deirdre horan llr / ecole polytechnique [email protected] c€¦ · deirdre horan --- 2013 fermi...
TRANSCRIPT
Introduction togamma-ray blazars
Deirdre HORANLLR / Ecole Polytechnique
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
1. Active galactic nuclei2. Blazars
3. Models of blazar emission4. The Fermi blazars
5. The TeV blazars6.The GeV-TeV Connection
7. The extra-galactic background light8. Intergalactic magnetic fields9. Characterising variability
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
c
OUTLINEc
Active galactic nuclei - 1/9 -c
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Active Galactic Nuclei
CHARACTERISTICS• central nucleus outshines the rest of the
galaxy• high luminosity (normally)• emission across entire spectrum ... radio
to keV, MeV, TeV➡non-thermal
• strong variability• radio-loud sources:
➡relativistic jets ... superluminal motion
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
TAXONO
MY
Active Galactic Nuclei
Beckmann & Shrader, astro-ph/1302.1397
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Active Galactic Nuclei
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
CLASSIFICATION
identified as Fermi sources
LSP, ISP, HSP LSP, ISP, HSPLow, intermediate & high
synchrotron peaked
LBL IBL HBL
Active Galactic Nuclei
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
CLASSIFICATION
identified as TeV sources
LSP, ISP, HSP LSP, ISP, HSPLow, intermediate & high
synchrotron peaked
LBL IBL HBL
Active Galactic Nuclei
Blazars2/9c
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
energy
power
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Blazars
• <5% of all AGN• jet points “at” us• f lat radio spectrum• radio loud AGN• large amplitude variability• optical polarisation• spectral energy distribution
CHARACTERISTICS
blob moves to P in time Δt
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Superluminal motion
Blazars
blob moves to P in time Δt
first pulse travels to observer in time D/c; the second, emitted time Δt later, has a shorter distance to travel: D-Δy. Difference in arrival time is:
observer
First proposed by Rees in 1966 (Nature, 211, 468) years before it was first observed when VLBI techniques were developed
therefore:
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Difference in arrival time is:
substitute for Δy & rearrange:
measured transverse velocity, vobs
Blazars
blob moves to P in time Δt
observer
Superluminal motion
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
So, if the plasma velocity was 0.95c and the angle to the observer was 5deg, the apparent velocity would be 1.5c. The effect is maximised when cosθ=β
BlazarsSuperluminal motion
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Blazars
The Doppler factor is a measure of the strength of the beaming:
Definitions:
The Lorenz factor: where
Relativistic beaming
• When an emitting plasma has a bulk relativistic motion relative to a fixed observer, its emission is beamed in the forward direction in the fixed frame
•The observed emission, Sobs is boosted in energy over that emitted in the rest frame, S
•Another relativistic effect occurs because the knots of plasma are moving at velocities close to that of light
•The flux density is thus changed by relativistic time dilation so an observer sees much more intense emission than if the plasma were at rest
If plasma velocity is 0.95c and θ is 5deg, the boosting
factor will be ~198
• The criterion for gammas to escape from a source is ...
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
BlazarsPair-production optical depth• High energy gamma rays collide with softer radiation to produce e+e- pairs• For gammas to escape from a source, the optical depth for this process τe must be sufficiently low • The cross section for this process is maximized for collisions between gamma rays of energy ...
and target photons of energy ...
