CALIFORNIA STATE UNIVERSITY, NORTHRIDGE

Dust Temperature Distributions of Herschel Detected

A thesis submitted in partial fulfillment of the requirements

For the degree of Master of Science in Physics

By

Jonathan Acuna

May 2019 The thesis of Jonathan Michael Paul Acuna is approved:

Dr Ana Cadavid Date

Dr Farisa Morales Date

Dr Damian Christian, Chair Date

California State University, Northridge

ii Acknowledgments

Thank you, Mom and Dad, for showing me the value of affordable living.

Thank you, TA officemates, for a environment conducive to hard work. Thank you,

Python Developers, for all the excellent libraries. Thank you, Department of Veteran

Affairs, for funding my education and looking after my health. Thank you, REI, for for providing a small measure of stress relief during the hard times. Thank you, Rob, for being a good friend. Thank you, Farisa, for believing where others did not. Thank you,

California State University, for providing everything needed for a Veteran to redefine the future.

iii Dedication

To my nephew Anthony Echegoyen, who’s young fascination with science inspired me to

work harder.

iv Table of Contents

Signature page...... ii Acknowledgements ...... iii Dedication ...... iv List of Figures ...... vi List of Tables...... vii Abstract...... viii Chapter 1: Introduction 1 1.1 Debris Disks...... 1 1.2 Debris Disk History...... 1 1.3 Instruments ...... 3 1.3.1 Spitzer/IRS ...... 4 1.3.2 Spitzer/MIPS...... 4 1.3.3 Herschel/PACS...... 5 1.3.4 Sky Surveys...... 6 1.4 Viability of Black Body Fitting...... 7 Chapter 2: Sample Selection 8 2.1 Selection process...... 8 2.2 Removal steps...... 8 2.3 Final Sample...... 9 2.4 Data Origins...... 9 Chapter 3: Data Reduction 11 3.1 Pipeline Description...... 11 3.2 Pipeline steps...... 12 3.2.1 Input ...... 12 3.2.2 Stitching and Saturation...... 13 3.2.3 Fitting...... 13 3.2.4 Plotting...... 15 3.2.5 Data/Table Storage...... 16 3.3 Pipeline Modules...... 16 Chapter 4: Results of Fitting 17 4.1 Numerical break-down...... 17 4.2 Single Belt Systems...... 19 4.3 Double Belt Systems...... 24 Chapter 5: Conclusion 28 References...... 30

v List of Figures

1.1 Image of planetary disks forming about the HL Tau. The gaps between belts are good indicators for . Image Credit: ALMA(ESO/NAOJ/NRAO); C. Brogan, B. Saxton (NRAO/AUI/NSF)...... 2 1.2 Image of Fomalhaut system with known shown effecting debris disk. This shows a link between planets and belt structure. Credit: NASA, ESA, and P. Kalas (University of California, Berkeley and SETI Institute)...... 2 1.3 Image shows the different Bandpasses for the PACS instrument. Each filter has a range of sensitive wavelengths. Credit. PACS observers manual, ESA. . . . . 6 3.1 The first input is only the photometric measurements (a). Saturation limits are added (b) and any measurements above the saturation marks are excluded from the fitting...... 15 4.1 Histogram showing distribution of debris disks. Number of disks vs temperatures of disks. There is a clear range for belt types. The Belts are overlaid and denoted by color...... 17 4.2 Stellar Temperature vs. Spectral Type. There is a linear relation between temperature and spectral type with very low residuals. The double ring systems have a stellar temperature bias, in that they tend to predominantly occur (~94%) around at or above ~6000 K or early type stars in our sample...... 18 4.3 Stellar Temperature vs. Age for 74 debris systems in our sample for which stellar age is known and for which dust temperatures were retrieved...... 19 4.4 SEDs showing the in cyan, best-fit black body representing a single belt debris ring in red. All instrument measurements are shown by color with the points used for fitting shown in black. If the measurement is above the saturation limit of the instrument (horizontal line) than the measurement was not used to find the optimal temperature for the debris ring. The uncertainties for each measurement are shown as vertical pink lines...... 22 4.5 SEDs for double-ring systems showing the photosphere in cyan, best-fit black body representing the inner warmer debris ring in red and the outer colder debris ring in blue. All instrument measurements are shown by color with the points used for fitting shown in black. If the measurement is above the saturation limit of the instrument (horizontal line) than the measurement was not used to find the optimal temperature for the debris ring. The uncertainties for each measurement are shown as vertical gray lines...... 26

vi List of Tables

4.1 This table shows the belt temperatures, star spectral type, star temperature and reduced chi squared values for all single belt systems...... 21 4.2 This table shows the belt temperatures for inner and outer rings, star spectral type, star temperature and reduced chi squared values for all double ring systems. 25

vii Abstract

Dust Temperature Distributions of Herschel Detected Debris Disk

By

Jonathan Michael Paul Acuna

Master of Science in Physics

Using Herschel/PACS photometry, Spitzer/IRS spectroscopy, and complemented by near- and mid-infrared all-sky photometry from 2MASS and WISE, we develop a python pipeline to analyze the dust emission from a sample of 336 stars. The infrared data ranges in wavelength between 1.235 and 160 µm, and the sources were selected from the Herschel Heritage Debris Disk (H2D2) program. We model each source’s excess by using a blackbody curve represented by the Plank function. Spectral fitting with my pipeline identified 235 debris disk systems, 54 of which are best modeled using two distinct rings of dust, and the remaining 181 disks appear as single-belt sources. For single-ring systems, the temperatures range from ~28 to ~361 K, with a median value of 108 K. For those systems best fitted with two-belts, the inner rings range in temperature from ~103 to ~351 K, with a median temperature of 337 K. The outer/ cold rings have a median dust temperature of 65 K, and range between ~39 to 145 K. For those debris systems with Spitzer/IRS data, the warm dust components are well-

viii characterized and two-belt fits were common; however, if Spitzer/IRS data is not available, then the Herschel cold/dust detections typically resulted in a single-belt fit.

