Thermal Dust Emission in the Microwave Frequency Range

(1)

Thermal Dust Emission in the Microwave Frequency Range

Daniel Christopher Herman

Thesis submitted for the degree of Master of Science in Astronomy

Institute of Theoretical Astrophysics University of Oslo

June 1, 2019

(2)

Copyright c 2019, Daniel Christopher Herman

This work, entitled Thermal Dust Emission in the Microwave Frequency Range is distributed under the terms of the Public Library of Science Open Access License, a copy of which can be found at http://www.publiclibraryofscience.org.

(3)

Abstract

Disentangling Galactic foreground emission from microwave frequency data sets is para- mount to extracting the Cosmic Microwave Background (CMB) signal. With the community of cosmologists searching for the elusive B-mode CMB polarization signature, it is vital that our collective ability to accurately model Galactic dust emission improves.

Understanding the physical nature of Galactic dust is also important to other elds of astronomy, as dust emission can glean information about the composition of dust grains, and the strength of the interstellar radiation eld.

In this thesis, I aim to dissect Galactic thermal dust modeling through a host of analytical methods. A set of physical and phenomenological dust models are reviewed to set the stage for my analysis. The parametric methods which have been used to apply phenomenological dust models to data are also described. Calibration of the Planck and DIRBE data using COBE/FIRAS data, within the relevant frequency ranges, is carried out to ensure that estimates to our modeling parameters remain unbiased. The correlation between thermal dust and the hydrogen column density is fundamental in this research, and is applied through multiple analytical approaches.

The results of the analysis are presented to highlight issues with current thermal dust modeling, particularly with published dust temperature maps. Constraints on the number of parameters required to model thermal dust are set, and motivations for a two-component dust model are laid out. Future work to improve upon this analysis and implementation of a physical dust model to component separation are also described here.

(4)

(5)

Acknowledgments

First and foremost, I would like to thank my family for the multiple levels of support they have so generously given throughout my education, even from 6,500km away. I would also like to thank Ingunn Wehus, Hans Kristian Eriksen, Trygve Leithe Svalheim, and Brandon Hensley for crafting me as a researcher, informing me when I have done something stupid, and always supplying me with more work than there are hours in a year. A special thanks to Erik Levén and the other Master's students for making the transition to a new country, continent, and culture a supportive and inviting one. I would not have succeeded without you all. Another big thank you to the OSI Ultimate team for inviting me in as your coach and your friend. Finally, much love to my friends from the Midwest, wherever you are in the world these days. You know who you are.

Daniel Christopher Herman

(6)

(7)

Preamble

The Planck satellite has given the elds of astrophysics and cosmology the rst high resolution view of the entire sky in the microwave regime. The data from the four years of observation has revealed the nature of the Cosmic Microwave Background's (CMB) anisotropies, giving the scientic community access to information about the conditions of the early universe. In addition, the Planck data also contains a wealth of information about the conditions of the galaxy thanks to the telescope's broad range of detector frequencies and the polarization sensitivity of the bolometers.

The ability to distinguish emission sources is of great importance to determining an accurate view of the CMB and the extragalactic background light. Much of the Planck High Frequency Instrument (HFI) data is contaminated by Galactic thermal dust emission, a dominant source of radiation in the microwave and far-infrared regimes that is the result of the heating of dust grains by starlight. While the community has been able to phenomenologically describe this emission well since the rst full-sky far- infrared surveys (COBE), eectively reproducing data through physically motivated simulations has proven dicult.

Creating a dust model that not only describes the observed emission across frequency space, but is physically motivated and is consistent with our understanding of the interstellar medium (ISM) is essential. An eective physical dust model would be instrumental in separating galactic emission from the background radiation, particularly being able to distinguish the polarization of dust radiation from the polarization of the CMB. The polarization of light in the CMB can glean information about some of the earliest moments of the history of the universe and is highly sought after. Outside the eld of cosmology, a physical dust model could inform astrophysicists about the conditions within the ISM, the strength of star light, and the process in which dust is formed within our galaxy.

An accurate dust model is also required in order to determine the strength of the cosmic infrared background monopole (CIB) and its anisotropies. As the CIB comes from dust emission of very distant galaxies, the shape of the spectral energy distribution (SED) is similar to that of our Galaxy's own dust emission.

In this thesis, I investigate recent attempts to create full-sky galactic thermal dust models by looking at the connection between thermal dust emission and the hydrogen column density. Using Planck and COBE/DIRBE data and ITA's in-house component separation codeCommander, the ecacy of single component and two-component dust models are investigated. Calibration of data sets in the sub-millimeter/far-infrared

(8)

has proven dicult for component separation without making assumptions about the dust SED, and an attempt to remedy this issue using the absolutely calibrated FIRAS products is also investigated in this thesis. Current and future work to more fully characterize the issues with thermal dust modeling are also outlined.

(9)

Introduction

(14)

(15)

Chapter 1

Modern Cosmology and its History

Throughout the millennia, humanity has been fascinated about the cosmos and our place in the universe. For most of human history, the ideas about our origins were based upon surface level observations and myths. With the creation of the rst telescope in 1610 humans could peer into the depths of space to begin to better understand the nature of the universe. Our progress as a world-wide collective has been remarkable over the last 400 years. This chapter contains a brief introduction to the modern cosmological theory, the ΛCDM model, the history of the analysis of the Cosmic Microwave Background, and future prospects.

1.1 Modern Cosmology

Cosmology is the study of the dynamics and evolution of the universe as a whole. Much of modern cosmology rests upon several transformative discoveries in the past 125 years, namely Einstein's discovery of the General Theory of Relativity, Lemaître's discovery of the expansion of the universe, the abundance of light elements in the universe, and the cosmic blackbody radiation known as the Cosmic Microwave Background (hereafter referred to as the CMB).

