Variability in Proto-Planetary Nebulae: IV. Light Curve Analyses of Four Oxygen-Rich, F Spectral-Type Objects
aa r X i v : . [ a s t r o - ph . S R ] M a r VARIABILITY IN PROTO-PLANETARY NEBULAE: IV.LIGHT CURVE ANALYSES OF FOUR OXYGEN-RICH, FSPECTRAL-TYPE OBJECTS
Bruce J. Hrivnak, Wenxian Lu, and Kristie A. Nault Department of Physics and Astronomy, Valparaiso University, Valparaiso, IN 46383, USA;[email protected]. [email protected]
ABSTRACT
We present new light curves covering 14 to 19 years of observations of four bright proto-planetary nebulae (PPNs), all O-rich and of F spectral type. They each display cyclical lightcurves with significant variations in amplitude. All four were previously known to vary in light.Our data were combined with published data and searched for periodicity. The results areas follows: IRAS 19475+3119 (HD 331319; 41.0 days), 17436+5003 (HD 161796; 45.2 days),19386+0155 (101.8 days), and 18095+2704 (113.3 days). The two longer periods are in agreementwith previous studies while the two shorter periods each reveal for the first time reveal a dominantperiod over these long observing intervals. Multiple periods were also found for each object. Thesecondary periods were all close to the dominant periods, with P /P ranging from 0.86 to 1.06.The variations in color reveal maximum variations in T eff of 400 to 770 K. These variations aredue to pulsations in these post-AGB objects. Maximum seasonal light variations are all less than0.23 mag ( V ), consistent for their temperatures and periods with the results of Hrivnak et al.(2010) for 12 C-rich PPNs. For all of these PPNs, there is an inverse relationship between periodand temperature; however, there is a suggestion that the period − temperature relationship maybe somewhat steeper for the O-rich than for the C-rich PPNs. Subject headings: planetary nebulae: general — stars: AGB and post-AGB — stars: oscillations — stars:variable: general
1. INTRODUCTION
Proto-planetary nebulae (PPNs) are objects inthe short-lived evolutionary phase between asymp-totic giant branch (AGB) stars and planetary neb-ulae (PNs). This transitional phase in the evolu-tion of low- and intermediate-mass (0.8 − ⊙ )stars is expected to be several thousand yearslong, depending upon the mass of the star (Bl¨ocker1995). This relatively short time scale contributedto the initial difficulty in identifying stars in thisstage prior to the availability of data from the In-fraRed Astronomical Satellite ( IRAS ), which be-came available in 1984.
IRAS allowed the de- Present address: Adler Planetarium, 1300S. Lake Shore Drive, Chicago, IL 60605, USA;[email protected] tection of candidate objects based on their mid-infrared emission from circumstellar dust formedduring the late-AGB phase. A good summary oftheir discovery and properties is given by Kwok(2000), while their place in the broader contextof post-AGB stars is described by Van Winckel(2003).It soon became apparent that some of the PPNswere oxygen-rich (O-rich) and some were carbon-rich (C-rich). This was initially based on theirmid-infrared spectra as obtained by
IRAS andlater by the
Infrared Space Observatory ( ISO ).Those that were O-rich showed amorphous sili-cate features at 9.7 and 18 µ m, both in emis-sion and absorption (Volk et al. 1991), and ISO observations also revealed crystalline silicates ata number of wavelengths between 20 and 43 µ m1Molster et al. 2002). Those that were C-rich in-stead showed infrared aromatic bands between 3and 12 µ m (Hrivnak et al. 2000) that are usu-ally identified as due to polycyclic aromatic hy-drocarbon (PAH) molecules. High-resolution vis-ible spectra supported these mid-infrared chem-ical classifications, with the O-rich showing Cto O ratios (C/O) of ∼ − ⊙ (Lattanzio & Wood 2004). Thus one mightexpect different pulsational properties between O-rich and C-rich PPNs, since they result from starsof different masses and luminosities.
2. PROGRAM OBJECTS
The four program objects are listed in Table 1,along with some basic information. The spectraof all four have been classified as F supergiants.All have high-resolution spectral abundance stud-ies which not only show that they are O-rich,but that they are iron-poor, with [Fe/H] rang-ing from − − Initial attention to the unusual properties ofIRAS 17436+5003 (HD 161796, V814 Her) wasdrawn by Bidelman (1981), who listed it amonga small group of four supergiants located at highgalactic latitude. Following the launch of
IRAS ,Parthasarathy & Pottasch (1986) noted its largeinfrared excess and suggested that it might bea post-AGB object, as did Hrivnak et al. (1989),who included it in a multi-wavelength study ofa eight PPN candidates of F − G spectral types.Imaging with the
Hubble Space Telescope ( HST )revealed a small elliptical nebula with size of 4.4 ′′ × ′′ surrounding the bright star (Ueta et al.2000). The mid-infared ISO spectrum showsthe broad amorphous silicate emission features at9.7 and 18 µ m and additional crystalline silicatefeatures in the 15 − µ m region (Molster et al.2002). The basic properties of IRAS 18095+2704(V887 Her) were initially discussed by Hrivnak et al.(1988), who identified the
IRAS source with athen un-cataloged 10th magnitude star. Its
HST image shows an elliptical or perhaps bipolar neb-ula with a size of 1.9 ′′ × ′′ surrounding thebright star (Ueta et al. 2000). The mid-infared ISO spectrum displays silicate emission at 9.7 and18 µ m, and weak emission features in the regionfrom 10 − µ m that are attributed to crystallinesilicates (Hrivnak et al. 2015b). This object is an2H maser (Eder et al. 1988, OH 53.8+20.1). The basic properties of IRAS 19386+0155(V1648 Aql) were initially discussed by van der Veen, Habing, & Geballe(1989) in their study of post-AGB transitional ob-jects. Pereira et al. (2004) carried out a visibleand infrared spectroscopic study to determine thechemical composition of the star and to model itsenvelope. The SED shows only one broad peakreaching maximum energy in the region from 4.5to 25 µ m. This seems to indicate a relatively ob-scured and reddened central star. It has not beenobserved with HST , but it has been observed andresolved in the mid-infrared, with a size of 2.6 ′′ and possessing a bright core and extended halo(Lagadec et al. 2011). The mid-infrared ISO spec-trum shows the 18 µ m silicate emission feature andfeatures in the 10 µ m region that we interpret asself-absorption in the middle of a silicate emis-sion feature. (Hrivnak et al. 2015b). OH maseremission has been detected (Lewis 2000). The basic properties of IRAS 19475+3119 (HD331319, V2513 Cyg) were broadly discussed byGarc´ıa-Lario et al. (1997).
