Multifrequency study of variability of Fermi/LAT Blazars

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Multifrequency Study of

Variability of

Fermi

/LAT

Blazars

by

V´ıctor Manuel Pati˜

no ´

Alvarez

Thesis submitted in partial fulfillment of the

requirements for the degree of

MASTER OF SCIENCE IN ASTROPHYSICS

at the

Instituto Nacional de Astrof´ısica, ´Optica y Electr´onica

July 2012 Tonantzintla, Puebla

Under the supervision of:

Ph.D. Alberto Carrami˜nana Alonso

Tenured Researcher INAOE, Mexico

Ph.D. Vahram Chavushyan

Ph.D. Luis Carrasco Baz´ua

©INAOE, 2012

The author hereby grants to INAOE permission to reproduce and to distribute publicly paper and electronic

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Agradecimientos

Deseo agradecer a mis supervisores, el Dr. Alberto Carrami˜nana, el Dr. Vahram

Chavushyan y el Dr. Luis Carrasco por su apoyo constante. Estoy muy agradecido por

la paciencia que me han tenido durante este a˜no de trabajo, adem´as de todo lo que he

aprendido de ellos.

Tambi´en me gustar´ıa agradecer a mis sinodales, la Dra. Itziar Aretxaga, el Dr. Ra´ul

M´ujica y la Dra. Irene Cruz-Gonz´alez por llevar a cabo la tarea de leer y examinar mi

tesis, as´ı como todas las sugerencias que me han dado.

Agradezco a los profesores que tuve durante el primer a˜no de materias, he aprendido

tanto desde que llegue aqu´ı, y en buena parte gracias a ellos.

Me gustar´ıa agradecer a tantas personas que he conocido aqu´ı en Puebla y que de una forma u otra han hecho mejor y más divertida mi estad´ıa en el INAOE. A Marco Vázquez, Eduardo Ibarra, Héctor Ibarra y V´ıctor Gómez por siempre compartir la mesa conmigo, a Paola Espinoza, a los tocayos César Mata y César Chávez, me aceptaron desde el principio aunque no me conocieran. A José Manuel por todas esas platicas tan

interesantes sobre diversos pasatiempos que tenemos en com´un. A Bernardo, porque

desde los primeros d´ıas que llegué aqu´ı me trato muy bien y como un amigo. Y como ser´ıa muy largo mencionar a todas las demás personas que he conocido durante mi estancia aqu´ı, sólo quiero decirles gracias a todos.

Me gustar´ıa agradecer a CONACYT, ya que sin la beca que recib´ıa puntual mensual-mente, no me hubiera sido posible realizar este trabajo.

Quiero agradecer a mi familia, principalmente a mis padres, mis ´ıdolos, sin su constante apoyo en todo lo que me he propuesto en la vida, ni siquiera estar´ıa aqu´ı en INAOE. Quiero agradecer a mi hermano, quien desde que tengo memoria ha sido mi principal

inspiración y motivación. Por último, pero no menos importante, me gustar´ıa agradecer

a alguien que ha cambiado mi vida para bien, agradezco que me haya tenido tanta

paciencia, agradezco su comprensi´on, sus consejos, sus rega˜nos (me los merec´ıa), pero

sobre todo agradezco que siempre ha estado ah´ı para mi cuando m´as la he necesitado; muchas gracias Karla, sin ti no hubiera podido.

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Abstract

In this work it was determined if there exist delays between the emissions in diﬀerent bands in 16 Fermi/LAT detected blazars, via the cross-correlation function (CCF). The bands we are working with are: gamma-rays (0.1-300 GeV), optical V band, near-infrared J, H and Ks bands (observation frame) and emission lines (object rest frame). We also want to investigate the performance of distinct methods used to obtain the cross-correlation function under diﬀerent conditions, and we pretend to point out their flaws and strengths, so that in the future we can make the correct decision about what method to use, depending on the specific characteristics of the data available.

The cross-correlation analysis was carried out by three diﬀerent methods discussed previously in the literature, the interpolation method (Gaskell & Sparke, 1986), the discrete cross-correlation function (Edelson & Krolik, 1988) and the Z-transformed discrete correlation function (Alexander, 1997). The idea behind using more than one method is to increase the sturdiness of the results obtained. Nonetheless, some modifications were made with respect to the original methods due to some problems present in these, mainly to correct for the nonlinearity of the AGN light curves. Our results show that for all objects, the three NIR bands vary simultaneously. For four objects of our sample (3C 273, Mrk 501, PKS 2155-304, and PMN J0808-0751), no correlation is found between any of the bands available in this study. For the remaining twelve, a correlation was found between the V band and the NIR bands; in most of them indicating that the V band and the NIR bands vary simultaneously or with small delay. For just 3 objects (3C 454.3, PKS 0235+164, and PKS 1510-089) was found a correlation between the gamma-ray emission and the V band; for the same three objects is found a correlation between gamma-ray emission and the NIR bands.

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In this work, we arrived to the conclusion that due to the diﬀerent flaws existent in the three methods to compute the CCF, there is not a single method better than the others; and if we want better robustness in the results it is necessary to use more than one method.

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Resumen

En este trabajo se determinó si existen retrasos entre las emisiones en diferentes ban-das en 16 blazares detectados por Fermi/LAT, utilizando la función de correlación cruzada (CCF). Las bandas con las que estamos trabajando son: rayos gamma (0.1-300 GeV), banda V óptica, bandas J, H y Ks del cercano infrarrojo (marco de referencia del observador) y l´ıneas de emisión (marco de referencia en reposo del objeto). También queremos investigar el desempeño de los distintos métodos us-ados para obtener la función de correlación cruzada bajo diferentes condiciones, y se pretende señalar sus fallas y fortalezas, de tal manera que en el futuro podamos tomar la decisión correcta sobre qué método usar, dependiendo de las caracter´ısticas espec´ıficas de los datos que se usaran.

El análisis de correlación cruzada se llevó a cabo por 3 diferentes métodos discutidos previamente en la literatura, el método de interpolación (Gaskell & Sparke, 1986), la función de correlación cruzada discreta (Edelson & Krolik, 1988) y la función de correlación discreta por transformada-Z (Alexander, 1997). La idea detrás de usar más de un sólo método es incrementar la robustez de los resultados obtenidos. No obstante, algunas modificaciones fueron hechas con respecto de los métodos originales debido a algunos problemas presentes en los mismos, principalmente para corregir por la no-linealidad de las curvas de luz de AGN.

Nuestros resultados muestran que para todos los objetos, las 3 bandas del cercano infrarrojo var´ıan simultáneamente. Para cuatro objetos de nuestra muestra (3C 273, Mrk 501, PKS 2155-304 y PMN J0808-0751), no se encuentra correlación entre ninguna de las bandas disponibles en este estudio; para los 12 restantes, se encuentra una correlación entre la banda V y las bandas del cercano infrarrojo; en la mayor´ıa de ellos indicando que la banda V y las bandas infrarrojas var´ıan de manera simultánea o con un retraso pequeño. Para solo 3 objetos (3C 454.3, PKS 0235+164 y PKS 1510-089) se encuentra una correlación entre la emisión de rayos gamma y la banda V; para los mismos tres objetos se encuentra una correlación entre la emisión de

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rayos gamma y las bandas del cercano infrarrojo.

En este trabajo llegamos a la conclusión de que debido a las diferentes debilidades que tiene cada uno de los métodos para calcular la CCF, no hay un sólo método que sea mejor que los otros; y si queremos una mejor robustez en nuestros resultados es necesario utilizar más de un sólo método.

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Preface

This work is devoted to investigate the statistical properties of multi-wavelength variability of a sample of blazars, as well as to explore the capabilities of the diﬀerent statistical methods utilized.

In Chapter 1 the reader will find general information about the AGN and the diﬀerent classifications for these objects.

In Chapter 2 the reader can find general information about the sample studied, as well as about the observations, telescopes used for the observations and methodology utilized to obtain the necessary information to analyze the data.

