Mid-infrared circumstellar emission of the long-period ...

Astronomy amp Astrophysics manuscript no draft_vh_paperI copyESO 2021August 20 2021

Mid-infrared circumstellar emission of the long-period Cepheid` Carinae resolved with VLTIMATISSE

V Hocdeacute1 N Nardetto1 A Matter1 E Lagadec1 A Meacuterand2 P Cruzalegravebes1 A Meilland1 F Millour1 B Lopez1P Berio1 G Weigelt3 R Petrov1 J W Isbell19 W Jaffe4 P Kervella5 A Glindemann2 M Schoumlller2 F Allouche1A Gallenne1 6 7 8 A Domiciano de Souza1 G Niccolini1 E Kokoulina1 J Varga4 17 S Lagarde1 J-C Augereau9R van Boekel4 P Bristow2 Th Henning19 K-H Hofmann3 G Zins2 W-C Danchi1 10 M Delbo1 C Dominik11

V Gaacutemez Rosas4 L Klarmann19 J Hron12 MR Hogerheijde4 11 K Meisenheimer19 E Pantin13 C Paladini2SRobbe-Dubois1 D Schertl3 P Stee1 R Waters14 15 M Lehmitz19 F Bettonvil4 M Heininger3 P Bristow2

J Woillez2 S Wolf16 G Yoffe4 L Szabados17 18 A Chiavassa1 S Borgniet5 L Breuval5 B Javanmardi5P Aacutebrahaacutem17 S Abadie2 R Abuter2 M Accardo2 T Adler19 T Agoacutecs21 J Alonso2 P Antonelli1 A Boumlhm19C Bailet1 G Bazin2 U Beckmann3 J Beltran2 W Boland5 P Bourget2 R Brast2 Y Bresson1 L Burtscher4

R Buter2 R Castillo2 A Chelli1 C Cid2 J-M Clausse1 C Connot3 RD Conzelmann2 M De Haan24 M Ebert19E Elswijk24 Y Fantei1 R Frahm2 V Gaacutemez Rosas5 A Gabasch2 E Garces2 P Girard1 A Glazenborg25FYJ Gonteacute2 JC Gonzaacutelez Herrera2 U Graser19 P Guajardo2 F Guitton1 H Hanenburg24 X Haubois2

N Hubin2 R Huerta2 J Idserda25 D Ives2 G Jakob2 A Jaskoacute16 L Jochum2 R Klein19 J Kragt21 G Kroes14 20S Kuindersma25 L Labadie17 W Laun19 R Le Poole5 C Leinert19 J-L Lizon2 M Lopez2 A Marcotto1

N Mauclert1 T Maurer19 LH Mehrgan2 J Meisner5 K Meixner19 M Mellein19 L Mohr19 S Morel1L Mosoni22 R Navarro24 U Neumann19 E Nuszligbaum3 L Pallanca2 L Pasquini2 I Percheron2 T Phan Duc2J-U Pott19 E Pozna2 A Ridinger19 F Rigal24 M Riquelme2 Th Rivinius2 R Roelfsema24 R-R Rohloff19

S Rousseau1 N Schuhler2 M Schuil24 K Shabun2 A Soulain19 C Stephan2 R ter Horst24 N Tromp24 F Vakili1A van Duin25 L B Venema25 J Vinther2 M Wittkowski2 and F Wrhel19

(Affiliations can be found after the references)

Received accepted

ABSTRACT

Context The nature of circumstellar envelopes (CSE) around Cepheids is still a matter of debate The physical origin of their infrared (IR) excesscould be either a shell of ionized gas or a dust envelope or bothAims This study aims at constraining the geometry and the IR excess of the environment of the bright long-period Cepheid ` Car (P=355 days)at mid-IR wavelengths to understand its physical natureMethods We first use photometric observations in various bands (from the visible domain to the infrared) and Spitzer Space Telescope spec-troscopy to constrain the IR excess of ` Car Then we analyze the VLTIMATISSE measurements at a specific phase of observation in order todetermine the flux contribution the size and shape of the environment of the star in the L band We finally test the hypothesis of a shell of ionizedgas in order to model the IR excessResults We report the first detection in the L band of a centro-symmetric extended emission around ` Car of about 17 R in full width athalf maximum producing an excess of about 70 in this band This latter value is used to calibrate the IR excess found when comparing thephotometric observations in various bands and quasi-static atmosphere models In the N band there is no clear evidence for dust emission fromVLTIMATISSE correlated flux and Spitzer data On the other side the modeled shell of ionized gas implies a more compact CSE (113plusmn002 R)and fainter (IR excess of 1 in the L band)Conclusions We provide new evidences for a compact CSE of ` Car and we demonstrate the capabilities of VLTIMATISSE for determiningcommon properties of CSEs While the compact CSE of ` Car is probably of gaseous nature the tested model of a shell of ionized gas is not ableto simultaneously reproduce the IR excess and the interferometric observations Further Galactic Cepheids observations with VLTIMATISSE arenecessary for determining the properties of CSEs which may also depend on both the pulsation period and the evolutionary state of the stars

Key words Techniques Interferometry ndash Infrared CSE ndash stars variables Cepheids ndash stars atmospheres

1 Introduction

Circumstellar envelopes (CSEs) around Cepheids have beenspatially resolved by long-baseline interferometry in the Kband with the Very Large Telescope Interferometer (VLTI) and

Based on observations made with ESO telescopes at Paranal obser-vatory under program ID 0104D-0554(A)

the Center for High Angular Resolution Astronomy (CHARA)(Kervella et al 2006 Meacuterand et al 2006) They were detectedaround four Cepheids including ` Car in the N band withVLTIVISIR and VLTIMIDI (Kervella et al 2009 Gallenneet al 2013) In the K band the diameter of the envelope appearsto be at least 2 stellar radii and the flux contribution is up to 5of the continuum (Meacuterand et al 2007) Both the size and flux

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contribution are expected to be larger in the N band as demon-strated by Kervella et al (2009) for ` Car Gallenne et al (2013)for X Sgr and T Mon and by Gallenne et al (2021 submitted)for other Cepheids Moreover a CSE has also been discovered inthe visible domain with the CHARAVEGA instrument aroundδCep (Nardetto et al 2016) The systematic presence of a CSE isstill a matter of debate While some studies have found no signif-icant observational evidence for circumstellar dust envelopes in alarge number of Cepheids (Schmidt 2015 Groenewegen 2020)Gallenne et al (2021 submitted) found a significant IR excessattributed to a CSE for 10 out of 45 Cepheids

Recently Hocdeacute et al (2020b) (hereafter Paper I) used ananalytical model of free-free and bound-free emission from athin shell of ionized gas to explain the near and mid-IR ex-cess of Cepheids They found a typical radius for this shell ofionized gas of about Rshell=115 R This shell of ionized gascould be due to periodic shocks occurring in both the atmo-sphere and the chromosphere which heat up and ionize the gasUsing VLTUVES data (Hocdeacute et al 2020a) found a radiusfor the chromosphere of at least Rchromo=15 R in long-periodCepheids In addition they found a motionless Hα feature inUVES high-resolution spectra obtained for several long-periodCepheids including ` Car This absorption feature was attributedto a static CSE surrounding the chromosphere above at least15 R and reported by various authors around ` Car (Rodgersamp Bell 1968 Bohm-Vitense amp Love 1994 Nardetto et al 2008)

Determining the IR excess and the size of the CSE is a keyto understand the physical processes at play In this paper westudy the long-period Cepheid ` Car Our aim is to determine itsIR excess from photometric measurements in various bands andSpitzer spectroscopy while inferring the size of the CSE andits flux contribution thanks to the unique capabilities providedby the Multi AperTure mid-Infrared SpectroScopic Experiment(VLTIMATISSE Lopez et al (2014) Allouche et al (2016)Robbe-Dubois et al (2018)) in the L (28-40 microm) M (45 - 5 microm)and N bands (8 - 13 microm)

We first reconstruct the IR excess in Sect 2 Then we presentthe data reduction and calibration process of VLTIMATISSEdata in Sect 3 We use a simple model of the CSE to repro-duce the visibility measurement of VLTIMATISSE in Sect 4In Sect 5 we discuss the physical origin of this envelope andpresent a model of a shell of ionized gas We summarize ourconclusions in Sect 6

2 Deriving the infrared excess of ` Car

21 Near-IR excess modeling with SPIPS

Due to their intrisic variability the photospheres of the Cepheidsare difficult to model along the pulsation cycle However it isan essential prerequisite for deriving both the IR excess in agiven photometric band and the expected angular stellar diame-ter at a specific phase of interferometric observations (required inSect 3) In order to model the photosphere we use SpectroPhoto-Interferometric modeling of Pulsating Stars (SPIPS) which is amodel-based parallax-of-pulsation code which includes photo-metric interferometric effective temperature and radial velocitymeasurements in a robust model fitting process (Meacuterand et al2015)SPIPS uses a grid of ATLAS9 atmospheric models1 (Castelli

amp Kurucz 2003) with solar metallicity and a standard turbulentvelocity of 2 kms SPIPS was already extensively described and

