Infrared Excesses in stars with and without planets
by
Ra´ulFelipe Maldonado S´anchez
Thesis submitted in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE IN ASTROPHYSICS
at the Instituto Nacional de Astrof´ısica, Optica´ y Electr´onica
August 2015
Tonantzintla, Puebla
Under the supervision of: Ph.D. Miguel Ch´avez Dagostino (INAOE) Ph.D. Emanuele Bertone (INAOE)
c INAOE, 2015 The author hereby grants to INAOE permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part.
To my family and friends
iii
Acknowledgments
I would like to offer my special thanks to my advisors Ph.D. Miguel Ch´avez Dagostino and Ph.D. Emanuele Bertone for all their support, advice and patience since the be- ginning of the project until the successful conclusion of this work, for helping me to improve this thesis and sharing me the necessary knowledge to do this research work.
My special thanks are extended to Ph.D. Olga Vega, Ph.D. Alicia Porras and Ph.D. Abraham Luna for being examiners of this thesis and giving me the advices and com- ments to improve this research work.
I am particularly grateful with all my classmates and friends: Eric, Carlos, Leticia, Emanuel, Ana, Gisela and Alan. They have shown me the meaning of a true friendship. The let me know that the study and learning in a perfect work team is easier and much funnier. I hope we still be friends for a long time and even collaborate in future projects.
I would like to express my very great appreciation to my colleague and friend Rodrigo Pineda, for his friendship and all his support through the master studies and during the development of this thesis, for encouraging me to continue in difficult times and showing me the importance of the study everyday.
I also want to thank Msc. Fernando Cruz S´aenzde Miera for his help in the develop- ment of this work.
I give my special thanks to my mom, sisters, brothers in law, nephews and nice, who are showing me their care and love everyday. The accomplishment of all my goals is because of their emotional support.
I really appreciate the knowledge acquired from all the teachers in the master, for their teachings in the classroom.
Finally, I thank CONACYT for the financial support in the master studies.
v
List of Figures
1.1 Spectral energy distributions of Vega, Fomalhaut, Eridani and β Pictoris.2 1.2 Diagram of the evolution of a typical circumstellar disk...... 3 1.3 Spectral Energy Distribution of the Herbig Ae star AB Aurigae.....4 1.4 Two parameter debris disk model...... 6 1.5 Spectral Energy Distributions of stars with prominent 22 µm excesses..9 1.6 Evolution of 24 µm excesses around Sun-like stars...... 11 1.7 β Pictoris coronagraphic images...... 13 1.8 Dust emission around Eridani at a wavelength of 850 µm...... 13
2.1 WISE satellite in its mapping configuration...... 16 2.2 Fit photometry profile differences between AllWISE and WISE All-Sky 17 2.3 Comparison of a real and spurious detection in WISE images...... 22 2.4 Spectral type distributions of stars with and without planets...... 23 2.5 Distance distribution of stars with and without planets...... 24 2.6 V magnitude distributions of stars with and without planets...... 24 2.7 Metallicity distributions of stars with and without planets...... 25
3.1 Color vs spectral type of stars with and without planets samples.... 28 3.2 Color excess distribution of the stars with and without planets sample. 29 3.3 Comparison between ATLAS9 and NEXTGEN synthetic spectra.... 33 3.4 Comparison of synthetic spectra with same Teff , surface gravity but different metallicity...... 35 3.5 Johnson, 2MASS and WISE filter response curves...... 36 3.6 Best fit of the Synthetic Spectral Energy Distribution for the star HD108874 using ATLAS9 models...... 37 2 3.7 χν distribution for the stars with and without planets...... 37 3.8 WISE vs Tycho-2 B-V color-diagrams...... 41
4.1 Distribution of uncertainties in the flux ratio W4/W3 in dependence of W4 flux...... 47 4.2 Distribution of total uncertainties propagated in the different IR-detection methods...... 48 4.3 Excess significance distribution of stars with and without planets.... 49
vii 4.4 Comparison between W4 and W3 observed and synthetic photometry as a function of W4 flux for each star in the combined samples of stars with and without planets...... 50 4.5 Comparison between W4, W3 and W2 observed and synthetic photom- etry in dependence of W4 flux for each star in the combined samples of stars with and without planets...... 51 4.6 Flux comparison of the WISE bands between the WISE catalogues avail- able in the literature...... 53 4.7 Spectral energy distribution of HD 106906...... 55 4.8 Spectral energy distribution of V342Peg (HR 8799)...... 56 4.9 Spectral energy distribution of BD-10 3166...... 57 4.10 Spectral energy distribution of CD-301812...... 58 4.11 WISE W4 pixel intensity distribution of CD-301812...... 58 4.12 WISE W2, W3 and W4 images of CD-301812...... 59 4.13 Spectral energy distribution of HD107146...... 60 4.14 Spectral energy distribution of HD85301...... 61 4.15 Spectral energy distribution of HD 136544...... 62
A.1 Empirically determined WISE vs. B-V photospheric color-color trends for all six WISE colors...... 69
B.1 Spectral energy distributions of HD106906 & HR7899...... 71 B.2 Spectral energy distributions of HD45184 & HD113337...... 72 B.3 Spectral energy distributions of HD114729A & HR6907...... 72 B.4 Spectral energy distributions of HD11506 & HD224693...... 72 B.5 Spectral energy distributions of HD130322 & HD98649...... 73 B.6 Spectral energy distributions of HD168443 & HD33643...... 73 B.7 Spectral energy distribution of HD4113...... 73 B.8 Spectral energy distributions of HD107146 & HD85301...... 74 B.9 Spectral energy distributions of HD60491 & HD125040...... 74 B.10 Spectral energy distributions of AFLep & HD136544...... 75 B.11 Spectral energy distributions of HD29137 & HD34745...... 75 B.12 Spectral energy distributions of HD8907 & LQHya...... 75 B.13 Spectral energy distributions of HD96418 & HR1981...... 76 B.14 Spectral energy distributions of HD205294 & HD44821...... 76 B.15 Spectral energy distributions of HD85638 & HD209253...... 76 List of Tables
3.1 Zero magnitude flux density for B, V, J, H, KS, W1, W2, W3, W4 bands. 30 3.2 Extinction law coefficients as a function of wavelength...... 30 3.3 Color corrections...... 32 3.4 Flux ratio comparison among the WISE bands in ATLAS9 synthetic spectra with different stellar parameters...... 34
4.1 Number and percentage of IR excesses (E) in stars with and without planets...... 43
C.1 Stellar parameters of the sample of stars with planets...... 77 C.2 Stellar parameters of the sample of stars without planets...... 81
D.1 Observed fluxes for stars with planets...... 100 D.2 Observed fluxes for stars without planets...... 106
ix
Contents
Acknowledgmentsv
1 Introduction1 1.1 Circumstellar Disks...... 1 1.1.1 Protoplanetary Disks...... 4 1.1.2 Debris Disks...... 5 1.2 Observing Debris Disks at IR wavelengths...... 7 1.3 Mid-IR observations: Warm debris disks...... 8 1.4 Planet interaction and disks...... 12 1.5 Aims of this work...... 14
2 The sample selection 15 2.1 IR Surveys...... 15 2.1.1 Wide-field Infrared Survey Explorer (WISE)...... 15 2.1.2 Two Micron All Sky Survey (2MASS)...... 18 2.2 The sample...... 19 2.2.1 Stars with planets...... 19 2.2.2 Stars without planets...... 20 2.3 Optical and Infrared photometry...... 21 2.3.1 Comparison of both samples...... 22
3 Methodology 27 3.1 Correction for extinction and magnitude to flux conversion...... 27 3.2 Photosphere fitting and synthetic photometry...... 32 3.3 Searching for Infrared Excesses...... 38 3.3.1 Method 1 (This work)...... 38 3.3.2 Method 2: Cruz-Saenz de Miera et al.(2014)...... 39 3.3.3 Method 3: Kennedy & Wyatt(2012)...... 39 3.3.4 Method 4: Morales et al.(2012)...... 40 3.3.5 Method 5: Patel et al.(2014)...... 40
4 Results 43 4.1 Comparing the two stellar samples...... 44
xi 4.2 Comparison among the methods...... 45 4.2.1 This work vs. Cruz-Saenz de Miera et al.(2014)...... 45 4.2.2 Kennedy & Wyatt(2012) vs. Morales et al.(2012)...... 45 4.2.3 Patel et al.(2014) vs. Morales et al.(2012)...... 46 4.3 Explaining differences among the methods...... 46 4.3.1 So, which is the best method?...... 51 4.4 Comparison between WISE data releases...... 52 4.5 Comments on some stars with planets...... 54 4.5.1 HD106906...... 54 4.5.2 V342Peg (HR 8799)...... 55 4.5.3 BD-10 3166...... 56 4.5.4 CD-301812 (WASP-79)...... 57 4.6 Comments on some stars without planets...... 59 4.6.1 HD107146...... 59 4.6.2 HD85301...... 60 4.6.3 HD 136544...... 61
5 Summary and Conclusions 63 5.1 Future work...... 65
A Apendix 67
B Apendix 71 B.1 Stars with planets SEDs...... 71 B.2 Stars without planets SEDs...... 74
C Apendix 77
D Apendix 99 Chapter 1
Introduction
1.1 Circumstellar Disks
Disks and rings are present in different astronomical objects and at different scale sizes, from galaxies to stars and planets. Circumstellar disks orbit stars at different evolutionary stages and they are commonly detected as an infrared (IR) excess in their spectral energy distributions (SED). In the case of main sequence (MS) stars, an IR excess was first discovered in Vega (Aumann et al., 1984) with the Infrared Astronomical Satellite (IRAS). This finding, together with the discovery of the first exoplanet around the MS star 51 Pegasi by Mayor & Queloz(1995), opened a new era in the field of stellar astrophysics. After the discovery of the ”Vega-like” phenomenon, a few other stars (Fomalhault, Eridani, β Pictoris) were also found to have an IR excess with fluxes at 25 µm and 100 µm significantly higher than those expected solely from the photosphere. The SED of this kind of excesses in the IR is consistent with models where dust particles in disks emit the extra energy, because they absorb the optical and ultraviolet light from the central star and re-radiate this energy thermally in the IR (Zuckerman, 2001). In Figure 1.1 we show the SEDs of the four stars showing the Vega-like phenomenon (sometimes known as the fabulous four).
