PROBING EXTRAGALACTIC DUST

THROUGH GAMMA-RAY BURST AFTERGLOWS

A Dissertation

presented to

the Faculty of the Graduate School

University of Missouri-Columbia

In Partial Fulfillment

of the Requirements for the Degree

of Doctor of Philosophy

by

Shunlin Liang

Dr. Aigen Li, Dissertation Supervisor

April 2010 The undersigned, appointed by the Dean of the Graduate School, have examined the dissertation entitled:

PROBING EXTRAGALACTIC DUST THROUGH GAMMA-RAY BURST AFTERGLOWS

presented by Shunlin Liang

a candidate for the degree of Doctor of Philosophy and hereby certify that in their opinion it is worthy of acceptance.

Dr. Bahram Mashhoon

Dr. Sergei Kopeikin

Dr. Angela Speck

Dr. Rainer Glaser

Dr. Aigen Li

ACKNOWLEDGMENTS

Many have made contributions to this dissertation. I especially want to express my appreciation to my advisor, Dr. Aigen Li, for his guidance, support and insightful suggestions. Dr. Aigen Li is indeed a rarity. He is enthusiastic, logical, forward- thinking, generous, focused, and insightful. While he is no ordinary exemplar for a graduate student, I could not have been luckier nor happier to have had such a person as a Ph.D. adviser. He constantly challenged me to attain technical excellence and strive for a deeper clarity in my work. He fostered my curiosity and enabled me, as both a person and a scientist, to shine. I cannot thank him enough for all that he has done for me. My past and current group members have been each extraordinarily influential.

It is a great pleasure to work as a group with Biwei Jiang, Fuyuan Xiang, Juhua Chen, Melanie Köhler, Moping Li, Jian Gao, and Ajay Mishra. My entire doctoral experience was enhanced through my friendship with them.

I heartily thank my thesis committee members: Dr. Bahram Mashhoon, Dr. Sergei Kopeikin, Dr. Angela Speck and Dr. Rainer Glaser. From the onset to the end, they consistently and thoughtfully encouraged me to build this thesis with an eye on the big picture. Thanks for their helpful discussions and suggestions.

This thesis is dedicated to all my friends and those three people that are closest to my heart, without whom thesis would not have been possible nor worthwhile. Mom,

Dad and my wife: Wei, thank you.

ii Contents

ACKNOWLEDGEMENTS ii

LIST OF TABLES v

LIST OF FIGURES vii

CHAPTER

1 Review of Gamma-Ray Bursts 1

1.1 History ...... 1

1.2 Fireball Model ...... 3

1.3 The Afterglow ...... 4

1.4 GRB Progenitor ...... 5

1.5 GRB Host Galaxies ...... 7

1.6 Interstellar Dust & Extinction ...... 9

2 The “Drude” Model: A Novel Approach to Derive Dust Extinction 18 2.1 Introduction ...... 18

2.2 Current Status ...... 21

2.3 Our Approach: The “Drude” Model ...... 25 2.4 GRB 000301C and GRB 021004: Test Cases ...... 26

2.5 Discussion ...... 27

iii 2.6 Conclusion ...... 29

3 The 2175 Å Interstellar Extinction Feature at High Redshifts 35

3.1 Introduction ...... 35

3.2 Dust Extinction Model ...... 36 3.3 Results ...... 36

3.4 Discussion ...... 38

3.5 Conclusion ...... 42

4 Probing Extragalactic Dust through Nearby Gamma-Ray Burst Af-

terglows 46 4.1 Introduction ...... 46 4.2 Dust Extinction Models ...... 49

4.3 Results ...... 50

4.4 Discussion and Conclusion ...... 62

5 Probing Extragalactic Dust through Distant Gamma-Ray Burst Af- terglows 83

5.1 Introduction ...... 83

5.2 Data Analysis & Dust Extinction Models ...... 84

5.3 Results ...... 86 5.4 DISCUSSION ...... 95

5.5 CONCLUSION ...... 98

6 Summary 124

Bibliography ...... 126

VITA 150

iv List of Tables

Table page

2.1 “Drude” fits to known extinction curves for λ = 0.1–1 µm widely adopted as “tem-

plates” in modeling GRB afterglow SEDs to derive GRB host dust extinction. . 30

2.2 Results of fitting to the afterglow SEDs of GRB 000301C and GRB 021004 with the

“Drude” approach (see §2.3, §2.4) or various template extinction laws. Note that

the “Drude” approach has more free parameters than the other approaches. . . . 30

2.3 Results of Drude-fitting to the artificial SED generated by reddening the power-

8 −0.5 law afterglow Fν (µJy) = 5.2×10 (ν/Hz) with AV = 0.5 mag extinction of MW,

SMC, and Calzetti-type (see Figure. 2.4)...... 30

3.1 Parameters for fitting the afterglow SEDs with the “Drude” model and the MW,

LMC and SMC template extinction laws...... 43

3.2 Dust size distributions for the extinction curves derived from the “Drude” model

and a mixture of silicate and graphite grains...... 44

4.1 Parameters for fitting the afterglow SEDs with the MW, LMC and SMC template

2 extinction laws. The goodness of the fit is measured by χ /Nobs, where Nobs is the

number of observational data points...... 67

4.2 Parameters for fitting the afterglow SEDs with the “Drude” approach...... 68

v 4.3 Dust size distributions for the extinction curves derived from the “Drude” approach

and modeled as a mixture of silicate and graphite grains...... 69

5.1 Parameters for fitting the afterglow SEDs with the MW, LMC and SMC template

2 extinction laws. The goodness of the fit is measured by χ /Nobs, where Nobs is the

number of observational data points...... 100

5.2 Parameters for fitting the afterglow SEDs with the “Drude” approach...... 101

5.3 Dust size distributions for the extinction curves derived from the “Drude” approach

and modeled as a mixture of silicate and graphite grains for GRBs at z > 2. . . 102

5.4 Dust size distributions for the extinction curves derived from the “Drude” approach

and modeled as a mixture of silicate and graphite grains for GRBs at z < 2. . . 103

5.5 ...... 104

5.6 Parameters for fitting the afterglow SEDs with the SN dust extinction law. . . . 104

vi List of Figures

Figure page

1.1 Light Curves of 12 GRBs, where the x-axis is the duration time for GRBs, and y-axis is the γ photon flux account. Taken from Bonnell

(1995)...... 14

1.2 This map shows the locations of a total of 2704 GRBs recorded by BASTE during its nine-years mission. The projection is in galactic

coordinates; the plane of the Milky Way Galaxy is along the horizon- tal line at the middle of the figure. The burst locations are color- coded based on the fluence, which is the energy flux of the burst in-

tegrated over the total duration of the event, while grey color is for the bursts whose fluence cannot be well determined due to incomplete data. Taken from Fishman et al. (2000)...... 14

1.3 A histogram showing the distribution of GRB redshift known to date (April 10, 2010). The median value of the 200 redshift is 1.58, and the mean value is 1.93. Taken from Liang & Li (in preparation)...... 15

1.4 The Lyα absorbers along the afterglow of GRB 050730. All significant lines (3σ) are indicated above for z = 3.969 (solid), z = 3.565 (dashed), z = 1.773 (dot-dashed) and unidentified (dotted) systems. The best-

fitting DLA profile is solid line. Taken from Starling et al. (2007). . . 15

vii 1.5 This map is to explain the explosion of a GRB. The dark circle repre- sents the newly formed spinning black hole at the center of an implod- ing star or a merging compact binary system. The long-lived afterglow

emission arises from the swept-up material, in where relativistic elec- trons radiating synchrotron light. The whole sequence of events will be compressed in time as viewed from Earth for the extreme velocity

of the jet. Taken from Piran (1999)...... 16

1.6 Left: a synchrotron spectrum of a relativistic shock with a power-law electron distribution. The panel shows that fast/slow cooling cases,

which are expected at earlier/late times. Right: the corresponding synchrotron light curve (ignoring self-absorption). Both panels assume a constant-density (rather than stellar wind-like) external environment.

Taken from Sari et al. (1998)...... 16

1.7 The plausible theoretical scenarios for the progenitors of GRBs, divided into two main classes: (1) collapsar model; and (2) binary compact

objects model. Taken from Bloom (2003)...... 17 1.8 HST images of 42 GRB host galaxies, in which an accurate projection of the early afterglow position is shown with a green circle. Comparing

these host galaxies, it shows that GRB host galaxies display a wide range in magnitude and morphology. Taken from Fruchter et al. (2006). 17

viii 2.1 Extinction laws widely adopted as “templates” in GRB host extinction studies: the

SMC law (upper panel: dashed black line; Pei 1992), the LMC law (upper panel:

−1 dashed blue line; Pei 1992), the linear Aλ ∝ λ law (upper panel: dashed cyan

line), the MW Galactic average extinction law (RV = 3.1; lower panel: dashed

black line; Pei 1992), the MW extinction law with RV = 4.5 for dense clouds

(lower panel: solid red line), the Calzetti starburst attenuation law (lower panel:

dashed blue line), and the Maiolino law for AGN dust tori (lower panel: dashed

cyan line; just like that of the MW with RV = 4.5). Also shown are the “Drude”

fits to these “template” extinction laws: SMC (upper panel: solid green line), LMC

(upper panel: solid red line), Linear (upper panel: solid magenta line), MW with

RV = 3.1 (lower panel: solid green line), and Calzetti (lower panel: solid magenta

line)...... 31

2.2 Upper panel: fitting the SED of the afterglow of GRB 000301C (filled black circles)

with the SMC (green) and LMC or MW (blue) template extinction laws and the

“Drude” approach (red; see Eq.2.2) for the host extinction curve. No extinction is

allowed in the MW and LMC models (i.e. the best fit with a MW- or LMC-type

extinction is given by AV ≈ 0): a small amount of AV would lead to large deviations

from the afterglow SED since the 2175 Å bump prominent in the MW and LMC

laws is absent in the afterglow SED. Lower panel: comparison of the SMC (green),

LMC (blue), MW (RV = 3.1; black) extinction laws with that derived from the

“Drude” approach (red)...... 32

2.3 Same as Figure. 2.2 but for GRB 021004...... 33

ix 2.4 Upper panel: Drude fits to the observer-frame UBVRIJHK “photometry data”

−β artificially-generated by reddening the intrinsic afterglow spectrum Fν ∝ ν of

a burst at z ≈ 2 (black line with red crosses superimposed for the observer-frame

UBVRIJHK bands) with the SMC (“data”: cyan squares; Drude fit: green line),

Calzetti (“data”: blue triangles; Drude fit: magenta line), and MW (“data”: black

circles; Drude fit: red line) extinction laws (with AV = 0.5 mag for each). Lower

panel: comparison of the SMC, Calzetti and MW extinction curves (solid lines)

with that inferred from the “Drude” approach (dashed lines)...... 34

3.1 Left panel (a): Fitting the SED of the afterglow of GRB 070802 (z ≈ 2.45) with

the “Drude” approach (red) and the MW (magenta), LMC (blue) and SMC (green)

templates for the GRB host extinction curve. Middle panel (b): Comparison of the

MW (magenta), LMC (blue), and SMC (green) extinction laws with that derived

from the “Drude” approach (red). Right panel (c): Fitting the derived extinction

curve (red solid line and black filled circles) with a mixture of amorphous silicate

(cyan dotted line) and graphite dust (green dashed line). The blue solid line plots

the resulting model extinction curve...... 44

3.2 Same as Figure. 3.1a,b but for GRB 050904 (Haislip et al. 2006; Tagliaferri et al.

2005) at three different epochs after burst...... 45

3.3 same as Figure. 3.1c but for GRB 050904 at three different epochs after burst. . 45

x 4.1 Upper panel (a): Fitting the SED of the afterglow of GRB 970508 with the “Drude” approach (red) and the MW (black), LMC (blue) and SMC (green) templates for the GRB host extinction curve. Upper

panel (b): Comparison of the MW (black), LMC (blue), and SMC (green) extinction laws with that derived from the “Drude” approach (red). Upper panel (c): Fitting the derived extinction curve (red solid

line and black filled circles) with a mixture of amorphous silicate (cyan dotted line) and graphite dust (green dashed line). The blue solid line plots the resulting model extinction curve. Middle Panel: Same as the

upper panel but for GRB 980703. Also shown in the middle panel (b)

is the MW extinction curve of RV = 3.5 (dashed line). Bottom panel: same as the upper panel but for GRB 990123...... 70

4.2 Same as Figure. 4.1 but for GRB 990510, GRB 991208, and GRB 991216. Also shown in the middle panel (b) is the extinction curve of the high latitude translucent cloud toward HD 210121 (thin cyan line) which

has the steepest far-UV rise ever observed in the Galaxy...... 71 4.3 Same as Figure. 4.1 but for GRB 000911, GRB 010222, and GRB 010921. 72

4.4 Same as Figure. 4.1 but for GRB 011121, GRB 020405, and GRB 020813. 73

4.5 Same as Figure. 4.1 but for GRB 030226, GRB 030328, and GRB 030329.

74

4.6 Same as Figure. 4.1 but for GRB 040924, GRB 041006, and GRB 050318. Also shown in the upper panel (b) is the so-called “Calzetti” attenua-

tion law of starburst galaxies (cyan line)...... 75

xi 4.7 Same as Figure. 4.1 but for GRB 050408, GRB 050525A, and XRF 050824X. Also shown in the upper panel (b), the middle panel (b) and the bot- tom panel (b) is the extinction curve of the high latitude translucent

cloud toward HD 210121 (thin cyan line) which has the steepest far-UV rise ever observed in the Galaxy...... 76

4.8 Same as Figure. 4.1 but for GRB 051111, GRB 060614, and GRB 060729.

Also shown in the middle panel (b) is the “Calzetti” law (cyan line). 77 4.9 Same as Figure. 4.1 but for GRB 061121, GRB 061126, and GRB 070125. Also shown in the bottom panel (b) is the “Calzetti” law (cyan line). 78

4.10 Same as Figure. 4.1 but for GRB 070306, GRB 071003, and GRB 080319B. Also shown in the upper panel (b) is the “Calzetti” law (cyan line). . 79 4.11 Same as Figure. 4.1 but for GRB 080330, GRB 080514B, and GRB 081008.

80

4.12 (a): Distribution of the derived host galaxy visual extinction AV ; (b): Distribution

of the total-to-selective extinction ratio RV ≡ AV /E(B − V ). (c): Distribution of

the hydrogen column densities NH along the lines of sight toward the bursts in their

host galaxies. (d): Dust-to-gas ratios in the host galaxies along the lines of sight

toward 25 GRBs. Also plotted are that of the MW, LMC and SMC. Open circles:

those bursts with a MW-type extinction; open triangles: those with a LMC-type

extinction; filled triangles: those with a SMC-type extinction; filled circles: those

with a MW-type extinction but with a very weak (or lacking) 2175 Å bump; open

stars: those with a featureless, steep extinction curve; filled stars: those with a

steep far-UV rise and a weak 2175 Å bump; open diamonds: those with a flat curve. 81

xii 4.13 Mass fractions of graphite dust as a function of redshift z for all 33 bursts at z < 2.

Also shown are the mass fractions of graphite of the MRN silicate-graphite model

(red dashed line; Mathis et al. 1977) and the WD silicate-graphite-PAH model

(green dot-dashed line; Weingartner & Draine 2001) ...... 82

4.14 Mass-weighted mean dust sizes as a function of redshift z. Also shown are the mean

dust sizes of the MRN silicate-graphite model (red dashed line; Mathis et al. 1977)

and the WD silicate-graphite-PAH model (green dot-dashed line; Weingartner &

Draine 2001)...... 82

5.1 Upper panel (a): fitting the SED of the afterglow of GRB 971214 with the “Drude” approach (red) and the MW (black), LMC (blue) and

SMC (green) templates for the GRB host extinction curve. Upper panel (b): comparison of the MW (black), LMC (blue), and SMC (green) extinction laws with that derived from the Drude approach

(red). Upper panel (c): fitting the derived extinction curve (red solid line and black filled circles) with a mixture of amorphous silicate (cyan dotted line) and graphite dust (green dashed line). The blue solid line

plots the resulting model extinction curve. 2nd Upper Panel: same as the upper panel but for GRB 000131. 3rd Upper Panel: same as the upper panel but for GRB 000926. Bottom panel: same as the upper

panel but for GRB 011211...... 105 5.2 Same as Figure 5.1 but for GRB 020124, GRB 030226, GRB 030323, and GRB 030429X...... 106

5.3 Same as Figure 5.1 but for GRB 050505, GRB 050730, GRB 050814, and GRB 050820B...... 107

xiii 5.4 Same as Figure 5.1 but for GRB 060206, GRB 060526, GRB 060607, and GRB 071025...... 108

5.5 Same as Figure 5.1 but for GRB 080129, GRB 080310, GRB 080413,

and GRB 080607...... 109 5.6 Same as Figure 5.1 but for GRB 080913, GRB 080916C, GRB 081029, and GRB 081118. Also shown in the bottom panel (b) is the so-called

“Calzetti” attenuation law of starburst galaxies (cyan line)...... 110

5.7 Same as Fig 5.1 but for GRB 081121, GRB 081222, GRB 090313 and GRB 090323...... 111

5.8 Fitting the derived extinction curve (red solid line and black filled circles) with a mixture of amorphous silicate (cyan dotted line) and graphite dust (green dashed line). The blue solid line plots the resulting

model extinction curve. The GRB hosts are selected at z < 2.0. . . 112

5.9 Fitting the derived extinction curve (red solid line and black filled circles) with a mixture of amorphous silicate (cyan dotted line) and

graphite dust (green dashed line). The blue solid line plots the resulting model extinction curve. The GRB hosts are selected at z < 2.0. . . 113 5.10 Fitting the derived extinction curve (red solid line and black filled

circles) with a mixture of amorphous silicate (cyan dotted line) and graphite dust (green dashed line). The blue solid line plots the resulting model extinction curve. The GRB hosts are selected at z < 2.0. . . 114

xiv 5.11 Upper panel (a): fitting the SED of the afterglow of GRB 050904 at t ≈ 0.47 days with the “Drude” approach (red) and the SN (blue) templates for the GRB host extinction curve. Upper panel (b): comparison of the

SN (blue) extinction laws with that derived from the Drude approach (red). Upper panel (c): fitting the derived extinction curve (red solid line and black filled circles) with a mixture of amorphous silicate (black

dotted line) and graphite dust (black dashed line). The black solid line plots the resulting model extinction curve. Middle Panel: same as the upper panel but for GRB 050904 at t ≈ 1.25 days. Bottom panel: same

as the upper panel but for GRB 050904 at t ≈ 3.40 days...... 115

5.12 (a)Upper panel: We present the GRB host extinction curves which have an extinction curve almost identified to that of the SMC (green

lines), LMC (blue lines), MW (red lines) and Calzetti (cyan lines) respectively. The GRB hosts are selected at z > 2.0. Bottom panel: We present the GRB host extinction curves which have an extinction

curve almost not identified to that of the SMC, LMC, MW and Calzetti respectively. (b)Same as (a), but for the GRB hosts are selected at z < 2.0...... 116

xv 5.13 (a)Histogram of the total sample (200 objects, blue region) of GRBs with measured redshift and 63 objects (red region) are selected, where 28 objects studied in this work, 33 objects in Liang & Li (2010), and 2

objects (GRB 000301C, and 021004) in Li et al. (2008). The redshift data come from http://www.mpe.mpg.de/jcg/grbgen.html. (b) Dis-

tribution of the hydrogen column densities NH along the lines of sight toward the bursts in their host galaxies. (c) Distribution of the derived

host galaxy visual extinction AV with mean value at 0.41 mag). (d) Dust-to-gas ratios in the host galaxies along the lines of sight toward

47 GRBs. Also plotted are that of the MW, LMC and SMC...... 117

xvi 5.14 (a) Derived strength (c1) of the far-UV extinction rise as a function

of redshift. (b) Derived strength (c4) of the 2175 Å extinction (in the source frame) as a function of redshift. (c) Derived extinction factor

RV (in the source frame) as a function of redshift. (d) Derived host

galaxy visual extinction AV (in the source frame) as a function of red-

shift. (e) The hydrogen column density NH (in the source frame) as a function of redshift. (f) Mass fractions of graphite dust as a function of redshift z for all 63 bursts. Also shown are the mass fractions of graphite of the MRN silicate graphite model (red dashed line; Mathis

et al. 1977) and the WD silicate-graphite polycyclic aromatic hydro- carbon model (green dot-dashed line; Weingartner & Draine 2001). (g) Mass-weighted mean dust sizes as a function of redshift z. Also shown

are the mean dust sizes of the MRN silicate-graphite model (dashed line; Mathis et al. 1977) and the WD silicate-graphite-PAH model (dot line; Weingartner & Draine 2001) (h) The metallicity as a function of

redshift. For the 63 bursts discussed, we do not see any strong evidence

for the dependence of c1, c4, RV , AV , NH , mgra or metallicity on z. . 118

5.15 (a)Derived strength (c1) of the far-UV extinction rise (in the source

frame) as a function of metallicity. (b) Derived strength (c4) of the 2175 Å extinction (in the source frame) as a function of metallicity.(c)

Derived host galaxy visual extinction AV (in the source frame) as a function of metallicity. For the 22 bursts selected, we do not see any

strong evidence for the dependence of c1, c4 or AV on metallicity. . . 119 5.16 The relationship of the intrinsic power-law slope of the optical afterglow

β to that of the X-ray afterglow βX ...... 120

xvii 5.17 We use Drude approach, FM and 9 order Polynomial model to fit the SN and QSO at z ≈ 6.2 extinction curve. The parameters for

Drude model: c1 = 4.6, c2 = 2.5, c3 = −110, c4 = 0.95, λ1 ≈ 0.10

(instead of 0.08) and λ2 ≈ 0.280 (instead of 0.2175). The parameters

for FM model: c1 = −3.8, c2 = 2.7, c3 = −2580, c4 = −0.5, RV = 2.1,

X0 = 8.8, and γ = 13.2. The parameters for 9 order Polynomial model:

c0 = −5.40, c1 = 15.79, c2 = −17.69, c3 = 10.38, c4 = −3.29, c5 = 0.58,

c6 = −0.057, c7 = 0.0027, c8 = −3.30E − 5, and c9 = −1.13E − 6. . . 121 5.18 We compare the CCM with SMC, LMC, Calzetti and HD210121 ex-

tinction curves. We find that CCM is not able to restore the SMC, LMC, Calzetti and HD210121 models. In (d), our Drude model can

have a best fit for CCM extinction curve with c1 = 7.86, c2 = 1.88,

c3 = −1.05, and c4 = 0.07...... 122 5.19 We use two dust extinction models to derive the best-fitting model on 3 high redshift (z > 5) GRBs...... 123

xviii PROBING EXTRAGALACTIC DUST THROUGH GAMMA-RAY BURST AFTERGLOWS

Shunlin Liang

Dr. Aigen Li: Dissertation Supervisor

ABSTRACT

Gamma-Ray Bursts (GRBs) are the most powerful explosions in the universe and a very interesting phenomenon in themselves. The gamma-rays and the X-ray flashes (XRFs) are the manifestations of the most violent, cataclysmic explosions in

the Universe. GRBs are followed by so-called afterglow emission detected in lower energy bands and on longer timescales, e.g. X-ray, UV, optical, near-infrared, radio emissions from a few hundred seconds to a few months. The following thesis does not

deal with the GRB phenomenon itself but it is studying their environment and host galaxies through optical spectroscopy and using them as light sources in the distant universe. This thesis is divided into six parts.

The first chapter of the thesis discusses the importance of dust on exploring the host galaxies of GRBs. In the second chapter, we present a detailed study on the ob- scuration and reddening by dust in GRB host galaxies. We propose a novel approach

- “Drude” model to derive the GRB host extinction law. We also present the gen- eral dust extinction models and explain why our “Drude” model is more favourable. With the template extinction laws all self-contained, and the capability of revealing

extinction laws differing from the conventional ones, it is shown that this is a power- ful approach in modeling the afterglow SEDs to derive GRB host extinction. In the third chapter, we select GRB 070802 at z ≈ 2.45 (which shows clear evidence for the

2175 Å extinction bump) and GRB 050904 at z ≈ 6.29, the 3rd most distant GRB observed to date and fit their afterglow spectra to determine the extinction of their host galaxies, with an emphasis on the 2175 Å extinction feature at high redshifts. We find that their extinction curves differ substantially from that of the Milky Way, the Small and Large Magellanic Clouds, the 2175 Å extinction feature appears to be also present in GRB 050904 at z ≈ 6.29. In the fourth and fifth chapter, we present a study of the dust properties for a large sample (33 objects) of long-GRB host galaxies at z ≤ 2.0 and another large sample (27 objects) at z ≥ 2.0, respectively. From the derived strength of the far-UV extinction rise, strength of the 2175 Å extinction, the total-to-selective extinction ratio RV , host galaxy visual extinction AV , dust compo- sition and the mass-weighted mean dust sizes of all 60 GRBs, we find no evidence of evolution of the dust properties (extinction, sizes and abundance) on redshifts. The thesis ends with summary, outlook and the references.

xx Chapter 1

Review of Gamma-Ray Bursts

1.1 History

Discovery – Gamma-ray bursts (GRBs) are short, sudden, and intense flashes of gamma-rays of ∼ 0.1−100MeV photons. The typical flux levels is 10−7−10−4 erg cm−2 s−1 and durations is 10−3 − 103 s (Figure 1.1). GRBs were first discovered accidentally in the late-1960s by the Vela satellites(Klebesadel et al 1973; Strong et al. 1974), whose mission was to monitor the γ-ray emission from nuclear weapons testing. The discovery of GRBs is a unexpected byproduct of this effort, as well as the discovery

of cosmic microwave background (CMB) in 1948. Since then, several dedicated satel- lites have been launched to observe the bursts and numerous theories (135 models, Nemiroff 1993) were proposed to explain their origin and most are Galactic origin.

Based on the observations, GRBs seem to occur at random times and from random locations in the sky. For the small number of GRBs been detected, the isotropic distribution of GRBs was not well confirmed for years.

“Great Debate” –Where GRBs are coming from, a “Great Debate” was argued by Paczyński (1995) and Lamb (1995): the cosmology distance or the Galactic dis- tance. In the debate, Paczyński (1995) argued for the cosmological origin of GRBs based primarily on two points: (1) the observed isotropy was taken as evidence for a

1 cosmological progenitor origin and (2) the paucity of faint bursts relative to the num- ber expected if the bursts originated homogeneously in Euclidean space also served as evidence for a cosmological origin (Fenimore et al. 1993; Fenimore & Bloom 1995).

On the other side, Lamb (1995) preferred a Galactic progenitor origin based on the same data. Bloom et al. (1995) explain that Lamb made a persuasive argument for Galactic scenarios despite the small theoretical parameter space then allowed by the isotropy and brightness distribution observations. In the early- to mid-1990s, the Burst and Transient Source Experiment (BATSE), high energy astrophysics experi- ment on NASA’s Compton Gamma-Ray Observatory orbiting around Earth detected

2704 GRBs (see Figure 1.2), placed the strongest constraints on the isotropic distri- bution with a high degree of confidence (Meegan et al. 1992), and ruled out most Galactic models.

Detector Development – After firmly establishing the isotropic distribution and cosmological location, the goal of the BASTE changed to providing GRBs positional information as quickly as possible over the newly formed GRB coordinate network

(GCN). This GCN service is intended to distribute GRB location information world- wide quickly and efficiently. Although BASTE alerted the scientific community of a GRB within seconds of the onset of the event, the radii of the error circles were tens of degrees in the first reports. Even for the brightest bursts, the radii of the error circles were reduced to a few degrees, still far too large for most optical searches. In 1997, the Italian-Dutch satellite BeppoSAX revolutionized our understanding of GRBs by quickly and precisely localization, leading to the afterglow era. On Feb 28, 1997, a GRB fell within the field of the Wide-Field Camera, where a X-ray flash was localized within a circles of 3’ in radius, and a fading X-ray source was found to within a circle of 50” in radius (Costa et al. 1997). This is the first detected afterglow of a GRB and some time later, the first radio afterglow was reported for GRB 970508 by Frail

2 et al. (1997).

After BASTE and BeppoSAX, Rossi X-ray Timing Explorer (RXTE), High Energy Transient Explorer 2 (HETE-2), INTErnational Gamma-Ray Astrophysics Laboratory

(INTEGRAL) and the recently launched Swift, have led to many more identifications of GRB afterglows at longer wavelengths (X-ray/UV/Optical/NIR/Radio). The mea- surement of high redshift distances and the wealth of data have enable astronomers to

understand the nature (e.g. progenitor, mechanism, environment) of the GRBs. The current number of reported GRB redshifts is 200 (Figure 1.3), with the first redshift (z = 0.835) reported for GRB 970508 (Metzger et al. 1997) and the highest redshift

(z = 8.2) for GRB 090423 (Tanvir et al. 2009). The mean redshift is around 1.93 with 200 GRBs above that value. These redshifts are determined either via absorp- tion lines (e.g. damped Lyα absorbers (DLAs), see Figure 1.4) from the fading optical

counterpart, or emission lines from the proposed host galaxy.

1.2 Fireball Model

Fireball model is the explosion mechanism for GRBs, which is well-constrained by

the observed fluences, redshift. Approximate 1051 − 1053 erg of γ-ray radiation is released within a few seconds in every GRB (see Figure 1.5, Piran 1999 for a review). The GRB variability timescale (10−3 − 103 s) also suggests that this energy is quickly

deposited by a “central engine” in a small volume of space (radius r . 1000 km) and is essentially optically thick to γ-ray radiation at early times. This opaque fireball of energy then expands adiabatically and relativistically until the γ-ray radiation can

escape. Therefore, GRB is thought to arise from the interaction of internal shocks initiated by the central engine (Fenimore et al. 1999). After the GRB, the relativistic blastwave expands outward and begins to sweep

3 up the ambient medium. Taking n = 1 cm−3 to be the density of the surrounding

2 2 1/3 medium, the blastwave begins to slow considerably by a radius R ≈ (E0/4mHc Γ ) ≈ 1016–1017 cm and some of the kinetic energy is then converted into internal motion within the shock (Mészáros & Rees 1993). Here mH is the mass of a hydrogen atom,

51 E0 (≈ 10 erg) is the total energy in the fireball and Γ is the bulk Lorentz factor. The transient afterglow phenomenon, thought to arise at this radius, is likely due to synchrotron radiation arising from the interaction of the relativistic ejecta and the ambient medium surrounding the burst site (van Paradijs et al. 2000; Kulkarni et al. 2000; Djorgovski et al. 2001).

1.3 The Afterglow

Based on the fireball model, the afterglows of the GRBs originate from the external shocks, and GRBs originates from the internal shock. Only a fraction of the kinetic energy can be dissipated by internal shocks, and the remaining energy will be followed and dissipated by external shocks. This theory made definite predictions about the spectrum energy distribution (SED) of the external shocks, as well as the afterglow.

Assuming the electrons in the swept-up material have different Lorentz factors and be distributed as a power-law N(Γ) ∝ Γ−p (where p is the electron energy index, e.g. Rybicki & Lightman 1979) and the resulting emitted spectrum is also a power-law

F ∝ t−αν−β(where α is the decay index and β is the spectral index, e.g. Sari et al. 1998).

During the dynamic interaction process, a fireball debris moving at closely c and interacting with interstellar gas, will result in nearly all of its particles moving at Γ À 1. The difference between non-relativistic and relativistic shocks affects the synchrotron radiation of the electrons they accelerate. As the fireball ploughs ahead,

4 it sweeps up an increasing amount of external medium, resulting in a decrease in Γ. Depending on the nature of the ambient medium (ISM or wind), Γ will decrease as a power of the time, asymptotically as t−3/8 (ISM) or t−1/4 (wind) in the adiabatic limit (Sari et al. 1998; Chevalier & Li 2000). As a consequence, the spectrum softens in time as the synchrotron peak frequency (νm) decreases. Thus, starting from GRB radiation, GRBs are expected to progressively evolve into an afterglow radiation, which peaks in the X-ray, then UV, optical, infrared and radio (e.g. Mészáros & Rees 1997).

In Figure 1.6, the SED consists of four power-law segments with three breaks. For

slowing cooling, there is a steeply rising synchrotron self-absorbed spectrum (β = 2)

at low frequencies up to a self-absorption break (νa), then followed by a shallower

slope (β = 1/3) up to νm. Above this break, the spectrum slope changes signs

(β = −(p − 1)/2) up to the cooling break νc and then takes the value β = −p/2. The

cooling break νc locates at where the electron cooling time becomes short compared to the expansion time. The observed flux is also predicted to have four power-law as

time (e.g. Zhang & Mészáros 2004 for a review).