In Chapter 3 the main topic is variability of AGN, antecedents and historical works in this matter, as well as a study to measure the variability of the sample in the diﬀerent bands available.

Chapter 4 is dedicated to explain the statistical methods utilized in the accomplish-ment of this work, also is explained compleaccomplish-mentary statistical work necessary to utilize the methods.

In Chapter 5 are stated the results obtained for the diﬀerent objects of the sam-ple.

In Chapter 6 is dedicated to the general conclusions from this work and future work related to my doctoral research.

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Chapter 1 Introduction

1.1 What are Active Galactic Nuclei?

Active Galactic Nuclei (AGN) are some of the most interesting objects in the universe for diﬀerent reasons:

• They are among the most luminous objects in the Universe.

• The physics of the process behind the energy production in these objects is not well understood.

• They have emission along the entire electromagnetic spectrum. • Most of them are variable at all wavelengths.

• Among other reasons.

The observational study of AGN began with the work of Edward A. Fath at Lick Observatory in 1908. He was studying the spectra of the nuclei of the brightest ”spiral nebulae”, now known as galaxies.

The AGN are very rare compared with typical (inactive) galactic nuclei, as shown by the relative numbers in Table 1.1.

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Table 1.1: Approximate Space Densities of AGN (from Osterbrock & Ferland, 2006).

Type Number (Mpc−3₎

Field Galaxies 10−1

Luminous galaxies 10−2

Seyfert Galaxies 10−4

Radio Galaxies 10−6

QSOs 10−7

Quasars 10−9

It is generally accepted that the energy production mechanism for AGN is the mass accretion into supermassive black holes at the center of galaxies, however, this process is not that simple; we do not just see the luminosity of the accretion disk directly, in this case, we would have emission only from UV to IR wavelengths, and we know this is not the only emission in AGN. Also, during the process of accretion, gravitational energy is being released in form of photons (mostly X-Rays).

The process of accretion causes a lot more sub-processes that have a great importance in the emission of AGN; one of them is the ionization of gas around the accretion disk, so we have hot free electrons, this place is known as the corona, and is responsible for part of the X-Ray emission in AGN, via Inverse Compton Emission with the photons of the accretion disk as source.

There is another region above the accretion disk that is ionized by the thermal continuum from the disk; a region of ionized gas that is not as hot as the corona, therefore, in it can occur recombination, excitation of ions (which have not lost all of their electrons), and hence, we can have emission lines in this region known as the broad line region (BLR). The dimensions of BLRs are small. For representative values, a density ne ≈109cm−3, a ionized gas mass ofMion >40M� and radius of

a few hundredths of pc.

A little away from the black hole and the accretion disk, a region of dense gas and dust surrounds the AGN, a dusty torus which optical depth is very high due to its density. Recent high-resolution IR observations indicate that the torus size might be no more than a few parsecs (Elitzur, 2005 and references therein)

An interesting characteristic of most AGN, is that they have jets, because the process of accretion onto the supermassive black hole generates a strong magnetic field, in which lots of charged particles are accelerated to relativistic and ultra-relativistic

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3 1.1. WHAT ARE ACTIVE GALACTIC NUCLEI?

velocities; in the jets is where the radio emission is produced, mostly by synchrotron emission from free electrons.

In the jets of the AGN also occurs the Inverse Compton process, this time responsible for part of the gamma-ray emission from these objects, unlike in the corona, where this process produces X-Rays photons; in the jet, where the free particles velocities are much higher, this process produces gamma-rays in a wide range of energies. It is thought that active galaxies are normal galaxies that are passing through a stage of activity in their nucleus. If we consider that all galaxies are occasionally active, we can derive a minimum mean active lifetime from the observed frequency of all AGN, which can be of at least 108 _{yr (McLure & Dunlop, 2004). It is possible that}

only a few percent of all galaxies have ever been active, but in that case the observed frequency of AGN means that they must have been active throughout the lifetime of the universe, 1₋2_×1010_{yr. Thus the minimum total energy released by an average}

AGN is _≈1060 _erg.

There are a lot of classifications for AGN, given their diﬀerent properties; for instance according to the shape of the spectra, the amount of emission at certain wavelengths, the properties of the host galaxy or the angle of the jet relative to the line of sight, among others. According to these, the AGN can be classified as quasars, blazars, ra-dio galaxies, BL Lacertae type (BL Lac), Quasi Stellar Object (QSO), Flat Spectrum Radio Quasar (FSRQ),LINERs, etc.

Now we will talk, about one of the great classifications of AGN: Seyfert galaxies, and Quasars.

1.1.1 Seyfert Galaxies

A great portion of the known AGN have emission lines, narrow and broad; the nature of these lines, depends mainly on the velocity of the emitter medium (e. g. fast moving clouds). Around this is an entire classification of AGN: Seyfert galaxies 1 and 2. Seyfert 1 galaxies are those with very broad H I, He I, and He II emission lines, with full-widths at half-maximum (FWHM) of order 1 ₋ 5 _× 103 _{km s}−1_,

while the forbidden lines, like [O III] λλ4959, 5007, [N II] λλ6548, 6583, and [S II]

λλ6716, 6731, tipically have FWHM of order 5_×102 _{km s}−1 _{(Osterbrock & Ferland,}

2006). Seyfert 2 galaxies on the other hand, have permitted and forbidden lines with approximately the same FWHM, typically 500 km s−1_{, similar to the FWHM of the}

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Figure 1.1: Optical spectra of various kinds of active galactic nuclei. The ”mean quasar” spectrum is from a composite generated by Paul Francis and colleagues (see Francis et al., 1991). NGC 4579 and NGC 4941 are from observations at Mt. Lemmon Observatory described in Keel (1983). Cygnus A was observed with the 4-meter telescope of Kitt Peak National Observatory (from Owen et al., 1990). The spectra for 0814+425 and 3C 390.3 is from the 5-m Hale telescope at Palomar (see Lawrence et al., 1996). The normal-galaxy spectrum of NGC 3368 is from the spectroscopic atlas of galaxies produced by (Kennicutt, 1992). The spectra for NGC 4151 is from an observation obtained at the Lick Observatory 3-m Shane telescope by Alexei Filippenko.

It is actually accepted that both types of Seyfert galaxies are basically the same kind of object, the diﬀerence being the angle of vision with respect to our line of sight (i. e. both objects have narrow and broad lines, just we do not see it in both). This is related to what lines can be broad, and those who are always narrow, because the forbidden lines (which are always narrow) can not be emitted in the same region as the broad lines.

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5 1.1. WHAT ARE ACTIVE GALACTIC NUCLEI?

To address this issue, let us think about why there are forbidden lines; this because the radiative decay probability is very low, so, in most environments (with relatively high density) there is no radiative decay, instead, there is collisional decay, and therefore, the line is not produced. This tells us that these lines can only be emitted in regions with low density. This does not happen with permitted lines, because the probability of radiative decay is very high, thus, they can be emitted even in dense environments.

According to the last paragraph, in the densest zones of the AGN (that can emit lines) forbidden lines cannot be produced, we are talking about the broad line region. Further from the central engine, there are regions of gas that are at lower densities, and in this environment is where the narrow (forbidden and permitted) lines are produced. According to our understanding of Seyfert galaxies, this occurs in both types of Seyfert, the diﬀerence is that in type 2 galaxies, we can not see the broad line region due to the dusty torus that surrounds the AGN, and blocks the light from this region. However, if we are not seeing towards the dusty torus of the AGN, we can see both broad and narrow lines. This can be understood better with the scheme of Fig. 1.2.

There are subclassifications of Seyfert galaxies intermediate between Seyfert 1 and 2 made by Donald Osterbrock and his associates, that take into account the existence of broad and narrow components of the H I lines, but this is the basic classification for this kind of galaxies (Krolik, 1999).

1.1.2 Quasars

Quasars are one of the big classes of AGN. The name was first adopted as an acronym of ”Quasi Stellar Radio Source”, however, nowadays the term is preferably used for AGN at high luminosity, rather than radio sources.

