Warm CO in evolved stars from the THROES catalogue. II. Herschel/PACS spectroscopy of C-rich envelopes
J. M. da Silva Santos, J. Ramos-Medina, C. Sánchez Contreras, P. García-Lario
AAstronomy & Astrophysics manuscript no. rotdiag c (cid:13)
ESO 2018December 20, 2018
Warm CO in evolved stars from the THROES catalogue
II. Herschel (cid:63) /PACS spectroscopy of C-rich envelopes
J. M. da Silva Santos , J. Ramos-Medina , C. Sánchez Contreras , and P. García-Lario Centro de Astrobiología (CSIC-INTA), ESAC, Camino Bajo del Castillo s / n, 28691 Villanueva de la Cañada, Madrid, Spain Institute for Solar Physics, Department of Astronomy, Stockholm University, AlbaNova University Centre, SE-106 91 Stockholm,Sweden. e-mail: [email protected] European Space Astronomy Center, PO Box 78, 28691, Villanueva de la Cañada, Madrid, SpainDecember 20, 2018
ABSTRACT
Context.
This is the second paper of a series making use of
Herschel / PACS spectroscopy of evolved stars in the THROES catalogueto study the inner warm regions of their circumstellar envelopes (CSEs).
Aims.
We analyze the CO emission spectra, including a large number of high- J CO lines (from J = J = ν = ff erent evolutionary stages from theAsymptotic Giant Branch (AGB) to the young planetary nebulae (PNe) phase. Methods.
We use the rotational diagram (RD) technique to derive rotational temperatures ( T rot ) and masses ( M H ) of the envelopelayers where the CO transitions observed with PACS arise. Additionally, we obtain a first order estimate of the mass-loss rates andassess the impact of the opacity correction for a range of envelope characteristic radii. We use multi-epoch spectra for the well studiedC-rich envelope IRC + T rot and M H . Results.
PACS sensitivity allowed the study of higher rotational numbers than before indicating the presence of a significant amount ofwarmer gas ( ∼ J CO observations at sub-mm / mm wavelengths. The masses are in the range M H ∼ − − − M (cid:12) , anti-correlated with temperature. For some strong CO emitters we infer a double temperature (warm T rot ∼
400 Kand hot T rot ∼
820 K) component. From the analysis of IRC + ff ect of line variability is perceptibleon the T rot of the hot component only, and certainly insignificant on M H and, hence, the mass-loss rate. The agreement between ourmass-loss rates and the literature across the sample is good. Therefore, the parameters derived from the RD are robust even whenstrong line flux variability occurs, with the major source of uncertainty in the estimate of the mass-loss rate being the size of theCO-emitting volume. Key words.
Stars: AGB and post-AGB – Stars: circumstellar matter – Stars: carbon – Stars: mass-loss – ISM: planetary nebulae
1. Introduction
The asymptotic giant branch (AGB) is a late evolutionary stageof low-to-intermediate mass stars (1 M (cid:12) < ∼ M (cid:63) < ∼ (cid:12) ) which islargely dominated by mass-loss processes. AGB stars can shedsignificant portions of their outer atmospheric layers in a dust-driven wind, with mass-loss rates of up to ˙ M ∼ − M (cid:12) yr − (e.g. Habing 1996; Höfner & Olofsson 2018). The material ex-pelled by the central star (with very low e ff ective temperaturesof T e ff ∼ + CSE’ system begins to evolve to the PlanetaryNebula (PN) phase, at which the CSE is fully or almost fully ion-ized due to the much higher central star temperatures ( T e ff ≈ -10 K) and more diluted envelopes. During the AGB-to-PN tran-sition, shocks – resulting from the interaction between slow andfast winds at the end of the AGB phase (or early post-AGB) –also play an important role changing the morphology, dynamics (cid:63)
Herschel is an ESA space observatory with science instruments pro-vided by European-led Principal Investigator consortia and with impor-tant participation from NASA. and chemistry of the CSEs (e.g. Kwok 2000; van Winckel 2003;Bujarrabal 2006).The CO molecule is an excellent tracer of the CSEs ofAGB stars, post-AGB objects and PNe (e.g Groenewegen et al.1996; Schöier & Olofsson 2001; Schöier et al. 2002; Teyssieret al. 2006). The rotational transitions of the ground vibrationallevel over a wide range of excitation energies sample from cold( ∼
10 K) to hot gas ( ∼ J = − J = − / sub-mm wave-lengths (e.g. Knapp et al. 1982; Knapp & Morris 1985; Knapp &Chang 1985; Olofsson et al. 1993; Bujarrabal et al. 1989; Joris-sen & Knapp 1998; Castro-Carrizo et al. 2010; Sánchez Contr-eras & Sahai 2012; Ramstedt & Olofsson 2014). Studies lookingat far-infrared (FIR) observations of even higher J CO transi-tions probing the warmest gas ( ∼ IS O ) (e.g. Just-tanont et al. 2000; Schöier et al. 2002) have continued more re-cently with
Herschel (e.g. Groenewegen et al. 2011; Bujarrabalet al. 2012; Khouri et al. 2014; Danilovich et al. 2015; Nicolaeset al. 2018). We abbreviate C O as simply CO throughout the paper. 1 of 30 a r X i v : . [ a s t r o - ph . S R ] D ec & A proofs: manuscript no. rotdiag
This is the second of a series of papers (Ramos-Medina et al.2018a, Paper I) where we analyze in an uniform and systematicway
Herschel / PACS spectra of a large sample of evolved starsfrom the THROES catalogue (Ramos-Medina et al. 2018b) tostudy their warm inner envelope regions using high- J CO tran-sitions at FIR wavelengths. As in other previous studies, we di-vide our sample in O-rich and C-rich targets (papers I and II, re-spectively) since these two major chemistry classes correspondto progenitor stars with di ff erent masses, which follow some-what di ff erent evolutionary paths, and also have a dissimilar dustcomposition, both facts potentially a ff ecting the mass-loss pro-cess. We include targets with di ff erent evolutionary stages: AGB,post-AGB (or pre-PNe) and young planetary nebulae (yPNe).The goal of our study (papers I and II) is to obtain a first esti-mate of the average excitation temperature ( T rot ) and mass ( M H )of the warm envelope layers traced by the PACS CO lines in auniform way using a simple analysis technique, the well-knownrotational diagram (RD) method. The RD technique is useful torapidly analyze large data sets (large number of lines and / or largesamples) and to provide some constraints on these fundamen-tal parameters. With the aim of benchmarking the results of theRD approximation, we obtain rough estimates of mass-loss rates( ˙ M ) and compare them to values in the literature, paying partic-ular attention to studies including at least a few high- J CO (FIR)transitions.The impact of possible non-LTE e ff ects on the results fromthe simple RD analysis was investigated in paper I. It was con-cluded that, though they are expected to be minor in general andprobably only a ff ecting the highest- J CO transitions studied here( J > ∼
27) at most, their existence cannot be ruled out in the low-est mass-loss rate stars and / or the outermost layers of the PACSCO-emitting volume. We also showed that even under non-LTEconditions, the masses derived from the RDs are approximatelycorrect (or, at the very least, not a ff ected by unusually large un-certainties) since the average excitation temperature describesrather precisely the molecular excitation (i.e., the real level pop-ulation). This is also corroborated by the good agreement foundbetween our estimates of ˙ M and those from detailed non-LTEexcitation and radiative transfer (nLTEexRT) studies that existfor a number of targets. We stress that the RD method enablesa characterization of the warm CSEs of evolved stars in a firstapproximation and that for a more robust and detailed study ofthe radial structure of the density, temperature and velocity in theCSEs, as well as for establishing potential mass-loss rate varia-tions with time, more sophisticated analysis is needed (e.g., Rydeet al. 1999; Schöier et al. 2002; De Beck et al. 2012).Upon submission of this manuscript (and after our paperI was accepted for publication) we became aware of a recentwork by Nicolaes et al. (2018) who independently presented Herchel / PACS (and SPIRE) range spectroscopy of a sample of37 AGB stars. These authors perform a similar RD analysis ofthe CO spectra and focus on deriving excitation temperatures (incontrast to our study, estimates of the envelope mass or mass-loss rates are not reported). Other di ff erences with respect to thework by Nicolaes et al. (2018) is that we introduce a canonicalopacity correction in the RDs and that we include post-AGBsand PNe.