1.4 GRB Progenitor

After the GRB emission and the afterglow phenomenon of long-duration bursts are

reasonably well-understood, one large outstanding question remains: what makes a gamma-ray burst? Or specifically, what are the astrophysical objects “progeni- tors” to produce GRBs? The following considerations should be used to principally

constrained the theoretical progenitor scenarios: (1) The implied (isotropic) energy release in γ-rays are typically 10−3–10−1 times the rest-mass energy of the Sun. Be- cause of the estimated efficiency of energy conversion of the initial input energy (either

5 Poynting flux or baryonic matter) to γ-rays ranges from ∼1% (e.g., Kumar 1999) to ∼60% (e.g., Kobayashi & Sari 2001), therefore, the best-estimated total energy re- lease (including neutrino and gravitational-wave losses) is roughly comparable to the

rest-mass energy of one solar mass; (2) The observed GRB variability timescale (few miliseconds) implies that the energy deposition takes place in a small region (radius of c×1 ms ≈ 300 km). Therefore, the progenitors of the GRBs are dense and massive astrophysical objects.

At current studies, the GRBs progenitors (see Figure 1.7) are mainly divided into two classes based on their duration and spectral hardness (1) the short-duration (T90

< 2s), hard-spectrum (high frequency) bursts and (2) the long-duration (T90 > 2s), soft-spectrum (low frequency) bursts. Short-duration GRBs are supposed to originate from the mergers of binary neutron stars, which are old and outside the galaxies.

Long-duration GRBs are widely accepted to originate from the deaths of massive stars (collapsar model or hypernova, Woosley 1993), which are embedded in a dense, metal-enriched molecular cloud (Frail et al. 2006; Campana et al. 2007). Further

evidence for the progenitor of the long-duration GRBs is the connection between long duration bursts and supernovae (SNe) (Hjorth et al. 2003; Woosley & Bloom 2006; Kaneko et al. 2007), where SNe has a dusty environment. Thus, long duration bursts

can possibly be found young stellar populations and high-mass star forming galaxies (Fruchter et al. 2006). While the progenitors of short-duration GRBs are believed to related to the coalescence of binary compact objects, an old stellar population

(neutron stars or black holes, e.g., Eichler et al. 1989; Narayan et al. 1992; Rosswog et al. 2003).

6 1.5 GRB Host Galaxies

There are numerous good reasons to study GRB host galaxies, especially for the high redshift GRB host galaxies. One of the most straightforward application is to obtain the host redshift, especially in cases where the redshift was not measured while the optical afterglow was bright. Since the hosts can be quite faint, spectroscopy may require a long integration time even on the largest telescopes. The redshift is essential for the calculation of the GRB energy, and lately becoming crucial in attempting to constrain cosmological parameters (Reichart et al. 2001; Dai et al. 2004).

Second good reason is that the systematically search and analysis of GRB hosts is

flux limited, while there is no flux limited for other galaxy selection mechanism. For instance, the Lyman-break selection (Shapley et al. 2003) is continuum flux limited and Lyα selection (e.g., Ouchi et al. 2003; Fynbo et al. 2003) is line flux limited.

Therefore, GRB-selected galaxies allow us to probe the faint end of the luminosity function, which span a wide range of apparent magnitudes from R = 14.3 (GRB 980425: Fynbo et al. 2000) to R > 29.5 (GRB 020124: Berger et al. 2002).

Further good reason is the GRB/SN connection and association with star-formation regions indicate that hosts should on average display properties synonymous with star formation. The general characteristics of GRB hosts are that they are predominately sub-luminous galaxies with very blue colors (Fruchter et al. 1999; Christensen et al. 2004) and their morphologies are often compact and sometimes suggestive of a merg- ing system (e.g. GRB 980613: Hjorth et al. 2002). Merging galaxies are excellent for star-formation study; and the gas content of the colliding galaxies falls rapidly into the combined potential well, setting off a burst originated from a massive star. Figure 1.8 shows a mosaic of 42 GRB host galaxies, observed by the Hubble Space

Telescope (HST). It clearly shows their varieties in morphology, requiring more than

7 one clear single morphological class to fit.

Spectroscopic measurements also provide direct estimation of recent star formation in GRB hosts, based on luminosities of emission lines such as the Lyα line (e.g.

Kulkarni et al. 1998; Møller et al. 2002; Vreeswijk et al. 2004), the [OII] λ = 3727 doublet (e.g. Bloom et al. 2003), and the Balmer lines (Christensen et al. 2004). After the internal host extinction correlation, the observed unobscured (or intrinsic)

−1 star-formation rates (SFRs) range from a few tenths of, to a few M¯ yr . Applying reddening corrections, the optical afterglow SED will be restored by a factor of a few in most cases and the resulting values are typical for a normal field galaxy population at comparable redshifts. However, GRB hosts are most likely similar to the young galaxies with the highest star formation rates (SFRs)(Christensen et al. 2004; Courty et al. 2004).

The most essential absorption line spectroscopy of GRB optical afterglow is damped Lyα absorbers (DLAs). This strongly suggests that GRBs explode in galaxies, or re- gions within galaxies, with high neutral hydrogen densities. The responsible HI gas could be related to the site of the GRB explosion, part of the star-forming region in which the GRB occurred, but also could be gas that not associated with the GRB and further away in the host galaxy. DLAs can also be used to determine the lower limit of the redshift of GRBs (see Figure 1.4). The column densities are in fact lower limits as the GRB itself occurs within the galaxy that is associated with the DLA system. When an independent extinction measurement is available, the derived gas/dust ratio is much larger that in the Milky Way (MW), but similar to that found in the Small Magellanic Cloud (SMC), where the SMC has lower abundances of heavy elements and dust than those of the MW (Hjorth et al. 2003).

With regards to the high (z > 2) GRB host galaxies, one of the most interesting use of GRBs is to probe the early phases of star and galaxy formation, metallicity

8 history of the universe, extinction curves as a function of redshift, and the resulting reionization of the Universe at 6 . z . 30 (e.g. Loeb & Barkana 2001; Kogut et al. 2003). If GRBs reflect the deaths of massive stars, their very existence and statistics would provide a superb probe of the primordial massive star formation and even the initial mass function (ISM).

Dust plays a crucial role in the formation and evolution history of stars and

galaxies in the early universe. The importance of correcting for dust extinction in the universe is now widely recognized. In order to reveal the structure and evolution of the early universe, to use Type Ia supernovae (SNe) as standard candles, and to infer

the cosmological star formation rate, it is essential to correct for the effects of dust extinction. To conclude, exploring the extinction (quantity, wavelength-dependence) and the

nature (size, composition, and quantity) of the dust in GRB host galaxies, we can have a good understanding of the host galaxies of GRBs by (1) correcting for the extinction of afterglows from X-ray to near-IR wavelengths to derive their intrinsic

luminosities; (2) constraining the nature of the GRB progenitors (i.e. collapsing massive stars or merging neutron stars); (3) tracing the physical conditions of (and processes occurring in) the environments where GRBs occur which hold clues for

understanding the mechanism for making a burst; (4) probing the interstellar medium (ISM) of high-redshift galaxies and the cosmic star formation history; and (5) testing the extinction curves evolve as redshift.

1.6 Interstellar Dust & Extinction

We are living in a dusty universe: dust is ubiquitously seen in a wide variety of astrophysical environments, ranging from circumstellar envelopes around cool red

9 giants to supernova ejecta, from diffuse and dense interstellar clouds and star-forming regions to debris disks around main-sequence stars, from comets to interplanetary space to distant galaxies and quasars. These grains, spanning a wide range of sizes from a few angstroms to a few micrometers, play a vital role in the evolution of galaxies as an absorber, scatterer, and emitter of electromagnetic radiation, as a driver for the mass loss of evolved stars, as an essential participant in the star and planet formation process, as an efficient catalyst for the formation of H2 and other simple molecules as well as complex organic molecules which may lead to the origins of life, as a photoelectric heating agent for the interstellar gas, and as an agent shaping the spectral appearance of dusty systems such as protostars, young stellar objects, evolved stars and galaxies. The space between the stars (interstellar space) of the Milky Way Galaxy and other galaxies is filled with gaseous ions, atoms, molecules (interstellar gas) and tiny dust grains (interstellar dust). The first direct evidence which pointed to the exis- tence of interstellar gas came from the ground-based detection of Na and Ca+ optical absorption lines (Hartmann 1904). This did not gain wide acceptance until Struve (1929) showed that the strength of the Ca+ K-line was correlated with the distance of the star. The true interstellar nature of this gas was further supported by the detection of the first interstellar molecules CH, CH+ and CN (Swings & Rosenfeld 1937, McKellar 1940, Douglas & Herzberg 1941). The presence of dark, obscuring matter in the Milky Way Galaxy was also recognized at the beginning of the 20th century (e.g. see Barnard 1919). Trumpler (1930) first convincingly showed that this “obscuring matter”, which dims and reddens starlight consists of small solid dust grains. The dust and gas are generally well mixed in the interstellar medium (ISM), as demonstrated observationally by the reasonably uniform correlation in the diffuse ISM between the hydrogen column density and the dust extinction color excess or

10 21 −1 −2 reddening E(B − V ) = AB − AV and NH /E(B − V ) ≈ 5.8 × 10 mag cm (Bohlin et al. 1978), where AB and AV are the extinction at the B (λ = 4400 Å ) and V (λ = 5500 Å ) wavelength bands. From this correlation one can estimate the gas-to- dust ratio to be ∼ 210 in the diffuse ISM. Despite its tiny contribution to the total mass of a galaxy, : interstellar dust has a dramatic effect on the physical conditions and processes taking place within the universe, in particular, the evolution of galaxies and the formation of stars and planetary systems (see the introduction section of Li & Greenberg 2003).

Our knowledge of interstellar dust regarding its composition, size and shape is mainly derived from its interaction with electromagnetic radiation: attenuation (ab- sorption and scattering) and polarization of starlight, and emission of IR and far-IR radiation. The principal observational keys, both direct and indirect, used to con- strain the properties of dust are the following: extinction, polarization, scattering, spectroscopic extinction and polarization features. In this dissertation, we mainly discuss the extinction and the 2175 Å feature.

Extinction is a combined effect of absorption and scattering: a grain in the line of sight between a distant star and the observer reduces the starlight by a combination of scattering and absorption (the absorbed energy is then re-radiated in the IR and far-IR).

The wavelength dependence of interstellar extinction – “interstellar extinction curve”, most commonly determined from the “pair-method”. In this method, the wavelength dependence of interstellar extinction is obtained by comparing the spec- tra of two stars of the same spectral type, one of which is reddened and the other unreddened. This extinction curve rises from the near-IR to the near-UV, with a broad absorption feature at about λ−1 ≈4.6 µm−1 (λ ≈ 2175 Å ), followed by a steep rise into the far-UV (λ−1 ≈10 µm−1). The extinction curve tells us the size (and to

11 a less extent, the composition) of interstellar dust. Since it is generally true that a grain absorbs and scatters light most effectively at wavelengths comparable to its size λ ≈ 2πa (Krügel 2003), there must exist in the ISM a population of large grains

with a & λ/2π ≈ 0.1 µm to account for the extinction at visible wavelengths, and a population of ultrasmall grains with a . λ/2π≈ 0.016 µm to account for the far-UV extinction at λ=0.1 µm (see Li 2004 for details).

The optical/UV extinction curves show considerable regional variations. Dust grains on different sightlines have different size distributions (and/or different com- positions). The optical/UV extinction curve in the wavelength range of 0.125 ≤ λ ≤

3.5 µm can be approximated by an analytical formula involving only one free param-

eter: RV ≡AV /E(B − V ), the total-to-selective extinction ratio (Cardelli, Clayton, & Mathis 1989), whereas the near-IR extinction curve (0.9 µm≤λ≤3.5µm) can be fitted

reasonably well by a power law A(λ)∼λ−1.7, showing little environmental variations.

The Galactic mean extinction curve is characterized by RV ≈ 3.1. Values of RV as small as 2.1 (the high latitude translucent molecular cloud HD 210121; Larson,

Whittet, & Hough 1996; Li & Greenberg 1998) and as large as 5.6 (the HD 36982 molecular cloud in the Orion nebula) have been observed in the Galactic regions. More extreme extinction curves have been reported for extragalactic objects. The optical/UV extinction curve and the value of RV depend on the environment: lower- density regions have a smaller RV , a stronger 2175 Å hump and a steeper far-UV rise (λ−1>4 µm−1), implying smaller grains in these regions; denser regions have a larger

RV , a weaker 2175 Å hump and a flatter far-UV rise, implying larger grains. In the Small Magellanic Cloud (SMC), the extinction curves of most sightlines display a nearly linear steep rise with λ−1 and an extremely weak or absent 2175 Å hump (Lequeux et al. 1982; Prévot et al. 1984). Grains in the SMC are smaller than those in the Milky Way diffuse ISM as a result of either more efficient dust destruction

12 in the SMC due to its harsh environment of the copious star formation associated with the SMC Bar or lack of growth due to the low-metallicity of the SMC, or both. Regional variations also exist in the SMC extinction curves.

The Large Magellanic Cloud (LMC) extinction curve is characterized by a weaker 2175 Å hump and a stronger far-UV rise than the average Galactic extinction curve (Nandy et al. 1981; Koornneef & Code 1981). Strong regional variations in extinction properties have also been found in the LMC (Clayton & Martin 1985; Fitzpatrick 1985,1986; Misselt, Clayton, & Gordon 1999): the sightlines toward the stars inside or near the supergiant shell, LMC 2, which lies on the southeast side of the 30 Dor star-forming region, have very weak 2175 Å hump (Misselt et al. 1999).

The 2175 Å hump is the strongest spectroscopic extinction feature. Its strength and width vary with environment while its peak position is quite invariant: the central wavelength of this feature varies by only ±0.46% (2σ) around 2175 Å (4.6 µm−1), while its FWHM varies by ±12% (2σ) around 469 Å (≈1 µm−1).

Its carrier remains unidentified 39 years after its first detection (Stecher 1965). It is generally believed to be caused by aromatic carbonaceous (graphitic) materials, very likely a cosmic mixture of polycyclic aromatic hydrocarbon (PAH) molecules (Joblin, Léger & Martin 1992; Li & Draine 2001; Draine 2003). For most sightlines, this feature is unpolarized. So far only two lines of sight toward HD 147933 and HD 197770 have a weak 2175 Å polarization feature detected (Clayton et al. 1992; Anderson et al. 1996; Wolff et al. 1997; Martin, Clayton, & Wolff 1999). Even for these sightlines, the degree of alignment and/or polarizing ability of the carrier should be very small (see Li & Greenberg 2003). Except for the detection of scattering in the 2175 Å hump in two reflection nebulae (Witt, Bohlin, & Stecher 1986), the 2175 Å hump is thought to be predominantly due to absorption, suggesting its carrier is sufficiently small to be in the Rayleigh limit.

13 Figure 1.1 Light Curves of 12 GRBs, where the x-axis is the duration time for GRBs, and y-axis is the γ photon flux account. Taken from Bonnell (1995).

2704 BATSE Gamma-Ray Bursts +90

+180 -180

-90

10-7 10-6 10-5 10-4 Fluence, 50-300 keV (ergs cm-2)

Figure 1.2 This map shows the locations of a total of 2704 GRBs recorded by BASTE during its nine-years mission. The projection is in galactic coordinates; the plane of the Milky Way Galaxy is along the horizontal line at the middle of the figure. The burst locations are color-coded based on the fluence, which is the energy flux of the burst integrated over the total duration of the event, while grey color is for the bursts whose fluence cannot be well determined due to incomplete data. Taken from Fishman et al. (2000).

14

200 GRBs

40

mean =1.93

median=1.58

30

20 Number of GRBs of Number

10

0

0 1 2 3 4 5 6 7 8

Redshift (z)

Figure 1.3 A histogram showing the distribution of GRB redshift known to date (April 10, 2010). The median value of the 200 redshift is 1.58, and the mean value is 1.93. Taken from Liang & Li (in preparation).

Figure 1.4 The Lyα absorbers along the afterglow of GRB 050730. All significant lines (3σ) are indicated above for z = 3.969 (solid), z = 3.565 (dashed), z = 1.773 (dot-dashed) and unidentified (dotted) systems. The best-fitting DLA profile is solid line. Taken from Starling et al. (2007).

15 The progenitor collapses or coalesceces, forming a spinning black hole... later, afterglow emission from The energy and then colliding shells the shock as it sweeps up escapes in the give rise to the GRB... the ambient medium. form of jets... Toward Earth

Fe−line emission site? Fe−line emission site? GRB location Afterglow location Dense cloud 18 pre−ejected Progenitor location 14 < <~ 10 cm ~ 10 cm material? < 10 8 cm

Figure 1.5 This map is to explain the explosion of a GRB. The dark circle represents the newly formed spinning black hole at the center of an imploding star or a merging compact binary system. The long-lived afterglow emission arises from the swept- up material, in where relativistic electrons radiating synchrotron light. The whole sequence of events will be compressed in time as viewed from Earth for the extreme velocity of the jet. Taken from Piran (1999).

6 10 a fast cooling a high frequency ν−1/2 tν 1/3 0 4 ν 10 1/6 −1/3 10 C t [t ] t−1/4 [t−4/7] B B C t(2−3p)/4 ν−p/2 4 J) 10 J)

µ (2−6p)/7

µ D [t ] 2 D 10 3 Flux (

Flux ( 10 ν2 −1/2 −1/2 −3/2 t t t t(2−3p)/4 [t−4/5] [t−2/7] [t−12/7] 0 A 2 H 10 10 t t t ν ν ν c m 0 a c m 1 10 8 10 12 14 16 18 −2 0 2 10 10 10 10 10 10 10 10 10

6 10 b b 1/3 slow cooling ν ν−(p−1)/2 low frequency t>t ν<ν 4 0 5 0 10 F G 10 1/2 t t3(1−p)/4 2 ν 1/6 −1/3 4 t [t ] 2 F G

J) 10 10 J) µ

E µ B ν−p/2 t(2−3p)/4 3

Flux ( 0 −3/2 −1/2 0 H Flux ( 10 10 t t t H

2 10 −2 10 t t t ν ν ν 0 m c a m c 1 10 8 10 12 14 16 18 −2 0 2 10 10 10 10 10 10 10 10 10 ν (Hz) t (days) Figure 1.6 Left: a synchrotron spectrum of a relativistic shock with a power-law elec- tron distribution. The panel shows that fast/slow cooling cases, which are expected at earlier/late times. Right: the corresponding synchrotron light curve (ignoring self- absorption). Both panels assume a constant-density (rather than stellar wind-like) external environment. Taken from Sari et al. (1998).

16 MS MS NS Double SN BH Neutron Star Eichler et al. 1989; MS NS NS Merger Paczynski 1992 SN

MS MS NS Black Hole− SN BH Narayan et al. 1991; Neutron Star MS BH BH Bethe & Brown 1998; Merger Janka et al. 1999 SN

MS MS


He Black Hole−


BH mass loss


Helium Star Fryer & Woosley 1998 MS NS BH Merger SN AIC

MS MS WD Black Hole− BH Fryer et al. 1999; White Dwarf mass loss MS NS BH Sigurdson & Rees 1999 Merger SN AIC MS MS ? ?

momentum?

angular Woosley 1993; Collapsar X−ray binary? MS BH MacFayden & (Hypernova) Woosley 1999

SN MS MS

mass loss Kluzniak & Ruderman 1998; DRACO X−ray binary? MS NS (magnetar) BH Dai & Lu 1998

SN AIC WD or MS Supermassive Black Hole− BH BH White Dwarf Merger Carter 1992

time

Figure 1.7 The plausible theoretical scenarios for the progenitors of GRBs, divided into two main classes: (1) collapsar model; and (2) binary compact objects model. Taken from Bloom (2003).

Figure 1.8 HST images of 42 GRB host galaxies, in which an accurate projection of the early afterglow position is shown with a green circle. Comparing these host galaxies, it shows that GRB host galaxies display a wide range in magnitude and morphology. Taken from Fruchter et al. (2006).

17 Chapter 2

The “Drude” Model: A Novel Approach to Derive Dust Extinction

2.1 Introduction

In addition to the Galactic foreground extinction, GRBs and their afterglows are subject to extinction caused by the dust within their host galaxies. Evidence for this includes —

• “Dark bursts” – an appreciable fraction of GRBs with X-ray and/or radio after-

glows lack an optical afterglow (Jakobsson et al. 2004a).1 A natural explanation for dark bursts is that they lie behind significant obscuring dust columns in their host galaxies which effectively suppresses the optical light [although some dark

bursts may be intrinsically faint or occur at high redshifts (say, z & 5) where the Lyα break has moved through the optical bands, leading to absorption of the optical light by the Lyα forest]. Indeed, Schady et al. (2007) found that

the X-ray afterglows of GRBs not detected by UVOT were more affected by extinction than those of GRBs with detected UVOT counterparts. The recent

1Prior to the launch of Swift, nearly ∼60% of the X-ray afterglows reportedly had no optical counterparts. Despite rapid and deep searches in the Swift era, it was found that ∼1/3 GRBs with bright X-ray afterglows remain undetected at optical wavelengths (Fiore et al. 2007, Schady et al. 2007).

18 detection of the near infrared (IR) afterglows of some GRBs (which would have been considered as “dark bursts” since their afterglows were not detected in any bluer bands) provides another piece of evidence for dust obscuration (e.g. see

Jaunsen et al. 2008, Tanvir et al. 2008).

• Reddening – some GRB afterglows with low redshifts appear very red, due to effects of extinction – ultraviolet (UV)/visible light is extinguished more by dust than red light (e.g. see Klose et al. 2000, Levan et al. 2006). Dust reddening

is also indicated by the significant deviation of the optical/near-IR spectral en- ergy distributions (SEDs) of many afterglows from that expected from standard models. Also because of dust reddening, the Balmer line ratios in the spectra

of some GRB host galaxies (e.g. see Djorgovski et al. 1998), known as the Balmer decrement, deviate from the expected ratios for the standard Case B recombination, which are fairly independent of physical conditions (Osterbrock

& Ferland 2006).

• Depletion – dust-forming heavy elements such as Si and Fe were found to be substantially depleted from the gas phase in some host galaxies (e.g. see Savaglio et al. 2003). This indirectly shows the presence of dust in GRB host galaxies

since the missing heavy elements must have been locked up in dust grains.

• Connection between long GRBs and massive stars – there are multiple strong lines of evidence that long-duration (& 2 s) GRBs are associated with the death of massive stars, occurring in regions of active star formation embedded in dense

clouds of dust and gas (see Woosley & Bloom 2006).

A precise knowledge of the extinction (quantity, wavelength-dependence) and the nature (size, composition, and quantity) of the dust in GRB host galaxies is crucial

19 for

• Correcting for the extinction of afterglows from X-ray to near-IR wavelengths to derive their intrinsic luminosities – this is particularly important for studying the luminosity distribution of GRB afterglows and their intrinsic SEDs (e.g. see

Kann et al. 2008);

• Constraining the nature of the GRB progenitors (i.e. collapsing massive stars or merging neutron stars) – if long-duration GRBs are indeed linked to the collapse of massive stars, it is most likely that their optical and near-IR afterglows will

suffer from significant attenuation in the star-forming molecular clouds heavily enshrouded by dust – the birth place of these short-lived (∼ 106 yrs) massive stars;

• Tracing the physical conditions of (and processes occurring in) the environments

where GRBs occur which hold clues for understanding the mechanism for mak- ing a burst, e.g., a flat or gray extinction law for GRB host galaxies would imply a dense circumburst environment where dust undergoes coagulational-growth or

a preferential destruction of small grains; and

• Probing the interstellar medium (ISM) of high-redshift galaxies and the cosmic star formation history – because of their intense luminosity which allows their detection at cosmological distances, GRBs are a powerful tool to study the

star formation history up to very high redshifts; e.g., the dust and extinction properties of GRB hosts would help understand the nature of dark bursts and the dark burst fraction which would place important constraints on the fraction

of obscured star formation in the universe (e.g. see Djorgovski et al. 2001b, Ramirez-Ruiz et al. 2002).

20 However, our current understanding of the dust extinction in GRB host galaxies is still very poor. Existing studies on this often draw conclusions in conflict with each other (see §2.2 for details). We argue that this could be caused by the prior

adoption of a template extinction law in fitting the observed GRB afterglow spectra to derive dust extinction (§2.2). We propose in this Chapter an alternative, robust method based on an analytical formula which can restore the widely adopted template

extinction laws (§2.3). For illustration, we apply this approach to GRB 000301C and GRB 021004 (§2.4). We demonstrate in §2.5 the uniqueness of the derived extinction laws. The robustness of this approach will be discussed in Chapter 3 (also see Liang

& Li 2009) in which the afterglow SEDs of > 50 GRBs of a wide range of properties are successfully modeled and for which the inferred extinction curves are diverse, with some differing substantially from any of the template extinction curves.

2.2 Current Status

At present, the amount of extinction (usually the rest-frame visual extinction AVr ) and the wavelength-dependence of the extinction (“extinction curve” or “extinction law”; Aλ/AV or Aν/AV if expressed in frequency) are commonly derived by fitting the UV, optical, and near-IR afterglow photometry (Fν; with the Galactic extinction corrected) with a power-law model (∝ ν−β; approximating their intrinsic spectra)

reddened by an assumed, template extinction law Aν/AV · ¸ −β AVr A(1+z)ν Fν = Fo (ν/Hz) exp − , (2.1) 1.086 AVr

where β is the intrinsic power-law slope of the afterglow, Fo is a normalization constant

(normalized to the overall afterglow flux level), A(1+z)ν is the rest-frame extinction, and z is the GRB redshift. The factor of “1.086” in eq.(2.1) arises from the conversion of extinction (in magnitude) to optical depth. As a priori, six template extinction

21 laws have been widely adopted in the literature to derive the dust extinction of GRB

−γ hosts: (1) a simple power-law Aλ/AV ∼ λ or even just a linear function of inverse

−1 wavelength Aλ/AV ∼ λ (“Linear” thereafter); (2) the Milky Way (MW) extinction curve (with a prominent bump at 2175 Å) characterized by RV , the total-to-selective extinction ratio (the Galactic average value is RV ≈ 3.1); (3) the featureless Small Magellanic Cloud (SMC) extinction curve which steeply rises with inverse wavelength

−1.2 from near-IR to far-UV (Aλ/AV ∼ λ ); (4) the Large Magellanic Cloud (LMC) curve being intermediate between that of the MW and the SMC; (5) the featureless “Calzetti” attenuation law for the dust in local starburst galaxies (Calzetti et al.

1994);2 and (6) the relatively flat “Maiolino” extinction law for the dust in the dense circumnuclear region of AGNs (Maiolino et al. 2001) where the dust size distribution is skewed toward large grains (see Figure. 2.1).

To our knowledge, exceptions to the “template” extinction approach described here are that of Chen et al. (2006) and Li et al. (2008), both of which were based on the fireball model. The latter approach is limited to bursts of which the X-ray and optical decay indices are the same. In most studies (which assume an extinc- tion template) a SMC-type extinction curve is preferred. This is probably because the 2175 Å extinction feature (which is prominent in the MW and LMC curves) is rarely seen in the afterglow spectra of GRBs. So far, its possible detection is only reported in four bursts: GRB 970508 (Stratta et al. 2004), GRB 991216 (Kann et al. 2006, Vreeswijk et al. 2006), GRB 050802 (Schady et al. 2007), and more definitely

GRB 070802 (Krühler et al. 2008; Elíasdóttir, Á., et al. 2009).

However, some studies favour a much flatter or even gray extinction curve (e.g.

2We should note that recent Spitzer observations in the near- and mid-IR argue against GRB hosts being strongly starbursting galaxies (Le Floc’h et al. 2006), although their morphological and average radio/submillimeter properties suggest that they are likely massive and actively star-forming galaxies (Berger et al. 2003; Conselice et al. 2005).

22 see Savaglio et al. 2003, Savaglio & Fall 2004, Stratta et al. 2005, Chen et al. 2006, Li et al. 2008, Perley et al. 2008a). With a SMC-type curve, the amount of visual

3 extinction AV or reddening derived by fitting the afterglow photometry tends to be

−1 small since the SMC curve rises so rapidly with λ that a small AV would imply a large UV extinction. This may explain the finding of “a strong clustering toward low extinction (AV . 0.2 mag)” in a detailed study of 19 GRBs by Kann et al. (2006), and later by Kann et al. (2008) for 15 GRBs. In contrast, for a flatter extinction law like that of Calzetti, Maiolino, MW with RV > 4, or that derived by Chen et al. (2006),

Li et al. (2008) and Perley et al. (2008a), a relatively large AV is often obtained.

The visual extinction AV can also be inferred from the dust depletion method based on the gas-phase heavy-element abundances estimated from the afterglow opti- cal absorption spectroscopy (Savaglio et al. 2003; Savaglio & Fall 2004). This analysis assumes both the dust depletion pattern and the visual extinction per unit dust col- umn AV /Ndust of GRB hosts to be the same as that of the MW. It is quite possible that GRB hosts may have a different depletion pattern and/or a different AV /Ndust conversion factor. The latter could result from a dust composition or size distribution differing from that of the MW.

One can also derive AV from the neutral hydrogen column density NH derived from Lyα absorption (Hjorth et al. 2003) or the equivalent NH obtained from soft X-ray absorption (mostly from oxygen K-shell absorption; Galama & Wijers 2001, Stratta et al. 2004, Watson et al. 2006). There is a puzzling discrepancy between the optical reddening E(B − V ) derived from the afterglow SED fitting and the visual extinction AV inferred from the dust depletion analysis or from NH measured from

3 Reddening is usually expressed as E(B−V ) ≡ AB −AV ≡ AV /RV , where AB is the extinction at the B band (λB ≈ 4400 . By definition, gray dust (for which the extinction is just weakly dependent on λ) is characterized by small reddening E(B − V ) and large RV . Apparently, for gray dust, a small reddening does not necessarily imply a small extinction since RV can be large.

23 the Lyα or X-ray absorption spectra, with the former considerably smaller than the latter.

This discrepancy problem could be alleviated if one invokes a flat or gray extinction

law. This is because (1) gray dust (& 1 µm) characterized with an extinction curve

weakly dependent on λ in the optical/UV could produce a high AV but little reddening (see Footnote-3), and (2) per unit mass gray dust is not as effective as submicron-

sized dust in absorbing and scattering optical light so that the AV /Ndust conversion factor for gray dust is smaller than that of the MW dust (with a typical size of ∼ 0.1 µm; see Li 2008). The latter would imply that the methods based on dust

depletion (see above) and Lyα/X-ray absorption may overestimate AV if the dust size distribution of GRB host galaxies is indeed biased toward large grains, as a result of dust coagulational growth in the dense circumburst environments or preferential

destruction of small dust by GRB emission (e.g. see Waxman & Draine 2000, Fruchter et al. 2001, Perna et al. 2003).

However, we should stress that the gray extinction hypothesis should not be con-

sidered as the only solution to the discrepancy problem (after all, SMC-type or even steeper extinction laws were derived for the hosts of some GRBs; see Liang et al.

2009). Indeed, the mismatch between the X-ray-derived AV and that derived from the optical SED modeling could be attributed to physically separate X-ray and opti- cal emission regions (e.g. see Prochaska et al. 2006, Watson et al. 2007). Prochaska et al. (2006) argued that for GRB 051111, the X-ray opacity comes from dust-free gas that is very local to the GRB (∼ 1 pc), while they placed a lower limit of > 50 pc on

the host galaxy absorption systems from the GRB. It has also been argued that AV is probably probing the dust outside of the dense molecular cloud around the GRB, since all dust within the cloud is likely to have been obliterated by the burst (e.g. see Perna & Lazzati 2002b, Prochaska et al. 2007). Moreover, if the dust depletion

24 pattern of GRB hosts is different from that of the Milky Way, the discrepancy be-

tween the depletion-derived AV and that from the optical SED modeling could be alleviated.

2.3 Our Approach: The “Drude” Model

In view of the shortcomings of the prior assumption of a template extinction law (see §2.2) and guided by Pei (1992), we propose a simple formula containing four

dimensionless parameters (c1, c2, c3, and c4) for the wavelength-dependence of the extinction for the dust in GRB host galaxies, instead of adopting any known extinction laws (see §2.2) as a template,

c1 Aλ/AV = c2 c2 (λ/0.08) + (0.08/λ) + c3 233 [1 − c / (6.88c2 + 0.145c2 + c ) − c /4.60] + 1 3 4 (λ/0.046)2 + (0.046/λ)2 + 90 c + 4 , (2.2) (λ/0.2175)2 + (0.2175/λ)2 − 1.95

where λ is in µm.4 While the first term in the right-hand side of Eq.(2.2) represents the far-UV extinction rise, the second term and the third term respectively account for the near-IR/visible extinction and the 2175 Å extinction bump. We call this the

“Drude” approach since Eq.(2.2) looks like a sum of Drude functions. As shown in

Figure. 2.1, this formula, with the free parameters cj (j = 1, ..., 4) adjusted using the Levenberg-Marquardt minimization algorithm (Press et al. 1992; see Table 2.1),

can reproduce the extinction curves widely adopted as template extinction laws in

4 Reichart (2001) proposed a seven-parameter formula for the dust extinction curve Aλ/AV of GRB hosts based on the expressions of Cardelli et al. (1989; “CCM”; for λ > 0.3 µm) and of Fitz- patrick & Massa (1990; “FM”; for 0.1 µm < λ < 0.3 µm). The problem with the Reichart (2001) formula (see his eqs. 61,66) is that the CCM expression is only valid for the Galactic extinction curves, it is not suitable for the SMC or LMC extinction (Gordon et al. 2003). Therefore, if a GRB host happens to have a SMC- or LMC-type extinction law, models based on the Reichart (2001) formula will not be able to restore the true extinction.