Most quasars have the curious feature that their emission is very variable along the entire spectra, some with characteristic time scales of a few months, or even a few days, which tell us that the major part of the energy released by an AGN comes from a region with sizes of a few light days; given that the variations in the emission cannot be transmitted from a region to another, faster than the speed of light (e.g. Edelson & Krolik, 1988; White & Peterson, 1994).

Like Seyfert galaxies, most quasars show broad emission lines; the strongest lines observed are the hydrogen Balmer Series (Hα, Hβ, Hγ), the explanation on how

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these are produced is basically the same as in Seyfert galaxies, following the Unified Model of AGN (e.g. Antonucci, 1993; Urry & Padovani, 1995). As mentioned above, it is generally accepted that a change in the viewing angle of the AGN can change the shape of its spectra, hence, their classification.

There have been important studies of quasars at all wavelengths, in fact, one of the most remarkable trends in gamma-ray astronomy in recent years has been the emergence of high-energy gamma-ray quasars as an important component of the gamma-ray sky (e.g. Abdo et al., 2009, 2010). At gamma-ray energies, these active galaxies are bright, most of these sources are preferentially detected at high energies, usually 100 MeV or more. In fact, they have been detected above 1 GeV, and some up to several TeV. Given the large distances to these objects and the strong emission of high-energy gamma rays, these can be considered as the most powerful particle accelerators in the Universe. Over 50 high-energy quasars are known at this time.

1.1.3 LINERs

Low ionization nuclear emission line regions (LINERs) are another sub-class of ob-jects that cannot be easily included in the unified model. They are intriguing cases because, as suggested by their low X-ray luminosities (L(2-10 keV) ∼ 1039−42 _erg

s−1_{), they could be the link between AGN (L(2-10 keV)} _∼₁₀41−45 _{erg s}−1_{) and}

nor-mal galaxies (Zhang et al., 2009; Rovilos et al., 2009). Their signature in the optical spectrum is the enhancement of low ionization lines.

1.2 Blazars

Blazars are one kind of radio loud active galactic nuclei (AGN), in which the angle of the jet relative to the line of sight is very small (a few degrees). This means the jet is practically pointing towards the observer (Blandford & Rees, 1978); therefore, the relativistic eﬀects in the jet are more important when studying these objects, for example, the shortening of time intervals, and hence, on rapid variability.

A defining characteristic of these objects is that they are very variable at all wave-lengths, and that almost every blazar has strong gamma-ray emission; therefore, these are key sources to study now that we have access to the data from the Fermi Gamma-Ray Space Telescope.

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7 1.2. BLAZARS

Figure 1.2: Scheme that shows how the viewing angle can change the type of object we are seeing. Image credit: NASA.

While all blazars emit variable, non-thermal radiation across the entire electromag-netic spectrum, they come in two main subclasses, whose major diﬀerence is in their optical properties:

1. Flat Spectrum Radio Quasars (FSRQs), which show strong, broad emission lines in their optical spectrum, just like radio quiet quasars; an example of the spectra is in Fig. 1.3.

2. BL Lacertae objects (BL Lacs), which are instead characterized by an optical spectrum, which at most shows weak emission lines, sometimes displays ab-sorption features, and in some cases can be completely featureless; an example of the spectra is in Fig. 1.4.

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Figure 1.3: Example spectra of a Flat Spectrum Radio Quasar. The reader may notice the broad line in the spectrum. Spectra from Steward Observatory public database (Smith et al., 2009).

Figure 1.4: Example spectra of a BL Lacertae type objects. The reader may notice the lack of features in the spectra. Spectra from Steward Observatory public database (Smith et al., 2009).

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9 1.2. BLAZARS

According to the peak-frequency of the synchrotron spectrum of these objects, blazars can also be classified as Low-frequency (LBL), or High-frequency synchrotron peaked BL Lac (HBL).

All these classifications are according to a varying combination of Doppler boosted radiation from the jet, emission from the accretion disk, the broad line region, and light from the host galaxy (Padovani et al., 2012).

Historically, the separation between BL Lacs and FSRQs has been made at the (rather arbitrary) rest-frame equivalent width (EW) of 5 ˚A for optical/NUV emission lines like Mg II λ2798, [O II] λ3727, and [O III] λ5007 (Stickel et al., 1991; Stocke et al., 1991). However, no evidence for a bi-modal distribution in the EW of the broad lines of radio quasars has ever been found and, on the contrary, radio-selected BL Lacs were shown to be, from the point of view of emission line properties, very similar to FSRQs but with a stronger continuum (Scarpa & Falomo, 1997).

Nevertheless, there are a number of BL Lac - FSRQ transition objects, which include even BL Lacertae itself, the prototype of the class, which displays at times moderately strong, broad lines (e.g. Vermeulen et al., 1995) and 3C 279, a well-studied FSRQ, which can appear nearly featureless in a bright state (e.g. Pian et al., 1999).

As the Energetic Gamma-Ray Experiment Telescope (EGRET) demonstrated that the extragalactic gamma-ray sky was dominated by blazars, there were great expec-tations concerning advances in blazar and AGN science from the Fermi/LAT (see Sec. 2.4). Many of these expectations have been, or are about to be, fulfilled. The importance of studying variability at different wavelengths is that we can con-strain fundamental parameters to understand how and where is produced the very luminous emission of blazars. If we can find that there exists a delay between two different wavelengths, it means that we can estimate the distances between the emis-sion regions of two different wavelengths. This parameters can be used to model the emission of blazars. It is also possible to estimate sizes of emission regions. We propose this study to verify if there exists a correlation between the gamma-rays and other bands of the electromagnetic spectrum in high-energy blazars.

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Ta b le 1. 2: S om e ch ar ac te ris tic s of th e d iﬀ er en t A G N ty p es (fr om K ro lik , 19 99 ). O b je ct P oi n tli ke B road b an d B road Li n es Nar ro w Li n es R ad io V ar iab le P ol ar iz ed R ad io-lou d q u as ar s Y es Y es Y es Y es Y es S om e S om e R ad io-q u ie t q u as ar s Y es Y es Y es Y es W eak W eak W eak B road lin e rad io gal ax ie s Y es Y es Y es Y es Y es W eak W eak Nar ro w lin e rad io gal ax ie s No No No Y es Y es No No O VV q u as ar s Y es Y es Y es Y es Y es Y es Y es B L Lac O b je ct s Y es Y es No No Y es Y es Y es S ey fe rt s ty p e 1 No Y es Y es Y es W eak S om e W eak S ey fe rt s ty p e 2 No Y es No Y es W eak No S om e LI NE R s No No No Y es No No No

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Chapter 2 Observations and Parameter

Derivation

The monitoring of astronomical objects has become very important since their vari-ability was discovered. AGNs are key targets for monitoring programs because of their rapid variability at all wavelengths (as large as a factor 2 on the same night). Our aim is to analyze the brightness variability of a number of objects in diﬀerent bands, one of them being the gamma-rays observed by Fermi/LAT.

The Fermi/LAT blazars are one kind of AGN which are detected to high energies (MeV, GeV, and even TeV). Most of the bolometric luminosity of these objects is emitted at gamma-rays. The angle of the jet with respect to the line of sight is very small (a few degrees). Most of these kind of objects are also known for being variable at all wavelengths.

We have Near InfraRed (NIR) J, H and Ks bands, and optical (V band and spectra) monitoring of Fermi/LAT Blazars. The time period covered by the observations is from the late 2007 up to mid-2011. The most relevant data for this work are: time of observation (Julian day), apparent magnitude of the object and error in the magnitude (for the case of photometry), and Hγ, Hβ and Mg IIλ2798 emission line flux with its error (for spectra).

The NIR data are from the Guillermo Haro Astrophysical Observatory (OAGH from spanish) using the Cananea Near-Infrared Camera (CANICA); while the optical data (V Band) are from three diﬀerent sources: most of the data is from Steward Observatory (Smith et al., 2009) using the SPOL CCD Imaging/Spectropolarimeter.