2. Observations
PACS is a photometer and medium resolution grating spectrom-eter (Poglitsch et al. 2010) onboard the Herschel Space Tele- scope (Pilbratt et al. 2010) probing the FIR wavelength range.The PACS spectrometer covers the wavelength range from 51 to210 µ m in two di ff erent channels that operate simultaneously inthe blue (51-105 µ m) and red (102-220 µ m) bands. The Field ofView (FoV) covers a 47 (cid:48)(cid:48) × (cid:48)(cid:48) region in the sky, structured inan array of 5 × (cid:48)(cid:48) × (cid:48)(cid:48) . PACSprovides a resolving power between 5500 and 940, i.e. a spec-tral resolution of approximately 55-320 km s − , at short and longwavelengths, respectively, and the PSF of the PACS spectrome-ter ranges from ∼ (cid:48)(cid:48) in the blue band to ∼ (cid:48)(cid:48) in the red band.The PSF is described in da Silva Santos (2016) and Bocchio et al.(2016). The technical details of the instrument can be found inthe PACS Observer’s Manual .The PACS (1D) spectral data were taken from the THROES(caTalogue of HeRschel Observations of Evolved Stars) web-site which contains fully reduced PACS spectra of a collec-tion of 114 stars, mostly low-to-intermediate mass AGB stars,post-AGB and PNe. The data reduction is explained in Ramos-Medina et al. (2018b) in full detail. The catalogue also consistsof a compilation of previous photometry measurements at 12,25, 60, 100 µ m with the Infrared Astronomical Satellite (IRAS).Table B.1 o ff ers a description of the observations used herewhere we provide the target name as listed in the header of thePACS FITS files and an alternative name for which some of thestars are more well known in the literature. We only analyzedthe spectra between [55-95] and [101-190] µ m because the fluxdensities are unreliable above 190 µ m, below 55 µ m and between95-101 µ m due to spectral leakage. Two observation identifiers(OBSIDs) per target, corresponding to the bands B2A, B2B andR1, are necessary to cover the full PACS wavelength range. Inthe case of IRC + Herschel
Science Archiveand, thus, are not included in the THROES catalogue. Instead,we used 4 + ff erent opera-tional days: OD = [745, 1087, 1257 and 1296] covering the spec-tral range [69-95, 140-190] µ m and OD = [894, 1113 and 1288]covering a narrower interval [77-95, 155-190] µ m. We searched for CO emission amongst the entire THROES cat-alog, but in this paper we focus on C-rich CSEs (29% of theentries) observed in PACS range mode. We found 15 evolvedstars with at least three CO emission lines with signal-to-noiseratio above 3.This sample contains bright infrared targets spanning a rangeof evolutionary stages from the AGB to the PN phase, but shar-ing similar carbon chemistry with strong CO emission at high ex-citation temperatures (up to E u / k ≈ M ∼ . × − M (cid:12) yr − de-rived from studies with large samples of carbon stars (Olofssonet al. 1993). We also include two mixed-chemistry post-AGBs(Red Rectangle and IRAS 16594-4656, Waters et al. 1998;Woods et al. 2005) and two mixed-chemistry yPNes (Hen 2-113and CPD-56 ◦ herschel.esac.esa.int/Docs/PACS/html/pacs_om.html https://throes.cab.inta-csic.es Fig. 1: IRAS color diagrams for the stars in the THROES catalogue. The colors are defined from the infrared fluxes at 12, 25 and60 µ m. The boxes on the left panel are the ones defined in van der Veen & Habing (1988), and the highlighted points correspond tothe stars studied in this paper.tance, e ff ective temperature and gas mass-loss rate, along withadditional references.Figure 1 shows the classic IRAS color-color diagram (vander Veen & Habing 1988) featuring the colors [25] − [60] = − . IRAS IRAS and [12] − [25] = − . IRAS IRAS of all the starsin THROES. The stars here studied are highlighted with coloredfilled symbols which we will use consistently throughout the pa-per. This diagram is known to be a good indicator of the evo-lutionary stage of low-to-intermediate evolved stars, with AGBspopulating the lower left corner and more advanced stages be-ing located on the diametrically opposed, so-called cold, side ofthe diagram. It also shows an evolution in terms of the mass-loss rate and / or progressively increasing optical depths (Bedijn1987). C-rich AGBs clearly constellate in a di ff erent box com-pared to the O-rich stars in Paper I, which has been interpretedas a consequence of di ff erent grains’ emissivities (Zuckerman &Dyck 1986). The AGB star that falls outside the expected boxwith a clear 25 µ m excess ([12] − [25] = .
1) is AFGL 3068(LL Peg), which is an "extreme carbon star": very dust-obscuredby optically thick shells due to high mass-loss rate (Volk et al.1992; Winters et al. 1997). The post-AGB object HD 44179, bestknown as The Red Rectangle, is also outlying in this same boxwith respect to objects in a similar evolutionary status beyond theAGB, which typically show much larger 25 µ m excess indicativeof detached cold dust (and gas) envelopes.
3. Observational results
The PACS continuum-subtracted spectra are plotted in Fig. 2sorted in terms of stellar e ff ective temperature ( T e ff increasesfrom top to bottom) and arbitrarily scaled for better compari-son of the CO spectra. The continuum was fitted using a non-parametric method after identifying the line-free regions of thespectrum for each target. A brief line-detection statistics sum-mary is given in Table B.3. Broad emission or absorption fea-tures due to instrumental artifacts are occasionally visible insome of the targets (e.g. near 62 µ m). The spectra of IRC + ff erent epochs are shown in the top panel ofFig. 3, and in more detail in Fig. C.2 in the Appendix. Straightaway we see significant di ff erences between thespectra of these targets such as the larger line density, resultingfrom a richer molecular content, in AGB stars compared to post-AGBs and yPNe as expected. In AGB stars the strongest spectrallines are due to CO emission, while post-AGBs and yPNe showmuch more prominent forbidden lines, except for AFGL 2688and AFGL 618. Additional molecular features with intense emis-sion are attributed to rotational transitions of common C-bearingspecies such as CO, HCN, CS, etc.Not so common in C-rich stars is the presence of OH, yet weidentify several OH doublet lines (at 79, 84, 119 and 163 µ m)in all yPNe and in the post-AGB star IRAS 16594-4656, withthe highest T e ff ∼
10 000K in its class and where the presenceof shocks is plausible. Two additional OH doublets at 65 and71 µ m, with high-excitation energy of about 500 and 600 K, re-spectively, are also observed in IRAS 16594-4656 and in theyPNe Hen 2-113. In those five ( T e ff >
10 000 K) targets, we alsoidentify pure rotational transitions of CH + , with the J = µ m being one of the most clearly detected and bestisolated lines . The 179.61 µ m CH + line could be blended withthe water 2 -1 transition. The highest- J lines of CH + are alsopresent in IRAS 16594-4656 and Hen 2-113. Interestingly, wedo not see CH + in the spectrum of the Red Rectangle, wheresharp emission features near 4225 Å were discovered and as-signed to this ion by Balm & Jura (1992). The detection of CH + in AFGL 618 and the more evolved PNe NGC 7027 had beenpreviously reported by Wesson et al. (2010, Herschel / SPIRE)and Cernicharo et al. (1997,
ISO data). As we see below in thissection, the targets with CH + and OH emission also show thestrongest atomic / ionic fine-structure lines.We identify lines due to H O (orto- and para-) transitionsin all AGBs, in the post-AGB AFGL 2688 and in the yPNeAFGL 618. The study of water lines in the C-rich AGB stars ofour sample (except for AFGL 2513) was already conducted byLombaert et al. (2016) who suggested that both shocks and UVphotodissociation may play a role in warm H O formation. Wa-ter lines had also been previously identified in the SPIRE spec-trum of AFGL 618 and AFGL 2688 Wesson et al. (2010). The lines of CH + covered by PACS are J = µ m, respectively. 3 of 30 & A proofs: manuscript no. rotdiag
55 60 65 70 75 80 85 90 95
AFGL 3068AFGL 3116IRAS 15194-5115CIT 6AFGL 2513V CYGV HYAAFGL 2688HD 44179IRAS 16594-4656AFGL 618IRAS 21282+5050CPD-568032Hen 2-113
Fig. 2: Continuum-subtracted PACS spectra of our sample. The vertical segments (at the top) and bars indicate the rotationaltransitions of CO (light gray, dotted lines), CO (dark gray), HCN (red), CS (yellow), OH (cyan), CH + (green) and forbiddenlines (blue) of [C ii ] 157 . µ m, [O i ] 63 . , . µ m, [N ii ] 121 . µ m.