1 httpwwwuseroatsinafitcastelligridshtml

used in several studies (Meacuterand et al 2015 Breitfelder et al2016 Kervella et al 2017 Gallenne et al 2017) Javanmardiet al (2021 accepted) Gallenne et al (2021 submitted) andPaper I SPIPS also takes into account the possible presence ofan IR excess by fitting an ad-hoc analytic power law IRex (seegreen curve in Fig 1a) We note that Gallenne et al (2021 sub-mitted) have shown that ` Car possibly has an IR excess usingSPIPS but its low detection level (29 plusmn 32 in K band) isnot significant compared to a single-star model (ie without IRexcess model) Breitfelder et al (2016) also provided a SPIPSfitting of ` Car which did not present any significant IR excessHowever this work was done by considering only the V J Hand K photometric bands ie not the mid-infrared bands whichare critical to detect such an IR excess Finally since a CSEaround ` Car has been detected by interferometry in the infrared(Kervella et al 2006 2009) we enable SPIPS to fit an IR excessin the following analysis SPIPS provides a fit to the photometryalong the pulsation cycle which is in agreement with the ob-servational data (description in Appendix A1) From Fig A1we emphasize that the SPIPS fitted model is well constrained bythe numerous observations and thus the physical parameters ofthe photosphere are accurately derived However as noted in theSPIPS original paper the uncertainties on the derived parame-ters are purely statistical and do not take into account systemat-ics While the fitting is satisfactory from the visible domain tothe near infrared SPIPS fits an IR excess for wavelengths aboveabout 12 microm Indeed the observed brightness (mobs) significantlyexceeds the predictions (mkurucz) The averaged IR excess over apulsation cycle is presented in Fig 1a In the next section wecombine this average IR excess with Spitzer mid-infrared spec-troscopy

22 Mid-IR excess from Spitzer observations

Space-based observations such as those of obtained with theSpitzer space telescope are useful to avoid perturbation causedby the Earth atmosphere which is essential for the study ofdust spectral features We use spectroscopic observations madewith the InfraRed Spectrograph IRS (Houck et al 2004) onboard the Spitzer telescope (Werner et al 2004) High spec-tral resolution (R=600) from 10 microm to 38 microm was used withShort-High (SH) and Long-High (LH) modules placed in the fo-cal plane instrument The full spectra were retrieved from theCASSIS atlas (Lebouteiller et al 2011) and the best flux cal-ibrated spectrum was obtained from the optimal extraction us-ing differential method which eliminates low-level rogue pix-els (Lebouteiller et al 2015) Table 1 provides an overview ofthe Spitzer observation The reference epoch at maximum light(MJD0=50583742) pulsation period (P=35557 days) and therate of period change (P=334plusmn10 syr) used to derive the pul-sation phase corresponding to the Spitzer observation are thosecomputed by the SPIPS fitting of ` Car We note that the mostup-to-date and independent value of rate of period change de-rived by Neilson et al (2016) (P = 2023 plusmn 138 sy) is slightlylower than the value estimated by SPIPS However adopting thislatter value would not change the result of this paper

In order to derive the IR excess of Spitzer observation andcorrect for the absorption of the interstellar matter (ISM) wefollowed the method developed in Paper I First we derived theIR excess of ` Car at the specific Spitzer epoch using

∆mag = mSpitzer minus mkurucz[φSpitzer] (1)

where mSpitzer is the magnitude of the Spitzer observation andmkurucz[φSpitzer] is the magnitude of the ATLAS9 atmospheric


Hocdeacute et al Mid-infrared circumstellar emission of the long-period Cepheid ` Carinae resolved with VLTIMATISSE

Table 1 Spitzer data set of ` Car (program number 40968) The Astronomical Observation Request (AOR) the date of observation the cor-responding Modified Julian Date (MJD) and the pulsation phase (φ) are indicated The physical parameters of ` Car derived by SPIPS at theSpitzer observation phase are indicated the effective temperature (Teff) the surface gravity (log g) and the limb-darkened angular diameter (θLD)Statistical uncertainties on Teff and θ are provided by SPIPS whereas uncertainty on log g is arbitrarily set to 10

Object AOR Date MJD φSpitzer Teff(φSpitzer) log g(φSpitzer) θLD(φSpitzer)(yyyymmdd) (days) (K) (cgs) (mas)

` Car 23403520 20080503 54589502 0648 4630+15minus15 098+010

minus010 2897+0002minus0002

05 1 2 3 5 10Wavelength λ(microm)

minus030

minus025

minus020

minus015

minus010

minus005

000

005

010

Exce

ss(∆

mag

)

ad-hoc IR excess

SPIPS model - photometric data

(a) SPIPS cycle-averaged IR excess

0 5 10 15 20 25 30Wavelength λ(microm)

minus025

minus020

minus015

minus010

minus005

000

005

010

015

Exce

ss(∆

mag

)

Spitzer excess corrected from ISM extinction

ISM extinction (∆mag gt 0)


(b) Reconstructed IR excess with SPIPS and SpitzerFig 1 (a) Averaged IR excess of ` Car as derived with the SPIPSalgorithm (red dots) and presented with the fitted ad-hoc analytic lawIRex = minus0053(λ minus 12)0501mag For each photometric band (describedin Appendix A) the red dots are the mean excess value averaged overthe cycle of pulsation of ` Car while the blue uncertainties correspondto the respective standard deviation (b) The IR excess of ` Car is re-constructed at the specific phase of Spitzer observation It includes theaveraged IR excess from SPIPS (red dots) and the Spitzer observations(blue line) corrected for the silicate absorption of the ISM along the lineof sight (orange curve) The silicate extinction has been derived usingsilicate refractive index from Draine amp Lee (1984) Green and gray ver-tical stripes represent the LM and N bands of MATISSE respectively

model interpolated at the phase of Spitzer observations (φSpitzer)using the parameters derived by SPIPS and given in Table 1We discarded wavelengths of Spitzer observations longer than30 microm due to extremely large uncertainties Secondly we cor-rected the spectrum for ISM extinction by subtracting a syn-thetic ISM composed of silicates from Draine amp Lee (1984)(see orange curve in Fig 1b) This calculation assumes a re-lation between the extinction E(B minus V) derived by SPIPS (ieE(B minus V)=0148 mag) and the silicate absorption from diffuseinterstellar medium (see Eq 4 in Paper I) Finally we combinethis result with SPIPS averaged IR excess in order to reconstructthe IR excess from the visible to the mid-infrared domain Thedetermined IR excess is presented in Fig 1b (red dots and blueline)

Similarly to the five Cepheids presented in Paper I we ob-serve a continuum IR excess increasing up to minus01 mag at 10 micromIn particular within the specific bands of MATISSE (see verticalstrips in Fig 1b) the IR excess is between minus005 and minus01 magat 35 microm and 45 microm (L and M bands) which represents an ex-cess of 5 to 10 above the stellar continuum In addition wefind no silicate emission feature in the Spitzer spectrum around10 microm (N band) within the uncertainties which points toward anabsence of significant amount of circumstellar dust with amor-phous silicate components

3 VLTIMATISSE interferometric observations

MATISSE is the four-telescope beam combiner in the L M andN bands of the Very Large Telescope Interferometer (VLTI)The VLTI array consists of four 18-meter auxiliary telescopes(ATs) and four 8-meter unit telescopes (UTs) and providesbaseline lengths from 11 meters to 150 meters As a spectro-interferometer MATISSE provides dispersed fringes and pho-tometries The standard observing mode of MATISSE (so-called hybrid) uses the two following photometric measurementmodes SIPHOT for L and M bands in which the photometry ismeasured simultaneously with the dispersed interference fringesand HIGH SENS for N band in which the photometric flux ismeasured separately after the interferometric observations Theobservations were carried out during the nights of 27 and 28February 2020 with the so-called large configuration of the ATsquadruplet (A0-G1-J2-J3 with ground baseline lengths from 58to 132 m) in low spectral resolution (R=λ∆λ asymp30) The logof the MATISSE observations is given in Table 2 The raw datawere processed using the version (155) of the MATISSE datareduction software 2 The steps of the data reduction process aredescribed in Millour et al (2016)

The MATISSE absolute visibilities are estimated by divid-ing the measured correlated flux by the photometric flux Ther-

2 The MATISSE reduction pipeline is publicly available at httpwwwesoorgscisoftwarepipelinesmatisse



mal background effects affect the measurement in the M and Nbands significantly more than in the L band Thus we use onlythe L band visibilities in our modeling and analysis while the Land M photometries are used for deriving the observed total flux(see Sect 32) In the N band the total flux of ` Car (asymp17 Jy)is at the lower limit of the ATs sensitivity with MATISSE foraccurate visibility measurements (sim 20 Jy as stated on the ESOwebpage of the MATISSE instrument) Thus we rather use thecorrelated flux measurements (not normalized by the photomet-ric flux) as an estimate of the N band photometry of ` Car Inthe following of the paper we discarded the 41 to 45 microm spec-tral region where the atmosphere is not transmissive and alsothe noisy edges of the atmosphere spectral bands As a resultwe analyze the following spectral region in L (31-375microm) forabsolute visibility and flux M (475-49microm) for flux and in N(82-12microm) for correlated flux