The temperature of dust particles depends on their distance from the star and their size relative to the wavelength of their maximum IR thermal emission. This means that small particles with respect to the peak of their IR emission will radiate inefficiently and their temperature will raise until they reach the temperature that a larger particle would have at the same location. Besides, particles much larger than the wavelength of interest will emit inefficiently in the IR, e.g. if we have millimeter wave observations, grains with sizes larger than 1 cm would contribute little to this total emission (Zuck- erman, 2001). If a disk consists of several components at different locations from the
1 2 CHAPTER 1. INTRODUCTION star, observations at different wavelengths can probe the multiple components: shorter wavelengths probe closer and warmer material, while longer wavelengths can detect cooler and fainter material. At distances about 0.01 to 0.03 AU, the emission of hot material with temperatures of 1500 K is traced at wavelengths near 2 µm. For distances of 0.1 AU to 1 AU, the∼ material has a temperature 300 K and∼ the emission peaks around 10 µm. At distances from 1 AU to 10 AU the∼ material emission peaks at 20 µm with a temperature 150 K. Finally, the temperature is 50 K for ma- terial∼ beyond 50 AU and the emission∼ of this material peaks at wavelengths∼ 60 µm ≥ (Dullemond & Monnier, 2010; Su,Chapter 2006 1.). Introduction
105
100
ε Eridani Vega 10-5 105
Flux [Jy]
100
β Pictoris Fomalhaut 10-5 1 10 100 1 10 100 Wavelength [µm]
Figure 1.1: Spectral energy distributions of the four stars with debris disks: Vega, β Pictoris, Figure 1.1: ϵSpectralEridani and energy Fomalhaut. distributions The photometric of the data firstpoints four are from stars the IRAS(Vega, (12, Fomalhault, 25, 60, 100 Eridani and β Pictoris) showingµm), 2MASS the Vega-like (J H and K phenomenon filters), AKARI and caused Spitzer by (24 the and presence 70 µm) missions. of debris All data disks. Photometric points representedwas obtained with through small the circles VizieR are search from engine. IRAS, The small 2MASS, circles AKARIrepresent the and photometricSpitzer missions. The continuous linepoints, are the thick synthetic lines are SEDs the synthetic from KURUCZ Kurucz models models for their (Cruz-Saenz respective ste dellar Miera effective et al., 2012). temperature, surface gravity and metallicity. Circumstellar disks evolve from protoplanetary to debris disks, hence their properties depend on their age. Williams & Cieza (2011, see also references therein) reviewed the evolution ofexcesses circumstellar around other disks nearby and stars, here as well we as for provide the study a onthefrequencyofthephe- brief summary of their work: the disk is formednomenon. by angular In fact, Aumann momentum[1985]soonconductedadetailedanalysisofallavailable conservation as the proto-star begins to accrete matter. Eventually,sources in the disks IRAS point start source to catalog lose mass and reported as the the disc starovery accretes of eight new matter stars at a rate of with7 infrared excess1 similar to8 that of Vega, this1 is, stars with prominent IR flux at three 6 1 about 10− M year− to 10− M year− for T-Tauri stars and of 10− M year− for Ae/Be∼ HerbigIRAS bands: stars 12,( 25Hillenbrand and∼ 60 µ.ThisworkincreasedthenumberofVega-likestarsto et al., 1992), and by photoevaporation∼ (mainly by X-ray andtwelve. UV Subsequent light from analyses the of IRAS central data (e.g. star).Backman In and early Gillett stages,[1987], Walker the accretion rate dominates overand Wolstencroft the photoevaporation[1988], Oudmaijer andet al. [ the1992], gasMannings in the and outer Barlow disk[1998 serves]) pro- as a reservoir for replenishingvided the an ever inner increasing (closer number to of the objects star) and regions.verified that tThehe preconception accretion that rate stars decreases with time and theon outer the main disk sequence will are no devoid longer of surrounding be able material, to supply hence material, stellar the spectral thus en- an inner hole is created at fewergy AUs distribution from (SED) the cannot star. always However, be represented the evolution by simple photospheric of the solid (in early material is quite investigations, blackbodies) models, was wrong. Early statistics on IRAS data showed
2 1.1. CIRCUMSTELLAR DISKS 3
different. Dust grains starts to collide and stick together, they are transported towards the midplane of the disk, decoupling from the gas. Dust coagulation process and the settling begins to create planetesimals and even larger rocky bodies. When the gas photoevaporates, dust with sizes 1 µm are blown away by the radiation pressure and drag forces might occur on the disks.≤ The dust particles are affected by a dissipative force called Poynting-Robertson (P-R) force. This force is produced by a tangential component of the radiation pressure that opposes the movement of the dust grains, it causes that they lose orbital energy and angular momentum and, as a consequence, get closer to the star (Burns et al., 1979). With this effect in action, dust evaporates when it reaches the sublimation radius and what is left after this event is a disk that lacks of significant amounts of gas and is populated with dust, planetesimals and even planets. This disk configuration is known as debris disk. Cold debris disks were first discovered by Aumann et al.(1984) and, later, presence of warm material (Carpenter et al., 2009; Cruz-Saenz de Miera et al., 2014; Patel et al., 2014) was also found in some other systems making cold and warm debris to coexist in many cases. Figure 1.2 AA49CH03-Williamsshows this evolutionary ARI 14 July 2011 phases 19:21 on the circumstellar disks. Below, we briefly describe the protoplanetary disk phase (Figure 1.2a) and the debris disk phase (Figure 1.2d). Debris disks are the main subject in this thesis.
Massive flared disk Settled disk a FUV photons b
Accretion
Evaporation flow
Photoevaporating disk
c d Debris disk EUV
Evaporation flow
FigureFigure 1.2: 6 Diagram of the evolution of a typical circumstellar disk. In blue is represented the gas materialThe evolution while of in a typical red the disk. dustThe gas (Williams distribution is & shown Cieza in blue, 2011 and the). dust in red. (a) Early in its evolution, the disk loses mass through accretion onto the star and far-UV (FUV) photoevaporation of the outer disk. (b)Atthesametime,grainsgrowintolarger bodies that settle to the mid-plane of the disk. (c) As the disk mass and accretion rate decrease, extreme-UV(EUV)-induced photoevaporation becomes important; the outer disk is no longer able to resupply the inner disk with material, and the inner disk drains on a viscous timescale ( 105 years). An inner hole is formed, accretion onto the star ceases, and the disk quickly dissipates from the ∼ inside out. (d ) Once the remaining gas photoevaporates, the small grains are removed by radiation pressure and Poynting-Robertson drag. Only large grains, planetesimals, and/or planets are left. This debris disk is very low mass and is not always detectable.
as a CTTS based on the presence of accretion indicators. Accretion may be variable on short timescales, but shows a declining long-term trend. Annu. Rev. Astro. Astrophys. 2011.49:67-117. Downloaded from www.annualreviews.org At the same time, grains grow into larger bodies that settle onto the mid-plane of the disk, where they can grow into rocks, planetesimals, and beyond. Accordingly, the scale height of the dust decreases and the initially flared dusty disk becomes flatter (Figure 6b). This steepens the slope of the mid- and far-IR SED as a smaller fraction of the stellar radiation is intercepted by Access provided by Instituto Nacional de Astrofisica, Optica y Electronica (INAOE) on 06/22/15. For personal use only. circumstellar dust (Dullemond & Dominik 2005). The near-IR fluxes remain mostly unchanged because the inner disk stays optically thick and extends inward to the dust sublimation temperature. The most noticeable SED change during this stage is seen in the decline of the (sub)millimeter flux, which traces the decrease in the mass of millimeter- and smaller sized particles (Andrews & Williams 2005, 2007a) (see Figure 7). As disk mass and accretion rate decrease, energetic photons from the stellar chromosphere are able to penetrate the inner disk and photoevaporation becomes important. When the accretion
98 Williams Cieza · AA48CH07-Dullemond ARI 16 July 2010 20:8
4 CHAPTER 1. INTRODUCTION all low-/intermediate-mass pre-main-sequence stars have disks. An often used indicator of the presence1.1.1 of a circumstellar Protoplanetary disk, or at Disks least of circumstellar material, is IR flux in excess of what can possibly be explained by a stellar photosphere of a reasonable size. By studying the fraction of stars with NIR excess flux in young clusters of ages from 0.5 to 5 million years, Haisch, Lada & LadaAccording (2001) established to Dullemond a clear & Monnier trend: that(2010 the), these “disk disks fraction” are composed decreases by with dust age, and or are in other words,enriched that disks with have gas a lifetimein a gas-to-dust of a few ratio million of about years. 100. They are found around pre-main A questionsequence is, stars, however, as T Tauriwhether stars one of can approximately be sure that one the solar NIR mass excess or is less indeed and Herbig from a disk and notAe from stars, some which circumstellar are few times envelope more or massive disk wind. than Although the Sun and we know will evolve from imaginginto A- that the coldtype outer main-sequence circumstellar stars material (Mathieu is indeed, 1994;disk-like, Waters & little Waelkens is known, 1998 about). Protoplanetary the nature of the materialdisks inward are well of what traced telescopes by a near-IR can spatially (NIR) excess resolve. often The called lack of”NIR correlation bump”, speciallybetween inAV and NIR excess (Cohen & Kuhi 1979) is inconsistent with a spherical dust geometry, and the spectral Herbig Ae/Be stars. This NIR bump is characteristic of these type of disks. Spherical shape of the IR excess for T Tauri stars and brown dwarfs can be explained fairly well with models envelopes or disks winds around these stars have been discarded as the sources of the of irradiated dusty disks with a flat (Adams & Shu 1986) or flared shape (Kenyon & Hartmann 1987, CalvetNIR bump et al. because 1992, Chiang the spectral & Goldreich shape of 1997, the excesses Menshchikov are well & explained Henning with 1997, models D’Alessio et al. 1998).of irradiated However, dust for with Herbig a flat Ae/Be or flared stars this shape was (Adams initially & not Shu so, clear1986; and D’Alessio still remains et al., under debate.1998 It appears). Hillenbrand that the et JHKL al.(1992 photometric) proposed points a Planck nicely component line up toof 1500form K a bump for modeling very similar, thoughthe not NIR identical, excess: to dust the evaporation peak of the was Planck taken function into account at a temperature at this temperature of about regime1,500 K. ∼ This isand perhaps a gap most in the clearly dust, seen filled in with the spectrum optically thinof the gas, prototype located Herbig in the very Ae star proximity AB Aurigae (Figureof 2 the). This proto-star NIR bump was proposed. was not at In all Figure expected 1.3 fromwe show any of the the SED above of the mentioned Herbig Ae models: They tendstar AB to yield Aurigae, relatively where smooth the NIR multicolor bump in the blackbody J, H, K, curves L passbands in which is evidenta continuous and is series of Planckrepresented peaks at by different the yellow temperatures solid line. add The up 1500 to K a smooth Planck component curve. Now is there shown appeared with the to be a singlegreen Planck solid peak line. in As the we spectrum, mentioned albeit before, often the with disk aevolves bit of and excess the emission gas present toward in the longer wavelengths.disk is Thisremoved NIR due bump, to radiation as it is often pressure called, from is the not star just and a small by formation feature: It of contains gas giant a large amountplanets of energy. (Baraffe The et bump al., 2010 alone). can contain up to half the IR flux from the entire system and nearly all the emission originating from the inner AU or so. It can therefore not be ignored; it must be understood in terms of some physical model.
10–7 AB Aurigae
) NIR bump –2
cm Stellar fux –1 10–8 (erg s ν F Planck ν Annu. Rev. Astro. Astrophys. 2010.48:205-239. Downloaded from www.annualreviews.org curve 1600K
Access provided by Instituto Nacional de Astrofisica, Optica y Electronica (INAOE) on 06/08/15. For personal use only. 10–9 0.1 1.0 10.0 100.0 λ (μm) Figure 2 The spectral energy distribution of the Herbig Ae star AB Aurigae. Red is the measured emission. Blue is the steller spectrumFigure 1.3: predictedSED of with Herbig a Kurucz Ae star ABstellar Aurigae. atmosphere Measured model. emission The in excess red, predicted of flux above stellar the spectrum atmosphere (the “IRfrom excess”) Kurucz is the models thermal in blue, emission Planck from curve the of dust 1600 in K the in green disk. The and the emission sum of in the the Planck near-IR curve (NIR) with clearly has a bump-likethe stellar structure atmosphere and in is gold often (Dullemond called the & NIR Monnier bump., 2010 In green,). a Planck curve at a temperature of 1,600 K is overplotted. The golden curve is the sum of the Planck curve and the stellar atmosphere.