Modern cosmological theories depend upon two foundational principles about the universe. First is the Cosmological Principle, which states that the universe we live in is isotropic and homogeneous: it appears the same in every direction, regardless of the point of observation. The second principle is the General Theory of Relativity, which connects the shape and behavior of spacetime to its energy content. The CMB is also of great importance for cosmology as it provides us with a snapshot of the young universe and its characteristics. The information within this radiation speaks volumes about the properties of the universe in its adolescence, and perhaps even information from earlier in its life. These are some of the reasons that theorists, observers and analysts are working to investigate this ancient signal.

The cosmological models we create are mathematical descriptions of the history of the universe, from its emergence to today. Information from the CMB and other extragalactic observations has been tied together to create a standard model of cosmology,

(16)

known as theΛCDMmodel. The model is called such because of the two main components in our model of the universe, dark matter and dark energy. This model describes an expanding universe which is dominated by dark energy, whose characteristics are en- capsulated in Λ, otherwise known as the cosmological constant, and cold dark matter, CDM. Both of these characteristics of the universe are empirically elusive. The models concerning their behaviors and origins are under constant scrutiny and investigation by the scientic community. According toΛCDMand observations, the energy content of the current universe is composed of69% dark energy,26%CDM, and a mere 5%regular matter with which we interact and of which we are made. The proportions of these three components and the manner in which they relate to each other is crucial to how the universe evolved into what we observe today. If not explicity referenced elsewhere, the contents of this chapter are based on "Modern Cosmology" by Scott Dodelson [1]

and "Lecture Notes on General Relativity" by Sean Carroll [2].

1.2 Universal Characteristics

TheΛCDMmodel is crafted to describe the contents of our universe, how they evolve, and how they interact with one another. Those with a basic interest in astronomy are familiar with the Hubble constant, H0. The Hubble constant is the present value of the Hubble parameter, H. The Hubble parameter is dened by the Hubble-Lemaître Law, which relates the speedv at which a object at distancedis moving away from an observer,

v=Hd. (1.1)

The most recent estimates for H₀ from the Planck Collaboration stand at 67.37± 0.54km/s/Mpc [3], however this value is not entirely consistent with local measurements of H0 [4]. This disagreement is an active topic of research and the resolution of this issue is of great importance to modern cosmological theories.

It has been observed that the rate of the expansion of the universe is not constant, it is accelerating. To understand the history of the universe, one must understand how it expanded in the past. This rate of expansion is tied directly to the ve basic components of our universe: baryons (b), dark matter (m), neutrinos (ν), photons (γ), and dark energy (ΛCDM). The relative densities of the above components are described in the following equation, whereΩx represents the relative density of component x,

Ωb+ Ωm+ Ων+ Ωγ+ ΩΛ= 1. (1.2) According to the General Theory of Relativity, the geometry of space-time is dependent upon the energy content within, and therefore the expansion of the universe changes with the relative densities. The Hubble parameter at a given timet is dened by the relation,

H(t) = a(t)˙ a(t) =H0

q

(Ω_b+ Ωm)a(t)⁻³+ (Ων+ Ωγ)a(t)⁻⁴+ ΩΛ, (1.3)

(17)

1.3 The Young Universe 5 whereais a time dependent parameter called the scale factor and a˙ is the derivative of awith respect to time. Today, the scale factor is unity, and decreases as we look back towards the Big Bang, asymptotically approaching zero. Inspecting equation 1.3, one can see that the relative densities of the components changes with time. According to current cosmological parameters, we can divide the history of the universe into three specic epochs: a radiation dominated era, a matter dominated era, and a dark energy dominated era. We currently live in a dark energy dominated universe, which is driving the acceleration of the expansion of the universe.

1.3 The Young Universe

The time scale of the early universe can be broken into three epochs, which I denote as infancy, youth, and adolescence. Details on the universe before recombination are not observable by means of electromagnetic radiation as light was unable to move freely through the universe. The era of recombination is what separates the adolescence and youth of our universe. Yet our current models, which are constrained by observations, can allow us to make educated guesses about the conditions before recombination.

1.3.1 Infancy

A common way to conceptualize the very beginning of the universe in modern cosmology is something akin to a singularity: everything compacted to an innite density in an innitesimal volume. The rst ∼10⁻⁴³ seconds of the universe constitutes what is commonly known as the Planck era. Theorists believe that in such an intense environ- ment, the four forces of nature that we recognize today (electric, weak/strong nuclear, and gravity) broke down and all combined together.

Following the Planck era, the universe enjoyed a brief period of extreme expansion called ination. It is believed, from observational hints, that this period of ination lasted only a brief moment and the size of the universe grew on the order of 60 e-folds (10²⁶ times its original size). The energy from ination is theorized to have decayed into normal particles in a process called reheating as ination came to an end. This process of ination allowed small, quantum uctuations in the universe to "freeze-out"

and grow to larger scale irregularities that seeded the growth of the galaxies and galaxy clusters we observe today.

Currently, there have been no direct observations of ination. The existence of ination is inferred by a few key problems in early universe observations. Ination helps explain how the universe became so isotropic and homogeneous, as the period of ination allowed the universe to grow to such a size where it could equilibrate before expanding to the point where portions of the universe could no longer exchange properties. Ination is used as a tool to describe this issue, known as the horizon problem. The horizon problem comes from the recognition that two widely separated points that did not have time to come into causal contact share the same temperature at the time the CMB was formed. Without something akin to ination, the universe would not have expanded

(18)

enough for equal temperatures in the CMB separated by large angular distances to have been produced by the same point.

As ination neared its end, baryons and anti-baryons were able to form, annihilating and creating photons, lling the universe with a dense radiation eld with roughly10⁹ more photons than protons.

1.3.2 Youth

After approximately a second of these extreme conditions the universe began to cool.

At this point the universe was full of the particles we observe today: protons, electrons, neutrinos and photons. We now enter the era where the universe and matter as we know it began to take shape. As the universe continued to expand, the temperature of the universe dropped to the point (T ≈1.5MeV) where primordial neutrinos were able to freely stream through the thick plasma [5]. Once the universe cooled down to roughly T ≈1eV, electrons were able to combine with protons to create the very rst elements of the universe. This era is known as Big-Bang Nucleosynthesis (BBN). This period of time is responsible for all of the neutral hydrogen and a majority of the helium and deuterium present today. The abundances of these particles is useful for constraining cosmological models.