25 GRB afterglow SED modeling, clearly demonstrating the advantages of the proposed formula over any template extinction laws with a fixed wavelength-dependence shape: with the widely-adopted conventional extinction laws self-contained in Eq.(2.2) and

the capability of revealing extinction laws differing from the conventional ones, the proposed formula is more flexible and more powerful in modeling the afterglow SEDs. Indeed, as shown in Liang & Li (2009, 2010), dust reddening models based on this

formula nicely reproduce the observed afterglow SEDs of distant GRBs at z > 4 (including GRB 050904 at z ≈ 6.3) and that of the “troublesome” GRB 061126 (Perley et al. 2008b) without resorting to an exotic extinction law.

2.4 GRB 000301C and GRB 021004: Test Cases

We apply the above-described technique (§2.3) to the optical afterglows of GRB 000301C at z ≈ 2.04 (Jensen et al. 2001) and GRB 021004 at z ≈ 2.33 (Fynbo et al. 2005a).

They are selected mainly because they are among the best-observed in terms of sam- pling in the time domain, and multiwavelength coverage. We fit their broadband

SEDs using Eqs.(2.1,2.2) with β, AV , c1, c2, and c3 allowed to vary as free param-

eters [Fo is not really a free parameter; for a given set of (β, AV , c1, c2, c3), Fo is uniquely determined by the overall flux level. Therefore, in the SED modeling we fit five free parameters to the six (seven) data points of GRB 000301C (GRB 021004)].5

We derive the best-fit parameters based on the Levenberg-Marquardt minimization algorithm (see Table 2.2). As shown in Figure 2.2 for GRB 000301C and in Figure 2.3 for GRB 021004, almost perfect fits to the observed SEDs are achieved through this

approach. The inferred extinction curves differ substantially from any of the template

5 We set c4 = 0 based on a visual inspection of the observed SEDs which clearly suggest the absence of a 2175 Å feature (see Figures. 2.2,2.3). With c4 treated as a free, positive parameter, even the best fits (given by c4 ≈ 0.0034, 0.0018 for GRB 000301C and GRB 021004, respectively; for comparison, c4 ≈ 0.051, 0.039 for MW and LMC, respectively) are not as good as that provided by models with c4 = 0. We place an upper limt of c4 ≈ 0.015 (0.0073) for GRB 000301C (GRB 021004).

26 extinction laws.

2.5 Discussion

We have also fitted the afterglow SEDs of GRB 000301C and GRB 021004 in terms of the MW, SMC, LMC, Calzetti, and “linear” template extinction curves (see Ta- ble 2.2 and Figures. 2.2,2.3). Since for a given template extinction law the wavelength- dependence of the extinction Aλ/AV is fixed, we are now left with only three param- eters: Fo, β, and AV . The models based on the MW and LMC extinction laws could not fit the observed SEDs at all. This is because the 2175 Å extinction feature which is prominent in the MW and LMC curves is absent in the SEDs of GRB 000301C and GRB 021004. In contrast, the SMC and “linear” models closely fit the afterglow SEDs of these two bursts, better than the “Drude” model proposed here as measured

2 by χ /Nd.o.f. (see Table 2.2). While the “Drude” model has three more parameters than the SMC and “linear” models, the quality of the fitting of the “Drude” model is even not as good as that of the SMC or “linear” model. Then, why do not we simply adopt the SMC or “linear” model? First of all, we should note that there are no physical reasons for a prior assump- tion of a known extinction law, either that of the SMC, LMC, “linear” or MW: the composition and size distribution (and therefore the extinction law) of the dust in the dense circumburst clouds of GRB hosts with a wide range of metallicities and evolu- tionary stages are not expected to resemble that of the MW, LMC, or SMC (e.g. see

Dwek 2005). In literature, a SMC-type extinction is often assumed for low-metallicity environments. However, there is no physical basis for this (except the lack of grain growth in these regions because of the lack of raw dust materials – the SMC dust,

27 on average, is substantially smaller than that of the Milky Way [see Weingartner & Draine 2001]). Moreover, it is known that the GRB hosts have a wide range of metallicities. Indeed, the reasons why the MW, LMC and SMC laws are often used for GRB afterglow SED modeling are mainly (1) little is known about the extinction laws of other galaxies, and (2) the Pei (1992) formula for the MW, LMC and SMC extinction laws is numerically convenient for computer implementation.

Second, although the SMC-type extinction is preferred in most of the present af- terglow SED modeling studies, only the “Drude” approach is capable of reproducing the SEDs of those reddened by gray extinction or by non-conventional extinction.

Indeed, it was shown that the afterglow SED of GRB 050904 at a redshift of z ≈ 6.3 cannot be explained by dust reddening with any of the conventional (MW, SMC, Calzetti) extinction curves; instead, it can be well reproduced by invoking the extinc- tion curve inferred for a distant quasar at z = 6.2 (Maiolino et al. 2004), suggesting that the properties of dust may evolve beyond z = 6 (Stratta et al. 2007).

Third, the “Drude” model would at least complement the models using template extinction curves, particularly for those bursts for which the “Drude” model gives

2 a larger χ /Nd.o.f. (but still fits the observed SEDs well). Given that the derived extinction AV and the intrinsic spectral slope β differ appreciably among different approaches (see Table 2.2), the SMC model (and other models) should be used along side with the “Drude” model to gain insight into the “true” extinction and the “true” spectral slope.

We finally demonstrate the uniqueness of the extinction curve inferred from the “Drude” approach. To this end, we generate three sets of afterglow “photometry

8 −0.5 data” by reddening the intrinsic afterglow spectrum Fν (µJy) = 5.2 × 10 (ν/Hz) of a burst at z ≈ 2 respectively with three template extinction laws: MW, SMC, and

Calzetti, each with AV = 0.5 mag. We then apply the “Drude” approach to these

28 three sets of artificially-created GRB afterglow data. As shown in Figure 2.4, we uniquely restore the MW, SMC, and Calzetti extinction laws: the inferred extinction curves are almost identical to that used to redden the intrinsic spectrum (the derived parameters [see Table 2.3] are essentially the same as those tabulated in Table 2.1).

2.6 Conclusion

Although it is well recognized that GRB afterglows are obscured and reddened by dust in their host galaxies, the wavelength-dependence and quantity of dust extinction are still poorly known. Current studies on this mostly rely on fitting the afterglow spectral energy distributions (SEDs) with template extinction models. The inferred extinction (both quantity and wavelength-dependence) and dust-to-gas ratios are of- ten in disagreement with that obtained from dust depletion and X-ray spectroscopy studies. We argue that this discrepancy could result from the prior assumption of a template extinction law. We propose an analytical formula to approximate the GRB host extinction law. With the template extinction laws self-contained, and the ca- pability of revealing extinction laws differing from the conventional ones, it is shown that this is a powerful approach in modeling the afterglow SEDs to derive GRB host extinction.

29 Table 2.1. “Drude” fits to known extinction curves for λ = 0.1–1 µm widely adopted as “templates” in modeling GRB afterglow SEDs to derive GRB host dust extinction.

2 c1 c2 c3 c4 χ /d.o.f. MW 14.4 6.52 2.04 0.0519 1.66 LMC 4.47 2.39 -0.988 0.0221 1.19 SMC 38.7 3.83 6.34 0. 1.36 Linear 66.2 4.97 22.1 0. 1.42 Calzetti 44.9 7.56 61.2 0. 1.68

Table 2.2. Results of fitting to the afterglow SEDs of GRB 000301C and GRB 021004 with the “Drude” approach (see §2.3, §2.4) or various template extinction laws. Note that the “Drude” approach has more free parameters than the other approaches.

2 2 Extinction c1 c2 c3 c4 AV β Fo χ /Ndata χ /Nd.o.f. Type (mag) (µJy)

Drude 0.025 0.048 -2.00 0. 0.32 0.61 3.99E10 0.33 1.98 MW ...... 0. 0.85 1.04E14 1.32 2.64 SMC ...... 0.11 0.62 4.68E10 0.64 1.28 LMC ...... 0. 0.85 1.04E14 1.32 2.64 Linear ...... 0.20 0.51 1.23E9 0.47 0.94 Calzetti ...... 0. 0.85 1.04E14 1.32 2.64 GRB 021004 Drude 0.015 0.15 -2.00 0. 0.13 0.78 6.13E12 0.47 1.64 MW ...... 0. 1.06 8.23E16 1.53 2.68 SMC ...... 0.15 0.67 1.58E11 0.36 0.53 LMC ...... 0. 1.06 8.23E16 1.53 2.68 Linear ...... 0.26 0.54 2.05E9 0.76 1.33 Calzetti ...... 0.95 0. 46.7 0.80 1.40

Table 2.3. Results of Drude-fitting to the artificial SED generated by reddening the power-law 8 −0.5 afterglow Fν (µJy) = 5.2 × 10 (ν/Hz) with AV = 0.5 mag extinction of MW, SMC, and Calzetti-type (see Figure. 2.4).

2 2 Reddening c1 c2 c3 c4 AV β Fo χ /Ndata χ /Nd.o.f. Type (mag) (µJy)

MW 14.3 6.49 2.02 0.0514 0.501 0.499 5.24E8 3.26E-4 4.35E-4 SMC 39.4 3.89 6.31 0. 0.500 0.501 5.26E8 1.32E-3 1.76E-3 Calzetti 45.2 7.51 61.7 0. 0.497 0.502 5.17E8 7.98E-4 1.06E-3

30 Figure 2.1 Extinction laws widely adopted as “templates” in GRB host extinction studies: the SMC law (upper panel: dashed black line; Pei 1992), the LMC law (upper panel: dashed blue line; Pei −1 1992), the linear Aλ ∝ λ law (upper panel: dashed cyan line), the MW Galactic average extinction law (RV = 3.1; lower panel: dashed black line; Pei 1992), the MW extinction law with RV = 4.5 for dense clouds (lower panel: solid red line), the Calzetti starburst attenuation law (lower panel: dashed blue line), and the Maiolino law for AGN dust tori (lower panel: dashed cyan line; just like that of the MW with RV = 4.5). Also shown are the “Drude” fits to these “template” extinction laws: SMC (upper panel: solid green line), LMC (upper panel: solid red line), Linear (upper panel: solid magenta line), MW with RV = 3.1 (lower panel: solid green line), and Calzetti (lower panel: solid magenta line).

31 Figure 2.2 Upper panel: fitting the SED of the afterglow of GRB 000301C (filled black circles) with the SMC (green) and LMC or MW (blue) template extinction laws and the “Drude” approach (red; see Eq.2.2) for the host extinction curve. No extinction is allowed in the MW and LMC models (i.e. the best fit with a MW- or LMC-type extinction is given by AV ≈ 0): a small amount of AV would lead to large deviations from the afterglow SED since the 2175 Å bump prominent in the MW and LMC laws is absent in the afterglow SED. Lower panel: comparison of the SMC (green), LMC (blue), MW (RV = 3.1; black) extinction laws with that derived from the “Drude” approach (red).

32 Figure 2.3 Same as Figure. 2.2 but for GRB 021004.

33 Figure 2.4 Upper panel: Drude fits to the observer-frame UBVRIJHK “photometry data” −β artificially-generated by reddening the intrinsic afterglow spectrum Fν ∝ ν of a burst at z ≈ 2 (black line with red crosses superimposed for the observer-frame UBVRIJHK bands) with the SMC (“data”: cyan squares; Drude fit: green line), Calzetti (“data”: blue triangles; Drude fit: magenta line), and MW (“data”: black circles; Drude fit: red line) extinction laws (with AV = 0.5 mag for each). Lower panel: comparison of the SMC, Calzetti and MW extinction curves (solid lines) with that inferred from the “Drude” approach (dashed lines).

34 Chapter 3

The 2175 Å Interstellar Extinction Feature at High Redshifts

3.1 Introduction

Dust is present in the high-redshift (z > 2) universe, as evidenced by the reddening of background quasars, the depletion of heavy elements in quasar absorption systems, and the far infrared (IR) to millimeter (mm) thermal emission of distant quasars. Dust plays a crucial role in the formation and evolution history of stars and galaxies in the early universe. The importance of correcting for dust extinction in the universe is now widely recognized. In order to reveal the structure and evolution of the early universe, to use Type Ia supernovae (SNe) as standard candles, and to infer the cosmological star formation rate, it is essential to correct for the effects of dust extinction. GRBs, owing to their intense luminosity (emitting up to ∼ 1053 erg), allow their detection up to very high redshifts at z & 10 (Lamb & Reichart 2000). Particu- larly, the association of long-duration bursts with massive stars (and therefore with dusty regions of high-mass star formation) and the featureless, power law-like spectral shapes of their afterglows, make GRBs an excellent probe of the dust at high-redshifts.

In this Chapter, we explore the dust extinction of the host galaxies of GRB 070802 at z ≈ 2.45 and GRB 050904 at z ≈ 6.29. We aim at a quantitative examination of

35 the nature of the dust in the early universe and attempt to address one of the hotly- debated questions in high-z astrophysics: do the dust properties evolve as a function of redshift (particularly at z > 5 where the dust source may be different)?

3.2 Dust Extinction Model

In this Chapter, we apply the “Drude” model discussed in Chap. 2.3 & 2.4 to explore the extinction properties of the dust in the distant universe through the afterglows

of high-redshifted. Compared to models based on template extinction curves, the “Drude” model is preferred because (1) it eliminates the need for a prior assumption of template laws – after all, there is no reason to assume that the “true” extinction

curves of GRB hosts should resemble any of those templates, and (2) the analytical formula (eq.2.2) on which the is based restores the widely-adopted MW, SMC, LMC, “Calzetti”, and “Maiolino” templates – if the “true” extinction curve of a GRB host

happens to resemble a certain template law, the “Drude” approach will allow us to restore it (see Li et al. 2008a).

3.3 Results

We apply the “Drude” model to GRB 070802 at z ≈ 2.45 and GRB 050904 at z ≈ 6.29. They are selected for the following reasons: (i) they span a wide range of redshifts, from the moderately high redshift of z ≈ 2.45 (GRB 070802) to the 3rd highest red- shift observed to date of z ≈ 6.29 (GRB 050904); (ii) the afterglow photometry of GRB 070802 provides the most definite evidence for the presence of the 2175 Å extinc- tion feature in a GRB host galaxy (Krühler et al. 2008; Elíasdóttir et al. 2009); and

(iii) the peculiar UKIRT z band (λrest ≈ 1275 Å) flux suppression of the GRB 050904 afterglow at 0.5 days and 1 day after the burst (Haislip et al. 2006; Stratta et al.

36 2007) was interpreted as evidence for an evolution of the dust properties at z > 6 (Stratta et al. 2007).

Using eqs.(2.1,2.2) and the Levenberg-Marquardt minimization algorithm, we fit

the broadband spectral energy distributions (SEDs) of the afterglows of these GRBs1

2 with β, AV , c1, c2, c3 and c4 allowed to vary as free parameters. Therefore, in the SED modeling we have six free parameters.3 It is unfortunate that the number of

model parameters (Npara = 6) exceeds the number of photometry data points Ndata

for GRB 050904 (Ndata = 4 for all three epochs; Haislip et al. 2006; Tagliaferri et al.

4 2005). With Ndata = 7, GRB 070802 has a better wavelength coverage. We therefore

2 use χ /Ndata as a quality measure of the fit. In Figure. 3.1 we plot the “Drude” model fit to the afterglow SED of GRB 070802 as well as the derived extinction curve. The results for GRB 050904 at three different

epochs after the burst are shown in Figure. 3.2. We see in these figures that (1) the “Drude” model provides excellent fits to the observed SEDs; (2) the derived extinc- tion curves differ substantially from the widely-adopted template extinction laws; (3)

the 2175 Å extinction feature appears to be also present in the afterglow spectra of GRB 050904, the 2nd most distant GRB observed to date, at epochs of 0.5 days and 1 day after the burst; (4) at an epoch of 3 days after the burst, the 2175 Å feature

appears to be absent in GRB 050904, suggesting that its carrier may have been de-

1For GRB 050904 we will consider three different epochs after the burst. 2 Fo is not really a free parameter; for a given set of (β, AV , c1, c2, c3, c4), Fo is uniquely determined by the overall flux level. 3Admittedly, the models based on template extinction laws have fewer parameters: with the shape of the extinction curve fixed, they only need to determine β and AV . The “Drude” approach needs four more parameters (i.e. c1, c2, c3 and c4) to describe the wavelength-dependence of the extinction. This is the nature of the “Drude” approach; because of this the “Drude” approach is more flexible in revealing the “true” extinction curve. 4For GRB 070802, we adopt the optical and near-IR photometry of Krühler et al. (2008) obtained by the 7-channel GRB Optical and Near-IR Detector (GROND) mounted on the 2.2 m ESO/MPI Telescope. The ESO VLT spectroscopy of GRB 070802 is in close agreement with the GROND photometry (see Figure. 5 of Elíasdóttir et al. 2009).

37 stroyed by the burst;5 and (5) there does not appear to show strong evidence for a dependence of dust extinction on redshifts (although the extinction curve does vary from one burst to another), as supported by a systematic study of > 20 GRBs at

z > 2: the overall wavelength dependence of extinction, the steepness of the far-UV extinction rise, and the presence and strength of the 2175 Å extinction bump, do not appear to show any dependence on redshifts (Liang & A. Li 2009). The model

parameters are tabulated in Table 3.1.

3.4 Discussion

In deriving the extinction of GRB hosts, a major problem with the models based

on template extinction laws is that the wavelength-dependence of the extinction is fixed. For a featureless, power-law-like afterglow SED, this often leads to a preference

of a SMC-type extinction and a small amount of AV (usually < 0.2 mag): obscured

−1.2 by a SMC-type extinction (which is roughly a power-law Aλ ∝ λ ), an intrinsic power-law-like afterglow SED remains featureless and becomes a steeper power-law.

However, if the dust is “gray” (i.e. the extinction Aλ only weakly varies with λ), the resulting dust-obscured afterglow SED will still be a featureless power-law, with the intrinsic power-law exponent unchanged. The possible presence of gray extinction has been suggested by a number of authors (e.g. see Savaglio et al. 2003, Savaglio

& Fall 2004, Stratta et al. 2004, 2005, Chen et al. 2006, Li et al. 2008b, Perley et al. 2008a). The “Drude” approach allows us to break the degeneracy between “gray” extinction and SMC-type extinction.

Attempts have also been made to fit the afterglow SEDs with the MW, SMC

5Indeed, one sees in Figure. 3.2 a gradual flattening of the far-UV extinction rise from 0.5 days to 1 day and 3 days after burst, as expected from a preferential destruction of small grains responsible for the far-UV extinction by the burst (see Perna et al. 2003), that is reflected in Table 3.2 with a gradual increase (decrease) of the cutoff sizes (the power-law size distribution indices).

38 and LMC template extinction laws. As shown in Figures 3.1, 3.2, no acceptable fits are obtained, except that the MW model for GRB 070802 and the SMC model for GRB 050904 at an epoch of 3 days after the burst fit the observed SEDs reasonably

well. But even for these two cases, the “Drude” approach fits better as can be seen in

2 Figures. 3.1, 3.2 and indicated by χ /Ndata (see Table 3.1). Elásdóttir et al. (2009) tried to fit the VLT/FORS2 spectroscopy and the GROND

photometry with the Fitzpatrick & Massa (1990; hereafter FM) parametrization as well as the MW-, LMC-, and SMC-type extinction. They found that satisfactory fits could be achieved only if one assumes a cooling break in the intrinsic spectrum, with

the FM parametrization providing the best fit. However, one should caution that the FM parametrization is only valid for λ < 2700 Å, while the GROND photometry of GRB 070802 extends from ∼ 1400 Å to ∼ 6400 Å (in the GRB rest-frame).

The afterglow SEDs of the bursts discussed here all show a flux suppression at λ ∼ 4 − 6 µm−1 and deviate appreciably from a power-law (except for GRB 050904 at 3 days after the burst). As shown in Figures 3.1, 3.2, the flux suppression is closely accounted for in terms of dust with a 2175 Å bump in its extinction. For GRB 070802, the derived 2175 Å bump is comparable or even slightly stronger than that of the MW: for MW c4 ≈ 0.05 while c4 ≈ 0.06 for GRB 070802. To validate the suggested detection of the 2175 Å extinction feature, we have also tried to fit

the afterglow SEDs with the “Drude” approach but setting c4 = 0 (i.e. no 2175 Å

extinction bump). It is found that the fits (with c4 = 0) are much worse, as reflected

2 from the substantially increased χ /Ndata (see Table 3.1). The 2175 Å bump, first detected by Stecher (1965), is the strongest spectroscopic interstellar extinction feature. This feature is seen in extinction curves along lines of

sight in the MW and LMC.6 But it is rarely seen in the afterglow spectra of GRBs. So

6Most SMC extinction curves have no detectable 2175 Å bump (Prévot et al. 1984). But there

39 far, its possible detection is only reported in four bursts: GRB 970508 (Stratta et al. 2004), GRB 991216 (Kann et al. 2006, Vreeswijk et al. 2006), GRB 050802 (Schady et al. 2007), and GRB 070802 (Fynbo et al. 2007, Krühler et al. 2008), with the

latter showing the clearest presence of the 2175 Å extinction feature in its afterglow spectrum. In addition, Ellison et al. (2006) reported the detection of this feature in an intervening absorber at z ≈ 1.11 toward GRB 060418. But the host galaxy of

GRB 060418 at z ≈ 1.49 seems to have a SMC-type extinction law.

The possible detection of the 2175 Å extinction feature has been reported for a number of low, intermediate, and moderately high redshift systems through (1) the

composite absorption spectrum of intervening MgII absorption systems (Malhotra 1997: 0.2 < z < 2.2) or radio galaxies (Vernet et al. 2001: z ∼ 2.5);7 (2) the individual absorption spectra of intervening MgII absorbers (Wang et al. 2004: 1.4 < z < 1.5;

Srianand et al. 2008: z ∼ 1.3);8 (3) the UV SEDs of massive, UV-luminous star- forming galaxies (Noll & Pierini 2005: 2 < z < 2.5; Noll et al. 2007: 1 < z < 2.5); and (4) the extinction curves of gravitational lensing galaxies (Toft et al. 2000: z ≈ 0.44;

Motta et al. 2002: z ≈ 0.83; Wucknitz et al. 2003: z ≈ 0.93; Muñoz et al. 2004: z ≈ 0.68). However, Vijh et al. (2003) found that the dust in 906 Lyman break galaxies at 2 < z < 4 does not exhibit the 2175 Å extinction feature. This is probably related to the survival and destruction of the carriers of the 2175 Å bump in different physical conditions.

Although the precise nature of the carrier of the 2175 Å extinction feature remains

exist regional variations in the SMC extinction curve. The SMC sight lines which show no 2175 Å bump all pass through the SMC Bar regions of active star formation (Prévot et al. 1984; Gordon & Clayton 1998). The 2175 Å bump is seen at least in one line of sight, Sk 143 (AvZ 456), which passes through the SMC wing, a region with much weaker star formation (Gordon & Clayton 1998). 7But York et al. (2006) found no evidence for the 2175 Å bump in the composite absorption spectra of 809 intervening QSO MgII absorbers at 1 < z < 1.9. 8The 2175 Å extinction feature, the 9.7 µm silicate absorption feature, and the diffuse interstellar bands are seen in the damped Lyα absorber at z ≈ 0.524 toward the BL lac object AO 0235+164 (Junkkarinen et al. 2004, Kulkarni et al. 2007).

40 unknown, it is generally accepted that it arises from small graphitic dust or a cosmic mixture of polycyclic aromatic hydrocarbon (PAH) molecules (Li & Draine 2001). In view of the detection of presolar graphite dust with a SN origin in primitive meteorites,

it is not unreasonable to expect a 2175 Å extinction bump for high-z objects since the dust at z > 5 is thought to originate from Type II SNe. On the other hand, PAHs have been detected in ultraluminous IR galaxies and submm galaxies at z > 2 through their vibrational bands at 6.2, 7.7, 8.6 and 11.3 µm (see Lutz et al. 2005, Yan et al. 2005). PAHs were also seen in the Cloverleaf lensed QSO at z ≈ 2.56 (Lutz et al. 2007). If PAHs are indeed responsible for the 2175 Å extinction, it would not be

surprising to see this feature in high-z galaxies.

Finally, we fit the inferred extinction curves using a mixture of spherical amor- phous silicate and graphite dust each with an exponential-cutoff power-law size dis-

tribution (e.g. see Kim et al. 1994)

Z amax sil −αsil Aλ/AV = Asil Cext(a, λ) a exp (−a/ac,sil) da amin Z amax gra −αgra +Agra Cext (a, λ) a exp (−a/ac,gra) da, (3.1) amin

where the lower (upper) cutoff size amin (amax) is taken to be 50 Å (1 µm) for both silicate and graphite dust; the power-law indices αsil, αgra and the exponential-cutoff sizes ac,sil and ac,gra are treated as free parameters; Asil and Agra are related to the

sil gra abundance of each species; and Cext (Cext ) is the extinction cross section of silicate (graphite) dust. As shown in Figure. 3.1c and Figure. 3.3, the silicate-graphite model closely reproduces the inferred extinction curves for both GRBs, including the 2175 Å extinction bump (see Table 3.2 for the size parameters). The major mismatch occurs at λ ∼ 7 µm−1 which is probably due to the sudden rise of the silicate electronic absorption (see Kim & Martin 1995). We note that both silicate and graphite are expected SN condensates (Todini & Ferrara 2001, Nozawa et al. 2003). They have

41 been identified as presolar grains in primitive meteorites originating from supernovae which are considered as the main source of dust at z > 5 (see Dwek et al. 2007).

By fitting the afterglow SEDs of GRB 050904 (z ≈ 6.29) with the extinction

curve inferred for the distant BAL QSO at z ≈ 6.2 (which displays a plateau at λ−1 ∼ 3.3 − 5.9 µm−1, Maiolino et al. 2004), Stratta et al. (2007) argued that the dust properties may evolve beyond z > 5. This seems to be supported by that the

dust at z > 5 is probably produced by Type II SNe while in the local universe AGB stars are a major source of dust. However, this study together with a preliminary analysis of > 20 GRBs at z > 2 based on the “Drude” approach does not indicate

any dependence of the dust extinction on redshift. A more thorough and systematic study of the dust extinction and IR emission properties of high-z GRBs is in progress and will be used to further explore whether the dust properties vary as a function of

redshift.

3.5 Conclusion

We explore the extinction properties of the dust in the distant universe through the

afterglows of high-redshifted GRBs based on the “Drude” model which, unlike previous studies, does not require a prior assumption of template extinction laws. We select GRB 070802 at z ≈ 2.45 (which shows clear evidence for the 2175 Å extinction bump)

and GRB 050904 at z ≈ 6.29, the 2nd most distant GRB observed to date. We fit their afterglow spectra to determine the extinction of their host galaxies. We find that (1) their extinction curves differ substantially from that of the Milky Way, the Small and

Large Magellanic Clouds (which were widely adopted as template extinction laws in literature); (2) the 2175 Å extinction feature appears to be also present in GRB 050904 at z ≈ 6.29; and (3) there does not appear to show strong evidence for a dependence

42 Table 3.1. Parameters for fitting the afterglow SEDs with the “Drude” model and the MW, LMC and SMC template extinction laws.

2 Extinction c1 c2 c3 c4 AV β Fo χ /Ndata Type (mag) (µJy)

GRB 070802 (z ≈ 2.54) Drude 0.08 0.32 -1.99 0.06 0.81 0.98 2.38E17 0.23 Drude 0.10 0.34 -1.98 0.00 0.83 0.97 1.70E17 1.86 MW ...... 0.81 1.39 9.39E22 0.84 SMC ...... 0.91 1.09 3.80E18 3.43 LMC ...... 1.57 0.002 628.3 0.66 GRB 050904 (z ≈ 6.29; 0.5 days after burst) Drude 0.91 1.62 -2.34 0.02 0.38 0.25 7.37E8 0.01 Drude 0.86 1.73 -2.30 0.00 0.42 0.27 1.43E9 1.20 MW ...... 0.01 1.42 1.12E26 5.51 SMC ...... 0.41 0.001 1.13E5 2.37 LMC ...... 0.46 0.35 2.23E10 3.94 GRB 050904 (z ≈ 6.29; 1 day after burst) Drude 1.31 1.07 -1.99 0.03 0.39 0.24 4.80E8 0.01 Drude 1.54 1.13 -1.99 0.00 0.46 0.26 9.41E8 1.12 MW ...... 0.16 1.73 6.11E30 5.58 SMC ...... 0.53 0.001 1.24E5 1.61 LMC ...... 0.84 0.03 6.01E5 2.07 GRB 050904 (z ≈ 6.29; 3 days after burst) Drude 1.58 1.18 -1.72 0.00 0.41 0.26 1.95E8 0.04 MW ...... 0.001 1.34 1.19E24 0.61 SMC ...... 0.33 0.16 4.10E6 0.06 LMC ...... 0.24 0.79 1.01E16 0.39

of dust extinction on redshifts. The inferred extinction curves are closely reproduced in terms of a mixture of amorphous silicate and graphite, both of which are expected supernova condensates and have been identified in primitive meteorites as presolar grains originating from supernovae (which are considered as the main source of dust at high-z).

43 Table 3.2. Dust size distributions for the extinction curves derived from the “Drude” model and a mixture of silicate and graphite grains.

GRB z Asil αsil ac,sil(µm) Agra αgra ac,gra(µm) 070802 2.45 0.30 2.84 0.039 0.70 3.03 0.11 050904 (0.5 days) 6.29 0.59 3.08 0.014 0.41 3.10 0.33 050904 (1 day) 6.29 0.63 3.05 0.021 0.37 3.08 0.52 050904 (3 days) 6.29 0.68 3.00 0.045 0.32 2.88 0.76

Figure 3.1 Left panel (a): Fitting the SED of the afterglow of GRB 070802 (z ≈ 2.45) with the “Drude” approach (red) and the MW (magenta), LMC (blue) and SMC (green) templates for the GRB host extinction curve. Middle panel (b): Comparison of the MW (magenta), LMC (blue), and SMC (green) extinction laws with that derived from the “Drude” approach (red). Right panel (c): Fitting the derived extinction curve (red solid line and black filled circles) with a mixture of amorphous silicate (cyan dotted line) and graphite dust (green dashed line). The blue solid line plots the resulting model extinction curve.

44 Figure 3.2 Same as Figure. 3.1a,b but for GRB 050904 (Haislip et al. 2006; Tagliaferri et al. 2005) at three different epochs after burst.

Figure 3.3 same as Figure. 3.1c but for GRB 050904 at three different epochs after burst.

45 Chapter 4

Probing Extragalactic Dust through Nearby Gamma-Ray Burst Afterglows

4.1 Introduction

The presence of dust in the host galaxies of gamma-ray bursts (GRBs) is now well recognized (see Li et al. 2008a for a summary), as revealed by dark bursts,1 reddening of GRB afterglows (Klose et al. 2000, Levan et al. 2006), depletion of dust-forming heavy elements (Savaglio et al. 2003), thermal emission of GRB host galaxies in the infrared (IR) and submillimeter wavelengths (Michalowski et al. 2008, 2009), and the association of long-duration bursts with the death of young massive stars (which suggests the residence of long bursts in dense, dusty star-forming regions; see Woosley & Bloom 2006 for a review). Very recently, Berger et al. (2009a) reported the discovery of a very red near-IR and optical afterglow of GRB 070724A, a short-duration GRB.

They argued that dust extinction (with an visual extinction of AV ≈ 2 mag) may also

1Dark bursts are those events with no detected optical afterglow or with detected optical flux significantly suppressed compared with that expected from the observed X-ray afterglow (Groot et al. 1998, Jakobsson et al. 2004a, van der Horst et al. 2009). Even in the Swift era, despite deep and prompt searches, an appreciable fraction (∼ 50%) of the bursts are identified as dark (e.g. see Melandri et al. 2008, Cenko et al. 2009, Perley et al. 2009a, Zheng et al. 2009). The optical darkness of GRB afterglows is largely attributed to the extinction of dust local to the GRB host galaxies (Cenko et al. 2009, Perley et al. 2009a).

46 be responsible for reddening the optical/near-IR afterglow of this short burst (which is much redder than expected in the standard afterglow model).