• The optical depth is then defined as:
... where N is the number of soft photons, R is the radius of the plasma “blob” (assumed shape) and σT is the Thompson-scattering cross section*
• A useful parameter that can then be derived** is the compactness of the source - it is a direct measure of the importance of the pair-production process
*Dondi & Ghisellini (1995) MNRAS, 273, 583**Urry & Padovani (1995) PASP, 107, 803
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Spectral Energy Distribution
energy
power
Blazars
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
HSPLSPISP
Before, definitions were based on ratio of flux at 5GHz to
that at 1 keV
BlazarsSpectral Energy Distribution
Models of blazar emission3/9c
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Models of blazar emission
energy
power “synchrotron” “inverse Compton”
Spectral Energy Distribution
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
energy
power
Lower energy emission due to synchrotron emission from relativistic e-s in the jet
Two fundamentally different approaches to explain the higher energy emission
•Leptonic & Hadronic
Models of blazar emission
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
energy
power
Lower energy emission due to synchrotron emission from relativistic e-s in the jet
Two fundamentally different approaches to explain the higher energy emission
•Leptonic & Hadronic• radiative output dominated by e-/e+
• high-energy photons most likely the result of inverse Compton scattering by the same e-s that produced the synch
• upscatter the low-energy photons responsible for first bump➡synchrotron self-Compton
• upscatter photons from the broad-line region, disc, torus ...➡external Compton
e- +B-field-> γsynch e- + γext
ore- + γsynch
Models of blazar emission
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
energy
power
Lower energy emission due to synchrotron emission from relativistic e-s in the jet
Two fundamentally different approaches to explain the higher energy emission
•Leptonic & Hadronic• both e-/e+ and p accelerated to ultra-
relativistic energies
• p’s exceed threshold for pγ photo-pion production on soft photon field in emission region
• high energy emission dominated by➡ proton synchrotron
• π0 decay products
• synchrotron and Compton emission from secondary products of charged pions➡external Compton
e- +B-field-> γsynch e- + γext
ore- + γsynch
Boettcher, M. (2012) Fermi & Jansky, astro-ph/1205.0539Boettcher M. (2013), ApJ (in press), Astro-PH/1304.0605
Models of blazar emission
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Models of blazar emission• leptonic models provide good fits to many blazars
RBS 0413 (Aliu et al. 2012, ApJ, 750, 94)
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Models of blazar emission• leptonic models provide good fits to many blazars
• X-ray and gamma-ray emission often correlated - a fact naturally explained by SSC models
Blazejowski, M. et al. 2005, ApJ, 630, 130
PRELIM
INARY
Fortson et aL. (2012) Gamma 2012
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Models of blazar emission• leptonic models provide good fits to many blazars
• in hadronic models, the cooling times are longer, which makes it more difficult to explain the rapid variability often seen in blazars
➡ proton synchrotron can produce rapid variability with very high energy protons in extremely magnetised, compact regions Holder, J. (2012), Astropart. Phys., 39, 61
• X-ray and gamma-ray emission often correlated - a fact naturally explained by SSC models
Aharonian et al. (2007), ApJ, 664, L71
Doppler factors of > 100 required
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Models of blazar emissionKrawczynski et al. (2004), ApJ 601, 151 “orphan” flare
from TeV blazar, 1ES 1959+650
hadronic models have been invoked to
explain this behavioure.g., Boettcher (2005), ApJ, 621, 176Sahu et al. (2013), Phys. Rev. D... (in press) astro-ph/1305.4985
• VHE emission discovered by H.E.S.S. (ATel July 2010)
• Hard Fermi spectrum (2.1) and nearby (z=0.049)
➡ excellent candidate for TeV emission
• X-ray observations taken simultaneously with VHE reveal onset of HE component at unusually low energies for a TeV BL Lac
PRELIMINARY
H.E.S.S. Collaboration et al. (2013 - in press) David SANCHEZ & Pascal FORTIN
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Models of blazar emission
• VHE emission discovered by H.E.S.S. (ATel July 2010)
• Hard Fermi spectrum (2.1) and nearby (z=0.049)
➡ excellent candidate for TeV emission
• X-ray observations taken simultaneously with VHE reveal onset of HE component at unusually low energies for a TeV BL Lac
PRELIMINARY
H.E.S.S. Collaboration et al. (2013 - in press) David SANCHEZ & Pascal FORTIN
Extensive Multifrequency Campaigns on the Classical TeV Blazars Mrk421 and Mrk501 in the Fermi Era
David Paneque, L.Stawarz, J.Finke, M. Georganopoulos, A.Reimer and D.Tescaro On behalf of the Fermi, MAGIC, VERITAS collaborations and the participants/groups of the MW campaigns
on Mrk421 and Mrk501 in 2009, which include GASP-WEBT, F-GAMMA and many others
Summary: We are performing an unprecedentedly long and dense monitoring of the multifrequency (radio to TeV) emission from the classical TeV blazars Mrk 421 and Mrk 501. These objects are among the brightest X-ray/TeV blazars in the sky and among the few sources whose Spectral Energy Distributions (SED) can be almost completely characterized by the current instruments. This is a multi-year, multi-instrument program involving the participation of VLBA, Swift, RXTE, MAGIC, VERITAS, Whipple, F-GAMMA, GASP-WEBT, and other collaborations and instruments which provide the most detailed temporal and energy coverage of these sources to date. In this conference, we report on some of the results we obtained with the multifrequency data from 2009. We show that, when Mrk421 and Mrk501 are in low states, their SEDs are very comparable and can be similarly modeled in the framework of a 1-zone Synchrotron self-Compton scenario with an electron energy distribution parameterized by three power laws with two breaks (in the electron energy distribution) at roughly the same energies, and a size of the emitting region comparable to the size of the partially resolved VLBA radio core.
