deflected by magnetic fields.

Introduction

Blazars

[Hubble Space Telescope, Very Large Array (VLA) ]

Introduction

Blazars

[Hubble Space Telescope, Very Large Array (VLA) ]

Radio Galaxy Hercules: Visible light by Hubble Space Telescope superposed with a radio image taken by the Very Large Array.

Blazars as Neutrino Sources:

• Type of active galactic nucleus with powerful jets aimed towards Earth.
• Sources of emission across the EM spectrum with high-energy gamma ray photons.
• Prominent candidates for the sources of high-energy neutrino emissions.

They are not deflected by magnetic fields, making them ideal for studying extreme environments. Also interact very weakly with matter.

IceCube Detector

Neutrino Observatory

• Location: Amundsen-Scott South Pole Station, Antarctica
• Volume: 1 km³ of instrumented Antarctic ice
• Detector Array:
  • 86 vertical strings, spaced 125 m apart
  • Strings extend to a depth of 2450 m, with 60 optical sensors each

[Illustration: Emily Cooper]

IceCube Detector

Neutrino Observatory

Detection Mechanism:

• Records Cherenkov light from relativistic particles produced by neutrino interactions
• Tracks high-energy muon neutrinos, enabling direction reconstruction with ~0.5° accuracy at 30 TeV

[Illustration: Emily Cooper]

Add everything related to the image: photomultiolier etc.

The IceCube-170922A Event

The IceCube-170922A Event

Neutrino recoded

• On September 22, 2017, a high-energy neutrino was detected.
• Most probable energy: \(290 \text{ TeV}\) (90% confidence level lower limit: \(183 \text{ TeV}\))
• Selected by the Extremely High Energy (EHE) online event filter

Research Focus

• The event was reported as a public alert.
• Further studies refined the directional reconstruction, with best-fitting coordinates of RA \(77.43^{+0.95}_{−0.65}°\) and Dec \(5.72^{+0.50}_{−0.30}°\)

EHE alerts are currently sent at a rate of about four per year, and are based on well-reconstructed, high-energy muon-track events

The Blazar TXS 0506+056

Gamma-rays detected by the Fermi Gamma-ray Space Telescope from 2008 to 2017

The direction of IceCube-170922A was consistent with the location of TXS 0506+056 and coincident with enhanced gamma-ray activity observed since April 2017 by the Large Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope

The northern sky, where TXS 0506+056 is located, is observed through Earth by IceCube IMPORTNTA

Consistent with position: Right Ascension (RA) 77.3582°, Declination (Dec) +5.69314°

Coincident with enhanced gamma-ray activity observed April 2017

The Blazar TXS 0506+056

“On the basis of this result, we consider the hypothesis that the blazar TXS 0506+056 has been a source of high-energy neutrinos beyond that single event.”

Searching for neutrino emission

IceCube neutrino data samples

Data Collection Periods

• Six periods: changing detector configurations, data-taking conditions, improved event selections

• Sample numbers: correspond to the number of detector strings that were operational.

Sample	Start Date	End Date
IC40	2008 Apr 5	2009 May 20
IC59	2009 May 20	2010 May 31
IC79	2010 May 31	2011 May 13
IC86a	2011 May 13	2012 May 16
IC86b	2012 May 16	2015 May 18
IC86c	2015 May 18	2017 Oct 31

During the first three periods, the detector was still under construction. The last three periods correspond to different data-taking conditions and/or event selections with the full 86- string detector.

Events

Expected Event Types

• Location: TXS 0506+056 is in the northern sky, observed through Earth by IceCube.
• Data Collection: ~70,000 neutrino-induced muon tracks recorded annually.

Astrophysical Neutrinos:

• Less than 1% of the detected events.
• Come from distant cosmic sources.
• Flux scales as \(dN/dE \sim E^{-2}\).

Background Events:

• Vast majority of detected events.
• Caused by neutrinos produced in the Earth’s atmosphere.
• Flux scales as \(dN/dE \sim E^{-3.7}\).

• Astrophysical Neutrinos: The distribution of energies for astrophysical neutrinos follows a pattern described by the formula \(dE/dN ~ E^{-2}\). This means that the number of neutrinos (N) decreases with energy (E) following a specific power-law distribution.
• Atmospheric Neutrinos: The energy distribution for atmospheric neutrinos follows a different pattern, approximately \(E-{3.7}\). This indicates a steeper decline in the number of neutrinos with increasing energy compared to astrophysical neutrinos.

Analysis Techniques

Time-integrated analysis

• Unbinned maximum likelihood technique
• Identify neutrino point sources by analyzing spatial clustering and energy distribution of detected neutrino events over an extended period.