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Extra data for 3C 454.3 was taken from Raiteri et al., 2011, the WEBT Project; and V band data for QSO B0133+476 was taken from the MISAO Project (Yoshida, 2012), specifically photometry taken by Miguel Rodriguez Marco with the SRO50 AAVSONet Robotic Telescope. Also we have optical spectra acquired at Steward Observatory using the SPOL CCD Imaging/Spectropolarimeter.

2.1 The Sample

This work was developed using a sample of 16 blazars detected by F ermi/LAT, for which we had access to photometric data in near-infrared bands and optical bands. The objects and some characteristics of these are shown in Table 2.1.

Table 2.1: Properties of 16 AGN from our sample

Object RA (J2000) Dec (J2000) Redshift Classification

3C 66A 02h22m39.6s +43◦_02’08” _0.444000 _BLLAC

3C 273 12h29m06.7s +02◦_03’09” _0.158339 _{Sy1; LPQ; FSRQ}

3C 279 12h56m11.1s -05◦47’22” 0.536200 HPQ(>3%); FSRQ; BLLAC 3C 345 16h42m58.8s +39◦_48’37” _0.592800 _{Opt.var. ;HPQ; FSRQ}

3C 454.3 22h53m57.7s +16◦_08’54” _0.859000 _{FSRQ; HPQ(}_>_3%)

BL Lac 22h02m43.3s +42◦16’40” 0.068600 Opt.var.; BLLAC Mrk 421 11h04m27.3s +38◦_12’32” _0.030021 _{S?; BLLAC}

Mrk 501 16h53m52.2s +39◦_45’37” _0.033663 _{E?; BLLAC}

PKS 0235+164 02h38m38.9s +16◦36’59” 0.940000 FSRQ; BLLAC PKS 0716+714 07h21m53.4s +71◦_20’36” _0.300000 _{HPQ; BLLAC}

PKS 1510-089 15h12m50.5s -09◦_06’00” _0.360000 _{Opt.var.; Sy1; HPQ}

PKS 1633+382 16h35m15.5s +38◦08’04” 1.813570 FSRQ; LPQ PKS 2155-304 21h58m52.0s -30◦_13’32” _0.116000 _{Opt.var.; BLLAC}

PMN J0808-0751 08h08m15.5s -07◦_51’10” _1.837000 _FSRQ

QSO B0133+476 01h36m58.6s +47◦51’29” 0.859000 HPQ; FSRQ W Comae 12h21m31.7s +28◦_13’59” _0.102000 _{Opt.var.; BLLAC}

The Steward Observatory optical program utilizes either the 2.3 m Bok Telescope on Kitt Peak, Arizona or the 1.54 m Kuiper Telescope on Mt. Bigelow, AZ. The Kuiper Telescope’s mount does not allow it to be operated at declinations north of ∼+61◦_{, whereas there is no such restriction with the Bok Telescope. All observations}

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13 2.2. PHOTOMETRY

are obtained using the SPOL spectropolarimeter (Schmidt et al., 1992). SPOL is a versatile, high-throughput (_∼ 30% instrument + telescope), moderate resolution (R _∼ 300-1000) instrument, that is also able to work as a spectropolarimeter and can obtain imaging polarimetry. The detector is a 1200 × 800 pixel2_{, thinned,}

antireflection-coated SITe CCD having �2.5e− _{read noise.}

CANICA is a near infrared (NIR) imaging instrument available at the 2.1-m telescope of the GHAO in Cananea, Sonora. The camera is based on the 1K x 1K Rockwell Science Center HAWAII (HgCdTe Astronomical Wide Area Infrared Imaging) focal plane array and includes a cryostat with two 15-position filter wheels and a pupil mask. The pixel scale of 0.32”/pixel is used, leading to a total field-of-view of 5.5’ x 5.5’ on the sky.

2.2 Photometry

The analysis of the photometry was performed as follows:

To transform the magnitudes into flux, the following formula was used:

f =f0×10−mag2.5 (2.1)

The values used for f0 are in Table 2.2.

Using standard error propagation, and taking into account the error in the measured magnitude and in the absolute calibration of the photometry for the NIR and optical bands, it was possible to estimate the error in the flux. It is worth mentioning that for this work, we just used all the photometric points (optical and infrared), that had error bars smaller than 15% because we want to avoid spurious results due to large errors.

Table 2.2: The Absolute Calibration of the Photometry

Band f0 Error

V 3.81_×10−20 _erg _cm−2_s−1_Hz−1 _{3810 Jy} _1%

J 1.624×10−20 _erg _cm−2_s−1_Hz−1 _{1624 Jy} _5%

H 1.105_×10−20 _erg _cm−2_s−1_Hz−1 _{1105 Jy} _5%

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2.3 Spectroscopy

The spectral data was taken from the publicly available database of the Steward Observatory Monitoring Program for Fermi Monitored Blazars. Basic information on the observatory and instrument was given in Sec. 2.1.

The spectral coverage is from 4000 to 7550 ˚A with a resolution of 15-25 ˚A, depending on the slit width chosen for the observation. Seven slits, each with a length of ∼50”, provide a range of widths from 1” - 13”.

The spectroscopic monitoring from the Steward Observatory, was used to elaborate emission line and continuum flux light curves. This was done just for the 4 sources with the best spectroscopic monitoring and showed emission lines. For each source a diﬀerent broad line was used, due to the redshift of the sources, and also to the position of the redshifted line in the optical spectra (mostly to avoid sky lines). Before measuring the line flux, the spectra was transformed to rest frame wavelength, applying a K-Correction in the process as multiplying by a factor (1 +z)3_{, using the}

IRAF Task ”dopcor”, and the redshift listed in NED. Additionally, the spectra were cut around the region of the emission line of interest, using the IRAF Task ”dispcor”, keeping∼400-500 ˚A to the left and right of the line, so as to measure the continuum of the spectra. Also, since we are interested in studying the flux of the emission lines (Hβ, Mg IIλ2798, Hγ), it is crucial to subtract the Fe II emission in both the optical and the ultraviolet spectral regions, in order to obtain the real emission line flux. This was performed with a software in IDL Language (Torrealba et al., 2012), the main steps we followed are described as follows:

Continuum Fitting and Subtraction. First, a local continuum with a power law of the formA_∗xB₊_C _{it was fitted to the spectrum around the line of interest}

(Fig. 2.1 Left Pannel) using the Levenberg-Marquardt least-squares minimal routinei_{. The zones in the spectra where the continuum is fitted must be}

provided by the user. The fitted continuum was subtracted from the spectra in order to proceed with the next step.

Subtract Iron from Spectra. The following Fe II templates of the NLS1 I Zw 1 galaxy (z = 0.0611; FWHM of _�900 km s−1_{) were used: (a) the template of}

V´eron-Cetty et al. (2004) based on spectra from the 4.2 m William Herschel and the 3.9 m Anglo-Australian telescopes for the optical band (from 3575-7530 ˚A); i_{We used the IDL routine MPFIT from}

http://cow.physics.wisc.edu/~craigm/idl/ fitting.html.

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15 2.3. SPECTROSCOPY

and (b) the template of Vestergaard & Wilkes (2001), based on spectra from the HST-FOS, for the UV-band (from 1250-3090 ˚A). These are the more accurate templates available in the literature. The intrinsic narrow lines of this source and its rich iron spectrum make the templates particularly suitable for use with AGN spectra. The iron emission was fitted to the continuum-less spectra in zones where there are no expected emission lines, and then the fitted iron emission was subtracted from the spectra (Fig. 2.1 Right Panel). In detail the fitting is performed as follows: 1) one must choose regions where we do not expect to have any kind of emission, after the subtraction of the iron from the spectra; 2) the rms is calculated in these intervals; 3) in the software, we have the possibility to change the broadening of the template depending on the specific resolution of the original spectra and we also have the possibility to change the shift and scale of the template in order to fit the observed emission. The goal is to obtain an rms in these zones at least one order of magnitude smaller than the height of the line, i.e. we seek a S/N ratio for the line greater than 10.