110 120 130 140 150 160 170 180 190
AFGL 3068AFGL 3116AFGL 2513CIT 6IRAS 15194-5115V CYGV HYAAFGL 2688HD 44179IRAS 16594-4656AFGL 618IRAS 21282+5050CPD-568032Hen 2-113
Fig. 2: Continued. & A proofs: manuscript no. rotdiag
60 80 100 120 140 160 18005001000
800 900 1000 1100 1200 1300150200250300800 900 1000 1100 1200 13001200140016001800
Fig. 3: Line and continuum variability of IRC + ff erent epochs (see alsoFig. C.2); the dotted lines sign the CO transitions. Bottom: Sine-wave fit to the continuum variability at two selected wavelengthsfor a fixed pulsation period of 630 days (solid lines) and free-period fit corresponding to 680 and 660 days for the blue and reddashed curves, respectively.The fine-structure lines [O i ] at 63.18 µ m and 145.53 µ mand [C ii ] at 157.74 µ m are very prominent in the spectra ofall post-AGBs and yPNe in our sample with the exception ofAFGL 2688. The post-AGB object IRAS 16594-4656 demon-strates clear signs of ionization since it shows a [C ii ] line evenstronger than that of AFGL 618, which has a hotter centralstar (Table B.1). Weak [N ii ] 121.89 µ m emission is also de-tected in Hen 2-113 and IRAS 21282 + µ m band of forsterite (Mg SiO ) is visible in CPD-56 ◦ Variability of the continuum at optical and IR wavelengths due tostellar pulsations is a common property of AGB stars. We presentPACS spectra at multiple epochs of the Mira-type C-rich starIRC + + Herschel / HIFI andIRAM 30m data. Line variability was attributed to periodicchanges in the IR pumping rates and also possibly in the dustand gas temperatures in the innermost layers of the CSE. Fromthe analysis of a 3 yr-long monitoring of the molecular emissionof IRC + Herschel (including HIFI, SPIRE and PACSdata), Teyssier et al. (2015) concluded that intensity changes ofCO lines with rotational numbers up to J =
18 are within the typ-ical instrument calibration uncertainties, but in the higher PACSfrequency range ( J ≥ > ∼ J , were found. More recently, He et al. (2017) reported 5%-30% intensity variability of additional mmlines with periodicities in the range 450-1180 days.In section 5.3 we study in greater detail what is the impact ofCO line variability on the estimate of T rot and M H from the ro-tational diagram analysis using PACS data for di ff erent epochs. We now focus on the purely rotational spectrum of CO in theground vibrational state ( v = J = −
13 ( E u ∼
581 K) to J = − E u ∼ µ m meanswe cannot detect the transitions J = J = + ∼ µ m, Fig. 3) prevents detection of CO transitions withupper-level rotational number between J u =
19 and J u = ∼ ∼ − )does not allow to spectrally resolve the CO profiles. This istrue not only for AGB CSEs with full-widths-at-half-maximum(FWHM) similar to or smaller than the terminal expansionvelocity of the envelopes (FWHM ∼ − , Table B.2),but also for post-AGB objects and yPNe, even in targets thatare known to have fast ( ≈
100 km s − ) molecular outflows likeAFGL 618 (e.g. Bujarrabal et al. 2010). For this reason we mea-sured CO fluxes by simply fitting a Gaussian function to thePACS lines.Due to insu ffi cient spectral resolution some reported linefluxes are a ff ected by line blend. These are identified with as-terisks in the tables and figures. Some of the well-known lineblends are CO J = J = J = with HCN J = µ m, respectively. Also,the CO transitions J = J = CO J = J = . µ m and 118 . µ m, respectively.Figure 4 compares the integrated flux of the CO ( J = F CO (15 − ) with the IRAS 100 µ m flux (IRAS ), thePACS continuum at 170 µ m (PACS ), i.e. near the CO ( J = J = and PACS continuum fluxes. The correlation between the CO J = F CO 15 − / PACS ) ratio and the IRAS[12]-[25] color (both distance-independent) for the AGB stars,which was noted in Paper I. For the more evolved targets thetrend is not so obvious, but the sample size is small. We also seethat, in general, the ratio between the molecular emission andthe dust emission is higher in less evolved objects than in themost evolved ones, which could be partially attributed to moreprominent CO photodissociation as the objects evolves along theAGB-to-PNe track. AFGL 618 and IRAS 16594-4656 are twoclear outliers in this relation since they show a line-to-continuumemission ratio as large as that of the AGB class. The Red Rect-angle (HD 44179) is well isolated in all the panels due to itscomparatively weak CO emission and low CO-to-dust ratio. Thissurely reflects the di ff erent nature of this object with respect tothe rest of post-AGB and yPNe in our sample, which is wellknown from previous works. The Red Rectangle belongs to aspecial class of post-AGB objects with relatively weak CO emis-sion coming from large ( ∼ / hot dust inthe disk, but lacking massive molecular outflows found in manyother evolved stars (e.g., Bujarrabal et al. 2016, and referencestherein).
4. Rotational diagram analysis
Following the same approach of Paper I, we have used the well-known and widely employed rotational diagram (RD) technique(e.g. Goldsmith & Langer 1999) to obtain a first estimate of the(average) excitation temperature ( T rot ) and total mass ( M H ) ofthe warm inner layers of the molecular envelopes of our sample.A canonical opacity correction factor, C τ , as defined by Gold-smith & Langer (1999), has been included to take into accountmoderate optical depth e ff ects (§ A.1). We refer to Paper I for amore detailed description of the method. To compute the optical depth of the line and to make the corre-sponding C τ correction, we need an estimate of the column den-sity of CO, which is computed in a simplified manner dividingthe total number of CO molecules ( N CO ) by the projected areaof the CO-emitting volume on the sky. The characteristic size ofthe envelope regions where the CO PACS emission is produced( r CO ) is one of the main sources of uncertainty since, except fora few targets (see below), these high- J CO-emitting layers areunresolved by PACS. Therefore, the value of r CO needs to beadopted based on several criteria. These criteria are described in -25 -24 -23 -17 -16 -15 -14 -26 -25 -24 -23 -17 -16 -15 -14 -1 0 1 2 310 -4 -3 -2 HD 44179 AFGL 2688AFGL 618IRC+10216AFGL 3068 HD 44179HD 44179 AFGL 2688AFGL 2688AFGL 618AFGL 618IRC+10216IRC+10216AFGL 3068AFGL 3068CPD-568032CPD-568032Hen 2-113Hen 2-113 Hen 2-113CPD-568032
Fig. 4: Correlation between CO line flux and continuum inten-sities. Top: CO J = −
14 vs IRAS 100 µ m flux. Middle: CO J = −
14 vs PACS 170 µ m continuum flux. Bottom: contin-uum normalized CO J = −
14 flux vs IRAS [12]-[25] color.The symbols and colors are the same as in Fig. 1.much detail in paper I, Appendix B. In the following, we providea brief summary of the general method and provide additionalarguments particularized to the C-rich targets here under study.For AGB CSEs, a first estimate of the size of the CO-emittingvolume can be derived from the envelope temperature struc- & A proofs: manuscript no. rotdiag
AFGL 3068
AFGL 3116
IRAS 15194-5115
CIT 6
AFGL 2513
V CYG
V HYA
AFGL 2688
HD 44179
IRAS 16594-4656
AFGL 618
Fig. 5: Rotational diagrams of the CO molecule. The gray line correspond to a single least-squares fit to the full range of transitionsfrom where a rotational temperature, T rot , and total gas mass, M H , is computed. The characteristic radius of the CO-emitting volume( r CO ) adopted is indicated. The red and blue lines correspond to a two-component model consisting of a "warm" and "hot" region,respectively. Asterisks mark line blends that were excluded in the fit.
500 1000 1500 2000 2500106108110112
IRAS 21282+5050
500 1000 1500 2000 2500104106108110112
CPD-568032
500 1000 1500 2000 2500104106108110112
HEN 2-113
Fig. 5: Continued.ture, T ( r ), estimated from detailed non-LTE molecular excita-tion and radiative transfer (nLTEexRT) calculations in the liter-ature. These have been done for many AGB CSEs using low- J CO transitions (typically J u < ∼ J levels (see e.g., Decinet al. 2010; Khouri et al. 2014; Danilovich et al. 2014; Maer-cker et al. 2016; Van de Sande et al. 2018). As deduced fromthese studies, the gas temperature is approximately 1000-2000 Kclose to the dust condensation radius ( ∼ (cid:63) ), and decreasesgradually towards the outermost layers approximately followinga power-law of the type ∼ / r α , with α ∼ + cm ( < ∼ R (cid:63) ) in AGB stars.An additional constraint on the radius can be imposed fromthe fact that the deepest layer traced by the observed CO emis-sion must be such that τ < × cm (Fig. A.1). We found that values around r CO ∼ [1-4] × cm result in line optical depths close to, but smallerthan unity (typically τ J = → ∼ C τ opacity correction factors for lines with J u <
19 and negligiblefor higher- J transitions. For r CO < × cm, the opacity of theCO J = r CO ∼ [1-4] × cm, is consistentwith the upper limits to the size of their envelopes deduced fromthe PACS spectral cubes and / or photometric maps by da SilvaSantos (2016) and with any other information on the molecu-lar envelope extent from the literature. IRC + σ above the instru- See also the temperature profiles for the O-rich AGBs in Fig. B.1 ofPaper I. ment PSF in both bands) that implies a deconvolved Gaussianradius of about 2 (cid:48)(cid:48) , that is ∼ × cm at d =
150 pc. This valueis in good agreement with the lower limit to r CO needed to sat-isfy the τ J = → < r CO ∼ × cm. Inthis case, we then rather confidently use an intermediate value of r CO = × cm.Contrary to AGBs, for post-AGBs and yPNe there are nomodel temperature profiles in the literature of the molecular gasin the CSEs (except for the rotating, circumbinary disk of theRed Rectangle, § 6.1.1).The range of representative radius adopted for post-AGBsand yPNe is r CO = [0.4-4] × cm (Table 1) based on a moder-ate opacity criteria, the extent of the emission in the PACS cubesand photometric maps, and on additional information on the ex-tent of the intermediate-to-outer molecular envelope from the lit-erature. In particular, in AFGL 2688, a deconvolved diameter of ∼ (cid:48)(cid:48) in the PACS blue band suggests that r CO < ∼ × cm (at d =
340 pc). Previous CO J = ∼ (cid:48)(cid:48) ( ∼ × cm) around the centerof the nebula (Cox et al. 2000). Since the CO J = r CO < ∼ × cm (as shown in Fig. A.1),we adopt as representative radius an intermediate value of r CO = × cm. HD 44179 (The Red Rectangle) is a point-source in the PACS photometric maps, therefore, for a distanceof 710 pc, r CO should be of the same order as in AFGL 2688,which is roughly consistent with interferometric observations(e.g., Bujarrabal et al. 2016). For IRAS 16594-4656, only a veryloose upper limit to the radius of r CO < × cm is inferred fromoptical images and H emission maps in this object (e.g., Hriv-nak et al. 2008). We explored the range, r CO ∼ . − × ,similar to AFGL 2688, and adopted as a reference value the mid-point value where τ J = → ∼ r CO < ∼ (cid:48)(cid:48) ∼ [1-2] × cm for AFGL 618, and ∼ [4-6] × cm for the rest. They are known to have central H ii regions that have recently formed as the star has become pro-gressively hotter along the PNe evolution. Because the CO en-velope surrounds the ionized nebula, a lower limit to r CO canbe established from the extent of the latter. Taking this intoaccount, we set a representative radius to r CO = × cm forAFGL 618 (Sanchez Contreras et al. 2017; Lee et al. 2013), and r CO = × cm for the rest (see e.g., Danehkar & Parker 2015;Castro-Carrizo et al. 2010). & A proofs: manuscript no. rotdiag
OD = 745 OD = 894
OD = 1087 OD = 1113
OD = 1257
OD = 1288
OD = 1296
Fig. 6: Rotational diagram of the CO molecule in IRC + ff erent epochs. Analogous to Fig. 5.Given the uncertainty in r CO , we have systematically ex-plored a range of radii around optimal / plausible values of r CO to asses the impact of this parameter in our results (Fig. A.1).The opacity correction increases the smaller r CO is, therefore theslope and y-intercept of the RD increase as a direct result of thefrequency-dependence of C τ (§ A.1), which results in lower val-ues of T rot and larger values of N CO , thus M H . This also meansthat, in practice, only the lowest-frequency-points are a ff ectedby C τ , while the highest-frequency transitions (i.e., highest ex-citation energies) are unaltered regardless of the radius that wechose within the reasonable constraints that we have put. In Paper I we examine and discuss extensively the impact of non-LTE excitation e ff ects (if present) on the values of T rot and M H derived from the RDs in a sample of 26 non C-rich evolved starswith mass-loss rates in the range ˙ M ∼ × − -1 × − M (cid:12) yr − .The C-rich targets studied here have on average larger mass-lossrates than those in Paper I, therefore, using a similar reasoning,the CO population levels are also most likely close to thermal-ization in the inner dense regions of the CSEs under study.This is further supported by nLTEexRT computations of aselection of high- J CO transitions observed with PACS (from J u =
14 to 38) by Lombaert et al. (2016). Their sample includedall our targets except for AFGL 2513 and IRC + M ∼ − -2 × − M (cid:12) yr − ) the CO molecule is predominantlyexcited through collisions with H , with a minor e ff ect of FIRradiative pumping due to the dust radiation field. The role ofdust-excitation on FIR CO lines was also investigated by Schöieret al. (2002) and found to be of minor importance for AGBswith typical mass-loss rates of ∼ − M (cid:12) yr − . We assess theFIR pumping e ff ect further in Section 5.3, where we study multi-epoch RDs of IRC + T rot may deviate from the kinetic temperature in regions wherethe local density is lower than the critical densities of the tran-sitions considered ( n crit ∼ × -3 × cm − , for J u =
14 and 27,respectively, and n crit ≈ -10 cm − for J u > J levels have the lowest critical densities(see above). If this is the case, in low mass-loss rate objects, thevalue of T rot deduced for the hot component could deviate fromthe temperature of the gas and approach to that of the dust withinthe CO-emitting volume. We note that, in any case, the gas anddust temperatures, although not equal, are not excessively diver-gent in the warm envelope regions around ∼ cm under study(e.g., Danilovich et al. 2014; Schöier et al. 2002).