Following roughly400,000years of an opaque universe, the universe made its next big transformation. Up until this point, the universe was so densely packed with electrons that photons could not escape due to Compton scattering. This marks the beginning of the Era of Recombination. As electrons combined with protons, the mean free path of photons begins to increase until photons scatter o electrons for the last time and stream freely into the at, transparent universe. These photons can be observed today as microwave radiation across the entire sky and constitute the Cosmic Microwave Background. The CMB is very important to understanding the early universe as the information it holds gives us a glimpse into the conditions of the universe when these photons scattered for the last time.

1.3.3 Adolescence

Following the nal scattering of photons, the universe entered the cosmological Dark Ages. Although light was free to escape into the universe at this time, light-producing structures such as stars and galaxies had not yet formed. The only light in the universe at this time was the CMB photons and photons released from neutral hydrogen atoms:

the 21-cm line emission.

During this era the universe continued to cool, and gravity began to pull matter and dark matter together, beginning the rst baryonic structure growth in the universe.

Assisted by dark matter, clouds of hydrogen collapsed, forming the rst stars. As galaxies grew, they were gravitationally drawn to one another and the rst galaxy clusters began to appear approximately 500 million years after the Big Bang [6]. The Dark Ages ended around the universe's billionth birthday, and since then has looked like the universe we are familiar with; lled with dust, stars, galaxies, etc.

(19)

1.4 Why Cosmologists Care About the CMB 7

1.4 Why Cosmologists Care About the CMB

The CMB is one of the richest tools for understanding our cosmological heritage. While cosmologists have learned a great deal about the nature of our reality from this early light, the CMB still contains information that can oer constraints for current and future cosmological theories, such as a theorized imprint of ination in the polarization of CMB photons.

Figure 1.1: Angular power spectrum of the CMB from Planck [7].

The angular power spectrum of the CMB gives cosmologists a wealth of information concerning the condition of the universe when the light scattered o of primordial electrons for the last time. For those unfamiliar, a power spectrum shows the strength of variation as a function of an observable. In this case, the angular power spectrum of the CMB shows the variation of temperature as a function of angular separation in the sky, as shown in gure 1.1.

Thanks to a long history of improving CMB observations, temporarily culminating in the Planck satellite, cosmologists have been able to put strong constraints on the nature of our universe. To a good approximation, the universe is geometrically at, the matter content of the universe is dominated by cold dark matter, and the rate of expansion of the universe is accelerating. While these precise observations have answered many questions, verifying some theories while rejecting others, there is much more to be discovered and much more analysis to be done.

(20)

1.5 Early CMB Detections and Theories

Following the discovery of the expansion of the universe by Lemaître and Hubble in 1927 and 1929 respectively, there have been many theories concerning the state of the universe before our time [8, 9]. For many years, the idea of a steady state universe with a constant relative matter density was theorized [10, 11]. At the same time, theories of an initial super-dense, extreme-temperature beginning of the universe began to surface.

Investigations of the subject by Dr. G. Gamow, R. Alpher, and R. Herman began as early as 1948 [12, 13, 14]. These papers predict a remnant temperature from this initial radiation to be on the order of a few Kelvin (∼5K according to the articles by Alpher and Herman).

Arno Penzias and Robert Wilson, working for Bell Laboratories in Holmdel, New Jersey were working with a radiometer horn in 1965. While testing this horn, the two scientists discovered that wherever they pointed their horn in the sky, they received an excess background signal that could not be explained through systematic means.

The unaccounted-for antenna temperature was found to be 3.5±1.0K at a frequency of 4080MHz (7.35cm) [15]. Penzias was informed about a preprint by Jim Peebles, who at the time worked at Princeton University. In Peebles' writing, he described a cosmic background radiation that would come from an early state of the universe in which the matter and radiation density is very high (T ≥10¹⁰K). Penzias shared the excess antenna temperature discovered by himself and Wilson with Robert Dicke from Princeton. After traveling to Bell Laboratories to check out the experiment themselves, Dicke, Peebles, P. G. Roll and D. T. Wilkinson [16], published a paper titled "Cosmic Black-Body Radiation" which interprets the discovery of the3.5K excess radiation and describes some constraints on cosmological models. Penzias and Wilson published a paper title "A Measurement of Excess Antenna Temperature At 4080 Mc/s" in tandem with the Princeton group. Penzias and Wilson would receive the Nobel Prize in 1978 for the rst detection of the Cosmic Microwave Background.

At the same time that these papers were published, Roll and Wilkinson had already begun a new experiment to search for this background radiation by constructing a similar radiometer horn sensitive at a wavelength of3.2 cm. The group decided to look at 3.2cm because of a known lack of galactic emission and low relative atmospheric absorption. The results conrmed the anomalous signal found by Penzias and Wilson by detecting a black body with temperature of3.0±0.5K [17].

Once this highly isotropic background radiation was discovered, astronomers began searching for any anisotropies that could be found in this radiation. The cosmological theories concerning a background radiation from the early, expanding universe predicted that structure observed today (galaxies, clusters, voids, etc.) were seeded by initial uctuations. If this idea were true, then the imprint from these initial uctuations should be seen in the CMB. The rst departure from isotropy to be pursued and discovered was the CMB dipole, which comes from the Earth's relative motion with respect to the surface of last-scattering reference frame. The rst results from Conklin (1969) [18], show a dipole with a magnitude of a few mK (∆T /T ∼10⁻³). This observation put an initial upper limit for observations of anisotropies on smaller scales.