However, little is known regarding the quantities and properties of the dust in

GRB host galaxies. While studies based on fitting the spectral energy distributions (SEDs) of afterglows in the ultraviolet (UV), visible and near-IR with a power-law (or broken power-laws) reddened by a known template extinction law such as that

of the Milky Way (MW) and the Large/Small Magellanic clouds (LMC/SMC) often suggest little extinction and a SMC-type extinction law (e.g. see Kann et al. 2006), dust depletion studies often favour large extinction and a flat or even gray extinction

law (e.g. see Savaglio et al. 2003, Savaglio & Fall 2004), in stark contrast to the featureless SMC extinction law which steeply rises with inverse wavelength (λ−1). But SED modeling also shows that large extinction is not uncommon. For some bursts, the visual extinction AV exceeds several magnitudes, e.g. AV ≈ 3.2 mag for

GRB 080607 (Prochaska et al. 2009), AV > 3.8 mag for GRB 970828 (Djorgovski et al. 2001b), 2 . AV . 5 mag for GRB 060923A (Tanvir et al. 2008), AV > 5.0 mag for GRB 061222A (Perley et al. 2009a), AV ≈ 5.5 mag for GRB 070306 (Jaunsen et al. 2008), and AV > 5.5 mag for GRB 070521 (Perley et al. 2009b), just to list a few. Furthermore, extinction laws very different from that of the SMC have been inferred for some bursts. The 2175 Å extinction bump, the most prominent UV extinction feature in the Galactic extinction law, is clearly seen in GRB 070802 (Krühler et al. 2008, Elíasdóttir et al. 2009, Liang & Li 2009), GRB 080607 (Prochaska et al. 2009), and probably in GRB 970508 (Stratta et al. 2004), GRB 991216 (Kann et al. 2006, Vreeswijk et al. 2006), GRB 050802 (Schady et al. 2007), and GRB 050904 (Liang & Li 2009). On the other hand, some bursts appear to have a featureless extinction law but much flatter than that of the SMC (e.g. see Chen et al. 2006, Li et al. 2008b, Perley et al. 2008a).

47 In view of the wide diverse nature of the quantity and wavelength dependence of the dust extinction of GRB host galaxies, we developed a technique (we call it the “Drude” approach) to fit the observed afterglow SEDs to derive the extinction and its wavelength dependence of the dust local to GRB hosts (see Li et al. 2008a). The advantage of this approach is that it does not require a priori assumption of a template extinction law (see §4.2). This is important as there is no reason to believe that the extinction curves of GRB host galaxies which exhibit a wide range of ages, luminosities, metallicities, and star-formation rates should resemble that of the known MW, LMC, SMC and other templates. Even in the Milky Way, there does not exist a universal extinction law: the extinction curve varies from one sightline to another. In the SMC and LMC, there are also regional variations (see Gordon et al. 2003). So far, only a few other galaxies have their extinction curves measured; the extinction curves of these external galaxies differ much from the standard MW, LMC and SMC laws (see §2.2 of Draine 2003). The “Calzetti” starburst attenuation law (i.e. the internal extinction by dust in starburst galaxies) determined by Calzetti et al. (1994) and the extinction curve inferred for a distant BAL QSO at a redshift z ≈ 6.2 by Maiolino et al. (2004)2 do not look like that of the MW, LMC, or SMC at all. Apparently, we should not expect a universal extinction law for GRB host galaxies.

Adopting the “Drude” approach (§3.2, also see Li et al. 2008a), in this Chapter we perform a systematic study of the dust extinction of the host galaxies for a sam- ple of 33 nearby or low-redshift (with z < 2) GRBs. In Chapter 5. we will explore high-redshifted GRB host galaxies (at z > 2) with an aim of studying the proper- ties of interstellar dust of the early universe and investigating whether (and how) they vary with z (Liang & Li 2010 in preparation). We compile the SEDs in the

2Stratta et al. (2007) successfully reproduced the observed afterglow SED of GRB 050904 at z ≈ 6.29 with the extinction curve of this high-redshift BAL QSO (but also see Liang & Li 2009).

48 UV/optical/near-IR bands of these GRB afterglows (§4.3), and determine both the quantity and wavelength-dependence of the extinction for the host galaxy of each GRB (§4.3). In §4.4 we discuss the deduced extinction curves and model them in terms of the silicate-graphite interstellar dust model. The dust properties and how the dust is correlated with gas are also discussed in §4.4.

4.2 Dust Extinction Models

In this Chapter, we apply the “Drude” model discussed in Chapter 2.3, 2.4 to explore the extinction properties of the dust in the distant universe through the afterglows of low-redshifted. Compared to models based on template extinction curves, the

“Drude” model is preferred because (1) it eliminates the need for a priori assumption of template laws (i.e. we do not need to choose a presumed dust extinction model), and (2) the analytical formula (eq.2.2) on which the “Drude” model is based restores the widely-adopted MW, SMC, LMC, and “Calzetti” templates – even if the “true” extinction curve of a GRB host happens to resemble a certain template law, the “Drude” approach will allow us to restore it (see Li et al. 2008a).

We should note that it is unfortunate that the “Drude” approach needs more free parameters3 – but this is the nature of the “Drude” approach: it allows the extinction curve to have a flexible shape, one has to have parameters to control the shape variation. While the approach of using “template” extinction curves has fewer parameters, their extinction shapes are fixed (but there is no priori reason why a GRB host should have an extinction shape like that of a fixed template). Note that

3Due to the sparsity of their photometric data, for some bursts the number of model parameters Npara exceeds the number of data points Nobs. For this reason, we measure the goodness of a model 2 fit in terms of χ /Nobs (see Tables 4.1,4.2). Future studies with the seven-band GROND imaging instrument and other photometric (Greiner et al. 2008) and even spectroscopic instruments (e.g. the FORS2 spectrograph on V LT ; see Fynbo et al. 2007) will allow us to place better constraints on model parameters.

49 the CCM parameterization of interstellar extinction curves with a single parameter

RV (Cardelli et al. 1989) is only valid for the Galactic sightlines and it does not apply to the LMC and SMC (Gordon et al. 2003),4 otherwise one could simply adopt the

CCM formula which has only one parameter (i.e. RV ) instead of eq.2.2 which has four parameters. The Fitzpatrick & massa (1990; “FM”) formula is good for the MW, SMC and LMC, but it is only valid for λ < 0.3 µm.

4.3 Results

To investigate the wavelength-dependence of dust extinction in the UV/optical/near- IR of the co-moving frame and its effects on the afterglow SEDs, one needs to select the samples which have the necessary wavelength coverage for determining the dust extinction. Foreground (Galactic) extinction have been corrected for each burst. For observations taken at slightly different epoches, we apply a correction using the

−α temporal dependence of GRB afterglows Fν(t) ∝ t (where α is the decay index of the fitted light curve) and bring all values to the same epoch. To this end, we investigate the host galaxies of long-duration bursts for which a wealth of data on the afterglow are available. We build a sample composed of 33 long bursts. The sample is selected by requiring that (i) they are nearby or at a redshift z < 2, and (ii) high- quality multiband (mainly UV/optical/near-IR) afterglow photometry is available.

This GRB host galaxy sample spans a redshift interval 0.125 < z < 1.98, with a median value z ' 1.1. In Tables 4.1,4.2 we respectively tabulate the model parameters for fitting the afterglow SEDs using the MW, LMC, SMC extinction templates and

4 The total-to-selective extinction ratio of the SMC bar is RV ≈ 2.87 (Gordon & Clayton 1998). The extinction curve of the SMC bar differs substantially from that predicted from the CCM formula with RV = 2.87: while the CCM RV = 2.87 curve has a moderately strong 2175 Å bump and a slightly steeper far-UV extinction rise than the MW average (with RV ≈ 3.1), the SMC extinction is featureless and steeply rises toward the far-UV. The LMC extinction law is also substantially different from that predicted from the CCM formula with RV ≈ 2.6, a value obtained by averaging over 10 LMC regions (Misselt et al. 1999).

50 the “Drude” approach. The fits are presented in Figures 4.1–11.

GRB 970508. We constructed the afterglow SED (ICRCVBU) of GRB 970508 at redshift z ≈ 0.835 (Metzger et al. 1997a,b), the second GRB for which an optical afterglow has been detected, with data from Galama et al. (1998) and Chary et al. (1998). The extinction in its host galaxy has been discussed by Reichart (1998), Wijers & Galama (1999), Stratta et al. (2004), Kann et al. (2006), Starling et al.

(2007) and others. Stratta et al. (2004) favoured a MW-type extinction with AV ≈

0.27 ± 0.16 mag. Kann et al. (2006) found AV ≈ 0.38 ± 0.11 mag for the preferred MW-type extinction. Starling et al. (2008) argued against any significant extinction, and thus they cannot distinguish between different extinction laws. In this Chapter, the best-fit model is provided by a MW-type extinction of AV ≈ 0.15 ± 0.04 mag but with a more prominent 2175 Å bump (see Figure. 4.1). If we neglect the U band photometry, the “Drude” model would result in an extinction law similar to that of the SMC with AV ≈ 0.49 ± 0.11 mag.

GRB 980703. We constructed the SED (KHJICRCVB) of GRB 980703 at z ≈ 0.966 (Djorgovski et al. 1998) with data from Vreeswijk et al. (1999a) at ∼ 1.2 days

after the burst. Kann et al. (2006) derived AV ≈ 1.32 ± 0.59 mag for the preferred

SMC-type extinction. In this Chapter, the “Drude” model results in AV ≈ 1.25 ±

0.45 mag and an extinction law similar to that of the MW with RV = 3.5 (i.e. the extinction curve has a weaker 2175 Å bump and flatter far-UV rise than that of the

Galactic diffuse ISM of RV ≈ 3.1; see Cardelli et al. 1989) characteristics of denser regions (see Figure. 4.1). The extinction appears to decrease with time (which was

regarded as an indication of dust destruction by the GRB): while Castro-Tirado et

al. (1999) estimated AV ≈ 2.2 mag at ∼ 0.9 days postburst, Vreeswijk et al. (1999a)

51 estimated AV ≈ 1.5 ± 0.11 mag at ∼ 1.2 days and Bloom et al. (1998) derived AV ≈ 0.9 ± 0.2 mag at ∼ 5.3 days, all assuming a MW-type extinction law. However, using the SMC extinction as a template, Starling (2008) examined this burst in detail and did not find any evidence of variable extinction.

GRB 990123. We constructed the SED (KHICRCVBU) of GRB 990123 at z ≈ 1.60 (Akerlof et al. 1999) with data from Galama et al. (1999). Kann et al. (2006) argued for a SMC-type extinction law with very little extinction AV ≈ 0.04±0.05 mag,

while Savaglio et al. (2003) estimated AV ≈ 1.1 mag from metal column abundances.

We found AV ≈ 0.30 ± 0.06 mag with an extinction law similar to that of the MW but lacking the 2175 Å extinction bump (see Figure. 4.1).5

GRB 990510. We constructed the SED (ICRCVB) of GRB 990510 at z ≈ 1.619 (Vreeswijk et al. 1999b) with data from Stanek et al. (1999) and Beuermann et al. (1999). Stanek et al. (1999) suggested that the deviation of the B band flux from the

−0.46±0.08 Fν ∝ ν power law fitted to the VRCIC fluxes may indicate an extinction of

AV ≈ 0.45 mag of the host galaxy or an intervening galaxy at z ≈ 1.62. Kann et al.

(2006) derived AV ≈ 0.18 ± 0.24 mag and a SMC-type extinction law. The “Drude” model also suggests a featureless extinction curve (with AV ≈ 0.37 ± 0.12 mag) like that of the SMC, but not as steep (see Figure. 4.2).

GRB 991208. We constructed the SED (KICRCVB) of GRB 991208 at z ≈ 0.706 (Dodonov et al. 1999, Djorgovski et al. 1999) with data from Castro-Tirado et al.

5While it is true that the extinction curve derived from the “ Drude” model deviates from the MW extinction law at λ−1 > 9 µm−1, we note that the uncertainty of the far-UV part of the MW extinction curve (i.e. the observed dispersion of the curve) is not small (e.g., at λ−1 = 10 µm−1 the uncertainty exceeds 30%; see Figure 1 of Zubko et al. 2004). The Galactic average extinction curve is based on the ANS satellite work by Savage et al. (1985) covering about 1000 sightlines. On the other hand, the extinction curve of the GRB host at λ−1 > 9 µm−1 would be better constrained if the afterglow data at λ−1 > 9 µm−1 was available.

52 (2001) and Chary et al. (2002). Kann et al. (2006) found that the MW-type extinction

with AV ≈ 0.80 ± 0.29 mag provides a better fit to the observed afterglow SED than the LMC and SMC models. The “Drude” approach derives an extinction law with

a weak 2175 Å bump and a far-UV rise even steeper than that of the SMC (see Figure. 4.2), similar to the extinction curve of the high latitude translucent cloud toward HD 210121 (Larson et al. 1996, Li & Greenberg 1998), which has the steepest

far-UV rise in the Galaxy. This model requires AV ≈ 0.47 ± 0.15 mag.

GRB 991216. We constructed the SED (KHJICRCVB) of GRB 991216 at z ≈ 1.02 (Vreeswijk et al. 1999c) with data from Garnavich et al. (2000) and Halpern et al. (2000). The “Drude” approach derives AV ≈ 0.14 ± 0.05 mag and an extinction curve very similar to that of the MW (see Figure. 4.2). The presence of the 2175 Å

bump in its extinction curve was supported by the detection of the broad absorption feature centered at ∼ 2360 Å (Vreeswijk et al. 2006). Kann et al. (2006) also found

that the MW-type extinction (with AV ≈ 0.13 ± 0.08 mag) is preferred.

GRB 000911. We constructed the SED (KSJICRCVB) of GRB 000911 at z ≈ 1.058 (Price et al. 2002a) with data from Lazzati et al. (2001) and Price et al. (2002a).

Masetti et al. (2005) found a SMC-type extinction of AV ≈ 0.32 mag, while Kann

et al. (2006) found the MW-type extinction of AV ≈ 0.27 ± 0.32 mag provides a slightly better fit than the LMC and SMC models. The “Drude” approach results in

AV ≈ 0.32 ± 0.10 mag and an extinction curve very similar to that of the MW (see Figure. 4.3). If we ignore the B band photometry, a SMC-type extinction would be preferred.

GRB 010222. We constructed the SED (KJICRCVBU) of GRB 010222 at z ≈ 1.477 (Jha et al. 2001) with data from Masetti et al. (2001). The “Drude” approach

53 derives AV ≈ 0.29 ± 0.08 mag with an extinction curve similar to that of the MW but

with the 2175 Å bump removed (see Figure. 4.3). In literature, both low and high AV values were suggested: (1) using the extinction curve model of Reichart (2001),6 Lee et al. (2001) found AV < 0.06 mag (with β = 0.75 fixed) and Galama et al. (2003) found AV ≈ 0.11 ± 0.02 mag; (2) Kann et al. (2006) were in favour of a SMC-type extinction with AV ≈ 0.14 ± 0.08 mag; and (3) Savaglio et al. (2003) argued for a much higher extinction of AV ≈ 0.7 mag from depletion studies of the dust-forming elements Fe and Si.

∗ ∗ GRB 010921. We constructed the SED (i r RCVBU) of GRB 010921 at z ≈ 0.45 (Bloom et al. 2001) with data from Price et al. (2002b). Kann et al. (2006) preferred a MW-type extinction with AV ≈ 0.81 ± 1.21 mag. Price et al. (2003) inferred a

LMC-type extinction of AV ≈ 1 mag. The “Drude” approach results in an extinction curve very similar to that of the SMC (see Figure. 4.3) with AV ≈ 1.02 ± 0.33 mag.

GRB 011121. We constructed the SED (KJICRCVBU) of GRB 011121 at z ≈ 0.36 (Infante et al. 2001) with data from Garnavich et al. (2003) and Greiner et

al. (2003a). While Kann et al. (2006) preferred a SMC-type extinction with AV =

0.39±0.14 mag, the “ Drude” approach derives AV ≈ 0.56±0.17 mag and an extinction curve very similar to that of the LMC but with a much weaker 2175 Å bump (see Figure. 4.4).7

6The seven-parameter analytical formula proposed by Reichart (2001) for the extinction curve Aλ/AV of GRB hosts was based on the expressions of Cardelli et al. (1989) for λ > 0.3 µm and of Fitzpatrick & Massa (1990) for 0.1 µm < λ < 0.3 µm. The problem with the Reichart (2001) formula (see his eqs. 61,66) is that the CCM expression is only valid for the Galactic extinction curves, it is not suitable for the SMC or LMC extinction (Gordon et al. 2003). Therefore, if a GRB host happens to have a SMC- or LMC-type extinction law, models based on the Reichart (2001) formula will not be able to restore the true extinction (while the “Drude” approach does). 7 The c4 parameter in Equation 2.2 which measures the strength of the 2175 Å bump is only ≈ 0.01 for GRB 011121, while c4 ≈ 0.022, 0.052 for the LMC and MW extinction laws, respectively.

54 GRB 020405. We constructed the SED (KSHJICRCVB) of GRB 020405 at z ≈ 0.69 (Masetti et al. 2002) with data from Masetti et al. (2003). While Stratta et al. (2005) argued for a flat, gray extinction curve with AV ≈ 2.3 mag based on a comparison of the X-ray and the optical data, Kann et al. (2006) found a moderate extinction of AV ≈ 0.25 mag for the SMC, LMC and MW template extinction laws. The “Drude” approach infers a featureless extinction curve steeply rising toward the far-UV with AV ≈ 0.72 ± 0.14 mag (see Figure. 4.4).

GRB 020813. We constructed the SED (KHJICRCVBU) of GRB 020813 at z ≈ 1.25 (Price et al. 2002c) with data from Barth et al. (2003). The “Drude” approach infers an extinction law just like that of the LMC but with the 2175 Å bump removed

(see Figure. 4.4). The inferred extinction AV ≈ 0.34 ± 0.12 mag is higher than that

derived by Kann et al. (2006; AV ≈ 0.12 ± 0.07 mag for SMC-type extinction), by

Covino et al. (2003; AV ≈ 0.12 ± 0.04 mag for MW-type extinction), and by Savaglio

& Fall (2004; AV < 0.19 mag from the analysis of metal column densities).

GRB 030226. We constructed the SED (KHJICRCVB) of GRB 030226 at z ≈ 1.98 (Greiner et al. 2003b) with data from Klose et al. (2004). Kann et al. (2006) found negligible extinction (AV ≈ 0.06 ± 0.06 mag for SMC-type extinction), in consistent

with Klose et al. (2004). The “Drude” approach infers AV ≈ 0.24 ± 0.04 mag and an extinction law resembling that of the LMC but with the 2175 Å bump removed and

a steeper far-UV rise at λ−1 > 8 µm−1 (see Figure. 4.5).

GRB 030328. We constructed the SED (ICRCVBU) of GRB 030328 at z ≈ 1.52 (Martini et al. 2003) with data from Maiorano et al. (2006). From the Fe II column density derived from the VLT optical spectrum of its afterglow, Maiorano et al. (2006) estimated AV < 0.1 mag. Kann et al. (2006) fitted the afterglow SED with a SMC-

55 type extinction of AV ≈ 0.05 ± 0.15 mag. The “Drude” approach derives AV ≈ 0.20 ± 0.06 mag with an extinction curve just like that of the MW but with the 2175 Å bump removed (see Figure. 4.5).

GRB 030329. We constructed the SED (HJICRCVBU) of GRB 030329 at z ≈ 0.168 (Greiner et al. 2003c) with data from Gorosabel et al. (2005). Bloom et al.

(2004) found AV ≈ 0.30 ± 0.03 mag (with β = 0.5 fixed; AV ≈ 0.94 ± 0.24 mag if β was treated as a free parameter) assuming a MW-type extinction. Kann et al. (2006) derived AV ≈ 0.54 ± 0.22 mag (β ≈ 0.30 ± 0.22) with a SMC-type extinction. The

“Drude” approach results in AV ≈ 0.30±0.12 mag (β ≈ 0.60±0.23) with a featureless extinction curve which is steeper than the MW curve but not as steep as that of the

LMC and SMC (see Figure. 4.5).

GRB 040924. We constructed the SED (KICRCV ) of GRB 040924 at z ≈ 0.859 (Wiersema et al. 2004) with data from Silvey et al. (2004). Due to the lack of data

at wavelengths bluer than the V band, Kann et al. (2006) found that the MW, LMC

and SMC extinction laws all provide excellent fits to the afterglow SED with AV ≈

0.21±0.62 mag and β ≈ 0.59±0.61 (MW), AV ≈ 0.22±0.62 mag and β ≈ 0.58±0.64

(LMC), and AV ≈ 0.16±0.44 mag and β ≈ 0.63±0.48 (SMC). The “Drude” approach yields a featureless, relatively flat extinction curve with AV ≈ 0.36 ± 0.10 mag and β ≈ 0.40 ± 0.14 (see Figure. 4.6). The derived extinction curve is almost identical

to that of the so-called “Calzetti” attenuation law of starburst galaxies. This also provides another piece of evidence for the advantage of the “Drude” approach: if the “true” extinction curve of a GRB host happens to resemble the “Calzetti” law which

is also widely used as a template, the “Drude” approach will allow us to restore it.

56 GRB 041006. We constructed the SED (HICRCVB) of GRB 041006 at z ≈ 0.716 (Price et al. 2004) with data from Soderberg et al. (2006). As shown in Figure. 4.6, both the “Drude” approach and the approach assuming a template extinction law

(MW, LMC and SMC) closely fit the afterglow SED (as due to the lack of data at wavelengths bluer than the B band). The “Drude” approach infers an extinction cure similar to that of the LMC but with a steeper far-UV rise at λ > 7.5 µm−1 and without

the 2175 Å bump. This model yields AV ≈ 0.15 ± 0.04 mag and β ≈ 0.32 ± 0.12, in

comparison with that of Kann et al. (2006): AV ≈ 0.11±0.23 mag and β ≈ 0.36±0.27

(MW), AV ≈ 0.14 ± 0.28 mag and β ≈ 0.32 ± 0.33 (LMC), and AV ≈ 0.12 ± 0.23 mag and β ≈ 0.34 ± 0.30 (SMC).

GRB 050318. We constructed the SED (V BU, UVW1, UVM2, UVW2) of GRB 050318 at z ≈ 1.44 (Berger & Mulchaey 2005) with data from Still et al. (2005) and Perri

et al. (2005a). Perri et al. (2005a) and Still et al. (2005) both derived β ≈ 1.1 ± 0.1.

The “Drude” approach yields AV ≈ 1.51 ± 0.54 mag and β ≈ 1.17 ± 0.42, with an extinction curve similar to that of the SMC (see Figure. 4.6).

GRB 050408. We constructed the SED (KHJIRVBU) of GRB 050408 at z ≈

1.2357 (Prochaska et al. 2005) with data from Wiersema et al. (2005), Milne et al. (2005), Kahharov et al. (2005), Flasher et al. (2005a), Foley et al. (2006), and de

Ugarte Postigo et al. (2007). The “Drude” approach yields AV ≈ 0.47 ± 0.08 mag (and β ≈ 0.62 ± 0.10) and an extinction curve even steeper than that of the SMC and exhibiting a weak 2175 Å bump, as probably revealed by the curvature in the UBV fluxes (see Figure. 4.7). In contrast, de Ugarte Postigo et al. (2007) and Kann

et al. (2007) were in favour of a SMC-type extinction with AV ≈ 0.74 ± 0.15 mag and β ≈ 0.28 ± 0.33. The extinction curve derived here is steeper than that of the MW

57 with RV = 2.5 but not as steep as that of HD 210121.

GRB 050525A. We constructed the SED (V BU, UVW1, UVM2, UVW2) of GRB 050525A

at z ≈ 0.606 (Foley et al. 2005) with data from Cobb & Bailyn (2005), Yanagi- sawa et al. (2005), Kaplan et al. (2005), Flasher et al. (2005b), Klotz et al. (2005), Blustin et al. (2006), and Della Valle et al. (2006a). The “Drude” approach yields

AV ≈ 0.85 ± 0.23 mag and β ≈ 0.63 ± 0.18 at ∼ 200 s postburst and an extinction

curve lying in between that of HD 210121 and that of the MW with RV = 2.5 (see Figure. 4.7). The derived extinction is much higher than that of Schady et al. (2007;

AV ≈ 0.16 ± 0.03 mag), Kann et al. (2007; AV ≈ 0.32 ± 0.20 mag), and Blustin et al.

(2006; AV ≈ 0.23 ± 0.15 mag).

XRF 050824X. We constructed the SED (KIRB) of XRF 050824X at z ≈ 0.83 (Fynbo et al. 2005b) with data from Schady et al. (2007a) and Sollerman et al.

(2007). The “Drude” approach deduces AV ≈ 0.23 ± 0.07 mag and β ≈ 0.21 ± 0.04 with an extinction curve lying in between that of HD 210121 and that of the MW

with RV = 2.5 (see Figure. 4.7), similar to GRB 050525A. Assuming a SMC-type

extinction, Kann et al. (2007) found AV ≈ 0.14 ± 0.13 mag and β ≈ 0.45 ± 0.18 [but

Sollerman et al. (2007) derived AV ≈ 0.4 ± 0.2 mag and β ≈ 0.56 ± 0.04]. We note that the limited wavelength coverage of these data does not allow one really to discern the SMC, LMC, MW and Drude extinction.

GRB 051111. We constructed the SED (KSHJIRV BU, UVW1, UVM2, UVW2) of GRB 051111 at z ≈ 1.55 (Hill et al. 2005) with data from Bloom (2005) and Yost et

al. (2007). Butler et al. (2006) and Kann et al. (2007) were both in favour of a SMC-

type extinction, with AV ≈ 0.23 ± 0.07 mag and AV ≈ 0.19 ± 0.02 mag, respectively.

The “Drude” approach deduces AV ≈ 0.38 ± 0.10 mag and β ≈ 0.37 ± 0.10 with an

58 extinction curve resembling that of the SMC but with a very weak 2175 Å bump (see Figure. 4.8). If we ignore the curvature of the RVB photometry, we would obtain a SMC-type extinction law.

GRB 060614. We constructed the SED (RV BU, UVW1, UVM2, UVW2) of GRB 060614 at z ≈ 0.125 (Price et al. 2006) with data from Della Valle et al. (2006b) and Mangano

et al. (2007). While Mangano et al. (2007) derived AV ≈ 0.05 mag with a SMC-like

extinction law, the “Drude” approach infers AV ≈ 0.42±0.18 mag and β ≈ 0.46±0.22 with a featureless, relatively flat extinction curve, similar to that of the “Calzetti” law (see Figure. 4.8).

GRB 060729. We constructed the SED (V BU, UVW1, UVM2, UVW2) of GRB 060729

at z ≈ 0.54 (Thoene et al. 2006) with data from Grupe et al. (2006, 2007). The “Drude” approach fits the afterglow SED at ∼ 100 ks postburst with an extinction curve resembling that of the LMC but with a steeper far-UV rise at λ−1 > 7 µm−1

(see Figure. 4.8). This model requires AV ≈ 0.45 ± 0.26 mag (and β ≈ 0.49 ± 0.17).

GRB 061121. We constructed the SED (Ri0V BU, UVW1, UVM2, UVW2) of GRB 061121 at z ≈ 1.314 (Bloom et al. 2006) with data from Yost et al. (2006), Melandri et al.

(2006), and Page et al. (2007). The “Drude” approach infers AV ≈ 1.10 ± 0.44 mag with an extinction curve resembling that of the MW but with a stronger 2175 Å bump (see Figure. 4.9).8 The MW-type extinction model fits the 2175 Å bump region very well, but fails at λ−1 < 3.7 µm−1. If we ignore both the U and B bands, we would then prefer a SMC-type extinction curve.

8 The c4 parameter of eq.2 which measures the strength of the 2175 Å bump is ≈ 0.10 for GRB 061121, while c4 ≈ 0.052 for the MW extinction law.

59 GRB 061126. We constructed the SED (KHJIRV BU, UVW1, UVM2) of GRB 061126 at z ≈ 1.1588 with data from Perley et al. (2008a). With a priori assumption of tem- plate extinction laws with a fixed wavelength dependence, Kann et al. (2007) found that the SMC-type extinction provides the best fit with AV ≈ 0.095 ± 0.055 mag, while Perley et al. (2008a) argued that a strong gray extinction may be responsible for the difference between the faint optical subluminosity and the bright X-ray af- terglow of this burst. The “Drude” approach infers AV ≈ 0.03 ± 0.01 mag with an extinction curve just like that of the MW but with the 2175 Å bump removed (see Figure. 4.9).

GRB 070125. We constructed the SED (KSJHIRVBU) of GRB 070125 at z ≈ 1.547 (Fox et al. 2007) with data from Updike et al. (2008a). Due to the lack of the 2175 Å bump, Updike et al. (2008a) found that a SMC-type extinction with

AV ≈ 0.11 mag is preferred. The “Drude” approach infers AV ≈ 0.45 ± 0.13 mag with a featureless, relatively flat extinction curve resembling that of the “Calzetti” law (see Figure. 4.9).

GRB 070306. We constructed the afterglow SED (RJHK) of GRB 070306 at z ≈

1.4959 (Jaunsen et al. 2008) with data from Jaunsen et al. (2008). Jaunsen et al. (2008) explored the overall extinction of the host galaxy by reddening a starburst galaxy template SED (Kinney et al. 1996) with various extinction laws. They found

the upper limit of AV in the range ∼ 0.1–0.5 mag, with the best fit given by a MW- type extinction (AV ≈ 0.17 mag). However, the afterglow of this burst seems to be highly extinguished: while it was not detected in the optical wavelengths, a near-IR

afterglow was clearly detected. Jaunsen et al. (2008) fitted the HK fluxes and the RJ upper limits of the afterglow of this burst by requiring the intrinsic spectral slope

60 of the near-IR afterglow to be βo = βx − 0.5 where βx ≈ 1.2 is the spectral slope of the X-ray afterglow (i.e., assuming a broken power-law with the cooling break occurring between the near-IR and X-ray bands). They found AV ≈ 5.4 ± 0.6 mag and a SMC-type extinction.

The “Drude” approach infers AV ≈ 1.40 ± 0.32 mag (and β ≈ 2.60 ± 0.43) and a flat extinction law (see Figure. 4.10). The major reason why we obtain a much lower

AV is that our β value is higher than that of Jaunsen et al. (2008) who fixed it to be β = 0.7. We do not want to overinterpret our results since we only have four data points among which two of them are just upper limits. We will investigate this burst

in a separate work, with special attention paid to the true β value.

GRB 071003. We constructed the SED (ugV rRiIz) of GRB 071003 at z ≈ 1.60435 with data from Perley et al. (2008b). While Perley et al. (2008b) found a SMC-type extinction and AV ≈ 0.21 mag, the “Drude” approach infers AV ≈ 0.51 ± 0.14 mag and an extinction law resembling that of the MW but with a much weaker 2175 Å bump and a steeper far-UV rise at λ−1 > 8.5 µm−1 (see Figure. 4.10).

GRB 080319B. We constructed the SED (KHJIRV BU, UVW1, UVM2, UVW2) of GRB 080319B at z ≈ 0.937 (Vreeswij et al. 2008) with data from Bloom et al. (2009). While Bloom et al. (2009) were in favour of a SMC-type extinction law with

AV ≈ 0.07±0.02 mag, the “Drude” approach deduces AV ≈ 0.05 mag and a featureless extinction law even steeper than that of the SMC (see Figure. 4.10).

GRB 080330. We constructed the SED (KHJIRVB) of GRB 080330 at z ≈ 1.51

(Malesani et al. 2008) with data from Cobb et al. (2008a). The “Drude” approach derives AV ≈ 0.41 ± 0.12 mag and an extinction law closely resembling that of the MW but lacking the 2175 Å bump (see Figure. 4.11).

61 GRB 080514B. We constructed the SED (NEWFIRM J, GROND J, GROND z0 ,

0 0 IC, Gemini i, GROND i, RC, GROND r , GROND g , B and U) of GRB 080514B at z ≈ 1.80 (Rossi et al. 2008) with data from Rossi et al. (2008). While Rossi et

al. (2008) found no evidence for dust in the host galaxy, the “Drude” approach infers

AV ≈ 0.24 ± 0.06 mag and and an extinction law resembling that of the MW but with a much weaker 2175 Å bump and a steeper far-UV rise at λ−1 > 9 µm−1 (see

Figure. 4.11).

GRB 081008. We constructed the SED (KHJIRB) of GRB 081008 at z ≈ 1.9685 (D’Avanzo et al. 2008) with data from Cobb et al. (2008b). The “Drude” approach infers AV ≈ 0.31 ± 0.23 mag and an extinction law resembling that of the LMC but lacking the 2175 Å bump and with a steeper far-UV rise at λ−1 > 6.5 µm−1 (see Figure. 4.11).