Likelihood Function \[L(\Phi_{100}, \gamma) = \prod_i \left( \frac{\color{#107895}{n_S(\Phi_{100}, \gamma)}}{N} \mathcal{S}(x_S, x_i, \sigma_i, E_i; \gamma) + \left(1 - \frac{\color{#107895}{n_S(\Phi_{100}, \gamma)}}{N}\right) \mathcal{B}(\sin \delta_i, E_i) \right) \]

• \(\color{#107895}{n_S (\Phi_{100},\gamma)}\) number of signal neutrinos for a signal flux model of the form \(\Phi(E) = \Phi_{100}(E/100 \text{ TeV})^{−\gamma}\):

\[ n_S = T \times \int_{100 \text{ GeV}}^{1 \text{ EeV}} A_{\text{eff}}(E, \sin \delta_i) \Phi(E) dE \]

Analysis Techniques

Time-integrated analysis

• Unbinned maximum likelihood technique
• Identify neutrino point sources by analyzing spatial clustering and energy distribution of detected neutrino events over an extended period.

Likelihood Function \[L(\Phi_{100}, \gamma) = \prod_i \left( \frac{n_S(\Phi_{100}, \gamma)}{N} \textcolor[RGB]{230,65,115}{\mathcal{S}(x_S, x_i, \sigma_i, E_i; \gamma)} + \left(1 - \frac{n_S(\Phi_{100}, \gamma)}{N}\right) \textcolor[RGB]{230,65,115}{\mathcal{B} (\sin \delta_i, E_i)} \right)\]

• \(\textcolor[RGB]{230,65,115}{\mathcal{S}}\) and \(\textcolor[RGB]{230,65,115}{\mathcal{B}}\) are the Probability Density Functions for the Signal and the Background.

• \(N\) is the total number of neutrino events,

Analysis Techniques

PDF of signal events

\[ \mathcal{S} = \frac{1}{2\pi \sigma_i^2} e^{-\frac{|x_S - x_i|^2}{2\sigma_i^2}} \times E_S(E_i, \sin \delta_i; \gamma) \]

• Spatial Component: Two-dimensional Gaussian distribution centered at the source position
• Energy Component: Probability of observing a neutrino with energy \(E_i\) at a given declination \(\delta_i\).

---

PDF of background events

\[ \mathcal{B} = P_B(\sin \delta_i) \times E_B(E_i, \sin \delta_i) \]

• Spatial Component: Uniform in right ascension
• Energy Component: derived from experimental data, representing the distribution of energies for background events.

Analysis Techniques

Time-dependent analysis

• Unbinned maximum likelihood technique
• Aims to identify clusters of neutrino events in space and in time.

Likelihood Function:

\[ L(\Phi_{100}, \gamma, T_0, T_W) = \prod_i \left( \frac{n_S(\Phi_{100}, \gamma)}{N} \textcolor[RGB]{230,65,115}{\mathcal{S}(x_S, x_i, \sigma_i, E_i; \gamma)} \times TS(t_i; T_0, T_W) + \left( 1 - \frac{n_S(\Phi_{100}, \gamma)}{N} \right) \textcolor[RGB]{230,65,115}{\mathcal{B}(\sin \delta_i, E_i)} \times TB(t_i) \right) \]

• The terms \(\textcolor[RGB]{230,65,115}{\mathcal{S}}\) and \(\textcolor[RGB]{230,65,115}{\mathcal{B}}\) were defined as before.

Analysis Techniques

Time-dependent analysis

• Unbinned maximum likelihood technique
• Aims to identify clusters of neutrino events in space and in time.

Likelihood Function:

\[ L(\Phi_{100}, \gamma, T_0, T_W) = \prod_i \left( \frac{n_S(\Phi_{100}, \gamma)}{N} \mathcal{S}(x_S, x_i, \sigma_i, E_i; \gamma) \times \textcolor[RGB]{76, 212, 162}{TS(t_i; T_0, T_W)} + \left( 1 - \frac{n_S(\Phi_{100}, \gamma)}{N} \right) \mathcal{B}(\sin \delta_i, E_i) \times \textcolor[RGB]{76, 212, 162}{TB(t_i)} \right) \]

• \(\textcolor[RGB]{76, 212, 162}{TS}\) and \(\textcolor[RGB]{76, 212, 162}{TB}\) are the Signal and Background Temporal Distribution Functions

Analysis Techniques

Signal Temporal Distribution Functions

Box-Shaped Time Window:

\[ TS(t_i; T_0, T_W) = \frac{1}{T_W} \]

\[ \quad \text{for} \quad T_0 - \frac{T_W}{2} < t_i < T_0 + \frac{T_W}{2} \]

Gaussian-Shaped Time Window:

\[ TS(t_i; T_0, T_W) = \frac{1}{\sqrt{2\pi (T_W/2)^2}} e^{-\frac{(t_i - T_0)^2}{2 (T_W/2)^2}} \]

---

Background Temporal Distribution Functions

Approximated as uniform over the observation period \(T\):

\[ TB(t_i) = \frac{1}{T} \]

Analysis Techniques

Statistic tests

Test Statistic (TS):

• For time-integrated analysis:

\[ TS = 2 \log \left( \frac{L(\Phi_{100}, \gamma)}{L(\Phi_{100} = 0)} \right) \]

• For time-dependent analysis:

\[ TS = 2 \log \left[ \frac{T_W}{T} \times \frac{L(\Phi_{100}, \gamma, T_0, T_W)}{L(\Phi_{100} = 0)} \right] \]

---

• The p-value is then computed from the TS.