HST imaging showsthat the nebula has an interesting, quadrupolarshape surrounded by a faint halo (Sahai et al.2007). The mid-infrared
ISO spectrum showssome features identified as crystalline silicates(Sarkar & Sahai 2006).
3. PHOTOMETRIC OBSERVATIONS
Photometric observations were carried out atthe Valparaiso University Observatory (VUO) us-ing the 0.4-m telescope and a CCD detector. Theybegan in 1994 and continue through the presenttime; those reported in this study run through2012, except for IRAS 19386+0155, for which westopped observations in 2007. Initial observationswere made primarily through the V filter, withsome occasionally through the R C filter, but thefrequency of R C observations increased and since2000 they they have been made together. Unfortu-nately a problem developed with the V filter whichcaused us to reject the V data from the 2000 and2001 seasons and part of 2002. This led to a gapin each of the V light curves. Beginning in 2007, B observations were also made for all of the sourcesexcept IRAS 19386+0155. In 2008 we upgradedfrom a Photometric Star I CCD, with a field ofview of 8 . ′ × . ′
7, to an SBIG 6303 CCD, with afield of view of 17 . ′ × . ′
9. Filter sets were usedwith each to match the standard Johnson B and V and Cousins R C systems. The observations werereduced with IRAF , using standard proceduresto remove cosmic rays effects, subtract the bias,and flat field the images. Aperture photometrywas carried out with an aperture of 11 ′′ diameter.Given the frequently partially-cloudy nights atour site, we carried out a program of differentialphotometry. Three comparison stars were usedfor each of the program stars. Ideal comparisonstars would be a good match in color and bright-ness, but that was not achievable in these casesdue to the brightness of the program stars andthe size of the field of view of our CCD detec-tors. The comparison stars used are listed in Ta-ble 2. When we changed to the larger format CCD,we were able to include new, brighter comparisonstars C and C for IRAS 17436+5003, and theseare the ones that we have listed in Table 2. Foreach PPN, the constancy of the primary compar-ison star, C , was examined with respect to theother two comparison stars. The precision of theobservations is not as high as we would like dueto the large differences in brightness between theprogram and comparison stars. This restricted theintegration times to avoid non-linearity in the pro-gram stars, but consequently lead to less precisionin the comparison star observations. We find thecomparison stars to be reasonably constant overtime, to within ± ± IRAF is distributed by the National Optical AstronomicalObservatory, operated by the Association for Universitiesfor Research in Astronomy, Inc., under contract with theNational Science Foundation. V and R C differential photometry for the four pro-gram stars from 1994 to 2007 is listed in Table 4,except for the 2007 observing sets that included B also. Those are listed in Table 5 along with BVR C observations made with the newer CCD beginningin 2008.
4. VUO LIGHT CURVES4.1. IRAS 17436+5003
The VR C light and color curves of IRAS17436+5003 are displayed in Figure 1. The lightcurves possess a total peak-to-peak variation of0.23 mag in V and 0.18 mag in R C , with a rel-atively large variation in the yearly amplitudesand a slight variation in the yearly means. Thisvariability is superimposed perhaps on a slight,non-monotonic trend of increasing brightness of ∼ V ) over the 19 years of our obser-vations. The peak-to-peak range within a seasonvaries greatly, from 0.05 (2004) to 0.21 (2010) magin V and from 0.06 (2004) to 0.18 (2010) mag in R C , with an average ratio of the seasonal range of R C to V of 0.90. The variations are even largerin B and ( B − V ), with an average ratio of the sea-sonal B to V of 1.36 over the six years in which wehave B observations. Samples of the B light andthe ( B − V ) color curves are shown in Figure 2.The differential comparison star measurements∆ V (C − C ) show a relatively large amount ofscatter (see Fig. 1) due to the faintness of thecomparison stars relative to IRAS 17436+5003( V =7.0) and, from 1994 − star relative to C . There is ev-idence of a general increase in brightness of C by 0.02 mag ( V ) from 1994 to 2007; this is rela-tively small and would not affect our main results.Inspection of the seasonal light curves of IRAS17436+5003 shows in general a cyclical variationwith a period in the range of ∼ −
50 day. Attimes, however, it appears as though the variationhas gone away, such as at the ends of the 2009 and2011 observing seasons (e.g., Fig. 2).The ( V − R C ) color of the system shows a vari-ation of 0.07 mag peak-to-peak (except for fouroutlying points), with most of the data within arange of 0.05 mag; the ( B − V ) color range is larger, reaching 0.12 in 2010, with most of the data withina range of 0.07 mag. An inspection of the lightand color curves shows that, in general, there is atrend of color with brightness, being redder whenfainter. This can perhaps be seen more clearly ina plots of ∆ V versus ∆( V − R C ) and ∆ V versus∆( B − V ), as shown in Figure 3. The VR C light curves for IRAS 18095+2704 areshown in Figure 4. They display a general trendof increasing brightness over the two decades ofobservations, increasing by 0.30 mag in V from1994 − R C from 1995 − V − R C ) color of the system, < − − V from 0.05 (1997) to 0.14 mag (2003) and in R C from 0.02 (1997) and 0.04 (1999) to 0.11 mag(2003). For years in which we have good coveragewith both filters, the average ratio of the ampli-tude in the two ( R C compared with V ) is 0.86.In the six years in which we observed consistentlywith all three filters, the average ratio of the am-plitude in B to V is 1.29. Samples of the morerecent B and color data, showing the cyclical vari-ations, are shown in Figure 2.Looking at the ( V − R C ) color (Fig. 4), it canbe seen that in general it follows the cyclical vari-ation, being redder when fainter. This is perhapsseen even more clearly in the ( B − V ) data (Fig. 2).Plotted in Figure 3 are the ∆ V versus ∆( V − R C )and ∆ V versus ∆( B − V ) data sets, with the mono-tonic trend in ∆ V brightness first removed usinga low-order polynomial fit. The ( V − R C ) color be-tween the two different CCD systems have beenadjusted by the small offset of − V − R C ) is 0.06 mag, with most within a rangeof 0.04 mag, the range in ∆( B − V ) is 0.09 mag,with most within a range of 0.05 mag.4 .3. IRAS 19386+0155 IRAS 19386+0155 also displays a general in-crease in brightness over the interval of observa-tion (1994 − V over 14 years. Duringthis time, there is a