4.4 Discussion and Conclusion

Unlike the models based on a pre-assumption of a specific extinction law which as a result restricts the derived extinction laws to one of the adopted templates, the “Drude” approach is more flexible in determining the true wavelength dependence of

the host extinction. As shown in §4.3, the “Drude” approach reveals a wide diversity of extinction laws for the sample of 33 GRBs:

• Some bursts exhibit an extinction law more or less like that of the MW (RV ≈

3.1 for GRB 991216 and 000911, and RV > 3.5 for GRB 980703), LMC (GRB 011121 but with a weaker 2175 Å bump), and SMC (GRB 010921, 050318 and 051111)

— this demonstrates that if the extinction law of a GRB host happens to be one of the widely adopted template extinction laws (e.g. the MW, LMC and SMC laws), the “Drude” approach is able to restore the true extinction law.

62 • Some bursts exhibit an extinction law just like that of the MW (with RV ≈ 3.1) but (i) with a stronger 2175 Å bump (GRB 970508 and 061121), (ii) with a much weaker 2175 Å bump (GRB 071003 and 080514B), or (iii) simply with the

2175 Å bump completely removed (GRB 990123, 010222, 030328, 061126 and 080330).

• Some bursts exhibit an extinction law like that of the high Galactic latitude translucent cloud HD 210121 (Larson et al. 1996, Li & Greenberg 1998) (or

lying in between that of HD 210121 and that of the MW with RV = 2.5) which is characteristics of a weak 2175 Å bump and a steep far-UV rise (GRB 991208, 050408, 050525A, and XRF 050824X).

• Some bursts exhibit a featureless extinction law which steeply rises toward

the far-UV (GRB 990510, 020405, 020813, 030226, 030329, 041006, 060729, 080319B, and 081008), with a varying degree of steepness.

• Some bursts exhibit a featureless, flat extinction law (GRB 040924, 060614, 070125, and 070306). Some of them are similar to the so-called “Calzetti” at-

tenuation law of starburst galaxies (GRB 040924, 060614, and 070125).

The extinction quantities, the shapes of the deduced extinction curves, and the presence or absence of the 2175 Å bump do not appear to correlate with redshifts (more details will be presented in Liang & Li 2010 in preparation).

For bursts lacking the 2175 Å bump, models based on a priori assumption of specific template extinction laws often infer a SMC-type extinction with a small AV . As demonstrated in this Chapter, among the 19 GRBs (of the entire sample of 33 bursts) which lack the 2175 Å bump, only three bursts (GRB 010921, 050318 and 051111) have an extinction curve similar to that of the SMC. The extinction curves

63 of the other 16 bursts display a wide range of shapes, ranging from being relatively

flat to very steep. The AV values derived from the “Drude” approach is generally ∼ 2–5 times larger than that derived from assuming a SMC template extinction law

provided that the “true” extinction law inferred from the “Drude” approach is not as steep as that of the SMC.

In Figure. 4.12 a we plot the distribution of AV . We see that the distribution of

AV peaks at ∼ 0.4 mag, with a strong clustering toward relative low extinction (AV <

0.6 mag), which is higher than that of Kann et al. (2006; AV < 0.2 mag) who were in favour of a SMC-type extinction. This also indicates that if the “true” extinction law of a GRB host galaxy is not like that of the SMC, one would underestimate

AV by taking the SMC extinction law to be the template. We should note that the distribution of AV inferred here may not reflect the “true” extinction distribution as the sample selected here is biased to bursts with bright optical afterglows and high quality photometry data (so highly extinguished bursts like dark bursts are unlikely included in this sample).

In Figure. 4.12 b we show the distribution of RV calculated from the deduced

extinction curves. We see that most of these bursts have RV in the range of ∼ 3.0– 3.4. But the actual extinction curves differ substantially from predicted from the

CCM formula using these RV values (needless to mention the absence of the 2175 Å bump which is present in the CCM formula). Even the very steep extinction curve

of GRB 080319B (see Figure. 4.10) has RV ≈ 3.06. This is not surprising since the CCM formula is known to be valid only for the Galactic sightlines (e.g. see Gordon et al. 2003).

We select a sample of 25 GRBs having known hydrogen column densities NH which range from 1.0×1019 cm−2 to 1.0×1023 cm−2 (see Kann et al. 2006 for references). In

Figure. 4.12 c we show the distribution of NH for these bursts. We see that the major-

64 21 22 −2 ity of these bursts have NH in the range of ∼ 1.0 × 10 – 1.5 × 10 cm . To explore

the dust-to-gas ratios of these bursts, we compare AV with NH in Figure. 4.12 d. Also plotted in Figure. 4.12 d are the extinction-to-gas ratios of the MW, LMC and SMC.9

We see that the majority of these bursts have a dust-to-gas ratio smaller than that of the MW, consistent with previous studies (e.g. see Galama & Wijers 2001, Stratta et al. 2004, Kann et al. 2006).10 But ∼ 40% of the bursts have a dust-to-gas ratio com-

parable to or higher than that of the LMC. In general, the dust-to-gas ratio derived

here is higher than deduced from previous studies which estimated AV from fitting the GRB afterglow SEDs with a SMC-type extinction law. Finally, the dust-to-gas

ratio does not seem to correlate with the shape of the extinction curve inferred from the “Drude” approach. We fit the inferred extinction curves using a mixture of spherical amorphous sil-

icate and graphite dust each with an exponential-cutoff power-law size distribution (e.g. see Kim et al. 1994). More details about this size distribution can be referred to Eq. 3.1 and Chapter 3.4. As shown in Figures 4.1–11, this simple dust model

closely fits the extinction curves of all 33 bursts. In Table 4.3 we present the model parameters.

In Figure. 4.13 we plot the mass fractions of graphite dust of all 33 bursts as a

function of redshift. It appears that the relative abundances of silicate to graphite

9 21 22 22 −2 −1 We adopt NH/E(B − V ) ≈ 4.93 ± 0.28 × 10 , 2 ± 0.5 × 10 , 4.4 ± 0.7 × 10 cm mag and RV ≈ 3.08, 3.16 and 2.93 for the MW (Diplas & Savage 1994), LMC (Koornneef 1982) and SMC (Bouchet et al. 1985), respectively. 10Why these GRB hosts have in general a lower dust-to-gas ratio than that of the MW? First, these hosts could be metal-poor compared with the MW so that there are fewer heavy elements to make the dust. Second, the bulk of the dust may be really “gray” (a > 1 µm) so that its presence cannot be revealed by the near-IR-visible-UV extinction curve derived from modeling the afterglow SEDs. The latter explanation is not unreasonable: in the dense dusty circumburst environment, the dust can grow through coagulation to large sizes. Therefore, a lower AV /NH ratio does not necessarily means a lower dust-to-gas ratio.

65 are in general lower than that of the MW diffuse ISM11

and do not appear to correlate with the redshifts of GRB hosts. In Figure. 4.14 we plot the mean dust sizes of all 33 bursts as a function of redshift.12

Again, it appears that there is no clear evidence for the dependence of hai on z. These issues will be explored in more detail in Chapter 5. (S.L. Liang & A. Li, in preparation).

To summarize, we have derived the quantities and wavelength dependences of the dust extinction along the lines of sight toward 33 nearby GRBs (with z < 2) from fitting their afterglow SEDs using the “Drude” approach which does not require a priori assumption of a specific extinction law. The deduced extinction curves display a wide diversity of shapes, ranging from relatively flat curves to curves which are featureless and steeply rise toward the far-UV, and from curves just like that of the MW, LMC and SMC which are widely used as extinction templates to curves resembling that of the MW and LMC but lacking the 2175 Å bump. The visual extinction AV derived from the “Drude” approach is generally larger by a factor of ∼ 2–5 than that inferred by assuming a SMC-type extinction law. The standard silicate-graphite interstellar grain model closely reproduces the extinction curves of all 33 GRB host galaxies, irrespective of their redshifts.

11 The silicate-graphite model of Mathis, Rumpl & Nordsieck (1977) who assumed a simple power law for the dust size distribution (dn/da ∼ a−3.5 with 50 < a < 0.25 µm for both silicate dust and graphite dust) gives mgra/ (mgra + msil) ≈ 0.36. The latest silicate-graphite-PAH model gives mgra/ (mgra + msil) ≈ 0.27 (Weingartner & Draine 2001). This model assumes two different size distributions which smoothly extend from a few angstroms to a few micrometers for silicate dust and graphitic dust. 12The mean dust sizes are derived by first averaging over the silicate (graphite) size distributions weighted by mass to obtain haisil (haigra) and then taking the mass-weighted average of haisil and haigra: hai = msil/ (mgra + msil) × haisil + mgra/ (mgra + msil) × haigra.

66 Table 4.1. Parameters for fitting the afterglow SEDs with the MW, LMC and SMC template 2 extinction laws. The goodness of the fit is measured by χ /Nobs, where Nobs is the number of observational data points.

MW Dust LMC Dust SMC Dust

2 2 2 GRB AV (mag) β log Fo (µJy) χ /Nobs AV (mag) β log Fo (µJy) χ /Nobs AV (mag) β log Fo (µJy) χ /Nobs 970508 0.24±0.08 0.14±0.06 3.26 0.38 0.16±0.05 0.10±0.04 3.47 2.42 0.13±0.04 0.25±0.06 5.27 1.46 980703 0.72±0.26 1.73±0.62 27.22 0.65 0.21±0.07 2.25±0.80 34.74 0.91 0.39±0.14 2.05±0.73 31.87 0.80 990123 0.21±0.13 0.44±0.10 7.66 0.88 0.14±0.06 0.34±0.08 6.10 0.48 0.17±0.08 0.40±0.06 6.99 0.45 990510 0.16±0.04 0.67±0.22 11.94 2.38 0.18±0.07 0.30±0.14 6.44 0.32 0.15±0.05 0.60±0.26 10.96 0.78 991208 0.86±0.29 0.16±0.07 5.65 0.08 0.78±0.18 0.17±0.05 5.78 0.10 0.90±0.20 0.11±0.04 4.95 0.07 991216 0.16±0.06 0.39±0.12 8.09 0.20 0.14±0.03 0.35±0.12 7.57 1.13 0.14±0.05 0.39±0.14 8.08 0.35 000911 0.44±0.17 0.55±0.28 10.08 0.51 0.17±0.03 0.77±0.22 13.28 0.45 0.30±0.08 0.64±0.10 11.41 0.41 010222 0.15±0.05 1.04±0.12 17.63 1.99 0.13±0.03 0.81±0.09 14.12 0.67 0.16±0.04 0.96±0.11 16.43 0.98 010921 0.83±0.27 0.91±0.29 15.72 0.03 1.23±0.39 0.11±0.03 3.92 0.03 1.33±0.43 0.19±0.06 5.16 0.03 011121 0.50±0.11 0.55±0.19 9.55 0.56 0.40±0.13 0.61±0.15 10.40 0.43 0.48±0.14 0.55±0.14 9.55 0.46 020405 0.16±0.05 0.96±0.20 15.35 1.07 0.17±0.06 0.93±0.23 14.98 1.02 0.20±0.09 0.91±0.15 14.63 1.02 020813 0.11±0.05 0.89±0.16 15.23 1.09 0.16±0.04 0.80±0.20 13.97 0.53 0.21±0.08 0.71±0.15 12.61 0.60 030226 0.10±0.03 0.61±0.14 10.93 3.17 0.14±0.03 0.43±0.11 8.20 0.56 0.12±0.04 0.43±0.10 8.30 1.24 030328 0.18±0.07 0.41±0.19 7.87 2.36 0.15±0.08 0.20±0.08 4.71 0.40 0.15±0.05 0.31±0.10 6.44 0.52 67 030329 0.53±0.23 0.32±0.10 7.22 0.36 0.38±0.14 0.43±0.15 8.78 0.34 0.49±0.17 0.34±0.13 7.50 0.36 040924 0.26±0.06 0.55±0.16 8.60 0.84 0.21±0.04 0.58±0.16 9.03 0.97 0.29±0.06 0.51±0.15 8.03 0.80 041006 0.12±0.03 0.39±0.13 7.52 0.42 0.13±0.02 0.36±0.12 7.16 0.47 0.15±0.02 0.36±0.12 7.09 0.42 050318 0.93±0.33 1.74±0.41 44.06 0.60 0.65±0.23 1.80±0.36 43.93 0.24 0.79±0.28 1.73±0.55 44.01 0.29 050408 0.23±0.04 1.34±0.22 21.00 2.58 0.75±0.12 0.27±0.04 5.34 0.39 1.02±0.17 0.11±0.02 3.04 0.84 050525A 0.38±0.11 1.77±0.50 28.19 0.10 0.17±0.05 1.97±0.56 31.03 0.15 1.33±0.37 0.11±0.03 3.91 0.06 050824X 0.30±0.09 0.16±0.04 3.79 0.35 0.34±0.06 0.14±0.02 3.08 0.17 0.35±0.08 0.14±0.03 3.08 0.21 051111 0.18±0.05 0.98±0.25 17.34 1.77 0.35±0.09 0.42±0.11 9.13 0.34 0.62±0.16 0.12±0.03 4.90 0.56 060614 0.26±0.12 0.69±0.16 12.23 0.52 0.17±0.16 0.67±0.14 11.93 0.44 0.24±0.10 0.69±0.20 12.23 0.47 060729 0.20±0.03 0.83±0.22 14.45 0.52 0.16±0.04 0.87±0.32 15.05 0.44 0.16±0.04 0.87±0.25 14.98 0.56 061121 1.28±0.52 0.93±0.38 16.60 2.97 0.65±0.26 1.29±0.52 21.57 3.51 1.54±0.62 0.11±0.04 4.51 1.79 061126 0.06±0.04 0.79±0.13 14.23 0.73 0.06±0.04 0.77±0.12 13.87 0.63 0.07±0.04 0.79±0.13 14.16 0.47 070125 0.15±0.02 0.73±0.24 13.30 6.53 0.14±0.04 0.52±0.15 10.11 0.56 0.17±0.04 0.67±0.20 12.47 1.86 070306 1.41±0.25 2.80±0.34 14.45 1.89 1.34±0.29 2.80±0.42 15.23 1.96 1.34±0.30 2.80±0.46 16.02 1.90 071003 0.13±0.08 1.13±0.20 18.13 0.79 0.10±0.05 0.91±0.16 14.82 0.69 0.24±0.05 0.70±0.12 11.78 0.51 080319B 0.10±0.08 0.08±0.06 4.24 2.35 0.14±0.05 0.08±0.06 4.24 1.32 0.08±0.06 0.05±0.02 4.24 1.67 080330 0.23±0.16 0.50±0.13 10.00 3.03 0.25±0.11 0.44±0.12 9.19 3.19 0.28±0.14 0.48±0.16 9.70 3.23 080514B 0.10±0.04 0.50±0.14 8.60 0.50 0.08±0.05 0.38±0.10 6.89 0.59 0.08±0.05 0.45±0.70 7.86 0.43 081008 0.20±0.10 1.21±0.91 20.52 5.56 0.38±0.28 0.11±0.08 4.15 1.44 0.16±0.12 1.10±0.82 18.86 3.83 Table 4.2. Parameters for fitting the afterglow SEDs with the “Drude” approach.

−2 a 2 GRB z log(NH/cm ) Ref. c1 c2 c3 c4 AV (mag) β RV log Fo (µJy) χ /Nobs 970508 0.835 21.80±0.40 (1) 0.24 1.32 -2.00 0.12 0.15±0.04 0.10±0.03 3.14 43.56 0.20 980703 0.966 22.56±0.20 (2) 1.33 3.33 -2.16 0.04 1.25±0.45 1.19±0.42 3.93 55.91 0.49 990123 1.60 21.73±0.40 (1) 1.60 2.90 -2.00 0.00 0.30±0.06 0.23±0.07 3.25 20.77 0.30 990510 1.619 22.00±0.30 (1) 1.94 2.49 -2.03 0.00 0.37±0.12 0.28±0.10 3.21 45.41 0.18 991208 0.706 – – 1.95 0.95 -1.90 0.04 0.47±0.15 0.48±0.12 2.99 52.71 0.05 991216 1.02 21.80±0.30 (3) 0.06 0.49 -2.00 0.06 0.14±0.05 0.36±0.16 3.12 44.04 0.16 000911 1.058 – – 0.62 2.62 -2.02 0.06 0.32±0.10 0.60±0.19 3.09 51.68 0.23 010222 1.477 22.08±0.20 (4) 4.68 4.79 -1.98 0.00 0.29±0.08 0.81±0.19 3.29 18.86 0.48 010921 0.45 – – 0.06 0.12 -1.99 0.01 1.02±0.33 0.52±0.17 4.07 51.02 0.01 011121 0.36 – – 0.06 0.17 -1.99 0.01 0.56±0.17 0.49±0.14 3.52 48.81 0.32 020405 0.69 21.70±0.30 (5) 0.21 0.74 -1.96 1.0E-4 0.72±0.14 0.44±0.23 3.26 21.20 0.90 020813 1.25 20.88±0.12 (6) 0.23 0.44 -1.96 0.00 0.34±0.12 0.46±0.09 3.31 12.29 0.46 030226 1.98 21.50±0.20 (7) 0.52 0.88 -1.96 1.0E-3 0.24±0.04 0.32±0.08 3.20 28.97 0.36 030328 1.52 20.78±0.18 (8) 0.22 1.28 -2.00 0.00 0.20±0.06 0.32±0.12 3.26 44.89 0.27 68 030329 0.168 20.30±0.05 (9) 0.02 0.28 -2.00 0.00 0.30±0.12 0.60±0.23 3.29 35.37 0.18 040924 0.859 – – 0.22 1.26 -1.94 0.00 0.36±0.10 0.40±0.14 3.26 19.64 0.56 041006 0.716 21.51±0.02 (8) 0.55 1.00 -2.00 0.00 0.15±0.04 0.32±0.12 3.19 37.82 0.20 050318 1.44 – – 1.59 1.20 -2.00 0.00 1.51±0.54 1.17±0.42 3.04 40.00 0.17 050408 1.2357 22.08±0.12 (10) 1.51 1.11 -2.17 0.03 0.47±0.08 0.62±0.10 3.00 55.56 0.30 050525A 0.606 21.34±0.09 (11) 1.22 0.85 -1.61 0.04 0.85±0.23 0.63±0.18 3.24 47.50 0.02 050824X 0.83 – – 1.45 0.92 -1.67 0.05 0.23±0.07 0.21±0.04 3.16 45.52 0.13 051111 1.55 21.90±0.15 (12) 0.61 0.50 -1.91 0.03 0.38±0.10 0.37±0.10 3.37 24.34 0.28 060614 0.125 20.48±0.12 (13) 0.30 2.86 -1.89 0.00 0.42±0.18 0.46±0.22 3.29 22.94 0.35 060729 0.54 21.30±0.08 (14) 0.50 0.91 -2.00 0.00 0.45±0.26 0.49±0.17 3.20 42.94 0.30 061121 1.314 21.91±0.10 (15) 8.45 5.34 -0.99 0.10 1.10±0.44 0.56±0.23 3.29 51.52 1.39 061126 1.1588 21.43±0.05 (16) 0.17 1.16 -2.00 0.00 0.03±0.01 0.90±0.15 3.07 41.53 0.20 070125 1.547 – – 0.14 0.21 -1.95 2.0E-3 0.45±0.13 0.22±0.06 3.99 36.78 0.25 070306 1.4959 21.59±0.04 (17) 0.50 0.32 -1.98 0.00 1.40±0.32 2.60±0.43 3.69 20.34 1.87 071003 1.60435 – – 0.22 1.08 -2.01 0.02 0.51±0.14 0.48±0.08 3.26 37.21 0.47 080319B 0.937 21.27±0.03 (18) 1.36 0.66 -1.97 0.00 0.05±0.02 0.12±0.04 3.06 52.42 0.48 080330 1.51 – – 0.24 1.30 -1.99 2.0E-3 0.41±0.12 0.28±0.07 3.26 14.73 2.19 080514B 1.8 21.15±0.30 (19) 0.30 1.68 -2.10 0.01 0.24±0.06 0.32±0.13 3.26 42.19 0.29 081008 1.9685 21.83±0.05 (20) 2.24 1.80 -1.99 1.0E-3 0.31±0.23 0.48±0.36 3.08 50.05 1.20

a(1)Galama & Wijers (2001); (2)Vreeswijk et al. (1999a); (3)Ballantyne et al. (2002); (4)Stratta et al. (2004); (5)Mirabal et al. (2003); (6)Butler et al. (2003); (7)Klose et al. (2004); (8)Butler et al. (2005); (9)Hjorth et al. (2003); (10)Foley et al. (2006); (11)Blustin et al. (2006); (12)Butler et al. (2006); (13)Dado et al. (2008); (14)Grupe et al. (2007); (15)Page et al. (2007); (16)Gomboc et al. (2008); (17)Jaunsen et al. (2008); (18)Bloom et al. (2008); (19)Rossi et al. (2008); (20)Racusin et al. (2008). Table 4.3. Dust size distributions for the extinction curves derived from the “Drude” approach and modeled as a mixture of silicate and graphite grains.

2 GRB Asil αsil ac,sil(µm) Agra αgra ac,gra(µm) χ /Nobs 970508 1.56E4 2.07 0.09 7.64 2.89 0.01 0.97 980703 6.17E3 2.13 0.11 9.73E-6 3.67 0.03 0.02 990123 4.50E-4 3.44 0.73 3.83E8 1.34 0.02 1.23 990510 0.03 3.26 0.04 0.10 3.00 0.95 4.20 991208 2.50E-4 3.63 0.04 1.00E-3 3.39 0.16 1.41 991216 0.03 3.12 0.27 1.93 2.86 0.02 1.95 000911 509.19 2.33 0.12 1.20E-3 3.40 0.02 0.04 010222 1.60E-4 3.52 0.72 2.87E9 1.10 0.03 2.11 010921 0.14 3.07 0.09 7.54E-4 3.46 0.79 2.53 011121 0.01 3.30 0.14 2.00E-3 3.24 0.68 0.07 020405 1.39E-4 3.55 0.41 1.97E8 1.34 0.03 0.56 020813 0.11 3.09 0.20 1.22E3 2.65 0.02 3.50 030226 8.85E-5 3.63 0.10 2.05E5 1.85 0.06 2.54 030328 0.03 3.19 0.07 0.08 3.00 0.83 2.89 030329 5.60E-5 3.62 0.17 1.99E3 2.24 0.06 1.25 040924 0.05 3.06 0.22 3.50E8 1.29 0.03 0.45 041006 2.40E-4 3.43 0.03 167.7 2.47 0.06 4.13 050318 3.55E-3 3.62 0.89 108.9 2.50 0.02 3.05 050408 4.04E-7 3.96 0.08 5.42E-6 3.42 0.84 4.60 050525A 0.01 3.20 0.39 176.0 3.16 0.02 0.23 050824X 0.01 3.24 0.27 0.17 3.03 0.02 0.08 051111 9.42E-4 3.44 0.35 5.01E8 1.45 0.01 0.23 060614 33.61 2.55 0.14 3.56E7 1.42 0.03 0.06 060729 5.38E-9 4.16 0.72 1.46 2.81 0.18 3.88 061121 0.06 3.05 0.33 0.01 3.34 0.02 0.09 061126 0.10 3.02 0.19 5.27 2.65 0.08 2.22 070125 0.07 3.06 0.29 145.7 2.35 0.03 0.05 070306 9.42E-3 3.17 1.00 0.045 2.94 0.10 4.73 071003 7.08E-4 3.40 0.64 181.7 2.44 0.04 0.75 080319B 9.86E-5 3.76 0.02 5.79E-4 3.43 0.22 2.36 080330 0.02 3.14 0.21 1.35E11 0.80 0.03 1.00 080514B 3.69E-3 3.27 0.47 0.81 2.80 0.08 0.80 081008 0.01 3.22 0.03 2.40E-3 3.13 0.91 0.90

69 Figure 4.1 Upper panel (a): Fitting the SED of the afterglow of GRB 970508 with the “Drude” approach (red) and the MW (black), LMC (blue) and SMC (green) templates for the GRB host extinction curve. Upper panel (b): Comparison of the MW (black), LMC (blue), and SMC (green) extinction laws with that derived from the “Drude” approach (red). Upper panel (c): Fitting the derived extinction curve (red solid line and black filled circles) with a mixture of amorphous silicate (cyan dotted line) and graphite dust (green dashed line). The blue solid line plots the resulting model extinction curve. Middle Panel: Same as the upper panel but for GRB 980703. Also shown in the middle panel (b) is the MW extinction curve of RV = 3.5 (dashed line). Bottom panel: same as the upper panel but for GRB 990123.

70 Figure 4.2 Same as Figure. 4.1 but for GRB 990510, GRB 991208, and GRB 991216. Also shown in the middle panel (b) is the extinction curve of the high latitude translu- cent cloud toward HD 210121 (thin cyan line) which has the steepest far-UV rise ever observed in the Galaxy.

71 Figure 4.3 Same as Figure. 4.1 but for GRB 000911, GRB 010222, and GRB 010921.

72 Figure 4.4 Same as Figure. 4.1 but for GRB 011121, GRB 020405, and GRB 020813.

73 Figure 4.5 Same as Figure. 4.1 but for GRB 030226, GRB 030328, and GRB 030329.

74 Figure 4.6 Same as Figure. 4.1 but for GRB 040924, GRB 041006, and GRB 050318. Also shown in the upper panel (b) is the so-called “Calzetti” attenuation law of star- burst galaxies (cyan line).

75 Figure 4.7 Same as Figure. 4.1 but for GRB 050408, GRB 050525A, and XRF 050824X. Also shown in the upper panel (b), the middle panel (b) and the bottom panel (b) is the extinction curve of the high latitude translucent cloud toward HD 210121 (thin cyan line) which has the steepest far-UV rise ever observed in the Galaxy.

76 Figure 4.8 Same as Figure. 4.1 but for GRB 051111, GRB 060614, and GRB 060729. Also shown in the middle panel (b) is the “Calzetti” law (cyan line).

77 Figure 4.9 Same as Figure. 4.1 but for GRB 061121, GRB 061126, and GRB 070125. Also shown in the bottom panel (b) is the “Calzetti” law (cyan line).

78 Figure 4.10 Same as Figure. 4.1 but for GRB 070306, GRB 071003, and GRB 080319B. Also shown in the upper panel (b) is the “Calzetti” law (cyan line).

79 Figure 4.11 Same as Figure. 4.1 but for GRB 080330, GRB 080514B, and GRB 081008.

80

18

14

(b) (a) 16

12

14

10

12

8 10

8

Number 6 Number

6

4

4

2

2

0 0

2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

R V

A V (magnitudes)

23

(d)

(c)

MC

S

4

LMC ) 22 2 - /cm H

MW

N Number

2 log (

21

0 20

20.0 20.5 21.0 21.5 22.0 22.5 23.0 0.1 0.2 0.5 1 2

-2

A (magnitude) v log (N /cm )

H

Figure 4.12 (a): Distribution of the derived host galaxy visual extinction AV ; (b): Distribution of the total-to-selective extinction ratio RV ≡ AV /E(B −V ). (c): Distribution of the hydrogen column densities NH along the lines of sight toward the bursts in their host galaxies. (d): Dust-to-gas ratios in the host galaxies along the lines of sight toward 25 GRBs. Also plotted are that of the MW, LMC and SMC. Open circles: those bursts with a MW-type extinction; open triangles: those with a LMC-type extinction; filled triangles: those with a SMC-type extinction; filled circles: those with a MW-type extinction but with a very weak (or lacking) 2175 Å bump; open stars: those with a featureless, steep extinction curve; filled stars: those with a steep far-UV rise and a weak 2175 Å bump; open diamonds: those with a flat curve.

81 Figure 4.13 Mass fractions of graphite dust as a function of redshift z for all 33 bursts at z < 2. Also shown are the mass fractions of graphite of the MRN silicate-graphite model (red dashed line; Mathis et al. 1977) and the WD silicate-graphite-PAH model (green dot-dashed line; Weingartner & Draine 2001)

Figure 4.14 Mass-weighted mean dust sizes as a function of redshift z. Also shown are the mean dust sizes of the MRN silicate-graphite model (red dashed line; Mathis et al. 1977) and the WD silicate-graphite-PAH model (green dot-dashed line; Weingartner & Draine 2001).

82 Chapter 5

Probing Extragalactic Dust through Distant Gamma-Ray Burst Afterglows

5.1 Introduction

The featureless, power-law-like afterglow spectra shape of GRBs, which are subject to reddening from interstellar dust of their host galaxies, is an excellent probe of the dust at high redshifts. Dust is an important astrophysical constituent. It regulates the cooling of the interstellar medium, attenuates light emitted by galaxies, and fragments collapsing molecular clouds into intermediate and low-mass stars. Dusty hyperluminous galaxies in the early universe provide unique environments for studying the role of massive stars in the formation and destruction of dust. At redshifts above 6, when the universe was less than 1 Gyr old, dust could have only condensed in the explosive ejecta of Type II supernovae (SNe), since most of the progenitors of the

AGB stars, the major alternative source of interstellar dust, did not have time to evolve off the main sequence. However, our precise knowledge of where and when this dust was made is still incomplete. Based on the detection of dust in the early universe (Bertoldi et al. 2003; Hines et al. 2006; Sloan et al. 2009), two processes are proposed to form dust:

83 (1) old sun-like stars near death generate dust, which takes a few billion years; (2) supernovae/hypernovae explosions revealed by infrared space missions, which evolves relatively quickly, only about tens of million years. Further observations show that

supernovae, the violent death of massive star, can make a major contribution to enriching the dust content of the universe (Maiolino et al. 2004). Especially in the most energetic event, GRBs, questions are raised about if GRBs can produce dust in

the quantities required to account for the dust they see in the early universe, or even they may destroy more dust than they create.

In Chapter 4. (also see Liang & Li 2010), we perform a systematic study of the

dust extinction of the host galaxies for a sample of 33 nearby or low-redshift (with z < 2) GRBs. In this Chapter, we will explore high-redshifted GRB host galaxies (at z > 2) with an aim of studying the properties of interstellar dust of the early

universe and investigate whether and how they vary with z. We compile the SEDs in the UV/optical/near-IR bands of these GRB afterglows (§5.3), and determine both the quantity and wavelength-dependence of the extinction for the host galaxy of each

GRB (§5.3). In §5.4 we discuss the deduced extinction curves and model them in terms of the silicate-graphite interstellar dust model. The dust properties and how the dust is correlated with gas are also discussed. In in §5.4, we also fit the evolution

of star formation rate on redshifts by a power law with exponential cutoff model. The main conclusion of this Chapter is summarized in §5.5.

5.2 Data Analysis & Dust Extinction Models

The ultraviolet (UV), optical, and near-IR afterglow data are downloaded from the Gamma-ray bursts Coordinates Network (GCN)1 and the references (see section Re- sults) within this paper. The sample is selected by requiring multiband (mainly

1http://gcn.gsfc.nasa.gov/

84 optical and NIR) photometry is available for the GRB afterglow. The selected high redshift host galaxies span a wide range of redshifts, from the moderately high red- shift of z ≈ 2.00 (GRB 030226) to the second highest redshift observed to date of

z ≈ 6.695 (GRB 080913) 2.

In order to derive the visual extinction AV in the GRB host galaxy along the line of sight, we need to correct the foreground Galactic extinction and the Lyman-forest

absorption by neutral hydrogen. The Galactic extinction law is referred from the

−1 −1 equation in Cardelli et al. (1989): < A(λ)/A(V ) >= a(λ )+RV b(λ ), where RV = A(V )/E(B−V ), E(B−V ) = A(B)−A(V ), and a(λ−1) and b(λ−1) are the wavelength

dependent parameters. To recover Lyman-forest lines blanketing absorption, we use the equation 15 in Madau (1995). The total effective line-blanketing optical depth P λobs 3.46 −3 −3 is derived by τeff = Aj ( ) , where Aj = (3.6 × 10 , 1.7 × 10 , 1.2 × j=1,4 λj −3 −4 10 , 9.3 × 10 ) and λj = (1216, 1026, 973, 950 ) for Lyα, β, γ and η, respectively.

The wavelength range of λobs is λj+1(1 + z) < λobs < λj(1 + z). One needs to select the samples which have the necessary wavelength coverage

for determining the dust extinction as to investigate the wavelength-dependence of dust extinction in the UV/optical/near-IR and its effects on the afterglow SEDs. To this end, we investigate the host galaxies of long-duration bursts for which a wealth

of data on the afterglow are available. For observations taken at slightly different epoches, we apply a correction using the temporal dependence of GRB afterglows

−α Fν(t) ∝ t (where α is the decay index of the fitted light curve) and bring all values to the same epoch.

In this Chapter, we apply the “Drude” model discussed in Chapter 2.3, 2.4 to explore the extinction properties of the dust in the distant universe through the

afterglows of high-redshifted GRBs.

2The highest redshifted GRB 090423 (z ≈ 8.26).