Recently, we had two “performance jumps” with respect to the past:
New Generation of IACTs online since ~7 years (low Eth, high sensitivity)
LAT in operation since ~3 year (~30 times more sensitive than EGRET)
Culprits for the relatively poor knowledge of these objects 1 - Time-evolving broad band spectra
2 - Poor sensitivity to study the high-energy part (E>0.1 GeV)
Coordination of instruments covering different energies needed
Long observation times (with EGRET and “old” IACTs) were needed for signal detection Data NOT simultaneous, and most of the knowledge we have on High Synchrotron Peaked BL Lac (BL Lac-HSP) relates to the high state
Enhanced observational capability can be used to improve our knowledge on BL Lac-HSP
~100 times more sensitive at E>~10 GeV
1 – We do NOT know well how blazars work
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Exquisite characterization of the high energy component, which can be detected with Fermi and Cherenkov Telescopes over 5 orders of magnitude (0.1 GeV – 10 TeV)
2- Motivation to observe (again) Mrk421 and Mrk501 3 – Campaigns on Mrk421 and Mrk501
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In general, blazars emit over a broad energy range + emission is variable. ! Contemporaneous multi-instrument observations are required to study them
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Both sources were found in relatively quiescent state with low variability. Agreement in overlapping energies among instruments (with different time coverage) indicates that we managed to get the true average SED of Mrk421 and Mrk501 during the 4.5 months campaign. The VHE spectra was EBL corrected using Franceschini et al 2008
Preliminary Host galaxy contribution at optical has been subtracted
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4 – Results obtained for Mrk501 (Abdo, A. A. et al. 2011, ApJ, 727, 129) and Mrk421 (Abdo, A. A. submitted to ApJ)
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R [cm] 5.2e16
B [G] 3.8e-2
delta 21.0
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#min 800
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#brk_1 5.e4
s2 2.7
#brk_2 3.9e5
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Mrk421: Finke’s code
R [cm] 1.3e17
B [G] 1.5e-2
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#min 600
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s2 2.7
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Mrk501: Stawarz’ code
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Electrons above o2(RW""emit X-rays
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The MW data collected during 4.5 month long campaigns allowed us to produce the most complete SED ever measured for both Mrk501 and Mrk421
! includes the full coverage of the !-ray component. ! Both sources were in relatively low/quiescent states.
The SED can be described with a 1-zone SSC model with an electron distribution with 2 breaks: break Internal to particle acceleration (20 GeV and 25 GeV electron energies for Mrk501 and Mrk421) break related to synchrotron cooling (500 GeV and 180 GeV electron energies for Mrk501 and Mrk421)
Electron distribution consistent with being produced through 1st order Fermi acceleration in relativistic, proton-mediated shocks X-ray produced mostly by electrons above 2nd break TeV dominated by electrons above 1st and 2nd break MeV/GeV (Fermi) produced mostly by electrons below 1st break, but also above 1st break
Similar SED modeling parameters for Mrk421 and Mrk501: is it by chance ?? Or is it a common property of these two objects ? ! Can we extend this behaviour to other HSP-BL Lacs ??
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Study of the classical (bright) TeV sources has the advantage that, Fermi+IACTs can strongly constrain the high energy component - Fermi data open a “new window” to study those objects ! Spectra reaching E>0.1 TeV; overlap with IACTs - Collection of MW data is ESSENTIAL for understanding these complex objects.