5. Results
The opacity-corrected RDs of the CO molecule are plotted inFig. 5 and in Fig. 6, where multi-epoch RDs for IRC + E u ∼
580 K to E u < ∼ E u ∼
10 of 30. M. da Silva Santos et al.: Warm CO in evolved stars from the THROES catalogue -4 -3 -2 -5 -4 -3 -2 Fig. 7: Summary of the RD results. Top: The colored symbolscorrespond to the opacity corrected values (single fit) which areconnected by dotted lines to the corresponding uncorrected val-ues in gray; on the sides we show the histograms of tempera-ture and mass of the single fits; in the case of IRC + T w < T single < T h .Their mean temperatures are T w ∼
400 K and T h ∼
820 K re-spectively. The corresponding masses are M w and M h with the former being 4-10 times larger than the latter. We find single-fitrotational temperatures in the range T rot ∼ N CO ∼ − , resulting in column densities of N colCO ∼ − cm − for the adopted radii (Table 1). To estimate the totalgas mass from CO we assumed the same fractional abundance X CO = × − (e.g. Teyssier et al. 2006) with respect to H for all targets. The single-fit values of the total mass of the CO-emitting volume range between M H ∼ × − M (cid:12) (V Cyg andHD 44179) and ∼ × − M (cid:12) (IRAS 21282 + M H ∼ × − M (cid:12) .Figure 7 shows the single-fit temperature versus mass for theopacity corrected diagram (colored symbols) and uncorrected(gray symbols). The opacity-correction results in changes in T rot of 10-15% in AGBs, and lower than 5% in post-AGBs and yPNe.In mass this typically corresponds to 60% in AGBs and lower inthe post-AGBs and AFGL 618 ( <
10% in M H ), and negligiblein the other three yPNes. Figure A.1 shows that τ J = − is closeto unity but it quickly falls o ff with increasing J meaning that C τ → E u / k > M h , in particular, is notunderestimated by opacity e ff ects.As in Paper I, we find an anti-correlation between M H and T rot , especially if we consider only the group of AGBs (Fig. 7). Ingeneral, post-AGBs and yPNe have the the highest masses. Oneclear exception to trend is The Red Rectangle, which is one ofthe least massive targets (with only a few ∼ − M (cid:12) yr − ) in con-trast to the rest of post-AGBs and yPNe. This is not surprisinggiven the nature of this object, which is the prototype of a specialclass of post-AGB objects with hot rotating disks and tenuouswinds very di ff erent from the massive and fast (high-momentum)outflows of standard pre-PNe (Bujarrabal et al. 2016, and refer-ences therein).We also investigated the correlation between the CO J = −
14 flux and the gas mass and find that the strongest COemitters have tendentially more massive envelopes, althoughthere is a significant scatter (Fig. C.1). Also, the targets withthe highest temperatures have the highest line-to-continuum(F
CO 15 − / PACS ) ratios. IRAS 21282 + J = −
14 emission, al-though its T rot ∼
170 K is the lowest in the sample. The Red Rect-angle appears isolated in a region of rather weak CO emission inspite of relatively high temperatures ( ∼ The mass-loss rates have been estimated by simply dividing thetotal mass by the crossing time of the CO-emitting layers, thatis:˙ M = M H v exp r CO (1)where v exp is the expansion velocity of the gas, which has beentaken from literature (Table B.2). For the characteristic radius ofthe CO-emitting region we use the same value ( r CO ) adoptedfor the opacity correction. We note that this estimate repre-sents a mean or "equivalent" mass-loss rate assuming constant-velocity spherically-symmetric mass-loss during the time when
11 of 30 & A proofs: manuscript no. rotdiag -7 -6.5 -6 -5.5 -5 -4.5-16.5-16-15.5-15-14.5-14
Fig. 8: Logarithm of the mass-loss rate versus total CO J = ∼ < ∼
300 yr forAGBs and post-AGBs / yPNe, respectively, given the values of v exp and r CO .The mass-loss rates are listed in Table 1. We find a range ofvalues of ˙ M ∼ − − − M (cid:12) yr − , with a median value in ourAGB stars of ˙ M ∼ × − M (cid:12) yr − . These values are not to betaken as representative of the whole class of C-rich evolved stars,since our sample is small and not unbiased. This is because theobjects in the THROES catalogue were originally selected for Herschel observations due to various reasons, probably includ-ing their strong CO emission.As in Paper I, we investigated a possible correlation between˙ M , and T rot , v exp . We see little evidence of an anti-correlationbetween ˙ M and T rot , although the relation is strongly influ-enced by AFGL 618, which is a strong outlier in this parame-ter space (Fig. C.1). In this, and maybe other objects (mainlypost-AGB / yPNe), we expect departures from the simple (con-stant mass-loss rate, spherically symmetric) model adopted toestimate the "equivalent" ˙ M . We compare the results obtainedhere and in Paper I in Section 6.3.Figure 8 shows the logarithm of the integrated flux of the CO J = −
14 line versus the logarithm of the mass-loss rate of thesingle component fit. The upper and lower limit of the errorbarsin ˙ M correspond to a range of radii around the representativeone (see Fig. A.1). We find a positive trend which is consistentwith a power-law relation similar to that found by Lombaert et al.(2016) in their sample of C-rich AGB CSEs with H O FIR emis-sion lines.Separate values of ˙ M for the hot and warm components arecomputed for completeness, but the di ff erence found ( M h < M w )should not be overinterpreted as a recent decrease of the mass-loss rate. The hot and warm components most likely trace adja-cent layers of the inner-winds of our targets, with the hot com-ponent presumably best sampling regions closer to the center.However, for simplicity and since we ignore the true CO exci-tation structure, we use the same radius to formally compute ˙ M for both components. We note that due to the 1 / r CO dependence,the values of M h and M w can be brought closer to the single- fit value if the warm and hot correspond to di ff erent r CO . Werefrain from discussing M h and M w separately since a more so-phisticated analysis, including nLTEexRT modeling, is neededin order to assess mass-loss time variability. For this reason weonly compare our single-component mass-loss rates to the liter-ature (§ 6.2). T rot and M H We have shown in Fig. 3 the temporal variability of the contin-uum and line fluxes in the case of the Mira-type variable AGBstar IRC + J CO lines ( E u > ff ects the val-ues of M H and T rot derived using the RD method but using dataacquired at di ff erent epochs. We use the same seven availableOBSIDS of IRC + + ff erent observingepochs are shown in Fig. 6, and the results of the RD analysis aretabulated in Table 1, together with the remaining targets. Sincethree of the OBSIDs corresponding to the ODs 894, 1133 and1288 have a more restricted wavelength coverage, the fits to theRDs have an inherently larger uncertainty because the fit is moresensitive to the low number statistics. The error-weighted mean(single-fit) rotational temperature and mass are T rot ∼
520 K and M H ∼ × − M (cid:12) , respectively.In Fig. 9, we plot the temperature and the mass, for single-and double-temperature components, versus the operational dayof the observations. The bottom panel shows that the total gasmass deduced from the single-fit of the RD or for the warm andhot components does not reflect the line flux variability sinceit stays essentially constant with time about the average value(dotted lines), well within the estimated uncertainties.In a similar manner, the temperature of the warm compo-nent does not clearly reflect the CO line flux variations, since allmulti-epoch values are in good agreement within uncertainties.The hot component is the one that shows the largest variations(perhaps periodic) of the temperature, with T h going ∼
100 K( ∼ ∼
640 K) at OD 1087, and then re-laxing back to normal values in the remaining epochs. This vari-ation is echoed in the single-fit value of T rot ( ∼ P =
630 days to theRD parameters, we find that such model accommodates rea-sonably well the data points corresponding to T h (and also thesingle-fit T rot ). It is also possible that IRC + / indicate periodic variability.In summary, probably due to a compensation between thechanges in the y-intercept and the slope of the RD due to CO lineflux variations, which are largest for transitions with the highest J , the total gas mass M H appears to be quite robust to FIR pump-ing (non-LTE) e ff ects. These, however, could have a measurable,yet moderate impact on the rotational temperatures. Which have been reprocessed and are part of the THROES catalogue.12 of 30. M. da Silva Santos et al.: Warm CO in evolved stars from the THROES catalogue
800 900 1000 1100 1200 1300-10123300400500600700800
Fig. 9: Rotational temperature and mass versus operational dayin IRC + T rot variation with fixedperiod of 630 days (solid line). Bottom: total gas mass over time.In each panel, the dotted lines are the average of each componentand the asterisks mark unused data points in the fit (see text). Thecolor code is the same as in Fig. 6.