31 Calibration of the squared visibility in the L band

Calibrators were selected using the SearchCal tool of theJMMC3 with a high confidence level on the derived angulardiameter (χ2 le 5 see Appendix A2 in Chelli et al (2016))Moreover calibrator fluxes in the L and N bands have to be ofthe same order than for the science target (ie asymp10 to 100 Jy in Land N) to ensure a reliable calibration (Cruzalegravebes et al 2019)These flux requirements induce the use of partially resolved cal-ibrators at the 132-m longest baseline The L band uniform-disk(UD) angular diameters for the standard stars as well as the cor-responding L and N band fluxes and the spectral type are givenin Table 3

We analyze these calibration stars with a special care Thefirst calibrator of this night q Car was observed in the frameof a different program and was not used in the interferometricvisibility calibration process Indeed it is a supergiant star ofspectral type KII which makes its angular diameter of 52 mastoo large (compared to ` Car) and rather uncertain in the L bandHowever q Car appears to be a suitable total flux calibrator for` Car in both L and M bands (see Sect 32) Indeed althoughq Car is an irregular long-period variable its photometric varia-tion in the visible is ∆magasymp01 4 (GCVS Samusrsquo et al 2017)thus its flux variation in the Rayleigh-Jeans domain ie in theL and M bands only represents about 1 Moreover q Car wasobserved at an air mass very close to the one of ` Car (see Ta-ble 2) In the analysis we discarded the calibrator B Cen sinceit has inconsistent visibilities as explained in Appendix B Thuswe used ε Ant to calibrate observation 1 For observation 2we also used ε Ant For observation 3 we bracketed the sci-ence target with the standard CAL-SCI-CAL strategy calibra-tion using β Vol The calibrated squared visibilities (V2) in Lband are presented in Fig 2 The visibility curve associated withthe limb-darkened angular diameter of the star (without CSE)which was derived from the SPIPS analysis at the specific phaseof VLTIMATISSE (φ=007) is shown for comparison

MATISSE also provides closure phase measurements whichcontain information about the spatial centro-symmetry of thebrightness distribution of the source For all the closure phasemeasurements we find an average closure phase of about 0in the L M and the N band from 82 to 925 microm (see Fig 3)

3 SearchCal is publicly available at httpswwwjmmcfrenglishtoolsproposal-preparationsearch-cal4 httpwwwsaimsusugroupsclustergcvsgcvsiiiiiidat

10 15 20 25 30 35 40 45Spatial frequency Bλ times107

03

04

05

06

07

08

09

10

V2

1

2

3

SPIPS θUD(φMATISSE) = 289 mas

Fig 2 The calibrated squared visibilities of ` Car as a function ofthe spatial frequencies in the L band for observations 1 2 and 3The theoretical visibility curve corresponding to a uniform disk ofθUD = 2887 plusmn 0003 mas in the L band as derived from the SPIPSanalysis (ie without CSE) is indicated for comparison

Table 2 Log of the observations for nights of 27 February (observa-tions 1 and 2) and 28 February 2020 (observation 3) with the Modi-fied Julian Date (MJD) the pulsation phase φ the seeing (in arcsecond)the air mass (AM) integrated water vapour (IWV) at 30 deg elevation(in millimeter) and the coherence time τ0 (in millisecond) are indicatedStars used in the visibility calibration strategy are marked with an as-terisk (see Sect 31) q Car and β Vol are used to calibrate the totalflux (see Sect 32) while e Cen is used to check the consistency of theother calibrators (see Appendix B) The calibrator B Cen is not usedsee Appendix B

Target Date φ seeing AM τ0(MJD) (primeprime) (ms)

q Car 5890711 078 140 601 ` Car 5890712 005 066 132 53

B Cen 5890713 085 139 612 ` Car 5890714 005 115 127 60

ε Ant 5890715 069 102 69e Cen 5890728 126 110 48bet Vol 5890799 079 151 63

3 ` Car 5890800 007 081 166 63bet Vol 5890801 091 142 157

In the N band we indicated the typical peak-to-valley disper-sion of the MATISSE closure phase measurements with an er-ror bar (asymp10 degrees) and we discarded the spectral region be-yond 10 microm due to extremely large uncertainties (see Fig 3)Down to a sub-degree level (resp 10 degrees level) our closurephase measurements are consistent with the absence of signifi-cant brightness spatial asymmetries in the environment around` Car in L and M bands (resp N band) That justifies our use ofcentro-symmetric models in the following of the paper



Table 3 Calibrator properties θUD is the uniform disk (UD) angulardiameter in L band from the JSDC V2 catalogue (Bourgeacutes et al 2014)FL and FN are the flux in the L and N bands from the Mid-infrared stel-lar Diameters and Fluxes compilation Catalogue (MDFC) (Cruzalegravebeset al 2019)

Calibrator θUD(mas) FL (Jy) FN(Jy) Sp Typeq Car 519plusmn060 2995plusmn506 458plusmn82 K25 IIB Cen 254plusmn028 723plusmn118 106plusmn10 K3 IIIε Ant 286plusmn030 881plusmn12 122plusmn18 K3 IIIe Cen 297plusmn029 889plusmn109 132plusmn16 K35 IIIbet Vol 290plusmn029 954plusmn235 146plusmn34 K2 III

1 2 3 4 5 6 8 10Wavelength (microm)

100

101

102

103

104

Flu

x(J

y)

SPIPS atmosphere ( = 007)

L band

M band

N band

Spitzer ( = 065)

8 9 10 11 12101

2 101

3 101

4 101

3 4 5

102

4 101

6 101

2 102

3 102

(a)

(b)

Fig 4 Averaged calibrated total flux for observations 1 2 and 3 inLM bands plus the correlated flux in N band for observation 3 Panels(a) and (b) refer to LM and N bands respectively SPIPS photospheremodel is interpolated at the phase corresponding to the MATISSE theobservation with parameters Teff(φobs)=5014plusmn15 K log g(φobs)=096plusmn010 and θUD(φobs)=2887 plusmn 0003 mas The Spitzer spectrum used inSect 22 is plotted for comparison

32 Flux calibration

In L and M bands we calibrate the total flux Ftotsci of ` Car using

Ftotsci =Itotsci

Itotcaltimes Ftotcal (2)

where Itotsci and Itotcal are the observed total raw flux of the sci-ence target and the calibrator respectively Ftotcal is the knownflux of the standard star We calibrate ` Car using standard starswith the closest air mass which are q Car and βVol for the obser-vations of the first and second night respectively Ftotcal is givenby their atmospheric templates from Cohen et al (1999) Sincethe air mass of both target and calibrator are comparable we donot correct for the air mass Moreover while a chromatic cor-rection exists for the N band (Schuumltz amp Sterzik 2005) it is notcalibrated (to our knowledge) for the L and M bands Then weaverage the three observations adding uncertainties and system-atics between each measurement in quadrature

Since ` Car is too faint in N band for accurate photometry(and thus absolute visibility) measurements we use the corre-

lated flux for the N band which is the flux contribution from thespatially unresolved structures of the source We calibrated thecorrelated flux of the science target Fcorrsci following

Fcorrsci =Icorrsci

Icorrcaltimes Ftotcal times Vcal (3)

where Icorrsci and Icorrcal are the observed raw correlated flux ofthe science target and the calibrator respectively and Vcal thecalibrator visibility For such an absolute calibration of the cor-related flux we need a robust interferometric calibrator with anatmospheric template given by Cohen et al (1999) Only β Volobserved during the second night meets these two requirementsThus we only calibrate the correlated flux measurements fromobservation 3 using the known flux of β Vol The calibratedcorrelated fluxes from the different baselines do not present anyresolved features allowing us to average the correlated flux fromthe different baselines Note that we have discarded the spectralregion between 93 and 10 microm due to the presence of a telluricozone absorption feature around 96 microm that strongly impacts thedata quality The calibrated total fluxes in L and M bands andthe averaged calibrated N band correlated flux are presented inFig 4

We draw here several intermediate conclusions First theagreement between the measured flux with MATISSE Spitzerand the SPIPS atmosphere model of ` Car is qualitatively sat-isfactory within the uncertainties However the MATISSE fluxmeasurements have rather large uncertainties (ge 10) makingit difficult to determine the IR excess of ` Car with a precisionat the few percent level Secondly we can see that the N bandcorrelated flux follows a pure Rayleigh-Jeans slope This indi-cates the absence of silicate emission which is consistent withthe Spitzer data (Sect 22) This is also in agreement with pre-vious MIDI spectrum given by Kervella et al (2009) Third aresolved environment around ` Car is seen in the visibility mea-surements in the L band Indeed the calibrated visibilities aresignificantly lower than the visibilities corresponding to a modelof the star without CSE as derived from the SPIPS algorithm atthe specific phase of VLTIMATISSE observations (see Fig 2)Since the interferometric closure phase is zero the resolved struc-ture around the star is centro-symmetric In the next section weapply a centro-symmetric model of envelope on the observed V2

measurements in L band in order to investigate the diameter andflux contribution of the envelope