(21)

1.6 Creating Cosmological Conjectures 9

1.6 Creating Cosmological Conjectures

Between the late 1960s and the 1980s, following the verication of the background radiation and an initial temperature estimate, theorists began exploring the implications of an expanding universe. E.R. Harrison showed in 1968 that random statistical uctuations in spacetime could not seed the formation of galaxies [19]. His following investigation regarding the nature of primordial quantum uctuations [20] led to Zel- dovich predicting metric uctuations on the order of 10⁻⁴−10⁻⁵ [21], leading to the formation of galaxies and galaxy clusters. Telescopes of the time lacked the sensitivity and angular resolution required to detect temperature uctuations this small, yet there was still much that could be discovered concerning the characteristics of the CMB.

1.7 Discovering the CMB Temperature

Figure 1.2: FIRAS observations of the CMB strength over the 2.27−21.33cm⁻¹ frequency range. The error bars are less than the line thickness [23].

(22)

1.7.1 COBE

Between 1989 and 1991, NASA's COBE satellite was used to probe the temperature of the CMB for the rst time. COBE was constructed in Maryland, USA at the God- dard Space Flight Center with three instruments on board designed to probe the CMB temperature, its anisotropies, and the infrared (IR) dust emission from our own galaxy and others. These instruments were called FIRAS (Far InfraRed Absolute Spectro- photometer), DIRBE (Diuse InfraRed Background Explorer), and DMR (Dierential Microwave Radiometer). COBE assumed a polar orbit around the Earth, facing away from the Earth and94^◦ to the Earth-Sun line. This always kept the Sun on the side of COBE so that the satellite's Sun shield would always protect the detectors [22]. The goal of the COBE mission was to determine the spectrum of the CMB, map out diuse galactic radiation in the infrared, and search for anisotropies in the CMB.

FIRAS showed that the CMB did indeed t a perfect blackbody with a temperature of T₀ = 2.7255±0.0009K (data shown and t in gure 1.2), as well as nding more information about CMB dipole anisotropy [23]. The DMR instrument also played a crucial role in early CMB detections. With an angular resolution of 7^◦, scanning the full sky at 31.5 GHz, 53 GHz, and 90 GHz, the data from DMR allowed researchers to measure the CMB power spectrum rst time [24].

1.8 Precision Cosmology

1.8.1 WMAP

Following the successful COBE mission, the WMAP (Wilkinson Microwave Anisotropy Probe) mission was proposed to NASA in 1995, and began its nine year observations following its June 2001 launch. WMAP ew with the intention of searching for anisotropies in the CMB at smaller angular scales, giving the scientic community a more precise power spectrum. WMAP took position at the Earth-Sun L2 point, such that the Earth and Sun were always behind the satellite's focal plane.

WMAP used pairs of polarization sensitive dierential microwave radiometers. In- stead of measuring the signal from a zero-point, the satellite measures the dierence in signal between two points on the sky. Compared to the DMR instruments7^◦ angular resolution, WMAP had sub-degree resolution, ranging from0.93^◦ at 22 GHz, to<0.23^◦ at 90 GHz.

The WMAP analysis teams produced full sky maps of the foregrounds (gure 1.3), full sky polarization maps, and created an angular power spectrum of the CMB up to l∼ 1200[26]. With these results, theorists could test model assumptions against real observations of the early universe, breaking degeneracies between some parameters and setting constraints on others [27].

(23)

1.8 Precision Cosmology 11

Figure 1.3: Strength of the galactic foregrounds at each of the ve WMAP bands [25].

1.8.2 Planck

With a breadth of knowledge concerning the CMB, noting the strengths and weaknesses of WMAP, the scientic community prepared for the next iteration of precision cosmology. The new CMB searching experiment came in the form of the European Space Agency's Planck satellite. Planck operated from 2009-2013, and like WMAP, took its position at L2 where it assumed a Lissajous orbit.

As an improvement to the WMAP satellite's ve bands, Planck had nine bands spread out over a broader frequency range, from 30 GHz up to 857 GHz. The addition of bands at higher frequencies allowed for greater accuracy with foreground removal, specically galactic thermal dust emission.

While WMAP took advantage of resolutions up to 14 arc-minutes at 90GHz, the Planck telescope had a base resolution of 33 arc-minutes at 30 GHz, and a maximum resolution of 5 arc-minutes at 857 GHz. The resolution and sensitivity of the Planck satellite was such that the largest uncertainties in the measurement of the CMB would come from the eectiveness of foreground removal. Analysis of the Planck data has yielded the CMB angular power spectrum up tol∼2500, a notable improvement from WMAP.

The Planck mission was originally planned to observe at least 95% of the sky over the course of 15 months. However, after detector calibration, the mission was extended twice, achieving four and half years of observation and producing ve full-sky maps.

The spacecraft received its nal decommissioning command on 23 October 2013, after which Planck removed itself from L2 and assumed a heliocentric orbit, keeping L2 open for future missions such as the James Webb Space Telescope. Data taken from the

(24)

Table 1.1: Cosmological parameters determined from WMAP and Planck data [3, 27].

Description Parameter WMAP best-t Planck best-t

Age of the universe t₀ (Gyr) 13.74±0.11 13.799±0.021 Hubble's constantkmMpc⁻¹s⁻¹ H0 70.0±2.2 67.74±0.46

Baryon density Ω_b 0.0463±0.0024 0.0486±0.0010

Cold dark matter density Ωc 0.233±0.023 0.2589±0.0057 Dark energy density ΩΛ 0.721±0.025 0.6911±0.0062 Density uctuations at8h⁻¹Mpc σ₈ 0.821±0.023 0.8159±0.0086 Scalar spectral index ns 0.972±0.013 0.9667±0.0040 Reionization optical depth τ 0.089±0.014 0.066±0.012

Planck satellite has allowed cosmologists to set tight constraints on observational cosmological parameters. Table 1.8.2 shows best t values for an assortment of cosmological parameters determined by WMAP and Planck data.

1.9 The Future of Cosmology

The results from the WMAP and Planck satellites have set a foundation for modern physics. The information deduced from the CMB holds huge implications for past and future theories concerning the nature of our universe. There is still much more to be found, and many more theories to be tested.