208 Dullemond Monnier · 1.1. CIRCUMSTELLAR DISKS 5
1.1.2 Debris Disks
Debris disk is a term for referring to all sub-planetary solids that are the aftermath of planet formation. After the protoplanetary stage, a star is expected to have in its surroundings at least one or all the following components: planets (from sub-Earth to super-Jupiter size); remnants of the protoplanetary disk (both dust and gas); plane- tesimals with growing solid particles and other planetesimals that are forming new dust through physical processes like collisions among them. As mentioned in Section 1.1, after the gas evaporation process in the protoplanetary disk, solids are settled into the midplane of the disk and some are carried onto the star by P-R drag reaching a radius where they sublimate due to the stellar radiation. The arrival of dust into the planetary region might have in consequence that planets, if they are present, would scatter this dust. This means that the star would clean its surroundings in timescales of 10 Myr, according to near IR observations (Wyatt, 2008). However, the existence of≤ disks with ages above 100 Myr implies mechanisms of dust replenishment. The mechanisms involve stirred dust produced by stellar flybys (Kroupa, 1998) or by Pluto- size bodies or even planets (Mustill & Wyatt, 2009), producing cascades of collisions between planetesimals, initiated with larger rocky bodies (Weinberger et al., 2011; Jackson & Wyatt, 2012). Thus, this kind of disks continues to evolve collisionally and dynamically.
The thermal IR emission of a debris disk is usually fitted with a SED of a blackbody with a single temperature. Nevertheless, gray body is also used for modeling debris disks because it describes the quasi-black body emission of the dust grains and takes into account their size, composition and morphology and their distance from the source. This emission is calculated through the equation:
1.9899B(λ, T ) B (λ, T ) = κ (1.1) g d2 abs
where Bg indicates the emission of the gray body, B(λ, T ) is the black body emission with temperature T, κabs is the absorption coefficient proposed by Draine(2006) and d is the distance to the source (Cruz-Saenz de Miera et al., 2012).
There are two quantities that can be derived from the fit: the dust temperature Td and the dust fractional luminosity fd, defined as the ratio between the bolometric luminosity of the dust and that of the star: fd = Ld/L . Wyatt(2008) proposed a way ∗ to calculate these quantities using the wavelength where the dust emission flux peaks d d λmax and the maximum flux itself Fmax, thus 6 CHAPTER 1. INTRODUCTION
d d 1µm Fmax λmax Td = 5100K d , fd = (1.2) λmax Fmax∗ λmax∗
where Fmax∗ is the maximum emission from the star and λmax∗ the wavelength where it is emitted. In order to better illustrate the role of Td and fd, Figure 1.4 shows a G2V stellar spectrum at a distance of 10 pc that contains different disk spectra at temperatures of 278 K, 88 K, and 28 K (yellow, red and blue solid lines respectively), 3 with a fractional luminosity of fd= 10− . These disks are located at 1 AU, 10 AU and 5 100 AU respectively. The debris disk spectrum at fractional luminosity levels of 10− 7 and 10− are shown in dashed and dotted lines. In the Solar System, mutual collisions ANRV352-AA46-10 ARI 25 July 2008between 4:42 Edgeworth Kuiper Belt (EKB) objects and erosion by interstellar dust grains release dust particles that spread over the EKB region (Jewitt et al., 2009). This means that the EKB would appear as an extended 50 AU disk with a Td 70 100 K and 7 ∼ − a fractional luminosity f 10− (Backman et al., 1995). d ∼
102 a Total emission 101 spectrum = 10–3 G2V at 10 pc = 10–5 100 T = 278 K, 1 AU = 10–7 T = 88 K, 10 AU T = 28 K, 100 AU –1 Disk 10 contribution = 10–3 Flux density (Jy) –5 10–2 = 10 = 10–7
10–3 10–1 100 101 102 103 Wavelength (µm)
10–1 Figure 1.4: The SED of a G2V star at 10pc in gray, with a debris disk of dust at temperatures of 278 K, 88 K, andb 28 K in yellow, red and blue, which dust radii corresponds to 1 AU, 10 AU, and 100 AUrespectively. 10–2 The tick lines show the total emission spectrum and thin lines show the disk contribution (Wyatt, 2008). 10–3 *
L –4 / 10 24 µm IR 70 µm L –5 850 µm at 10 pc = 10 f
10–6
10–7 AB KB
10–8 100 101 102
Annu. Rev. Astro. Astrophys. 2008.46:339-383. Downloaded from www.annualreviews.org Radius (AU)
10–1 c MOV G2V AOV 10–2 Access provided by Instituto Nacional de Astrofisica, Optica y Electronica (INAOE) on 06/11/15. For personal use only.
10–3 * L / 24 µm IR –4 L 10 70 µm
= 850 µm at 10 pc f 10–5
10–6
10–7 100 101 102 103 Radius (AU)
342 Wyatt 1.2. OBSERVING DEBRIS DISKS AT IR WAVELENGTHS 7 1.2 Observing Debris Disks at IR wavelengths
Observations of debris disks help to study their properties and to identify possible correlations with their host stars properties and, thus, to understand the diversity of planetary systems architectures. One of the objectives is to place the Solar System’s debris disk, composed of warm dust in the terrestrial zone (the asteroid belt at 0.5- 3 AU), and cold dust in the EKB, in context of the other systems (Matthews et al., 2014). As expected, these disks might be detected at different wavelengths, unveiling different dust composition and physical properties.
Far-Infrared to Millimiter Observations • Some debris disks are detected only at long wavelengths ( 60 µm), that corresponds to cold dust with temperatures 50 K orbiting from 10 to≥ 100 AU. For many systems, a single dust disk is enough to≤ fit their SED. These outer disks are much brighter 5 3 analogues of our EKB with fractional luminosities range from 10− to 10− (Krivov, 2010). The dust masses in debris disks, determined through sub-mm measurements, 3 are in range of 10− to 1 Earth masses (Sheret et al., 2004). Some debris disks reveal, in spectroscopic observations, features of the mineralogy of the dust grains, e.g. a mixture of amorphous and crystalline silicates, silica and other species, including water ice. However, the interpretation of the spectra is difficult and involves degeneracies, since the same spectra can be fitted with different mixtures of material (Chen et al., 2008; Lisse et al., 2009; Krivov, 2010). Observations at millimeter wavelengths are valuable for studies of system dynamics because of the higher sensitivity of this wavelengths to larger dust grains, with long resonant lifetimes that best traces the structure of the disk (Wyatt, 2006).
In the past decade, several surveys have measured the incidence of debris disks in spectral types A to M at 70 and 160 µm. The most relevant are FEPS∗ (Rieke et al., 2005), using the Spitzer observatory, DEBRIS (Sibthorpe et al., 2013) and DUNES† (Eiroa et al., 2013), carried out with the Herschel satellite. Matthews et. al (2014, and references therein) make a comparison of detection rates of debris disks among the different surveys, making emphasis that for A stars, the detection rates are 33% and 25% at 70 µm and 100 µm respectively, while for solar type stars (FGK) the detection rate ranges from 10% in the case of FEPS survey to 17% reported in the DEBRIS survey. DUNES increased the detection rate up to 20% (Eiroa et al., 2013). Also, Trilling et al.(2008) reported that an apparent decrease of excess rates from A to K spectral types is due to an age effect as expected by the circumstellar disk evolution.
∗Formation and Evolution of Planetary Systems †DUst around NEarby Stars 8 CHAPTER 1. INTRODUCTION
Near-IR Observations • Systems with very hot dust, which have temperatures around 1000 K have been disco- vered through near-IR photometry. It is proposed that this kind of disks has grains with size 1 µm in a separation radius of 0.2 AU from the central star. These exozodiacal≈ clouds, as designated in analogy to the solar system zodiacal dust, has an 8 4 estimated dust mass of 8 10− Earth masses and a fractional luminosity of 5 10− . For instance, near-IR emission≈ × has been observed in Vega. A major dynamical× event, similar to the Late Heavy Bombardment (Wyatt, 2008) in the solar system, might explain the presence of small dust grains in the inner disk of this star (Absil et al., 2006).
1.3 Mid-IR observations: Warm debris disks
Most of the known debris disks are analogues to our Kuiper Belt and show no evidence of warm dust grains in the inner regions, nevertheless, new kind of disks were detected thanks to extensive surveys in the Mid-IR. These disks were called warm debris disks and the emission in excess found at wavelengths between 5 µm and 35 µm suggests the presence of material closer to the star. Recent studies with the Wide Infrared Survey Explorer (WISE) (Cruz-Saenz de Miera et al., 2014; Patel et al., 2014) have found stars with infrared excesses at Mid-IR. In Figure 1.5 we show the SED from Cruz-Saenz de Miera et al.(2014) of four stars with prominent 22 µm excesses (in the W4 WISE band), which might correspond to warm debris disks with temperatures 4 Td in the range of 100 K to 450 K and fractional luminosities fd from 4 10− to 2 × 1.25 10− . × Several physical processes have been proposed to explain the formation and presence of warm dust around stars. As mentioned before, the presence of debris disks around stars with ages 100 Myr implies a second generation dust production. In the spe- cific case of warm≥ dust, gravitational interaction among the particles in debris disks might produce a collisional cascade that populate regions at smaller stellocentric dis- tances. Williams & Wetherhill(1994) suggest that collisional grinding of planetesimals to micron-sized grains is produced by gravitational interaction between planets embed- ded in the planetesimal belt. Besides, Pluto size objects, as well as asteroids and short period comets together, are considered also sources of the interplanetary dust observed at few AU from the star (Gr¨unet al., 2001). Currie et al.(2007) have proposed that warm dust is also product of terrestrial planet formation, i.e. rocky planets in the habitable zone. This theory is reinforced with the evidence of the chaotic early times of our solar system. Jackson & Wyatt(2012) proposed the formation of our Moon as a collision between the primitive Earth and a gigantic object near the size of Mars. 1.3. MID-IR OBSERVATIONS: WARM DEBRIS DISKS 9
Wyatt(2008) proposed that dust is mainly produced by collisions of large rocky bodies and the dust is carried in zones closer to the star by P-R drag. A similar scenario was proposed by Reidemeister et al.(2011), where they proposed that stellar wind drag, similar as the P-R force but with particles instead of photons, is responsible of the warm6 dustF. around Cruz-Saenz Eridani. de Miera, M. Chavez, E. Bertone and O. Vega
HD 39415 HD 119718 1.00 1.000
0.10
0.01 Tdisc = 244 K Tdisc = 103 K 0.100 Fdisc = 6.50E-03 Fdisc = 4.25E-04
1.0 HD 115371 YZ Cep WISE 22 [Jy] Flux [Jy]
0.1 0.010
0.01
Tdisc = 197 K Tdisc = 442 K Fdisc = 1.75E-04 Fdisc = 1.25E-02 0.001 0.001 1 10 1 10 0.001 0.010 0.100 1.000 Wavelength [µm] MIPS 24 [Jy]
FigureFigure 1.5: SEDs 5. Spectral of four stars energy that display distributions prominent 22 µ ofm excesses. four stars Observational that display data points Figure 8. Comparison between WISE-W4 and Spitzer-MIPS at J, H, KS and the WISE bands in red dots. Continuous line correspond to the best fit photosphere fromprominent Kurucz models 22 plusµmexcesses.Observationaldatapoints(reddots) the blackbody. Each panel shows the disk temperature and the fractional 24 µm. Blue circles and red triangles are sources from Eiroa et al. luminosity (Cruz-Saenz de Miera et al., 2014). mark the J, H, and KS 2MASS magnitudes, extracted from SIM- (2013) and Chen et al. (2011), respectively. Data from Chen etal. BAD, and four WISE bands. The continuous lines correspond to (2011) consist of the 65 stars in their sample that accomplished Itthe is also best worth fit to of mention the stellar that other photosphere processes are plus involved a black in the body.destruction In ea ofch warm the WISE quality selection criteria adopted in this work. Green dust.panel In weKenyon indicate & Bromley the( black2004) models, body temperature a planetesimal belt and produces fractional lowlu- levels squares are the excess candidates included in the present work. of debris emission in the early stages of planetary accretion, then dust production reachesminosity a maximum that delivers and destructive the best collisional fit. cascades initiate by interaction of km- Error bars are smaller that the symbol size for most stars. The sized bodies. This means that, according to these models, rocky planetesimals grow agreement of the two instruments is evident down to the lowest into planets in 1-10 Myr at distances around 0.3-3 AU, icy planetesimals become W4 flux level in our sample of excess candidates indicated with planets in 10-30 Myr and, after icy planets formed,∼ a depletion of planetesimals occurs due to25 repeated collisions and the lack of replenishment of dust from the outer disk. As the dotted line.