4 Gaussian envelope model

In this section we fit a geometrical model on the measured Lband visibilities ` Car and its CSE are modeled with an uniformdisk (UD) and a surimposed Gaussian distribution as in the pre-vious studies on ` Car CSE (Kervella et al 2006 2009) The UDdiameter corresponds to the one at the specific phase of the ob-servation derived by SPIPS that is θUD = 2887 plusmn 0003 mas inthe L band To model the CSE we superimposed a Gaussian in-tensity distribution centered on the stellar disk This CSE Gaus-sian model has two parameters which are the CSE diameter θCSEtaken as the Full Width at Half Maximum (FWHM) and theCSE flux contribution normalized to the total flux We then per-formed a reduced χ2

r fitting to adjust the total squared visibilityof the model V2

tot over the MATISSE observation in L band Wecomputed the total squared visibility of the star plus CSE model



using

V2tot( f ) =

(F |VUD( f )| + FCSE |VCSE( f )|

)2(4)

where f =Bpλ is the spatial frequency (Bp the length of the pro-jected baseline) F and FCSE are the normalized stellar andCSE flux contribution to the total flux respectively normalizedto unity F + FCSE = 1 VUD( f ) is the visibility derived from theUD diameter of the star given by

VUD( f ) = 2J1(πθUD f )πθUD f

(5)

where J1 is the Bessel function of the first order VCSE( f ) is thevisibility of a Gaussian intensity distribution

VCSE( f ) = exp[minus

(πθCSE f )2

4ln2

] (6)

We perform the fit on observations 1 2 and 3 simultaneouslysince ` Car is not expected to vary significantly between φ=005and 007 The derived visibility model is shown in Fig 5 and wepresent the best-fit parameters in Table 4 The visibility modelturns out to be consistent within the error bars with the threeobservations However the reduced χ2

r is low (ie 02) thus thedata are overfitted by the model and the uncertainties on thebest-fit parameters are underestimated In that case to obtainmore reliable uncertainties on the best-fit parameters we fit in-dependently the three observations and we take the uncertaintyas the standard deviation as of the resulted parameters We re-solve a CSE with a radius of 176plusmn028 R accounting for about70plusmn14 of the flux contribution in the L band that gives anIR excess of minus007 mag Both the size and the flux contributionare in agreement with previous studies which have found a com-pact environment of size 19plusmn14 R in K band with VINCI and30plusmn11 R in N band with MIDI (Kervella et al 2006) with fewpercents in flux contribution in both cases As noted by Kervellaet al (2006) the large uncertainties in the K band diameter isdue to a lack of interferometric data for baselines between 15 to75 m We also note that cycle-to-cycle amplitude variations dis-covered in ` Car (Anderson 2014 Anderson et al 2016) couldslightly affect the diameter in the K band On the other handKervella et al (2009) found extended emission between 100 and1000 AU (asymp100-1000 R) using MIDI and VISIR observationsin the N band Thus it is possible that the CSE have both a com-pact and an extended component which are observable at dif-ferent wavelengths The CSE flux contribution of 7 is also inagreement with the MATISSE total flux within the uncertainties(see Fig 4) as well as the determined IR excess of about minus005to minus01 mag we derived from Fig 1b in Sect 22

Table 4 Fitted parameters of a Gaussian CSE with flux contributionFCSE() and FWHM θCSE(mas) which is also expressed in stellar ra-dius RCSE(R) Parameters FCSE and θCSE are weakly correlated witha correlation coefficient of 009 The uncertainties on the parametersare obtained using the standard deviation of the best-fit parameters forthe three observations fitted independently These results are comparedwith those obtained with VINCI in K band and MIDI in N band fromKervella et al (2006)

This work VINCI MIDIL K N

fCSE() 70plusmn14 42plusmn02 -θCSE(mas) 506plusmn081 58plusmn45 80plusmn30RCSE(R) 176plusmn028 19plusmn14 30plusmn11

χ2r 02 065 -


03

04

05

06

07

08

09

10

V2

1

2

3SPIPS θUD = 289 mas

FIT RCSE = 176R fcse = 70 χ2 = 02

Fig 5 Fitted Gaussian CSE around ` Car for the combined observa-tions 1 2 and 3 in the L band The error on the visibility model isobtained using the covariance matrix of the fitting result

5 Physical origin of the IR excess

51 Dust envelope

The absence of emission features in the N band in both MA-TISSE and Spitzer spectra rules out the presence of dust fromtypical oxygen rich star mineralogy with amorphous silicates oraluminum oxide which present a characteristic spectral shapein N band A pure iron envelope which presents a continuumemission is also unlikely to be created We already consideredthen rejected these possibilities in Paper I (see the Figures 8 and9 in it) We note that the presence of large grains of silicate witha size of about 1 microm and more would lead to a broader emis-sion which could completely disappear (Henning 2010) How-ever the reason why large grains would preferentially be createdin the envelope of Cepheids remains to be explained In addi-tion considering the best-fit of the Gaussian CSE model at adistance of 176 R from the stellar center ie 076 R from thephotosphere the temperature would exceed 2000 K thereforedust cannot survive since it would sublimate (Gail amp Sedlmayr1999) These physical difficulties to reproduce the IR excess withdust envelopes were also recently pointed out by Groenewegen



(2020) who fitted the SEDs of 477 Cepheids (including ` Car)with a dust radiative transfer code

52 A thin shell of ionized gas

In Paper I we suggested the presence of a thin shell of ionizedgas with a radius of about 115 R to explain the reconstructedIR excess of five Cepheids We use the same model for ` Carwith a shell of ionized gas to test its consistency with IR ex-cess and interferometric observations In this part we performa reduced χ2

r fitting of the shell parameters on the IR excessreconstructed in Sect 22 This simple model has three physi-cal parameters which are the shell radius the temperature andthe mass of ionized gas An additional parameter is applied asan offset to the whole reconstructed IR excess from Fig 1b al-lowing the model to present either a deficit or an excess in thevisible domain if necessary Indeed the key point is when con-sidering a shell of ionized gas this shell is expected to absorbthe light coming from the star in the visible domain which iscurrently not considered in the SPIPS algorithm when recon-structing the IR excess (the V magnitude is forced to be zero seeFig 1a) However thanks to the VLTIMATISSE measurementsof flux contribution of the CSE in the L band (7) we can fixthis offset parameter consistently to 003 magnitude to force theIR excess in L band from SPIPS (that is asymp10) to be also 7within the uncertainties We present the result of the modeling(χ2

r =055) constrained by the spectrum of ` Car in Fig 6 We finda thin shell radius of Rshell=113plusmn002 R which is lower than theGaussian CSE of 176plusmn028 R constrained by MATISSE obser-vations On the other hand this model also reproduces the Spitzerspectrum better than the SPIPS predicted photometries In par-ticular its value in the L band is about 1 (see Fig 6) whichis not consistent with the value derived using L band visibilities(sim 7) This model has also derived weak near-infrared excessfor several stars in Paper I (see its Figure 11) This behaviour isphysically explained by the free-bound absorption of hydrogenbefore the free-free emission dominates at longer wavelengthWe have explored the spatial parameters to test if a larger ion-ized envelope has the potential to match MATISSE observationswith the IR excess However our model is not able to accuratelyreproduce all the observations Also even if our model is com-plex considering the physics involved (free-free and bound-freeopacities description) its geometrical description is rather sim-ple with a constant density and temperature distribution Thusit might not be adapted to the modeling of a larger envelope

53 Limit of the model

The derived parameters of the shell of ionized gas depend onthe initial IR excess derived by SPIPS Any systematics in thiscalculation could in turn affect the IR excess and the parametersof the shell of ionized gas As noted by Hocdeacute et al (2020b)the derived distance of SPIPS would be systematically affectedif the shell of ionized gas is not taken into account because ofits absorption in the visible This systematic should be only fewpercents (10∆m25) all parameters being unchanged The directimplementation of the gas model into the SPIPS fitting has to betested in forthcoming studies to correct this uncertainty More-over Gallenne et al 2021 (submitted) studied the ad-hoc IR ex-cess derived by SPIPS for a larger sample of stars and found thatangular diameter and the colour excess are the most impactedparameters when no ad-hoc IR excess model is included How-ever in the case of ` Car these parameters appear to be well con-

strained by angular diameter measurements the reddening andthe distance are also in agreement with values found in the liter-ature (see Appendix A)

λ(microm)

020

015

010

005

000

minus005

minus010

minus015

minus020

Exce

ss(∆

mag

)

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Ionized shell (T ρ) = cst

SPIPS model

0 5 10 15 20 25 30

Wavelength λ(microm)

minus010

minus005

000

005

010

Res

idu

al(m

ag)

3 4 5

minus010

minus005

000

Fig 6 ` Car IR excess fitting result of ionized gas shell following themethod described in Paper I Yellow region is the error on the magni-tude obtained using the covariance matrix of the fitting result We finda thin shell of ionized gas with radius Rshell=113plusmn002 R temperatureTshell=3791plusmn85 K mass of ionized gas M=910times10minus8plusmn85times10minus9 M using an ad-hoc offset of +003 mag on the data in order to match the IRexcess found by VLTIMATISSE and the one of SPIPS (see the text)and χ2

r =055 The subplot shows the comparison between the flux con-tribution derived from the Gaussian CSE (dashed line) the IR excessfrom SPIPS (red point) and IR excess from a shell of ionized gas in theLM band (red line)