suggestion that the ( V − R C )color was bluer by 0.02 mag in the first severalyears, but this result is uncertain since it is basedon only a small number of R C observations in theyears 1995-1997 compared with the later observa-tions from 1999 and from 2002 through 2007.A cyclical variation is also seen in the seasonaldata, with a varying amplitude. The amplituderanges in V from 0.07 (1996, 1997, 1999) to 0.20mag (2003). There are many fewer R C observa-tions in the early years, but from 2003 through2007, the ratio of amplitudes ( R C compared with V ) is 0.84.When comparing the seasonal ( V − R C ) colorvariations with the seasonal cyclical variations inbrightness (Fig. 5), one can see a general patternof the object being redder when fainter. This canbe seen clearly in Figure 3, following the removalof the brightness trend in V using a low-order poly-nomial fit. The range in color is small, ∼ The light curves of IRAS 19475+3119 show nolong-term trends in brightness, although they doshow some small variations in the mean seasonalbrightness and some changes in the seasonal rangein brightness. These are seen in Figure 6. Theseasonal range in V brightness varies from lows of0.07 (1995, 1997) and 0.08 (2010) mag to highs of0.19 (2009) and 0.17 (2003) mag. The range in R C is typically less, with an average ratio ( R C com-pared with V ) of 0.94, and the range in B is typi-cally more in the six years in which it is observed,with an average ratio ( B to V ) of 1.29. Visualinspection of the seasonal light curves shows cycli-cal variations in brightness, and in several of theseasons (1996, 1998, 2003, 2008, 2009, and 2010)one can discern a cycle length of 30 −
50 day (seeFig. 2).The overall color of the system does not varymuch, with the ∆( V − R C ) value mostly withinthe range of 0.035 mag and ∆( B − V ) value mostlywithin the range of 0.04 mag. When one examines the seasonal light and color curves, one can see atrend, with the object fainter when redder (seeFig. 2). Such a trend can be seen clearly whenlooking at the overall brightness-color curves, asshown in Figure 3.
5. COMBINED LIGHT CURVES & PE-RIOD ANALYSES
All four of these PPNs are known to be variablein light and have been included in prior studies byother investigators. This is particularly true ofthe brightest of these sources, IRAS 17436+5003,which has been observed by several investigators,particularly Fernie. The other three sources havebeen observed extensively by Arkhipova and col-laborators, as described below. Their
UBV obser-vations are carried out with a single-channel pho-toelectric photometer using a 27 ′′ aperture, andthey tied their observations to the UBV systemby observations of standard stars. Data are alsoavailable for two of the objects in the V band fromthe All Sky Automated Survey (ASAS; Pojmanski2002) .The availability of these additional observationsaffords an opportunity to enlarge the data sample,either in time or density or both, with the promiseof better documented light curves. These in turncan yield better determined results for the periodanalysis, including the determination of multipleperiods. This is, of course, predicated on the abil-ity to accurately combine the different data sets.All of the investigators made differential observa-tions, as we did, and to combine them requires ac-curate standardized measurements of the variouscomparison stars. Since different investigators usedifferent comparison stars and different aperturesizes, this can potentially lead to slight zero-pointoffsets in the magnitudes in the different data sets.To correct for such offsets, we compared the vari-ous data sets where they overlapped in time, to de-termine and correct for any such offsets. These arediscussed for each star. These individually-derivedoffsets are well established, based on a minimumof 18 nights, and are listed in Table 6, along withaccess to the published data sets. We briefly dis-cuss these other studies, star by star, along withthe resulting combined light curves, and we thenproceed to the period analyses of each. V data sets and then examined the data insubsets. For IRAS 18095+2704 and 19386+0155,the general trends were first removed. The lightcurves each show some variations in the yearlymeans. We first searched the data sets for pe-riodicity with these included, in case there werelonger-term periodicities that these represented.For none of these PPNs was a significant longer-term periodicity found, so we then normalized, oradjusted, the yearly data by the yearly means andthen did the final period analyses on the adjusteddata sets. Due to its brightness and its unusual distinctionof being a high-latitude object with a supergiantspectrum, IRAS 17436+5003 (HD 161796) becamethe target of many variability studies even beforeit was identified as a PPN. The most extensiveof these was by Fernie and collaborator (Fernie1983, 1986, 1989, 1990a,b, 1991; Fernie & Seager1993, 1995), who carried on a long series of obser-vations including most years from 1980 through1998. They always include V observations andfrom 1986 to 1998 the observations are UBV . Be-ginning in 1986, the observations were made withan automated photoelectric telescope at a goodsite, and the number of annual observations in-creased significantly.We combined with our V observations the longand consistent data set of Fernie’s. In compar-ing the data of Fernie’s with ours during the over-lap from 1984 to 1998, we find that there are 22dates on which we observed on the same night,and from these we find an average offest of 0.000 ± − V light curve is displayed in Fig-ure 7. The agreement of the different data sets isgood in the regions of overlap and very usefully increases the temporal coverage. The light curveshows a general increase in brightness of 0.04 magfrom 1984 to 2012, but the increase is not strictlymonotonic. The yearly amplitude is seen to varythroughout this interval by a factor of three tofour. The combination of our data with those ofFernie and Percy & Welch gives us a relatively-long time interval of 34 years of data for IRAS17436+5003. This affords a good opportunity tonot only find the best period(s) for the entire dataset, but to also examine the observations in smallertime intervals to investigate period changes. Thedata sets were first adjusted to the mean bright-ness of each year. Years with fewer than ten datapoints were not included.The analysis of the entire V data set (set A)revealed in several closely-spaced frequencies, ascan be seen in Figure 8. The analysis revealeddominant periods of P = 45.15 ± = 47.36 days, and P = 46.75 days. There are intotal eight significant periods in the data; we havelisted the first six in Table 7. The data, phased toP = 45.15 days, are also displayed in Figure 8.They show a reasonably good phased light curve,considering the observed range in amplitude seenin the light curve. The fit of the periods and ampli-tudes to the normalized light curve is remarkablygood for most of the time interval, as can be seenin the lower five panels of Figure 7. It is only inthe last decade, 2003 − −