This implies that identifying double belt systems relies heavily on detections between 5.2 and 38 µm. Finally, the temperature ranges found for the two-belt debris system are reminiscent of the temperatures of our own solar system’s asteroid and Kuiper belts, indicative of a common dust temperature horizon around main sequence stars.

ix Chapter 1

Introduction

The purpose of this research is to analyze the photometric data of 376 stellar systems. All sources are members of the Herschel Heritage Debris Disk (H2D2) program. This is the first study to systematically analyze a sample of this size, testing for similarities and characteristics of systems with debris disks. The motivation for this type of study is that debris disks are signposts for planetary systems. This type of analysis could lead to a new detection method for planetary systems.

1.1 Debris Disks

Circumstellar debris disks were first discovered in the 1980s by the Infrared

Astronomical Satellite (IRAS). These disks are likely formed around Mature stars and can have their boundaries defined by shepherding planets. There is a disproportionate lifespan however between the dust in a debris disk and the parent star. The debris disks last only as long as there is a source feeding dust into them. Because of this the disks must have some type of replenishing mechanism, either from comets or asteroids. The disks can be used as indicators to identify properties of their parent systems. The disk architecture specifically has a lot of value when trying to understand a host system, like our own which has planet types separated by disks.

1.2 Debris Disk History

It is thought that there is a link between the debris disk distributions and locations of nearby orbiting bodies. The prevailing theory is that the disks are composed of solid water and astro-sil particulates and maintain temperatures based on the amount of stellar

1 radiation they receive from their parent

stars and the distance of the disks. These

disks maintain an equilibrium temperature

because the dust emits radiation at levels

proportional to the ambient flux they

absorb. Like all orbiting bodies the

particulates in the debris disks their

parent stars in ellipses and can range in Figure 1.1. Image of planetary disks forming about the star HL Tau. The gaps between belts cross sectional radii by as much as a few are good indicators for planets. Image Credit: ALMA(ESO/NAOJ/NRAO); C. Brogan, B. astronomical units, see figure 1.1. The Saxton (NRAO/AUI/NSF)

eccentricity of the disks could also be an indicator for the eccentricity of any nearby

planets. Fomalhaut (figure 1.2) has a debris disk system with an observed orbiting body.

Since their initial discovery, hundreds of debris disk rings have been confirmed. Initial

work done with debris disks focused on

stars with infrared excess, trying to relate

belt properties to planetary system

evolution phases. This early star work was

done with a sample of nearby A type stars

observed by the Spitzer/MIPS, first at 24

Figure 1.2. Image of Fomalhaut system with µm (Rieke et al. 2005) and later at 70 µm known planet shown effecting debris disk. This shows a link between planets and belt (Su et al. 2006). The early work showed structure. Credit: NASA, ESA, and P. Kalas (University of California, Berkeley and SETI Institute) that approximately 30% of stars have a

2 stronger emission above that of the stellar photosphere, implying emission from dust belts around the stars. This is a larger excess than was found for main sequence stars

(∼15%; Bryden et al. 2006; Trilling et al. 2008) and for low- M type stars (<10%;

Gautier et al. 2007; Plavchan et al. 2009). The largest percentage of disks have been discovered around A-type stars. The dust system around Fomalhaut, another A-type star, was also found to host a planet located on the inner edge of an offset belt. Few dust systems were initially found to have warm dust until the work done by Werner et al, in

2004. Soon after, Spitzer/IRS (Houck et al. 2004) and Spitzer/MIPS (Rieke et al. 2004) were used to discover an abundance of warm dust disks (∼200 K; Morales et al., 2009) with evidence for multiple belts within single stellar systems. Other works have found correlations between the temperature of our asteroid belt and that of warmer inner belts

(Morales et al., 2011) by comparing between characteristics in the various belts.

1.3 Instruments

Our understanding of debris disks has been greatly expanded by the Spitzer Space

Observatory (Werner et al. 2004). Initially launched in 2003 into heliocentric orbit,

Spitzer has used its instruments to provide spectroscopic and photometric data. Spitzer has made observations around main-sequence stars that are thought to be planetary systems or a system in which planets may form (Werner et al. 2006). Disk structure was hinted at by both the Spitzer and Hubble space telescopes (Su et al. 2005; Kalas et al.

2006). Spitzer was able to detect a large sample of stars with infrared excesses, specifically at the 24 and 70 micrometer (µm) wavelengths.

3 1.3.1 Spitzer/IRS

The InfraRed Spectrograph (IRS) is one of three Instruments aboard the Spitzer

Space Observatory. There are four separate modules used by the instrument, each able to take data at different wavelengths. The four modules are the Short-Low 1 & 2 and Long-

Low 1 & 2 (SL1, SL2, LL1, LL2) and together are able to provide low resolution

(R~100) and moderate resolution (R~600) capabilities between 5.2 and 38 µm.

Spectroscopic data can be collected by one of the two modes aboard the IRS. The Staring mode is a single target point and shoot and is the basic mode for the IRS. The Mapping mode is based on a grid designated by the observer around a central position with spectra being taken at each grid point. The IRS also has two filters. The first filter works between 13 and 18 µm while the second is between 18 and 26 µm. There is also built-in software to identify point sources and line them up in the appropriate IRS slit. This lining up process is known as the Peak-up mode and was used to provide imaging capacity between 8 and 24 µm by calibrating images between 16 and 22 µm covering a

1x1 arc minute area. Spectroscopic data used for this work is from the low resolution modules detecting circumstellar dust between 5 and 35 µm.