Add Continuum to Iron-less Spectra. After subtracting the iron emission from the spectra, the same continuum that was subtracted, is added to the iron-less spectra to obtain the total spectra without iron emission (Fig. 2.2).

The flux line for each spectrum is measured after the iron subtraction and re-addition of the continuum were done. This is calculated as the integration above the fitted continuum, over the range of wavelengths covered by the line (over 140 ˚A from base to base for the four objects). The range of integration and the lines of interest for each object are shown in Table 2.3.

Table 2.3: Lines measured in each object and range of integration of the lines.

Object Line Range (˚A)

3C 273 Hβ (4861 ˚A) 4760 - 4975 3C 279 Mg II (2798 ˚A) 2725 - 2875 3C 454.3 Mg II (2798 ˚A) 2725 - 2875 PKS 1510-089 Hγ (4341 ˚A) 4264 - 4410

The integration of the lines is done with a purpose-built software in IDL Language. The basic method of integration is the trapezium method, with ∆λ = 10−3 _˚_{A, and}

values in the spectrum were interpolated linearly to match the requirements of the integration software. First, for each interval of width ∆λ the area of the entire trapezium (from fλ = 0 to the fλ in the spectrum) was obtained, then, from the

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Figure 2.1: Left Panel: Fitting of the continuum with a power law of the form

A∗xB₊_C_{. The black line is the observed spectra, meanwhile the red dashed line}

is the continuum fitted. Right Panel: Fitting of the iron emission template to the continuum-less spectra. The points represent the observed spectra after continuum subtraction, the green line is the iron template fitted to the observed spectrum and the blue line represent the spectra (continuum-less) after Fe II subtraction.

fitted continuum power law, the value of the continuum was calculated at the center of this interval, in order to make a rectangle of width equal to that of the interval, and height, that of the continuum obtained from the center of the interval; next, to the area of the entire trapezium was subtracted the area of the rectangle, and the result is added to the results of every interval in the range of integration, to obtain the line flux.

There are also Equivalent Widths available for all of the spectra, that were calculated with the same software as the line flux, as follows: once we obtain the area belonging to the line on one interval, this is divided by the height of the continuum in the middle point in the interval, and the contributions of all the intervals are added to obtain the total equivalent width. The reason why the equivalent width was not

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17 2.3. SPECTROSCOPY

Figure 2.2: Final Iron-less Spectra.

obtained in the common fashion, just by the division of the total line flux by the continuum flux, is because the continuum is not constant in the range where the line is integrated, as can be seen in Figs. 2.1, 2.2.

Continuum fluxes are also available, at 2800 ˚A and 3000 ˚A for 3C 279 and 3C 454.3, at 4900 ˚A and 5100 ˚A for 3C 273, and at 4900 ˚A for PKS 1510-089.

The validity of this software was tested by measuring the line flux for a random sample including 20 % of the spectra, with the IRAF task ”splot”, integrating (using the E key) over the ranges specified in table 3. All fluxes obtained in this way are consistent within the error bars with those obtained with the software in IDL. Strictly speaking, there are three diﬀerent sources of error in measuring the line flux: 1) the error in the flux calibration; 2) random error due to dispersion of the spectra and the signal to noise ratio; 3) and the error introduced by the subtraction of the iron emission.

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the error due to flux calibration.

The random error due to the general statistical characteristics of the spectra, can be calculated through the formula of Tresse et al. (1999).

σF =σcD

�

2Npix+

EW

D (2.2)

where F is the line flux, EW is the equivalent width, D is the dispersion of the spectra in ˚A/pix,Npix is the number of pixels covering the integration range of the

line, andσc is the standard deviation of the continuum measured near the line.

From here we can also calculate the error in the equivalent width, as follows:

σEW =

EW F σcD

�

EW

D + 2Npix+

�

EW D

�2�

Npix (2.3)

The third source of error is that introduced by the subtraction of the iron emission. This error was estimated taking into account the eﬀect of the S/N ratio of the line with respect to the noise in the continuum, in the parts of the line were there was subtracted iron emission. In order to know the parts of the line where the subtraction was performed, we looked into the templates of iron emission (both optical and UV), and checked the range in wavelength where the iron emission around the lines of interest, was 10 % of the nearest local maximum. Once that was done the uncertainty due to subtraction of iron emission is estimated as follows:

σFiron =

rms maxs

(Fline−Fironless) (2.4)

where rms is obtained after the iron subtraction, maxs is the line-peak in the

continuum-less spectrum, Fline is the line flux; and Fironless is the fraction of the

line flux, in the range of integration where there was not iron subtraction. The ratio

rms/maxs is basically the inverse of the S/N ratio of the line-peak, and the second

term Fline−Fironless is introduced so that the S/N is scaled to the fraction of the

line flux that could be aﬀected by the iron subtraction.

Once we obtain the error due to diﬀerent factors, these errors are added in quadrature to obtain the total error in the emission line flux.

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19 2.4. GAMMA-RAY DATA

2.4 Gamma-Ray Data

The gamma-ray light curves were obtained using data from the Fermi Gamma-Ray Observatory, with the Large Area Telescope (LAT).

LAT is a pair-production telescope. The tracking section has 36 layers of silicon microstrip detectors to record the tracks of charged particles, interleaved with 16 layers of tungsten foil (12 thin layers, 0.03 radiation length, at the top or front of the instrument, followed by 4 thick layers, 0.18 radiation length, in the back section) to promote γ-ray pair conversion. Below the tracker lies an array of CsI crystals to determine theγ-ray energy. The tracker is surrounded by segmented charged-particle anticoincidence detectors (plastic scintillators with photomultiplier tubes) to reject cosmic-ray backgrounds. LAT’s improved sensitivity compared to EGRET stems from a large peak eﬀective area (_∼8000cm2_{, or} _∼ _{6 times greater than EGRET’s),}

large field of view (∼ 2.4 sr, or nearly five times greater than EGRET’s), good background rejection, superior angular resolution (68% containment angle ∼0.6◦ at 1 GeV) for the front section and about a factor of 2 larger for the back section versus ∼ 1.7◦ _{at 1 GeV for EGRET; and improved observing eﬃciency (keeping the sky}

in the field of view with scanning observations versus inertial pointing for EGRET) (Abdo et al., 2009).

The process of obtaining Gamma-Ray Light Curves is a little bit more diﬃcult, because unlike infrared or optical photometry, we do not have standard stars in Gamma-Ray because normal stars does not emit in gamma-rays. The methodology to obtain Gamma-Ray Fluxes is described as follows:

Identification Identify all the Gamma-Ray sources in the field you are working on.

Model Create a model of the emission (e.g. power law, broken power law, log parabola, etc.), considering the point sources (sources of interest), the Galactic and Extragalactic Diﬀuse Sources and others sources that may be identified in the field.

Likelihood Analysis Perform a likelihood analysis to find the flux of the source of interest and the significance of this detection (In the case of a light curve, a likelihood analysis should be carried out to get each one of the fluxes).

For our analysis we used a time bin of 7 days for almost of the objects, in order to get a good S/N ratio; except for one object, 3C 454.3, where a time bin of two days was chosen given the brightness of this object. Also for most light curves, we choose an energy interval of 0.1 to 300 GeV, except for BL Lac where we defined an energy

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interval of 1 to 300 GeV; because this light curve had a visual resemblance to the light curves in the other bands, unlike the 0.1-300 GeV light curve; also the fact that at 1 GeV we have a smaller IRF (Instrument Response Function) which makes the identification of the source photons more reliable.

The Fermi mission is providing a set of tools called the Fermi Science Tools for the analysis of both LAT and GBM data. This suite was developed by the Fermi Science Support Center (FSSC) and the instrument teams, and was reviewed by the Fermi Users’ Group.

In the Fermi Science Support Center, there is a section of User Contributed Software. Two scripts from here were used, one to generate point source models, and one to generate light curves. For this second script, however, the models and other parameters used in the script were for demonstration purposes only, and therefore, this script was modified to fulfill our scientific needs.