20 observational programs at far-IR, sub-mm and mm that are 15 required to better characterise the material around Sun-like stars.
Frequency 10
5 ACKNOWLEDGMENTS 0 We thank the anonymous referee for constructive com- 0 100 200 300 400 ments that improved the presentation of this work. MC and Tdisc [K] FCSM would like to thank CONACyT for financial support through grant number 134985. This publication makes use of Figure 6. Distribution of the black body temperature of the disc candidates of our sample. The shaded area indicates the distribu- data products from the Wide-field Infrared Survey Explorer, tion of those objects that also display a 3σ excess in W3. which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California In- stitute of Technology, funded by the National Aeronautics and Space Administration. This research has made use of the 50 SIMBAD database, operated at CDS, Strasbourg, France.
40
30 REFERENCES
Frequency 20 Aumann H. H., Beichmann C. A., Gillett F. C., de Jong, T. Houck, J. R. et al., 1984, ApJL, 278, L23 10 Chen C. H., Mamajek E., Bitner M. A., Pecaut M., Su K. Y. L., et al., 2011, ApJ, 738, 122 0 Dermott S. F., Durda D. D., Grogan K., Kehoe, T. J. J. -4 -3 -2 -1 2002, in Asteroids III, ed. W. F. Bottke Jr. et al. (Tucson, Log F disc Univ. Arizona Press), 423 Figure 7. Distribution of the fractional luminosity of the disc Eiroa C., Fedele D., Maldonado J., Gonz´alez-Garc´ıa B. M., candidates of our sample. The shaded area indicates the distribu- Rodmann J., et al., 2010, A&A, 518, L131 tion of those objects that also display a 3σ excess in W3. Eiroa C., Marshall, J. P., Mora, A., Montesinos B., Absil, O., et al. 2013, A&A, 555, 11 Fujiwara H., Ishihara D., Kataza H., Onaka T., Yamashita T. et al., 2009, in proceedings of the conference AKARI,
c 2013 RAS, MNRAS 000,1–7 ⃝ 10 CHAPTER 1. INTRODUCTION a consequence, debris dust production eventually declines. This implies that dust mass drops systematically with time. Rieke et al. (2005 and references therein) proposed that debris luminosity peaks around an age of 10-30 Myr and then declines toward 1 older ages; in particular, they proposed that 24 µm emission declines as t− by erosive collisions. Nevertheless, although planet gravitational interaction is thought to be responsible of formation of warm dust, it is also possible that this interaction might be the cause of the decrease in dust mass. Quillen(2006) has proposed that massive planets, at least Neptune size, are required for clearing regions in disks and also planet migration could be constantly eroding away the inner regions of the disk forming gaps in the terrestrial zone.
According to Krivov (2010 and references therein), a balance between the production of dust by collisional cascades and its loss due to radiation pressure is expected. If such balance exists, the amount of particles with different sizes and orbits stay constant relative to each other; however, Wyatt et al.(2012) claimed that debris disks incidence rate is higher around stars with planets of low mass.
Some physical properties have been derived for these inner disks: for example, the 8 6 typical masses are estimated in the range of 10− and 10− Earth masses (Krivov, 2010). Studies at 24 µm, done by Rieke et al.(2005) for A stars with ages in the range of 5-850 Myr, found that younger stars exhibit excess emission more frequently than older stars and the fractional excesses inversely fall with age. Observationally, Su (2006) found a rate for A stars of 32% at 24 µm. Also, different surveys with IRAS, ISO‡, and Spitzer have shown that Mid-IR excesses are rare in FGK stars (Wyatt, 2008). Trilling et al.(2008) found a fraction of 4% warm excesses in field stars with a median age of 5Gyr using the Spitzer survey. As shown in Figure 1.6 (a), the fraction of FGK stars with∼ 24 µm excesses falls with time from 20% - 40% at the youngest ages to a few percent on a 100 Myr scale. The fall off mimics the behavior of A type stars except that it is an order of magnitude faster (see Figure 1.6(b)). The difference in timescales and the lifetime of Sun-like stars in the MS stage explains in some way the rarity of warm dust excesses in field FGK stars (Wyatt, 2008).
‡Infrared Space Observatory ANRV352-AA46-10 ARI 25 July 2008 4:42
1.3. MID-IR OBSERVATIONS: WARM DEBRIS DISKS 11
102 HD 113766 a BD+20307 F5-K7 stars F0-F4 stars ) * –2
24 t F
/ HD 23514 24 F 101
t –1 Excess ratio (
η Corvi HD 69830
100
0 50 102 103 104 Age (Myr)
70 b 60 10–30 B5-A9 stars (Siegler) FGK stars (Siegler) Annu. Rev. Astro. Astrophys. 2008.46:339-383. Downloaded from www.annualreviews.org 50 NGC 2547 FGK stars (Meyer) 31–89 40 Access provided by Instituto Nacional de Astrofisica, Optica y Electronica (INAOE) on 06/11/15. For personal use only.
30 Sco Cen 90–189
190–500 IC2391 20 10 –32 100–320
Fraction of stars with 24-µm excess (%) 10 501–800 32–100 Field Pleiades 320 –1000 1000–3200 Hyades 0 101 102 103 Age (Myr)
Figure 1.6: Evolution of 24 µm excesses around Sun-like stars (Siegler et al., 2007). In Panel (a): www.annualreviews.org Evolution of Debris Disks 367 24 µm excess ratio as a function of age. In Panel (b): Fraction of stars• with 24 µm excesses as a function of age. Filled circles are FGK stars, squares for A and B stars. The numbers in the blue and red marks represent the timescale binning for the stars in each sample. Figure taken from Wyatt (2008). 12 CHAPTER 1. INTRODUCTION 1.4 Planet interaction and disks
Since the discovery of the first Jupiter size exoplanet around the main sequence star 51 Pegasi (Mayor & Queloz, 1995), many more exoplanets around Sun-like stars have been identified by several methods like radial velocity, transit, astrometry, microlen- sing, timing and direct imaging (see Perryman 2011 for further explanation of the detection methods). The majority of all exoplanet searches have taken place at optical wavelengths, with mature stars as primordial candidates. We have previously men- tioned that debris disk are perturbed by the presence of planets and, therefore, it is convenient to briefly elaborate on these interactions.
Murray & Dermott(1999) analyzed perturbations produced by planets on the disks. The secular perturbation occurs when the planetary system has a planet with an or- bital plane misaligned with the disk plane. Eventually, the disk plane tends to align with the planet plane and this alignment takes place in long term scales, that can take 10 Myr or more before reaching the steady state. Several scenarios for secular pertur- bations are proposed depending of the planet orbit inclination. First, if the planet has an orbital plane misaligned with the disk mid plane, a warp will propagate through the disk. Second, if there is a planet with an eccentric orbit, there would be spiral pertur- bations that propagate through the planetesimal disk and, in consequence, make the planetesimals change their initial circular orbits to a spiral form orbit. This will cause catastrophic collisions that will produce collisional cascades. Another consequence of this secular perturbation is the formation of asymmetric brightness on the side of the disk closer to the star. (Mustill & Wyatt, 2009; Wyatt, 1999; Matthews et al., 2014). This warp phenomenon is been observed in β Pic disk at 80 AU and was used to infer the presence of a planet at a distance of 9 AU, with a mass of 9 Jupiter masses (MJ §). This hypothetical planet was identified later by direct imaging. Figure 1.7 shows β Pic images obtained with the Space Telescope Imaging Spectrograph (STIS) on board the Hubble Space Telescope. The warp can be seen in the vicinity ( 100 AU) of the star (Lagrange et al., 2010; Heap et al., 2000). ∼ ±
Another kind of perturbations in debris disks are produced by resonances in the vicinity of a planet. The resonances overlap each other causing chaos in the region nearby where they are produced. As a consequence, dust is removed from its initial location, and the planet induces the perturbations that shape the inner edge of the debris disks, cleaning the region where the planet orbits. This means that it is possible that planets are orbiting stars within the gaps of debris disks. On the other hand, it is also possible that the formation of clumpy structures occurs. This implies that if a planet is migrating throughout the disk, its resonances will sweep the material and some planetesimals and dust might migrate also with the planet, producing a pinpointed signature where the planet might be located inside the clumps. This phenomenon can be seen around
§ −4 1 MJ = 9.54 10 M × 440 HEAP ET AL. Vol. 539
3.3. Evaluation of the Results di†erences in the six di†erent solutions for the disk Since there are no experimental data available for evalu- (observations at three roll angles times two wedge ating the e†ectiveness of the occulting mask and Lyot stop, positions). As such, they should represent a total error we compared the derived PSF for b Pic with theoretical including both observational uncertainties and errors in the models. Figure 5 compares the radial proÐle of the derived data processing. Along the spine of the disk, the signal-to- PSF with that computed from Telescope Imaging Model- noise ratio exceeds 100 over the region from 30 to 150 AU ling (TIM) models (Burrows & Hasan 1993). This plot from the star. Above and below the spine of the disk, the demonstrates the two main advantages of coronagraphy. brightness, and consequently, the S/N, drop rapidly. First, the 1A occulting wedge provides a rejection factor of 4. OBSERVED PROPERTIES OF THE b PIC DISK up to 8000. Were it not for the wedge, the star would produce count rates of up to nearly a billion e~ s~1 pixel~1. 4.1. Disk Morphology But because the star is occulted, the dynamic range of the b Figure 8 shows the resulting images of the b Pic disk Pic scene is lowered to a point where it can easily be accom- based on the WedgeB1 observations. At the top is a false- modated by the CCD detector. For example, atr \ 0A.5 (10 color image of the disk on a log scale. The bottom shows the AU), the occulted star contributes 26,000 e~ s~1 pixel~1, disk with intensities normalized to midplane brightness and well below the full-well capacity of the CCD (144,000 e~ the vertical scale (i.e., perpendicular to the spine of the disk) pixel~1) for a 1 s exposure. Since the readout noise of the expanded by a factor of 4 in order to show the shape of the summed image (eight or 16 exposures for WedgeB2 and disk more clearly. The main visual impressions are the WedgeB1, respectively) is below 1 e~ s~1 pixel~1, its smoothness of the disk and the presence of a warp close (in 1.4. PLANETdynamic range INTERACTION is about 1 ] 106. Second, the AND wings of DISKS the projection) to the star. The smoothness of the disk in the 13 PSF are a factor of 2 lower than the TIM model for the STIS images is in sharp contrast to previous images telescope performance. This level of suppression accords (Burrows et al. 1995; Mouillet et al. 1997), which are with the expected action of the Lyot stop, but further obser- marked by swirls and radial spikes. We interpret this Eridani,vations which are needed presents to complete some the characterization of this of clumpy the texture structure in previous images in the to incomplete 850 µ eliminationm maps of the collected STIS coronagraphic mode. PSF. The pronounced warp in the disk was detected in with theFigure James 6 compares Clerk the radial Maxwell proÐles of Telescope light from the (JCMT).previous images, In but Figure only theSTIS 1.8 images we are reproduce able to the star and from the midplane of the disk. The star contributes follow it in close to the star. Below, we report on quantitat- 850 µmmore map light by tothe Greaves disk interior to etr \ al.3A and(1998 also beyond). The 9A; perturbationsive measurements of the presented disk, including the in radial the Ñux above gra- lines this is because the sky background is included in the PSF. dient and vertical Ñux distribution, the warp, and the are alsoFigure presented 7 shows the in disk works image with of contours Wisdom of the associ-(1980),innermost Faber region & of Quillen the disk(r \(12007A.5), which), heretoforeWyatt has(2003), ated signal-to-noise (S/N) ratios superposed. The errors not been seen in images of its dust-scattered light. To Mustill &used Wyatt to compute( the2011 S/N for), eachMatthews pixel were estimated et al. from(2014describe). the disk, we use a cylindrical coordinate system
FIG. 8.ÈSTIS/CCD coronagraphic images of the b Pic disk (WedgeB2 observations). The half-width of the occulted region is0A.75 \ 15 AU. At top is the disk at a logarithmic stretch. At bottom is the disk normalized to the maximum Ñux, with the vertical scale expanded by 4. Figure 1.7: STS/CCD coronagraphic images of β Pictoris disk (Heap et al., 2000).