1.9.1 CMB Polarization

One of the most pressing questions remaining in probing the nature of the CMB is the polarization of CMB photons. In the early universe, uctuations in the density of matter during ination caused gravitational waves to propagate through the plasma of the early universe, stretching and compressing space as they moved. When a photon scattered o of an electron in this stretched space, the polarization direction of the photon was aected. It is theorized that there should be a detectable remnant from this time in the polarization of CMB photons. In CMB analysis, two dierent types of polarizations are classied: the E and B-modes. E-mode polarization is curl free, while B-mode polarization is divergence free, as illustrated in gure 1.4. If ination really did occur in the way that we have modeled it, this signal may be detectable in the CMB as B-modes.

(25)

1.9 The Future of Cosmology 13

Figure 1.4: BICEP-2 B-mode signal (left) [28], and an example of the shape of E and B-mode polarizations (right) [29].

1.9.2 Experimental Endeavors

There are many current and proposed projects related to CMB polarization. A recent project, BICEP-2, published a paper in 2014 stating that they had detected a true CMB B-mode signal (gure 1.4). However, the Planck team was convinced that this signal was not a true detection of CMB B-modes, but instead an excess contamination due to galactic foregrounds that the BICEP-2 analysis team had not yet taken into account.

With its seven polarization sensitive bands, Planck had been able to map out polarization contamination quite well for both synchrotron and thermal dust emission. After months of joint analysis, a paper was published verifying the Planck teams suspicions about the validity of the signal. This error in analysis highlights the importance of modeling and removing foregrounds.

There are other current projects looking to detect these elusive B-modes at small scales, such as SPIDER and LSPE. Concerning galactic foreground polarization signals that could prevent viewing CMB B-modes, C-BASS [30], S-PASS [31], and QUIJOTE are on the hunt. The LiteBIRD satellite, which will probe the sky for polarized radiation between 40 and 400 GHz, was selected by JAXA to move forward on May 21, 2019.

(26)

(27)

Chapter 2

The Microwave Sky

Retrieving an accurate detection of the Cosmic Microwave Background is not a trivial task. There are many signals that are emitted in the Galaxy in the microwave regime. Each of these components dominate for dierent frequency ranges. How these foreground components are modeled aects the accuracy with which we can detect the true CMB signal. There are ve main components, namely spinning dust (also known as Anomalous Microwave Emission (AME)), synchrotron radiation, free-free emission, molecular line emission, and thermal dust radiation. The presence of zodiacal light also aects our observations, as it responsible for strong emission in the far-infrared (FIR).

The spectral energy distribution (SED) and strength of each foreground in CMB analysis frequency space is shown in gure 2.1 for both the temperature and polarization cases. In this section the physics and frequency behavior of each of the components are explained.

Figure 2.1: Frequency dependence of foregrounds for temperature (left) and polarization (right) [32].

(28)

2.1 Synchrotron Emission

Synchrotron radiation is produced when electrons move through a magnetic eld. As electrons move through the eld, they are accelerated by the Lorentz force. These electrons become "trapped" by magnetic eld lines, such that they revolve around magnetic eld lines as depicted in gure 2.2. For non-relativistic electrons, the frequency of the radiations caused by this cyclic movement is entirely dependent upon the strength of the magnetic eld. However, as an electron becomes relativistic, the period of oscillation around the eld line decreases and the power of the radiation increases. In this case, the emission of the radiation is strongly beamed in the direction of motion of the electron, and the frequency of this electromagnetic radiation is dependent on the characteristic energy of the electron. Therefore, this radiation is often only observed for a eeting moment as the beam of radiation passes across the observer's eld of view.

In the case of foregrounds, free, highly energetic electrons get trapped by Galactic magnetic eld lines. Across the Galaxy, the magnetic eld lines are not all homogeneous, and the speed of electrons varies as well. As these speeding electrons become trapped by the magnetic eld, they begin to radiate. Because the electrons radiate very rapidly along a specic axis, the radiation they create is highly polarized (∼75%). The fact that synchrotron radiation is so strongly polarized is of great importance in E-mode and B- mode CMB analysis since the synchrotron signal dominates over the CMB polarization signal as seen in gure 2.1.

The distribution of relativistic electron energies leads us to expect that the frequency dependence of synchrotron radiation goes as P(ω) ∝ ω^β^s where we denote β_s as the spectral index for synchrotron radiation [33]. The Planck Collaboration 2015 results show that the spectral index of synchrotron radiation throughout the Galaxy is consistent with a nearly constant value of β_s =−3.11 for frequencies above 20 GHz [34].

However, details on the spectral index below 20 GHz are not well dened as there is not enough data to measure it properly. Current synchrotron sky surveys include S-PASS and C-BASS at 2.3 GHz and 5 GHz respectively [30, 31], will help constrainβ_s at lower frequencies.

Figure 2.2: Schematic of an electron cycling around a magnetic eld line [35].

(29)

2.2 Free-Free (Bremsstrahlung) Emission 17

2.2 Free-Free (Bremsstrahlung) Emission

Figure 2.3: A graphic showing the process of bremstrahlung or braking radiation [36].

Free-free emission, otherwise known as Bremsstrahlung (braking radiation), is caused by free electrons interacting with ions. In the astrophysical case, these free (unbound) electrons are thermally hot, meaning that their characteristic energies are a result of the temperature of their en- vironment. This radiation is emitted when these high speed electrons become close enough to ions such that the electron is accelerated. A cartoon of this interaction is shown in gure 2.3. Free electrons in our galaxy are generally tied to star-forming regions where stellar radiation ionizes atoms in dust clouds. Specically, there is a correlation between free electrons in space and Hα radiation, as both types of radiation are emitted in the same high temperature regions in the Galaxy. Initial full sky CMB analysis used galactic Hα templates to predict where free-free emission is strong within the Galaxy [37]. Hαtemplates trace

the electron column density, which, along with the electron temperatureT_edetermines the strength of the emission. The electron temperature changes the value of the power- law index, however the power-law is well approximated byβ ≈ −2.13.

(30)

A_s

10 30 100 300

KRJ@ 408 MHz

Figure 2.4: Full sky map of synchrotron emission from Planck Collaboration 2015 analysis [34].