46 days. Fernie also drew attentionto some epochs in which the star appeared to notvary (Fernie 1993). Some of this complexities seemto be resolved by our inclusion of multiple periods.The data were then examined in subsets andthe results are also listed in Table 7. The anal-ysis of the Fernie and Percy & Welch data (setB, 1979 − = 45.08 ± = 46.54 days, and P = 47.45 days; these are6early the same as the first three periods seen inthe entire data set. This is perhaps not surprising,since their data comprise two-thirds of the numberin the entire data set. The analysis of the com-plete VUO data (set C, 1994 − = 47.30 ± in theentire data set (A), and a value for P that agreeswith P in the entire data set. Similar results werefound in the VUO R C data (set D, 1997 − V data infive or six year intervals. The 1994 − = 44.09 and P = 42.38 days; the sec-ond of these agrees with P of the entire VUO V data set (C). The 2003 − = 41.47 and P = 56.87 days; this value of P does not appears in any of the other data sets.The 2008 − = 47.42 andP = 57.70, and P = 38.14 days; P agrees withthe value found for P in the complete VUO dataset (C) and P is similar to the value of P foundin the 2003 − P that arefound in only certain time intervals (sets E, F).This suggests that there are indeed changes in thedominant periods with time. However, there doesnot appear to be a monotonic increase or decreasein the period over time, as seen by the compari-son of the P values in subsets E, F, and G. Onecan also meaningfully compare the ratio of thetwo dominant periods, particularly in the longerdata sets (A, B, C, D). They are all close in value,ranging from 1.03 to 1.06, with an average valueof 1.05. IRAS 18095+2704 was observed by Arkhipova et al.(1993, 2000, 2010) for 19 years, beginning withonly a few observations in 1990 − ± B and V . Their observa-tions show a clear trend of increasing brightness,as we found, with an increase of 0.37 mag in V ,0.35 mag in B , and 0.32 mag in U over 19 years,with the (B − V) color staying approximately con-stant. Examining some older photographic ob- servations, they find that this brightness trendextends back to the earliest measurements fromthe mid-1930s. From their 2000 − ± V data with theirs, we firstcompared the two data sets. There are 24 nightsin common between the two data sets, with a sys-tematic difference (VUO − Arkhipova) of − − − ± ∼
105 days. However, we did not combine thesedata with ours.A combined V light curve was formed by addingthe Arkhipova et al. data set from 1993 to 2008to ours, using the offset determined. This is dis-played in the top panel of Figure 9, and shows anincrease in brightness of 0.40 mag over this 20-year interval. To prepare the combined data setfor analysis, we first removed the trend in eachdata set separately using a low-order polynomial,and then adjusted the seasonal light curves to thesame mean levels. This adjusted V light curve isshown in the bottom panel of Figure 9. Close ex-amination of the seasonal light curves shows goodagreement between the two data sets and servesto better document the cyclical variability. We began with a period analysis of the com-bined, adjusted V light curve of IRAS 18095+2704,which covers the longest time interval, 1993 to2012, and has the largest number of data points(set A). The frequency spectrum showed several7elatively strong peaks, and the subsequent anal-ysis indicated multiple periods in the data. Thestrongest period was P = 113.3 ± are shown Figure 8, and the presence ofthese additional periods is seen in the frequencyspectrum. Six significant periods are found in thedata, and these are listed in Table 7.In Figure 9 is also shown the fit of the firstfour periods, along with their associated ampli-tudes and phases, to the observed light curve. Thefit is reasonably good, given the complex natureof the light curve and the long interval of obser-vations (20 years), and improves slightly with theinclusion of the two additional significant periods.Subsets of this V light curve and of some ofthe light curves with other filters were also investi-gated. We began by dividing the combined V dataset into two ten-year time intervals. For the timeinterval 1993 − = 98.2 days, close to P in the full V data set,and an additional significant period of 107.5 days(close to P in the full data set). For the interval2003 − = 111.8 days, close to P in the full V data set, andadditional periods of 110.2, 103.1 (close to P inthe full data set), 68.3, and 97.2 days; the periodsof 111.8 and 110.2 in the 2003 − V data setare close to and beat against one another. Notethat a formal analysis of the ASAS 2003 − V light curve results in a period of 110 ± B light curve, formed by re-moving the trends from the Arkhipova et al. andthe VUO data, including the determined B offset,and adjusting to the individual seasons. Excludedwere two years with fewer than 10 observations.This data set (D) yielded periods in agreementwith those found for the combined V light curve,P = 113.5 days and additional periods of 103.0,154.5, 97.9, and 116.3 days, and with larger ampli-tudes than found for the V analysis. We also inves-tigated the VUO R C light curves from 1998 − − R C lightcurves have smaller amplitudes. These periods are also recorded in Table 7. Based on the combined,full V light curve (set A), we find a ratio of P /P = 0.86. Arkhipova et al. (1993, 2000, 2010) also ob-served IRAS 19386+0155 for 19 years, again be-ginning with only a few observations in 1990 − ± B and V .Their observations show a clear trend of increas-ing brightness with time. They determined an in-crease in V of 0.2 mag but find that surprisinglythe (B − V) color gets redder by 0.1 mag duringthis time. From the 2000 − /P = 0.96. They note that during this cyclicalvariation the system is bluer when brighter, as wefound.To combine our V data, we compared the twodata sets and found that there are 12 nights incommon, with a systematic difference (VUO − Arkhipova) of +0.060 mag and another 26 suc-cessive nights of observations, with a difference of+0.061. This yielded a weighted value of +0.060mag, with those on successive nights receiving halfweight.IRAS 19386+0155 was also observed with in theASAS sky survey from 2002 through 