This presentation shows “first” results from the 2009 MW campaigns on Mrk421/Mrk501. Work ongoing to extract further results from these MW campaigns from 2009, as well as from the campaigns we had in 2010.
This is a multi-instrument and multi-year effort: Extensive (6 months) campaigns were done in 2010 and are ongoing in 2011 for Mrk421 and Mrk501. Stay tuned for new results.
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Mrk421: Finke’s code
Mrk501: Stawarz’ code
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Preliminary
Preliminary
Preliminary
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Models of blazar emission
• VHE emission discovered by H.E.S.S. (ATel July 2010)
• Hard Fermi spectrum (2.1) and nearby (z=0.049)
➡ excellent candidate for TeV emission
• X-ray observations taken simultaneously with VHE reveal onset of HE component at unusually low energies for a TeV BL Lac
PRELIMINARY
Difficult to model with a single zone homogeneous SSC model due to the unprecedented width of the HE component compared to the LE component
H.E.S.S. Collaboration et al. (2013 - in press) David SANCHEZ & Pascal FORTIN
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Models of blazar emission
The Fermi blazars4/9c
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
1873 sources1298 identified/associated
Nolan et al. (2012), ApJS, 199, 31
84% AGN* *74%
blazarsDeirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
The Fermi blazars
2FGL
LBAS (Abdo et. al 2009, ApJ 700, 597)Based on 0FGL, 3 months data, ~10σ 106 high-confidence blazars
1LAC (Abdo et. al 2010, ApJ 715, 429)Based on 1FGL, 11 months data, ~5σ523 (blazars) / 599 (total) in clean sample
1 2
32LAC (Ackermann et. al 2011, ApJ 743, 171)Based on 2FGL, 24 months data, ~5σ 862 (blazars) / 886 (total) in clean sample
BL LacFSRQUnknown
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Figure credit: S. Fegan
The Fermi blazars
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Ackermann et. al 2011, ApJ 743, 171
curve represents the detection
limit
The Fermi blazars
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
The Fermi blazars
Ackermann et. al 2011, ApJ 743, 171*8 misaligned blazars
4 NLSyIs10 AGN of other type
2 starburst s
*Abdo et. al 2010, ApJS 188, 405
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Finke, J. (2012), Fermi-Jansky (astro-ph/1301.6081)
“If the seed photon source for external Compton scattering is the broad line region (BLR), and the BLR strength is correlated with the power injected into electrons in the jet, one would expect that more luminous jets have stronger broad emission lines and greater Compton cooling, and thus a lower νsy. As the power injected in electrons is reduced, the broad line luminosity decreases, there are fewer seed photons for Compton scattering, and consequently the peak synchrotron frequency moves to higher frequencies. This is also reflected in the lower luminosity of the Compton-scattered component relative to the synchrotron component as νsy moves to higher frequencies.”
Fossati et Al. (1998), MNRAS, 299, 433
Finke, J. (2012), Fermi-Jansky (astro-ph/1301.6081)
The Fermi blazars
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Ackermann et. al 2011, ApJ 743, 171
The Fermi blazars
BL Lacs: LSP ISP HSP
• Work is underway to publish the 1st Fermi-LAT catalog of sources > 10 GeV• Shape of the spectrum at > 10 GeV might not be well characterized if we use a single fit in the energy range 0.1 GeV – 100 GeV
➡ Lower energies have larger statistical weight
• The variability at the highest Fermi-LAT energies could be different from that at the
lowest energies, which might indicate the presence of a separate population of particles
which may radiate from the same/different location
➡ Are sources more variable at HE than at LE ? or the other way around ?
• Understand better the population of sources emitting above 10 GeV
➡ What are the sources dominating the highest LAT energies?