The detection, flux measurement and spectral modeling of Fermi LAT sources is accomplished by a maximum likelihood optimization technique, as described in the Cicerone webpage (see also e.g. Abdo et al., 2009).

In order to consider a flux obtained in a certain bin, as a significative detection, we take as threshold a T S > 25 (i.e. S/N ratio �5). The points with large errors were not taken into account to create the light curves. First we discarded points with errors equal or greater than 100%, second, we analyze a distribution of the errors for each source, and we discard points with errors larger than 3σ.

To get a more detailed explanation of the statistical analysis to obtain the fluxes, please refer to App. B.

2.5 Light Curves

Once we finish all the steps mentioned in this chapter, we get the object’s light curves. The total number of observations (time bins for gamma-ray) we have for each band are stated in Table 2.4.

It might be worth noting that in the gamma-ray, V band and spectral monitoring, 3C 454.3 has the best sampling of all our objects. Meanwhile, for the NIR bands the object Mrk 421 has the best sampling.

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21 2.5. LIGHT CURVES

Table 2.4: Total number of multiwavelength observations.

Object Gamma-Ray V Band J Band H Band Ks Band Spectra

3C 66A 154 91 49 47 46

-3C 273 158 114 52 52 51 109

3C 279 159 110 29 32 30 104

3C 345 33 39 24 29 20

-3C 454.3 514 429 76 71 71 207

BL Lac 49 190 68 59 58

-Mrk 421 159 134 98 100 98

-Mrk 501 152 127 57 56 51

-PKS 0235+164 142 115 35 37 31

-PKS 0716+714 158 77 44 43 40

-PKS 1510-089 163 115 37 37 35 102

PKS 1633+382 162 106 30 36 28

-PKS 2155-304 169 89 10 10 9

-PMN J0808-0751 42 - - 26 38 27

-QSO B0133+476 158 164 38 42 35

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-Chapter 3

Variability

AGN are perfect objects to study brightness variability, given that they vary at all wavelengths from radio to gamma-ray.

Even broad emission lines in quasar-like objects vary, because the lines arise from photoionization by a continuum extending to ultraviolet and in some objects to X-ray energies; obviously if the photoionizing continuum varies, the emission line spectrum should vary as well. Variability studies are useful for diﬀerent things, like constraining the sizes of emitting regions of diﬀerent wavelengths.

3.1 Previous Work

The study of variability at gamma-rays is particularly interesting, because most of the bolometric luminosity of blazars is emitted at gamma-rays (Sbarrato et al., 2011). The EGRET experiment onboard the Compton Gamma-Ray Observatory

already detected rapid variability with time scales of few hours (e.g. _∼ 8 h for 3C 279 Wehrle et al., 1998, _∼ 4 h for PKS 1622-297 Mattox et al., 1997). The early results obtained from the Large Area Telescope (LAT) onboard theF ermi Gamma

-Ray Space T elescope also show rapid variability of few hours (e.g. Foschini et al., 2010; Subramanian et al., 2012).

Some quasar are variable in every waveband in which they have been studied, not only in the continuum, but in the broad emission lines as well. Optical continuum variability of quasars was established even before the emission line redshifts were

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understood (e.g. Matthews & Sandage, 1963).

An interesting example of AGN variability is that of Seyfert galaxies at X-rays. The X-ray emission consists of several components, including a power law in the medium energy X-ray range (1-10 keV; α�0.9, wherefν ∝ν−α), a soft excess usually below

1 keV, and a reflection bump in the 10-30 keV range. Both the soft excess and the medium X-ray power law component are variable, albeit diﬀerently; the soft excess is more strongly variable and is often but not always, correlated with the emission at medium energy X-rays. There are very few cases where the soft and medium X-ray variations appear uncorrelated (Ulrich et al., 1997).

The very large eﬀort in monitoring high-z quasars has recently come to fruition. There are now enough data in various samples to separate the eﬀects of luminos-ity and redshift on the variabilluminos-ity, avoiding the inherent correlation that exists in magnitude-limited samples. The observation that optical-UV spectra of both low and high-luminosity AGN vary more at short than at long wavelengths (as found for high-luminosity AGN by Cutri et al., 1985) accounts completely for the observed increase of variability with redshift (Giallongo et al., 1991; Trevese et al., 1994; Di Clemente et al., 1996; Cristiani et al., 1996).

An alternative model (diﬀerent than the standard black hole + accretion disk model) views radio quiet AGN as giant young stellar clusters (Terlevich et al., 1992). In this case, variability results from the random superposition of ”events”: supernova explosions generating rapidly evolving compact supernova remnants (cSNRs) due to the interaction of their ejecta with the high density circumstellar environment. This model is supported by the striking similarity between the optical spectra of AGN and of cSNRs (e.g. Filippenko, 1989). The characteristics of an event (i.e. its light curve, amplitude, and time scale) result from the combination of radiative cooling, expanding shocks, shells formation, among others (Terlevich et al., 1992). Still, the light curves of AGN of various absolute luminosities and redshifts can be predicted from this model and are found to be consistent with the observed dependence of the structure function (the curve of growth of variability with time) on luminosity and redshift, however, it still has problems explaining the X-ray variability and periodicity found for some AGN (Cid Fernandes et al., 1996; Cristiani et al., 1996).

Variability of distant quasars could also result from microlensing by compact bodies in intervening galaxies. The cosmological implications would be very important: if there were such lenses along all sight-lines to high-z AGN, then Ω in compact objects would be close to one (Press & Gunn, 1973; Blandford & Narayan, 1992).

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25 3.1. PREVIOUS WORK

motivation for monitoring emission line variations in AGN (e.g. Gaskell & Sparke, 1986; Gaskell & Peterson, 1987). The mass is estimated in the following way. Vari-ations in the emission line strengths of AGN are observed to echo the continuum variations with a time delay, which can be interpreted as the light travel time be-tween the central source and the surrounding high velocity gas clouds (the BLR). Combining the radial distance to the line-emitting gas with its velocity (assuming virialized motions) allows determination of the mass of the central black hole. It is clearly important to assess whether the gas is gravitationally bound, as well as to search for kinematic evidence of accretion and/or ordered gas motions such as infall or a rotating disk. Reverberation (or echo) mapping is a technique for inferring the structure and velocity field of the BLR from the time delays between continuum and line variations (Peterson, 1993). The basic assumptions are that the BLR is ionized by a central continuum point source, the light travel time between continuum and gas clouds is much longer than the ionization or recombination times, and the line intensity is linearly correlated with the incident continuum flux (e.g. Peterson, 1993).

The BLR can respond only to continuum variations that last long enough to penetrate its volume significantly, and the amplitude of the continuum variations must also be large enough to alter the gas clouds emissivity. That is, the BLR filters out continuum variations that are too fast or too small.

For example, in NGC 4151 the continuum variations occurring in _∼1 day did not result in any detectable variations of the C IV line intensity (Crenshaw et al., 1996), although their amplitude, by a factor 1.3, was suﬃcient to produce line intensity variations in slower conditions.

Because the velocity and line emissivity vary with the radial distance (stratification), the line intensity and profile variations differ according to the duration and the amplitude of the continuum event (Netzer & Maoz, 1990). Care should be exercised when comparing delays of line responses during different episodes or in different AGN. Only comparisons between events with similar continuum amplitudes are valid. Another important issue is the variability of line profiles. Comparison of line profile variability during month-long campaigns separated by one or more years reveals that the line response is not stationary. This phenomenon, observed in the High Ionization Lines (HIL) and the Low Ionization Lines (LIL), is probably caused by changes in the distribution of the BLR gas in a few years (NGC 4151: Ulrich et al., 1991; Perry et al., 1994; NGC 3516: Wanders & Horne, 1994; NGC 5548: Wanders & Peterson, 1996). Although it is not possible at this time to offer a definitive interpretation

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of these changes, they suggest the presence of time variable inhomogeneities on the surface of the disk (possibly due to the magnetic field) which can (a) enhance the Balmer lines emission in some locations (e.g. bumps on the disk surface would intercept more continuum flux), thus altering the Hβ profile and (b) strengthen the gas extraction from the disk surface (at local enhancements of the magnetic field), thus lifting additional HIL clouds above the disk and producing shoulders and other features in the C IV line (Fig. 3.1).