54 Perspectives

An interesting physical alternative is to consider free-free emis-sion produced by negative hydrogen ion Hminus with free electronsprovided by metals Indeed for an envelope of 2 R the aver-age temperature is about 3000 K and the hydrogen is neutralThus in that case most of the free electrons would be pro-vided by silicon iron and magnesium which have a mean firstionization potential of 789 eV As neutral hydrogen is able toform negative hydrogen ion Hminus could generate an infrared ex-cess with free-free emission This phenomenon is known to pro-duce a significant IR excess compared to dust emission in theextended chromosphere of cool supergiant stars such as Betel-geuse (Gilman 1974 Humphreys 1974 Lambert amp Snell 1975Altenhoff et al 1979 Skinner amp Whitmore 1987) Moreover thephoto-detachment potential occurs at 16 microm for the Hminus mech-anism thus free-free emission should dominate the IR excessabove this wavelength as it is suggested by the SPIPS cycle-averaged IR excess This single photo-detachment has also theadvantage to avoid the important bound-free absorption in thenear-infrared produced in the preceding model We thus suggest



that the compact structure we resolved around ` Car has the po-tential to produce IR excess through Hminus free-free mechanism byanalogy with extended chromosphere of cool supergiant starsFurther investigations are necessary to confirm this hypothesis

6 Conclusions

Determining the nature and the occurrence of the CSEs ofCepheids is of high interest to quantify their impact on thePeriod-Luminosity relation and also for understanding themass-loss mechanisms at play In this paper we constrain boththe IR excess and the geometry of the CSE of ` Car usingboth Spitzer low-resolution spectroscopy and MATISSE inter-ferometric observations in the mid-infrared Assuming an IR ex-cess ad-hoc model we used SPIPS to derive the photosphericparameters of the star in order to compare with Spitzer and MA-TISSE at their respective phase of observation This analysisallows to derive the IR excess from Spitzer and also to derivethe CSE properties in the L band spatially resolved with MA-TISSE These observations lead to the following conclusions onthe physical nature of ` Carrsquos CSE

1 We resolve a centro-symmetric and compact structure inthe L band with VLTIMATISSE that has a radius of about176 R The flux contribution is about 7

2 We find no clear evidence for dust emission features around10 microm (N band) in MATISSE and Spitzer spectra which sug-gests an absence of circumstellar dust

3 Our dedicated model of shell of ionized gas better reproducesthe mid-infrared Spitzer spectrum and implies a size for theCSE lower than the one derived from VLTIMATISSE ob-servations (113plusmn002 R versus 176plusmn028 R) as well as alower flux in the L band (1 versus 7)

4 We suggest that improving our model of shell of ionized gasby including the free-free emission from negative hydrogenion would probably help reproducing the observations iethe size of the CSE and the IR excess in particular in the Lband

While the compact CSE of ` Car is likely gaseous the exactphysical origin of the IR excess remains uncertain Further ob-servations of Cepheids depending on both their pulsation periodand their location in the HR diagram are necessary to under-stand the CSErsquos IR excess This could be a key to unbias Period-Luminosity relation from Cepheids IR excess

Acknowledgements The authors acknowledge the support of the French AgenceNationale de la Recherche (ANR) under grant ANR-15-CE31-0012- 01 (projectUnlockCepheids) The research leading to these results has received fundingfrom the European Research Council (ERC) under the European Unionrsquos Hori-zon 2020 research and innovation program under grant agreement No 695099(project CepBin) This research was supported by the LP2018-72019 grant ofthe Hungarian Academy of Sciences This research has been supported by theHungarian NKFIH grant K132406 This research made use of the SIMBAD andVIZIER5 databases at CDS Strasbourg (France) and the electronic bibliographymaintained by the NASAADS system This research also made use of Astropya community-developed corePython package for Astronomy (Astropy Collabo-ration et al 2018) Based on observations made with ESO telescopes at Paranalobservatory under program IDs 0104D-0554(A) This research has benefitedfrom the help of SUV the VLTIuser support service of the Jean-Marie MariottiCenter (httpwwwjmmcfrsuvhtm) This research has also made use ofthe Jean-Marie Mariotti Center Aspro service 6

5 Available at httpcdswebu-strasbgfr6 Available at httpwwwjmmcfraspro

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Optical Instrumentation Engineers (SPIE) Conference Series Vol 9907 Op-tical and Infrared Interferometry and Imaging V 99070C

Altenhoff W J Oster L amp Wendker H J 1979 AampA 73 L21Ammons S M Robinson S E Strader J et al 2006 ApJ 638 1004Anderson R I 2014 AampA 566 L10Anderson R I Meacuterand A Kervella P et al 2016 MNRAS 455 4231Astropy Collaboration Price-Whelan A M Sipocz B M et al 2018 AJ 156

123Berdnikov L N amp Turner D G 2002 VizieR Online Data Catalog 213Bohm-Vitense E amp Love S G 1994 ApJ 420 401Bourgeacutes L Lafrasse S Mella G et al 2014 in Astronomical Society of the

Pacific Conference Series Vol 485 Astronomical Data Anaylsis Softwardand Systems XXIII ed N Manset amp P Forshay 223

Breitfelder J Meacuterand A Kervella P et al 2016 AampA 587 A117Breuval L Kervella P Anderson R I et al 2020 AampA 643 A115Capitanio L Lallement R Vergely J L Elyajouri M amp Monreal-Ibero A

2017 AampA 606 A65Castelli F 1999 AampA 346 564Castelli F amp Kurucz R L 2003 in IAU Symposium Vol 210 Modelling of

Stellar Atmospheres ed N Piskunov W W Weiss amp D F Gray A20Chelli A Duvert G Bourgegraves L et al 2016 AampA 589 A112Cohen M Walker R G Carter B et al 1999 AJ 117 1864Cruzalegravebes P Petrov R G Robbe-Dubois S et al 2019 MNRAS 490 3158Draine B T amp Lee H M 1984 ApJ 285 89ESA ed 1997 ESA Special Publication Vol 1200 The HIPPARCOS and TY-

CHO catalogues Astrometric and photometric star catalogues derived fromthe ESA HIPPARCOS Space Astrometry Mission

Gaia Collaboration Brown A G A Vallenari A et al 2018 AampA 616 A1Gail H-P amp Sedlmayr E 1999 AampA 347 594Gallenne A Kervella P Meacuterand A et al 2017 AampA 608 A18Gallenne A Meacuterand A Kervella P et al 2013 AampA 558 A140Gilman R C 1974 ApJ 188 87Groenewegen M A T 2020 AampA 635 A33Henning T 2010 ARAampA 48 21Hocdeacute V Nardetto N Borgniet S et al 2020a AampA 641 A74Hocdeacute V Nardetto N Lagadec E et al 2020b AampA 633 A47Houck J R Roellig T L van Cleve J et al 2004 ApJS 154 18Humphreys R M 1974 ApJ 188 75Ishihara D Onaka T Kataza H et al 2010 AampA 514 A1Kervella P 2007 AampA 464 1045Kervella P Meacuterand A amp Gallenne A 2009 AampA 498 425Kervella P Meacuterand A Perrin G amp Coudeacute du Foresto V 2006 AampA 448

623Kervella P Trahin B Bond H E et al 2017 AampA 600 A127Lambert D L amp Snell R L 1975 MNRAS 172 277Laney C D amp Stobie R S 1992 AampAS 93 93Lebouteiller V Barry D J Goes C et al 2015 ApJS 218 21Lebouteiller V Barry D J Spoon H W W et al 2011 ApJS 196 8Lopez B Lagarde S Jaffe W et al 2014 The Messenger 157 5Madore B F 1975 ApJS 29 219Meacuterand A Aufdenberg J P Kervella P et al 2007 ApJ 664 1093Meacuterand A Kervella P Breitfelder J et al 2015 AampA 584 A80Meacuterand A Kervella P Coudeacute du Foresto V et al 2006 AampA 453 155Meacuterand A Kervella P Coudeacute du Foresto V et al 2005 AampA 438 L9Millour F Berio P Heininger M et al 2016 in Society of Photo-Optical

Instrumentation Engineers (SPIE) Conference Series Vol 9907 Proc SPIE990723

Monson A J Freedman W L Madore B F et al 2012 ApJ 759 146Nardetto N Fokin A Mourard D et al 2004 AampA 428 131Nardetto N Gieren W Kervella P et al 2009 AampA 502 951Nardetto N Groh J H Kraus S Millour F amp Gillet D 2008 AampA 489

1263Nardetto N Meacuterand A Mourard D et al 2016 AampA 593 A45Nardetto N Mourard D Mathias P Fokin A amp Gillet D 2007 AampA 471

661Neilson H R Engle S G Guinan E F Bisol A C amp Butterworth N 2016

ApJ 824 1Neugebauer G Habing H J van Duinen R et al 1984 ApJ 278 L1Pel J W 1976 AampAS 24 413Richichi A Percheron I amp Davis J 2009 MNRAS 399 399Robbe-Dubois S Lagarde S Antonelli P et al 2018 in Society of Photo-

Optical Instrumentation Engineers (SPIE) Conference Series Vol 10701 Op-tical and Infrared Interferometry and Imaging VI 107010H