A_ff

0 10 100 1000

cm⁻⁶pc

Figure 2.5: Full sky map of free-free emission from Planck Collaboration 2015 analysis [34].

(31)

2.3 Anomalous Microwave Emission 19

2.3 Anomalous Microwave Emission

Initial attempts to subtract foreground emission at low frequencies yielded some surpris- ing results. Within a year, Kogut et al. (1996) [38], de Oliveira-Costa et al. (1997) [39]

and Leitch et al. (1997) [40] published papers mentioning an excess of galactic emission within the 10-50 GHz range. This unexpected emission seemed to be correlated with both the DIRBE240µm, 140µm and 100µm maps, which are strongly contaminated by thermal dust emission. Leitch et al. were the rst to coin the term Anomalous Microwave Emission (AME).

Since there is a high correlation between this anomalous radiation and the dust structure of the Galaxy, many theories concerning how this dust may emit this radiation have arisen over the decades. Draine and Lazarian (1998) [41] theorized that small spinning grains would emit electric dipole radiation within the frequency range where AME is present. It is due to this theory that the emission in this range is often referred to as spinning dust. In their paper, Draine and Lazarian argue that free-free emission cannot account for this anomalous emission because the energy required to heat electrons to this level (T ≥10⁶K) is far greater than the energy released by supernovae.

The true nature of this emission is still not well understood 20 years later, but the ability to separate this emission from other foregrounds as well as the CMB has been made possible by modeling on purely phenomenological grounds.

Asd

0.01 0.1 1 10

mKRJ @ 30 GHz

Figure 2.6: Full sky map of spinning dust (AME) emission from Planck Collaboration 2015 analysis [34].

(32)

2.4 Line Emission

Line emission from molecular energy transitions also adds an appreciable amount of emission in the microwave sky. Carbon monoxide (CO) line emission has a large eect as multiple rotational energy transitions occur within this frequency range. CO emission is due to discrete changes in the rotational energy of the rigid molecule. Because the energy levels are discrete, the emission is easy to predict and correlate across frequencies.

The emission is observed at sharp frequencies corresponding to the J = 1 → 0 (115 GHz),J = 2→1 (230 GHz) and J = 3→2 (345 GHz) transitions. Due to the choice of the Planck satellite's detector bands, the emission from CO is non-zero and must be modeled. Carbon monoxide molecules are formed alongside interstellar dust during star formation, and therefore the CO emission is strong in regions with strong thermal dust emission. However, the emission from CO is not as diuse as thermal dust: it is distinct and sharp.

ACO10

0 10 100

KRJkm s⁻¹

Figure 2.7: Full sky map of CO 1-0 line emissionfrom Planck Collaboration 2015 [34].

(33)

2.5 Zodiacal Light 21

2.5 Zodiacal Light

While most of the foreground contamination in the microwave sky comes from outside of the solar system, there is one local component which must be taken into account.

Satellites used for CMB detection are designed and positioned so as to avoid contamination by sunlight. However, dust grains along the ecliptic in our solar system absorbs some of the light from the sun. This unwanted emission creates a distinct pattern visible in data sets. The strength and shape of zodiacal light (hereafter referred to as zodi) changes with the year and location of the satellite making observations. As a result, zodi corrections need to be done for each data set.

Figure 2.8: Zodiacal light template for the Planck 857 GHz channels.

(34)

2.6 Thermal Dust

Ad

0.01 0.1 1 10

mKRJ @ 545 GHz

Figure 2.9: Full sky map of thermal dust emission from Planck Collaboration 2015 analysis [34].

Star dust, as it is commonly referred to, is created through the generation of stars and is the key to the creation of planets, asteroids, as well as simple and complex molecules. When a star dies, the outer layers are blown o either by radiation or through a violent event such as supernovae. These layers are rich in metals, and move through space in nebulae or molecular clouds. As carbon and silicon traverse these nebulae, they begin to create simple molecules and clump together creating small dust grains. The dust grains absorb star light, which causes them to heat up. The dust grains radiate away this energy as electro-magnetic radiation in the infrared and microwave regime. This is thermal dust emission.

While the CMB signal is weak in the infrared, the behavior of thermal dust is important to component separation work since the signal dominates for most of the Planck High Frequency Instrument data. The thermal dust spectrum looks like that of a modied blackbody so our understanding of the behavior of the dust at higher frequency ranges aects our modeling between 100 and 1000 GHz. Details on the modied blackbody model are described at length in section 2.7.1. The emission from thermal dust is between 5−15% polarized and therefore understanding thermal dust is important to detecting the polarization of the CMB. The contribution of polarized dust emission over frequencies is shown in gure 2.1.

Thermal dust plays a role in many elds of astronomy due to the breadth of frequencies that galactic dust aects. Beginning with visible and ultraviolet light, thick

(35)

2.6 Thermal Dust 23

Figure 2.10: Full sky optical map of the Milky Way Galaxy as seen by the Gaia telescope [42].

clouds of dust absorb much of the star light causing dusty regions to look black as seen in gure 2.10. In the mid-IR, galactic dust switches from strong absorption to emission where large peaks can be found at specic wavelengths. These wavelengths correspond to polycyclic aromatic hydrocarbons (PAHs) [43] (gure 2.11). Moving further up the wavelength regime to the far-IR and into the microwave where CMB analysis takes place, dust takes a shape similar to a blackbody, with a changing frequency dependence. For this reason, much of the dust modeling done for CMB analysis assumes a modied blackbody shape, described in section 2.7.

2.6.1 Optical Properties

There are two primary properties of dust that are observable for astronomers: the dust extinction and the dust emission. As mentioned above, dust absorbs photons that come from regular stellar emission, specically in the optical and UV wavelengths. As a result of this absorption, the light from background stars looks both dimmer and more red. Mapping the reddening of background sources due to dust is particularly useful in extragalactic astronomy [44].