Figure 3.1: Examples of long- and short-term variations of the C IV line in NGC 4151. Variations within days are shown on each panel. One can appreciate the variations on time scales of years by comparing the two panels and considering that between 1985 and 1990 the C IV line was observed to be perfectly symmetrical. [From Ulrich et al. (1991)] Ordinates in 10−14 _{erg s}−1 _cm−2 _˚_A−1_.

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27 3.2. VARIABILITY OF BLAZARS

3.2 Variability of Blazars

Blazars exhibit the most rapid and the largest amplitude variations of all AGN (Stein et al., 1976; Angel & Stockman, 1980). The combination of extreme variability and relatively weak spectral features suggests the continuum is emitted by a relativistic jet close to the line of sight and hence that the observed radiation is strongly amplified by relativistic beaming (Blandford & Rees, 1978). Here we take the point of view that all blazars, whether weak-lined like BL Lac objects or strong-lined like flat spectrum radio-loud quasars (FSRQ), contain essentially similar relativistic jets. They may diﬀer in other aspects of nuclear activity; in particular, BL Lac objects may have less luminous accretion disks and BLRs than FSRQ (Ulrich et al., 1997).

Early multiwavelength studies provided the first global support for the idea of bulk relativistic motion in blazars: the observed radio emission was suﬃciently luminous and rapidly variable that, assuming it was due to synchrotron radiation, high X-ray fluxes would be expected from Compton upscattering of the synchrotron photons (the so-called synchrotron self-Compton process), unless the radio emission was rel-ativistically beamed (Hoyle et al., 1966; Jones et al., 1974a,b).

Optical variability extends to very short time scales, and intra-night small- amplitude variability has been observed in a number of blazars (Jang & Miller, 1995; Heidt & Wagner, 1996). The short time scale variations of radio-selected BL Lacs (LBL) are systematically larger in amplitude and have shorter duty cycles than those of X-ray selected (HBL) BL Lac objects (Heidt, 1996). Within the radio-selected sample, there is a tendency for greater optical activity among higher luminosity sources (Heidt & Wagner, 1996).

The spectral variability in the UV band is generally small, with only a weak tendency for larger amplitude variability at shorter UV wavelengths (Edelson, 1992; Pian & Treves, 1993; Paltani & Courvoisier, 1994). Along the 90s, the two blazars with the most UV observations, Mrk 421 and PKS 2155304, both HBL, show spectral hardening with increasing intensity only in a statistical sense (Ulrich et al., 1984; Maraschi et al., 1986; George et al., 1988a; Urry et al., 1988).

In HBL, rapid large-amplitude X-ray variability is the rule (flux doubling on time scales of hours). The spectra harden systematically with increasing intensity (Urry et al., 1986; Treves et al., 1989; George et al., 1988b; Giommi et al., 1990; Sembay et al., 1993; Sambruna et al., 1994). Comparing the UV and X-ray variability of HBL suggests that both spectral changes and variability amplitude are greater beyond the synchrotron peak, which is in the soft X rays for these objects.

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Gamma-ray emission, in some cases extends to the TeV range (Fig. 3.2). Mrk 421 was the first extragalactic source detected at such energies with the Whipple Obser-vatory (Punch et al., 1992), although it was only weakly detected at GeV energies with EGRET (Lin et al., 1992). The increased sensitivity of Fermi/LAT, however, has granted the detection of Mrk 421 as a bright gamma-ray source (Abdo et al., 2009). The TeV flux of Mrk 421 is variable by up to a factor of 10 on time scales of a day (Kerrick et al., 1995) and by a factor of 5 on time scales of 30 min (Gaidos et al., 1996). Shorter time scales are not presently accessible owing to low event rates. Large-amplitude TeV variability must be frequent as such variations are com-monly detected, in contrast with the quiet behavior of the same source in the GeV range.

Figure 3.2: Spectral energy distributions for two blazars in high and low states: Mrk 421 (filled and open squares) and PKS 0528+134 (filled and open circles). In both cases, the object is more highly variable at frequencies larger than that of the peak than at smaller frequencies. [From Macomb et al. (1995, 1996); Sambruna et al. (1996).] The case of 3C 279 is illustrated in Maraschi et al. (1994).

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29 3.3. MEASURING VARIABILITY

Some important conclusions have been drawn from the EGRET and Whipple dis-coveries. First, the gamma-ray emitting region must be transparent (i.e. the optical depth to pair production must be low), yet for minimal assumptions about ambient X-ray photon densities, the size limit imposed by the rapid gamma-ray variability implies very high optical depths. Therefore gamma rays must be relativistically beamed (Maraschi et al., 1992; Becker & Kafatos, 1995; Dondi & Ghisellini, 1995; Gaidos et al., 1996).

Second, blazars emit a large fraction of their luminosity at very high energies. If the long-term gamma-ray light curve of 3C 279 is typical, even if the EGRET detections are biased toward exceptional states of gamma-ray activity, the average power output in gamma rays is comparable to that at all other wavelengths.

Third, the second peak of the spectral power distribution remarkably seems to fall at the highest energies for those objects whose first peak is also at high frequency: it probably lies near 0.11 GeV for low-frequency peaked BL Lac (LBL) and 10-100 GeV for HBL (see Fig. 3.2), although this is based on very incomplete data. A likely origin of the gamma-ray emission is Compton scattering of lower energy photons by the same relativistic electrons producing the low frequency component. The correlation of variability at high and low frequencies is a crucial test for this class of models. Therefore, a multifrequency study is very important to constraint the emission mod-els for these objects.

3.3 Measuring Variability

For all objects in our sample, and in all of observed bands (V, J, H, Ks, gamma-rays, spectral continuum, and emission lines), we calculated a variability parameter Fvar

as explained in Vaughan et al. (2003).

If we have a vector of N values x, with its corresponding error barsσx then we can

define a variability parameter Fvar as

Fvar =

�

S2₋_σ2

err

¯

x2 (3.1)

Where S2 _{is the variance of} _x_{, ¯}_x_{is the mean of} _x _and_σ2

err is the mean square error,

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σ2

err =

1

N

�

i=1

σ2_x,i (3.2)

The uncertainty associated to this variability parameter is

err(Fvar) =

� � � � �

��

1 2N

σ2

err

¯

x2_F

var

�2

+

 

�

σ2

err

N

1 ¯

x

 

2

(3.3)

According to Vaughan et al. (2003) the above equation is valid for both Gaussian and Poisson distributed flux errors. It is worth reiterating that this error accounts only for measurement errors on the fluxes; it does not account for the intrinsic scatter in the fluxes inherent in any red noise process.