Rodgers A W amp Bell R A 1968 MNRAS 138 23Samusrsquo N N Kazarovets E V Durlevich O V Kireeva N N amp Pas-

tukhova E N 2017 Astronomy Reports 61 80Schmidt E G 2015 ApJ 813 29



Schuumltz O amp Sterzik M 2005 in High Resolution Infrared Spectroscopy inAstronomy 104ndash108

Scowcroft V Seibert M Freedman W L et al 2016 MNRAS 459 1170Skinner C J amp Whitmore B 1987 MNRAS 224 335Smith B J Price S D amp Baker R I 2004 ApJS 154 673Werner M W Roellig T L Low F J et al 2004 ApJS 154 1Wright E L Eisenhardt P R M Mainzer A K et al 2010 AJ 140 1868

1 Universiteacute Cocircte drsquoAzur Observatoire de la Cocircte drsquoAzur CNRSLaboratoire Lagrange Franceemail vincenthocdeocaeu

2 European Southern Observatory Karl-Schwarzschild-Str 2 85748Garching Germany

3 Max-Planck-Institut fuumlr Radioastronomie Auf dem Huumlgel 69 D-53121 Bonn Germany

4 Leiden Observatory Leiden University Niels Bohrweg 2 NL-2333CA Leiden the Netherlands

5 LESIA Observatoire de Paris Universiteacute PSL CNRS SorbonneUniversiteacute Universiteacute de Paris 5 place Jules Janssen 92195Meudon France

6 Nicolaus Copernicus Astronomical Centre Polish Academy of Sci-ences Bartycka 18 00-716 Warszawa Poland

7 Unidad Mixta Internacional Franco-Chilena de Astronomiacutea (CNRSUMI 3386) Departamento de Astronomiacutea Universidad de ChileCamino El Observatorio 1515 Las Condes Santiago Chile

8 Departamento de Astronomiacutea Universidad de Concepcioacuten Casilla160-C Concepcioacuten Chile

9 Univ Grenoble Alpes CNRS IPAG 38000 Grenoble France10 NASA Goddard Space Flight Center Astrophysics Division Green-

belt MD 20771 USA11 Anton Pannekoek Institute for Astronomy University of Amster-

dam Science Park 904 1090 GE Amsterdam The Netherlands12 Department of Astrophysics University of Vienna Tuumlrkenschanzs-

trasse 1713 AIM CEA CNRS Universiteacute Paris-Saclay Universiteacute Paris

Diderot Sorbonne Paris Citeacute F-91191 Gif-sur-Yvette France14 Institute for Mathematics Astrophysics and Particle Physics Rad-

boud University PO Box 9010 MC 62 NL-6500 GL Nijmegen theNetherlands

15 SRON Netherlands Institute for Space Research Sorbonnelaan 2NL-3584 CA Utrecht the Netherlands

16 Institut fuumlr Theoretische Physik und Astrophysik Christian-Albrechts-Universitaumlt zu Kiel Leibnizstraszlige 15 24118 Kiel Ger-many

17 Konkoly Observatory Research Centre for Astronomy and EarthSciences Eoumltvoumls Loraacutend Research Network (ELKH) Konkoly-Thege Mikloacutes uacutet 15-17 H-1121 Budapest Hungary

18 CSFK Lenduumllet Near-Field Cosmology Research Group BudapestHungary

19 Max Planck Institute for Astronomy Koumlnigstuhl 17 D-69117 Hei-delberg Germany

20 Institute for Astrophysics University of Vienna 1180 Vi-ennaTuumlrkenschanzstrasse 17 Austria

21 I Physikalisches Institut Universitaumlt zu Koumlln Zuumllpicher Str 7750937 Koumlln Germany

22 Zselic Park of Stars 0642 hrsz 7477 Zselickisfalud Hungary23 Sydney Institute for Astronomy (SIfA) School of Physics The Uni-

versity of Sydney NSW 2006 Australia24 NOVA Optical IR Instrumentation Group at ASTRON Oude

Hoogeveensedijk 4 7991 PD Dwingeloo the Netherlands25 ASTRON (Netherlands) Oude Hoogeveensedijk 4 7991 PD

Dwingeloo the Netherlands



300 325 350 375 400 425 450 475 500


minus20

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sure

ph

ase

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ree)

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(a) 1 LM bands

82 84 86 88 90 92


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(deg

ree)

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300 325 350 375 400 425 450 475 500


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(deg

ree)

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82 84 86 88 90 92


minus40

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has

e(d

egre

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ree)

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(f) 3 N band

Fig 3 Closure phase for observations 1 2 and 3 for LM and the N bands for each ATs triplet The double arrows in the N bandpanels represent the typical peak-to-valley variation



Appendix A SPIPS data set and fitted pulsationalmodel of the star sample

Figure A1 is organized as follows pulsational velocity effectivetemperature and angular diameter curves according to the pulsa-tion phase are shown on the left panels while the right panelsdisplay photometric data in various bands Above the figure theprojection factor set to p = 1270 is indicated along with thefitted distance d using parallax-of-pulsation method the fittedcolor excess E(B minus V) and the ad-hoc IR excess law In thiswork we arbitrarily set the p-factor to 127 following the gen-eral agreement around this value for several stars in the literature(Nardetto et al 2004 Meacuterand et al 2005 Nardetto et al 2009)However there is no agreement for the optimum value to useand it is also the case for ` Car In the case of this star (Nardettoet al 2007 2009) found a p-factor of 128plusmn002 and 122plusmn004using different observational techniques which both are in agree-ment with 127 within about 1 sigma Thus a possible system-atic cannot be excluded although the distance derived by SPIPS(d = 5192plusmn45 pc) is in agreement for example with the distanceobtained using Gaia parallaxes (505plusmn28 pc) (Gaia Collaborationet al 2018) or the one derived using a recent period-luminositycalibrated for Cepheids in the Milky Way (544plusmn32 pc) (Breuvalet al 2020)

Gallenne et al (2021 submitted) have shown that the ab-sence of IR excess model in the SPIPS fit can affect the deriva-tion of the angular diameter and the colour excess In our fitusing IR excess model we emphasize the good agreement ofthe angular diameter model with the data (panel b) and alsothe consistency of the derived colour excess with the one givenby Stilism 3D extinction map (Capitanio et al 2017) that is0148 plusmn 0006 versus 0116 plusmn 026 In the photometric panelsthe gray dashed line corresponds to the magnitude of the SPIPSmodel without CSE It actually corresponds to the magnitudeof a Kurucz atmosphere model mkurucz obtained with the AT-LAS9 simulation code from Castelli amp Kurucz (2003) with so-lar metallicity and a standard turbulent velocity of 2 kms Thesemodels are indeed suitable for deriving precise synthetic pho-tometry (Castelli 1999) in comparison with MARCS modelsgiving rough flux estimates7 The gray line corresponds to thebest SPIPS model which is composed of the latter model with-out CSE plus an IR excess model In the angular diameter panelsthe gray curve corresponds to limb-darkened (LD) angular diam-eters For stars with solar metallicity when effective temperatureis low enough CO molecules can form in the photosphere andabsorb light in the CO band-head at 46 microm (Scowcroft et al2016) This effect is observed in the Spitzer I2 IRAC dataset Inthis case these data were ignored during the fitting of SPIPSPanels presenting a horizontal blue bar contain only one datawith undetermined phase of observation thus these photometricmid-infrared bands were not used in the IR excess reconstructionin Sect 21 and 22

Appendix B Verification of the diameters of thecalibrators

In order to verify the consistency of the standard stars of the firstnight (27 February) we consider all calibrators available dur-ing the night (B Cen e Cen ε Ant) and we inter-calibrate themThus each calibrator is calibrated using the two others We per-formed six different calibrations in total following Table B1 and

7 httpsmarcsastrouuse

Fig B1 The results are also compared with the known valuesfrom the literature

From these results the diameters of ε Ant and e Cen are inexcellent agreement with those given by the JSDC when they arecalibrated from one to another and the visibilities are well fittedby an uniform disk (UD) model (see Figures B1a and B1b)On the contrary we find important inconsistencies when deriv-ing the diameter of B Cen or using it as a calibrator (see Fig-ures B1c to B1f) In particular this standard star is suspectedto be 20 larger tan the diameter given by the JSDC (asymp 3 masinstead of 25 mas) Moreover a simple UD model seems to beunsuitable for fitting the observed visibilities (see black curve inFigures B1e and B1f) On the other hand the diameter of B Cenis also well established by interferometry in the K band (Richichiet al 2009) and was used many times as an interferometric cali-brator (Kervella et al 2006 Kervella 2007) We emphasize thatthe transfer function was very stable during this night thus thisresult cannot be attributed to the atmospheric conditions (see co-herence time in Table 2) Since the origin of this discrepancyremains unknown this analysis prevented us for using B Cen tocalibrate the Cepheid ` Car