Key Findings and Outcomes

Neutrinos from the direction of TXS 0506+056

Results of Time-Dependent Analysis

[arXiv:1807.08794v1]

• \(\textcolor[RGB]{255,141,60}{\text{Orange Curve:}}\) corresponds to the analysis using the Gaussian-shaped TDF.
  • Central time \(T_0\) and width \(T_W\) are plotted for the most significant findings
  • p-value: height of the peak
• \(\textcolor[RGB]{18,54,190}{\text{Blue Curve}}\): corresponds to the analysis using the Box-shaped TDF.
  • The curve traces the outer edge of the superposition of the best-fitting time windows over all times \(T_0\)
  • significance: height of that window

Neutrinos from the direction of TXS 0506+056

Results of Time-Dependent Analysis

[arXiv:1807.08794v1]

• IC86b from 2012 to 2015, contains a significant excess which is identified by both time-window shapes.
• The excess consists of \(13 \pm 5\) events above the expectation from the atmospheric background.

Figure 1: Time-dependent analysis results. The orange curve corresponds to the analysis using the Gaussian-shaped time profile. The central time T0 and width TW are plotted for the most significant excess found in each period, with the P value of that result indicated by the height of the peak. The blue curve corresponds to the analysis using the box-shaped time profile. The curve traces the outer edge of the superposition of the best-fitting time windows (durations TW) over all times T0, with the height indicating the significance of that window. In each period, the most significant time window forms a plateau, shaded in blue.

• The large blue band centered near 2015 represents the best-fitting 158-day time window found using the box-shaped time profile.

• The vertical dotted line in IC86c indicates the time of the IceCube-170922A event.

Neutrinos from the direction of TXS 0506+056

Results of Time-Dependent Analysis

• The significance depends on the energies of the events, their proximity to the coordinates of TXS 0506+056, and their clustering in time.

[arXiv:1807.08794v1]

• Event Weight: product of event’s spatial term and energy term in the unbinned likelihood analysis at the location of TXS 0506+056 and assuming \(\gamma = 2.1\)

• Muon Energy Proxy: approximate value in units of TeV of the reconstructed muon energy.

Figure 2: Time-independent weight of individual events during the IC86b period. Each vertical line represents an event observed at the time indicated by calendar year (top) or MJD (bottom). Overlapping lines are shifted by 1 to 2 days for visibility. The height of each line indicates the Event Weight: the product of the event’s spatial term and energy term in the unbinned likelihood analysis evaluated at the location of TXS 0506+056 and assuming the best-fitting spectral index γ = 2.1 (30).

• The color for each event indicates an approximate value in units of TeV of the reconstructed muon energy (Muon Energy Proxy), which the analysis compares with expected muon energy distributions under different hypotheses.

• The dashed curve and the solid bracket indicate the best-fitting Gaussian and box- shaped time windows, respectively. The distribution of event weights and times outside of the best-fitting time windows is compatible with background.

Neutrinos from the direction of TXS 0506+056

Results of Time-Dependent Analysis

• The Gaussian is centered at \(T_0 =\) 13 December 2014 \(\pm\) 21 days
• Duration \(T_W = 110^{+35}_{-24}\) days.
• The best-fitting parameters:
  1. fluence \(E^2J_{100} = (2.1^{+0.9}_{-0.7}) \times 10^{-4} \text{ TeV cm}^{-2}\) at \(100 \text{ TeV}\)
  2. spectral index \(\gamma = 2.1 \pm 0.2\)
  3. P-value \(0.0002\) \(\rightarrow\) Significance \(3.5 \sigma\)

---

• For the box-shaped time window the results are similar to those of the Gaussian window but the uncertainties are discontinuous and not well-defined.

Neutrinos from the direction of TXS 0506+056

Results of Time-Dependent Analysis

1. Joint uncertainty on Gaussian shape fitted parameters holding the time parameters fixed (T0 = 13 December 2014, TW = 110 days)
2. Skymap showing the p value of the time-dependent analysis performed at the coordinates of TXS 0506+056 (cross) and at surrounding locations, during IC86b data period.