1.3.2 Spitzer/MIPS

The Multiband Imaging Photometer (MIPS) for Spitzer is another of Spitzer’s three instruments. MIPS is able to produce images at spectral bands centered around 24,

70 and 160 µm. There is also a capability to produce low resolution spectra between 55 and 95 µm. The MIPS instrument contains three detection arrays to resolve the airy disks. An airy disk is created when light is diffracted after passing through a small

4 aperture. There is a central disk and surrounding rings. The center is brighter than each concentric ring. The size of the airy disk is dependent on the aperture size and light wavelength. The three arrays view simultaneously creating the multi band image during telescope motion. The field of view for the 24 µm camera is approximately 5 arcminutes.

The MIPS instrument contains four modes of operating referred to as Astronomical

Observation Templates (AOTs). The first is known as the Scan Mapping AOT and is used to image large areas using a single or multiple band setup in near propinquity. The second is known as the Photometry and Super Resolution AOT and is used to image point sources and targets up to two arcminutes. The third mode is known as the Spectral

Energy Distribution (SED) AOT and works with the 70 µm band to acquire low resolution (R~20) spectra. The final mode is used to measure the intensity of zodiacal light and other extended emission sources and is the Total Power AOT. At the 24 and 70 micrometer wavelengths the instrument detected excess above the stellar photosphere.

This discrepancy pointed to a large distribution of small dust particles around the parent stars.

1.3.3 Herschel/PACS

The Photoconductor Array Camera and Spectrometer (PACS) instrument possesses two bolometer arrays used for imaging photometry. The PACS also contains separate bolometers made from stressed and unstressed Germanium Galium used for imaging line spectroscopy. The observed wavelengths for PACS range from 60 to 210

µm, figure 1.4. This range contains the wavelengths of emission for forming planetary systems and is thus ideal for studying dusty and grainy regions. In addition, distant star

5 Figure 1.3. Image shows the different Bandpasses for the PACS instrument. Each filter has a range of sensitive wavelengths. Credit. PACS observers manual, ESA. forming are red-shifted into the PACS wavelength sensitivity range. Current instruments have a limited ability to resolve most known debris disk systems. Because of this temporary shortcoming in available observing devices the properties and distributions of the debris disks must be extrapolated using SEDs. Spitzer has two instruments, the IRS and the MIPS which provide large photometric data samples for the

SEDs.

1.3.4 Sky Surveys

We used photometric data from two all sky surveys. The Two Micron All Sky

Survey (2MASS) was a large scale sky observing attempt covering roughly 70% of the sky. Three bands J, H and K were used for detections at 1.25, 1.65 and 2.17 µm. The

Wide-Field Infrared Survey Explorer (WISE) is another large scale observing mission which observed with four modules at 3.3, 4.6, 12 and 22 µm. All of our sources are

6 detected with 2MASS and all except six are detected with WISE due to saturation and/or other effects.

1.4 Viability of Black Body Fitting

Current instruments have a limited ability to resolve most known debris disk systems. Because of this temporary shortcoming in available observing devices the properties and distributions of the debris disk structure must be extrapolated using SEDs.

For this purpose, we compiled multi-mission photometric data, to analyze SEDs, assuming that grains around stars are distributed in narrow rings around their parent stars.

So we uniformly adopt blackbody curves represented by the Planck function to describe the flux from the grains. The grains range in size and emit along the near infrared spectrum. The Planck function takes wavelength and temperature as inputs and outputs a calculated flux or intensity. The grains in the disks are absorbing stellar radiation, reaching thermal equilibrium and emitting in the near infrared. The wavelength of emission is limited to the size of the emitting grains. With all the near infrared emission of the grains, the disks outshine the stars in the near infrared wavelengths. The optical properties, grain size and distance from the star are what determine the information that can be gained from the SEDs. This is a simple model for a complex environment which works because of several factors. First, that the dust particles in the debris disks emit radiation based on their grain size. That due to their grain size that emission is in the near infrared. That the debris disks are large enough in area to produce a combined flux sufficient enough to be detected above that of the star.

7 Chapter 2

Sample Selection

2.1 Selection process

All 336 stars in this sample have been observed and detected by the Herschel/

PACS instrument and have photometric data for at least two of the three wavelengths (70,

100, 160 in µm) from an initial 376 sources in the H2D2 sample. Our study focuses on dust around main sequence stars. The star selection was drawn from currently known sources of mature stars with debris disks studied with Herschel. The selection of stars was made to analyze a large sample of mature stars and this is the first time such a large sample of stars with debris disks is studied uniformly. These stars are similar in spectral type and size to our own , in that they are mature stars, but reminiscent of a young solar system. This sample included many A-Type stars with similar mass to our Sun but of a younger age (<1Gyr) that are relatively close by (<200pc). A motivation for this project is to characterize the dust (i.e., its temperature) and find any trends.

2.2 Removal steps

Of the original 376 H2D2 stars, 40 were removed. Known young stellar objects

(YSOs), and asymptotic giant branch objects (AGBs), and white dwarf (WD) stars with orbiting debris disks were removed because, though they possess debris disks, the central star is either still forming (in the case of YSOs) or are so evolved that the star itself is or has ejected material into interplanetary space (in the case of AGBs and WDs) in the form of planetary nebulae residuals.

8 2.3 Final Sample

The final sample contains 336 mature stars (Ages < ~1Gyr). For each star we prepared a datafile which contains the photometric and spectroscopic data, uncertainties and corresponding wavelength and the instrument that collected the datapoint. The range of photometric data points varies per star file from ~10 to several hundred depending on the different instruments used for collection. Because of the discrepancy in the number of data points there are some targets which produced more robust results due to the larger number of available data points.