6. Discussion
The detection of high- J CO rotational lines is an indication of asignificant amount of molecular gas under relatively high tem-perature conditions. From our simple RD analysis we inferredthat the average gas temperatures of the layers sampled by FIRCO lines are much larger ( T rot ∼ −
900 K) than those typ-ically derived from mm / sub-mm observations, which are sensi-tive to < ∼
100 K gas from the intermediate-to-outer layers of theenvelopes of evolved stars (at ≈ -10 cm, see e.g. De Becket al. 2010; Schöier et al. 2011).In a number of targets we identified a double-temperature("warm" and "hot") component. Deviations from a single straightline fit to the RD have been found also in some of the O-richobjects in Paper I and in other previous works using, for ex-ample, ISO and / or Herschel / SPIRE CO spectra in a number ofAGB and post-AGB CSEs (e.g., Justtanont et al. 2000; Wes-son et al. 2010; Matsuura et al. 2014; Cernicharo et al. 2015b;Cordiner et al. 2016). AFGL 618 and IRAS 16594-4656 are thetargets whose RDs show the most obvious departure from linear-ity. IRAS 16594-4656 is particularly interesting since we found amuch cooler warm-component of just T w ∼
220 K, and a break-point at lower energies ( E u / k ≈ . T w ∼
450 K up to E u / k ≈ . M H and T rot ratios (Fig. 10), andfind that they are correlated. If the temperature profiles in the en-velope follow a power-law of the type T ( r ) ∝ r − α , with α beinga constant, then the trend in Fig. 10 should also follow approxi-mately a power-law function. We find α ∼ .
4, which is similarto the value found for the O-rich targets studied in Paper I. Thevalue of α is in agreement with past works that suggested thatthe kinetic temperature distribution is shallower, with values of α down to ∼ ∼ × -3 × cm) CSE lay-ers (De Beck et al. 2012; Lombaert et al. 2016; Matsuura et al.2014) than for the outer regions, where the steepest temperaturevariations ( α ∼ > ∼ cm; Teyssier et al. 2006).In addition to the average power-law exponent obtained byfitting all the targets simultaneously, we can also derive a valuefor each individual case applying: α = − log( T h / T w )log( M h / M w ) (2)as shown in the bottom panel of Fig. 10. In the case ofIRC + α = . ± .
06 which is in good agreementwith the power-law exponent in the inner CSE between 9 and 65stellar radii (i.e., up to ∼ × cm) deduced from detailednon-LTE excitation and radiative transfer models (De Beck et al.2012).Therefore, the empirical relation found between the hot-to-warm ratio of M H and T rot is consistent with the double- T rot component in some of our targets stemming (at least partially)from the temperature stratification across the inner envelope lay-ers. The two components in the RD do not necessarily imply twodistinct / detached shells of gas at di ff erent temperatures, but theymost likely reflect the temperature decay laws. As explained inPaper I, in case of LTE deviations (not impossible in the lowestmass-loss rate objects), the value of α obtained from this sim-ple approach would more closely represent the dust (rather thanthe gas) temperature distribution. This needs confirmation by de-tailed nLTEexRT models to the individual targets, which will bedone in a future publication. It is not possible to directly compare most of our results withliterature because past studies have been focusing on the cold,outer components of CSEs. Prior to
Herschel there was a studybased on ISO LWS data in roughly the same wavelength rangeby Justtanont et al. (2000) who also performed RD analysis(without opacity correction). They found T rot ∼ ±
90) K and T rot ∼ ±
30) K for AFGL 618 and AFGL 2688 respectively.We obtained similar results without opacity correction, but intro-ducing this e ff ect lowered these values to T rot ∼ ±
30) K and T rot ∼ ±
20) K. In AFGL 618 the central star is hot enough( T e ff ∼ T e ff ∼ J = − J = −
20 to infer the kinetic temperature profile across the CSEof IRAS 15194-5115. According to their model, T kin ∼
400 Kat r CO ∼ (1-2) × cm, which is in excellent agreement withour opacity-corrected single component T rot ∼
410 K for r CO = × cm. This is because, as already pointed out by Ryde et al.(1999), these high- J levels are mainly populated by collisions,therefore they are proxies for the kinetic temperature, at least out
13 of 30 & A proofs: manuscript no. rotdiag
Paper I -6 -5 -4 Fig. 10: Hot / warm temperature ratio versus hot / warm mass ra-tio for AGBs and post-AGBs and the power-law index. Top: thelines correspond to power-law fits with index α = . α = .
44 for the uncorrectedRDs (dashed); the open symbols correspond to the O-rich AGBstars in Paper I. Bottom: power law index for each individualtarget versus mass-loss rate (single fit).to a few ∼ cm. Also using ISO data, Schöier et al. (2002)presented a kinetic temperature model for CIT 6 that shows that T kin ∼ −
500 K at approximately r CO ∼ (1-2) × cm, whichis consistent with the warm component ( T w ∼
460 K) that weinfer and the representative radius r CO = × cm adopted.The hot component ( T w ∼
830 K) found by us would imply thatregions closer to the star have an important contribution to theemission of the highest- J lines.The only star whose inner / warmer (gaseous) CSE hadbeen studied in detail before using Herschel / PACS data isIRC + J CO spectral lines to infer the kinetic temperature profile asa function of radial distance. They find T kin ∼ −
600 K at r CO ∼ (1-2) × cm. Here we applied the opacity correctionfor r CO = × cm which seems to be the layer at which T kin ∼
300 K in their model. This is also the average value of T w that we found by fitting only the lowest J transitions, wichdoes not change appreciably with time despite strong line fluxvariability (Fig. 9). The hot component ( ∼ r CO ∼ × cm according to their model. Using Herschel / SPIRE data, Wesson et al. (2010) also per-formed RD analysis of CO spectra and derived T rot ∼ T rot ∼ T h ∼
900 K.For HD 44179 (the Red Rectangle) we obtained T rot ∼
440 K, which is about 2-3 times larger than the range of val-ues inferred by Bujarrabal & Alcolea (2013) from
Herschel / HIFIlower- J CO observations. It is not surprising that we find a largervalue since the higher J lines probed by PACS are probablyformed deeper inside the rotating circum-binary disk at the coreof this object. Meanwhile follow up analysis has shown moreclearly an outflow with ∼
500 K (Bujarrabal et al. 2016), butalso seems that such temperature conditions could exist in a re-gion of the inner disk with a radius of about r CO ∼ × cm,unresolved by PACS. The opacity correction would still be mod-erate for this value ( τ J = − ∼ . T rot ≈
410 K which is still within the un-certainties. For the remaining yPNes (IRAS 21282 + As in Paper I, we have compared the values of the mass-loss ratesderived from our simple RD analysis with other values foundin the literature mostly from low- J observations, paying specialattention to a few targets with detailed non-LTE excitation andradiative transfer analysis of CO data including at least somehigh- J transitions observed with Herschel . This is also a way ofascertaining the robustness of the RD method.Figure 11 shows our estimate of the mass-loss rate versusthat found in the literature (see Table B.2). For each target themarkers correspond to the single temperature component for theradius mentioned in Table 1, and the error bars represent the un-certainty in the radius for the adopted v exp . We show the com-puted opacities for the considered radii in each target in the sup-plementary Fig. A.1. The range of values found in literature areshown by the gray shaded area whose bounds are set by the max-imum and minimum ˙ M plus uncertainties when reported (factorof ∼ v exp and X CO here adopted.Similarly to the non C-rich THROES targets in Paper I, ourmass-loss rates are in good agreement with values in the litera-ture within the large uncertainties. In our case, these are domi-nated by the uncertainty in r CO . We see that the range of radiiwe explored yields a ˙ M that fits within the shaded area. In manycases, the error bars are truncated at the upper limit above whichthe line opacities would be too large to allow reliable estimatesof the masses and mass-loss rates (see Fig. A.1). For example, inthe case of AFGL 3068 this seems to imply smaller radius thanwhat we have adopted to better match the values in literature.In the case of IRC + r CO = × cm (instead of r CO = × cm) would result in a mass-loss of ˙ M ≈ . × − M (cid:12) yr − (not displayed) that would bestmatch the estimate from mm observations. However in these cir-cumstances the expected opacities in the lowest J lines wouldbe too large ( τ (cid:29) T w and T h areconsistent with kinetic temperature profile models as explained
14 of 30. M. da Silva Santos et al.: Warm CO in evolved stars from the THROES catalogue A F G L A F G L I R A S - C I T A F G L V C YGV