2009. We ex-amined the data set of 766 V observations, whichhad a average uncertainty of ± − V light curve was thus formed byadding the Arkhipova et al. data from 1993 − The combined VUO and Arkhipova et al. V light curve of IRAS 19386+0155 was analyzed for8ariability. The trend of increasing brightness wasfirst removed by fitting it with a low-order poly-nomial. The light curve analysis shows two dom-inant periods in the data, with P = 101.8 ± = 98.6 ± are shownin Figure 8. These are the same periods foundby Arkhipova et al. (2010) based on their dataset alone. Three additional significant periods arefound in the combined data, and these are listedin Table 7. Similar results were found, whetheror not we adjust the data to the means of the in-dividual seasons. We have listed in the table andshown in the figures the results with data adjusted(set A). The fit is reasonably good over this 16-year interval. Based on the combined, full V lightcurve (set A), we find a ratio of P /P = 0.97.We then investigated the periodicities using sub-sets of the adjusted V data − from 1993 − − − and also the VUO R C data from 2002 − V data set.We also investigated the ASAS V data set from2002 − ± − ± ± − IRAS 19475+3119 was observed by Arkhipova et al.(2006) over a four-year interval from 2002 to 2005,resulting in 104
UBV measurements. They re-ported that the object showed semi-regular bright-ness variations with a maximum range of 0.17 magin V , and a larger range in the shorter bandpasses.This agrees with the variations that we find. Theyalso reported that they did not find a statistically-significant period for the entire data set, but pe-riods were found for individual years of 43 ± ± UBV measurements.Since their data set falls within the time rangeof ours, including their data will not extend thebase line but will increase the density of obser-vations during that five-year interval of overlap.Comparing V observations from the two data setsrevealed an offset in observations made on thesame day of (VUO − Arkhipova) of − − − V light curve with the offset included isdisplayed in Figure 11. Visual inspection seasonby season shows good agreement between the twodata sets. A period analysis of IRAS 19475+3119 was firstcarried out on the combined V light curve. We an-alyzed the light curve both with and without ad-justing the data to the seasonal means. The sameresults were obtained in both cases, with two sig-nificant periods, P = 40.95 ± =38.85 ± R C light curve (set B) also resultedin two similar periods. These period results arelisted in Table 7. The frequency spectrum andthe phased light curve plot based on P for thecombined and adjusted V data are shown in Fig-ure 8. Both the V and R light curves also gaveevidence of a third period, P = 48.1 days, with aS/N = 3.9, slightly below our significance level of4.0. However, given that it is seen in both of thedata sets, we regard it as significant. These eachyield a ratio of P /P = 0.95.In Figure 11 is displayed the adjusted V lightcurve for the combined data, fitted with the threeperiods and associated amplitudes and phases.The fit for this star is not as good as that foundfor the other three, and we attribute much of thisto the complexity of the pulsations of this star.A better fit could likely be obtained with time-dependant amplitudes. PPNs have been shown toproduce shocks as they pulsate (L`ebre et al. 1996;Zaˇcs et al. 2009). A spectroscopic and photomet-ric study of the similar (F5 I, P ∼
39 days) butcarbon-rich PPN IRAS 07134+1005 (HD 56126,CY CMi), with a similarly complex light curve,displayed strong evidence for shock waves in its9tmosphere (Barth`es et al. 2000).We also analyzed the light curves in subsets andusing the other filters. Analyses of the V (set C)and R C (set D) light curves from 2002 − and P to the full data sets.Only the V light curve for the interval 1994 −
6. DISCUSSION
We have analyzed light curves that span timeintervals from 16 to 34 years for four bright, O-richPPNs, all with F spectral types, Dominant periodswere determined for all four, with values rangingfrom 41 to 113 days. Similar, although less robustvalues, had been found in previous studies. Thesevalues fall within the range found for other F − Gspectral type PPNs, in particular the 12 C-richones analyzed by Hrivnak et al. (2010) that spanthe period range of 38 to 153 days. A similar rangewas found for eight C-rich PPNs in the MagellanicClouds (Hrivnak et al. 2015a, Paper III).We also analyzed the light curves within subsetsof five to ten year time intervals. These analysesoften resulted in different dominant period valuesin different time intervals, indicating that signif-icant period changes do occur. In a majority ofcases, P increased with time, but not in all cases.In a previous period analysis of two C-rich PPNswith similarly long sets of observations, we foundthat in one case there was no significant change inP and in the other P decreased (Hrivnak et al.2013). With this present small sample, we con-clude that no clear trends in period change emergewhen comparing the data sets for an individualstar in different time intervals. The results ofthe larger sample of 12 PPNs had suggested thatP decreases with time (Hrivnak et al. 2010), butthat result is not seen over the longer two-decadetime span of these studies.Multiple periods were found for all four PPNs,and they were always close in value to the dom-inant period. Similar results have been found in detailed light curve studies of other PPNs(Hrivnak et al. 2013, 2015a). The ratios of P /P for these four range from 0.86 to 1.05, with anaverage value of 0.96. These are summarized inTable 8. They are similar to the ratios found inprevious studies by Hrivnak et al. (2013, PaperII) for two PPNs (0.95), by Hrivnak et al. (2015a,Paper III) for seven PPNs (0.86 − − − − luminosity relationships derived for post-AGB stars (Bl¨ocker 1995; Vassiliadis & Wood1994). At present, there are only a few investi-gations of pulsation of post-AGB stars, and theagreement with observations is not good. Aikawa(2010) ran linear, radial pulsation models of post-AGB stars with masses of 0.6 and 0.8 M ⊙ andpresented graphically the results for the temper-ature range 5000 − g in the rangeof 0.0 − eff =6300 K and T eff = 7000 K and log g in the rangeof 0.2 to 1.0, the closest parameters to our stars.The fundamental modes were all stable except forthose with T eff = 6300 K and log g ≤ ⊙ but of temperatures in the range of 5600 to 6000K, cooler than our stars. We previously comparedthem with our observational results of two coolerPPNs, but they also resulted in periods that weretoo short and pulsational amplitudes that