2.4 Data Origins

The collection of photometric data is the measured flux. This analysis relies on near-, mid- and far-infrared photometric measurements from the four instruments described in section 1.3; Herschel/PACs, Spitzer/IRS, WISE and 2MASS. There is variance from the IRS data however. This is dependent on the position of the source during the observation which can lead to inconsistencies in the brightness of data points.

Some IRS calibration lead to an increase in the uncertainties for the IRS low resolution modules in a per source case. Therefore, the IRS spectroscopic measurements had to be recalibrate to the MIPS 24 µm data point. All data files which contained the IRS low- mode modules were calibrated to the MIPS 24 datapoint because of MIPS’ excellent

(<2%) calibration uncertainty. The length of each exposure is also a factor and the saturation limits are taken into account. When a data point was found over the saturation limit for the instrument it was not included in the fitting process. Considerable work was done on the IRS data before it was refined into it current form. The width of the

9 instrumental point-spread function determined the width of the aperture when extracting the spectra. The spectra was then calibrated by subtracting the background from an assumed point source spectra (a more in-depth explanation can be found in the IRS manual). This was done by the Spitzer Science Center’s IRS data reduction pipeline version S15.3.0. We use post basic calibrated data and recalibrate to MIPS 24 µm due to

IRS’ larger uncertainties.

10 Chapter 3

Data Reduction

3.1 Pipeline Description

For the purposes of this paper the entire code that was written for the analysis of the photometric data will be referred to as the pipeline. The pipeline is designed to process a large number of data files but can also be used to process a single data files as needed. This is done in the initial steps of the pipeline by selecting the indexes for analysis within the desired directory folder. In addition to the main processing portion of the pipeline there are also subsidiary portions that store functions which are called through out the main portion. The main channel is divided into the following sections; input, stitching and selection, fitting, plotting and data/table storage. Within the pipeline each file is opened, the appropriate star model is called and the flux from all the needed sources is compiled. Once compiled, the data is fitted first with a single black body curve and then with two. A statistical F-Test is used to determine which is more statistically viable based on the number of data points and the comparative reduced chi squared values. The datafiles can be in the same folder containing the code or located elsewhere as long as the user inputs the correct datafile directory. The Herschel/PACs instruments has wavelength saturation limits. Any Herschel points above the saturation limits were removed before the fitting routine. The purpose of the code is to look at a file containing photometric data and determine the number and temperature of debris disks contained around the file’s source star. A python library was written to complete all the needed

11 tasks for analysis. In addition several modules are called to streamline sections of the code.

3.2 Pipeline steps

The first few lines of the pipeline call in all the libraries needed throughout the code.

This includes the subsidiary python scripts containing all the functions and fitting routines. The pipeline runs through the main sections. Each data file contains a specific amount of data points. Initial lists are created which are used later to store results. Each star file is passed through the pipeline sequentially. Once the data is inputed, it is sorted according to instrument and saturation limits and stored in a flux list. The flux list is passed to the fitting routine which fits a single and pair of blackbody curves. The two fits are compared statistically using their reduced chi squared values by the Ftest to determine which is more significant given the number of parameters and the degrees of freedom.

The case with more significance is moved along for plotting and value storage and is presented in the results.

3.2.1 Input

The input section is where the user indicates which data files to analyze. This is done by selecting the appropriate folder directory. The entire folder can be analyzed or specific files within the directory based on the indexes indicated. Once a data file is opened the header is read into the code and the star’s temperature recorded. Every analysis process uses either the NextGen or the Kurucz star models depending on the star temperature.

Based on the temperature the appropriate star model is opened and the stellar flux

12 information is stored. There are also calls for user input, which turn on and off the plotting routines. This was done to save runtime and processing power.

3.2.2 Stitching and Saturation

For the files that contain Spitzer/IRS photometry, module stitching is performed. The first step in this process is to determine which modules are used. If the IRS LL1 (~20 to

~37 µm) module exists in the star file, then it is renormalized to the MIPS 24 µm photometric point by convolving the MIPS24 filter response function with the IRS LL1 spectra. Subsequently, the rest of the modules are “stitched” together by extrapolating from each one and renormalizing them to the LL1 module. Once the IRS modules are normalized, the new IRS fluxes are then combined with the rest of the 2MASS, WISE and

Herschel measured fluxes per star-dust system to moves into the fitting stage.

In addition, each instrument has a saturation limit, which is checked against the measured photometry. If the flux exceeds the saturation limit of the instrument, then that flux point is not used in the fitting step. However, photometric points above saturation limits are plotted (shown in Section 3.4) for visual inspection and confirmation.

3.2.3 Fitting

We assume that the debris disks in our sample are made of dust particles distributed in rings or belts around the parent star. The infrared emission from the grains is modeled as blackbody curves represented the Planck function:

or (3.1)

13 Classically, the inputs are wavelength (λ) and temperature (T) and the output is flux (B).

In this study however we use the function in an indirect manner with T being an unknown free fitting parameter. I call a special “curve_fit" function from the python library Scipy.

This special function optimizes a model to the measured fluxes by dynamically changing the temperature parameter in the Planck function. For this study we assume a range of wavelength inputs from 1 to 500 micrometers, which generates a continuous curve.

There are two unknown factors here, the temperature and the normalization of the blackbody. By altering the temperature input, the curve is shifted in a horizontal direction. The normalization factor moves the curve in a vertical direction. A reduced chi squared value is used to find and fit the optimal parameters to the IR excess flux of each star, where

(3.2)

And a statistical F-test us used to discriminate between single- and double-belt systems:

(3.3)

These resultant fitted temperatures are listed in the results section—Chapter 4. Secondly, this stage determines whether the Source has a single belt or two belts. I fit both a single belt and a double belt to the flux data. Once both sets are fitted, their reduced Chi

Squared values are compared using the F-Test to determine which has more statistical

14 significance. The model with a higher significance is moved forward and its belt temperature(s) is stored.