•Identify promising candidates for IACTs ... new VHE discoveries
D. Paneque, Fermi Symposium (2012)
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
See Lamb & Macomb (1997), 488, L872
The Hard Source List - a catalog above 10 GeVThe Fermi blazars
The TeV blazars5/9c
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
145 sources114 identified/associated
84% AGN*
TeVCat
*95%blazars
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
The TeV blazars
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
As of writing this talk, there are 145 sources in TeVCat - 57 Extragalactic
The TeV blazars
HBLs IBLs LBLs FR1s FSRQs
New TeVCat options
coming soon
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
As of writing this talk, there are 145 sources in TeVCat - 57 Extragalactic
5%5%
4%2%
72%
12%
7 IBL3 FSRQ
41 HBL
1 LBL
3 Radio Galaxies
2 Starbursts
Only two sources are not AGN!
Most numeroussource class in TeV sky
The TeV blazars
The GeV-TeV Connection6/9c
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Total No.Sources
Total No.Identified*
No. AGN
% AGN that are blazars
GeV... Fermi 2FGL 1873 1298 (69%) 1092 (84%) 74%
TeV... TeVCat 145 117 (81%) 55 (47%) 96%
*Identified / Associated
49 of the 55 TeV AGN are in 2FGL
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
The GeV-TeV Connection
Senturk, Errando, Böttcher & Mukherjee (2013), ApJ 764, 119• Analysed 27 months of Fermi data for the TeV AGN that had spectral infrormation available (26 objects)
• Compared the TeV AGN with the AGN from 2FGL
• Computed SEDs for all objects
• The combined GeV-TeV spectra of some blazars (1ES 0229+200, 1ES 0347-121, 1ES 1101-232, 1ES 1218+304, H 1426+428) suggest an inverse-Compton peak beyond 1 TeV
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
The GeV-TeV Connection
• TeV instruments are pointed and have relatively small fields of view
• Low duty cycles (~10%)
➡ Need targets
• Fermi has a very large field of view - sees a fifth of the sky at any given time
• Surveys entire sky every three hours
➡ Transients, cataloging
0
12
24
36
48
60
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
39 HBL 7 IBL 1 LBL 3 FRI 3 FSRQ
Since Fermi was launched,29 TeV AGN detected - 14 thanks to LAT data
Fermi
0
15
2009 2010 2011 2012
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
The GeV-TeV Connection
Name Class % Crab
SHBL J001355.9-185406 HBL 1.0
1ES 0229+200* HBL 1.8
1ES 0347-121* HBL 2.0
PKS 0548-322* HBL 1.3
1ES 1312-423 HBL 0.4
HESS J1943+213 HBL 1.5
49 of the 55 TeV AGN are in 2FGL
*Detections reported in the literature since 2FGL
• At the time of publication, there were 6 TeV AGN that were not detected in 2FGL
• Since then, 8 TeV AGN have been detected - they were all in 2FGL
➡ still 6 TeV AGN not in 2FGL
• all HBL• among the weakest TeV AGN
• 3 have subsequently been reported as detections (non-Fermi pubs)
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
The GeV-TeV Connection
The extragalactic background light7/9c
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
The further away the object we detect, the more its TeV photons are absorbed by the EBL - this results in a break in the spectrum
energy energy energy energy
no. p
hoto
ns
no. p
hoto
ns
no. p
hoto
ns
no. p
hoto
ns
Increasing distance
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
ΓHE
ΓVHE
The extra-galactic background light
Sanchez, Fegan, Giebels (2013) in press, astro-PH/1303.5923
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Abdo et Al. (2009), ApJ, 707, 1310
The extra-galactic background light
WWW..MPI-HD.MPG.DE astro-PH/1212.3409
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
HESS data on seven blazars were used to search for the absorption signature of the EBL - it was detected at 9 sigma - results are only slightly above the lower
limits calculated by summing galaxies visible in sky surveys
The extra-galactic background light
Intergalactic magnetic fields8/9c
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Intergalactic magnetic fields• when we detect TeV gamma rays from a distant source, we know that the signal has already been attenuated - only a fraction of those emitted arrive on Earth
• the gamma rays collide with photons of the EBL en route from the source and pair produce➡ if there were NO magnetic fields in the universe, these charged pairs would not get deflected, they would travel in original direction until they Compton upscattered an EBL photon to MeV-GeV energies*
• in this way, the original TeV gamma rays get reprocessed
to lower energy radiation
• IF we could identify a distant, steady** TeV source which had NO GeV emission, this could be an indication that the B-fields between the source and us deflected the charged pairs such that the reprocessed lower energy emission was “removed” (scattered) from the signal ** if the source is at a lower level now than when the TeV emission that we are detecting was emitted, it could be argued that, since the radiation due to the deflected pairs has longer to travel, it would be delayed by some time - and it hasn’t arrived yet