Table B1 Diameters in milliarcseconds obtained by the inter-calibration between B Cen ε Ant and e Cen The targets of the cali-bration are indicated in the upper part of the table together with theirangular diameter in L band from the JSDC catalogue in parenthesesThe first column indicates the calibrator used to obtain the derived UDangular diameters in each cell The red cells represent discrepant valuescompared to the JSDC catalogue at more than 1σ This deviation fromthe derived θUD to the JSDC value is derived by |θUD minus θJSDC|σJSDC

e Cen ε Ant B Cen(297plusmn029) (286plusmn030) (254plusmn028)

e Cen - 291plusmn001 309plusmn002ε Ant 296plusmn001 - 310plusmn002B Cen 241plusmn002 239plusmn002 -



Fig A1 The SPIPS results of ` Car Velocity Anderson (2014) Effective temperature No data Angular diameter Kervella et al (2006)Photometry Madore (1975) Pel (1976) Neugebauer et al (1984) Laney amp Stobie (1992) ESA (1997) Berdnikov amp Turner (2002) Smith et al(2004) Ammons et al (2006) Wright et al (2010) Ishihara et al (2010) Monson et al (2012) Gaia Collaboration et al (2018)



10 15 20 25 30 35 40

Spatial frequency Bλ times107

03

04

05

06

07

08

09

10

V2

JSDC θUD =286plusmn030 mas

FIT θUD =291plusmn001 mas χ2 =018

(a) ε Ant calibrated with e Cen

10 15 20 25 30 35 40


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(b) e Cen calibrated with ε Ant

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(d) e Cen calibrated with B Cen

10 15 20 25 30 35 40


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(e) B Cen calibrated with ε Ant

10 15 20 25 30 35 40


03

04

05

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07

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V2



(f) B Cen calibrated with e Cen

Fig B1 Inter-calibration of the different calibrators and comparison with JSDC diameters (a) and (b) ε Ant and e Cen diameters are inagreement with the JSDC when they are calibrated from each other (c) and (d) On the contrary the diameter of ε Ant and e Cen are inconsistentwith the JSDC catalogue when they are calibrated with B Cen (e) and (f) B Cen diameter is inconsistent with the JSDC catalogue


1 Introduction

2 Deriving the infrared excess of 60 Car





32 Flux calibration



51 Dust envelope



54 Perspectives

6 Conclusions

A SPIPS data set and fitted pulsational model of the star sample

B Verification of the diameters of the calibrators


contribution are expected to be larger in the N band as demon-strated by Kervella et al (2009) for ` Car Gallenne et al (2013)for X Sgr and T Mon and by Gallenne et al (2021 submitted)for other Cepheids Moreover a CSE has also been discovered inthe visible domain with the CHARAVEGA instrument aroundδCep (Nardetto et al 2016) The systematic presence of a CSE isstill a matter of debate While some studies have found no signif-icant observational evidence for circumstellar dust envelopes in alarge number of Cepheids (Schmidt 2015 Groenewegen 2020)Gallenne et al (2021 submitted) found a significant IR excessattributed to a CSE for 10 out of 45 Cepheids

Recently Hocdeacute et al (2020b) (hereafter Paper I) used ananalytical model of free-free and bound-free emission from athin shell of ionized gas to explain the near and mid-IR ex-cess of Cepheids They found a typical radius for this shell ofionized gas of about Rshell=115 R This shell of ionized gascould be due to periodic shocks occurring in both the atmo-sphere and the chromosphere which heat up and ionize the gasUsing VLTUVES data (Hocdeacute et al 2020a) found a radiusfor the chromosphere of at least Rchromo=15 R in long-periodCepheids In addition they found a motionless Hα feature inUVES high-resolution spectra obtained for several long-periodCepheids including ` Car This absorption feature was attributedto a static CSE surrounding the chromosphere above at least15 R and reported by various authors around ` Car (Rodgersamp Bell 1968 Bohm-Vitense amp Love 1994 Nardetto et al 2008)

Determining the IR excess and the size of the CSE is a keyto understand the physical processes at play In this paper westudy the long-period Cepheid ` Car Our aim is to determine itsIR excess from photometric measurements in various bands andSpitzer spectroscopy while inferring the size of the CSE andits flux contribution thanks to the unique capabilities providedby the Multi AperTure mid-Infrared SpectroScopic Experiment(VLTIMATISSE Lopez et al (2014) Allouche et al (2016)Robbe-Dubois et al (2018)) in the L (28-40 microm) M (45 - 5 microm)and N bands (8 - 13 microm)

We first reconstruct the IR excess in Sect 2 Then we presentthe data reduction and calibration process of VLTIMATISSEdata in Sect 3 We use a simple model of the CSE to repro-duce the visibility measurement of VLTIMATISSE in Sect 4In Sect 5 we discuss the physical origin of this envelope andpresent a model of a shell of ionized gas We summarize ourconclusions in Sect 6

2 Deriving the infrared excess of ` Car


Due to their intrisic variability the photospheres of the Cepheidsare difficult to model along the pulsation cycle However it isan essential prerequisite for deriving both the IR excess in agiven photometric band and the expected angular stellar diame-ter at a specific phase of interferometric observations (required inSect 3) In order to model the photosphere we use SpectroPhoto-Interferometric modeling of Pulsating Stars (SPIPS) which is amodel-based parallax-of-pulsation code which includes photo-metric interferometric effective temperature and radial velocitymeasurements in a robust model fitting process (Meacuterand et al2015)SPIPS uses a grid of ATLAS9 atmospheric models1 (Castelli

amp Kurucz 2003) with solar metallicity and a standard turbulentvelocity of 2 kms SPIPS was already extensively described and

1 httpwwwuseroatsinafitcastelligridshtml

used in several studies (Meacuterand et al 2015 Breitfelder et al2016 Kervella et al 2017 Gallenne et al 2017) Javanmardiet al (2021 accepted) Gallenne et al (2021 submitted) andPaper I SPIPS also takes into account the possible presence ofan IR excess by fitting an ad-hoc analytic power law IRex (seegreen curve in Fig 1a) We note that Gallenne et al (2021 sub-mitted) have shown that ` Car possibly has an IR excess usingSPIPS but its low detection level (29 plusmn 32 in K band) isnot significant compared to a single-star model (ie without IRexcess model) Breitfelder et al (2016) also provided a SPIPSfitting of ` Car which did not present any significant IR excessHowever this work was done by considering only the V J Hand K photometric bands ie not the mid-infrared bands whichare critical to detect such an IR excess Finally since a CSEaround ` Car has been detected by interferometry in the infrared(Kervella et al 2006 2009) we enable SPIPS to fit an IR excessin the following analysis SPIPS provides a fit to the photometryalong the pulsation cycle which is in agreement with the ob-servational data (description in Appendix A1) From Fig A1we emphasize that the SPIPS fitted model is well constrained bythe numerous observations and thus the physical parameters ofthe photosphere are accurately derived However as noted in theSPIPS original paper the uncertainties on the derived parame-ters are purely statistical and do not take into account systemat-ics While the fitting is satisfactory from the visible domain tothe near infrared SPIPS fits an IR excess for wavelengths aboveabout 12 microm Indeed the observed brightness (mobs) significantlyexceeds the predictions (mkurucz) The averaged IR excess over apulsation cycle is presented in Fig 1a In the next section wecombine this average IR excess with Spitzer mid-infrared spec-troscopy


Space-based observations such as those of obtained with theSpitzer space telescope are useful to avoid perturbation causedby the Earth atmosphere which is essential for the study ofdust spectral features We use spectroscopic observations madewith the InfraRed Spectrograph IRS (Houck et al 2004) onboard the Spitzer telescope (Werner et al 2004) High spec-tral resolution (R=600) from 10 microm to 38 microm was used withShort-High (SH) and Long-High (LH) modules placed in the fo-cal plane instrument The full spectra were retrieved from theCASSIS atlas (Lebouteiller et al 2011) and the best flux cal-ibrated spectrum was obtained from the optimal extraction us-ing differential method which eliminates low-level rogue pix-els (Lebouteiller et al 2015) Table 1 provides an overview ofthe Spitzer observation The reference epoch at maximum light(MJD0=50583742) pulsation period (P=35557 days) and therate of period change (P=334plusmn10 syr) used to derive the pul-sation phase corresponding to the Spitzer observation are thosecomputed by the SPIPS fitting of ` Car We note that the mostup-to-date and independent value of rate of period change de-rived by Neilson et al (2016) (P = 2023 plusmn 138 sy) is slightlylower than the value estimated by SPIPS However adopting thislatter value would not change the result of this paper

In order to derive the IR excess of Spitzer observation andcorrect for the absorption of the interstellar matter (ISM) wefollowed the method developed in Paper I First we derived theIR excess of ` Car at the specific Spitzer epoch using

∆mag = mSpitzer minus mkurucz[φSpitzer] (1)

where mSpitzer is the magnitude of the Spitzer observation andmkurucz[φSpitzer] is the magnitude of the ATLAS9 atmospheric





` Car 23403520 20080503 54589502 0648 4630+15minus15 098+010

minus010 2897+0002minus0002


minus030

minus025

minus020

minus015

minus010

minus005

000

005

010

Exce

ss(∆

mag

)

ad-hoc IR excess




minus025

minus020

minus015

minus010

minus005

000

005

010

015

Exce

ss(∆

mag

)




