3.2.4 Plotting

If during the input stage, the plots are turned on, then all the compiled fluxes are graphed as an SED for visual inspection or presentation. Each SED plot has a vertical axis of stellar flux in units of Janskies (Jy) and a horizontal axis for wavelength in units of µm. The SED contains flux from multiple missions and instruments represented by the different colors as shown in Figure 3.1 (a). Also indicated on the plots are the saturation

(a) Photometric measurements (b) SED with saturation limits

Figure 3.1. SED for HD 71722. The plot on the left (a) shows the photometric measurements only. Saturation limits are added (b) to the SED for HD 71722, and any measurements above the saturation marks are excluded from the χ2 fitting. limits per instrument as horizontal bars as in Fig. 3.1 (b). A summation represents the combination of the debris disks and the stellar flux for comparison with the the flux data.

The final plots, shown in chapter 4, also contain blackbody curves, stellar models and flux summation lines.

15 3.2.5 Data/Table Storage

At the end of the fitting stage there are three lists stored in the code. These lists are the temperatures of each debris belt. Each temperature index has information stored with it including source name and if it is a multi-belt system, an indicator for warm inner belts or cold outer belt. The pipeline opens these temperature lists and writes them into a .csv file, storing the .csv as a separate file once completed.

3.3 Pipeline Modules

The bulk of the pipeline takes place in the main script module. This script calls subsidiary modules as needed. There are three principle ”subsidiary” modules and six complementary modules. The three subsidiaries are the ”functions”, ”single” and

”double” modules. The functions module contains 36 individual functions written for the pipeline that are all called as needed. The “single” and “double” modules are both called and used once the flux list is compiled; in other words, once the fluxes have been recalibrated and recombined as described in Section 3.2.2. These are the fitting routines that optimize for either a single- or double-blackbody curve to the measured fluxes, and to test for goodness of fit.

There is also a “convolution” module, which is used once per star-disk system, and only if there exists Spitzer/IRS and Spitzer/MIPS24 data. This module is used to normalize the IRS data as described in Section 3.2.2.

16 Chapter 4

Results of Fitting

4.1 Numerical break-down

Of 336 star files in our Herschel debris disk sample, the pipeline, described in

Chapter 3, found dust temperatures for 235 systems. There are 101 star files that were not fit due to processing runtime errors, and/or degeneracy in possible fitting parameters, and so the dust belt temperatures could not be found. We find that of the those systems that are successfully fit there are 181 best described by single-belt debris disks and 54 by double-belt debris disk models. The histogram in figure 4.1 shows the resultant range in best-fit dust temperatures for both single- and double-belt systems.

Figure 4.1: Histogram showing distribution of debris disk temperatures. Single-belt systems (plotted in red) are more numerous (181), versus double-belt systems (plotted in green + blue for the outer and inner dust components respectively) which add up to 54 systems. We note that the single- and double-belt systems cover similar ranges in dust temperatures (~28 to ~360 K) reminiscent of asteroidal and Kuiper-like dust temperatures in our solar system.

17 Figure 4.1 shows a distinct temperature range for each debris ring type: single, inner and outer, shown in red, green, and blue respectively. There is also a larger number of belts with lower temperatures, which can be seen by the red spike around 100 K. Interestingly, when a system is fit with a two-belt model, there seems to be a deficit of 100 K dust.

Figure 4.2. Stellar Temperature vs. Spectral Type. There is a linear relation between temperature and spectral type with very low residuals. The double ring systems have a stellar temperature bias, in that they tend to predominantly occur (~94%) around stars at or above ~6000 K or early type stars in our sample.

As illustrated in figure 4.2, the single-ring systems are uniformly spread over the full range of spectral types and star temperatures explored here. This may indicate that any system could evolve into a single ring system, or that stellar spectral type and/or star temperature are not determining factors for the formation of single belt systems.

18 Figure 4.3. Stellar Temperature vs. Age for 74 debris systems in our sample for which stellar age is known and for which dust temperatures were retrieved.

Of the 129 debris disk systems with measured ages in our sample, 74 are plotted in figure

4.3 and show a tendency of double-belt systems forming around the “younger” stars (i.e.

<~1 Gyr). From Figures 4.2 and 4.3, double-belt systems are more common around the

“younger” early the stars, perhaps because a more massive star has a more massive disk to begin with, or because brighter stars are more effective at illuminating their surrounding debris.

4.2 Single Belt Systems

The minimum temperature deduced for a single-belt systems is ~28 K in the case of an

M-dwarf star (see table in figure 4.4). The maximum single-belt temperature however is

19 ~361 K for a debris system around an A-type star. The median temperature of the single belts is 108 K. The specific temperatures for all single-belt systems are shown in figure

4.4. The table is divided into columns by star name, spectral type, star temperature, dust temperature and reduced chi squared value. All of our dust temperatures have an uncertainty of +/- 5 .