This absorption of stellar photons causes the dust grains to heat up, which in turn causes the dust grains to emit thermally. The characteristic temperature at which these dust grains emit is dependent on the intensity of the interstellar radiation eld (ISRF), the dust grain size distribution, the dust grain composition and the dust-to-gas ratio.

(36)

Fig. 2.Dust emission for the DHGL medium. Grey symbols and curves indicate the observed emission spectrum (see Sect.4.1) forN_H = 10²⁰H cm⁻². The mid-IR (∼5−15μm) and far-IR (∼100−1000μm) spectra are from ISOCAM/CVF (ISO satellite) and FIRAS (COBE satellite), respectively. The triangle at 3.3μm is a narrow band measurment from AROME balloon experiment. Squares are the photometric measurments from DIRBE (COBE). Black lines are the model output and black squares the modeled DIRBE points taking into account instrumental transmission and color corrections.

Fig. 3.Long wavelength emission of dust in the DHGL medium.

Grey symbols and curves indicate the observed emission spectrum (see Sect.4.1) forNH = 10²⁰H cm⁻². The spectrum is a FIRAS (COBE satellite) measurment. Squares and diamonds are the photometric measurments from DIRBE (COBE) and WMAP, respectively. Black lines are the model output and black squares the modeled DIRBE points taking into account instrumental transmission and color corrections.

4.2. The model

To model the DHGL data set we use three dust components:

(i) PAHs; (ii) hydrogenated amorphous carbon (hereafter amC) and (iii) amorphous silicates (hereafter aSil). The properties of

each type are described in the AppendixA. In the course of dust evolution, composite or core-mantle (silicate-carbon) grains are likely to appear that would lead to a similar polarization of both the 3.4μm absorption band of amorphous carbon and the 9.7μm band of the silicates (seeAdamson et al. 1999;Li & Greenberg 2002). We do not consider such composite grains here because recent spectropolarimetric measurements byChiar et al.(2006) indicate that the 3.4μm band is not polarized while the 9.7μm band along the same sightline is polarized. Although such observations should be pursued, these results may indicate that the carriers of the 3.4 and 9.7μm features belong to physically separated dust populations where the former are poorly elongated or not well aligned with the magneticﬁeld while the latter are.

Further constraints on this issue will be obtained fromPlanck measurements of polarized dust emission in the submm range.

The size distribution and abundance of the dust components have been adjusted in order to reproduce both the extinction and emission. The required size distributions are shown in the form of their mass distributions in Fig.1. The population of amorphous carbon dust has been divided into small (SamC) and large (LamC) grains, but the overall size distribution of carbonaceous grains (PAH and amC) is continuous. Following previous studies (e.g.Weingartner & Draine 2001a), the smallest grains (PAH and SamC) size distributions are assumed to have log- normal distributions (witha0the centre radius andσthe width of the distribution). The LamC and aSil size distributions fol- low a power law (∝a^α) starting atamin and with an exponen- tial cut-oﬀof the form e⁻^[(a−a^t^)/a^c^]^γfora≥ at(1 otherwise) at large sizes. As noted byKim & Martin(1995), such a form in the cut-oﬀis required to explain the observed polarization in the near-IR: the polarization capabilities of the present dust model will be discussed in a future paper. The abundances and A103, page 6 of14

Figure 2.11: Dust SED for 1-1000 µm. Data from ISOCAM/CVF and FIRAS are in grey. Modeled dust emission is given by the black lines. Reproduced from Compiègne et al. 2011 [45].

2.6.2 Physical Properties

Typically, dust accounts for∼1%of the mass of interstellar gas. This dust is commonly composed of metals such as carbon, oxygen, magnesium, silicon and iron. Dust grains are constantly recycled in the interstellar medium. Therefore dust is quite diuse and is always changing densities throughout the Galaxy.

Dust grains are generally assumed to be on the order of 1 nm to 1 µm[46] in size.

However, the actual size distribution of the dust grains is dicult to measure. Dust can also be composed of many dierent types of metals, which are directly dependent on which stars caused the dust to form.

In physical dust models that have been investigated over the years, there are three main types of dust grains that are modeled: carbonaceous grains, silicate grains, and PAHs. These grains have been chosen due to distinct absorption features observed in dusty regions. The size distributions of these particles, their shapes, dielectric func- tions and alignment with galactic magnetic elds may vary, making the modeling very complex.

2.7 Thermal Dust Models

In this section a more in-depth description of the modeling and the physicality of these models is discussed. Historically, thermal dust modeling in component separation has been carried out in a phenomenological fashion. Since the COBE satellite data, it

(37)

2.7 Thermal Dust Models 25 has been understood that thermal dust emission can be well described by a modied blackbody curve. While this method has been eective at removing the dust in the frequency range where we can receive the CMB signal (gure 2.1), this model does not necessarily describe the physical behavior of the dust.

2.7.1 The Modied Blackbody

Modeling galactic thermal dust emission from a purely phenomenological perspective allows us to describe this emission in a simple manner, with few parameters. Generally, this phenomenological model assumes that thermal dust emits like a blackbody, but with a spectral dependence. Emission from thermal dust at a given frequencyν is given empirically by a modied blackbody (MBB) model,

Iν =τνBν(T), (2.1)

where I_ν is the intensity of the radiation from dust, B_ν(T) is the Planck function for blackbody emission at temperature T, andτν is the frequency dependent dust optical depth which modies the shape of the dust SED. The optical depth term is the product of the dust opacity cross section per unit mass,κ_ν, and the dust mass column density:

τ_ν =κ_νrm_pN_H, (2.2)

where the dust mass column density is separated into its components. The dust mass column density is a product ofN_HI, the hydrogen column density,m_p, the proton mass, andr, the dust-to-gas ratio. This leads us to a model which can physically describe the thermal dust emission,

Iν =κνmprN_HBν(T_d). (2.3) In phenomenological models, κ_ν is assumed to take a power-law shapeκ_ν =κ₀(ν/ν₀)^β where κ0 is dened at a reference frequency ν0. We can contract equation 2.3 into a simpler model where all of the variables that can alter the optical depth of the dust are contained in a single frequency dependent component:

I_ν =τ_ν₀ν ν₀

βobs

B_ν(T_d). (2.4)

This leaves us with a simple two parameter model, with the observablesβ_d, the spectral index, and T_d, the dust temperature. The amplitude of the dust emission itself, τ₀ is also determined. Historically, the spectral index has been assumed to have a value of

∼2.0which is motivated by laboratory experiments [44].