were10oo small (Hrivnak et al. 2013). This commendsfurther pulsational modeling of post-AGB stars inthe temperature range of 6000 − − G stars, we(Hrivnak et al. 2010) found a monotonic, approxi-mately linear decrease in period ( P ) with effectivetemperature ( T eff ) over the range of 5000 to 8000K. While we do not have a long enough observinginterval to see an individual star change in T eff or P , we can interpret this trend of decreasing P with increasing T eff to represent the averageexpected evolution of these stars as they evolvefrom large, cool AGB stars to the small, hot cen-tral stars of PNs. Since they evolve toward highertemperatures at approximately constant luminos-ity, they must be decreasing in size and increasingin density (ongoing mass loss is small). There-fore, assuming radial pulsations, we would expecta decrease in period as they evolve. A compar-ison with five C-rich PPNs in the Large Magel-lanic Cloud (LMC) showed that they also follow asimilar monotonic trend, although perhaps offsetslightly to lower T eff or shorter P (observationsof more periodic LMC PPNs are needed to con-firm this offset). In Figure 12 is plotted the P and T eff values for the four O-rich PPNs examined inthis study, together with the 12 C-rich ones fromthe Milky Way Galaxy. Note that we have in-cluded two points each for IRAS 17436+5003 andIRAS 19475+3119, since there are two different T eff values published for each. A straight line fitto the data points for these 4 O-rich PPNs wouldbe nearly vertical and possess a much steeper thanthat found for the C-rich ones. However, thispresent sample is small and all of the points, ex-cept one of those for IRAS 17436+5003, fall withinthe range of the C-rich data points. When we com-pare the pulsation amplitude (∆V) with their pe-riods and temperatures (see Table 8), they agreewell with the monotonic trends found for the C-rich sample; all of the objects with periods shorterthan 120 days and temperatures higher than 6000K have maximum amplitudes ≤ P − T eff relationship forthese four O-rich PPNs appears to have a muchsteeper slope than is found for the 12 C-rich PPNs.This may not be significant, since it is based on only four objects over a smaller temperaturerange (1000 K), and the O-rich PPNs generally fallwithin the distribution of the C-rich sample. If it isreal, one suggestion is that it relates to the differ-ence in metallicity between the two longer-periodobjects (P ≈
110 day, [Fe/H] ≈− ≈
45 day, [Fe/H] ≈− − − and IRAS 19386+0155 by 0.13 magover 14 years or 0.009 mag yr − . Similar mono-tonic trends, some decreasing and some increas-ing, have been found in the light curves of otherPPNs of F − G spectral types. Including these four,periods have been determined for a total of 26PPNs of F − G spectral types, 19 in the MWGand 7 in the Magellanic Clouds, for which ob-servations cover intervals of at least nine years(Hrivnak et al. 2010; Arkhipova et al. 2010, 2011;Hrivnak et al. 2015a). Of these, five show mono-tonic increases of ∼ − − , two showmonotonic decreases of ∼ − , and oneshows a light curve that is constant in brightnessfor six years, then shows a sudden drop of 0.12mag in one year, and then a gradual increase of0.019 mag over nine years. Two others show somelarger changes ( ∼ − − V)= 0.23-0.32 for F2 − ≥ µ m) grains, which would appear grey and not colorselective, as noted by Arkhipova et al. (2010).All four of these PPNs are redder, and thuscooler, when fainter. This is what is com-monly found in PPNs of F − G spectral types(Arkhipova et al. 2010, 2011; Hrivnak et al. 2010,2015a). Hrivnak et al. (2013) found in the de-tailed study of two PPNs that included contem-poraneous light, color, and velocity curves, thatthe stars were smallest when brightest and hottest.This differs from what is found in Cepheid vari-ables, in which there is a phase lag of ∼ B − V ) changesand the temperatures determined from the spec-troscopic analyses, these color changes were trans-formed to temperature changes using the color-temperature table of Cox (2000, Table 15.7). Thisresulted in maximum temperature changes of 400to 770 K, which are attributed to pulsation. Ofthe two PPNs with multiple spectroscopically-determined temperature values, for one of them(IRAS 17436+5003) the difference between thetwo spectroscopic temperatures is less than therange determined from the color range, and forone of them (IRAS 19475+3119), the differenceis slightly greater, but within the uncertainty ofthe temperature determinations. We investigatedthe epochs of the high-resolution spectra used todetermine the temperatures, to see if they couldbe correlated with specific phases in the lightcurves. For IRAS 17436+5003, the higher tem-perature spectrum was obtained near maximum brightness and bluest color (see Fig. 7), while thelower temperature spectrum was obtained whenthere were no contemporaneous light curves. ForIRAS 18095+2704, the spectrum was taken nearmaximum brightness and bluest color (see Fig. 9),and for IRAS 19386+0155, between maximum andaverage brightness (see Fig. 10). Of the two spec-tra of IRAS 19475+3119, the higher tempera-ture one was obtained near maximum brightnessand the lower temperature one at an epoch withfew photometric observations and no clear phas-ing of the brightness. Thus, for the two objectswith multiple spectroscopic temperature determi-nations, the higher temperatures are associatedwith the greater brightness in the light curves, con-sistent with the brightness-color correlations foundfrom the light curves.
7. SUMMARY AND CONCLUSIONS
In this paper, we have carried out a detailedlight curve and period study of four bright PPNs.They each had previous light curve and periodstudies, but by combining these data sets withours, we have significantly increased the samplesize and the time intervals of observation. The pri-mary results are listed below. They serve to helpelucidate the pulsation properties of intermediate-and low-mass post-AGB during this short transi-tion stage from the AGB to the PN phases.1. The four vary in light with changing am-plitudes; these amplitudes vary between 0.05 and0.25 mag, peak to peak.2. Two of them also show long-term trendsof increasing brightness, with values of 0.13 and0.30 mag over 14 and 19 years, respectively, cor-responding to 0.01 − − . Long-termtrends have been observed in about 30% of thewell-studied PPNs, with five showing clear mono-tonic trends of increased brightness and two of de-creased brightness. We attribute these to changesin the circumstellar dust opacity.3. A dominant period was found in each ofthe four, with values ranging from 41 to 113 days.Similar periods had previously been found forthree of these based in smaller data sets. These Sahin et al. (2011) obtained two separate spectra, observed10 months apart. Since they based the analysis primarilyon the first of these, this is the epoch we investigated. − G spectral types of 38 to 153 days.4. In each of the four PPNs, multiple peri-ods were determined. These account for muchof the variation in amplitude seen in the lightcurves. In all cases, the secondary period is closeto the primary period, with an average value ofP /P of 0.96. This is similar to the range of val-ues of 0.9 − − G spectral type PPNs.These four O-rich ones have a steeper slope to theirtrend, but the sample is too small to determineif the slopes differ between PPNs with differentchemistries.6. All four are redder when fainter, in agree-ment with the brightness-color relationship foundin other well-studied PPNs. The maximum(B − V) color changes range from 0.055 to 0.105mag, which imply changes in effective tempera-ture of 400 −