Spectral Reduced Spectral Reduced Star Name Type Star Temp Belt Temp ChiSquare Star Name Type Star Temp Belt Temp ChiSquare BD-19 1062 K3V(e) 4650 67.34 32.85 HD 218340 G3V 5780 108.19 3.63 F0+VkA5m GJ 285 M4.0Ve 3080 157.14 626.27 HD 218396 A5 7460 52.91 100.46 GJ 433 M1.5 3600 39.13 439.65 HD 218511 K6V 4290 100.49 9.29 GJ 54 M2.5V 3340 57.68 261.92 HD 21997 A3IV/V 8300 68.74 71.32 GJ 581 M3V 3330 108.78 11.30 HD 22049 K2Vk: 5090 131.85 49.80 GJ 649 M2V 3680 95.41 378.79 HD 220825 A2VpSrCrSi 9030 192.89 1.38 GJ 9298 K4V 4160 88.88 3.88 HD 221756 A1Va 8450 108.42 106.61 HD 102438 G6V 5620 222.36 0.67 HD 222368 F7V 6240 199.69 0.52 HD 102458 G4V 5770 236.53 2.08 HD 223352 A0Vnp 9530 201.27 1.98 HD 102647 A3Va 8630 115.08 3.52 HD 223408 F6V 6270 88.98 24.08 HD 105857 A2V 8270 200.22 1.54 HD 224309 A3V 8780 135.56 70.96 HD 106252 G0 5830 56.84 0.29 HD 22484 F9IV-V 6000 105.32 0.29 HD 107649 F5V 6370 299.54 4.51 HD 2262 A5IVn 7950 162.64 1.58 HD 109573 A0V 9390 113.47 118.06 HD 23208 G8V 5350 92.17 32.80 HD 1100 K0III 4810 68.85 33.58 HD 23281 A5III-IV 7590 304.93 19.44 HD 110058 A0V 8080 126.11 35.03 HD 23380 F2V 6770 103.71 32.19 HD 111631 M0V 3950 27.96 49.66 HD 23484 K2V 5090 65.18 4.67 HD 113766 F3/5V 6810 295.64 2.18 HD 23586 F0 6520 332.51 16.90 HD 114082 F3V 6590 111.17 1.08 HD 23642 A0VpSi+Am 8820 129.56 1.62 HD 11413 A1Va_lB 8150 74.54 104.32 HD 24141 kA3hF0mF0 7890 178.55 1.33 HD 115371 F3V 6550 271.95 18.93 HD 24636 F3IV/V 6780 126.42 0.84 kA15hA3m HD 115892 A3va 9140 200.84 4.97 HD 24649 F6V 6260 86.63 41.83 HD 117620 F2/3V 6670 126.68 19.95 HD 24817 A0Vn 8810 269.87 1.47 HD 119152 F0V 7100 123.95 47.92 HD 26736 G5V 5660 89.04 32.19 HD 120178 F5V 6240 304.55 3.88 HD 278932 G5 5660 100.77 142.53 HD 120362 G5V 5320 84.95 24.37 HD 28069 F7V 6240 84.97 25.14 HD 12039 G4V 5670 117.88 24.26 HD 282477 G0 5260 228.03 74.05 kA5hF0VmF HD 121191 A5IV/V 8310 153.47 412.65 HD 28355 0 7590 109.76 4.82 HD 124520 G3V 5753 36.47 48.01 HD 3003 A0V 9060 188.15 3.31 HD 125283 A2Vn 8630 203.98 7.30 HD 30051 F2/3IV/V 6740 88.76 38.58 HD 128165 K3V 4840 111.78 8.73 HD 31392 G9V 5290 60.99 2.29 HD 128311 K3V 4860 114.85 5.60 HD 35289 F3V 6700 297.18 10.75 HD 131496 K0 4790 56.89 44.13 HD 35416 F3V_m-1.5 6790 122.24 43.52 HD 13161 A5III 8150 85.85 0.73 HD 35650 K6V 4140 36.70 254.41 HD 132254 F8-V 6220 317.60 1.03 HD 35656 B9V 10010 132.21 82.58 HD 13246 F7V 6180 232.15 23.88 HD 35850 F8V(n)k: 6130 90.12 46.89 HD 132658 F5 6820 241.87 12.17 HD 36546 B8 8740 150.81 80.70 F0VspEuGd HD 137949 Sr 6790 77.72 36.26 HD 37004 A3V 8140 127.72 81.39 HD 139006 A1IV 9840 124.42 5.14 HD 37487 F0 6980 104.72 47.08 HD 139731 F0V 6820 120.90 19.11 HD 37546 F5V 6570 84.38 21.08 HD 1404 A2V 8920 177.90 1.96 HD 37594 A9V 7370 61.45 55.72 HD 140614 F3V 6700 77.27 38.92 HD 37852 B8V 6740 264.29 24.97 HD 14082B G2V 5790 153.46 20.41 HD 38273 F2V 6690 97.26 33.74 HD 145504 F0V 6470 258.08 2.00 HD 38397 G0V 5950 49.00 39.69 HD 145964 B9V 9520 113.28 1.11 HD 38529 G8III/IV 5330 79.96 1.22 HD 149807 F2IV/V 6090 194.39 41.46 HD 38805 A3V 8500 105.69 129.04 HD 151360 F3V 6910 123.50 19.06 HD 39091 G0V 5890 310.79 0.98 HD 159170 A5V 7870 204.64 2.35 HD 40136 F2V 7060 275.49 1.35 HD 159502 F5 6950 318.70 14.55 HD 44958 A5V 7630 80.68 63.96 HD 160305 F8/G0V 6050 84.20 30.26 HD 4747 G8/K0V 5310 98.04 23.89 HD 165459 A1V 8240 104.51 47.19 HD 48370 K0V(+G) 5240 44.16 60.39 HD 166636 A1V 9080 105.43 42.66 HD 48682 F9V 6070 59.19 1.28 HD 169830 F7V 6260 317.17 1.10 HD 51296 A5 7560 361.16 13.79