2.7.2 The Two Component Dust Model

When tting a modifed blackbody to the thermal dust emission observed by COBE, Finkbeiner et al. (1999) [47] noted that an improvement to the t was found when the sum of two modied blackbodies was used. The total dust SED could be composed

(38)

of two separate dust components with distinctly dierent characteristics. These components can be described by the combination of two separate MBBs: a hot and a cold component. This work was initially put forward by Reach et al. [48], which was later investigated again by Finkbeiner et al. [47] using COBE/FIRAS/DIBRE data, and most recently using Planck data in 2015 by Meisner and Finkbeiner [49]. The results from each of these studies has shown a preference for a two component dust model, as the two component model describes the full spectrum more completely. More recently Zheng et al. (2016) [50] used a blind component separation process to identify and remove foregrounds, nding a preference for a two-component model.

The shape of this two-component model spectrum is given by:

I_ν ∝h f₁q₁ ν

ν₀ β1

B_ν(T₁) +f₂q₂ ν ν₀

β2

B_ν(T₂)i

. (2.5)

The two component model is structured very intuitively, following the approach of single MBBs. The intensity of the dust emission is a sum of two separate MBBs with emission contributions f₁ and f₂. The sum of these two contributions is equal to unity. The variablesq1 andq2represent the ratio of the emission cross section to optical absorption cross section.

As will be discussed in chapter 6, there is good reason to believe that there are at least two dierent dust components present in the Milky Way, each with its own SED and spatial distributions in the Galaxy.

2.7.3 Physical Dust Models

In the interest of taking the next step in thermal dust analysis, many groups have created physical dust models in hopes of elucidating the physical nature of thermal dust in our galaxy [43, 45, 46]. Physical dust models are concerned with the composition of dust in the interstellar medium (ISM), its relation to hydrogen column density, and the polarization of the thermal dust.

Physical dust models have looked at three distinct types of dust grains to be responsible for the absorption of star light in the UV and visible, with emission in the IR and FIR. In the 1980s, the distinct spikey infrared emission features seen in gure 2.11 were identied as being caused by polycyclic aromatic hydrocarbons (PAHs). Amorph- ous carbonaceous dust is also considered to have an appreciable eect on thermal dust emission, as it can explain the 217 nm bump in observed extinction curves [45]. How- ever, carbon does not appear to be the only element responsible for appreciable dust emission. Silicate grains have also been identied as a constituent of galactic dust due to the recognizable bump in the dust absorption spectra at 9.7µm.

These types of dust have been observed through spectra, however the emission from these grains is dependent on a few key parameters. How much emission comes from the dust is dependent on the abundance of dust, the size of the grains that cause the emission, and the intensity of the ISRF.

The typical size of a dust grain is approximately 0.1 µm, and dust accounts for

∼1%of the mass of the ISM. Dust grains are expected to be aspherical, and are often

(39)

2.7 Thermal Dust Models 27 modeled this way due to the fact that spherical dust grains would not emit polarized radiation. Of course, if these aspherical dust grains were randomly oriented, there would be no net polarization. However, galactic magnetic elds induce grain alignment.

Carbonaceous dust grains have been shown to be polarization independent, which leads to the assumption that the polarization of dust emission depends on the composition of the dust grains [51]. It is expected that silicate grains are responsible for much, if not all of the polarization of dust emission and extinction.

In order to accurately predict the absorption and emission of radiation, the respect- ive cross sections must be calculated for each type of dust grain. The cross section is dependent on the geometry of the grains, so how these grains are structured is fundamental in creating a physical dust model. As physical dust modeling has progressed, there has been more focus on the distribution of the shape and size of dust grains. In the past two decades, increases in computational power and the introduction of the Planck data sets has allowed more thorough testing of physical dust models.

2.7.3.1 Draine & Li (2007)

The silicate-graphite-PAH model crafted by Draine and Li (2007) (hereafter DL07) [43]

was used to describe the IR and FIR emission while simultaneously predicting the IR absorption features discovered by the Infrared Space Observatory (ISO). In this model, a mixture of carbonaceous, amorphous silicate, and PAH grains are assumed. Graphite is also assumed to constitute an appreciable amount of the carbonaceous dust. The purpose of this model is to estimate PAH abundances, the intensity of starlight, and determine the total dust masses. Specic to this model is the distinction between two charge states of PAHs: either neutral or ionized (positively or negatively charged). The main parameters t in this model are the intensity of the ISRF (U) and the PAH fraction (q_PAH).

This model reproduces average Milky Way dust extinction and calculates a dust emission spectra based o of varying ISRF values. This model has been fundamental in physical dust modeling as it has given basic constraints on the size of PAHs and amorphous carbonaceous/silicate grains by creating a model that agrees well with FIRAS sub- millimeter dust emission.

With new data from the Planck satellite, the Planck Collaboration (2016) [52]

showed that the DL07 model under-predicted dust emission per unit extinction by a factor of 1.5 when looking at the observed dust SED perA_V at high Galactic latitudes.

2.7.3.2 Compiègne et al. (2011)

Compiègne et al.(2011) createdDustEM[45] to attempt to reproduce the dust extinction spectra while tting the dust emission SED. In contrast to the DL07 model, most of the carbonaceous grains that are not PAHs are assumed to be amorphous and still well describe the absorption bands at 3.4, 6.85 and 7.25 µm. The DustEM model focuses on tting three dust components: PAHs, hydrogenated amorphous carbon, and amorphous silicates (aSil). The carbonaceous grains are separated into PAHs, small

Thermal Dust Emission in the Microwave Frequency Range