770 K.We have begun photometric studies of addi-tional, fainter O-rich PPNs, which will help toenlarge the sample and increase the range in tem-perature. These should help to better define theperiod-temperature-amplitude relationships forO-rich PPNs and allow a more robust compari-son with C-rich PPNs.We want to acknowledge the many VU un-dergraduate summer research students who par-ticipated in this long-term research program:Danielle Boyd, Laura Nickerson, Paul Barajas, Ja-son Webb, Bradley Spitzbart, George Lessmann,Will Herron, Richard Maupin, Emily Cronin,Ryan Doering, Shannon Pankratz, Andrew Juell,Daniel Allen, Justin Lowry, Kathy Cooksey, Jef-frey Eaton, Nicolas George, Katie Musick, SarahSchlobohm, Brian Bucher, Kara Klinke, KristinaWehmeyer, Bradley Rush, Byung-Hoon Yoon, Jef- frey Massura, Marta Stoeckel, Larry Selvey, Ja-son Strains, Ansel Hillmer, Erin Lueck, JosephMalan, Callista Steele, Ryan McGuire, Christo-pher Wagner, Samuel Schaub, Zachary Nault,Wesley Cheek, Joel Rogers, Rachael Jensema,Christopher Miko, Austin Bain, Hannah Rotter,and Aaron Seider. The ongoing work of PaulNord in maintaining the equipment is gratefullyacknowledged. We thank Kevin Volk for ongo-ing conversations about evolved stars. We alsothank the anonymous referee for her/his sugges-tions which improved the presentation of these re-sults. Equipment support for the VU Observatorywas partially provided by grants from the NationalScience Foundation College Science Instrumen-tation Program (8750722), the Lilly “Dream ofDistinction” Program, and the Juenemann Foun-dation. BJH acknowledges onging support duringthis project from the National Science Foundation(9315107, 9900846, 0407087, 1009974, 1413660),NASA through the JOVE program, and the Indi-ana Space Grant Consortium. This research hasmade use of the SIMBAD database, operated atCDS, Strasbourg, France, and NASA’s Astrophys-ical Data System.13
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This 2-column preprint was prepared with the AAS L A TEXmacros v5.2. able 1Program Objects IRAS ID V a (V − R C ) a ,b Sp.T. T eff log g [Fe/H] [C/O] Ref. c Other ID(mag) (mag) (K)17436+5003 7.0 0.2 F3 Ib d − − d − − · · · − − − − − − − − · · · a Variable. b Includes circumstellar and interstellar reddening. c References for the spectroscopic analyses: (1) Luck et al. (1990), (2) Klochkova et al. (2002), (3) Sahin et al.(2011), (4) Pereira et al. (2004). (5) Arellano Ferro et al. (2001). Note that there is an earlier spectroscopic studyof IRAS 18095+2704 by Klochkova (1995), but the one cited is at ∼ d Classified as A7 I by Sua´rez et al. (2006). able 2Standard Magnitudes of Program and Comparison Stars a Object GSC ID V (B − V) (V − R C ) (R C − I C ) Run b IRAS 17436+5003 03518-00402 7.00 · · · · · · · · · · · · · · · C d · · · · · · C e · · · · · · IRAS 18095+2704 02100-00044 10.30 · · · · · · · · · f · · · · · · C h · · · · · · C · · · · · · IRAS 19386+0155 00483-00956 11.09 1.16 0.77 0.86 3C · · · C i · · · C i i i · · · IRAS 19475+3119 02669-01757 9.27 · · · · · · · · · · · · · · · C · · · · · · C · · · · · · a Uncertainties in the observations are as follows − V : ± B − V ): ± V − R C ): ± R C − I C ): ± b Standardized observations were made at the VUO on UT (1) 22 August 1995 and (2)26 June 2012, and are averaged together for the comparison stars, and at (3) the Kitt PeakNational Observatory on 23 June 1994. c Evidence of a general increase in brightness from 1994 − V ). d HD 234482 e HD 234480 f TYC 2100-387-1 g Suggestion of a gradual monotonic increase in brightness of 0.025 mag ( V ) from 1994 to2007 and a gradual increase and then decrease over a range of 0.03 mag ( V ) from 2008 to2012. h TYC 2100-238-1 i Uncertainty of ± j Suggestion of variation ≤ k Suggestion of long-term ( ≥ ∼ able 3Statistics of the VUO PPN Light and Color Curves IRAS ID Years Number of Observations Average Uncertainty (mag) a ∆V ∆R C ∆(V − R C ) ∆B σ (∆V) σ (∆R C ) σ (∆(V-R C )) σ (∆B)17436+5003 1994 − − − · · · · · · − a The average statistical uncertainty in a single differential measurement. able 4Differential Standard VR C Magnitudes and Colors for the Four PPNs from 1994 − a ,b Program Star HJD − − C HJD − − R C )IRAS 17436+5003 49557.6197 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − Note.—
Average uncertainties in the brightness are as follows: ± V ), ± C ), ± − R C )), with maximum uncertainties ∼ a Table 4 published in its entirety in the electronic edition of the Astronomical Journal. A portion of Table 4 isshown here for guidance regarding form and content. b The 2007 observations that contain all three
BVR C filters are listed instead in Table 5. able 5Differential Standard BVR C Magnitudes for the Four PPNs from 2007 − a ,b Program Star HJD − c ∆B ∆V ∆R C HJD − c ∆B ∆V ∆R C IRAS 17436+5003 54283.6210 − − − · · · − · · · IRAS 17436+5003 54287.6152 − − − − − − − − − − − − − − − − − − − − − − − − − · · · − − − − − · · · − − − · · · IRAS 17436+5003 54305.6554 − − − − − − − − − − − − − − − − − − Note.—