HYA I RC + A F G L HD I R A S - A F G L I R A S + C P D - H e n2 - -7 -6 -5 -4 Fig. 11: Comparison between the mass-loss rate in this work andthe literature. The markers correspond to the representative radiilisted in Table 1 for each target and the error bars are mass-lossrates for a given range of radii. The shaded area encloses therange of values found in literature scaled to the same parametershere assumed (see text).in Section 6.1. We find an average value of four OBSIDs of˙ M ∼ × − M (cid:12) yr − , which is lower than the range ˙ M ∼ (1-3) × − M (cid:12) yr − scaled from Teyssier et al. (2006); De Becket al. (2010, 2012); Guélin et al. (2017). However the value ob-tained for the warm component agrees with the lower limit ofthis range (because of the larger M H ). We obtain T w ∼
300 Kand ˙ M w ∼ × − M (cid:12) yr − for a radius of r CO = × cm, ingood agreement with the results of radiative transfer modelingof the same high J CO lines by Decin et al. (2010). Scaling their˙ M to the same d and X CO gives ˙ M ∼ × − M (cid:12) yr − with anuncertainty of a factor 2.For V Hya we obtained ˙ M ∼ × − M (cid:12) yr − which islower than ˙ M ∼ × − M (cid:12) yr − from Camps (2011) whoperformed radiative transfer calculations using the same PACSspectrum. In this case, however, the spatio-kinematic structureof the molecular outflow is more complex than assumed here. Inparticular, multiple kinematic (fast and slow) components seemto be present Hirano et al. (2004); Sahai et al. (2009), which notonly translates into a larger uncertainty in the characteristic valueof v exp in the PACS CO-emitting layers, but also implies that the"equivalent" mass-loss rate is particularly questionable.As for V Hya, for pPNe and yPNe, the assumption ofconstant-velocity spherically- symmetric mass loss may also nothold. For completeness, the mass-loss rates estimates for thesetargets are shown Table B.2, but they are subject to larger uncer-tainties and have to be interpreted with caution. We have checkedthat, even in these cases, our values are in good agreement withprevious estimates (making similar simplifying assumptions) inthe literature. For example, for the Red Rectangle, we obtained˙ M ∼ × − M (cid:12) yr − which is within the (scaled) range of˙ M ∼ (0.2-1.4) × − M (cid:12) yr − reported by De Beck et al. (2010). In summary, our results are consistent with the literaturewithin the typical uncertainties, but it is hard to tell what is theexact cause of the slight discrepancies from case to case. Oneobvious reason is that the simple RD method and our assump-tion of a characteristic value of r CO (unknown, but crudely con-strained from first principles and observations) only provides arough estimate of the mass-loss. We also note, that the bulk ofthe CO emission under study is produced in the warm inner lay-ers of the CSEs of our targets down to a location where τ ∼
1. Forvery optically thick CSEs, there may be an additional amount ofgas that is not fully recovered after the moderate opacity correc-tion applied. Another reason for ˙ M discrepancies is the di ff erentnumber of transitions and range of E u covered by di ff erent stud-ies. Non-LTE excitation and radiative transfer models of the COemission including a wide range of J - transitions is needed to ob-tain accurate estimates of the mass-loss rates and, in particular,to address ˙ M time modulations. In the Appendix we provide Fig. C.1 where we plot together theresults presented here to the ones obtained for the sample of O-rich and S-type stars in Paper I.We find that the range of T rot is approximately the sameamong C-rich and O-rich stars, but the O-rich AGBs have lessmassive CSEs by typically one order of magnitude, and lowerexpansion velocities. This in turn reflects on lower mass-lossrates on average. The scenario is reversed in the groups of PNeswith the few O-rich PNes having more warm gas than the carboncounterparts. Probably the O-rich AGB stars studied in Paper Iare typically low massive stars with very large evolution times,while the O-rich post-AGBs and PNe are very massive objectsthat have undergone through the Hot Bottom Burning stage.We stress that despite these trends being indicative of cleardi ff erences in the properties of the CSEs of the targets in theTHROES catalogue, they may not be a general property of C-rich versus non C-rich targets, since our samples are not nec-essarily unbiased and they are definitely not statistically signifi-cant.
7. Summary
In this paper (Paper II), we use
Herschel / PACS FIR spectraof a sample of 15 C-rich evolved stars, including AGBs, post-AGBs and yPNe, from the THROES catalogue (Ramos-Medinaet al. 2018b). These data contain valuable information about thephysical-chemical properties of evolved stars as shown, for in-stance, by the striking di ff erences of spectral features (molecu-lar, atomic / ionized and solid state) as a function of evolutionarystage. In this work, we focus on the rotational spectrum of CO(up to J = −
44) which was used as a proxy for the molecu-lar component of the gas in the warm regions of the CSEs. Ourfindings can be summarized as follows: – Due to
Herschel’s higher sensitivity compared to ISO, therange of detected CO transitions has been extended to highrotational levels of up to J u =
45 in low-to-intermediate massevolved stars. Rotational diagrams using high-excitationCO ( v =
0) rotational emission lines, with upper-level energies E u ∼
580 to 5000 K, have been plotted to estimate rotationaltemperatures ( T rot ), total molecular mass in the CO-emittinglayers ( M H ) and average mass-loss rates during the ejectionof these layers ( ˙ M ).
15 of 30 & A proofs: manuscript no. rotdiag – The range of temperatures found in our sample, T rot ∼ / sub-mm observations, and even Herschel / HIFI and SPIRE obser-vations, confirming that PACS CO lines probe deeper layersyet poorly studied to date (typically, ≈ cm for AGBs and ≈ cm for post-AGBs and yPNes).) – The total gas mass of the warm envelope layers sampled byPACS data are between M ∼ − − − M (cid:12) , with post-AGBs and yPNe being overall more massive. – We find clearly di ff erent temperature distributions for the dif-ferent classes with AGBs having typically hotter gas (up to T rot ∼ T rot < ∼
500 K) and yPNes( T rot < ∼
400 K). The yPN AFGL 618 is a clear outlier witha very high amount ( M H ∼ × − M (cid:12) ) of rather hot (up toT h ∼
900 K) gas, similar to the most massive AGBs in thesample. – For AFGL 3116, CIT 6, AFGL 2513, V Hya, IRAS 16594-4656 and AFGL 618 a double temperature (hot and warm)component is inferred from the RDs. The mean temperaturesof the warm and hot components are ∼
400 K and ∼
820 K,respectively. The mass of the warm component ( ∼ − -8 × − M (cid:12) ) is always larger than that of the hot component,by a factor ∼ – The warm-to-hot M H and T rot ratios in our sample are cor-related and are consistent with an average temperature radialprofile of T ∝ r − . , that is, slightly shallower than in theouter envelope layers, in agreement with recent studies. – The mass-loss rates estimated are in the range ˙ M ≈ − -10 − M (cid:12) yr − , in agreement (within the uncertainties) withvalues found in the literature for our targets. – We investigated the impact of CO line flux variability on thevalues of M H and T rot derived from the simple RD analy-sis. We studied in detail the case of the Mira-variable AGBstar IRC + ff erent epochs are minimally a ff ected. Only the hot com-ponent does show the sign of line variability ( δ T / T ∼ – Similarly to Paper I, we find an anti-correlation between T rot and M H , which may result from a combination of CO linecooling and opacity e ff ects, and we find a correlation be-tween ˙ M and v exp , which is consistent with the wind ac-celeration mechanism being more e ffi cient the more lumi-nous / massive the star is. These trends had been reported inprevious studies using low- J CO transitions.We show that high- J CO emission lines probed by
Her-schel / PACS are good tracers of the warm gas ( T ∼ −
900 K)surrounding evolved carbon stars. Using the simple RD tech-nique, we have provided systematic and homogeneous insightinto the deepest layers of these CSEs, though it relies on sev-eral approximations. Detailed non-LTE excitation and radiativetransfer calculations are needed to determine the temperaturestratification of the CSEs, to infer mass-loss rates and to addresstheir time-variability.
Acknowledgements.
We thank the referee for the useful comments and remarks.PACS has been developed by a consortium of institutes led by MPE (Germany)and including UVIE (Austria); KU Leuven, CSL, IMEC (Belgium); CEA, LAM(France); MPIA (Germany); INAF-IFSI / OAA / OAP / OAT, LENS, SISSA (Italy);IAC (Spain). This development has been supported by the funding agenciesBMVIT (Austria), ESA-PRODEX (Belgium), CEA / CNES (France), DLR (Ger-many), ASI / INAF (Italy), and CICYT / MCYT (Spain). This publication makesuse of data products from the THROES catalog, which is a project of the Cen-tro de Astrobiología (CAB-CSIC) with the collaboration of the Spanish Virtual Observatory (SVO), funded by the European Space Agency (ESA). J.M.S.S. ac-knowledges financial support from the ESAC Faculty and the ESA Education Of-fice under the ESAC trainee program. The Institute for Solar Physics is supportedby a grant for research infrastructures of national importance from the SwedishResearch Council (registration number 2017-00625). C.S.C. acknowledges fi-nancial support by the Spanish MINECO through grants AYA2016-75066-C2-1-P and by the European Research Council through ERC grant 610256:NANOCOSMOS.