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31 3.3. MEASURING VARIABILITY Ta b le 3. 1: M u lt iw av el en gt h va ri ab il it y p ar am et er . O b je ct G am m a V B an d J B an d H B an d K s B an d E m is si on Li n e 4 C on ti n u u m 3C 66A 0. 310 ± 0. 020 0. 222 ± 0. 002 0. 240 ± 0. 010 0. 262 ± 0. 010 0. 279 ± 0. 011 -2 -2 3C 273 0. 532 ± 0. 014 0. 032 ± 0. 005 0. 047 ± 0. 013 0. 089 ± 0. 009 0. 079 ± 0. 011 0. 034 ± 0. 001 0. 048 ± 0. 000 3C 279 0. 315 ± 0. 015 0. 783 ± 0. 002 0. 581 ± 0. 015 0. 597 ± 0. 015 0. 531 ± 0. 016 0. 517 ± 0. 008 0. 803 ± 0. 002 3C 345 -1 0. 435 ± 0. 008 0. 341 ± 0. 013 0. 401 ± 0. 013 0. 387 ± 0. 016 -2 -2 3C 454. 3 1. 035 ± 0. 004 0. 582 ± 0. 001 0. 851 ± 0. 009 0. 861 ± 0. 010 0. 834 ± 0. 010 0. 076 ± 0. 002 0. 584 ± 0. 000 B L Lac 0. 346 ± 0. 072 0. 428 ± 0. 001 0. 281 ± 0. 008 0. 305 ± 0. 009 0. 319 ± 0. 010 -2 -2 M rk 421 0. 241 ± 0. 019 0. 279 ± 0. 002 0. 219 ± 0. 006 0. 192 ± 0. 006 0. 270 ± 0. 006 -2 -2 M rk 501 0. 475 ± 0. 021 0. 054 ± 0. 001 0. 076 ± 0. 011 0. 068 ± 0. 012 0. 115 ± 0. 011 -2 -2 P K S 0235+ 164 0. 254 ± 0. 019 1. 134 ± 0. 002 1. 056 ± 0. 014 1. 132 ± 0. 013 0. 947 ± 0. 014 -2 -2 P K S 0716+ 714 0. 242 ± 0. 018 0. 321 ± 0. 002 0. 389 ± 0. 011 0. 395 ± 0. 011 0. 400 ± 0. 012 -2 -2 P K S 1510-089 0. 588 ± 0. 012 0. 525 ± 0. 003 0. 549 ± 0. 011 0. 562 ± 0. 013 0. 544 ± 0. 012 0. 144 ± 0. 003 0. 415 ± 0. 001 P K S 1633+ 382 0. 278 ± 0. 019 0. 705 ± 0. 003 0. 746 ± 0. 014 0. 798 ± 0. 015 0. 777 ± 0. 020 -2 -2 P K S 2155-304 0. 399 ± 0. 020 0. 364 ± 0. 002 0. 220 ± 0. 022 0. 256 ± 0. 020 0. 261 ± 0. 031 -2 -2 P M N J 0808-0751 0. 637 ± 0. 046 -2 0. 733 ± 0. 015 0. 810 ± 0. 012 0. 738 ± 0. 018 -2 -2 Q S O B 0133+ 476 -1 -3 0. 706 ± 0. 014 0. 805 ± 0. 014 0. 663 ± 0. 018 -2 -2 W C om ae 0. 367 ± 0. 019 0. 282 ± 0. 004 0. 324 ± 0. 010 0. 308 ± 0. 009 0. 298 ± 0. 010 -2 -2 1T h e val u es ar e u n d et er m in ed b ec au se w e h av e th at th e m ean sq u ar e er ro r is lar ge r th an th e var ian ce of th e li gh t cu rv e, in d ic at in g n o m eas u rab le var iab il it y. 2 W e d o n ot h av e th is li gh t cu rv e. 3 F or th is li gh t cu rv e w e ju st h av e th e er ror d u e to th e ab sol u te cal ib rat ion of th e p h ot om et ry , b u t n ot th e er ror in th e m eas u re d m agn it u d e, th er ef or e, an es ti m at ion of th e var iab il it y p ar am et er w ou ld b e ov er es ti m at ed . 4 T h e em is si on li n e h as a si m il ar p rob le m th an in n ot e 3, gi ve n th at w e d o n ot h av e th e cal ib rat ion er ror for th e sp ec tr a, b u t w e d o n ot ex p ec t th is to aﬀ ec t m u ch th e var iab il it y p ar am et er es ti m at ed .

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Chapter 4 Statistical Analysis

4.1 Cross Correlation Analysis

The Cross-Correlation function has been used in science for more than 50 years. It is a very useful tool for analyzing time series. A specific application in astronomy is to quantify lags between diﬀerent types of emission in Active Galactic Nuclei (e.g. between continuum and emission-line flux variations, see Gaskell & Sparke, 1986; Gaskell & Peterson, 1987).

In this work we used three diﬀerent methodologies of the cross-correlation function: the interpolation method of Gaskell & Sparke (1986), the discrete correlation function of Edelson & Krolik (1988) and the Z-Transformed discrete correlation function of Alexander (1997); in order to quantify the lags between four diﬀerent parts of the electromagnetic spectrum, specifically, the NIR (J, H and Ks bands), the optical (V-band), the gamma-ray and line flux emission.

4.2 The Interpolation Method

To use this method, we need the data from both light curves to be taken uniformly (i.e. data in the same moment for both curves and with equal spacing). Given that this is extremely diﬃcult to do in real life, the alternative that Gaskell & Sparke (1986) suggest is to make linear interpolation in the data, so we can get two vectors

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of the same size, with fluxes in the same moment and observation times equally spaced.

In practice, if you do not have equal epochs of observation, then you should take into account, that you just want to do interpolation, not extrapolations. This is so, given that we use linear interpolation, we can get very large fluxes, or unphysical negative fluxes. To avoid this, you should take as starting point of the cross-correlation analysis, the initial point of the curve that starts later in time; and as ending point, the final point of the curve that finish earlier in time.

In the original paper of Gaskell & Sparke (1986) they used this method to look for correlations between continuum and line flux measurements, and one particular step they did was to extend the continuum measurement backward and forward: they took values before the starting point, the same as the first point, and all the values after the ending point, the same as the last point, (according to their work, this minimizes the introduction of spurious correlations). This was done because of the limited sampling they had. Given that we have enough sampling, we do not need to do this. Also, even when the interpolation method works by assuming a certain understanding of the behavior of the light curve, applying this step might in fact cause the opposite eﬀect the authors were looking to avoid (see also White & Peterson, 1994).

Once you have two vectors of flux (from diﬀerent light curves) covering a time interval

T, one should make a vector of lags, that as maximum can have values from −T to +T. However, this is exact only when you have the fluxes in the light curves spaced by one unit of time (e.g. days); in the case when you have points in the light curves separated by more than one unit of time, say ∆t, the vector of lags should have values:

Li =

li

∆t (4.1)

where li is the real lag, in the same units than ∆t; and Li must always be an

integer.

This method will basically move the time axis of one of the light curves to greater or lower values, according to the lag; then, in the interval of time when both light curves intersect, it computes the correlation coeﬃcient between these segments of the light curves.

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35 4.2. THE INTERPOLATION METHOD

−T to +T, both of these lags would be computed with just one point in each light curve (because just one point will coincide once the light curve has been displaced that much), and lags close to these also will have just a few points. In this situation a correlation coeﬃcient is not statistically significant. In this work, we took as minimum li = −0.8T, and as maximum li = +0.8T with the purpose of leaving at

least 20% of the light curves to obtain a correlation coeﬃcient

Now, if we have vectors xand y, and a vector of lags L, we can calculate the Cross-Correlation Function Pxy(L) by using the Eq. 4.2 as defined by Fuller (1976):

Pxy(L) =

                                        

N−|L|−_� 1

k=0

(xk+|L|−x¯)(yk−y¯)

� � � ��N�−1

k=0

(xk−x¯)2

��N_�−1

k=0

(yk−y¯)2

� F or L <0

N−L−_�1

k=0

(xk−x¯)(yk+L−y¯)

� � � ��N�−1

k=0

(xk−x¯)2

��N_�−1

k=0

(yk−y¯)2

� F or L≥0

(4.2)

where ¯xis the mean of the points in thex curve that are involved in the calculation of the correlation coeﬃcient, and similarly for ¯y. This value is recalculated for each lag.

In some works found in the literature (e.g. Gaskell & Sparke, 1986; Gaskell & Peterson, 1987), to perform the Cross-Correlation Analysis, they take ¯xas the mean of the entire light curve, so one does not have to recalculate this value for each lag. According to White & Peterson (1994), however, this is only valid, if we assume that the light curve is stationary, i.e., the mean and standard deviation do not change with time, but this is something we cannot assume for AGN light curves, and they propose to take into account for the computation of the mean, just the points involved in the correlation for each lag.

Once you’re done with this step, then to represent graphically the Cross-Correlation Function, you should plot L × ∆t vs. Pxy(L).

Multifrequency study of variability of Fermi/LAT Blazars