20 HD 174474 A2V 8370 309.97 20.53 HD 5133 K2.5Vk: 4960 63.73 1.02 HD 176894 F0 6790 77.66 72.22 HD 53143 G9V 5280 63.19 77.23 HD 179520 F3V 6920 241.63 25.06 HD 5388 F6V 6330 94.40 44.36 HD 179930 M0Vk: 3840 86.39 98.40 HD 5578 K3Ve 4600 31.31 26.90 HD 179933 A0V 9430 244.54 985.98 HD 57703 F2 6590 54.18 0.90 HD 180161 G8V 5250 60.68 28.39 HD 57969 A1V 8420 132.64 85.61 A0V+M7/8 HD 181296 V 9260 135.86 92.53 HD 59507 A2V 8870 129.77 103.71 HD 182681 B8.5V 9680 84.62 196.55 HD 59659 F7V 6250 84.01 26.23 HD 183216 G2V 5890 51.46 3.38 HD 60737 G0 5760 71.83 0.97 HD 183970 F5 6150 86.87 51.54 HD 66552 B9V 10080 290.93 97.35 HD 184327 A1/2V 8820 120.47 73.85 HD 6798 A3V 9190 86.93 112.76 HD 186025 F3/5IV/V 6090 295.63 11.61 HD 71043 A0V 9370 256.19 3.98 HD 187085 G0V 6010 343.98 1.85 HD 7112 G5V 5710 90.40 44.60 HD 187897 G5 5810 64.55 1.23 HD 71988 A3 7470 78.73 34.41 HD 188228 A0Va 10010 86.21 0.42 HD 72659 G2V 5850 52.58 0.53 HD 189002 F6V 5930 97.68 36.29 HD 72687 G5V 5680 188.31 0.77 HD 191089 F5V 6550 98.10 41.93 HD 73350 G8/K0(IV) 5730 212.28 16.58 HD 192263 K1/2V 4930 66.65 2.32 HD 74389 A2V 8790 269.15 72.43 HD 192544 A0III 7630 111.98 84.12 HD 75616 F5 6340 73.24 0.62 HD 196544 A1IV 8940 102.01 72.74 HD 7570 F9VFe+0.4 5960 216.30 0.65 HD 19668 G8/K0V 5330 138.76 3.08 HD 76151 G3V 5650 155.15 0.75 HD 198093 G2/3V 5940 95.83 23.91 HD 77056 G8V 5440 132.87 27.73 HD 198160 A2III 7890 91.18 47.37 HD 83033 F3V 6820 97.90 47.07 HD 198472 F5/6V 6410 97.25 35.15 HD 85672 A0 7970 78.80 94.30 HD 19994 F8.5V 6000 318.89 3.07 HD 8686 F3V 6650 134.23 29.82 HD 201219 G5 5490 62.07 0.67 HD 88463 F2IV 6730 99.58 34.88 HD 201377 A3III/IV 8050 175.98 39.41 HD 89452 K0 5240 46.11 27.95 HD 201906 A1V 9140 119.08 118.01 HD 90905 G1V 6010 114.61 3.81 HD 202206 G6V 5500 60.54 1.91 HD 94131 F0/2V 6910 69.14 45.74 HD 202628 G5V 5720 50.42 27.65 HD 95086 A8III 7560 68.59 78.41 kA4hA9mA HD 20320 9V 7590 80.54 2.61 HD 95418 A1IVps 9840 114.78 10.80 HD 20794 G8III 5530 63.34 213.02 HD 9826 F9V 6120 210.43 0.90 HD 208585 K0 4960 94.28 79.64 HD 99945 kA2hF1mF0 7420 67.61 56.44 HD 21086 F8 6070 255.83 29.33 HIP 11437 K7V 4280 69.59 5.27 HD 21641 B8.5V 10050 311.45 120.10 HIP 84914 G0 5900 85.76 38.16

Table 4.1. This table shows the belt temperatures, star spectral type, star temperature and reduced chi squared values for all single belt systems.

We note that 122 or ~67% of single-belt systems have dust temperatures of <~150

Kelvin. The results are also plotted per source via SEDs for visual inspection. Each SED contains the stellar model in cyan, the best fit single debris-ring in red and the instruments with saturation limits. The debris-rings in figure 4.5. are generated with the

Planck function. The input parameters are wavelength (ranging from 1 to 500 µm) and temperatures shown in figure 4.4.

21 λ(µm) λ(µm)

λ(µm) λ(µm)

λ(µm) λ(µm)

Figure 4.4. SEDs showing the photosphere in cyan, best-fit black body representing a single belt debris ring in red. All instrument measurements are shown by color with the points used for fitting shown in black. If the measurement is above the saturation limit of the instrument (horizontal line) than the measurement was not used to find the optimal temperature for the debris ring. The uncertainties for each measurement are shown as vertical pink lines.

22 λ(µm) λ(µm)

λ(µm) λ(µm)

λ(µm) λ(µm)

Figure 4.4. Continued

23 4.3 Double Belt Systems

54 debris disks are best fit with two dust components as described in Chapter 3. We find that the inner dust belts have a minimum temperature of ~103 K, also in the case of a M- type star in our sample. The maximum warm dust temperature on the other hand is ~351

K for a G-type star, and close to the warmest temperature deduced for the single-belt systems of ~360 K. The median warm dust temperature is ~337 K, reminiscent of temperatures observed for our asteroid belt (100 - 350 K; Morales et al., 2009). For the outer debris components, the minimum dust temperatures range from ~39 K to a maximum of ~145 K, with a median temperature of ~65 K. Our deduced median dust temperature is again close to what we see for Kuiper belt objects of ~40-60 K (T ∼50 K;

Jewitt & Luu 2004). All of our dust temperatures have a uncertainty of +/- 5 Kelvin.