03

04

05

06

07

08

09

10

V2

1

2

3





q Car 5890711 078 140 601 ` Car 5890712 005 066 132 53

B Cen 5890713 085 139 612 ` Car 5890714 005 115 127 60

ε Ant 5890715 069 102 69e Cen 5890728 126 110 48bet Vol 5890799 079 151 63

3 ` Car 5890800 007 081 166 63bet Vol 5890801 091 142 157







100

101

102

103

104

Flu

x(J

y)


L band

M band

N band

Spitzer ( = 065)

8 9 10 11 12101

2 101

3 101

4 101

3 4 5

102

4 101

6 101

2 102

3 102

(a)

(b)


32 Flux calibration


Ftotsci =Itotsci





Fcorrsci =Icorrsci











using

V2tot( f ) =


)2(4)



(5)



(πθCSE f )2

4ln2

] (6)






χ2r 02 065 -


03

04

05

06

07

08

09

10

V2

1

2


FIT RCSE = 176R fcse = 70 χ2 = 02



51 Dust envelope












λ(microm)

020

015

010

005

000

minus005

minus010

minus015

minus020

Exce

ss(∆

mag

)

Spitzer corrected


SPIPS model

0 5 10 15 20 25 30


minus010

minus005

000

005

010

Res

idu

al(m

ag)

3 4 5

minus010

minus005

000



54 Perspectives





6 Conclusions



























































300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(a) 1 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(b) 1 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(c) 2 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40C

losu

rep

has

e(d

egre

e)G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(d) 2 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(e) 3 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(f) 3 N band




















10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2






1 Introduction






32 Flux calibration



51 Dust envelope



54 Perspectives

6 Conclusions






` Car 23403520 20080503 54589502 0648 4630+15minus15 098+010

minus010 2897+0002minus0002


minus030

minus025

minus020

minus015

minus010

minus005

000

005

010

Exce

ss(∆

mag

)

ad-hoc IR excess




minus025

minus020

minus015

minus010

minus005

000

005

010

015

Exce

ss(∆

mag

)




















03

04

05

06

07

08

09

10

V2

1

2

3





q Car 5890711 078 140 601 ` Car 5890712 005 066 132 53

B Cen 5890713 085 139 612 ` Car 5890714 005 115 127 60

ε Ant 5890715 069 102 69e Cen 5890728 126 110 48bet Vol 5890799 079 151 63

3 ` Car 5890800 007 081 166 63bet Vol 5890801 091 142 157







100

101

102

103

104

Flu

x(J

y)


L band

M band

N band

Spitzer ( = 065)

8 9 10 11 12101

2 101

3 101

4 101

3 4 5

102

4 101

6 101

2 102

3 102

(a)

(b)


32 Flux calibration


Ftotsci =Itotsci





Fcorrsci =Icorrsci











using

V2tot( f ) =


)2(4)



(5)



(πθCSE f )2

4ln2

] (6)






χ2r 02 065 -


03

04

05

06

07

08

09

10

V2

1

2


FIT RCSE = 176R fcse = 70 χ2 = 02



51 Dust envelope












λ(microm)

020

015

010

005

000

minus005

minus010

minus015

minus020

Exce

ss(∆

mag

)

Spitzer corrected


SPIPS model

0 5 10 15 20 25 30


minus010

minus005

000

005

010

Res

idu

al(m

ag)

3 4 5

minus010

minus005

000



54 Perspectives





6 Conclusions



























































300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(a) 1 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(b) 1 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(c) 2 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40C

losu

rep

has

e(d

egre

e)G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(d) 2 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(e) 3 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(f) 3 N band




















10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2






1 Introduction






32 Flux calibration



51 Dust envelope



54 Perspectives

6 Conclusions











03

04

05

06

07

08

09

10

V2

1

2

3





q Car 5890711 078 140 601 ` Car 5890712 005 066 132 53

B Cen 5890713 085 139 612 ` Car 5890714 005 115 127 60

ε Ant 5890715 069 102 69e Cen 5890728 126 110 48bet Vol 5890799 079 151 63

3 ` Car 5890800 007 081 166 63bet Vol 5890801 091 142 157







100

101

102

103

104

Flu

x(J

y)


L band

M band

N band

Spitzer ( = 065)

8 9 10 11 12101

2 101

3 101

4 101

3 4 5

102

4 101

6 101

2 102

3 102

(a)

(b)


32 Flux calibration


Ftotsci =Itotsci





Fcorrsci =Icorrsci











using

V2tot( f ) =


)2(4)



(5)



(πθCSE f )2

4ln2

] (6)






χ2r 02 065 -


03

04

05

06

07

08

09

10

V2

1

2


FIT RCSE = 176R fcse = 70 χ2 = 02



51 Dust envelope












λ(microm)

020

015

010

005

000

minus005

minus010

minus015

minus020

Exce

ss(∆

mag

)

Spitzer corrected


SPIPS model

0 5 10 15 20 25 30


minus010

minus005

000

005

010

Res

idu

al(m

ag)

3 4 5

minus010

minus005

000



54 Perspectives





6 Conclusions



























































300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(a) 1 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(b) 1 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(c) 2 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40C

losu

rep

has

e(d

egre

e)G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(d) 2 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(e) 3 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(f) 3 N band




















10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2






1 Introduction






32 Flux calibration



51 Dust envelope



54 Perspectives

6 Conclusions







100

101

102

103

104

Flu

x(J

y)


L band

M band

N band

Spitzer ( = 065)

8 9 10 11 12101

2 101

3 101

4 101

3 4 5

102

4 101

6 101

2 102

3 102

(a)

(b)


32 Flux calibration


Ftotsci =Itotsci





Fcorrsci =Icorrsci











using

V2tot( f ) =


)2(4)



(5)



(πθCSE f )2

4ln2

] (6)






χ2r 02 065 -


03

04

05

06

07

08

09

10

V2

1

2


FIT RCSE = 176R fcse = 70 χ2 = 02



51 Dust envelope












λ(microm)

020

015

010

005

000

minus005

minus010

minus015

minus020

Exce

ss(∆

mag

)

Spitzer corrected


SPIPS model

0 5 10 15 20 25 30


minus010

minus005

000

005

010

Res

idu

al(m

ag)

3 4 5

minus010

minus005

000



54 Perspectives





6 Conclusions



























































300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(a) 1 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(b) 1 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(c) 2 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40C

losu

rep

has

e(d

egre

e)G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(d) 2 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(e) 3 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(f) 3 N band




















10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2






1 Introduction






32 Flux calibration



51 Dust envelope



54 Perspectives

6 Conclusions




using

V2tot( f ) =


)2(4)



(5)



(πθCSE f )2

4ln2

] (6)






χ2r 02 065 -


03

04

05

06

07

08

09

10

V2

1

2


FIT RCSE = 176R fcse = 70 χ2 = 02



51 Dust envelope












λ(microm)

020

015

010

005

000

minus005

minus010

minus015

minus020

Exce

ss(∆

mag

)

Spitzer corrected


SPIPS model

0 5 10 15 20 25 30


minus010

minus005

000

005

010

Res

idu

al(m

ag)

3 4 5

minus010

minus005

000



54 Perspectives





6 Conclusions



























































300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(a) 1 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(b) 1 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(c) 2 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40C

losu

rep

has

e(d

egre

e)G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(d) 2 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(e) 3 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(f) 3 N band




















10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2






1 Introduction






32 Flux calibration



51 Dust envelope



54 Perspectives

6 Conclusions












λ(microm)

020

015

010

005

000

minus005

minus010

minus015

minus020

Exce

ss(∆

mag

)

Spitzer corrected


SPIPS model

0 5 10 15 20 25 30


minus010

minus005

000

005

010

Res

idu

al(m

ag)

3 4 5

minus010

minus005

000



54 Perspectives





6 Conclusions



























































300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(a) 1 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(b) 1 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(c) 2 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40C

losu

rep

has

e(d

egre

e)G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(d) 2 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(e) 3 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(f) 3 N band




















10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2






1 Introduction






32 Flux calibration



51 Dust envelope



54 Perspectives

6 Conclusions





6 Conclusions



























































300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(a) 1 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(b) 1 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(c) 2 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40C

losu

rep

has

e(d

egre

e)G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(d) 2 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(e) 3 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(f) 3 N band




















10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2






1 Introduction






32 Flux calibration



51 Dust envelope



54 Perspectives

6 Conclusions

































300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(a) 1 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(b) 1 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(c) 2 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40C

losu

rep

has

e(d

egre

e)G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(d) 2 N band

300 325 350 375 400 425 450 475 500


minus20

minus15

minus10

minus05

00

05

10

15

20

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(e) 3 LM bands

82 84 86 88 90 92


minus40

minus30

minus20

minus10

0

10

20

30

40

Clo

sure

ph

ase

(deg

ree)

G1-J2-J3

A0-G1-J2

A0-G1-J3

A0-J2-J3

(f) 3 N band




















10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2






1 Introduction






32 Flux calibration



51 Dust envelope



54 Perspectives

6 Conclusions




















10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2




10 15 20 25 30 35 40


03

04

05

06

07

08

09

10

V2






1 Introduction






32 Flux calibration



51 Dust envelope



54 Perspectives

6 Conclusions



Mid-infrared circumstellar emission of the long-period ...

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Transcript of Mid-infrared circumstellar emission of the long-period ...