* the mean free path for e+/e- is low ~kpc
Vovk, Taylor, Semikoz & Neronov (2012), ApJ, 747, L14
Place constraints on the intergalactic B-field strength using the direct and cascade components of the GeV-TeV spectrum of 1ES 0229+200
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Intergalactic magnetic fields
Characterising variability
9/9c
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Characterising variabilityQuantifying the variability of blazars
Nandra et al. (1997) ApJ 476, 70
excess variance
N points in each light curve Xi
is the unweighted arithmetic mean of the Xi
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Putting an upper limit on the excess variance➡ When no (negative) excess variance is measured in the data, we can estimate the level of intrinsic variance that could be present in the lightcurve but that would still allow us to arrive at this value for excess variance
1. Simulate lightcurves by generating, for each datapoint Fi +/- dFi (F is the ith data point and dF is the ith uncertainty, i =1:N), a normal distribution centred on the mean of the measured lightcurve with width of sqrt(dFi2 + VARIANCE2)
2. For each level of VARIANCE, generate a large number of lightcurves
Characterising variability
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Sample lightcurves for different levels of VARIANCE
Characterising variability
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Putting an upper limit on the excess variance➡ When no (negative) excess variance is measured in the data, we can estimate the level of intrinsic variance that could be present in the lightcurve but that would still allow us to arrive at this value for excess variance
1. Simulate lightcurves by generating, for each datapoint Fi +/- dFi (F is the ith data point and dF is the ith uncertainty, i =1:N), a normal distribution centred on the mean of the measured lightcurve with width of sqrt(dFi2 + VARIANCE2)
2. For each level of VARIANCE, generate a large number of lightcurves
3. Calculate the excess variance for each of these lightcurves and histogram these for each level of VARIANCE
Characterising variability
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Histograms of excess variance for each VARIANCE added
Characterising variability
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Putting an upper limit on the excess variance➡ When no (negative) excess variance is measured in the data, we can estimate the level of intrinsic variance that could be present in the lightcurve but that would still allow us to arrive at this value for excess variance
1. Simulate lightcurves by generating, for each datapoint Fi +/- dFi (F is the ith data point and dF is the ith uncertainty, i =1:N), a normal distribution centred on the mean of the measured lightcurve with width of sqrt(dFi2 + VARIANCE2)
2. For each level of VARIANCE, generate a large number of lightcurves
3. Calculate the excess variance for each of these lightcurves and histogram these for each level of VARIANCE
4 For each VARIANCE level, find the excess variance that 95% (or whatever your required confidence level is) of the excess variances are above
Characterising variability
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Histograms of excess variance for each VARIANCE added
Characterising variability
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Putting an upper limit on the excess variance➡ When no (negative) excess variance is measured in the data, we can estimate the level of intrinsic variance that could be present in the lightcurve but that would still allow us to arrive at this value for excess variance
1. Simulate lightcurves by generating, for each datapoint Fi +/- dFi (F is the ith data point and dF is the ith uncertainty, i =1:N), a normal distribution centred on the mean of the measured lightcurve with width of sqrt(dFi2 + VARIANCE2)
2. For each level of VARIANCE, generate a large number of lightcurves
3. Calculate the excess variance for each of these lightcurves and histogram these for each level of VARIANCE
4 For each VARIANCE level, find the excess variance that 95% (or whatever your required confidence level is) of the excess variances are above
Characterising variability
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Putting an upper limit on the excess variance➡ By finding where the measured value of excess variance intersects with the curve generated by the 95% values, we can determine the level of VARIANCE that could be present in the lightcurve but that would still lead to us getting the measured value 5% of the time or less
Characterising variability
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware
Note on rate and its uncertainty in Fermi data
Characterising variability
Thank you for
c
Deirdre HORAN --- 2013 Fermi Summer School --- Lewes, Delaware