Star Name Spectral Type Star Temp Inner Belt Temp Outer Belt Temp Reduced ChiSquare GJ 14 M0.5V 4020 102.84 41.62 1.38 HD 105211 F2V 7010 252.30 51.25 0.59 HD 10647 F9V 6140 200.84 54.41 2.03 HD 106906 F5V 6540 267.63 101.96 0.74 HD 107146 G2V 5850 314.64 49.23 0.63 HD 10939 A1V 9030 208.50 60.11 1.78 HD 110411 A0Va_lB 8540 315.27 82.95 0.71 HD 110897 F9V_Fe-0.3 6080 302.42 47.20 0.85 HD 111520 F5/6V 6280 172.23 72.09 1.11 HD 115600 F2IV/V 6840 263.59 106.37 0.61 HD 120534 A5V+(F) 7140 331.08 86.25 0.50 HD 121189 F3V 6810 308.85 120.08 0.46 HD 127821 F4IV 6640 330.30 49.39 1.47 HD 131835 A2IV 7840 182.95 78.21 21.40 HD 136246 A1V 8510 144.99 47.44 0.98 HD 138965 A1V 8630 192.57 63.43 1.95 HD 141378 A5IV-V 8300 339.64 67.20 1.38 HD 145229 G0 5950 315.38 56.26 0.37 HD 153053 A5IV/V 7820 140.87 54.96 1.38 HD 15745 F0 6950 124.37 79.02 2.10 HD 159492 A5IV/V 7770 167.99 55.27 2.88 HD 161868 A1VnkA0mA0 9030 172.30 72.76 1.14 HD 164249 F6V+M2Ve 6590 230.26 70.77 0.54 HD 166 K0V 5410 294.28 79.97 0.52 HD 16743 F0/2III/IV 6910 171.96 56.17 1.20 HD 17848 A2V 8450 253.79 61.01 1.01 HD 181327 F6V 6450 107.86 66.14 1.51 HD 183324 A0IVp 8630 176.97 64.21 1.44 HD 192425 A1Va 8540 243.11 59.00 2.16 HD 195627 F0V 7320 283.93 60.78 2.12 HD 202917 G7V 5510 327.69 70.19 0.99 HD 205674 F3/5IV 6700 190.88 52.98 1.16 HD 207129 G2V 5890 204.42 50.52 1.08 HD 215766 B9V 10070 342.30 133.69 1.39 HD 216435 G0V 5820 220.54 56.13 0.63

24 HD 219482 F6V 6240 269.41 82.60 0.70 HD 221853 F0 6690 194.57 84.50 0.58 HD 31295 A0Va_lB 8630 215.90 65.14 2.35 HD 32297 A0V 7890 253.32 82.93 0.95 HD 38206 A0V 9680 242.93 66.32 0.77 HD 38678 A2IV-V(n) 8450 185.54 39.38 3.26 HD 38858 G2V 5750 154.77 47.56 0.90 HD 40540 A8IV(m) 7280 190.05 80.55 0.91 HD 54341 A0V 9680 255.65 60.73 2.11 HD 70313 A3Va 8300 199.82 65.74 1.45 HD 71722 A0V 8870 295.82 81.06 1.24 HD 76543 A5III 8060 170.84 56.95 1.17 HD 76582 F0IV 7680 132.57 48.65 0.59 HD 79108 A0V 9680 269.94 74.59 0.73 HD 82943 F9VFe+0.5 5760 327.62 54.40 2.58 HD 84870 A3 7530 202.74 53.75 0.91 HD 9672 A1V 8800 260.64 66.95 6.38 HD 98673 A7Vn 8030 317.28 111.18 0.96 HIP 8920 G0 6060 351.35 144.59 10.68

Table 4.2. This table shows the belt temperatures for inner and outer rings, star spectral type, star temperature and reduced chi squared values for all double ring systems.

The double-ring results are also plotted per source via SEDs for visual inspection. Each double-ring SED contains the stellar model in cyan, the best fit debris-rings in red for the warmer inner belt and blue for the outer colder belt. The instruments are also shown with saturation limits. The debris-rings in figure 4.7. are generated with a double Planck function. The input parameters are wavelength (ranging from 1 to 500 µm) and temperatures shown in figure 4.6.

25 λ(µm) λ(µm)

λ(µm) λ(µm)

λ(µm) λ(µm)

Figure 4.5. SEDs for double-ring systems showing the photosphere in cyan, best-fit black body representing the inner warmer debris ring in red and the outer colder debris ring in blue. All instrument measurements are shown by color with the points used for fitting shown in black. If the measurement is above the saturation limit of the instrument (horizontal line) than the measurement was not used to find the optimal temperature for the debris ring. The uncertainties for each measurement are shown as vertical gray lines.

26 λ(µm) λ(µm)

λ(µm) λ(µm)

λ(µm) λ(µm)

Figure 4.5. Continued.

27 Chapter 5

Conclusion

In this thesis we characterized circumstellar dust by studying its infrared excess flux above the stellar photosphere, as measured by Spitzer Space Telescope and the

Herschel Space Observatory. We χ2 fit the 2MASS, WISE, Spitzer//MIPS, and Herschel/

PACS photometry and Spitzer/IRS spectroscopic data via SED analysis, assuming a

NextGen or Kurucz synthetic stellar photosphere, and model the dust using the Planck function.

The complete pipeline was written using Python 2.7. The code calculates dust temperatures for single- and double-belt debris disks around 235 star systems. We set out to identify the temperature ranges of the debris belts and look for correlations between other stellar systems and our own. The number of belts in a system is identified using the statical F-test, which distinguished the level of confidence between two chi squared values for a system.

Our analysis of infrared excesses suggests the following:

• There is a distinct temperature range for each belt type. (i.e., single-belt dust ranges

from 28 to 361 K, where the double-belt systems have warm dust form 103 to 351 K,

and cold dust from 39 to 145 K.)

• Single belt systems are more numerous by a factor of ~3.35.

• The Planck function is a good first approach for obtaining the characteristic

temperature of circumstellar dust grain.

28 • There is a striking similarity between the temperatures found for double-belt systems

and debris in our own solar system. Both the asteroid and Kuiper belts are within the

temperature distributions presented in Chapter 4.

We note that the Herschel/PACS photometric measurements, especially the 160

µm waveband, are points in each SED that drove the fits by tightly constraining the cold dust-temperatures, revealing the contribution of the outer/cold regions for each debris disk system.

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