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Appendix A.1: Opacity correction
In case of optically thick emission, an optical depth correctionfactor C τ should be added to the RD to compensate for an un-derestimation of the mass within the CO-emitting volume. Theoptical depth at the line center ( τ ) of a given CO ( J u - J l ) transitionis: τ = A ij λ N colu π V × [ e ( h ν/ kT ) −
1] (A.1) where V = v exp √ π/ (2 (cid:112) log 2) [km s − ] with v exp being the ex-pansion velocity of the gas, N colu = N u /π r is the column den-sity of the upper level, A ij is the Einstein coe ffi cient for sponta-neous emission and λ is the peak wavelength. It follows that thecorrection factor is written as: C τ = τ − e − τ (A.2)To compute C τ , we perform a first fit of the RD datapoints,ln (cid:16) N u g u (cid:17) , starting with null opacity correction (ln C τ =
0) whichyields initial (or opacity-uncorrected) values of T rot and N CO . Weuse these values to calculate τ and C τ and to apply the opacitycorrection, that is, ln (cid:16) N u g u (cid:17) = ln (cid:16) N u g u (cid:17) + ln C τ . A second fit toln (cid:16) N u g u (cid:17) is then performed, which renders the so-called opacity-corrected values of T rot and N CO (Table 1).We want to highlight that, as explained in Goldsmith &Langer (1999), the opacity correction is only reliable for moder-ate values of the optical depth. For this reason, for all objects inour sample, the minimum acceptable value of r CO used to com-pute the CO column density is always chosen so that it resultsin values of τ close to, but smaller than, unity (Fig. A.1). Indeed,the envelope layers where τ ∼ / C τ →
0) from deeper, optically thicker regions. As seen inFig. A.1, for r CO < ∼ × cm the opacity of the CO J = E u =
580 K), which is the optically thickest transition in our sam-ple, becomes larger than 1 in all our targets. The expected sizeof the CO-emitting volume in our sample is discussed in detailin Section. 4.The optical depth of the line is also sensitive to the expansionvelocity of the gas (Eq. A.1), which is unconstrained from PACSdata and has been assumed to be the terminal expansion velocityof the AGB CSE from the literature (values and references aregiven in Table B.1). In the case of pAGBs and yPNe, we adoptthe average expansion velocity of the bulk of the envelope fromdi ff erent previous works. The uncertainty of v exp is normally lessthan 10%. Appendix A.2: Model selection with BIC
Here we describe the method used to automatically find a breakpoint in the linear relation in the rotational diagram using theBayesian information criterion (BIC) .Our approach concerns the minimization of the RSS (resid-ual sum of squares) by computing the BIC for a range of possiblelocations of break points. The BIC can be regarded as a roughestimate of the Bayes factor (Schwarz 1978), and it is given by: BIC = n ln( RS S / n ) + k ln( n ) (A.3)where a penalty term, k ln( n ), penalizes model complexity de-pending on the number of parameters k and data points n (seealso Maindonald & Braun 2010). We also tested the Akaike’s in-formation criterion (AIC) (Akaike 1974), but we concluded thatfor this particular application it tends to overfit essentially be-cause the penalty term is smaller. In fact, due to the small num-ber of data points, we are not interested in splitting the rotationaldiagram too much in order to obtain robust results. It can happenthat BIC suggests more than one breakpoint due to the smalleraccuracy of the higher J line fluxes, and in that case only the Implemented in R using the package strucchange (Zeileis et al.2002). 19 of 30 & A proofs: manuscript no. rotdiag -1 AFGL 3068 -2 -1 AFGL 3116 -2 -1 V HYA -2 -1 IRAS 15194-5115 -2 -1 CIT 6 -2 -1 AFGL 2513 -2 -1 V CYG -2 -1 IRC+10216, 4 OBSIDS
Fig. A.1: Optical depth at line center ( τ ) as a function of the energy of the upper level ( E u ). τ was computed for a range of radii;the characteristic radius adopted ( r CO , Table 1) is marked with a thick line. In each panel, the inset shows the values of T rot and M H after the C τ correction has been applied for the corresponding radii, along with the opacity-uncorrected results (open triangle).first break point is taken into account. Obvious line blends wereexcluded upon the computation of both statistics.Figure A.2 shows the BIC test in a graphical way where wesee that the BIC curve is usually minimal at 0 or 1 breakpoints.For example for AFGL 2513 it is shown that the residuals of thefit keep decreasing with 2 breakpoints, although this is stronglypenalized by the BIC, so a 2-component fit is favored. On thecontrary, in AFGL 3068, IRAS 15194-5115 and IRC + ffi ces to reproduce the data.We note that these methods do not prove that a double tem-perature component is physically true, neither they provide analternative explanation for the trends in the data. They simply highlight hidden patterns in the residuals which can be causedby many e ff ects, being line blend the most obvious among them,or heteroscedasticity. Appendix B: Tables
20 of 30. M. da Silva Santos et al.: Warm CO in evolved stars from the THROES catalogue -3 -2 -1 AFGL 2688 -2 -1 HD 44179 -2 -1 IRAS 16594-4656 -3 -2 -1 AFGL 618
15 20660680700720 -3 -2 -1 IRAS 21282+5050
50 100 150150160170 -4 -3 -2 -1 CPD-568032 -4 -3 -2 -1 Hen 2-113
Fig. A.1: Continued.
21 of 30 & A proofs: manuscript no. rotdiag
Table B.1: Characterization of PACS observations.Target name Alt. name Class R.A. (J2000) DEC (J2000) OBSID Obs. dateAFGL 3068 LL Peg C-rich AGB 23 h m s .
39 17 o (cid:48) (cid:48)(cid:48) . h m s .
67 43 o (cid:48) (cid:48)(cid:48) .
52 13422125121342212513 2011-01-11IRC + h m s .
41 13 o (cid:48) (cid:48)(cid:48) .
60 1342221889134224132813422453951342246381134225375413422557411342256262 2011-05-292011-10-252012-05-052012-05-302012-10-212012-11-212012-11-30IRAS 15194-5115 II Lup C-rich AGB 15 h m s . − o (cid:48) (cid:48)(cid:48) . h m s .
28 30 o (cid:48) (cid:48)(cid:48) .
48 13421977991342197800 2010-06-05AFGL 2513 V1969 Cyg C-rich AGB 20 h m s .
25 31 o (cid:48) (cid:48)(cid:48) . h m s .
27 48 o (cid:48) (cid:48)(cid:48) . h m s .
25 21 o (cid:48) (cid:48)(cid:48) . h m s .
74 36 o (cid:48) (cid:48)(cid:48) .
68 13421992331342199234 2010-06-26HD 44179 Red Rectangle mixed post-AGB 6 h m s . − o (cid:48) (cid:48)(cid:48) . h m s . − o (cid:48) (cid:48)(cid:48) . h m s .
66 36 o (cid:48) (cid:48)(cid:48) .
28 13422258381342225839 2011-08-07IRAS 21282 + h m s .
42 51 o (cid:48) (cid:48)(cid:48) .
76 13422207411342223375 2011-05-122011-06-30CPD-568032 Hen 3-1333 mixed yPNe 17 h m s . − o (cid:48) (cid:48)(cid:48) . h m s . − o (cid:48) (cid:48)(cid:48) .
20 13422251421342225143 2011-08-02
Notes.
Target name, alternative name, evolutionary classification, coordinates given by right ascension (R.A) and declination (DEC), observationidentifier (OBSID) and observation date. The spectra correspond to bands B2B and R1 in IRC + Table B.2: Properties of stars and their CSEs taken from the bibliography.Target name Var. T e ff (K) d (pc) v exp (km s − ) ˙ M (M (cid:12) yr − ) referencesAFGL 3068 Mira 2000 1100 13 (0.9, 6) × − (0.8, 6.8) × −
2, 10, 23, 29AFGL 3116 Mira 2000 630 14 (4.6, 12) × − (1, 11.8) × −
2, 10, 23IRC + × − (0.05, 3.2) × −
2, 12, 23, 24, 31IRAS 15194-5115 Mira 2400 500 23 (0.4, 1.5) × − (0.08, 2.5) × −
2, 10, 13CIT 6 SRa 2450 440 21 (5, 6) × − (1.2, 11) × −
2, 10, 23AFGL 2513 Mira 2500 1760 26 2 × − (1, 4) × −
6, 14V Cyg Mira 2580 271 15 (0.4, 6.3) × − (0.08, 1.7) × −
2, 10, 15V Hya SR / Mira 2650 380 24 (0.25, 6) × − (0.03, 3) × −
1, 10, 17, 25AFGL 2688 7250 340 20 (0.7, 2) × − (0.06, 0.6) × −
3, 8, 19, 27HD 44179 7750 710 8.3 10 − -10 − − -10 −
5, 7, 10, 32IRAS 16594-4656 10000 1800 14 1 × − (0.4, 3.7) × −
9, 18AFGL 618 33000 900 80 (0.3, 2) × − (0.06, 0.7) × −
4, 16, 26, 27, 30IRAS 21282 + × − (1.5, 7.5) × −
11, 21, 26CPD-568032 30000 1530 22.6 (1.2-4) × − (1.2-4) × −
20, 28Hen 2-113 30900 1230 23 (6.3-8) × − (6.3-8) × −
20, 28
Notes.