85 5.3 Results

We build a sample composed of 28 long bursts. The sample is selected by requir- ing that (i) they are at a redshift z > 2, and (ii) high-quality multiband (mainly

UV/optical/near-IR) afterglow photometry data are available. This GRB host galaxy sample spans a redshift interval 2.00 < z < 6.95, with a median value z ' 3.3. In Tables 5.1,5.2, we respectively tabulate the model parameters for fitting the afterglow

SEDs using the MW, LMC, SMC extinction templates and the Drude approach. The fits are presented in Figures 5.1–5.7.

GRB 971214. We constructed the SED (KJIC RC V ) of GRB 971214 at z ≈ 3.42 (Kulkarni et al. 1998) with data from Halpern (1998); Ramaprakash et al. (1998); and Wijers & Galama (1999). Halpern (1998) found a strong spectral curvature in their data and inferred a large extinction E(B − V ) ≈ 0.4 on the assumption of average

Galactic extinction law, and a very steep spectrum with β ≈ 2.5. Kann et al. (2006) found the best fit in SMC dust law with AV ≈ 0.44 ± 0.21 mag and β ≈ 0.5 ± 0.58. Starling et al. (2008) also derived the best-fitting model of a power law plus SMC extinction with E(B−V ) ≈ 0.031. The Drude approach derives AV ≈ 0.20±0.06 mag and β ≈ 0.14 ± 0.04 and an extinction curve almost identified to that of the SMC (see Fig. 5.1).

GRB 000131. We constructed the SED (KHJIRV ) of GRB 000131 at z ≈ 4.50

(Andersen et al. 2000) with data from Andersen et al. (2000). Andersen et al. (2000) found the best fit with a power law spectrum with Lyman forest absorption and SMC reddening (AV ≈ 0.18 mag, and β ≈ 0.70). Kann et al. (2006) found the best fit with a straight power law (no dust model constrain) shows no extinction

(AV ≈ 0 mag) and β ≈ 0.66± 0.34. The Drude approach derives AV ≈ 0.56±0.30 mag

86 and β ≈ 0.10 ± 0.05 and an extinction curve almost identified to that of the SMC (see Fig. 5.1).

GRB 000926. We constructed the SED (KHJIC RC VBU) of GRB 000926 at z ≈ 2.07 (Fynbo et al. 2000) with data from Fynbo et al. (2001). Fynbo et al. (2001) found best fit was achieved for a SMC extinction law with modest extinction of

AV ≈ 0.18 ± 0.06 mag and a spectral index β ≈ 1.00 ± 0.18. Kann et al. (2006)

derived a good agreement (AV ≈ 0.15 ± 0.07 mag and β ≈ 1.01 ± 0.16 for SMC dust)

with Fynbo et al. (2001). The Drude approach derives AV ≈ 0.35 ± 0.11 mag and β ≈ 0.80 ± 0.25 and an extinction law closely resembling that of the LMC but lacking the 2175 Å bump (see Fig. 5.1).

GRB 011211. We constructed the SED (KJIC RC VB) of GRB 011211 at z ≈ 2.14 (Fruchter et al. 2001) with data from Holland et al. (2002) and Jakobsson et al.

(2003). Holland et al. (2002) found a very low AV ≤ 0.03 mag and β ≈ 0.61±0.15 by using the extinction law (RV = 3.1) of Cardelli, Clayton, & Mathis (1989). Jakobsson et al. (2003) found that SMC dust gives the best fit with AV ≈ 0.08 ± 0.08 mag and β ≈ 0.56 ± 0.19. Kann et al. (2006) found that SMC dust gives a best fit with a moderate AV ≈ 0.25 ± 0.06 mag and β ≈ 0 ± 0.15. The Drude approach derives

AV ≈ 0.24 ± 0.06 mag and β ≈ 0.14 ± 0.03 and an extinction law closely resembling that of the LMC but lacking the 2175 Å bump (see Fig. 5.1).

GRB 020124. We constructed the SED (KsJIC RC BM ) of GRB 020124 at z ≈ 3.22 (Hjorth et al. 2003) with data from Hjorth et al. (2003). Hjorth et al. (2003)

found AV ≤ 0.2 mag by fixing β > 0.5 for SMC dust, deeming β < 0.5 unrealistic. They additionally employ a synthetic B-band point derived from extrapolating the spectrum and found β ≈ 0.31 ± 0.43 from a free fit of SMC dust. Without B-

87 band point, Kann et al. (2006) found the best fit with AV ≈ 0.11 ± 0.85 mag and

β ≈ 0.28 ± 0.33 for SMC dust. The Drude approach infers AV ≈ 0.24 ± 0.10 mag and β ≈ 0.35 ± 0.14 and an extinction law closely resembling that of the LMC but lacking the 2175 Å bump (see Fig. 5.2).

GRB 030226. We constructed the SED (KHJIC RC VB) of GRB 030226 at z ≈ 2.00 (Ando et al. 2003) with data from Klose et al. (2004) and Pandey et al. (2004).

Pandey et al. (2004) derived an extinction law similar to that in starburst galaxies (Calzetti et al. 1997) with β ≈ 0.55 and E(B − V ) ≈ 0.15 mag. Klose et al. (2004)

found β ≈ 0.70 ± 0.03, with no evidence for additional reddening AV ≈ 0 mag by dust (Milky Way-like dust, as well as SMC-like dust) in the GRB host galaxy. Kann et al. (2006) found a consistent result with Klose et al. (2004), a SMC dust model

with AV ≈ −0.06 ± 0.04 mag and β ≈ 0.77 ± 0.06. The Drude approach infers

AV ≈ 0.10 ± 0.01 mag and β ≈ 0.58 ± 0.07 and an featureless extinction curve, steeply rising to far-UV (see Fig. 5.2).

GRB 030323. We constructed the SED (KSHJIC RC VB) of GRB 030323 at z ≈ 3.37 (Vreeswijk et al. 2003) with data from Vreeswijk et al. (2004). Vreeswijk et

al. (2004) do not fit the light curves, but analyse the SED at different post-burst times from observations at near-identical epochs. They fix β ≈ 0.28, derived from

the α-β relations (βexp = (α + 1)/2). Using this value, they found the best fit with

MW dust extinction curve (AV ≈ 0.5). Kann et al. (2006) found the SED of this burst is unusual: the B band can not be included due to Lyman dampening, and the spectrum (a strong DLA) shows that the V band is also unreliable. With the

exception of the KS band, the SED shows a strong curvature without being very

steep. Kann et al. (2006) tried to fit the SED with the KS band (removing the KS

88 band results in very good fits that have β ≤ 0). Fixing β ≈ 0.28, Kann et al. (2006)

yield AV ≈ 0.70, AV ≈ 0.41 and AV ≈ 0.26 mag for MW, LMC and SMC dust curves,

respectively. If fixing the β ≈ 0.28, we also derive a consistent result (AV ≈ 0.75,

AV ≈ 0.52 and AV ≈ 0.35 mag for MW, LMC and SMC dust curves, respectively) with Kann et al. (2006), but with slightly larger error bars (7.12, 3.52 and 4.95) than the none β fixed model (5.48, 3.02 and 4.50) respectively. The Drude approach derives

AV ≈ 0.50 ± 0.07 mag and β ≈ 0.14 ± 0.02 and an extinction law closely resembling that of the LMC but lacking the 2175 Å bump (see Fig. 5.2).

GRB 030429X. We constructed the SED (KsHJIC RC V ) of GRB 030429X at z ≈ 2.65 (Weidinger et al. 2003) with data from Jakobsson et al. (2004). Jakobsson et al. (2004) found that the optical/near-infrared spectral energy distribution is best

fit with β ≈ 0.36 ± 0.12 reddened by an SMC-like extinction law with (a modest)

AV ≈ 0.34±0.04 mag. Kann et al. (2006) found a best fit with a lower β ≈ 0.22±0.24

and a slightly higher AV ≈ 0.40±0.10 mag for SMC dust model. The Drude approach

derives AV ≈ 0.40 ± 0.07 mag and β ≈ 0.26 ± 0.05 and an extinction law closely resembling that of the SMC (see Fig. 5.2).

GRB 050505. We constructed the SED (KsHJRC ) of GRB 050505 at z ≈ 4.27 (Berger et al. 2005) with data from Hurkett et al. (2006). Hurkett et al. (2006) derived a a good fit by the SMC-like extinction curve with AV ≈ 0.3 mag and the low-frequency index β1 ≈ 0.41±0.05 and high-frequency index β2 ≈ 0.90 . The Drude approach derives AV ≈ 1.145 ± 0.67 mag and β ≈ 0.37 ± 0.22 and an extinction law closely resembling that of the MW (see Fig. 5.3).

GRB 050730. We constructed the SED (KJIRV ) of GRB 050730 at z ≈ 3.97 (Chen et al. 2005) with data from the following sources: Pandey et al. (2006) and

89 Perri et al. (2005). Due to the high redshift (z ∼ 3.97) of the burst, the Ly-α break lies between the R and I pass-bands, making NIR frequencies essential to determine the correct spectral index of the burst. Pandey et al. (2005) used only I, J, K

data to determine the spectral index at the epoch of the SED with β ≈ 0.56 ± 0.06 and a negligible extinction AV ≈ 0.01 mag in the host (as well as Starling et al.

0 2005). Using an i IC JK SED, Kann et al. (2007) found β0 ≈ 0.82 ± 0.041 (β0 being the spectral slope without any extinction correction) and β ≈ 0.52 ± 0.045,

AV ≈ 0.10 ± 0.015 mag for the preferred SMC dust. Chen et al. (2005) found a steep β ≈ 1.88 ± 0.01 from the continuum fitting of an echelle spectrum. The Drude

approach derives AV ≈ 0.29 ± 0.06 mag and β ≈ 0.17 ± 0.03 and an extinction law closely resembling that of the MW (see Fig. 5.3).

GRB 050814. We constructed the SED (KJIR) of GRB 050814 at z ≈ 5.29 (Jakob-

sson et al. 2006) with data from Jakobsson et al. (2006). Jakobsson et al. (2006)

found a best fit with an extinction of AV ≈ 0.9 mag with β ≈ 1.0 fixed using the parametrization of Calzetti et al. (2000). Curran et al. (2008) found a lower extinc-

tion AV ≈ 0.23 mag and a similar β ≈ 0.9 ± 0.5 by using the Pei model for the MW, SMC or LMC, or the Calzetti model for a star forming region. Both Jakobsson et al. (2006) and Curran et al. (2008) do not mention which dust model is the best

fit. The Drude approach deduces AV ≈ 0.92 ± 0.33 mag and β ≈ 0.17 ± 0.05 with an extinction curve similar to that of the MW with a relatively stronger 2175 Å bump (see Fig. 5.3).

0 GRB 050820B. We constructed the SED (KHJz IC RC V gBU) of GRB 050820B at z ≈ 2.60 (Prochaska et al. 2005) with data from the following sources: Vestrand et al. (2006), Cenko et al. (2006) and references therein. Cenko et al. (2006) found

90 β1b ≈ 0.57±0.06 and β2 ≈ 0.77±0.08, and AV ≈ 0 mag for all dust extinction curves. Kann et al. (2007) derived a steeper unextincted slope than Cenko et al. (2006) with

β ≈ 0.96±0.028, and a very low host extinction AV ≈ 0.065±0.008 mag, in agreement

with Cenko et al. (2006). The Drude approach derives AV ≈ 0.12 ± 0.03 mag and β ≈ 0.60±0.13 and an extinction law closely resembling that of the SMC (see Fig. 5.3).

GRB 060206. We constructed the SED (IRVB) of GRB 060206 at z ≈ 4.04 (Fynbo & Limousin 2006) with data from the following sources: Stanek et al. (2007), Curran et al. (2007), Monfardini et al. (2006) and Thöne et al. (2008a). Monfardini et al.

(2006) found β ≈ 0.7 using a broken power law. Thöne et al. (2008a) found that the SED is well fit with a single power law with β ≈ 0.93 ± 0.01 and a 3σ upper limit for the intrinsic optical/UV extinction of E(B − V ) < 0.01. The Drude approach

deduces AV ≈ 0.12 ± 0.02 mag and β ≈ 0.62 ± 0.09 with an extinction curve steeply rising to the far-UV (see Fig. 5.4).

0 0 0 GRB 060526. We constructed the SED (KSHJIC i RC r V g B) of GRB 060526 at z ≈ 3.22 (Berger & Gladders 2006) with data from Dai et al. (2007) and Thöne et al. (2008b). The decreasing flux in the B, g0 and V bands is due to the Lyman forest

0 0 blanketing. Thöne et al. (2008b) found the best fit for the SED (KSHJIC i RC r ) by

SMC dust with AV ≈ 0.049 ± 0.041 mag and β ≈ 0.495 ± 0.144. The Drude approach

derives AV ≈ 0.23 ± 0.07 mag and β ≈ 0.26 ± 0.08 with an extinction curve similar to that of the LMC but with a weak 2175 Å bump (see Fig. 5.4).

GRB 060607A. We constructed the SED (HirgB) of GRB 060607A at z ≈ 3.08

(Ledoux et al. 2006) with data from the following sources: Molinari et al. (2007), Ziaeepour et al. (2008) and Nysewander et al. (2009). Nysewander et al. (2009) found

+0.14 AV ≈ 0.41−0.30 mag and β ≈ 0.70 by using an extinction curve model of Reichart

91 (2001). The Drude approach derives AV ≈ 0.20 ± 0.02 mag and β ≈ 0.38 ± 0.03 with an extinction curve similar to that of the LMC but with a weak 2175 Å bump (see Fig. 5.4).

GRB 071025. We constructed the SED (KHJYIR) of GRB 071025 at z ≈ 5.2 Pagani et al. (2007) with data from Perley et al. (2009). Perley et al. (2009) found AV ≈ 1.09 mag and β ≈ 0.96 by using supernova-dust model of Maiolino et al.

(2004). The Drude approach derives AV ≈ 0.40 ± 0.09 mag and β ≈ 0.96 ± 0.21 with an extinction curve steeper than that of the LMC (see Fig. 5.4).

0 0 0 GRB 080129. We constructed the SED (KSHJz r i ) of GRB 080129 at z ≈ 4.35 (Greiner et al. 2009a) with data from Greiner et al. (2009a). Greiner et al. (2009a) found a strong foreground extinction (≈ 3.4 mag) The Drude approach derives AV ≈ 0.19 ± 0.02 mag and β ≈ 0.42 ± 0.05 with a featureless, relatively flat extinction curve (see Fig. 5.5).

GRB 080310. We constructed the SED (KHJIVBU) of GRB 080310 at z ≈ 2.42 (Prochaska et al. 2008) with data from Perley et al. (2008). Perley et al. (2008) found the best-fit with AV ≈ 0.10 ± 0.05 mag and β ≈ 0.56 ± 0.13 for SMC dust model. The Drude approach derives AV ≈ 0.09 ± 0.01 mag and β ≈ 0.64 ± 0.07 and with an extinction curve less steeper than SMC (see Fig. 5.5).

GRB 080413. We constructed the SED (KHJIRVB) of GRB 080413 at z ≈ 2.43 (Thöne et al. 2008) with data from Cobb (2008a). The Drude approach infers

AV ≈ 0.14 ± 0.03 mag and β ≈ 1.15 ± 0.28 with an extinction curve similar to that of the LMC but without a 2175 Å bump (see Fig. 5.5).

92 GRB 080607. We constructed the SED (KHJI, clear, V ) of GRB 080607 at z ≈ 3.04 (Prochaska et al. 2008) with data from Updike et al. (2008). Prochaska et al.

(2009) found the best fit with RV ≈ 4.0 ± 0.23, AV ≈ 3.2 ± 0.5 mag, β ≈ 0.67 ± 0.05 and a positive detection of the 2175 Å bump for Fitzpatrick & Massa (1990) dust

model. The Drude approach derives AV ≈ 1.21±0.23 mag and β ≈ 1.06±0.20 and an extinction law closely resembling that of the MW with a 2175 Å bump (see Fig. 5.5).

GRB 080913. We constructed the SED (KHJz0i0) of GRB 080913 at z ≈ 6.72 (Fynbo et al. 2008) with data from Greiner et al. (2009b). Greiner et al. (2009b)

found that the best fit power law has β ≈ 1.12 ± 0.16 and no evidence for extinction

in the host frame is found (AV ≈ 0.0 mag, which means no differences between SMC,

MW, and LMC dust models). The Drude approach derives AV ≈ 0.27 ± 0.08 mag and β ≈ 0.48 ± 0.14 and an extinction law closely resembling that of the LMC with a slightly weak 2175 Å bump (see Fig. 5.6).

0 0 0 GRB 080916C. We constructed the SED (KSHJz i r ) of GRB 080916C at z ≈ 4.35 (Greiner et al. 2009c) with data from Greiner et al. (2009c). Greiner et al.

(2009c) found that the SED is best fit with no extinction AV ≈ 0.0 mag in the

host frame, a power law of spectral index β ≈ 0.38, and AV ≈ 0.98 mag for the

foreground galactic reddening. The Drude approach deduces AV ≈ 0.17 ± 0.03 mag and β ≈ 0.11 ± 0.02 with an extinction curve resembling that of the MW but with a

very weak 2175 Å bump (see Fig. 5.6).

GRB 081029. We constructed the SED (KHJIRV ) of GRB 081029 at z ≈ 3.85

(D’Elia et al. 2008) with data from Cobb et al. (2008b). The Drude approach derives

AV ≈ 0.13 ± 0.02 mag and β ≈ 0.88 ± 0.11 and an extinction law closely resembling that of the LMC but lacking the 2175 Å bump (see Fig. 5.6).

93 GRB 081118. We constructed the SED (KHJz0i0r0g0) of GRB 081118 at z ≈ 2.58 (D’Elia et al. 2008) with data from Loew et al. (2008). The Drude approach infers

AV ≈ 0.96 ± 0.37 mag and β ≈ 0.61 ± 0.23 with a featureless, relatively flat Calzetti type extinction curve (see Fig. 5.6).

GRB 081121. We constructed the SED (KHJz0i0r0g0) of GRB 081121 at z ≈ 2.51 (Berger & Rauch 2008) with data from Loew et al. (2008). The Drude approach

infers AV ≈ 0.14 ± 0.06 mag and β ≈ 0.23 ± 0.09 and an extinction law less steeper than SMC (see Fig. 5.7).

GRB 081222. We constructed the SED (KHJz0i0g0) of GRB 081222 at z ≈ 2.77 (Cucchiara et al. 2008) with data from Updike et al. (2008). The Drude approach derives AV ≈ 0.66 ± 0.12 mag and β ≈ 0.06 ± 0.01 and an extinction law closely resembling that of the MW with a 2175 Å bump (see Fig. 5.7).

GRB 090313. We constructed the SED (z0i0r0g0) of GRB 090313 at z ≈ 3.38 (Chornock

et al. 2009) with data from Perley (2009b) and Berger (2009). Perley (2009b) found

that the optical SED is well-fit assuming a moderate (AV ≤ 0.4 mag) amount of SMC-like dust extinction. This value was later refined by Kann et al. (2009) to

AV ≈ 0.34 ± 0.15 mag. The Drude approach derives AV ≈ 0.56 ± 0.35 mag and β ≈ 0.14 ± 0.09 and an extinction law closely resembling that of the SMC (see Fig. 5.7).

GRB 090323. We constructed the SED (z0i0r0g0) of GRB 090323 at z ≈ 3.57 (Chornock

et al. 2009) with data from Updike et al. (2009). Kann et al. (2009) found that the SED is well-fit by a small amount of SMC dust. The Drude approach derives

AV ≈ 0.55 ± 0.10 mag and β ≈ 0.12 ± 0.02 and an extinction law closely resembling

94 that of the SMC (see Fig. 5.7).

5.4 DISCUSSION

Unlike the models based on a pre-assumption of a specific extinction law which as a result restricts the derived extinction laws to one of the adopted templates, the Drude approach is more flexible in determining the true wavelength dependence of the host extinction. As shown in §2.2, the Drude approach reveals a wide diversity of extinction laws for the sample of 28 GRBs:

• Some bursts exhibit a featureless extinction law just like that of SMC (GRB 971214, 000131, 030429X, 050820B, 071025, 090313, 090323) with a varying degree of steepness.

• Some bursts exhibit an extinction law just like that of the MW/LMC (with

RV ≈ 3.1) but (i) with a stronger 2175 Å bump (GRB 050505, 050814, 070802, 080607, 081222), (ii) with a much weaker 2175 Å bump (GRB 050730, 060206, 060526, 080913, 080916C), or (iii) simply with the 2175 Å bump completely re-

moved (GRB 000926, 011211, 020124, 030226, 030323, 060607A, 080310, 080413, 081029, 081121).

• Some bursts exhibit a featureless, flat extinction law (GRB 080129, 081118).

Applying the “Drude” model to fit the observation spectra afterglow of 28 GRBs, we find that the afterglow photometry of GRBs (050505, 050730, 050814, 070802,

080607 and 081222) provide evidence for the presence of the 2175 Å extinction feature in their GRB host galaxies (Krühler et al. 2008; Elíasdóttir et al. 2008; Liang & Li 2009; Prochaska et al. 2009). The extinction quantities, the shapes of the deduced

95 extinction curves, and the presence or absence of the 2175 Å bump do not appear to correlate with redshifts (see Fig. 5.14b).

For bursts lacking the 2175 Å bump, models based on a priori assumption of

specific template extinction laws often infer a SMC-type extinction with a small AV . As demonstrated in this work, among the 23 GRBs (of the entire sample of 28 bursts) which lack the 2175 Å bump, seven bursts have an extinction curve similar to that

of the SMC, The extinction curves of the other 16 bursts display a wide range of

shapes, ranging from being relatively flat to very steep. The AV values derived from the Drude approach is generally ∼ 2–5 times larger than that derived from assuming

a SMC template extinction law provided that the “true” extinction law inferred from the Drude approach is not as steep as that of the SMC. Dust sublimation might explain the lack of the 2175 Å feature for small size grains

is tent to be sublimated and the dust size distribution is dominated by larger grains. One naive interpretation would be that at these high redshift z > 5 we are approaching the epoch when dust had no time to form in large quantities, both because of the

lower metallicities and because AGB stars did not have enough time to inject dust into the ISM. Higher gas density may favor the growth of grains and yielding to a flatter extinction curve, which would significantly reduce the reddening by dust.

An additional or alternative possibility is that these extreme redshifts the main dust production mechanism is different. While at low redshift z < 5, dust is predominantly produced in AGB stars, at very high redshift z > 5 dust may be predominantly

produced by SNe (Schneider et al. 2003; Nozawa et al. 2003; Todini & Ferrara 2001).

We select a sample of 24 GRBs having known hydrogen column densities NH which range from 1.0 × 1019 cm−2 to 1.0 × 1023 cm−2 (see Kann et al. 2006 for references).

In Fig. 13b we show the distribution of NH for these bursts. We see that the majority

21 22 −2 of these bursts have NH in the range of ∼ 1.0 × 10 – 1.5 × 10 cm . To explore the

96 dust-to-gas ratios of these bursts, we compare AV with NH in Fig. 13d. Also plotted in Fig. 13d are the extinction-to-gas ratios of the MW, LMC and SMC.3

We see that the majority of these bursts have a dust-to-gas ratio smaller than

that of the MW, consistent with previous studies (e.g. see Galama & Wijers 2001, Stratta et al. 2004, Kann et al. 2006). But ∼ 30% of the bursts have a dust-to-gas ratio comparable to or higher than that of the LMC. In general, the dust-to-gas ratio

derived here is higher than deduced from previous studies which estimated AV from fitting the GRB afterglow SEDs with a SMC-type extinction law. Finally, the dust- to-gas ratio does not seem to correlate with the shape of the extinction curve inferred

from the Drude approach.

We fit the inferred extinction curves using a mixture of spherical amorphous sili- cate and graphite dust with the same exponential-cutoff power-law size distribution

(e.g. see Kim et al. 1994)

R a max sil gra −αdust Aλ/AV = (Asil C (a, λ) + Agra C (a, λ)) a exp (−a/ac) da (5.1) amin ext ext

where the lower (upper) cutoff size amin (amax) is taken to be 50 Å (1 µm) for both silicate and graphite dust; the power-law indices αdust and the exponential-cutoff sizes

sil gra ac are treated as free parameters; Cext (Cext ) is the extinction cross section of silicate (graphite) dust. As shown in Fig. 5.1-5.7, this simple dust model closely fits the extinction curves of all 28 bursts. In Table 5.3, we present the model parameters.

In Fig. 5.14, we plot the derived strength (c1) of the far-UV extinction rise, the

strength (c4) of the 2175 Å extinction, the extinction factor RV , host galaxy visual ex-

tinction AV , the hydrogen column density NH , dust abundance Mdust mass-weighted mean dust sizes as a function of redshift z. and the metallicity as a function of red-

3 21 22 22 −2 −1 We adopt NH/E(B − V ) ≈ 4.93 ± 0.28 × 10 , 2 ± 0.5 × 10 , 4.4 ± 0.7 × 10 cm mag and RV ≈ 3.08, 3.16 and 2.93 for the MW (Diplas & Savage 1994), LMC (Koornneef 1982) and SMC (Bouchet et al. 1985), respectively.

97 shift. For the 28 bursts at z > 2 discussed in this work, we do not see any strong evidence for the dependence of c1, c4, RV , AV , NH , Mdust or metallicity on z. In Fig. 5.15, we also find no strong evidence for the dependence of the derived host galaxy visual extinction AV , the strength (c1) of the far-UV extinction and the strength (c4) of the 2175 Å extinction on metallicity.

In Fig. 5.16, we find no evidence for the relationship of β = βX − 0.5. In Fig. 5.17, 3 models (Drude, FM and Polynomial) are used to fit the SN dust extinction curves. The fitting parameters are presented in Table 5.4. In Fig. 5.18, we compare the CCM with SMC, LMC, Calzetti and HD210121 extinction curves. We find that CCM is not able to restore the SMC, LMC, Calzetti and HD210121 models. In Fig 18.d, our

Drude model can have a best fit for CCM extinction curve with c1 = 7.86, c2 = 1.88, c3 = −1.05, and c4 = 0.07. In Fig. 5.19, We use two dust extinction models to derive the best-fitting model on 3 high redshift (z > 5) GRBs.

5.5 CONCLUSION

In this work, we have derived the quantities and wavelength dependence of the dust extinction along the lines of sight toward 28 GRBs (with z > 2) from fitting their afterglow SEDs using the Drude approach which does not require a priori assumption of a specific extinction law. The deduced extinction curves display a wide diversity of shapes, ranging from relatively flat curves to curves which are featureless and steeply rise toward the far-UV, and from curves just like that of the MW, LMC and SMC which are widely used as extinction templates to curves resembling that of the MW and LMC but lacking the 2175 Å bump. From the plot of the derived strength of the far-UV extinction rise, the strength of the 2175 Å extinction, the extinction factor

RV , host galaxy visual extinction AV , the hydrogen column density NH , and mass-

98 weighted mean dust sizes as a function of redshift z, we find no evidence that dust evolve as redshift.

99 Table 5.1. Parameters for fitting the afterglow SEDs with the MW, LMC and SMC template 2 extinction laws. The goodness of the fit is measured by χ /Nobs, where Nobs is the number of observational data points.

MW Dust SMC Dust LMC Dust

2 2 2 GRB AV (mag) β log Fo χ /Nobs AV (mag) β log Fo χ /Nobs AV (mag) β log Fo χ /Nobs (µJy) (µJy) (µJy)

971214 0.16±0.04 0.44±0.12 7.20 0.55 0.18±0.05 0.13±0.03 2.30 0.11 0.26±0.07 0.14±0.03 2.35 0.17 000131 0.45±0.24 1.38±0.75 22.0 5.37 0.56±0.30 0.12±0.06 3.05 1.92 0.81±0.44 0.13±0.06 3.21 3.04 000926 0.14±0.03 1.26±0.39 20.3 4.03 0.20±0.06 0.91±0.28 15.2 0.23 0.27±0.08 0.91±0.29 15.3 1.39 011211 0.10±0.03 0.46±0.11 7.83 4.94 0.21±0.05 0.15±0.03 2.62 1.00 0.19±0.05 0.27±0.07 5.05 2.80 020124 0.16±0.06 0.67±0.27 10.6 0.42 0.21±0.08 0.35±0.14 5.87 0.15 0.29±0.12 0.33±0.13 5.61 0.18 030226 0.08±0.03 0.60±0.07 10.5 1.53 0.15±0.04 0.47±0.05 8.53 0.74 0.15±0.01 0.54±0.06 9.65 0.66 030323 0.52±0.07 0.69±0.10 11.3 5.48 0.40±0.05 0.10±0.01 2.56 4.59 0.58±0.08 0.10±0.01 2.68 3.02 030429X 0.07±0.02 1.00±0.19 16.1 5.51 0.42±0.08 0.17±0.03 3.65 0.79 0.10±0.02 0.97±0.18 15.4 3.60 050505 0.81±0.48 0.45±0.27 8.41 0.72 0.13±0.06 1.84±1.09 28.8 1.64 0.09±0.06 1.81±1.07 28.3 1.44 050730 0.25±0.05 0.36±0.07 8.41 0.32 0.16±0.03 0.16±0.03 5.36 0.72 0.28±0.05 0.13±0.02 4.62 0.17 050814 0.91±0.32 0.11±0.04 4.12 0.03 0.48±0.20 0.11±0.02 3.93 3.06 0.69±0.27 0.11±0.06 4.07 2.15 050820B 0.14±0.02 1.02±0.23 17.0 8.24 0.09±0.02 0.58±0.13 10.3 0.31 0.10±0.03 0.80±0.18 13.7 1.67 050904a 0.005±0.002 1.53±0.34 24.7 1.51 0.44±0.10 0.03±0.01 2.27 0.07 0.27±0.06 0.91±0.20 15.7 1.11 050904b 0.005±0.001 1.31±0.26 21.1 0.04 0.05±0.01 1.12±0.22 18.3 0.01 0.05±0.01 1.21±0.24 19.5 0.02 050904c 0.02±0.004 1.37±0.68 21.4 0.20 0.19±0.09 0.77±0.38 12.5 0.06 0.16±0.08 1.04±0.51 16.5 0.11 060206 0.12±0.02 0.74±0.11 13.3 0.17 0.14±0.02 0.56±0.09 10.6 0.16 0.14±0.02 0.66±0.10 12.0 0.07 060526 0.16±0.05 0.58±0.18 10.4 0.21 0.14±0.04 0.26±0.08 5.62 0.14 0.23±0.07 0.24±0.07 5.45 0.04 060607 0.08±0.03 0.56±0.05 11.8 3.51 0.16±0.01 0.45±0.04 10.1 4.72 0.13±0.03 0.51±0.04 11.1 2.85 071025 0.10±0.02 2.34±0.51 37.5 4.60 0.67±0.14 0.10±0.03 4.40 10.3 0.95±0.21 0.16±0.04 4.60 3.20 080129 0.07±0.02 0.53±0.06 9.72 0.44 0.10±0.03 0.29±0.03 6.12 0.77 0.09±0.02 0.42±0.05 8.07 0.43 080310 0.12±0.03 0.68±0.08 13.1 2.10 0.08±0.02 0.58±0.06 11.5 0.70 0.12±0.03 0.64±0.07 12.4 0.90 080413 0.15±0.02 1.27±0.31 21.0 3.31 0.12±0.03 1.16±0.28 19.4 2.52 0.12±0.03 1.22±0.30 20.3 2.79 080607 0.98±0.18 1.51±0.29 26.4 7.51 0.10±0.02 2.72±0.51 43.8 10.8 0.14±0.02 2.76±0.52 44.4 9.70 080913 0.20±0.06 1.36±0.39 22.5 0.54 0.31±0.09 0.34±0.10 7.20 0.26 0.38±0.11 0.65±0.19 11.9 0.03 080916 0.12±0.02 0.28±0.05 5.33 0.19 0.14±0.02 0.16±0.02 2.79 0.38 0.06±0.02 0.15±0.03 3.38 0.02 081029 0.08±0.02 1.09±0.13 19.3 1.21 0.13±0.01 0.85±0.10 15.7 2.57 0.08±0.02 0.98±0.12 17.7 1.71 081118 0.14±0.04 1.42±0.55 22.2 0.40 0.10±0.04 1.31±0.51 20.6 0.49 0.07±0.04 1.37±0.53 21.5 0.43 081121 0.10±0.04 0.40±0.16 8.26 0.12 0.16±0.04 0.27±0.11 6.33 0.02 0.09±0.03 0.34±0.13 7.37 0.04 081222 0.89±0.17 0.11±0.02 4.82 1.32 0.09±0.02 1.23±0.23 21.1 10.0 0.32±0.06 0.83±0.16 15.3 8.23 090313 0.26±0.16 2.20±1.38 34.9 0.02 0.49±0.31 0.08±0.07 3.44 0.05 0.44±0.27 1.20±0.75 19.9 0.03 090323 0.31±0.05 2.28±0.40 36.9 0.02 0.47±0.08 0.10±0.02 4.11 0.41 0.45±0.08 1.22±0.21 20.9 0.10

a,b,c(t = 0.47 days; t = 1.25 days; and t = 3.40 days, respectively.)