L134 GREAVES ET AL. Vol. 506
Fig. 1.—Dust emission around e Eri at a wavelength of 850 mm. The false-color scale is linear from 2.8 mJy beam21 (3.5 j pixel21) to 8.5 mJy beam21 (at the peak). The star is marked by the star symbol, the circle shows the 150 beam size, and 10 corresponds to 3.22 AU. The apparent size of Pluto’s orbit at 3.22 pc Dustdistance emissionis also shown. The pos aroundition of the star is R.A.Eridani5 03h32m56.s0, decl at. 5 209 a727 wavelength9290.8 and is equinox 2000, e ofpoch 1 850998. The pµropm.er motion Theof the star falsewas color scale is Figure 1.8: only 00.5 over the 6 month observing period. linear from 2.8 mJy beam−1 to 8.5 mJy beam−1. the star is marked with the star symbol. The circle of less than 1), and calibration data were obtained from Mars in a peak signal-to-noise ratio per beam of 10. Photospheric shows the beama sizend Uran ofus. P 15”ointing a andccuracy 1”was 2 correspond0, which is small compa tored 3.22emiss AUion of (1.7Greaves5 0.2 mJy ha ets als al.o be,e n1998subtract).ed in the with the beam size of 150 at 850 mm (FWHM). The data image. The photospheric flux was estimated by independent were reduced using the SCUBA User Reduction Facility (Jen- extrapolations using 2.2 and 3.4 mm data (Carter 1990) and the ness & Lightfoot 1998) and are rebinned in a right IRAS 12 mm flux (corrected for an effective temperature of ascension–declination frame with 20 cells. 5000 K). Dust emission around e Eri was also tentatively de- The 850 mm map of e Eri is shown in Figure 1. The data tected at 450 mm (Table 1). have been smoothed with a 80 point-spread function, resulting The image shows extended flux around the star out to about
TABLE 1 Flux Measurements for e Eri
Wavelength (mm) Dust Flux Photospheric Flux Unit Comments 850 ...... 40 5 3 1.7 5 0.2 mJy r 350 from star 450 ...... 185 5 103 6 5 1 mJy r ∑ 350 from star 100 ...... 1.78 0.11 Jy IRAS∑ 60 ...... 1.34 0.29 Jy IRAS 25 ...... 0.27 1.63 Jy IRAS 12 ...... ) 6.66 Jy IRAS 3.4 ...... ) 70.3 Jy SAAO 2.2 ...... ) 139.7 Jy SAAO 1300 ...... (17–24) 0.7 mJy Photometry, 110–240 beams Note.—The flux data were from this work, the IRAS point-source catalog, Carter 1990, Zuckerman & Becklin 1993, Chini, Kru¨gel, & Kreysa 1990, and Chini et al. 1991. The photospheric emission at 2.2–12 mm was extrapolated to find dust excesses (see also Gillett 1986). Only the 12 mm point was used for the IRAS wavelengths, and color corrections were made for a 5000 K photosphere (12–25 mm) and the dust spectral energy distribution (60–100 mm). 14 CHAPTER 1. INTRODUCTION
Greaves et al.(2006) have found that the incidence of debris disks do not correlate with metallicity of MS stars, whereas it has been found by Fischer & Valenti(2005) that the metallicity of stars with giant planets is likely super solar. More recently, Marshall et al.(2014) have found several trends between the stellar metallicity, the presence of a debris disk and the mass of the massive exoplanets around stars. They found that low metallicity stars are more likely to host low mass planets and these stars are more likely to have a detectable debris disk. However, there is not yet a significant evidence for a trend relating the eccentricity of the innermost planets with the fractional luminosity of the disks, which suggests that known exoplanets in the systems have little influence on the presence of dust.
1.5 Aims of this work
Given that planets are the final stage of agglomeration of smaller bodies from dust to planetesimals, and debris disks are the result of collisional grinding of these planete- simals, we might expect the presence of planets in the terrestrial zone located a few AUs from the star and warm debris disks to be correlated. This idea is reinforced by the hypothesis that the gravitational interaction of a planet with the dust particles is responsible for the continuous production and replenishing of warm dust. However, it also has been discussed that the cleaning processes of the innermost regions of debris disks are also caused by planets. Thus, it is interesting to see if the number of stars with Mid-IR excesses is correlated with the presence or absence of planets in order to understand which physical processes are dominating in these planetary systems. To achieve this, we analyze two samples of stars, one composed of stars with planets and the other composed of stars without planets (stars with no detected planets), using IR data from the four WISE bands (W1, W2, W3, W4) and searching for IR excesses at 22 µm with a comparison of the observed and the expected flux ratio W4/W3 in order to see if the correlation between warm debris disks and the presence of planets exists. Nevertheless, we also analyze other methods to search for IR excesses that have been used by other authors to understand which method provides better detection of the excess significance, thus avoiding unreliable IR excesses.
The structure of this thesis is as follows: In Chapter 2 we present a description of the photometry data used and the sample selection. In Chapter 3 we describe the methodology used in this work, as well as details of the different methods that have been implemented for detecting infrared excesses. In chapter 4 we report the results obtained and the analysis of these results. Finally, we present the conclusions and future work in chapter 5. Figures and tables of interest are shown in the appendix section. Chapter 2
The sample selection
The 2 Micron All Sky Survey (2MASS) and the Wide Infrared Survey Explorer (WISE) conducted sensitive observations of the entire sky at near and mid-IR wavelengths. These massive surveys complement the pioneering work of IRAS, particularly in the context of the present work. This chapter focuses on the description of 2MASS and WISE and the sample we have selected for investigating the prevalence of Mid-IR excesses in MS stars with and without planets. The next two sections of this chapter describe some scientific goals, characteristics and quality of the data releases of these surveys.
2.1 IR Surveys
2.1.1 Wide-field Infrared Survey Explorer (WISE)
WISE was a NASA mission (2009-2011) which had as objective to map the entire sky in the mid-infrared passbands at 3.4 µm (W1), 4.6 µm (W2), 12 µm (W3) and 22 µm (W4). It had a telescope with 40 cm of aperture, cryogenically cooled. It used four focal plains that simultaneously took images of a 47 47 arcmin field of view. Moreover, the exposure time was 7.7 s for W1 and W2, and 8.8× s for W3 and W4. The Full Width Half Maximum of the Point Spread Functiona were 6.1” for W1, 6.4” for W2, 6.5” for W3 and 12.0” for W4. In Figure 2.1 we show a sketch of the WISE satellite (Wright et al., 2010).
Two data releases have been delivered. The first one, called All-Sky (Cutri et al., 2012), covered more than 90% of the sky. These data were reduced in a way that
15 16 CHAPTER 2. THE SAMPLE SELECTION improved the calibrations. WISE photometry was conducted using profile fitting of the point spread function of the instrument instead of aperture photometry, where the photon integration was done inside a region of appropriate size. However, it is known that the All-Sky data release had several limitations, which were:
Possible differences in the measured positions of the objects between the catalog • and the atlas.
The profile fitting in the photometry can systematically underestimate the fluxes • for the faintest sources, with W 1 > 14.0 mag and W 2 > 13.5 mag.
The catalog has unreliable entries. •
Figure 2.1: Sketch of WISE satellite in its mapping configuration (Wright et al., 2010).
The second data release, named AllWISE (Cutri, 2013), was delivered in November 2013 and included combined data of previous epochs of WISE, such as NEOWISE, which provided photometry measurements of asteroids and comets, and Cryogenic WISE, which obtained data before their cooling systems ended operations. Taking into account these combinations, the sensitivity and the photometric precision was improved as compared to the previous All-Sky data release. Photometry comparisons between the two data releases were done in the entire sky and Figure 2.2 shows pho- tometry profile differences between AllWISE and WISE All-Sky surveys in W4 band at a declination of +120 and right ascension of 127.50 as an example. Black dots show the relative differences in the W4 mag for sources present in the AllWISE and All-Sky surveys. In the figure, we can see that the photometry of both data releases are in agreement for sources with W4 magnitudes from 2 to 6. For magnitudes W4 6, All-Sky photometry delivered fainter fluxes than AllWISE. The situation is reversed≥ for magnitudes 8. Therefore, non negligible differences (as large as 0.1 mag) are present. ≥
The improvements in AllWISE catalogue with respect to All-Sky catalogue are sum- 2.1. IR SURVEYS 17 marized in the following points:
AllWISE has more sensitivity in W1 and W2 due to the inclusion of the preview • observational epochs, such as NEOWISE and Cryogenic WISE in the mission mapping.
AllWISE photometry is more reliable in the four bands than the previous release • because of a better estimation of the background in single exposures.
The astrometry has improved because the proper motion of the stars has been • corrected using 2MASS catalogue as reference.