[arXiv:1807.08794v1]

Figure 3: Time-dependent analysis results for the IC86b data period (2012-2015). - (a) Change in test statistic, ∆TS, as a function of the spectral index parameter γ and the fluence at 100 TeV given by E2J100. The analysis is performed at the coordinates of TXS 0506+056, using the Gaussian-shaped time window and holding the time parameters fixed (T0 = 13 December 2014, TW = 110 days). The white dot indicates the best-fitting values. The contours at \(68\%\) and \(95\%\) confidence level assuming Wilks’ theorem (36) are shown in order to indicate the statistical uncertainty on the parameter estimates. Systematic uncertainties are not included.

• 2. Skymap showing the P value of the time-dependent analysis performed at the coordinates of TXS 0506+056 (cross) and at surrounding locations. The analysis is performed on the IC86b data period, using the Gaussian-shaped time-window. At each point, the full fit for (Φ, γ, T0, TW) is performed. The P value shown does not include the look-elsewhere effect related to other data periods. An excess of events is detected consistent with the position of TXS 0506+056.

Neutrinos from the direction of TXS 0506+056

Results of Time-Dependent Analysis

• Outside the 2012-2015 time period, the next most significant excess is found using the Gaussian window in 2017 and includes the IceCube-170922A event.
• Centered at 22 September 2017 with duration \(T_W = 19\) days, \(\gamma = 1.7 \pm 0.6\), and fluence \(E^2J = 0.2^{+0.4}_{-0.2} × 10^{−4} \text{ TeV cm}^{−2}\) at \(100 \text{ TeV}\).
• No other event besides the IceCube-170922A event contributes significantly to the best-fit.

[arXiv:1807.08794v1]

Neutrinos from the direction of TXS 0506+056

Results of Time-Integrated Analysis

• The analysis is performed using the full data sample

Best fitting parameters:

• Full 9.5-year sample best fit \(\textcolor[RGB]{230,65,115}{(a \; posteriori)}\):
  • \(\Phi_{100} = (0.8^{+0.5}_{-0.4}) \times 10^{-16} \text{ TeV}^{-1} \text{ cm}^{-2} \text{s}^{-1}\),
  • \(\gamma = 2.0 \pm 0.3\).
  • P value: \(0.002\% (4.1σ)\).

• 7-year sample best fit \(\textcolor[RGB]{230,65,115}{(No \; IC86c)}\):
  • \(\Phi_{100} = (0.9^{+0.6}_{-0.5}) \times 10^{-16} \text{ TeV}^{-1} \text{ cm}^{-2} \text{s}^{-1}\),
  • \(\gamma = 2.1 \pm 0.3\).
  • P value: \(1.6\% (2.1σ)\).

[arXiv:1807.08794v1]

Blazar TXS 0506+056 as neutrino source

Blazar TXS 0506+056 as neutrino source

TXS 0506+056 Redshift and Luminosity

• Redshift:

  • \(z = 0.3365 \pm 0.0010\)
  • Essential for determining the isotropic luminosity in both neutrinos and gamma rays.

• Luminosity during enhanced activity:

  • Neutrino luminosity: \((1.2^{+0.6}_{−0.4}) × 10^{47} \text{erg} \text{ s}^{-1}\) average over \(158\) days
  • Higher than the gamma-ray luminosity during the same period.

---

Some gamma rays from neutrino production are absorbed or have energies outside the Fermi-LAT detection range.

Blazar TXS 0506+056 as neutrino source

Position and Inclination

The explanation for why TXS 0506+056 is the first blazar associated with a significant neutrino excess may depend on:

1. Detection Likelihood:

• Favorable declination increases IceCube detection chances.
• IceCube is highly sensitive to high-energy neutirinos near the equatorial plane, viewed from the South Pole.
• more than an order of magnitude more luminous than nearby blazars such as Markarian 421, Markarian 501, and 1ES 1959+650 (more northern declinations)

2. Intrinsic properties

- Neutrino excess may depend on the blazar's jet inclination relative to our line of sight.

Conclusions

• TXS 0506+056 is confirmed as a high-energy neutrino source with 3.5σ evidence from 2014-2015.
• Evidence is independent of IceCube-170922A, reinforcing the blazar’s role in neutrino production.
• Isotropic neutrino luminosity is higher than gamma-ray luminosity.
• Findings support blazars as key sources of high-energy astrophysical neutrinos.

Backup Slides

Estimation of \(L\) for the null hypothesis

Denomination of Test Statistic (TS): \[ L(\Phi_{100} = 0)? \]

• Probability distribution of the test statistic under the null hypothesis estimated by performing the time-(in)dependent analysis at the location of TXS0506+056 on samples of randomized data.
• In the time-dependent case, random samples are produced by randomly reassigning the times among the events within the same data period used to compute the like- lihood.
• The equatorial coordinates are then recomputed using the new times.
• All other event properties remain unchanged.