100 Table 5.2. Parameters for fitting the afterglow SEDs with the “Drude” approach.

d e 2 GRB z log(NH) Ref. c1 c2 c3 c4 AV β βX Ref. RV log Fo χ /Nobs (cm−2) (mag) (µJy)

971214 3.420 21.20±0.10 (1) 0.16 0.27 -1.97 0.01 0.20±0.06 0.14±0.04 1.2±0.4 (1) 3.50 2.90 0.16 000131 4.500 – – 0.20 0.27 -1.97 0.01 0.56±0.30 0.10±0.05 – – 3.55 3.00 1.65 000926 2.066 21.30±0.30 (2) 0.16 0.43 -1.96 0.00 0.35±0.11 0.80±0.25 0.7±0.2 (1) 3.30 14.0 0.17 011211 2.140 20.40±0.20 (3) 0.16 0.27 -1.97 0.01 0.24±0.06 0.14±0.03 1.2±0.1 (1) 3.50 3.22 1.62 020124 3.198 21.70±0.20 (4) 0.16 0.27 -1.97 0.01 0.24±0.10 0.35±0.14 – – 3.50 6.05 0.13 030226 2.000 20.50±0.30 (5) 0.10 0.27 -1.97 0.01 0.10±0.01 0.58±0.07 0.9±0.2 (1) 3.42 10.5 0.52 030323 3.372 21.90±0.07 (6) 0.15 0.27 -1.97 0.01 0.50±0.07 0.14±0.02 – – 3.49 3.21 4.45 030429X 2.650 21.60±0.20 (7) 0.15 0.25 -1.98 0.01 0.40±0.07 0.26±0.05 – – 3.48 5.18 1.27 050505 4.270 22.05±0.10 (8) 7.98 6.93 3.11 0.04 1.14±0.67 0.37±0.22 0.53 (2) 3.30 7.53 0.58 050730 3.967 22.15±0.10 (9) 0.23 0.77 -1.96 0.03 0.29±0.06 0.17±0.03 0.79 (3) 3.25 5.71 0.00 050814 5.300 – – 0.42 1.61 -1.94 0.06 0.91±0.93 0.17±0.17 0.51 (4) 3.25 5.21 0.00 050820B 2.612 21.00±0.10 (10) 0.17 0.29 -1.97 0.00 0.12±0.03 0.60±0.13 0.77 (5) 3.45 11.0 0.07 050904a 6.290 21.60±0.10 (11) 3.28 1.44 -1.61 0.01 0.39±0.09 0.17±0.04 – – 2.93 4.72 0.00 050904b 6.290 21.60±0.10 (11) 2.97 1.89 -1.46 0.01 0.07±0.01 1.13±0.23 – – 3.05 18.9 0.01 050904c 6.290 21.60±0.10 (11) 3.01 2.32 -1.67 0.01 0.27±0.13 0.82±0.40 – – 3.13 13.7 0.00 060206 4.048 20.85±0.10 (12) 0.65 0.89 -1.92 0.01 0.12±0.02 0.62±0.09 0.95 (6) 3.19 11.8 0.09 060526 3.221 20.20±0.20 (13) 0.20 0.51 -1.95 0.01 0.23±0.07 0.26±0.08 1.03 (7) 3.29 5.84 0.03 060607 3.082 16.85±0.10 (14) 0.53 0.88 -1.85 0.02 0.20±0.02 0.38±0.03 0.53 (5) 3.22 9.43 0.77 071025 5.200 20.95±0.05 (15) 4.00 2.50 -2.00 0.01 0.40±0.09 0.96±0.21 – – 3.12 17.4 3.85 080129 4.349 21.80±0.20 (16) 0.12 0.72 -1.94 0.00 0.19±0.02 0.42±0.05 – – 3.28 8.40 0.20 080310 2.420 18.70±0.10 (17) 1.44 0.93 -1.64 0.02 0.09±0.01 0.64±0.07 0.88 (5) 3.17 12.8 0.73 080413 2.433 21.85±0.15 (17) 0.10 0.37 -1.97 0.01 0.14±0.03 1.15±0.28 0.89 (8) 3.32 19.8 2.85 080607 3.036 22.58±0.04 (18) 0.04 0.65 -2.00 0.04 1.21±0.23 1.06±0.20 0.24 (9) 3.29 20.2 7.15 080913 6.695 22.00±0.40 (19) 3.84 1.23 -1.49 0.04 0.27±0.08 0.48±0.14 – – 2.89 9.60 0.05 080916 4.350 21.60±0.20 (20) 0.48 1.11 -1.85 0.01 0.17±0.03 0.11±0.02 0.5±0.3 (10) 3.22 3.00 0.01 081029 3.848 – – 0.15 0.27 -1.97 0.01 0.13±0.02 0.88±0.11 – – 3.49 16.6 1.97 081118 2.580 – – 0.14 2.00 -2.00 0.00 0.96±0.37 0.61±0.23 – – 3.29 10.9 0.36 081121 2.512 21.00±0.10 (21) 0.11 0.27 -1.98 0.01 0.14±0.06 0.23±0.09 – – 3.39 5.85 0.03 081222 2.770 20.70±0.10 (22) 0.33 0.79 -1.94 0.08 0.66±0.12 0.06±0.01 1.06±0.07 (11) 3.24 4.09 0.58 090313 3.375 21.10±0.30 (23) 0.18 0.27 -1.97 0.01 0.56±0.35 0.14±0.09 – – 3.53 4.06 0.06 090323 3.570 22.80±0.40 (24) 0.19 0.29 -1.97 0.01 0.55±0.10 0.12±0.02 – – 3.44 4.45 0.00

a,b,c(t = 0.47 days; t = 1.25 days; and t = 3.40 days, respectively.)

d(1)Reichart (1998); (2)Fynbo et al. (2002); (3)Vreeswijk et al. (2006); (4)Hjorth et al. (2003); (5)Shin et al. (2006); (6)Vreeswijk et al. (2004); (7)Jakobsson et al. (2004); (8)Berger et al. (2006); (9)Chen et al. (2005); (10)Prochaska et al. (2007); (11)Totani et al. (2005); (12)Fynbo et al. (2006); (13)Berger & Gladders (2006); (14)Chen et al. (2007); (15)Pagani et al. (2007); (16)Greiner et al. (2009a); (17)Ledoux et al. (2009); (18)Prochaska et al. (2009); (19)Greiner et al. (2009b); (20)Greiner et al. (2009c); (21)Godet et al. (2008); (22)Grupe et al. (2008); (23)Mao et al. (2009); (24)Perri et al. (2009) e(1)Nardini et al. (2006); (2)Berger et al. (2006); (3)D’Elia et al. (2005); (4)Jakobsson et al. (2006b); (5)Fox et al. (2008); (6)Fynbo et al. (2006); (7)Jakobsson et al. (2006); (8)Vreeswijk et al. (2008); (9)Prochaska et al. (2009); (10)Greiner et al. (2009); (11)Liang et al. (2009).

101 Table 5.3. Dust size distributions for the extinction curves derived from the “Drude” approach and modeled as a mixture of silicate and graphite grains for GRBs at z > 2.

2 d GRB Asil Agra αdust ac(µm) < a >(µm) mgra/(mgra + msil) χ /Nobs Metallicity Ref. 971214 1.93E-3 1.99E-4 3.37 0.26 8.45E-3 6.16E-2 0.50 – – 000131 1.30E-4 1.26E-5 3.59 0.45 8.06E-3 5.84E-2 0.26 – – 000926 2.62E-3 1.67E-4 3.33 0.38 8.60E-3 3.91E-2 0.31 8.54±0.05 (1) 011211 2.00E-3 1.86E-4 3.37 0.28 8.46E-3 5.61E-2 0.43 7.8±0.4 (2) 020124 1.95E-3 1.84E-4 3.38 0.27 8.43E-3 5.70E-2 0.43 – – 030226 7.10E-3 1.17E-3 3.25 0.26 8.74E-3 9.54E-2 0.16 – – 030323 2.09E-3 2.46E-4 3.37 0.27 8.45E-3 7.01E-2 0.36 7.4±0.2 (3) 030429X 1.53E-3 8.47E-5 3.41 0.24 8.35E-3 3.41E-2 2.47 – – 050505 4.52E-3 3.91E-3 3.24 0.19 8.69E-3 0.35 1.65 7.49 (4) 050730 1.68E-3 8.02E-4 3.35 0.23 8.47E-3 0.23 1.03 6.7±0.2 (5) 050814 1.12E-3 2.01E-3 3.33 0.18 8.47E-3 0.53 0.01 – – 050820B 2.86E-3 1.11E-4 3.34 0.28 8.53E-3 2.43E-2 1.41 8.1±0.1 (6) 050904a 6.19E-2 2.55E-2 3.14 0.23 9.01E-3 0.31 0.13 – – 050904b 6.22E-2 2.39E-2 3.03 0.17 9.25E-3 0.38 0.29 – – 050904c 6.89E-3 1.20E-2 3.20 0.26 8.87E-3 0.17 0.09 – – 060206 4.57E-3 5.26E-4 3.30 0.26 8.61E-3 6.87E-2 0.04 7.85 (7) 060526 1.83E-3 4.67E-4 3.35 0.28 8.50E-3 0.14 0.47 – – 060607 2.32E-3 1.01E-3 3.33 0.24 8.52E-3 0.22 0.12 8.69 (8) 071025 3.08E-3 2.12E-4 3.35 0.22 8.46E-3 4.22E-2 8.37 – – 080129 2.60E-2 5.56E-3 3.12 0.29 9.13E-3 0.12 0.39 – – 080310 8.42E-3 1.83E-3 3.26 0.19 8.64E-3 0.12 0.07 7.29 (9) 080413 2.23E-3 4.52E-4 3.34 0.33 8.55E-3 0.11 0.18 – – 080607 1.00E-2 1.02E-2 3.19 0.14 8.73E-3 0.39 2.85 – – 080913 3.32E-3 7.50E-4 3.36 0.14 8.34E-3 0.13 0.33 – – 080916 1.31E-3 3.67E-4 3.37 0.40 8.51E-3 0.15 0.40 – – 081029 2.32E-3 3.47E-4 3.36 0.25 8.46E-3 8.73E-2 0.90 – – 081118 1.57E-2 5.36E-3 3.15 0.32 9.06E-3 0.18 0.11 – – 081121 1.60E-3 1.59E-4 3.39 0.28 8.41E-3 5.95E-2 0.95 – – 081222 3.96E-3 3.00E-3 3.29 0.14 8.49E-3 0.32 0.85 – – 090313 2.02E-3 1.55E-4 3.38 0.25 8.42E-3 4.70E-2 0.94 – – 090323 2.14E-3 2.34E-4 3.38 0.23 8.41E-3 6.53E-2 1.79 – –

a,b,c(t = 0.47 days; t = 1.25 days; and t = 3.40 days, respectively.) d(1)Fynbo et al. (2002); (2)Mirabal et al. (2003); (3)Vreeswijk et al. (2004); (4)Beger et al. (2006); (5)Starling et al. (2005); (6)Ledoux et al. (2005); (7)Fynbo et al. (2006); (8)Prochaska et al. (2008); (9)Fox et al. (2008)

102 Table 5.4. Dust size distributions for the extinction curves derived from the “Drude” approach and modeled as a mixture of silicate and graphite grains for GRBs at z < 2.

2 a GRB z Asil Agra αdust ac(µm) < a >(µm) mgra/(mgra + msil) χ /Nobs Metallicity Ref. 970508 0.84 4.25E-2 2.10E-3 2.89 0.08 9.28E-3 0.12 0.97 – – 980703 0.97 9.49E-2 6.50E-2 3.01 0.15 9.26E-3 0.30 1.15 7.60 (1) 990123 1.60 1.09 0.16 2.84 0.17 9.93E-3 8.46E-2 0.45 – – 990510 1.62 4.12E-2 4.59E-3 3.10 0.27 9.17E-3 6.66E-2 1.11 – – 991208 0.71 2.70E-4 3.03E-5 3.58 0.16 7.97E-3 6.68E-2 7.45 8.02 (2) 991216 1.02 7.46E-4 5.81E-4 3.41 0.17 8.29E-3 0.33 6.15 – – 000911 1.06 0.89 1.20E-3 3.40 0.02 7.49E-3 6.71E-2 0.04 – – 010222 1.48 0.26 4.01E-2 2.94 0.22 9.66E-3 9.00E-2 0.88 – – 010921 0.45 6.75E-4 7.76E-5 3.47 0.28 8.25E-3 6.84E-2 0.35 8.24 (3) 011121 0.36 4.50E-4 4.56E-5 3.48 0.50 8.28E-3 6.10E-2 1.34 7.50 (1) 020405 0.69 1.78E-2 2.87E-3 3.18 0.22 8.88E-3 9.32E-2 4.78 8.33 (1) 020813 1.25 1.36E-3 6.16E-5 3.40 0.35 8.42E-3 2.81E-2 2.53 – – 030226 1.98 3.57E-3 2.26E-4 3.31 0.32 8.62E-3 3.88E-2 0.87 – – 030328 1.52 3.74E-3 6.28E-4 3.27 0.56 8.80E-3 9.69E-2 2.88 – – 030329 0.17 6.44E-3 1.28E-3 3.25 0.25 8.73E-3 0.11 9.35 8.13 (4) 040924 0.86 3.00 0.66 2.76 0.13 1.00E-2 0.12 4.26 8.10 (5) 041006 0.72 4.28E-4 2.78E-5 3.49 0.37 8.24E-3 3.99E-2 9.90 – – 050318 1.44 1.21E-2 1.1E-14 3.24 0.23 8.74E-3 5.9E-13 0.01 – – 050408 1.24 0.26 1.10E-7 3.01 0.14 9.23E-3 2.76E-7 0.25 – – 050525A 0.61 2.21E-3 7.31E-4 3.36 0.18 8.40E-3 0.17 0.01 – – 050824X 0.83 3.38E-3 1.41E-3 3.32 0.17 8.48E-3 0.21 1.57 – – 051111 1.55 1.39E-4 2.62E-5 3.59 0.34 8.04E-3 0.11 0.09 – – 060614 0.13 0.86 0.20 2.83 0.19 1.00E-2 0.13 0.48 – – 060729 0.54 3.07E-3 6.0E-13 3.33 0.36 8.59E-3 1.3E-10 0.08 – – 061121 1.31 8.00E-4 1.67E-3 3.36 0.13 8.33E-3 0.57 1.85 – – 061126 1.16 6.51 0.54 2.70 0.14 1.04E-2 5.03E-2 1.38 – – 070125 1.55 3.10E-2 2.39E-3 3.12 0.30 9.14E-3 4.71E-2 0.36 – – 070306 1.50 0.13 0.11 2.94 0.22 9.66E-3 0.34 6.45 – – 071003 1.60 3.42E-2 2.46E-3 3.12 0.28 9.12E-3 4.41E-2 0.40 – – 080319B 0.94 9.85E-5 5.78E-4 3.43 0.22 8.29E-3 0.20 2.36 – – 080330 1.51 6.86E-2 1.56E-2 3.05 0.20 9.24E-3 0.13 5.16 – – 080514B 1.80 6.37E-2 2.12E-2 3.05 0.21 9.26E-3 0.18 0.27 – – 081008 1.97 1.24E-2 1.39E-4 3.23 0.26 8.79E-3 7.12E-3 0.05 – –

a(1)Savaglio et al. (2009); (2)Levesque et al. (2009); (3)Levesque et al. (2010); (4)Gorosabel et al. (2005); (5)Wiersema et al. (2008).

103 Table 5.5 Parameters for fitting the SN dust extinction with the “Drude” model, FM template extinction law, and 9 order Polynomial.

Drude∗ 2 c1 c2 c3 c4 χ /N 4.60 2.50 -110 0.95 0.15 FM 2 c1 c2 c3 c4 RV xo γ χ /N 4.60 2.50 -110 0.95 2.08 8.80 13.25 0.23 Polynomial (9 order) 2 c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 χ /N -1.84 5.37 -6.02 3.53 -1.11 0.19 -0.02 9.32E-4 -1.12E-5 3.84E-7 0.02

∗ 0 λ0 = 0.28 (0.2175 in our previous paper), and λ0 = 0.10 (0.08 in our previous paper).

Table 5.6. Parameters for fitting the afterglow SEDs with the SN dust extinction law.

2 GRB AV (mag) β log Fo(µJy) χ /Nobs 050814 0.11±0.03 0.76±0.25 12.9 0.34 050904a 0.13±0.02 1.13±0.17 18.5 3.0E-4 050904b 0.02±0.003 1.25±0.14 19.7 7.0E-3 050904c 0.06±0.01 1.24±0.20 19.1 0.02 071025 0.29±0.07 0.91±0.15 15.8 0.06 080913 0.06±0.01 1.24±0.12 20.0 0.31

a,b,c(t = 0.47 days; t = 1.25 days; and t = 3.40 days, respec- tively.)

104 Figure 5.1 Upper panel (a): fitting the SED of the afterglow of GRB 971214 with the “Drude” approach (red) and the MW (black), LMC (blue) and SMC (green) templates for the GRB host extinction curve. Upper panel (b): comparison of the MW (black), LMC (blue), and SMC (green) extinction laws with that derived from the Drude approach (red). Upper panel (c): fitting the derived extinction curve (red solid line and black filled circles) with a mixture of amorphous silicate (cyan dotted line) and graphite dust (green dashed line). The blue solid line plots the resulting model extinction curve. 2nd Upper Panel: same as the upper panel but for GRB 000131. 3rd Upper Panel: same as the upper panel but for GRB 000926. Bottom panel: same as the upper panel but for GRB 011211.

105 Figure 5.2 Same as Figure 5.1 but for GRB 020124, GRB 030226, GRB 030323, and GRB 030429X.

106 Figure 5.3 Same as Figure 5.1 but for GRB 050505, GRB 050730, GRB 050814, and GRB 050820B.

107 Figure 5.4 Same as Figure 5.1 but for GRB 060206, GRB 060526, GRB 060607, and GRB 071025.

108 Figure 5.5 Same as Figure 5.1 but for GRB 080129, GRB 080310, GRB 080413, and GRB 080607.

109 Figure 5.6 Same as Figure 5.1 but for GRB 080913, GRB 080916C, GRB 081029, and GRB 081118. Also shown in the bottom panel (b) is the so-called “Calzetti” attenua- tion law of starburst galaxies (cyan line).

110 Figure 5.7 Same as Fig 5.1 but for GRB 081121, GRB 081222, GRB 090313 and GRB 090323.

111 Figure 5.8 Fitting the derived extinction curve (red solid line and black filled circles) with a mixture of amorphous silicate (cyan dotted line) and graphite dust (green dashed line). The blue solid line plots the resulting model extinction curve. The GRB hosts are selected at z < 2.0.

112 Figure 5.9 Fitting the derived extinction curve (red solid line and black filled circles) with a mixture of amorphous silicate (cyan dotted line) and graphite dust (green dashed line). The blue solid line plots the resulting model extinction curve. The GRB hosts are selected at z < 2.0.

113 Figure 5.10 Fitting the derived extinction curve (red solid line and black filled circles) with a mixture of amorphous silicate (cyan dotted line) and graphite dust (green dashed line). The blue solid line plots the resulting model extinction curve. The GRB hosts are selected at z < 2.0.

114 Figure 5.11 Upper panel (a): fitting the SED of the afterglow of GRB 050904 at t ≈ 0.47 days with the “Drude” approach (red) and the SN (blue) templates for the GRB host extinction curve. Upper panel (b): comparison of the SN (blue) extinction laws with that derived from the Drude approach (red). Upper panel (c): fitting the derived extinction curve (red solid line and black filled circles) with a mixture of amorphous silicate (black dotted line) and graphite dust (black dashed line). The black solid line plots the resulting model extinction curve. Middle Panel: same as the upper panel but for GRB 050904 at t ≈ 1.25 days. Bottom panel: same as the upper panel but for GRB 050904 at t ≈ 3.40 days.

115 Figure 5.12 (a)Upper panel: We present the GRB host extinction curves which have an extinction curve almost identified to that of the SMC (green lines), LMC (blue lines), MW (red lines) and Calzetti (cyan lines) respectively. The GRB hosts are selected at z > 2.0. Bottom panel: We present the GRB host extinction curves which have an extinction curve almost not identified to that of the SMC, LMC, MW and Calzetti respectively. (b)Same as (a), but for the GRB hosts are selected at z < 2.0.

116

25

200 GRBs 40 (a) (c)

63 GRBs 20

30

15

20

10 Number Number

10

5

0 0

0 2 4 6 8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Redshif t (z) A (mag)

V

10

(d) (b) 23

8

SMC ) 2 - LMC

22

6

MW / cm H

Number 4

21 log( N

2

20

0

0.0 0.5 1.0 1.5 2.0 20.0 20.5 21.0 21.5 22.0 22.5 23.0

-2

A (mag)

V log ( N / cm )

H

Figure 5.13 (a)Histogram of the total sample (200 objects, blue region) of GRBs with measured redshift and 63 objects (red region) are selected, where 28 ob- jects studied in this work, 33 objects in Liang & Li (2010), and 2 objects (GRB 000301C, and 021004) in Li et al. (2008). The redshift data come from http://www.mpe.mpg.de/jcg/grbgen.html. (b) Distribution of the hydrogen column densities NH along the lines of sight toward the bursts in their host galaxies. (c) Distribution of the derived host galaxy visual extinction AV with mean value at 0.41 mag). (d) Dust-to-gas ratios in the host galaxies along the lines of sight toward 47 GRBs. Also plotted are that of the MW, LMC and SMC.

117 Figure 5.14 (a) Derived strength (c1) of the far-UV extinction rise as a function of redshift. (b) Derived strength (c4) of the 2175 Å extinction (in the source frame) as a function of redshift. (c) Derived extinction factor RV (in the source frame) as a function of redshift. (d) Derived host galaxy visual extinction AV (in the source frame) as a function of redshift. (e) The hydrogen column density NH (in the source frame) as a function of redshift. (f) Mass fractions of graphite dust as a function of redshift z for all 63 bursts. Also shown are the mass fractions of graphite of the MRN silicate graphite model (red dashed line; Mathis et al. 1977) and the WD silicate-graphite polycyclic aromatic hydrocarbon model (green dot-dashed line; Weingartner & Draine 2001). (g) Mass-weighted mean dust sizes as a function of redshift z. Also shown are the mean dust sizes of the MRN silicate-graphite model (dashed line; Mathis et al. 1977) and the WD silicate-graphite-PAH model (dot line; Weingartner & Draine 2001) (h) The metallicity as a function of redshift. For the 63 bursts discussed, we do not see any strong evidence for the dependence of c1, c4, RV , AV , NH , mgra or metallicity on z.

118 Figure 5.15 (a)Derived strength (c1) of the far-UV extinction rise (in the source frame) as a function of metallicity. (b) Derived strength (c4) of the 2175 Å extinction (in the source frame) as a function of metallicity.(c) Derived host galaxy visual extinction AV (in the source frame) as a function of metallicity. For the 22 bursts selected, we do not see any strong evidence for the dependence of c1, c4 or AV on metallicity.

119

4

1

X

.1

X

.01

1 4 .01 .1

Figure 5.16 The relationship of the intrinsic power-law slope of the optical afterglow β to that of the X-ray afterglow βX .

120 Figure 5.17 We use Drude approach, FM and 9 order Polynomial model to fit the SN and QSO at z ≈ 6.2 extinction curve. The parameters for Drude model: c1 = 4.6, c2 = 2.5, c3 = −110, c4 = 0.95, λ1 ≈ 0.10 (instead of 0.08) and λ2 ≈ 0.280 (instead of 0.2175). The parameters for FM model: c1 = −3.8, c2 = 2.7, c3 = −2580, c4 = −0.5, RV = 2.1, X0 = 8.8, and γ = 13.2. The parameters for 9 order Polynomial model: c0 = −5.40, c1 = 15.79, c2 = −17.69, c3 = 10.38, c4 = −3.29, c5 = 0.58, c6 = −0.057, c7 = 0.0027, c8 = −3.30E − 5, and c9 = −1.13E − 6.

121 Figure 5.18 We compare the CCM with SMC, LMC, Calzetti and HD210121 extinc- tion curves. We find that CCM is not able to restore the SMC, LMC, Calzetti and HD210121 models. In (d), our Drude model can have a best fit for CCM extinction curve with c1 = 7.86, c2 = 1.88, c3 = −1.05, and c4 = 0.07.

122 Figure 5.19 We use two dust extinction models to derive the best-fitting model on 3 high redshift (z > 5) GRBs.

123 Chapter 6

Summary

In this thesis, we presented a systematic study of the properties of extragalactic dust of gamma-ray bursts (GRBs).

First, in view of the shortcomings of the prior assumption of a template extinction law, we propose a novel approach - the “Drude” model to derive the wavelength- dependence of the extinction for the dust in GRB host galaxies, instead of adopting

any known extinction laws as a template. This “Drude” approach can reproduce the extinction curves widely adopted as template extinction laws in GRB afterglow SED modeling, clearly demonstrating the advantages of the proposed formula over any

template extinction laws with a fixed wavelength-dependence shape: with the widely- adopted conventional extinction laws self-contained in Eq.(2.2) and the capability of revealing extinction laws differing from the conventional ones, the proposed formula

is more flexible and more powerful in modeling the afterglow SEDs. Second, we explore the extinction properties of the dust (particularly the 2175 Å extinction feature) in the distant universe through the afterglows of high-redshifted

GRBs based on the “Drude” model. We select GRB 070802 at z ≈ 2.45 (which shows clear evidence for the 2175 Å extinction bump) and GRB 050904 at z ≈ 6.29, the 3rd most distant GRB observed to date. We fit their afterglow spectra to determine the extinction of their host galaxies and found (i) their extinction curves differ substan-

124 tially from that of the MW, SMC and LMC; and (ii) the 2175 Å extinction feature appears to be also present in GRB 050904 at z ≈ 6.29.

Third, we select a large sample (33 objects at z < 2 and 27 objects at z > 2) of GRBs. We explore the dust properties of the distant universe by applying var- ious dust extinction models (“Drude” model, Milky Way, Large Magellanic Cloud, and Small Magellanic Cloud) to fit the observed optical-NIR afterglows. From the derived strength of the far-UV extinction rise, the strength of the 2175 Å extinction, the total-to-selective extinction ratio RV , host galaxy visual extinction AV , the hy-

drogen column density NH , dust abundance Mdust, mass-weighted mean dust sizes as a function of redshift z, we find no evidence that dust evolves as redshift.

Fourth, we investigate the dependence of metallicity and star formation rate on redshift. No evidence can be found that metallicity evolves as redshift. However, the

star formation rate does evolve as redshift and we propose a power law distribution with exponential cutoff model to investigate the evolution of star formation rate on

redshifts. Our model gives the best fit with the power index (α2 = 1.93 ± 0.20) and the cutoff point at (z = 2.20 ± 0.16). Finally, due to the bright future of GRB astronomy provided by the Swift mission, the number of high redshift bursts appears to be detecting will shed light on the early

Universe.

125 Bibliography

[1] Akerlof, C., et al. 1999, Nature, 398, 400

[2] Anderson, C.M., et al. 1996, AJ, 112, 2726

[3] Andersen, M. I., et al. 2000, A&A, 364, L54

[4] Ballantyne, D. R., et al. 2002, A&A, 389, L74

[5] Barnard, E.E. 1919, ApJ, 49, 1

[6] Barth, A. J., et al. 2003, ApJL, 584, L47

[7] Berger, E., et al. 2002, ApJ, 581, 981

[8] Berger, E., Cowie, L. L., Kulkarni, S. R., Frail, D. A., Aussel, H., & Barger,

A. J. 2003, ApJ, 588, 99

[9] Berger, E., & Mulchaey, J. 2005, GCN Circ. 3122

[10] Berger, E., & Gladders, M. 2006a, GCN Circ. 5170

[11] Berger, E., Penprase, B. E., Cenko, S. B., Kulkarni, S. R., Fox, D. B., Steidel, C. C., & Reddy, N. A. 2006b, ApJ, 642, 979

[12] Berger, E. 2009a, GCN Circ. 8984

[13] Berger, E., Cenko, S. B., Fox, D. B., & Cucchiara, A. 2009b, ApJ, 704, 877

126 [14] Bertoldi, F., Carilli, C. L., Cox, P., Fan, X., Strauss, M. A., Beelen, A., Omont, A., & Zylka, R. 2003, A&A, 406, L55

[15] Beuermann, K., et al. 1999, A&A, 352, L26

[16] Blandford, R. D., & McKee, C. F. 1976, Physics of Fluids, 19, 1130

[17] Bloom, J. S. 2005, GCN Circ. 4256

[18] Bloom, J. S., et al. 1998, ApJL, 508, L21

[19] Bloom, J. S., et al. 2001, GCN Circ. 1135

[20] Bloom, J. S., et al. 2003, ApJ, 594, 674

[21] Bloom, J. S., van Dokkum, P. G., Bailyn, C. D., Buxton, M. M., Kulkarni,

S. R., & Schmidt, B. P. 2004, AJ, 127, 252

[22] Bloom, J. S., Perley, D. A., & Chen, H. W. 2006, GCN Circ. 5826

[23] Bloom, J. S., et al. 2009, ApJ, 691, 723

[24] Blustin, A. J., et al. 2006, ApJ, 637, 901

[25] Bohlin, R.C., Savage, B.D., & Drake, J.F. 1978, ApJ, 224, 132

[26] Bouchet, P., Lequeux, J., Maurice, E., Prevot, L., & Prevot-Burnichon, M. L. 1985, A&A, 149, 330

[27] Bouwens, R. J., Illingworth, G. D., Franx, M., & Ford, H. 2008, ApJ, 686, 230

[28] Butler, N. R., et al. 2003, ApJ, 597, 1010

[29] Butler, N. R., Ricker, G. R., Ford, P. G., Vanderspek, R. K., Marshall, H. L., Jernigan, J. G., Garmire, G. P., & Lamb, D. Q. 2005, ApJ, 629, 908

127 [30] Butler, N. R., et al. 2006, ApJ, 652, 1390

[31] Campana, S., et al. 2007, ApJL, 654, L17

[32] Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245

[33] Castro-Tirado, A. J., et al. 1999, ApJL, 511, L85

[34] Castro-Tirado, A. J., et al. 2001, A&A, 370, 398

[35] Calzetti, D., Kinney, A. L., & Storchi-Bergmann, T. 1994, ApJ, 429, 582

[36] Cenko, S. B., et al. 2006, ApJ, 652, 490

[37] Cenko, S. B., et al. 2009, ApJ, 693, 1484

[38] Chary, R., et al. 1998, ApJL, 498, L9

[39] Chary, R., Becklin, E. E., & Armus, L. 2002, ApJ, 566, 229

[40] Chary, R., Berger, E., & Cowie, L. 2007, ApJ, 671, 272

[41] Chen, H.-W., Prochaska, J. X., Bloom, J. S., & Thompson, I. B. 2005, ApJL,

634, L25

[42] Chen, H.-W., Prochaska, J. X., & Gnedin, N. Y. 2007, ApJL, 667, L125

[43] Chen, S. L., Li, A., & Wei, D. M. 2006, ApJL, 647, L13

[44] Chevalier, R. A., & Li, Z. 2000, ApJ, 536, 195

[45] Christensen, L., et al. 2004, A&A, 425, 913

[46] Clayton, G.C., & Martin, P.G. 1985, ApJ, 288, 558

[47] Clayton, G.C., et al. 1992, ApJ, 385, L53

128 [48] Cline, T. L., Desai, U. D., Klebesadel, R. W., and Strong, I. B. 1973, ApJ, 185, L1

[49] Cobb, B. E., & Bailyn, C. D. 2005, GCN Circ. 3506

[50] Cobb, B. E. 2008a, GCN Circ. 7553

[51] Cobb, B. E. 2008b, GCN Circ. 8356

[52] Cobb, B. E. 2008c, GCN Circ. 7609

[53] Cobb, B. E. 2008d, GCN Circ. 8452

[54] Colgate, S. A. 1968, Canadian Journal of Physics, 46, 476

[55] Conselice, C. J., et al. 2005, ApJ, 633, 29

[56] Costa, E., et al., 1997, Nature, 387, 783

[57] Courty, S., et al. 2004, MNRAS, 354, 581

[58] Curran, P. A., et al. 2007, MNRAS, 381, L65

[59] Curran, P. A., Wijers, R. A. M. J., Heemskerk, M. H. M., Starling, R. L. C., Wiersema, K., & van der Horst, A. J. 2008, A&A, 490, 1047

[60] Covino, S., et al. 2003, A&A, 404, L5

[61] Dado, S., Dar, A., De Rújula, A., & Plaga, R. 2008, ApJ, 678, 353

[62] Dai, X., Halpern, J. P., Morgan, N. D., Armstrong, E., Mirabal, N., Haislip, J. B., Reichart, D. E., & Stanek, K. Z. 2007, ApJ, 658, 509