Figure 2.2: Photometric differences between AllWISE and WISE All-Sky as function of AllWISE magnitude in the ecliptic plane. Black dots are individual sources. Green dots and error bars are the average fitting and the photometry residuals in bins of 0.5 mag width in W4 in a region of the sky of +120 in declination and right ascension of 1270∗
Some scientific goals
WISE achieved sensitivities of 5σ in point sources better than 0.08, 0.11, 1 and 6 mJy (16.5, 15.5, 11.2 and 7.9 Vega magnitudes respectively) in the four bands, respectively. This allowed to reach deeper magnitudes than 2MASS Ks data in W1 for sources with a spectrum similar to a A0 star. Furthermore, it was able to go even deeper for K
∗from wise2.ipac.caltech.edu 18 CHAPTER 2. THE SAMPLE SELECTION type stars and galaxies with old stellar populations. In comparison, IRAS survey had sensitivities at 12 µm, 25 µm and 60 µm of 0.5 Jy for the three bands (Neudebauer et al., 1984), implying that for 12 µm and 25 µm, WISE is 100 times more sensitive than IRAS. ∼
Data from the WISE survey have been used in scientific cases involving many astro- physical scenarios. For the purposes of this work, we only mention some of them that are of our interest and can be summarized as follows: WISE studied the Solar System’s zodiacal cloud and the asteroid system, with a better angular resolution than IRAS, which had 0.5 arcmin at 12 µm and 2 arcmin at 100 µm, in order to observe dust bands and comet trails. Also, the mission provided a robust statistical database for study- ing star formation and the evolution of circumstellar disks around thousands of stars in the solar neighborhood. These observations helped to understand the dynamics of the system and refined the timescales for disk clearing in early evolutionary stages of stars. Using WISE longer wavelengths, excess at 22 µm are easily detectable. For instance, the simultaneous four color photometry detect optically thick disk emission for solar-like stars in the Taurus and Ophiucus star-forming regions (Wright et al., 2010).
2.1.2 Two Micron All Sky Survey (2MASS)
The 2MASS project was designed for surveying sky in the near infrared. It used two telescopes of 1.3 m of diameter, one located at Mt. Hopkins, Arizona, and the other at Cerro Tololo Interamerican Observatory (CTIO), Chile. Each telescope was equipped with a three channel camera that observed simultaneously in the J (1.25 µm), H (1.65 µm) y Ks (2.17 µm) bands. The point sources brighter than 1 mJy were detected and characterized in each band, with a signal-to-noise ratio greater than 10. Furthermore, the spatial resolution of this instrument was 2.0 arcesc. The scanning of the northern sky begun on June 1997 and finished on December 2000. In the South observatory the scanning started on March 1998 and ended on February 2001 (Skrutskie et al., 2006).
The main science goals were:
A look to the Milky Way almost free of the darkening effect caused by interstellar • dust revealed the structures of luminous mass in the Galaxy.
The first photometric census of all sky from the galaxy, with magnitude greater • than Ks = 13.5 mag, including galaxies in the dusty zones where it was impossible to complete the optical census. 2.2. THE SAMPLE 19
A statistical base to look for rare but important astronomical objects, as cold • or extremely red (e.g. low luminosity stars or brown dwarfs), as well as objects highly darkened in optical wavelengths (e.g. globular clusters in the galactic plane).
The data were released on March 2003 (Cutri et al., 2003) and 99.998% of the sky was mapped, with almost 300 million stars and over 1 million galaxies and many other objects of unknown nature.
2.2 The sample
In order to achieve the objectives of this work, we need a properly selected sample of stars. One set corresponds to an updated collection of stars for which planetary companion have been found. The other, also arising from exoplanetary surveys, is composed of stars with not yet detected planets. In the following, we will describe the selection criteria of the working dataset.
2.2.1 Stars with planets
The sample of stars with planets was constructed based upon “The Extrasolar Planet Encyclopedia” web page∗. The team responsible of this database have gathered data from February 1995 up to date. On July 2015, the database consists of 1932 discovered exoplanets in 1222 stellar systems. The reported planetary systems have been detected by different methods, including radial velocity, transits, micro-lensing, direct imaging and astrometry. The database also offers planetary parameters like planet mass, radius, orbital period, distance to the parent star, ellipticity, etc. Additionally, the catalogue includes stellar parameters of the host stars like metallicity, spectral type, temperature, distance from the Sun, etc. However, the sample of stars with planets taken into account for this work was obtained in April 2015, as the last update. Thus, we begin with a sample of 1207 stars with planets.
Up to 20% of the current confirmed extrasolar planets have been discovered by the very successful Kepler Mission (Batalha, 2014). The WISE Mid-IR excesses associated to these targets were studied in detail by Kennedy & Wyatt(2012). In their work, they concluded that all but one excess at 22 µm are caused by background extragalactic sources and not produced by debris disks around the stellar systems. Considering Kennedy & Wyatt(2012) conclusion about the IR excesses in the Kepler field, 444
∗http://exoplanet.eu 20 CHAPTER 2. THE SAMPLE SELECTION stars with planets catalogued as Kepler Object of Interest (KOI) and Kepler Input Catalogue (KIC) are not considered in the sample selection. Thus, eliminating the 444 stars from the initial number of stars with planets, we remained with 763 stars with planets at the beginning of the sample selection.
2.2.2 Stars without planets
There have been many surveys with the goal of finding exoplanets in the last 10 years. For the purposes of the present work we based our sample of stars without plan- ets on the results of the Searching Program Guaranteed Time Observations (GTO) High Accuracy Radial velocity Planet Searcher (HARPS). GTO HARPS is a project designed to look for planets by measuring the radial velocity of stars. The Echelle spectrograph HARPS offers a radial velocity precision of about 1 m/s (Sousa et al., 2008, 2011). From this GTO HARPS program, 1033 stars were initially selected (April 2015). These stars are considered as low rotators, not evolved and with low chromo- spheric activity, effect that may jeopardize precise radial velocity measurements. Since this studies were carried out several years ago, there was the chance that some stars previously catalogued as not having planets might have a confirmed planet nowadays, thus, we compared both samples of stars with and without planets and found that 145 stars from this GTO program were later on confirmed as exoplanetary hosts. This reduced our sample to 888 stars.
Other stars without planets used in this work were taken from Valenti & Fischer (2005) work. They spectroscopically analyze a sample of stars observed with the High- Resolution Echelle Spectrograph (HIRES) at the 10 m telescope Keck, with University College London Echelle Spectrometer (UCLES) at the 4 m Anglo-Australian telescope located at Siding Spring Observatory, and with the Hamilton Echelle Spectrograph at Lick Observatory. These stars were initially selected having low chromospheric activity and not being binaries.
Comparing the stars between Sousa et al.(2008, 2011) and Valenti & Fischer(2005) catalogues, we found 148 stars in common. Furthermore, 146 Valenti & Fischer(2005) stars are now confirmed as planet hosts and were not included in Sousa et al.(2008, 2011) sample. Thus, the final sample of stars taken from Valenti & Fischer(2005) work includes 746 stars without planets. Finally, adding the stars without planets from Valenti & Fischer(2005) and Sousa et al.(2008, 2011), we ended up with a total number of 1634 stars without planets to analyze. 2.3. OPTICAL AND INFRARED PHOTOMETRY 21 2.3 Optical and Infrared photometry
We collected mid-infrared photometry from AllWISE catalogue with the following constraints:
The signal-to-noise ratio S/N 5 in W4 photometry. • ≥ W1, W2, W3 and W4 photometry must include uncertainties (some sources • brighter than 0 magnitude in any WISE band do not have uncertainties).
The selected sources must be free from any artifact or contamination. These • artifacts can include diffraction spikes caused by nearby bright sources, halos of dispersed light or optical ghosts due to a brighter source in the vicinity.
The pixel saturation in W3 and W4 must be zero. • By applying the previous criteria, the two samples of stars reduced to 1215 stars without planets and 309 stars with planets.
The J, H, and KS photometry is collected from the All-Sky catalogue of 2MASS. The restrictions applied on this catalogue are as follows:
J, H and KS photometry must be accompanied by the corresponding uncertain- • ties.
The quality flag of the photometry must be A or B, with a S/N 10 and S/N 7, • respectively, in the catalogue. Data with lower quality flags C,≥ D, E, F and≥ X are discarded.
Taking into account these restrictions, the number of stars in both samples is reduced again, leaving the samples with 1121 stars without planets and 271 stars with planets. Stars like Eridani, Fomalhaut and β Pic do not fulfill the 2MASS restrictions, thus, these well known stars were not considered in our sample.
We subsequently used the Astronomical Database SIMBAD to obtain the B and V photometry and to select MS and subgiants stars and excluded objects of luminosity classes III, II and I, as well as pre-main sequence objects (T-Tauri, Ae/Be Herbig) and stars in binary or multiple systems. This reduced our sample of stars with planets to 232 stars and the sample of stars without planets to 964.
Finally, since the WISE catalog is known to include spurious detections (e.g., Cruz- Saenz de Miera et al. 2014), we therefore proceeded to carefully inspect each image 22 CHAPTER 2. THE SAMPLE SELECTION
Figure 2.3: Spurious WISE image in W4 band of HD 192020 (up). Reliable image in W4 of HD 3277 (down). and excluded false detections in W4. This effect is consequence of the profile fitting used to obtain the photometry, since the fit on the noise level may raise the flux level artificially. Some examples of true and false detections can be seen on Figure 2.3.
After considering all the previous steps, the final samples consist in 910 stars without planets and 202 stars with planets.
2.3.1 Comparison of both samples
After selecting the samples of stars with and without planets, we needed to ensure that the results obtained in this work were not biased due to discrepancies in both samples. Thus, it was necessary to see if both samples were compatible with each other. For this, we plotted the spectral type, distance, V magnitude and metallicity distribution histograms of both samples and applied a two-sample Kolmogorov Smirnov (KS) test considering the null hypothesis that both independent samples are taken from the same continuous distribution. In brief, the KS test consists in comparing the maximum distance between the cumulative distributions of the two samples with a critical value, that depends on the sample sizes.
Figure 2.4 shows the histograms of the spectral type distributions of both stellar sam- ples. From this plot we can see that the spectral types for the stars with planets range from B6 to K7, with a peak in K0, followed in number by G0 and then G5. On the other hand, the stars without planets spectral types range from F2 to K8, with G5-type stars being the most numerous, followed by G0 and F8. 2.3. OPTICAL AND INFRARED PHOTOMETRY 23
Spectral Type of stars 140 with planets without planets 120
100
80
Number 60
40
20
0 B6 B7 B8 B9 A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 G0 G1 G2 G3 G4 G5 G6 G7 G8 G9 K0 K1 K2 K3 K4 K5 K6 K7 K8 K9 Spectral Type
Figure 2.4: Spectral type distributions of stars with and without planets.
To carry out the KS test, we first computed the maximum distance D between the two samples formed by n1 and n2 entries. Then, we compared it with the critical value D , which depends on the chosen significance value α and can be calculated with the c p equation Dc = c(α) (n1 + n2)/n1n2, where c(α) = 1.63 for a confidence level α= 99% (Massey, 1952). If D > Dc, the null hypothesis is rejected.