Type of variability, e ff ective temperature ( T e ff ), distance ( d ), expansion velocity ( v exp ) and range of gas mass-loss rate ( ˙ M ) includinguncertainty, with and without scaling to the same X CO , d and v exp used in this paper on the right and left columns, respectively. In case there is onlyone ˙ M value in literature with no estimated uncertainty we assumed an error factor of 3 which is the typical uncertainty in mass-loss rates of AGBstars (e.g. De Beck et al. 2010; Ramstedt et al. 2008). References. (1)
Bergeat & Chevallier (2005), (2)
Ramstedt & Olofsson (2014), (3)
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Sánchez Contreras et al. (2004), (5)
Bujarrabal et al. (2016) (6)
Guandalini et al. (2006), (7)
Men’shchikov et al. (2002), (8)
Ishigaki et al. (2012), (9)
Mishra et al. (2015) (10)
DeBeck et al. (2010), (11)
Hasegawa & Kwok (2003), (12)
Cernicharo et al. (2015a), (13)
Ryde et al. (1999), (14)
Groenewegen et al. (2002), (15)
Neufeldet al. (2010), (16)
Huang et al. (2016), (17)
Knapp et al. (1997), (18)
Woods et al. (2005), (19)
Milam et al. (2009), (20)
De Marco & Crowther (1998), (21)
Likkel et al. (1988), (22)
Bujarrabal et al. (2016), (23)
Teyssier et al. (2006), (24)
De Beck et al. (2012), (25)
Knapp et al. (1999), (26)
Meixner et al.(1998), (27)
Bujarrabal et al. (2001), (28)
Leuenhagen et al. (1996), (29)
Sánchez Contreras & Sahai (2012), (30)
Wesson et al. (2010), (31)
Guélin et al.(2018), (32)
Bujarrabal & Alcolea (2013)
Table B.3: Carriers of some of the spectral lines detected towards our sample of C-rich evolved stars.Target Name Molecular Atomic / ionized DustCO HCN CS OH H O CH + [OI]63 . µ m [NII]121 . µ m [OI]145 . µ m [CII]157 . µ m forsterite69 µ mAFGL 3068 (cid:88) (cid:88) (cid:88) (cid:88) AFGL 3116 (cid:88) (cid:88) (cid:88) (cid:88)
IRC + (cid:88) (cid:88) (cid:88) (cid:88) IRAS 15194-5115 (cid:88) (cid:88) (cid:88) (cid:88)
CIT 6 (cid:88) (cid:88) (cid:88) (cid:88)
AFGL 2513 (cid:88) (cid:88) (cid:88) (cid:88)
V Cyg (cid:88) (cid:88) (cid:88) (cid:88)
V Hya (cid:88) (cid:88) (cid:88) (cid:88)
AFGL 2688 (cid:88) (cid:88) (cid:88)
HD 44179 (cid:88) (cid:88) (cid:88) (cid:88) (cid:88)
IRAS 16594-4665 (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88)
AFGL 618 (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88)
IRAS 21282 + (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) CPD-568032 (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88)
Hen 2-113 (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88)
23 of 30 & A proofs: manuscript no. rotdiag T a b l e B . : L i n e fl ux e s o f C O r o t a ti on a lt r a n s iti on s i n a s a m p l e o f C -r i c h e vo l v e d s t a r s . T r a n s iti on ν r e s t ( M H z ) λ r e s t ( µ m ) E up / k ( K ) A ij ( s − ) F ( × − W m − ) C O ( ν = ) C I T VH y a I R A S - A F G L V C yg J = → . . . . ± . . ± . . ± . . ± . . ± . J = → . . . . ± . . ± . . ± . . ± . . ± . J = → . . . . ± . . ± . . ± . . ± . . ± . J = → . . . . ± . . ± . . ± . . ± . . ± . J = → . . . . ± . . ± . . ± . . ± . . ± . J = → . . . . ± . . ± . . ± . . ± . . ± . J = → . . . . ± . . ± . . ± . . ± . . ± . J = → . . . ± . . ± . ± . ± . . ± . J = → . . . . ± . . ± . . ± . . ± . . ± . J = → . . . ± ± ± . ± . . ± . J = → . . . ± . ± . ± ∗ . ± . . ± . J = → . . . ± . ± . . ± . . ± . . ± . ∗ J = → . . . . ± . . ± . . ± . ∗ . ± . . ± . J = → . . . ± . . ± . . ± . . ± . . ± . J = → . . . . ± . . ± . ∗ . ± . . ± . ∗ . ± . ∗ J = → . . . . ± . . ± . . ± . . ± . . ± . J = → . . . . ± . . ± . ... . ± . . ± . J = → . . . . ± . . ± . ... . ± . . ± . J = → . . . ± . ± . ... . ± . ∗ . ± . ∗ J = → . . . ± ∗ . ± . ... . ± . ∗ . ± . ∗ J = → . . . . ± . ∗ . ± . ......... J = → . . . ± . ± . ∗ ......... J = → . . . . ± . . ± . ......... J = → . . . ± ∗ . ± . ∗ ......... J = → . . . . ± . ∗ . ± . ......... J = → . . . . ± . ∗ . ± . ......... J = → . . . ± ∗ . ± . ∗ ......... J = → . . . . ± . ∗ . ± . ∗ ......... J = → . . . . ± . . ± . ......... J = → . . . ............... N o t e s . T h ee lli p s i s m a r k a b s e n t o r no i s y ( S N R < ) li n e s , a nd a s t e r i s k s ( * ) fl a g li n e b l e nd s w h i c h m a yh a v eca u s e dov e r e s ti m a t e d fl ux e s .
24 of 30. M. da Silva Santos et al.: Warm CO in evolved stars from the THROES catalogue T a b l e B . : C on ti nu e d . A F G L A F G L A F G L HD I R A S - A F G L H e n2 - C P D - I R A S + . ± . . ± . ± . ± . . ± . ± . ± . . ± . . ± .
06 2 . ± . . ± . ± . ± . . ± . ± . ± . . ± . . ± .
05 2 . ± . . ± . ± . ± . . ± . ± . ± . . ± . . ± .
06 2 . ± . . ± . ± . ± . . ± . ± . ± . . ± . . ± .
04 2 . ± . . ± . ± . ± . . ± . ± . ± . . ± . . ± .
07 2 . ± . . ± . ± . ± . . ± . ± . ± . . ± . . ± . . ± . . ± . ± . ± . . ± . ± . ± . ± . . ± .
09 2 . ± . . ± . ± . ± . . ± . ± . ± . . ± . . ± .
08 2 . ± . . ± . ± . ± . . ± . ± . ± . . ± . ... . ± . . ± . ± . ± . . ± . ± . ± . . ± . ... . ± . . ± . ± ∗ ... . ± . ± . ± . . ± . ... . ± . . ± . ± ... . ± . ± . ± . . ± . ... . ± . . ± . ± ... . ± . ± . ± . . ± . ... . ± . ∗ . ± . ± ... ± ∗ ± ∗ ... b a d fi t ... ... . ± . ∗ ± ... . ± . a d fi t ∗ ......... ... . ± . ± ... . ± . ∗ ± ......... ... . ± . ± ... . ± . ............ ... . ± . ± ∗ ... . ± . ∗ ............ ... . ± . ∗ ± ... . ± . ............ ... . ± . ± ... . ± . ∗ ............ ... . ± . ± .................. ... ± ∗ ± ∗ .................. ... . ± . ∗ ± .................. ... . ± . ± .................. ... . ± . ± .................. ...... ± .................. ...... ± ∗ .................. ...... ± .................. ...... ± .................. ...... ± ..................
25 of 30 & A proofs: manuscript no. rotdiag T a b l e B . : C O li n e fl ux e s o f s e v e nob s e r v a ti on s o fI RC + . A s t e r i s k s fl a gkno w n li n e b l e nd s . T r a n s iti on ν r e s t ( M H z ) λ r e s t ( µ m ) E up / k ( K ) A ij ( s − ) F ( × − W m − ) C O ( ν = ) OD OD OD OD OD OD OD J = → . . . ± ± ± ± ± ± ± J = → . . . ± ± ± ± ± ± ± J = → . . . ± ± ± ± ± ± ± J = → . . . ± ± ± ± J = → . . . ± ± ± ± J = → . . . ± ± ± ± ± ± ± J = → . . . ± ± ± ± ± ± ± J = → . . . ± ± ± ± ± ± ± J = → . . . ± ± ± ± ± ± ± J = → . . . ± ± ± ± ± ± ± J = → . . . ± ± ± ± ± ± ± J = → . . . ± ± ± ± J = → . . . ± ∗ ± ∗ ± ∗ ± ∗ J = → . . . ± ± ± ± J = → . . . ± ± ± ±
26 of 30. M. da Silva Santos et al.: Warm CO in evolved stars from the THROES catalogue breakpoints breakpoints
Fig. A.2: Bayesian information criterion and residual sum ofsquares as a function of number of breakpoints. The BIC is givenby the solid line and the RSS is given by the dashed line. Thestatistic was not computed for IRAS 21282 + ffi -cient number of points.
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Appendix C: Supplement figures
28 of 30. M. da Silva Santos et al.: Warm CO in evolved stars from the THROES catalogue
200 400 600 80010 -6 -5 -4 -3 -2 -1
200 400 600 80010 -7 -6 -5 -4
200 400 600 80010 -4 -3 -2 -6 -4 -2 -4 -3 -2 -1 0 1 2 310 -7 -6 -5 -4 AFGL 618 IRAS 17347-3139HD 44179
10 20 30 40 50 60 70 8010 -7 -6 -5 -4 Fig. C.1: Supplementary plots. Temperature, mass, mass-loss-rate, line to continuum ratio and IRAS color of our sample of C-rich(filled symbols) and O-rich stars in Paper I (open symbols and magenta pentagrams). The color code is the same as in Fig. 1.
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0 2505007500 2505007500 2505007500 2505007500 2505007500 250500750 70 75 80 85 90 950 250500750 140 150 160 170 180 190
Fig. C.2: Spectra of IRC + ff erent epochs. Each row corresponds to a di ff erent observing day (from top to bottom: OD =745, 894, 1087, 1113, 1257, 1288, 1296). Same color code for the top tick marks as in Fig.2.