[63] Dai, Z. G., Liang, E. W., & Xu, D. 2004, ApJ, 612, L101

129 [64] D’Avanzo, P., D’Elia, V., & Covino, S. 2008, GCN Circ. 8350

[65] de Ugarte Postigo, A., et al. 2007, A&A, 462, L57

[66] Della Valle, M., et al. 2006a, ApJL, 642, L103

[67] Della Valle, M., et al. 2006b, Nature, 444, 1050

[68] Diplas, A., & Savage, B. D. 1994, ApJ, 427, 274

[69] Djorgovski, S. G., Kulkarni, S. R., Bloom, J. S., Goodrich, R., Frail, D. A., Piro, L., & Palazzi, E. 1998, ApJL, 508, L17

[70] Djorgovski, S. G., Dierks, A., Bloom, J. S., Kulkarni, S. R., Filippenko, A. V., Hillenbrand, L. A., & Carpenter, J. 1999, GCN Circ. 481

[71] Djorgovski, S. G., et al. 2001a, Gamma-ray Bursts in the Afterglow Era, 218

[72] Djorgovski, S. G., Frail, D. A., Kulkarni, S. R., Bloom, J. S., Odewahn, S. C., & Diercks, A. 2001b, ApJ, 562, 654

[73] Dodonov, S. N., Afanasiev, V. L., Sokolov, V. V., Moiseev, A. V., & Castro-

Tirado, A. J. 1999, GCN Circ. 475

[74] Douglas, A.E., & Herzberg, G. 1941, ApJ, 94, 381

[75] Draine, B. T. 2003, ARA&A, 41, 241

[76] Dwek, E. 2005, in AIP Conf. Proc. 761, The Spectral Energy Distributions of Gas-Rich Galaxies: Confronting Models with Data, ed. C. C. Popescu & R. J. Tuffs (Melville: AIP), 103

[77] Dwek, E., Galliano, F., & Jones, A. P. 2007, Nuovo Cimento B Serie, 122, 959

130 [78] Eichler, D., Livio, M., Piran, T., & Schramm, D. N. 1989, Nature, 340, 126

[79] Elíasdóttir, Á., et al. 2009, ApJ, 697, 1725

[80] Ellison, S. L., et al. 2006, MNRAS, 372, L38

[81] Fenimore, E. E., et al. 1993, Nature, 366, 40

[82] Fenimore, E. E., & Bloom, J. S. 1995, ApJ, 453, 25

[83] Fenimore, E. E., Ramirez-Ruiz, E., & Wu, B. 1999, ApJ, 518, L73

[84] Fiore, F., et al. 2005, ApJ, 624, 853

[85] Fiore, F., Guetta, D., Piranomonte, S., D’Elia, V., & Antonelli, L. A. 2007,

A&A, 470, 515

[86] Fishman, G. J. 1999, A&AS, 138, 395

[87] Fitzpatrick, E. L. 1985, ApJ, 299, 219

[88] Fitzpatrick, E. L. 1986, AJ, 92, 1068

[89] Fitzpatrick, E. L., & Massa, D. 1990, ApJS, 72, 163

[90] Flasher, J., et al. 2005a, GCN Circ. 3561

[91] Flasher, J., et al. 2005b, GCN Circ. 3567

[92] Foley, R. J., Chen, H.-W., Bloom, J., & Prochaska, J. X. 2005, GCN Circ. 3483

[93] Foley, R. J., et al. 2006, ApJ, 645, 450

[94] Fox, A. J., Ledoux, C., Vreeswijk, P. M., Smette, A., & Jaunsen, A. O. 2008, A&A, 491, 189

131 [95] Fox, D. B., Berger, E., Price, P. A., & Cenko, S. B. 2007, GCN Circ. 6071

[96] Frail, D. A., et al. 1997, Nature, 389, 261

[97] Frail, D. A., et al. 2006, ApJL, 646, L99

[98] Fruchter, A., et al. 1999, ApJ, 516, 683

[99] Fruchter, A., Krolik, J. H., & Rhoads, J. E. 2001, ApJ, 563, 597

[100] Fruchter, A. S., et al. 2006, Nature, 441, 463

[101] Fynbo, J. P. U., et al. 2000, ApJ, 542, L89

[102] Fynbo, J. P. U., et al. 2001, A&A, 373, 796

[103] Fynbo, J. P. U., et al. 2002, A&A, 388, 425

[104] Fynbo, J. P. U., et al. 2003, A&A, 407, 147

[105] Fynbo, J. P. U., et al. 2005a, ApJ, 633, 317

[106] Fynbo, J. P. U., et al. 2005b, GCN Circ. 3874

[107] Fynbo, J. P. U., et al. 2006, A&A, 451, L47

[108] Fynbo, J. P. U., et al. 2007, Messenger, 130, 43

[109] Galama, T. J., et al. 1998, ApJL, 497, L13

[110] Galama, T. J., et al. 1999, Nature, 398, 394

[111] Galama, T. J., & Wijers, R. A. M. J. 2001, ApJL, 549, L209

[112] Galama, T. J., et al. 2003, ApJ, 587, 135

132 [113] Garnavich, P. M., Jha, S., Pahre, M. A., Stanek, K. Z., Kirshner, R. P., Garcia, M. R., Szentgyorgyi, A. H., & Tonry, J. L. 2000, ApJ, 543, 61

[114] Garnavich, P. M., et al. 2003, ApJ, 582, 924

[115] Godet, O., & Oates, S. 2008, GCN Circ. 8543

[116] Gordon, K. D., & Clayton, G. C. 1998, ApJ, 500, 816

[117] Gordon, K. D., Clayton, G. C., Misselt, K. A., Landolt, A. U., & Wolff, M. J. 2003, ApJ, 594, 279

[118] Gorosabel, J., et al. 2005, A&A, 444, 711

[119] Gomboc, A., et al. 2008, ApJ, 687, 443

[120] Gou, L. J., Mészáros, P., Abel, T., & Zhang, B. 2004, ApJ, 604, 508

[121] Greiner, J., et al. 2003a, ApJ, 599, 1223

[122] Greiner, J., Guenther, E., Klose, S., & Schwarz, R. 2003b, GCN Circ. 1886

[123] Greiner, J., Peimbert, M., Estaban, C., Kaufer, A., Jaunsen, A., Smoke, J., Klose, S., & Reimer, O. 2003c, GCN Circ. 2020

[124] Greiner, J., et al. 2008, PASP, 120, 405

[125] Greiner, J., et al. 2009a, ApJ, 693, 1912

[126] Greiner, J., et al. 2009b, ApJ, 693, 1610

[127] Greiner, J., et al. 2009c, A&A, 498, 89

[128] Groot, P. J., et al. 1998, ApJL, 493, L27

133 [129] Grupe, D., et al. 2006, GCN Circ. 5365

[130] Grupe, D., et al. 2007, ApJ, 662, 443

[131] Grupe, D., et al. 2008, GCN Circ. 8691

[132] Haislip, J. B., et al. 2006, Nature, 440, 181

[133] Halpern, J. P., Thorstensen, J. R., Helfand, D. J., & Costa, E. 1998, Nature,

393, 41

[134] Halpern, J. P., et al. 2000, ApJ, 543, 697

[135] Hartmann, J. 1904, ApJ, 19, 268

[136] Heng, K., Lazzati, D., Perna, R., Garnavich, P., Noriega-Crespo, A., Bersier,

D., Matheson, T., & Pahre, M. 2008, ApJ, 681, 1116

[137] Hill, G., Prochaska, J. X., Fox, D., Schaefer, B., & Reed, M. 2005, GCN Circ. 4255

[138] Hines, D. C., Krause, O., Rieke, G. H., Fan, X., Blaylock, M., & Neugebauer, G. 2006, ApJL, 641, L85

[139] Hjorth, J., et al. 2002, ApJ, 576, 113

[140] Hjorth, J., et al. 2003a, Nature, 423, 847

[141] Hjorth, J., et al. 2003b, ApJ, 597, 699

[142] Holland, S. T., et al. 2002, AJ, 124, 639

[143] Holland, S. T., et al. 2003, AJ, 125, 2291

[144] Hopkins, A. M., & Beacom, J. F. 2006, ApJ, 651, 142

134 [145] Hurkett, C. P., et al. 2006, MNRAS, 368, 1101

[146] Imhof, W. L., Nakano, G. H., Johnson, R. G., Kilner, J. R., Regan, J. B., Klebesadel, R. W., and Strong, I. B. 1974, ApJ, 191, L7

[147] Infante, L., Garnavich, P. M., Stanek, K. Z., & Wyrzykowski, L. 2001, GCN Circ. 1152

[148] Jakobsson, P., et al. 2003, A&A, 408, 941

[149] Jakobsson, P., et al. 2004a, A&A, 427, 785

[150] Jakobsson, P., Hjorth, J., Fynbo, J. P. U., Watson, D., Pedersen, K., Björnsson,

G., & Gorosabel, J. 2004b, ApJL, 617, L21

[151] Jakobsson, P., et al. 2006, A&A, 447, 897

[152] Jaunsen, A. O., et al. 2008, ApJ, 681, 453

[153] Jensen, B. L., et al. 2001, A&A, 370, 909

[154] Jha, S., et al. 2001, ApJ, 554, L155

[155] Jiang, L., et al. 2006, AJ, 132, 2127

[156] Joblin, C., Léger, A., & Martin, P. 1992, ApJ, 393, L79

[157] Junkkarinen, V. T., Cohen, R. D., Beaver, E. A., Burbidge, E. M., Lyons,

R. W., & Madejski, G. 2004, ApJ, 614, 658

[158] Kahharov, B., Ibrahimov, M., Sharapov, D., Pozanenko, A., Rumyantsev, V., & Beskin, G. 2005, GCN Circ. 3261

[159] Kaneko, Y., et al. 2007, ApJ, 654, 385

135 [160] Kann, D. A., Klose, S., & Zeh, A. 2006, ApJ, 641, 993

[161] Kann, D. A., et al. 2007, arXiv:0712.2186

[162] Kaplan, D., Garnavich, P., Rosenberg, J., & Stanek, K. Z. 2005, GCN Circ.

3507

[163] Kim, S.-H., Martin, P. G., & Hendry, P. D. 1994, ApJ, 422, 164

[164] Kim, S.-H., & Martin, P. G. 1995, ApJ, 442, 172

[165] Kinney, A. L., Calzetti, D., Bohlin, R. C., McQuade, K., Storchi-Bergmann,

T., & Schmitt, H. R. 1996, ApJ, 467, 38

[166] Kistler, M. D., Yüksel, H., Beacom, J. F., Hopkins, A. M., & Wyithe, J. S. B. 2009, ApJL, 705, L104

[167] Klebesadel, R. W., Strong, I. B., and Olson, R. A. 1973, ApJ, 182, L85

[168] Klose, S., et al. 2000, ApJ, 545, 271

[169] Klose, S., et al. 2004, AJ, 128, 1942

[170] Klotz, A., Boër, M., Atteia, J. L., Stratta, G., Behrend, R., Malacrino, F., & Damerdji, Y. 2005, A&A, 439, L35

[171] Kobayashi, S., & Sari, R. 2001, ApJ, 551, 934

[172] Kogut, A., et al. 2003, ApJS, 148, 161

[173] Koornneef, J., & Code, A.D. 1981, ApJ, 247, 860

[174] Koornneef, J. 1982, A&A, 107, 247

[175] Krühler, T., et al. 2008, ApJ, 685, 376

136 [176] Kulkarni, S. R. 1998, Nature, 393, 35

[177] Kulkarni, S. R., et al., 2000, Proc. SPIE, 4005, 9

[178] Kulkarni, V. P., York, D. G., Vladilo, G., & Welty, D. E. 2007, ApJL, 663, L81

[179] Kumar, P. 1999, ApJ, 523, L113

[180] Lamb, D. Q. 1995, PASP, 107, 1152

[181] Lamb, D. Q., & Reichart, D. E. 2000, ApJ, 536, 1

[182] Larson, K. A., Whittet, D. C. B., & Hough, J. H. 1996, ApJ, 472, 755

[183] Lazzati, D., Perna, R., & Ghisellini, G. 2001a, MNRAS, 325, L19

[184] Le Floc’h, E., Charmandaris, V., Forrest, W. J., Mirabel, I. F., Armus, L., & Devost, D. 2006, ApJ, 642, 636

[185] Lee, B. C., et al. 2001, ApJ, 561, 183

[186] Lee, W. H., & Kluzniak, W. 1995, Acta Astronomica, 45, 705

[187] Lee, W. H., & Ramirez-Ruiz, E. 2007, New Journal of Physics, 9, 17

[188] Levan, A. J., et al. 2006, ApJ, 647, 471

[189] Ledoux, C., Petitjean, P., Møller, P., Fynbo, J., & Srianand, R. 2005, IAU Colloq. 199: Probing Galaxies through Quasar Absorption Lines, 433

[190] Ledoux, C., Vreeswijk, P. M., Smette, A., Fox, A. J., Petitjean, P., Ellison, S. L., Fynbo, J. P. U., & Savaglio, S. 2009, A&A, 506, 661

[191] Lequeux, J., Maurice, E., Prévot-Burnichon, M.-L., Prévot, L., & Rocca- Volmerange, B. 1982, A&A, 113, L15

137 [192] Li, A., & Greenberg, J. M. 1998, A&A, 339, 591

[193] Li, A., & Draine, B.T. 2001, ApJ, 554, 778

[194] Li, A., & Greenberg, J.M. 2003, in Solid State Astrochemistry, ed. V. Pirronello, J. Krelowski, & G. Manicó (Dordrecht: Kluwer), 37

[195] Li, A. 2004, in Penetrating Bars through Masks of Cosmic Dust, ed. D. L. Block,

I. Puerari, K. C. Freeman, R. Groess, & E. K. Block (Dordrecht: Kluwer), 535

[196] Li, A. 2008, in: Small Bodies in Planetary Sciences (Lecture Notes in Physics

Series, vol 758 ), I. Mann, A. Nakamura, & T. Mukai (eds.), Springer, Chapter 6, 167

[197] Li, A., Liang, S. L., Kann, D. A., Wei, D. M., Klose, S., & Wang, Y. J. 2008a,

ApJ, 685, 1046

[198] Li, Y., Li, A., & Wei, D. M. 2008b, ApJ, 678, 1136

[199] Liang, S. L., & Li, A. 2009, ApJL, 690, L56

[200] Liang, S. L., & Li, A. 2010, ApJ, 710, 648

[201] Loeb, A., & Barkana, R. 2001, ARA&A, 39, 19

[202] Loew, S., Greiner, J., Yoldas, A., Kuepcue Yoldas, A., & Szokoly, G. 2008,

GCN Circ. 8529

[203] Loew, S., Kruehler, T., & Greiner, J. 2008, GCN Circ. 8540

[204] Lutz, D., Valiante, E., Sturm, E., Genzel, R., Tacconi, L. J., Lehnert, M. D., Sternberg, A., & Baker, A. J. 2005, ApJL, 625, L83

[205] Lutz, D., et al. 2007, ApJL, 661, L25

138 [206] Madau, P. 1995, ApJ, 441, 18

[207] Madau, P., & Phinney, E. S. 1996, ApJ, 456, 124

[208] Maiolino, R., Marconi, A., & Oliva, E. 2001, A&A, 365, 37

[209] Maiolino, R., Schneider, R., Oliva, E., Bianchi, S., Ferrara, A., Mannucci, F., Pedani, M., & Roca Sogorb, M. 2004, Nature, 431, 533

[210] Maiorano, E., et al. 2006, A&A, 455, 423

[211] Malesani, D., Fynbo, J. P. U., Jakobsson, P., Vreeswijk, P. M., & Niemi, S.-M. 2008, GCN Circ. 7544

[212] Malhotra, S. 1997, ApJ, 488, L101

[213] Mangano, V., et al. 2007, A&A, 470, 105

[214] Mannucci, F., Buttery, H., Maiolino, R., Marconi, A., & Pozzetti, L. 2007, A&A, 461, 423

[215] Mao, J., Margutti, R., Sakamoto, T., Schady, P., Burrows, D. N., Roming, P.,

& Gehrels, N. 2009, GCN Report, 204, 1

[216] Martin, P.G., Clayton, G.C., & Wolff, M.J. 1999, ApJ, 510, 905

[217] Martini, P., Garnavich, P., & Stanek, K. Z. 2003, GCN Circ. 1980

[218] Masetti, N., et al. 2001, A&A, 374, 382

[219] Masetti, N., Palazzi, E., Pian, E., Hjorth, J., Castro-Tirado, A., Boehnhardt, H., & Price, P. 2002, GCN Circ. 1330

[220] Masetti, N., et al. 2003, A&A, 404, 465

139 [221] Masetti, N., et al. 2005, A&A, 438, 841

[222] Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425

[223] McKellar, A. 1940, PASP, 52, 187

[224] Meegan, C. A., et al. 1992, Nature, 355, 143

[225] Melandri, A., et al. 2006, GCN Circ. 5827

[226] Melandri, A., et al. 2008, ApJ, 686, 1209

[227] Mészáros, P., & Rees, M. J. 1993, ApJ, 405, 278

[228] Mészáros, P., & Rees, M. J. 1997, ApJ, 476, 232

[229] Metzger, M. R., et al. 1997a, IAU Circ., 6676

[230] Metzger, M. R., et al. 1997b, Nature, 387, 879

[231] Michałowski, M. J., Hjorth, J., Castro Cerón, J. M., & Watson, D. 2008, ApJ,

672, 817

[232] Michałowski, M. J., et al. 2009, ApJ, 693, 347

[233] Milne, P. A., Williams, G. G., & Park, H.-S. 2005, GCN Circ. 3258

[234] Mirabal, N., Paerels, F., & Halpern, J. P. 2003, ApJ, 587, 128

[235] Misselt, K. A., Clayton, G. C., & Gordon, K. D. 1999, ApJ, 515, 128

[236] Molinari, E., et al. 2007, A&A, 469, L13

[237] Møller, P., et al. 2002, A&A, 396, L21

[238] Monfardini, A., et al. 2006, ApJ, 648, 1125

140 [239] Motta, V., et al. 2002, ApJ, 574, 719

[240] Muñoz, J. A., Falco, E. E., Kochanek, C. S., McLeod, B. A., & Mediavilla, E. 2004, ApJ, 605, 614

[241] Nandy, K., Morgan, D.H., Willis, A.J., Wilson, R., & Gondhalekar, P. M. 1981, MNRAS, 196, 955

[242] Narayan, R., Paczynski, B., & Piran, T. 1992, ApJL, 395, L83

[243] Nemiroff, R. J. 1993, American Journal of Physics, 61, 619

[244] Norris, J. P., Cline, T. L., Desai, U. D., and Teegarden, B. J. 1984, Nature,

308, 434

[245] Noll, S., & Pierini, D. 2005, A&A, 444, 137

[246] Noll, S., Pierini, D., Pannella, M., & Savaglio, S. 2007, A&A, 472, 455

[247] Nozawa, T., Kozasa, T., Umeda, H., Maeda, K., & Nomoto, K. 2003, ApJ, 598,

785

[248] Nysewander, M., & Haislip, J. 2006, GCN Circ. 5236

[249] Osterbrock, D. E., & Ferland, G. J. 2006, Astrophysics of Gaseous Nebulae and Active Galactic Nuclei (2nd ed; Sausalito: Univ. Sci. Books)

[250] Ota, K., et al. 2008, ApJ, 677, 12

[251] Ouchi, M., et al. 2003, ApJ, 582, 60

[252] Paczyński, B. 1986, ApJL, 308, L43

[253] Paczyński, B. 1995, PASP, 107, 1167

141 [254] Paczyński, B. 1991, ApJ, 370, 597

[255] Paczyński, B. 1998, Gamma-Ray Bursts, 4th Hunstville Symposium, 428, 783

[256] Page, K. L., et al. 2007, ApJ, 663, 1125

[257] Pandey, S. B., Sagar, R., Anupama, G. C., Bhattacharya, D., Sahu, D. K., Castro-Tirado, A. J., & Bremer, M. 2004, A&A, 417, 919

[258] Pandey, S. B., et al. 2006, A&A, 460, 415

[259] Pei, Y. C. 1992, ApJ, 395, 130

[260] Perley, D. A., et al. 2008, ApJ, 672, 449

[261] Perna, R., & Belczynski, K. 2002a, ApJ, 570, 252

[262] Perna, R., & Lazzati, D. 2002b, ApJ, 580, 261

[263] Perna, R., Lazzati, D., & Fiore, F. 2003, ApJ, 585, 775

[264] Perley, D. A., et al. 2008a, ApJ, 672, 449

[265] Perley, D. A., et al. 2008b, ApJ, 688, 470

[266] Perley, D. A., Bloom, J. S., & Li, W. 2008c, GCN Circ. 7406

[267] Perley, D. A., et al. 2009a, AJ, 138, 1690

[268] Perley, D. A. 2009b, GCN Circ. 8997

[269] Perri, M., et al. 2005a, A&A, 442, L1

[270] Perri, M., Capalbi, M., Giommi, P., Grupe, D., Burrows, D. N., Angelini, L., & Greiner, J. 2005b, GCN Circ. 3722

142 [271] Perri, M., & Stratta, G. 2009, GCN Circ. 9031

[272] Piran, T. 1999, Physics Reports, 314, 575

[273] Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1992, Numerical Recipes in FORTRAN: The Art of Scientific Computing (2nd ed.; Cambridge: Cambridge Univ. Press)

[274] Prévot, M. L., et al. 1984, A&A, 132, 389

[275] Price, P. A., et al. 2002a, ApJ, 573, 85

[276] Price, P. A., et al. 2002b, ApJL, 571, L121

[277] Price, P. A., Bloom, J. S., Goodrich, R. W., Barth, A. J., Cohen, M. H., & Fox,

D. W. 2002c, GCN Circ. 1475

[278] Price, P. A., et al. 2003, ApJ, 584, 931

[279] Price, P. A., Roth, K., Rich, J., Schmidt, B. P., Peterson, B. A., Cowie, L., Smith, C., & Rest, A. 2004, GCN Circ. 2791

[280] Price, P. A., Berger, E., & Fox, D. B. 2006, GCN Circ. 5275

[281] Prochaska, J. X., Bloom, J. S., Chen, H.-W., Foley, R. J., & Roth, K. 2005, GCN Circ. 3204

[282] Prochaska, J. X., Chen, H.-W., & Bloom, J. S. 2006, ApJ, 648, 95

[283] Prochaska, J. X., Chen, H.-W., Dessauges-Zavadsky, M., & Bloom, J. S. 2007,

ApJ, 666, 267

[284] Prochaska, J. X., Dessauges-Zavadsky, M., Ramirez-Ruiz, E., & Chen, H.-W. 2008, ApJ, 685, 344

143 [285] Prochaska, J. X., et al. 2009, ApJL, 691, L27

[286] Racusin, J. L., Schady, P., & Palmer, D. 2008, GCN Report, 173

[287] Ramaprakash, A. N., et al. 1998, Nature, 393, 43

[288] Ramirez-Ruiz, E., Trentham, N., & Blain, A. W. 2002, MNRAS, 329, 465

[289] Reichart, D. E. 1998, ApJL, 495, L99

[290] Reichart, D. E., Lamb, D. Q., Fenimore, E. E., Ramirez-Ruiz, E., Cline, T. L., & Hurley, K. 2001a, ApJ, 552, 57

[291] Reichart, D. E. 2001b, ApJ, 553, 235

[292] Rhoads, J. E., & Fruchter, A. S. 2001, ApJ, 546, 117

[293] Rol, E., et al. 2007, ApJ, 669, 1098

[294] Rossi, A., et al. 2008, A&A, 491, L29

[295] Rosswog, S., Ramirez-Ruiz, E., & Davies, M. B. 2003, MNRAS, 345, 1077

[296] Rosswog, S. 2005, ApJ, 634, 1202

[297] Ruderman, M. 1975, New York Academy Sciences Annals, 262, 164

[298] Sari, R., Piran, T., & Narayan, R. 1998, ApJ, 497, L17

[299] Savaglio, S., Fall, S. M., & Fiore, F. 2003, ApJ, 585, 638

[300] Savaglio, S., & Fall, S. M. 2004, ApJ, 614, 293

[301] Schady, P., et al. 2007, MNRAS, 377, 273

[302] Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525

144 [303] Schneider, D. P., et al. 2003, AJ, 126, 2579

[304] Shapley, A. E., et al. 2003, ApJ, 588, 65

[305] Shemi, A., & Piran, T. 1990, ApJL, 365, L55

[306] Shin, M.-S., et al. 2006, arXiv:astro-ph/0608327

[307] Silvey, J., et al. 2004, GCN Circ. 2833

[308] Sloan, G. C., et al. 2009, Science, 323, 353

[309] Soderberg, A. M., et al. 2006, ApJ, 636, 391

[310] Sollerman, J., et al. 2007, A&A, 466, 839

[311] Srianand, R., Gupta, N., Petitjean, P., Noterdaeme, P., & Saikia, D. J. 2008,

MNRAS, 391, L69

[312] Stanek, K. Z., Garnavich, P. M., Kaluzny, J., Pych, W., & Thompson, I. 1999, ApJL, 522, L39

[313] Stanek, K. Z., et al. 2007, ApJL, 654, L21

[314] Starling, R. L. C., Wijers, R. A. M. J., Wiersema, K., Rol, E., Curran, P. A., Kouveliotou, C., van der Horst, A. J., & Heemskerk, M. H. M. 2007, ApJ, 661,

787

[315] Starling, R. L. C. 2008, A&A, 488, 915

[316] Stecher, T. P. 1965, ApJ, 142, 1683

[317] Still, M., et al. 2005, ApJ, 635, 1187

145 [318] Stratta, G., Fiore, F., Antonelli, L. A., Piro, L., & De Pasquale, M. 2004, ApJ, 608, 846

[319] Stratta, G., Perna, R., Lazzati, D., Fiore, F., Antonelli, L. A., & Conciatore, M. L. 2005, A&A, 441, 83

[320] Stratta, G., Maiolino, R., Fiore, F., & D’Elia, V. 2007, ApJL, 661, L9

[321] Strong, I. B., Klebesadel, R. W., and Olson, R. A. 1974, ApJ, 188, L1

[322] Struve, O. 1929, MNRAS, 89, 567

[323] Swings, P., & Rosenfeld, L. 1937, ApJ, 86, 483

[324] Tagliaferri, G., et al. 2005, A&A, 443, L1

[325] Tanvir, N. R., et al. 2008, MNRAS, 388, 1743

[326] Tanvir, N. R., et al. 2009, Nature, 461, 1254

[327] Thöne, C. C., et al. 2006, GCN Circ. 5373

[328] Thöne, C. C., Greiner, J., Savaglio, S., & Jehin, E. 2007, ApJ, 671, 628

[329] Todini, P., & Ferrara, A. 2001, MNRAS, 325, 726

[330] Toft, S., Hjorth, J., & Burud, I. 2000, A&A, 357, 115

[331] Todini, P., & Ferrara, A. 2001, MNRAS, 325, 726

[332] Trumpler, R. J. 1930, PASP, 42, 214

[333] Updike, A. C., et al. 2008a, ApJ, 685, 361

[334] Updike, A. C., Milne, P. A., & Williams, G. G. 2008b, GCN Circ. 7848

146 [335] Updike, A., Afonso, P., Clemens, C., & Greiner, J. 2008c, GCN Circ. 86931

[336] Updike, A. C., Filgas, R., Kruehler, T., Greiner, J., & McBreen, S. 2009, GCN Circ. 9026

[337] van der Horst, A. J., Kouveliotou, C., Gehrels, N., Rol, E., Wijers, R. A. M. J., Cannizzo, J. K., Racusin, J., & Burrows, D. N. 2009, ApJ, 699, 1087

[338] van Paradijs, J., Kouveliotou, C., & Wijers, R. A. M. J. 2000, Ann. Rev. Astr.

Ap., 38, 379

[339] Verma, A., Lehnert, M. D., Förster Schreiber, N. M., Bremer, M. N., & Douglas, L. 2007, MNRAS, 377, 1024

[340] Vernet, J., Fosbury, R. A. E., Villar-Martin, M., Cohen, M. H., Cimatti, A., di Serego Alighieri, S., & Goodrich, R. W. 2001, A&A, 366, 7

[341] Vestrand, W. T., et al. 2006, Nature, 442, 172

[342] Vijh, U. P., Witt, A. F., & Gordon, K. D. 2003, ApJ, 587, 533

[343] Vreeswijk, P. M., et al. 1999a, ApJ, 523, 171

[344] Vreeswijk, P. M., et al. 1999b, GCN Circ. 324

[345] Vreeswijk, P. M., et al. 1999c, GCN Circ. 496

[346] Vreeswijk, P. M., et al. 2004, A&A, 419, 927

[347] Vreeswijk, P. M., et al. 2006, A&A, 447, 145

[348] Vreeswijk, P. M., Smette, A., Malesani, D., Fynbo, J. P. U., Milvang-Jensen, B., Jakobsson, P., Jaunsen, A. O., & Ledoux, C. 2008, GCN Circ. 7444

147 [349] Wang, F. Y., & Dai, Z. G. 2009, MNRAS, 400, L10

[350] Wang J., Hall P. B., Ge J., Li A., & Schneider D. P. 2004, ApJ, 609, 589

[351] Watson, D., et al. 2006, ApJ, 652, 1011

[352] Waxman, E., & Draine, B.T. 2000, ApJ, 537, 796

[353] Weingartner, J. C., & Draine, B. T. 2001, ApJ, 548, 296

[354] Wheaton, W. A. et al. . 1973, ApJ, 185, L57

[355] Wiersema, K., Starling, R. L. C., Rol, E., Vreeswijk, P., & Wijers, R. A. M. J.

2004, GCN Circ. 2800

[356] Wiersema, K., Rol, E., Starling, R., Tanvir, N., Bloomfield, D. S., & Thompson, H. 2005, GCN Circ. 3699

[357] Wijers, R. A. M. J., & Galama, T. J. 1999, ApJ, 523, 177

[358] Witt, A.N., Bohlin, R.C., & Stecher, T.P. 1986, ApJ, 305, L23

[359] Wolff, M.J., Clayton, G.C., Kim, S.H., Martin, P.G., & Anderson, C.M. 1997, ApJ, 478, 395

[360] Woosley, S. E. 1993, ApJ, 405, 273

[361] Woosley, S. E., & Bloom, J. S. 2006, ARA&A, 44, 507

[362] Wucknitz, O., Wisotzki, L., Lopez, S., & Gregg, M. D. 2003, A&A, 405, 445

[363] Yan, L., et al. 2005, ApJ, 628, 604

[364] Yanagisawa, K., Toda, H., & Kawai, N. 2005, GCN Circ. 3489

148 [365] York, D. G., et al. 2006, MNRAS, 367, 945

[366] Yost, S. A., Schaefer, B. E., & Yuan, F. 2006, GCN Circ. 5824

[367] Yost, S. A., et al. 2007, ApJ, 657, 925

[368] Yüksel, H., Kistler, M. D., Beacom, J. F., & Hopkins, A. M. 2008, ApJL, 683, L5

[369] Zhang, B., & Mészáros, P. 2004, Int. J. Mod. Phys. A, 19, 2385

[370] Zheng, W.-K., Deng, J.-S., & Wang, J. 2009, Res. Astron. Astrophys., 9, 1103

[371] Ziaeepour, H., et al. 2008, MNRAS, 385, 453

[372] Zubko, V., Dwek, E., & Arendt, R. G. 2004, ApJS, 152, 211

149 VITA

Shunlin Liang was born on April 20th, 1978 in Shunde, China. He received a

Bachelor and Master degree in Astronomy from Nanjing University, Nanjing, China in July 2001 and 2004, respectively. During his graduate study in Nanjing University, he was working with Dr. Zigao Dai on Gamma-ray Burst. In August 2005, he came to University of Missouri-Columbia in the United States, and joined the Department of Physics and Astronomy for his Ph.D study in Astrophysics. Since then, he has been working with Dr. Aigen Li on cosmic dust. He will receive his Ph.D. in May,

2010.

150 Publications

1. Liang, S.L., and Li, A. "Probing Extragalactic Dust through Nearby Gamma-

Ray Burst Afterglows". The Astrophysical Journal., vol. 710, pp. 648-662, 2010.

2. Liang, S.L., and Li, A. "Probing Cosmic Dust of the Early Universe through High-Redshift Gamma-Ray Bursts". The Astrophysical Journal Letters, vol.

690, pp. L56-L60, 2009.

3. Li, A., Liang, S.L., Kann, D.A., Wei, D.M., Klose, S., and Wang, Y.J. "On Dust Extinction of Gamma-ray Burst Host Galaxies". The Astrophysical Jour- nal., vol. 685, pp. 1046-1051, 2008.

Work in Progress

1. Liang, S.L., and Li, A. "Probing Extragalactic Dust through Distant Gamma- Ray Burst Afterglows". To be submitted to The Astrophysical Journal.

151