The statistic KS value computed in the spectral type distributions of stars with and without planets is D= 0.064, The critical KS value for the chosen significance level is Dc=0.126. In this case D < Dc, thus, the null hypothesis is not rejected and we conclude that the samples of stars with and without planets are coming from the same parent distribution with a confidence level of 99%. This result indicates that both samples are compatible and all the stars homogeneously sample the spectral types.
For the distance from the Sun distribution histograms shown in Figure 2.5, the KS statistic value calculated is D=0.276. Since D > Dc in this case, the null hypothesis is rejected and we conclude that the distance distributions are not coming from the same parent distribution with a confidence level of 99%; in other words, they are independent. This outcome is referring that the stars without planets were chosen from the solar neighborhood, while some stars with planets are located further and are not selected in the solar vicinity. 24 CHAPTER 2. THE SAMPLE SELECTION
Distance of stars 180 with planets 160 without planets
140
120
100
80 Number
60
40
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0 100 101 102 103 log(distance) (pc)
Figure 2.5: Distance distributions of stars with and without planets.
For the case of the V magnitude distribution histograms shown in Figure 2.6, the KS value obtained is D=0.109. In this case, D < Dc and the null hypothesis is accepted, we concluded that both samples are coming from the same parent population in a confidence level of 99%. This implies that both samples are compatible between them. We can prove this result visually since the V magnitude ranges from 6 to 10 in both histograms and most of the stars in the sample of stars with planets are peaking at 8 mag bin while in case of stars without planets are peaking at 7 mag bin.
V magnitude of stars 100 with planets without planets
80
60 Number 40
20
0 5 6 7 8 9 10 11 V magnitude (mag)
Figure 2.6: V magnitude distributions of stars with and without planets. 2.3. OPTICAL AND INFRARED PHOTOMETRY 25
For metallicity distribution histograms shown in Figure 2.7, the KS value calculated was D=0.295 Then, we also conclude that both samples are independent each other and do not come from the same parent distribution of metallicities with a confidence level of 99% as D > Dc. An average metallicity of [Fe/H]=-0.6 is calculated in the sample of stars without planets. This result is in agreement with other works (e.g. Casagrande et al. 2011; Haywood 2001), where they report metallicities in the solar neighborhood of [Fe/H]=-0.06 and [Fe/H]=-0.7 respectively. On the other hand, the sample of stars with planets shows an average [Fe/H]=0.07. this result is due to the fact that Fischer & Valenti(2005) found that there is a positive correlation between giant planets and metallicity. Thus, knowing that 60% of stars in our sample have planets with masses 1 MJ (Jupiter mass), we expected to find the sample of stars with planets more metallic≥ than the stars without planets.
Metallicity of stars 180 with planets 160 without planets
140
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80 Number
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0 2.0 1.5 1.0 0.5 0.0 0.5 1.0 Metallicity log(Fe/H)
Figure 2.7: Metallicity distributions of stars with and without planets.
For the study presented in this work, we have selected 202 stars with planets and 910 stars without planets. The statistical analysis indicates that these samples are statisti- cally similar in their spectral type and V magnitude distributions. This result indicates that the samples are not biased in these parameters. However, we found that the sam- ple with planets is biased to higher metallicities than the other sample. In the following chapter we describe the analysis of the WISE data, and show the method applied to correct the observed fluxes for interstellar extinction, the prescription to identify IR excess, as well as a comparison with other IR excess identification criteria. 26 CHAPTER 2. THE SAMPLE SELECTION Chapter 3
Methodology
3.1 Correction for extinction and magnitude to flux conversion
Correction by interstellar extinction is important because we need to remove the effects of obscuration by interstellar dust in the observed SED of the stars in our samples. On one side, 17% and 13% of stars with and without planets, respectively, are located close to the galactic plane ( b 10 degrees). On the other side, some stars are at distances in excess of 100 pc whose| |≤ light might be affected by absorption of interstellar material. Additionally, the set of theoretical SEDs used to predict the stellar contribution in the search for IR excesses are calculated as flux vs. wavelength, thus we require to transform WISE magnitudes and other ancillary data of our targets to compatible flux units.
First of all, to achieve the correction by extinction process, the color excess E(B V ) = − (B V ) (B V )0 is calculated for each star, where (B V )0 is the intrinsic color, which− depends− − of the spectral type of the star, taken from− the spectral type-intrinsic color calibration proposed by Pecaut et al.(2012) for MS stars. In Figure 3.1 we show the distribution of B V colors with respect to the spectral type in both samples. In red dots the B V color− is plotted for the stars in the samples while the solid line represents the Pecaut− et al.(2012) calibration. As we can see, there are some objects that are bluer (B V below the solid black line) than expected. The bluest object is found in the sample− of stars without planets and the reddest object is found in the other sample.
27 28 CHAPTER 3. METHODOLOGY
Stars without planets 1.4 Intrinsic B-V (Pecaut et al. 2012) Sample's B-V 1.2
1.0
0.8
B-V (mag) 0.6
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0.0 F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 G0 G1 G2 G3 G4 G5 G6 G7 G8 G9 K0 K1 K2 K3 K4 K5 K6 K7 K8 K9 M0 Spectral type
Stars with planets 1.5 Intrinsic B-V (Pecaut et al. 2012) Sample's B-V
1.0
B-V (mag) 0.5
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B5 B6 B7 B8 B9B9.5A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 G0 G1 G2 G3 G4 G5 G6 G7 G8 G9 K0 K1 K2 K3 K4 K5 K6 K7 K8 K9 Spectral type
Figure 3.1: Color vs spectral type of stars without planets (upper panel) and with planets (lower panel). In red points the B V color for each star. The black continuous line represent the spectral type-intrinsic color calibration− of Pecaut et al.(2012).
After the calculation of the color excess E(B V ) and plotting the distributions of the color excesses shown in Figure 3.2, we proceeded− to make a Gaussian fitting to each distribution in order to get the mean µ and the standard deviation σ of both sample histograms. We decided to correct those stars with E(B V ) µ + σ. To eliminate the outliers in the color excess distributions, we carried out− an iterative≥ sigma clipping process with a threshold of 3σ. Thus, the Gaussian fitting applied to the distributions of color excess shows that the stars without planets with E(B V ) > 0.055 mag are to be corrected by stellar extinction. For stars with planets the− correction is applied for the stars with E(B V ) > 0.078 mag. − 3.1. CORRECTION FOR EXTINCTION AND MAGNITUDE TO FLUX CONVERSION29
Color excess distribution of stars without planets 160 µ +σ 140 µ σ − Gaussian Fit 120
100
80 Number
60
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0 1.0 0.8 0.6 0.4 0.2 0.0 0.2 0.4 (B V) (B V) − − − 0
Color excess distribution of stars with planets 30 µ +σ µ σ − 25 Gaussian Fit
20
15 Number
10
5
0 0.2 0.0 0.2 0.4 0.6 (B V) (B V) − − − 0
Figure 3.2: Color excess distribution of stars with (lower panel) and without (upper panel) planets. The blue line shows the best gaussian fits applied to the distributions. The red and black vertical lines indicate the 1σ symmetrical threshold.
To correct for interstellar extinction and to convert magnitude to flux, the following equation must be applied.
−mλ+Aλ Fc = F010 2.5 (3.1)
where F0 is the zero magnitude flux density in the Vega scale (all zero points are reported in Table 3.1), mλ is the apparent magnitude in the λ band and Aλ is the extinction coefficient derived form the coefficient ratio Aλ/AV shown in Table 3.2 taken 30 CHAPTER 3. METHODOLOGY
from the interstellar extinction curve of Rieke & Lebofsky(1985). AV is calculated by taking into account the total selective extinction ratio RV = AV /EE(B V ), assuming − the canonical value RV =3.1.
Table 3.1: Zero magnitude flux density for B, V (Bessell, 1979), J, H, KS (ipac.caltech.edu/2mass), W1, W2, W3, W4 (wise2.ipac.caltech.edu) bands.
Band F0 (Jy) B (Johnson) 4266.7 V (Johnson) 3836.3 J (2MASS) 1594.0 H (2MASS) 1024.0 KS (2MASS) 666.7 W1 (WISE) 306.682 W2 (WISE) 170.663 W3 (WISE) 29.045 W4 (WISE) 8.284
Table 3.2: Extinction law coefficients as a function of wavelength (Rieke & Lebofsky, 1985).
λ E(λ-V)/E(B-V) Aλ/Av
(1) (2) (3) U 1.64 1.531 B 1.00 1.324 V 0.0 1.00 R -0.78 0.748 I -1.60 0.482 J -2.22 0.02 0.282 H -2.55 ± 0.03 0.175 K -2.744 ± 0.024 0.112 L -2.92 ± 0.03 0.058 M 3.02 ± 0.03 0.023 N 2.93± 0.052 8.0µ -3.03 0.020 0.003 8.5µ -2,96 0.043± .006 9.0µ -2.87 0.074 ±0.011 9.5µ -2.83 0.087 ± 0.013 10.0µ -2.86 0.083±0.012 10.5µ -2.87 0.074±0.011 11.0µ -2.91 0.060 ±0.0009 11.5µ -2.95 0.047± 0.007 12.0µ -2.98 0.037±0.006 12.5µ -3.00 0.030±0.005 13.0µ -3.01 0.027 ± 0.004 ± 3.1. CORRECTION FOR EXTINCTION AND MAGNITUDE TO FLUX CONVERSION31
By applying the general formula of error propagation, we acquire the following equa- tion:
F0 (A m)/2.5 dF = 10 j − ln(10)dm (3.2) 2.5
In the case of W3 (12 µm), Table 3.2 shows A /A = 0.037 0.006. In other words, 12µm V ± dAj = AV dc, where dc is the uncertainty of the constant in the ratio A12µm/AV . Thus we also applied for this particular case,
s 2 2 F0 F0 dF = 10(Aj m)/2.5ln(10)dm + 10(Aj m)/2.5ln(10)A dc (3.3) −2.5 − 2.5 − v
For the rest of the stars, which do not need to be corrected by extinction, we used the classical magnitude to flux conversion formula:
m Fν = Fν010− 2.5 (3.4)
Furthermore, Wright et al.(2010) mention that WISE calibration fluxes are flux den- α sities for astronomical sources with power-law spectra Fν α ν− in general. The index α ranges from -3, -2, -1, 0, 1, 2, 3 and 4 and is used for color corrections such that Fν0 = F0/fc, where fc is the flux correction. In the case of WISE photometry 2 used in this work, Fν α ν− for the Rayleigh-Jeans regime (Mid-IR) of stellar SED, thus, Fc = 1 according to Table 3.3.
Finally, we used the general formula for error propagation in order to derive the un- certainty on the flux, assuming Gaussian-distribution error:
s 2 ∂f F0 −m df = dm = ln(10)10 2.5 dm (3.5) ∂m 2.5 32 CHAPTER 3. METHODOLOGY
Table 3.3: Color corrections from Wright et al.(2010).
3.2 Photosphere fitting and synthetic photometry
A detection of a debris disk happens when the observed infrared flux is larger than the expected flux of the star alone. For this, a synthetic spectrum is used to predict the stellar contribution in the IR interval. In this work we used ATLAS9 spectra (Castelli & Kurucz, 2003) for the calculation of synthetic photometry. Previous studies in the searching of infrared excesses, (e.g. Kennedy & Wyatt(2012), Morales et al. (2012)), have also used ATLAS9 synthetic spectral energy distributions (sSED). The in properties are as follows.