Average uncertainties in the brightness are as follows: ± B ), ± V ), and ± C ), with maxi-mum uncertainties ∼ a Table 5 is published in its entirety in the electronic edition of the Astronomical Journal. A portion of Table 5 is shown herefor guidance regarding form and content. b The 2007 observations that contain only VR C filters are listed instead in Table 4. c The time represents the mid-time of the V observations. The times for the B and R C observations differ from this byapproximately the following: IRAS 17436+5003: +0.0011 and − − − able 6Offsets Between the Published Data Sets and VUO Data Sets a IRAS ID Source Dates Bandpass Offset (mag)17436+5003 Fernie b − c − d − − d − − d − e − − f − − a Offset = VUO − published data set. b c Percy & Welch (1981), where the data are listed. d Arkhipova et al. (1993, 2000, 2010); data available on-line from VizieRat http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=J/PAZh/26/705 andhttp://vizier.u-strasbg.fr/viz-bin/VizieR?-source=J/PAZh/36/281. e f Arkhipova et al. (2006); data available on-line from VizieR athttp://vizier.u-strasbg.fr/viz-bin/VizieR?-source=J/PAZh/32/48.21 able 7Periodogram Study of the Light Curves of Four O-Rich PPNs a IRAS ID Set Filter Years No. P A P A P A P A P A P A Obs. (days) (mag) (days) (mag) (days) (mag) (days) (mag) (days) (mag) (days) (mag)17436 A V V V · · · · · · · · · · · · · · · · · · R C · · · · · · · · · · · · · · · · · · V · · · · · · V · · · · · · · · · · · · V · · · · · · · · · · · · · · · · · · V V b
327 98.2 0.015 107.5 0.013 · · · · · · · · · · · · · · · · · · · · · · · · V · · · · · · B · · · · · · R C · · · · · · R C · · · · · · · · · · · · · · · · · · · · · · · · V · · · · · · V · · · · · · · · · · · · · · · · · · V · · · · · · · · · · · · R C · · · · · · · · · · · · · · · · · · · · · · · · V · · · · · · · · · · · · · · · · · · R C · · · · · · · · · · · · · · · · · · V · · · · · · · · · · · · · · · · · · R C · · · · · · · · · · · · · · · · · · · · · · · · V · · · · · · · · · · · · · · · · · · · · · · · · a The formal, least-squares uncertainties determined using Period04 for each object in period P and amplitude A are approximately as follows:IRAS 17436: ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± b A similarly good fit is achieved with P =98.5 days, A =0.013 mag and P =102.8 days, A = 0.012 mag able 8Results of the Period and Light Curve Study of Four Oxygen-Rich PPNs IRAS ID P P /P P preva SpT T effb ∆V c ∆(V − R C ) b ∆(B − V) b ∆T eff b Comments(day) (day) (K) (mag) (mag) (mag) (K)17436+5003 45.2 1.06 40 −
46 F3 Ib 6600, 7100 0.21 0.065 0.095 700 · · · · · · a Previously published periods: IRAS 17436+5003: Fernie, series of papers; IRAS 18095+2704: Arkhipova et al. (2010); IRAS19386+0155: Arkhipova et al. (2010); IRAS 19475+3119: Arkhipova et al. (2006). b T eff determined from model atmosphere analyses as cited in Table 1 c The maximum brightness and color range observed in a season and the corresponding maximum temperature change based on∆(B − V) and color − temperature calibration of Cox (2000, Table 15.7). ig. 1.— Plots showing the differential light andcolor curves of IRAS 17436+5003 obtained at theVUO from 1993 − ) with respect to the sec-ondary (C ) comparison stars on the same scaleas the PPN light curves. The absence of V datafrom 2000 to part of 2002 is due to a filter prob-lem. Zero-point offsets are added to convenientlydisplay all three light curves on the same plot. Fig. 2.— Plots showing samples of the differen-tial B and ( B − V ) curves from the 2009 and 2010seasons obtained at the VUO. The changing cycli-cal behavior of the light and color curves can beseen, as can the correlation between brightnessand color. Error bars are included.Fig. 3.— Plots showing the change in color withchange in brightness. A clear trend is seen, withthe objects being redder when fainter. The ob-servations with the initial VUO CCD are plottedas filled circles and with the newer CCD as opencircles. For IRAS 18095+2704, an adjustment in( V − R C ) of 0.01 mag has been applied to correctfor the small offset in color between the old andnew CCD systems, as described in the text.24ig. 4.— Plots showing the differential light andcolor curves of IRAS 18095+2704 obtained at theVUO, plotted similar to Figure 1.Fig. 5.— Plot showing the differential light andcolor curves of IRAS 19386+0155 obtained at theVUO from 1993 − V light curve ofIRAS 17436+5003, with our data shown as filledcircles, the data of Fernie shown as open circles,and the data of Percy & Welch shown as filledtriangles. Bottom five panels: The seasonally-adjusted V light curve fitted with the six peri-ods and amplitudes listed in Table 7. The fit isgenerally good throughout except for the mostrecent data (bottom panel). Note that there issome repetition of the data and the fitted curvesat the edges of the five lower panels. The verticaldashed line shows the time when published high-resolution spectra were taken.25ig. 8.— The frequency spectrum of the combinedand seasonally-adjusted V light curves of the fourtargets, together with their associated phase plotsbased on the frequency peaks (P ). The presenceof secondary period peaks in the data is evident.Fig. 9.— Top panel: Combined V light curve ofIRAS 18095+2704, with our data shown as filledcircles and the data of Arkhipova et al. shownas open circles. Bottom two panels: The trend-removed, seasonally-adjusted V light curve on anexpanded scale, fitted with the four periods andamplitudes listed in Table 7. The fit is reasonableon most seasons given the complex nature of thelight curve. In some seasons, the periods lookslike they agree but not the fixed amplitudes. Thevertical dashed line shows the time when publishedhigh-resolution spectra were taken. Fig. 10.— Top: Combined V light curve of IRAS19386+0155, with our data shown as filled circlesand the data of Arkhipova et al. shown as opencircles. Bottom: The trend-removed, seasonally-adjusted V light curve fitted with the five periodsand amplitudes listed in Table 7. The fit is reason-ably good over this 16-year interval. The verticaldashed line shows the time when published high-resolution spectra were taken.26ig. 11.— Top: Combined V light curve of IRAS19475+3119, with our data shown as filled circlesand the data of Arkhipova et al. shown as opencircles. Bottom three panels: The seasonally-adjusted V light curve fitted with the three pe-riods and amplitudes listed in Table 7. The fit isnot so good, particularly in the amplitudes. Weattribute this to the complex nature of the lightcurves, likely due to the presence of shock wavesin the atmosphere. Note that there is some repeti-tion of the data at the edges of the two lower pan-els. The vertical dashed line shows the time whenpublished high-resolution spectra were taken. Fig. 12.— A plot of pulsation period versus T eff .The 12 C-rich objects are shown with open cir-cles (Hrivnak et al. 2010) and the four O-rich ob-jects from this study are shown with filled cir-cles. Those with less certain values are shownwith smaller symbols. The straight line is a fitto the 12 C-rich objects. Two of the O-rich ob-jects (IRAS 17436+5003 and 19475+3119) havetwo points each because they have two differenttemperature measurements. (We have assumedreasonable error bars of ±
250 K and ± ±
250 K, ± ±±