There are 476 synthetic model spectra with several combinations of effective • temperature (Teff ), metallicity ([M/H]) and surface gravity (log g).
All the models have the same number of 72 plain-parallel layers from log τRoss = • 6.875 to log τ = +2.00, with steps of ∆τ = 0.125 − Ross Ross All models and theoretical fluxes are computed with abundances scaled to the • solar composition.
In all model spectra, a micro turbulence of 2.0 km/s is assumed. • The ATLAS9 model spectra are available for different effective temperature, from 3500 K to 13000 K in steps of 250 K, and, from 13000 K to 50000 K in 1000 K steps. For surface gravity, the spectra are available in the range of 0.0 log(g) 5.0 with 0.5 dex steps. For metallicity, the interval is 2.5 [M/H] 0.5,≤ with steps≤ of 0.5 dex. − ≤ ≤ 3.2. PHOTOSPHERE FITTING AND SYNTHETIC PHOTOMETRY 33
The whole wavelength coverage of the synthetic SEDs ranges from 9.09 nm to 160 µm with variable spacing. In the IR, ∆λ is 0.005 µm for 0.999 µm λ 1.5975 µm; 0.01 µm for 1.605 µm λ 3.195 µm; 0.02 µm for 3.21 µm λ ≤6.39≤µm; 0.04 µm for 6.42 µm λ 9.98≤µm;≤ 10 µm for 10.2 µm λ 20 µm and≤ 20≤µm for 20 µm λ 160 µm. ≤ ≤ ≤ ≤ ≤ ≤
The analysis of the differences among different model atmospheres at IR regimes has been carried out by other authors. For example, Sinclair et al.(2010) found that ATLAS9 and MARCS present discrepancies no larger than 2% at 24 µm for stellar parameters compatible with F, G and K spectral types. ATLAS9 and NEXTGEN agree even better. Cruz-Saenz de Miera et al.(2012) found a merely 0.62% differences at 5000 K, 0.97% at 6000 K and 2.05% at 7000 K between the fluxes at 24 µm (see Figure ≈3.3). Therefore, we concluded≈ that the proposed analysis of WISE fluxes does not depend on the theoretical data.
Figure 3.3: Comparison between ATLAS9 and NEXTGEN synthetic spectral energy distribution covering all the wavelengths available at ATLAS9 (1-160 µm, the pink vertical dashed line marks a limit of 20 µm. Figure taken from Cruz-Saenz de Miera et al.(2012).
The SED morphology depends essentially on the stellar parameters (Teff , [M/H] and log g). Although we do not expect important differences in the Rayleigh-Jeans (R-J) tail (λ > λmax, where λmax is the peak wavelength of Wien’s law) for the metallicity and surface gravity, we considered convenient to explore if there are significant differences while varying these parameters for a fixed Teff . For each test, we decided to use 34 CHAPTER 3. METHODOLOGY
synthetic spectra of ATLAS9 models with Teff =5000 K, 6000 K and 7000 K and modifying the other two stellar parameters. When metallicity varies from -2.5 to +0.5, we selected log g=4.5 for the three temperatures; for variations in log g from 0.5 to 5.0, we used [M/H]=0.0 for the same three temperatures. Then, we calculated flux ratios between the spectra with the largest flux difference in each WISE band. The results are in Table 3.4 where we show that for different temperatures, the flux do not significantly change. We noted that the largest discrepancies are found in the W2 band for a temperature of 5000 K, while the most significant agreement is found in the W4 band at Teff =7000 K. We decided to make this test using this three temperatures and the specified log g and [M/H] since most of the stars in our samples ranges among these parameters. The effects of stellar parameters is shown in Figure 3.4 in which the WISE bands appear as solid vertical lines in black for W1, green for W2, blue for W3 and red for W4.
Table 3.4: Flux ratio comparison among the WISE bands in ATLAS9 synthetic spectra. This ratio is calculated between the spectra with the largest flux difference in each WISE band. The first column shows the parameters that remained constant along the test.
Constant parameters W1 flux ratio W2 flux ratio W3 flux ratio W4 flux ratio
Teff = 5000 K, log(g)=4.5 0.978 0.886 0.984 0.961 Teff = 5000 K, [M/H]=0.0 0.987 0.944 0.979 0.986 Teff = 6000 K, log(g)=4.5 0.987 0.969 0.979 0.992 Teff = 6000 K, [M/H]=0.0 0.984 0.978 0.987 0.988 Teff = 7000 K, log(g)=4.5 0.954 0.958 0.976 0.995 Teff = 7000 K, [M/H]=0.0 0.941 0.968 0.988 0.992
It was necessary to find the synthetic spectrum that best fitted the observed photo- metry of each star in order to obtain a better estimation of the expected stellar flux. To achieve this, the best fit model is found using χ2 minimization algorithm called MPFIT (Markwardt, 2009). In this algorithm, χ2 is calculated in several iterations and the program gives as a result, the parameters that gives de minimum χ2. The free parameters to be fitted were Teff and a scalar value that was needed to normalize the flux in Jy units of the synthetic spectrum to the observed photometry. The bands considered in the fit were B, V, J, H, and Ks. Their uncertainties were taken from the SIMBAD data base, for B, V, and from the 2MASS All-Sky catalogue for J, H, KS. Metallicity and surface gravity were taken as fixed parameters in the searching of the best fit because, as we demonstrated, changes due to variations in [M/H] and log g in the synthetic flux are negligible for the purposes of these study in the R-J regime. Thus, we acquired the metallicity and surface gravity for each star in the samples from the PASTEL Catalogue (Soubiran et al., 2010) and Extrasolar Planets Encyclopedia web page∗.
∗http://exoplanet.eu 3.2. PHOTOSPHERE FITTING AND SYNTHETIC PHOTOMETRY 35
SED, T=7000K, log(g)=4.5 SED, T=7000K, [M/H]=0.0
8 10 108
7 10 7 10
) 106 ) 1 1 6
− − 10 105 1 1 5 − − 10 s 4 s
2 10 2
m m 4
c 3 c 10 / 10 [M/H]=-2.5 / log(g)=0.5 g g
r [M/H]=-2.0 r 3 log(g)=1.0
e 2 e 10 ( 10 [M/H]=-1.5 ( log(g)=1.5
x x 1 [M/H]=-1.0 2 log(g)=2.0 u 10 u l l 10
F [M/H]=-0.5 F log(g)=2.5 0 10 1 [M/H]=0.0 10 log(g)=3.5 [M/H]=+0.2 log(g)=4.5 10-1 [M/H]=+0.5 100 log(g)=5.0
10-1 100 101 10-1 100 101 Wavelength (µm) Wavelength (µm)
SED, T=5000K, log(g)=4.5 SED, T=5000K, [M/H]=0.0 107 107
6 10 6 10 ) ) 1 1
− − 5 105 10 1 1 − − s s 104 2 104 2 m m c c
/ [M/H]=-2.5 / log(g)=0.5 103 g g
r [M/H]=-2.0 r log(g)=1.0 103 e e
( [M/H]=-1.5 ( log(g)=1.5 102 x [M/H]=-1.0 x log(g)=2.0 u u l 102 l F [M/H]=-0.5 F log(g)=2.5 101 [M/H]=0.0 log(g)=3.5 1 [M/H]=+0.2 log(g)=4.5 10 100 [M/H]=+0.5 log(g)=5.0
10-1 100 101 10-1 100 101 Wavelength (µm) Wavelength (µm)
Figure 3.4: Comparison of ATLAS9 model spectra with same Teff =7000 K (upper panels) and Teff =5000 K (lower panels). Vertical lines show the position of WISE band wavelengths W1 (black); W2 (green), W3 (blue) and W4 (red). When log g=4.5 and metallicty varies (left panels), [M/H]=0.0 and log g varies (right panels).
Aimed at finding the best fit spectra and identifying IR excesses, we require the set of synthetic photometric fluxes at the relevant wavelength bands. For this, we used the response curves of the Johnson† and 2MASS‡ filter bands (see Figure 3.5). These response curves are convolved to the synthetic spectrum and then we applied equation (3.6) for getting the synthetic photometry.
R F (ν)R(ν)dν P = (3.6) ν R R(ν)dν with F (ν) the model spectra and R(ν) the filter response curve. The values of the fitted parameters are reported in Appendix C. After finding the best fit of the photosphere for each star in the sample, the next step was to calculate the synthetic photometry for the WISE passbands. The WISE filters response curves are also shown in Figure 3.5§. †http://voservices.net/filter/ ‡http://www.ipac.caltech.edu/2mass §http://wise2.ipac.caltech.edu 36 CHAPTER 3. METHODOLOGY
Johnson filter response curves 1.0 U B V 0.8 R I
0.6
0.4 Transmission
0.2
0.0 3000 4000 5000 6000 7000 8000 9000 10000 Wavelength ( )
2MASS filter response curves 1.0
0.8
0.6
0.4 Transmission
0.2 J H
KS 0.0 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Wavelength (µm)
WISE filter response curves 1.0 W1 W2 W3 0.8 W4
0.6
0.4 Transmission
0.2
0.0 0 5 10 15 20 25 30 Wavelength (µm)
Figure 3.5: Response curves for five Johnson filters (upper panel). Solid lines depict the curves of B and V. In the middle and lower panels we show, respectively, the curves for 2MASS and WISE filters.
Figure 3.6 shows, as an example, the fit of the star HD108874, with a Teff =5563 K, 2 log g=4.44 and [Fe/H]=0.26. In Figure 3.7, we show the histograms of the reduced χν of the fits for all stars. The histograms of stars with and without planets peak at χ2 1.4 ν ∼ 3.2. PHOTOSPHERE FITTING AND SYNTHETIC PHOTOMETRY 37
2 and 70% of the stars of the samples have χν 3.0. We can conclude, therefore, that the bulk∼ of the photospheric emission is well reproduced≤ by our fits.
HD108874 Synthetic photometry Best fit 100 BVJHK photometry WISE photometry
10-1 Flux (Jy)
10-2
100 101 Wavelength (µm)
Figure 3.6: Best fit of the Synthetic Spectral Energy Distribution for the star HD108874 found with MPFIT algorithm. In blue solid line we show the best fit synthetic spectrum, in green dots the synthetic photometry for B, V, J, H, KS, W1, W2, W3, W4 bands, in black stars the observed BVJHK and in red stars the WISE photometry.
160 stars without planets 140 stars with planets
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80 Number 60
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20
0 0 2 4 6 8 10 12 14 16 Reduced χ2
2 Figure 3.7: χν distributions for the stars with and without planets (orange and blue respectively) studied in this work, obtained by MPFIT algorithm. 38 CHAPTER 3. METHODOLOGY 3.3 Searching for Infrared Excesses.
In the present work, the search for IR excesses is conducted through a comparison of the reddest WISE bands with the fluxes expected from the stellar photosphere, as described in the previous chapter. Since, to date, there are a number of investigations using WISE data, we considered convenient to also incorporate a description of the most relevant methods and compare our results with those of other authors. This comparison will serve to find potential discrepancies and to discuss the validity of the different procedures.
3.3.1 Method 1 (This work)
In this work, we compared W4/W3 observed flux ratio and the expected ratio of the stellar contribution, taken into account the associated flux uncertainties. This can be done applying the following equations: