NGC-2437 (Messier 46), NGC-2438 And Its Central White ...tommadigan.net/NGC-2437-M46-and-NGC-2438_Its... · NGC-2437 (Messier 46), NGC-2438 And Its Central White Dwarf as a Model

NGC-2437 (Messier 46), NGC-2438

And

Its Central White Dwarf as a Model End State for Solar Class Stars

Thomas Madigan James Cook University Master of Astronomy Pilot Research Project 21 May 2011

NGC-2437 (Messier 46), NGC-2438 And Its Central White Dwarf as a Model End State for Solar Class Stars

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Table of Contents NGC-2437 (Messier 46), NGC-2438 .............................................................................................................................................1 And.................................................................................................................................................................................................1 Its Central White Dwarf as a Model End State for Solar Class Stars.............................................................................................1

Table of Contents .......................................................................................................................................................................2 Covering Page Illustration..........................................................................................................................................................3 Preface........................................................................................................................................................................................4 Abstract ......................................................................................................................................................................................4 Format ........................................................................................................................................................................................5 Data Products .............................................................................................................................................................................5

Methodology ..........................................................................................................................................................................5 1. Various Color Indices..................................................................................................................................................5 2. Apparent Visual Magnitude ........................................................................................................................................5 3. Specific Color Excess..................................................................................................................................................5 4. Normalized B – V Index .............................................................................................................................................6 5. Effective Blackbody Temperature...............................................................................................................................6 6. Bolometric Correction.................................................................................................................................................6 7. Absolute Bolometric Magnitude .................................................................................................................................6 8. Absolute Visual Magnitude.........................................................................................................................................6 9. Fully Corrected Distance.............................................................................................................................................6 Distance to NGC-2437 ...........................................................................................................................................................7 Field Star Stellar-evolutionary trends and population ............................................................................................................7 “Turn-off” point for NGC-2437 and the more distant Perseus-arm stars ...............................................................................7 Age of NGC-2437 ..................................................................................................................................................................9 NGC-2419 and NGC-2437 Turn Off Points...........................................................................................................................9 HR Diagram and Stellar Profile for NGC-2437 ...................................................................................................................10 Analysis of and distance to NGC-2438 and its White Dwarf Central Star...........................................................................10

Conclusion................................................................................................................................................................................13 Association of NGC-2437 and NGC-2438...........................................................................................................................13 Two Stellar Populations .......................................................................................................................................................13 HR Diagram and Turnoff .....................................................................................................................................................13 NGC-2438 as a model End State for Solar Class Stars ........................................................................................................13

Tables and Illustrations ............................................................................................................................................................14 Figure 1 ................................................................................................................................................................................14 Figure 2 ................................................................................................................................................................................15 Table 1 comparing select test-case stars with our empirically derived Absolute Bolometric Magnitude ............................15 Figure 3 ................................................................................................................................................................................16 Table 2 comparing select test-case stars with our empirically derived Absolute Visual Magnitude....................................16 Table 3 providing the spatial distance distributions of both stellar populations as illustrated in Figure 5 ...........................18 Figure 6 illustrating the galactic coordinate grid ..................................................................................................................19 Table 4 indicating stellar population distribution by distance for NGC-2437......................................................................20 Figure 7b illustrating the distance distribution of the more distant Perseus-arm stars. ........................................................21 Table 5 indicating stellar population distribution by distance for the more distant Perseus-arm stars .................................21 Figure 8 illustrating the B – V spread for NGC-2437 ..........................................................................................................22 Table 6 indicating mean B – V and stellar population of NGC-2437 for a one sigma width...............................................22 Figure 10 illustrating the M(V) spread for NGC-2437 with the mean centered at 2.67 .......................................................23 Table 7 indicating the absolute visual magnitude spread for NGC-2437 cluster stars .........................................................24 Figure 12 illustrating the absolute magnitude distribution of the more distant Perseus arm stars........................................25 Table 8 indicating the absolute visual magnitude spread for the more distant Perseus-arm stars ........................................25 Figure 13 illustrating the absolute magnitude distribution of all field stars included in this study ......................................26 Table 9 provides the details for Figure 12............................................................................................................................26 Figure 14 illustrating the “Turn-off” point for NGC-2437 and the more distant Perseus-arm stars.....................................28 Table 10 indicating frequency of B – V index in terms of Spectral Class............................................................................28 NGC-2437 and NGC-2438 Images and Illustrations............................................................................................................29 Figure 15 illustrating NGC-2438 in Red light (600 nm) ......................................................................................................30 Figure 16 illustrating NGC-2438 in the Red light of Hydrogen Alpha (656.3 nm)..............................................................31


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Figure 17 illustrating NGC-2438 in the Red light of Singly ionized Sulfur (672 nm) .........................................................32 Figure 18 illustrating NGC-2438 in the V Band (530 nm)...................................................................................................33 Figure 19 illustrating NGC-2438 in the Blue-Green light of Doubly ionized Oxygen (501 nm).........................................34 Figure 20 illustrating NGC-2438 in the B Band (420 nm) ...................................................................................................35 Figure 21 illustrating the fully integrated L-RGB image of NGC-2438...............................................................................36 Figure 22 processed to bring out the more subtle colors of the various field stars...............................................................37 Figure 24 illustrating the extended shell and halo surrounding NGC-2438 .........................................................................38 Figure 23 with the various elements represented by their respective line emissions............................................................39

Appendix A ..............................................................................................................................................................................40 Sample Photometric Data .....................................................................................................................................................40

Appendix B ..............................................................................................................................................................................41 Photometric Data For NGC-2438 and its Central White Dwarf...........................................................................................41 Temperature, Luminosity and Distance Calculations based on Standard Candle Distance and Luminosity Modeling .......41 Distance determination using an accepted PN Expansion Rate and an Estimated Minimum Expansion Time since AGB.41 Image scale and Angular Dimensions ..................................................................................................................................41 Manually Integrated Intensity Map (Blue) ...........................................................................................................................42 Manually Integrated Intensity Map (Blue) ...........................................................................................................................42 Manually Integrated Intensity Map (Visible) .......................................................................................................................42

Appendix C ..............................................................................................................................................................................43 The 0.61 Meter Flagship Instrument of LightBuckets..........................................................................................................43

Appendix D ..............................................................................................................................................................................44 The Johnson-Cousins Standard ............................................................................................................................................44

Appendix E...............................................................................................................................................................................46 SExtractor Input Controls.....................................................................................................................................................46 Input controls for V-Band analysis of NGC-2437................................................................................................................46 Convolution map for Source Intensity Gaussian ..................................................................................................................47 SExtractor Output Controls (Generic)..................................................................................................................................47 Sample SExtractor Output....................................................................................................................................................48

References ................................................................................................................................................................................49

Covering Page Illustration Planetary Nebula NGC-2438 surrounded by the stars of Galactic Cluster NGC-2437 (M-46). Image scale: 0.57 arc-seconds/ pixel with the nebula subtending 1 arc-minute Instrument: 0.61 meter Ritchey-Chretein Image credit Thomas Madigan Image is an RGB/ OIII/ Ha and SII composite


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Preface This work is the culmination of a decision process that began 4 years ago. We decided on the current topic after considering a number of our own unanswered questions set against the backdrop of yet other unanswered questions in astronomy and astrophysics or answers to those questions that, to this day, remain ambiguous or uncertain. The decision to move forward with this research was made in early March 2010 and, since then, data acquisition and analysis has been ongoing. In this work, I will present the fruits of that research and analysis. Most assuredly we will present new science and answer a number of questions. This work also concludes the two previous works submitted, more specifically the first work that presents our findings regarding NGC-2419, the most distant globular cluster associated with the Milky Way galaxy. The title of this final work for the Master of Astronomy program, my thesis, “NGC2437 (Messier 46), NGC-2438 And Its Central White Dwarf as a Model End State for Solar Class Stars”, was ultimately decided upon based on the richness of the content and region of the sky containing these objects, the widely varying disciplines that will be brought to bear in discussing them specifically, how they relate to other topics in astronomy and astrophysics more generally and, finally, what new and intriguing questions may arise followed by their own unique paths of inquiry and discovery. NGC-2438 was discovered in 1786 by William Herschel. Ever since then, the question always arose: was this object physically associated with the galactic cluster NGC-2437 (M-46) or is it a foreground or background object? When one first observes NGC-2437 and notes the ghostly presence of NGC-2438, that immediate question begs asking. While the question may seem simple on its face, the answer is not so easily obtained and, in order to answer it, 2 other questions need to be answered: (2) what is the distance to NGC-2437 and (3), what is the distance to NGC-2438. Thus, the process of inquiry and discovery began, concluding with this work.

Abstract In addition to the 2 questions presented above, we discuss our findings regarding the stellar populations and evolution of NGC-2437 and the nature of NGC-2438 and its central, white dwarf star. We originally set out to demonstrate that this PNe is a typical, end-of-life state for solar-class stars but, through a comprehensive process of inquiry, analysis and discovery, we conclude that it and its white dwarf central star are anything but solar-class1. As well, some doubt still persists regarding the independence of NGC-2437 and NGC-24382. We unequivocally dispel that uncertainty and answer the first of three questions posed above, demonstrating that NGC-2438 is not physically associated with NGC-2437 nor is it “on the periphery of NGC-2437” as some have suggested; it is a foreground object over 0.5 kpc closer. Additionally, through our findings, we assert the veracity of newly published maps of the Milky Way galaxy in the direction of the Peseus Arm out to 5 kpc, these maps produced from Spitzer Space telescope data and images. In addition to these findings, we:

1. determine the distance to NGC-2437; 2. determine the age of NGC-2437 using the “turn off” technique through painstaking analysis of our

NCC-2437 photometric data and recent Hipparcos data;

1 Gathier, R.; Pottasch, S. R., 1988; Magnitudes of central stars of planetary nebulae; European Southern Observatory; Astronomy and Astrophysics (ISSN 0004-6361), vol. 197, no. 1-2, May 1988, p. 266-270 2 Atlas of the Messier Objects: Highlights of the Deep Sky (p 193-195); Stoyan, R., et al; Cambridge University Press 2008


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3. present an analysis of NGC-2437 stellar-evolutionary trends and population 4. present an analysis of the more distant Perseus arm population in the narrow region of sky

occupied by NGC-2437 at a galactic longitude of 115º 5. present an analysis of and distance to NGC-2438 and its White Dwarf Central Star 6. compare and contrast the analysis of NGC-2419, presented and discussed in our previous work.

In this work, we will show that the population of NGC-2419, presented and discussed previously, is markedly different than the population of NGC-2438 (M-46), illustrating the widely disparate ages of their respective populations; NGC-2419 is comprised of highly evolved red giants set against a backdrop of aging population II Main Sequence stars; NGC-2437 is comprised of relatively young A class stars by comparison. Although we do present an aging “turnoff” analysis of each cluster, the stellar populations are markedly different.

FormatThis study is multi-faceted with many different components. As such, we adopt a concise style with the intention of presenting our data and findings in the clearest manner possible. The data for each of the components is graphically presented in the Tables and Illustrations section accompanied by a detailed description of that data and chart as presented; a general narrative and overview for each section is included in the main body of the work. Following the main body of the work we present a conclusion.

Data Products Without exception, this entire work has relied heavily on the analysis of original image and photometric data acquired by the 0.61 meter Ritchey–Chrétien Reflector of Lightbuckets, Rodeo, NM, USA (Appendix C).

MethodologyWe continue our use of Source Extractor (Appendix E) to measure the raw flux of each cluster star from BVRI wavebands. We made extensive use of MS Excel both as a sorting and charting tool but also as a solver and data analysis tool. As we did in our previous studies, we made extensive use of the photometric tools available in MaxIM DL, a FITS imaging and photometric suite that runs on top of the ASCOM platform and requires the installation of the PinPoint application for any photometric analyses. We selected several field stars as reference stars whose photometric properties are known and published in GSC 1.0 or 1.1. Once determined, the magnitudes of these reference stars were used to compute the apparent visual magnitude of any given star included in the study. As we did previously, we used SExtractor (Appendix E) to determine the raw flux intensity of each star image in a given image and imported that output into MS Excel, color-coding the data with the appropriate filler: I-band data is color coded with a deep red filler; R-band data is coded with a bright red filler, etc (Appendix A). Following the import, we then sorted by abscissa within ordinate (X within Y) to “combine” all points for each star. Once “combined”, we populated the adjacent rows and columns as follows:

1. Various Color Indices were determined using Pogson’s relation to compute the various color indices (B – V) with (V – R) and (R – I) in a few cases. As is the case for all papers in the 2 previous works, culminating with this paper, all color indexing and photometry was accomplished according to the Johnson-Cousins BVRI standard (Appendix D). Equipment limitations prevented any near UV analysis, photometry or imaging.

2. Apparent Visual Magnitude was computed using Pogson’s relation, based on the predetermined field reference star whose properties were available in GSC 1.0 or 1.1;

3. Specific Color Excess was determined using the NASA/ IPAC Galactic Dust Extinction Service and Coordinate Transformation & Galactic Extinction Calculator, a utility based largely on the

comprehensive 1998 study by Schlegel, D.J, et al3. Using the Galactic Dust Extinction Service and the 1998 study by Schlegel, D.J, et al, we determine the B – V correction for the given galactic longitude of 115º as 0.359.

4. Normalized B – V Index for interstellar reddening was determined for each field star. 5. Effective Blackbody Temperature of each field star was determined using (1) and (4) and the

1998 empirical derivation of Reed, C.4; 6. Bolometric Correction was determined for each field star using the 1998 empirical derivation of

Reed, C.5; 7. Absolute Bolometric Magnitude was computed in conjunction with (4) and (5), the fitting of our

photometric data using the linear regression methods contained in MS Excel’s solver along with its charting and analytical tool set to the Hipparcos HR Diagram (Figure 1)6, empirically produced using the photometric data of 22,000 stars from that mission’s catalog. We thus, empirically derive the following expression for Absolute Bolometric Magnitude in terms of the B – V Color Index: (Figure 2). Substituting the sun’s B – V index of 0.656 as a test case, we compute its Absolute Bolometric Magnitude to be +4.712, very close to the accepted value of +4.75.

5.8909( ) 0.8475BolM B V= − +

a. We thus compute the absolute bolometric magnitude of each member star using this expression based on:

i. with the exception of a few foreground stars, each field star is a member of either one stellar population or another, the closer, cluster population or the more distant Perseus arm population; placing all stars at either of these 2 specific distances normalizes the distance, providing the necessary theoretical basis for intrinsic luminosity determination;

ii. the preponderance of all field stars being Main Sequence stars. This empirical expression is applicable to Main Sequence stars exclusively. Due to the 2nd power dependence of luminosity on radius, evolved stars that have left the Main Sequence, starting their ascent along the RGB, cannot be evaluated as such.

8. Absolute Visual Magnitude was determined by subtracting the Bolometric Correction from the Absolute Bolometric Magnitude

9. Fully Corrected Distance was computed using Pogson’s relation and the distance modulus for each field star using the fully normalized and corrected absolute visual magnitude and the apparent visual magnitude determined in (2).


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3 ApJ: 500:525È553, 1998 June 20: Maps of Dust Infrared Emission for Use in Estimation of Reddening and Cosmic Microwave Background Radiation Foregrounds; Schlegel, D.J, et al 4 C. Reed, 1998; The Composite Observational-Theoretical HR Diagram 5 C. Reed, 1998; The Composite Observational-Theoretical HR Diagram 6 Badiali, M., et al, 2007; Age and Morphology of the Main Sequence from HIPPARCOS HR Diagram Data


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Distance to NGC-2437 Previous distance determinations of NGC-2437 were made using proper motion and parallax studies7. In 1963, C.R. O’Dell of the University of California, Berkeley, published a study8 regarding the possible association of NGC-2437 and NGC-2438. He unambiguously concludes that no association now exists but that there may have been a previous, chance encounter. We unequivocally confirm these determinations, dispel any ambiguities or uncertainty as to the independence of NGC-2437 and NGC-2438 and assert that no association now exists or that it ever did, through a chance encounter or otherwise. We draw these conclusions from our exhaustive photometric analysis of the cluster member stars. In a related study, we analyze the more distant stars of the Perseus arm as a separate, more distant stellar population and present that study as a confirmation of recent renderings of the Milky Way galaxy using the Spitzer Space telescope9 and other, supporting infrared observations. This study is presented as a separate article further in this work. Our study reveals the presence of two distinct stellar populations (Fig 4, 5 and 6), the closer, slightly more luminous stars of NGC-2437 and the more distant stars of the Perseus arm. We determine the mean distance to NGC-2437 to be 1.8 (+/- 0.610) Kpc (Figure 7) or 5.9 (+/- 1.96) Kly, a result that is in close agreement with the accepted value of 1.7 Kpc or 5.4 Kly. We determine the mean distance to the more distant, Perseus arm stars to be 2.4 (+/- 0.714) Kpc. Evident from this comparison is the greater certainty in distance to NGC-2437 with a narrower standard deviation. This greater certainty would also serve to constrain the other, related conclusions [based on an accurate distance determination]. Conclusions such as intrinsic luminosity, absolute visual magnitude and spectral class would be affected by a change in distance. Such effects would be dramatically observed in our comprehensive HR Diagram, presented in Figure 14. An accurate HR Diagram would necessarily require an accurate distance determination, specifically when specific population studies are undertaken, such as ours. It needs to be noted that any segregations of, and conclusions based on, distance were made in accordance with the conclusion that 2 separate populations of stars are represented in this study, stars whose distances are presented in Figure 5. Field Star Stellar-evolutionary trends and population “Turn-off” point for NGC-2437 and the more distant Perseus-arm stars We present a representative sampling of almost 800 field stars (Figure 13) with the preponderance of those stars the more distant Perseus arm stars, most of them slightly less luminous than the NGC-2437 cluster stars with an absolute visual magnitude of 3.34. Following Figure 13 is Figure 14, a comprehensive HR Diagram of NGC-2437 and all field stars included in this study.

7 Publications of the Astronomical Society of the Pacific 119: 1349. arXiv:0710.2900; In Search of Possible Associations between Planetary Nebulae and Open Clusters; Majaess D. J., Turner D., Lane D. (2007); Notes from Observatories, On the Association of NGC 2437 and NGC 2438; O’Dell, C.R.; 1963, U. Cal, Berkeley; Publications of the ASP, Vol. 75, No. 445, p.370-372Monthly Notices of the Royal Astronomical Society. arXiv:0809.0327 : AAOmega radial velocities rule out current membership of the planetary nebula NGC 2438 in the open cluster M46; Kiss, L. L., Szabó, Gy. M., Balog, Z., Parker, Q. A., Frew, D. J. (2008) 8 Notes from Observatories, On the Association of NGC 2437 and NGC 2438; O’Dell, C.R.; 1963, U. Cal, Berkeley; Publications of the ASP, Vol. 75, No. 445, p.370-372 9 http://www.spitzer.caltech.edu/images/1927-ssc2008-10a1-The-Milky-Way-Galaxy

http://en.wikipedia.org/wiki/Publications_of_the_Astronomical_Society_of_the_Pacific

http://en.wikipedia.org/wiki/ArXiv

http://en.wikipedia.org/wiki/Monthly_Notices_of_the_Royal_Astronomical_Society

http://en.wikipedia.org/wiki/ArXiv

http://arxiv.org/abs/0809.0327

http://www.spitzer.caltech.edu/images/1927-ssc2008-10a1-The-Milky-Way-Galaxy

Since 40% of those stars are member stars of NGC-2437, stars whose distance measurement have a smaller standard deviation and thus, a more reliable distance determination, we conclude that the stars represented at the classic “Turn Off” point are member stars of NGC-2437. It is necessary, for population studies such as this, that all stars be at a common distance. Clearly, there are other stars at varying distances from the cluster, member stars of the more distant Perseus arm and closer, foreground stars. As stated on page 11 (Figures 2 and 3), it can be concluded that the preponderance of stars included in this study are Main Sequence stars. Any positional inconsistencies in Figure 14 are, therefore, based on distance, not intrinsic luminosity. Clearly, there are some evolved stars as illustrated by the “Turn Off” and the correct location of sub-giant class stars. We refrain from any further spectral and luminosity classifications because of the “mix” of stars from the two distinct populations but do provide the locations were they should be. It is interesting to note the differences between the cluster “Turn Off” for NGC-2437 and NGC-2419, the most remote globular cluster linked to the Milky Way. We discuss this more in depth below. It should be noted that, based on our conclusion that all field stars belong to two distinct populations and, for precisely this reason, the plot of B – V vs. Apparent Visual Magnitude will produce a fairly well-defined HR Diagram for those two populations. As stated above, when the distance is normalized, a meaningful mapping of luminosity vs. temperature can be obtained. Much insight can be gained from studying this chart, not the least of which is the placement of a solar-class star, indicated in yellow. When producing this image, precise ray tracing was performed, positioning the “sun” on the extrapolated Main Sequence slopes for the two populations as well as aligning it along the vertical axis corresponding to its B – V index of 0.656. The Main Sequence extrapolations were performed using a “best fit” slope. Upon inspection, we determine an apparent visual magnitude range of +18.75 – +17.20 for a solar class (G2V) star if placed at the respective mean distances of the 2 populations. Using that result, the sun’s absolute visual magnitude of +4.83 and the distance modulus, we compute the distance range of such a star:


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pc

pc

5 518.92 5

3.7846.1 0.71

m M LogDLogD

LogDD K

− = −==

= ±

The Main Sequence midline representing the 6.1 +/– 0.7110 Kpc solar-class star clearly represents the more distant population, at a point beyond the mean distance of the Perseus arm stars contained in this study; they would represent the 2 sigma Gaussian “tail” for that population.

5 517.37 5

3.4742.97 0.61

m M LogDLogD

LogDD K

− = −==

= ±

The Main Sequence midline representing the 2.97 +/– 0.6111 Kpc solar-class star, at a distance at the low side of the one sigma limit, would be consistent with our distance determinations and results. Granted,

10 We adopt the one sigma uncertainty for the more distant Perseus-arm stars 11 We adopt the one sigma uncertainty for the cluster stars


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the normalization methods were based on a best fit slope using our photometric data and Hipparcos data, the result is consistent with the distance determined for NGC-2437. Upon inspection, the brightest star presents with an apparent visual magnitude of +10 while the faintest of the stars present with an apparent visual magnitude of +18.6, this low limit achieved with a 360 integration time. It is interesting to note here, that the sun would present at approximately this magnitude at 5.7 Kpc, a distance contained in the 2 sigma tail of the Perseus arm population distribution. Age of NGC-2437 In Table 10 we present our findings regarding the cluster “Turn Off” stars’ spectral class, determining that the preponderance of these stars are early A, Vega, Sirius, Fomalhaut class stars. Using the results obtained in our 2009 study12 and adopting a productive lifetime of an A0V – A4V class star we estimate the age of the turn off stars and, in turn, the cluster to be 900 my (900 million years). This result is at variance with the current estimated age of 300 my13, a value, in the opinion of this author, that is questionable and needs additional substantiation based on the preponderant spectral class of the cluster stars. According to our study, Vega, an A0V class star, has a productive, hydrogen burning lifetime of 804 my and Fomalhaut, an A3V class star, has a productive hydrogen burning lifetime of 1.3 gy. Since, presumably, the formation of the cluster predates the formation of the earliest of these turn off stars – it is older and contains somewhat longer-lived, less luminous stars, we adopt an age greater than these evolved, early A class stars. Furthermore, in support of this conclusion, there are slightly later A (Fomalhaut, A3V – A4V) class stars as members of the “turn off’ population with somewhat longer, productive lifetimes [that have also started to evolve off the Main Sequence]. The cluster can be no younger than 900 my. Determination of the respective spectral classes was accomplished by fitting the B – V data to values computed and presented in Table 2 and, during the process, measuring those results against Figure 1. NGC-2419 and NGC-2437 Turn Off Points In our previous work, we presented a study of the ancient and most distant Milky Way globular cluster, NGC-2419. We took specific note of that cluster’s evolved stellar population and, due to aperture limitations, were unable to image the magnitude +23(+) “turn off” population of that cluster, solar class stars that range from late F to early G and present with a feeble apparent visual magnitude of +23 and fainter. Even though we were unable to acquire image data for the NGC-2419 turn off population, we did acquire image data for the more luminous, evolved giant and horizontal branch stars of that cluster. When apparent visual magnitude was plotted against spectral class (B – V color index), we produced the upper “tail” of the classic HR profile of an evolved cluster. We note the comparatively disparate turnoff population of NGC-2419 as compared to the NGC-2437 turn off population with the former consisting of late F to early G stars and the later consisting of early A class stars. Based on their respective turn off populations, clearly, NGC-2419 is eons older than NGC-2437. Because of the disparate stellar populations of both clusters, there were very few similarities. The one, notable similarity was the presence of Horizontal Branch stars with a notable paucity of such stars represented in our NGC-2437 data. Our NGC-2419 HR profile illustrates that the evolved, giant members of that cluster present with a B – V range of 0.4 – 0.6. In Figure 14, we present candidate giants and supergiants, stars that would be of the same type and class as the large, luminous evolved members of NGC-2419. Without an

12 Stellar Lifetime Based on Stellar Mass; Madigan, 2009, as part of degree work 13 Limited references available for this topic; http://en.wikipedia.org/wiki/Messier_46; Notes from Observatories, On the Association of NGC 2437 and NGC 2438; O’Dell, C.R.; 1963, U. Cal, Berkeley; Publications of the ASP, Vol. 75, No. 445, p.370-372

http://en.wikipedia.org/wiki/Messier_46


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independent, corroborative distance determination, those stars remain candidate giants for the purposes of this study. HR Diagram and Stellar Profile for NGC-2437 Figure 14 illustrates the “Turn Off” point for NGC-2437 stars. It also includes the Main Sequence tracks for the two populations presented in this study, the location of sub-giant class field stars, possible Giants, Supergiants, Horizontal Branch stars and the placement of a solar-class (G2V) star at the mean distance for both populations (this would provide a modicum of comparison for the sun and the field stars in terms of luminosity). For reference, we also include in Figure 14 the placement of the 2 bright field stars discussed with Figure 22. Analysis of and distance to NGC-2438 and its White Dwarf Central Star As one of the compelling points of interest that led up to the choice of these 2 objects, NGC-2437 and NGC-2438, we present our analysis of NGC-2438 and its White Dwarf Central star. Since we’ve already determined the magnitudes of almost 1,000 stars in the field containing NGC-2438, the choice of a suitable comparison star by which we could determine the distance to the white dwarf and hence, the distance to NGC-2438, should be trivial. Indeed, based on that choice comparison star, we determine the apparent visual magnitude of the central white dwarf to be +16.85 (Appendix B), a value that agrees quite well with the accepted value of +17.2014. Although the white dwarf central star data was clearly available [in the FITS image data], the photometric suite of tools in MaxIM DL failed to detect it. This necessitated mapping the data in MS Excel, pixel by pixel, and then manually integrating the representative pixels out to the FWHM intensity (Appendix B). The manually integrated B and V intensities were then used in our distance and luminosity calculations (Appendix B). A number of inconsistencies became apparent as we worked through our calculations. The standard determination of distance based on apparent and absolute visual magnitude using the distance modulus (adopting the notion that the WD could be modeled as a Blackbody with a Teff of 8,100 K) did not agree by two orders of magnitude with the distance determined using a standard accepted expansion rate of 20 km/sec for planetary nebulae and an nominal expansion period (since the star’s AGB phase commenced, producing the planetary nebula) of approximately 10 Kyr (Appendix B). As an aside, it should be noted here that the relative brevity of the Planetary Nebula phase of any star’s end-state evolutionary behavior would preclude any past association of NGC-2438 with NGC-2437 (M-46). If one adopts 10 Kyr as the time frame since the star entered the AGB, eventually resulting in the planetary nebula, even a star with a high radial proper motion would not cover the distance between the two objects during that time. In our calculations we adopt a nominal WD radius equal to one terrestrial radius (6,400 Km) and apply the Planck Law to determine the intrinsic WD luminosity (if a Blackbody model is adopted). In an attempt to reconcile the two widely disparate results, we held the radius of the star fixed at one terrestrial radius while varying the temperature from a low, using the normalized B – V temperature (8,100 K), to a high of 110,000 K. The following is the result of that calculation (also contained in Appendix B): Comp Temp(b,v) Radius Solar Radii

8096 6400000 0.00956 13519 6400000 0.00956

14 Gathier, R.; Pottasch, S. R., 1988; Magnitudes of central stars of planetary nebulae, page 267; European Southern Observatory; Astronomy and Astrophysics (ISSN 0004-6361), vol. 197, no. 1-2, May 1988, p. 266-270


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110000 6400000 0.00956

Luminosity Luminosity (sun) Log Luminosity (sun)1.25371E+23 0.000325638 -3.49 9.75008E+23 0.002532487 -2.60 4.27322E+27 11.09927303 1.05

Log D(pc) Distance (pc) Distance (ly)

1.62805124 42.46696654 138.4423109 1.89322613 78.20348919 254.9433748 2.294832806 197.166354 642.762314 It is clear, even if we adopt an upper-limit Teff of 110,000 K, we are only at 197 pc, still only at the 20% distance mark, far short of the 1.2 Kpc determined using standard expansion rate models (Appendix B). As well, adopting a Teff of 110,000 K, the central White Dwarf star would present with a luminosity of 11 times solar, something else that is questionable. Additionally, a Teff of 110,000 K exceeds the Eddington limit by over a factor of 2. The accepted upper limit for Teff is 50,000 K, after which the core’s gamma radiation pressure will push off the outer, non-fusing envelope of gas! One of the fundamental premises of any significant astronomical distance determination is the ability to model a star as a Blackbody. By comparing the relative flux of the B and V bands (as well as other bands – the theory is identical), we can deduce the temperature of the star’s surface independent of distance and, by applying the Planck Radiation law, the bolometric luminosity of the star if the assumption is made that the star is on the Main Sequence, an evolutionary path where the size (and hence the absolute luminosity) can be constrained very precisely. This B – V color index is precisely based on the notion that a star can be modeled as a Blackbody. This, indeed, is true for the preponderance of all stars, except for the White Dwarf Central star of NGC-2438! As it turns out, this star belongs to a rare class of star that cannot be reliably modeled as a Blackbody, that it is a very hot, non-thermal emitter! Recent studies, discussed in a 1988 paper15 by Pottasch, Gathier, et al, have brought to light a relatively new class of very hot WD star modelled as a hot, non-thermal emitter or NTE. So how do we determine the effective temperatures and radiative properties of these very hot NTE stars? As it turns out, there is such a method. As discussed in the captions associated with our line emission images of NGC-2438, the continuum flux at a given wavelength that corresponds to a particular line emission will be absorbed by the nebular gas and reradiated as line emission [by the planetary nebula]. This conclusion is consistent with our results as discussed in the various captions. What needs to be done is to measure the stellar flux for a wavelength not represented in the PN but emitted by the star and compare that to the nebular flux intensity of a reference line, such as HeII at 479.3nm. We would thus measure the stellar flux for a Rydberg series emitter that does not present in the PN and then compare that to the stellar flux of the reference line. Such a Rydberg series line would be the Balmer 4 – 2 transition or the H Beta line at 486 nm. The resultant Zanstra Temperature16 would thus be determined by measuring the intensity ratio of H Beta/ HeII and would be an accurate indicator of the star’s effective temperature. In the 1988 paper by Gathier, Pottasch, et al, a Zanstra Temperature of 112,000 K for Hydrogen and 131,000 K for Helium was obtained respectively for the NGC-2438 WD central star. It can be concluded that the disparity in Zanstra Temperatures between Hydrogen and Helium is a good indicator that the star cannot be modelled as a blackbody but as a hot, NTE. If a the Zanstra Temperature ratio was close to or equal to unity, a 15 Gathier, R.; Pottasch, S. R., 1988; Magnitudes of central stars of planetary nebulae; European Southern Observatory; Astronomy and Astrophysics (ISSN 0004-6361), vol. 197, no. 1-2, May 1988, p. 266-270 16 Zanstra, H., 1927; An Application of the Quantum Theory to the Luminosity of Diffuse Nebulae; ApJ, vol. 65, p.50

blackbody model would be indicated but that is not the case. This would at least account for the wide disparity in results obtained using the 2 methods described above with the later method (the expanding gas model) the more reliable. Although the standard candle method is, by far, the simplest and most straight forward, it is fundamentally flawed in that a blackbody cannot be assumed for these rare, hot NTE WD stars. Although an explanation is presented for the disparity, we clearly need to determine which result is the more reliable; but how? If there could be a means to independently determine the distance to a star of similar class and state of evolution, we could determine the distance by adopting a modified distance modulus where both stars, the reference WD and our subject WD, would be of comparable luminosities and thus, of comparable absolute magnitudes. We would then only have to apply the inverse square law to determine the distance to our subject WD. To the best of our knowledge, this technique has never been attempted until now. Well, it turns out that just such a distance determination was conducted17 with one of the test cases being NGC-6720 (M-57), the famous Ring Nebula in Lyra! We modify Pogson’s relation as follows, employing the inverse square law, the justification for this based on the notion that both stars are at similar evolutionary states. This, in turn, is based on the brevity of the PN phase of stellar evolution relative to the productive lifetime of a star; if two PN’s present where the central WD is viable and visible, chances are they are a similar in age, with similar absolute magnitudes and in similar evolutionary states.

Pogson’s relation: 22 1

1

2.5log mm mm

⎛ ⎞− = − ⎜

⎝ ⎠⎟ ; based on the inverse square law, where flux varies as the

inverse second power of the distance, we write Pogson’s relation thus: 2 1 5logm m D− = − , where D is the relative distance; we derive the absolute distance below. It must be pointed out here that this method is only accurate if both WD stars are at similar evolutionary states whose evolutionary histories are similar, otherwise the equivalence won’t hold. In this case, that condition is satisfied. Using the 2007 paper by Harris, Dahn, et al, to obtain the distance and magnitude of the NGC-6720 WD central star and our

magnitude determination of the NGC-2438 WD central star, we write: 22 1

1

5 mm m Logm

⎛ ⎞− = − ⎜

⎝ ⎠⎟ , and then,

since the ratio of m2 and m1 are represented as an inverse square of the distance, we can write 2 1

5( ) ( ) 10

m m

Final InitialD D x−⎛ ⎞

⎜ ⎟−⎝ ⎠= ; ( ) ( )15.75 16.85704 10

5Final pcD x + −⎛= ⎜ −⎝ ⎠⎞⎟ where 704 pc is the distance to NGC-

6720. Evaluating this expression, we compute the distance to the WD central star of NGC-2438 to be 1.168 (+/- 0.2) Kpc or 3.8 (+/- 0.6) Kly, a value consistent with the accepted value of 3 Kly. We adopt and carry along the one sigma uncertainty of 0.55 mas as published in the 2007 paper by Harris, Dahn, et al for NGC-6720. The distance to NGC-2438, as determined here, is consistent with and agrees very well with the accepted expansion rates and post AGB evolutionary time frames (Appendix B) of Planetary Nebulae. In closing, we determine the inner, bright, physical core [of PN NGC-2438] to be 0.57 Ly, a value consistent with other, similarly evolved planetary nebulae such as NGC-6720.


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17 Harris, Dahn, Canzian, Guetter, et al, 2007; Trigonometric Parallaxes of Central Stars of Planetary Nebulae; The Astronomical Journal, 133:631 – 638, 2007 February


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Conclusion Association of NGC-2437 and NGC-2438 One of the purposes of this study, now concluded, was to determine if there exists any interdependence, now, or in the past, between NGC-2437 and NGC-2438. We have determined the distance to NGC-2437 to be 1.8 (+/- 0.6) Kpc and the distance to NGC-2438 to be 1.168 (+/- 0.2) Kpc, a difference of over 0.6 Kpc or 2 Kly! We therefore unambiguously conclude that no association exists now and dispel any ambiguities or uncertainty as to any previous association between the two objects. NGC-2438 is a foreground object, much younger than the cluster given the brief, punctuated evolution of planetary nebulae, objects that appear, expand and evaporate into the Interstellar Medium on timescales that are measured in tens of thousands of years compared to the evolution of a galactic cluster, objects whose lifetimes are measured in hundreds of millions of years, if not longer. We assert that no association now exists or that it ever did, either through a chance encounter or otherwise. Two Stellar Populations We present clear and compelling evidence for 2 distinct stellar populations towards NGC-2437/ 38 at galactic longitude 115º. Further, we articulate the various properties of those 2 populations and present them in chart form with concise explanations of each presented as captions. HR Diagram and Turnoff We present a comprehensive HR Diagram for both stellar populations where we “age” NGC-2437 using the “Turn Off” method. Based on our study, we determine the age of NGC-2437 to be at least 900 mya. We indicate the placement of the cluster’s Horizontal Branch stars and the placement of candidate giant and supergiant stars. NGC-2438 as a model End State for Solar Class Stars We conclude that NGC-2438 is not a model end state for solar class stars and that it had at least a 3 solar mass progenitor. This conclusion is based on the relatively rare character of it’s fiercely hot White Dwarf central star as a NTE whose effective surface temperature is at least 50,000 K and possibly as hot as 110,000 K. We adopt the hybrid distance-modulus method described in the previous section to determine the distance to the NGC-2438 WD. That distance is 1.168 (+/- 0.2) Kpc.

Tables and Illustrations

Figure 1 illustrating the HR Diagram produced using the Hipparcos photometric data of 22,000 stars. Note the author’s overlay grid, used to correlate B – V index and Absolute Magnitude


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Figure 2 We present our empirically derived, best-fit plot of NGC-2437 field-star photometric data with

Hipparcos data, plotting Absolute Bolometric Magnitude, M(bol), as a function of B – V. Using the sun, Altair, Fomalhaut, Sirius and Vega, we compare our computed results with accepted values using our derived, straight-line solution and thus, present the following table. Table 1 comparing select test-case stars with our empirically derived Absolute Bolometric Magnitude

Star B - V M(V) Accepted Value M(V)

Computed Value Spectral

Class Sun 0.656 4.75 4.71193 G2V Atair 0.22 2.18 2.143498 A7V Fomalhaut 0.09 1.377681 A3V Sirius 0.01 0.906409 A1V Vega 0 0.38 0.8475 A0V


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Figure 3 We present our empirically derived, best-fit plot of NGC-2437 field-star photometric data with

Hipparcos data, plotting Absolute Visual Magnitude, M(V), as a function of B – V, after application of the Bolometric Correction. Using the sun, Altair, Fomalhaut, Sirius and Vega, we compare our computed results with accepted values using our derived, straight-line solution and thus, present the following table. The result is in excellent agreement with the accepted values for the cooler of these Main Sequence, comparison stars. The increasingly divergent computed and accepted values for the earlier, more luminous stars Sirius and Vega would be consistent with the slope of the Main Sequence increasing with increasing luminosity. Table 2 comparing select test-case stars with our empirically derived Absolute Visual Magnitude

Star B - V M(V) Accepted Value M(V) Computed

Value Spectral

Class Sun 0.656 4.83 4.944818 G2V Atair 0.22 2.21 2.255962 A7V Fomalhaut 0.09 1.73 1.454239 A3V Sirius 0.01 1.42 0.960871 A1V Vega 0 0 0.8992 A0V Based on figures 2 and 3, it can be concluded that the preponderance of all stars included in this study are Main Sequence stars.


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Figure 4 illustrating the two separate stellar populations and the mean distance to each. These 2 separate populations are identified by the distinct break in absolute visual magnitude just above M(V) = 2.00. This break would be consistent with the larger, more distant and more diverse population of the Milky Way’s Perseus arm stars as compared to the closer and more luminous early to mid A stars of NGC-2437. The presence of these two distinct stellar populations, accompanied by the paucity of any stars in a very narrow region just above M(V) = 2.00, would be consistent with recent renderings of the Milky Way using IR observations with the Spitzer Space Telescope (Fig 5). Indeed, our data maps very well with this data and, in effect, confirms its veracity. Respectively, the distances are 1.8 Kpc to NGC-2437 and 2.4 Kpc to the more distant Perseus arm stars.


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Figure 5 clearly illustrating the two, distinct stellar populations of NGC-2437, centered at 2 kpc and the more distant, more diverse stars of the Milky Way’s Perseus arm, centered at over 3 kpc Table 3 providing the spatial distance distributions of both stellar populations as illustrated in Figure 5

Distance (pc) Frequency 2.493598669 11032.588829 1072062.684059 2253092.779289 2384122.874519 975152.969749 496183.064978 227213.160208 10


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Figure 6 illustrating the galactic coordinate grid18 and the two stellar populations described in Figures 4 and 5. We spatially fit the map with our NGC-2437 and Perseus arm data. We note the structures towards galactic longitude 115, the direction towards NGC-2437/ NGC-2438 and the more distant Perseus Arm stars. The 2 stellar populations, as represented in Figure 4, are clearly the analogs of this region of the galaxy, complete with the distinct “break” in absolute magnitude, separated by luminosity and distance; note the intervening paucity of stars, highlighted by the empty space between NGC-2437 at 1.8 Kpc and the second, more distant population, encircled at 2.4 Kpc. Galactic latitude, in this diagram, is indicated in 5 Kly units.


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18 http://www.spitzer.caltech.edu/images/1927-ssc2008-10a1-The-Milky-Way-Galaxy

http://www.spitzer.caltech.edu/images/1927-ssc2008-10a1-The-Milky-Way-Galaxy

Figure 7 illustrating the distance distribution of NGC-2437 (M-46) cluster stars. Note the mean distance centered just below 1.8 Kpc, a value consistent with the accepted value of 5.4 kly.

Table 4 indicating stellar population distribution by distance for NGC-2437. In choosing the population stars that were included in this spread, it is a given that all stars are part of the same cluster population and are, therefore, at a comparable luminosity and distance. At a one sigma distance from the mean of 1.781 Kpc, there are no more than 308 stars, at a two sigma distance, there are no more than 449 stars. Given the two sigma spread of over 1.2 Kpc, a value comparable with the cluster’s mean distance, it is unlikely that these additional 141 stars are cluster stars. We therefore constrain the maximum cluster population to no more than 308 stars, a value consistent with an estimated upper limit of 500.

Mean Distance(pc) 1781 Population (one sigma width) 308 One Sigma (pc) 610 1171 - 2392 pc Two Sigma (pc) 1220 Population (two sigma width) 449 561 - 3001 pc


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Figure 7b illustrating the distance distribution of the more distant Perseus-arm stars. Table 5 indicating stellar population distribution by distance for the more distant Perseus-arm stars

Mean Distance(pc) 2426 Population (one sigma width) 353 One Sigma (pc) 714 1712 - 3140 pc


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Figure 8 illustrating the B – V spread for NGC-2437 Table 6 indicating mean B – V and stellar population of NGC-2437 for a one sigma width Mean (B - V) 0.270822184Population (one sigma width) One Sigma (B -V) 0.168032872 1171 - 2392 pc 308


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Figure 9 illustrating the B – V spread for NGC-2437 with the mean centered at 0.2552

Figure 10 illustrating the M(V) spread for NGC-2437 with the mean centered at 2.67


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Figure 11 illustrating the M(V) spread for NGC-2437 with the mean centered at 2.67 Table 7 indicating the absolute visual magnitude spread for NGC-2437 cluster stars

M(V) Frequency % of Total Spectral Class B - V 0.8413 1 0.209205 A0V 0

1.081651 3 0.6276151 A0V 0 1.322003 10 2.0920502 A1V 0.03 1.562354 45 9.4142259 A2V 0.07 1.802705 62 12.970711 A3V 0.09 2.043056 47 9.832636 A5V 0.26 2.283408 42 8.7866109 A9V 0.3

This illustration provides a histogram of the absolute visual magnitude spread of NGC-2437. It is clear that the preponderance of the stars in this cluster are early A-class stars with 13% of their population being Fomalhaut-class (A3V) stars. It is a given that all stars are at the same distance and, therefore, are of comparable age and luminosity. The distributions presented in Figures 8, 9, 10 and 11 were based on the distance determinations highlighted in Figure 7 and Table 4.


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Figure 12 illustrating the absolute magnitude distribution of the more distant Perseus arm stars Table 8 indicating the absolute visual magnitude spread for the more distant Perseus-arm stars

M(V) Frequency % of total 0.734467 1 0.350.968199 1 0.351.201932 2 0.711.435665 4 1.421.669398 1 0.351.903131 7 2.482.136864 8 2.842.370596 18 6.382.604329 29 10.282.838062 43 15.253.071795 50 17.733.305528 43 15.253.539261 34 12.063.772993 14 4.964.006726 15 5.324.240459 8 2.84

More 4 1.42


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NGC-2437 (Messier 46), NGC-2438 AIts Central White Dwarf as a Model End State for S

nd olar Class Stars

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Figure 13 illustrating the absolute magnitude distribution of all field stars included in this study Table 9 provides the details for Figure 12

M(V) Frequency Percentage 0.734466669 1 0.13%1.386628715 30 3.92%2.038790761 150 19.61%2.690952807 164 21.44%3.343114853 216 28.24%3.995276899 104 13.59%4.647438945 44 5.75%5.299600991 27 3.53%5.951763036 19 2.48%

Total Stars Studied 765 Cluster stars

Perseus Arm Stars In this breakdown we see a correlation between the number of early-mid, A class stars with an M(V) of approximately 2 or less with the aggregate population of NGC-2437 cluster stars (see Figure 11). We therefore conclude that the pink-highlighted stars are cluster stars and the blue-highlighted, less-luminous F-class stars are the more distant Perseus arm stars. This conclusion would be consistent with their respective populations: the population of NGC-2437 cluster stars are, quite simply, closer and limited to the cluster; the Perseus arm population stars are limited to the myriad stars of a prolific, star-forming region of the Milky Way: the Perseus arm. Clearly, there would be some overlap between the two groups but, it would be safe to conclude that the majority of the more luminous stars in this study belong to NGC-2437.

NGC-2437 (Messier 46), NGC-2438 And

Its Central White Dwarf as a Model End State for Solar Class Stars Page 27

Figure 14 illustrating the “Turn-off” point for NGC-2437 and the more distant Perseus-arm stars This illustration plots the apparent visual magnitude vs. the B – V index for the aggregate of all 766 field stars included in this study. We present the “Turn Off” point for NGC-2437 stars. It also includes the Main Sequence tracks for the two populations presented in this study, the location of sub-giant class field stars, possible Giants, Supergiants, Horizontal Branch stars and the placement of a solar-class (G2V) star at the mean distance for both populations (this would provide a modicum of comparison for the sun and the field stars in terms of luminosity). For reference, we also include the placement of the 2 bright field stars discussed with Figure 22. Table 10 indicating frequency of B – V index in terms of Spectral Class

B - V Frequency Spectral Class -0.0162 1

0.029782353 4 A1V 0.075764706 23 A2V 0.121747059 38 A4V 0.167729412 32 A5V 0.213711765 33 A6V 0.259694118 21 A7V 0.305676471 27 A9V 0.351658824 25 0.397641176 25 0.443623529 17 0.489605882 16 0.535588235 9

Turnoff stars

*Note: spectral class determined by fitting data to values computed and listed in table 2


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NGC-2437 and NGC-2438 Images and Illustrations We present all our images of NGC-2438, with Figure 23, the final, fully-integrated image as the concluding image in this section. Integration times for all images and photometric data included in this study were 360 seconds using the 0.61m Ritchey–Chrétien reflector of Light Buckets, Rodeo, New Mexico, operating at F/8. Full instrumentation specifics are found in Appendix C. All color indexing, photometry, RGB and L-RGB imaging was accomplished according to the Johnson-Cousins (U)BVRI standard (Appendix D). Equipment limitations prevented any near UV photometry or imaging. All image processing and enhancement was accomplished using MaxIM DL, version 5.07 and Adobe Photoshop, version CS2. Photometry was accomplished using MaxIM DL, SExtractor (Source Extractor), version 2.8.6 (Appendix E), a Linux-only client, and MS Excel, version 2003.

Figure 15 illustrating NGC-2438 in Red light (600 nm) Note the presence of the central White Dwarf. Since there is no line emission at this particular wavelength, the WD is visible.


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Figure 16 illustrating NGC-2438 in the Red light of Hydrogen Alpha (656.3 nm) Note the apparent absence of the central White Dwarf in this narrow band image. This observation is consistent with the position that the planetary nebula is absorbing and reradiating the light at the specific wavelength (of H Alpha, in this case). The 656.3 nm light from the WD is highly absorbed by the abundant hydrogen and reradiated as H Alpha line emission by the planetary nebula; the continuum flux at a given wavelength that corresponds to a particular line emission will be absorbed by the nebular gas and reradiated as line emission [by the planetary nebula].


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Figure 17 illustrating NGC-2438 in the Red light of Singly ionized Sulfur (672 nm) Note the faint but recognizable image of the central White Dwarf in this narrow band image. Aside from the high relative flux of hydrogen alpha (Figure 16), this observation is consistent with the position that the ratio of sulfur to hydrogen is very small. In fact, it turns out that this particular White Dwarf is a member of a class of White Dwarf that cannot be modelled as a Blackbody19, that it is a very hot, non-thermal emitter. In the previous, narrow-band image, the relative abundance of Hydrogen as compared to the relative paucity of Sulfur, as represented in this image, would explain the presence of the WD in this image but not the previous. Stated differently, the 656.3 nm light from the WD is highly absorbed by the relatively abundant hydrogen and reradiated as H Alpha line emission by the planetary nebula; not so for the sulfur.


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19 Magnitudes of central stars of planetary nebulae; Gathier, R.; Pottasch, S. R., 1988

Figure 18 illustrating NGC-2438 in the V Band (530 nm)


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Figure 19 illustrating NGC-2438 in the Blue-Green light of Doubly ionized Oxygen (501 nm) Note the apparent absence of the central White Dwarf in this narrow band image. This observation is consistent with the position that the planetary nebula is absorbing and reradiating the light at the specific wavelength (of OIII, in this case). The 501 nm light from the WD is highly absorbed by the relatively abundant oxygen and reradiated as O III line emission by the planetary nebula.


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Figure 20 illustrating NGC-2438 in the B Band (420 nm)


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Figure 21 illustrating the fully integrated L-RGB image of NGC-2438 This image was processed and enhanced to bring out the very hot (and very blue) central White Dwarf.


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Figure 22 processed to bring out the more subtle colors of the various field stars Note the 2 yellow-orange foreground field stars on the right. The indicated distances are based on a Main Sequence luminosity and, without an independent confirmation of distance (parallax), we cannot assign a luminosity class and have, instead, simply indicated their spectral class. This data was culled from the master data spread sheet (attached as a separate document). If, as late G and early K stars, they are on the Main Sequence, they would clearly not be member stars of either population under study but much closer. They are, however, among the brightest of the field stars but also among the closest at 127 and 69 parsecs respectively if a Main Sequence luminosity is adopted. They are labelled and represented in Figure 14 as “field stars”. It is interesting to note that they present with the decidedly yellow-orange cast of cooler, sub-solar class stars with the early K star the slightly brighter, more orange of the 2.

B - V Color Normalized B - V Log T T Mag (mv) Mag (Abs-Bol) Bolom

Correctn Mag

(Abs-Vis) Fully Corrected Dist

pc/ Ly Spec Class

0.3727 0.7317 3.751 5639 10.9 5.162 -0.2101 5.3722 127.3/ 415 G70.5024 0.8614 3.716 5199 10.47 5.928 -0.3488 6.277 68.80/ 224 K1


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Figure 24 illustrating the extended shell and halo surrounding NGC-2438 Image credit Daniel Lopez, Instituto de Astrofisica de Canarias This image was obtained by Daniel Lopez of the Astrophysical Institute of The Canaries (Instituto de Astrofisica de Canarias) using the IAC-80 telescope at Tenerife Observatory, Mt. Tiede, The Canary Islands. Although this image was obtained with a 0.8m telescope, an aperture comparable to the telescope used for this study, and does capture the extended shell and halo of the object, the white dwarf central star is rather subdued in comparison to our image. Note: Our determination of distance using expansion models would necessarily need to take into account these faint, outer shells. Although we would not necessarily alter our distance determination, we would need to modify the expansion rate.


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Figure 23 with the various elements represented by their respective line emissions Although a NII and HeII filter weren’t specifically used, these ions of Nitrogen and Helium can be inferred as being present and would be represented in the R and B band nebular emission. According to the Johnson-Cousins standard (Appendix D), the NII line at 658 nm has a relative intensity of 83% and the HeII line at 487 nm has a relative intensity of 50%.


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Appendix A Sample Photometric Data

Flux Max X_Pos Y_Pos Select B - V Color Normalized B - V Log T T Mag M(v)

Mag (Bol) BC

Mag Abs-V

Dist Pc

Dist Ly

48924.1 1328.792 440.643 v -0.1911 0.1679 3.90422 8020.8 10.381.8326-0.1515 1.9841 478.7 1560.7 227.0241 773.245 440.731 2420.603 1212.502 440.845

45507.5 1328.84 440.888 i 36.25994 1021.108 440.907 58341.05 1327.973 441.016 b 30800.38 1329.298 441.392 r As explained in our previous work, Source Extractor (Appendix E) was used to parse the individual FITS data sets and extract the various intensities. That extraction is output as Flux Max, X and Y positions, respectively. We choose to sort by absicca within ordinate and then merge with and operate on that data, using it in the various computations. The various wave bands are labeled and color coded, allowing for relatively easy assimilation and reconciliation. Legend: B V R I(c)


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Appendix B

Photometric Data For NGC-2438 and its Central White Dwarf Temperature, Luminosity and Distance Calculations based on Standard Candle Distance and Luminosity Modeling20

Star # Blue Int21 V Int22 Mb/Mv B - V Bolometric Correction Corrected BV Indic v-Mag Comp Bol-Mag V-Mag

0 56040 46355 1.208931075 -0.206003853 -0.159504615 0.152996147 16.84792187 13.54816106 13.70766567 Computed Log Temp Temp Comp Temp(b,v) Radius (Km) Solar Radii

3.9083 8096 8096 6400000 0.00956

Luminosity (W) Luminosity (sun) Log Luminosity (sun) Computed Sp Type Log D(pc) Distance (pc) Distance (ly)1.25371E+23 0.000325638 -3.49 WD 1.62805124 42.46696654 138.4423109

Distance determination using an accepted PN Expansion Rate and an Estimated Minimum Expansion Time since AGB23 Distance (pc - by exp) Distance (Ly) Radius (pc - by expansion) Radius (Ly - by expansion) Abs Visual Mag (from Exp)

1167.77 3806.93 0.17 0.57 6.51 Comp Temp(b,v) Radius Solar Radii Luminosity Luminosity (sun) Log Luminosity (sun)

8096 6400000 0.00956 1.25371E+23 0.000325638 -3.49 13519 6400000 0.00956 9.75008E+23 0.002532487 -2.60

110000 6400000 0.00956 4.27322E+27 11.09927303 1.05

Log D(pc) Distance (pc) Distance (ly)1.62805124 42.46696654 138.44231091.89322613 78.20348919 254.94337482.294832806 197.166354 642.762314

Image scale and Angular Dimensions NGC-2438 Size (arc-sec) x 741 846= 59.85 NGC-2438 Size (arc-sec) y 684 794= 62.7

20 Blackbody Modeling 21 Normalized integrated intensity (Blue): 56040 22 Normalized integrated intensity (Visible): 46355 23 Detail included as separate attachment


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Manually Integrated Intensity Map (Blue) 0 0 0 0 0 0 00 2696 2977 3209 3360 3332 0

0 2947 3242 3403 3419 3247 00 3022 3335 3594 3542 3280 00 2848 3157 3221 3271 3152 00 2677 2905 2992 2957 2755 00 0 0 0 0 0 0

Raw integrated intensity 78540 Normalized integrated intensity 56040 Manually Integrated Intensity Map (Visible)

2106 2319 2374 2583 21062172 2472 2599 2633 24722274 2518 2627 2631 24372264 2548 2592 2455 22552172 2230 2293 2274 2149

Raw integrated intensity 59555Normalized integrated intensity 46355 Note: The raw integrated intensity is simply the aggregate sum of all intensities. The normalized integrated intensity subtracts out an average background intensity from each pixel, a value determined by comparing the central nebular background with the darkest region of the background sky. This correction is especially important in the specific case of a White Dwarf within a Planetary Nebula where the nebular intensity surrounding the central White Dwarf would serve to obscure the true intensity of the White Dwarf. The FWHM intensity is found at the third cell from the center cell.

Appendix C The 0.61 Meter Flagship Instrument of LightBuckets24

Telescope Specifications Manufacturer: RC Optical Systems, Inc., Flagstaff, Arizona, USA Aperture: 0.61 meters (24”) Effective Focal ratio: F/8 Location: Rodeo, New Mexico, USA Elevation: 1.26 Km Filters available: L, B, G, V, R, Ic, OIII, SII, Ha Filter Carousel Size: 9 position w/ 50mm round CCD Manufacturer: Apogee Model: Alta U42 Pixel Size: 13.5µ x 13.5µ QE: >90% @ 550nm Chip Size: 4.2 M-Pixel, 2048 x 2048 Field Of View: 20 x 20 arcminutes Image Scale: 0.57 arc-seconds/ pixel



24 http://www.lightbuckets.com

http://www.lightbuckets.com/



Appendix D The Johnson-Cousins Standard The following tables describe the percentage of incident radiation at the given wavelength (specified in nanometers) with the centroid located at 1.000 Blue (B) Wavelength Transmitted energy 360 0.0 370 0.030 380 0.134 390 0.567 400 0.920 410 0.978 420 1.000 430 0.978 440 0.935 450 0.853 460 0.740 470 0.640 480 0.536 490 0.424 500 0.325 510 0.235 520 0.150 530 0.095 540 0.043 550 0.009 560 0.000 Red (R) Wavelength Transmitted energy

Visible (V)Wavelength Transmitted energy 470 0.000 480 0.030 490 0.163 500 0.458 510 0.780 520 0.967 530 1.000 540 0.973 550 0.898 560 0.792 570 0.684 580 0.574 590 0.461 600 0.359 610 0.270 620 0.197 630 0.135 640 0.081 650 0.045 660 0.025 670 0.017 680 0.013 690 0.009 700 0.000

550 0.00 560 0.23 570 0.74 580 0.91 590 0.98 600 1.00 610 0.98 620 0.96 630 0.93 640 0.90 650 0.86 660 0.81 670 0.78 680 0.72 690 0.67 700 0.61 710 0.56 720 0.51 730 0.46 740 0.40 750 0.35 800 0.14 850 0.03



Infrared (Ic)Wavelength Transmitted energy 700 0.000 710 0.024 720 0.232 730 0.555 740 0.785 750 0.910 760 0.965 770 0.985 780 0.990 790 0.995 800 1.000 810 1.000 820 0.990 830 0.980 840 0.950 850 0.910 860 0.860 870 0.750 880 0.560 890 0.330 900 0.150 910 0.030 920 0.000 Ultraviolet (U) Wavelength Transmitted energy 300 0.00 305 0.016 310 0.068 315 0.167 320 0.287 325 0.423 330 0.560 335 0.673 340 0.772 345 0.841 350 0.905 355 0.943 360 0.981 365 0.993 370 1.000 375 0.989 380 0.916 385 0.804 390 0.625 395 0.423 400 0.238 405 0.114 410 0.051 415 0.019 420 0.000



Appendix E SExtractor Input Controls

Input controls for V-Band analysis of NGC-2437 # Default configuration file for SExtractor 2.3b2 # EB 2003-02-07 #-------------------------------- Catalog ------------------------------------ CATALOG_NAME M46-V.cat # name of the output catalog CATALOG_TYPE ASCII_HEAD # "NONE","ASCII_HEAD","ASCII","FITS_1.0" # or "FITS_LDAC" PARAMETERS_NAME default.param # name of the file containing catalog contents #------------------------------- Extraction ---------------------------------- DETECT_TYPE CCD # "CCD" or "PHOTO" FLAG_IMAGE flag.fits # filename for an input FLAG-image DETECT_MINAREA 5 # minimum number of pixels above threshold DETECT_THRESH 1.5 # <sigmas> or <threshold>,<ZP> in mag.arcsec-2 ANALYSIS_THRESH 1.5 # <sigmas> or <threshold>,<ZP> in mag.arcsec-2 FILTER Y # apply filter for detection ("Y" or "N")? FILTER_NAME default.conv # name of the file containing the filter DEBLEND_NTHRESH 32 # Number of deblending sub-thresholds DEBLEND_MINCONT 0.000 # Minimum contrast parameter for deblending CLEAN Y # Clean spurious detections? (Y or N)? CLEAN_PARAM 1.0 # Cleaning efficiency MASK_TYPE CORRECT # type of detection MASKing: can be one of # "NONE", "BLANK" or "CORRECT" #------------------------------ Photometry ----------------------------------- PHOT_APERTURES 5 # MAG_APER aperture diameter(s) in pixels PHOT_AUTOPARAMS 2.5, 3.5 # MAG_AUTO parameters: <Kron_fact>,<min_radius> SATUR_LEVEL 500000000.0 # level (in ADUs) at which arises saturation MAG_ZEROPOINT 0.0 # magnitude zero-point MAG_GAMMA 4.0 # gamma of emulsion (for photographic scans) GAIN 0.5 # detector gain in e-/ADU PIXEL_SCALE 0.57 # size of pixel in arcsec (0=use FITS WCS info) #------------------------- Star/Galaxy Separation ---------------------------- SEEING_FWHM 1.2 # stellar FWHM in arcsec STARNNW_NAME default.nnw # Neural-Network_Weight table filename #------------------------------ Background ----------------------------------- BACK_SIZE 64 # Background mesh: <size> or <width>,<height> BACK_FILTERSIZE 3 # Background filter: <size> or <width>,<height> BACKPHOTO_TYPE LOCAL # can be "GLOBAL" or "LOCAL" #------------------------------ Check Image ---------------------------------- CHECKIMAGE_TYPE NONE # can be one of "NONE", "BACKGROUND", # "MINIBACKGROUND", "-BACKGROUND", "OBJECTS", # "-OBJECTS", "SEGMENTATION", "APERTURES", # or "FILTERED" CHECKIMAGE_NAME check.fits # Filename for the check-image #--------------------- Memory (change with caution!) ------------------------- MEMORY_OBJSTACK 2000 # number of objects in stack MEMORY_PIXSTACK 200000 # number of pixels in stack MEMORY_BUFSIZE 1024 # number of lines in buffer #----------------------------- Miscellaneous --------------------------------- VERBOSE_TYPE NORMAL # can be "QUIET", "NORMAL" or "FULL"



Convolution map for Source Intensity Gaussian CONV NORM # 3x3 “all-ground” convolution mask with FWHM = 2 pixels. 1 2 1 2 4 2 1 2 1

SExtractor Output Controls (Generic) default.param # VECTOR_ASSOC FLUX_MAX # ALPHAPEAK_SKY # ALPHAPEAK_J2000 # DELTAPEAK_SKY # DELTAPEAK_J2000 # MAG_ISO # MAG_AUTO # MAG_ISOCOR # MAG_WIN # MAG_SOMFIT # MAG_PSF # MAG_MODEL # MAG_DISK X_IMAGE Y_IMAGE # THETA_IMAGE # ELONGATION # ELLIPTICITY FWHM_IMAGE # ERRX2_IMAGE # ERRY2_IMAGE Out of the hundreds of available output controls for SExtractor, only 4 were used for my analysis. The output data is presented in columns as read from the controls list (default.param). A brief description of each follows: FLUX_MAX: The maximum intensity per object (stars are considered Gaussians) as extracted from the FITS data array X_IMAGE: The X position or abscissa of the source as extracted from the FITS data array Y_IMAGE: The Y position or ordinate of the source as extracted from the FITS data array FWHM_IMAGE : The Full-width, half-maximum value of the source (determined from the source intensity as extracted from the FITS data array via the Point Spread Function) Note: we include all 4 SExtractor text files as separate attachments.



Sample SExtractor Output # 1 FLUX_MAX Peak flux above background [count] # 2 X_IMAGE Object position along x [pixel] # 3 Y_IMAGE Object position along y [pixel] # 4 FWHM_IMAGE FWHM assuming a gaussian core [pixel] 113.0315 1143.578 1.423 1.22 17.27808 1456.516 1.726 5.53 19.03113 867.113 1.841 4.75 551.8174 1834.683 2.027 1.63 60.0896 489.126 5.316 1.60 44.17773 850.647 6.028 1.65 90.5769 1232.633 5.221 1.65 232.7032 140.307 8.341 1.78 84.98767 393.842 2.377 16.64 80.83704 1050.479 2.622 9.01 36.03149 1397.908 2.352 12.69 20.01379 1505.734 3.436 8.48 79.84399 1586.692 2.633 8.86 171.281 206.501 8.231 1.53 94.85181 1542.839 11.983 1.80 33.12817 4.500 11.496 5.57 151.9308 222.204 2.414 10.77 55.93347 1386.740 13.956 1.75 14.64526 1200.778 14.911 4.50 49.89697 1382.688 16.004 1.59 47.9978 257.681 19.534 3.32 24.13391 6.841 5.835 10.81 151.0895 62.464 15.239 1.48 17.05432 1426.649 14.174 6.07 72.67737 1718.672 19.038 1.67 95.32471 1291.723 3.947 8.91 83.79187 1354.920 2.884 9.32 102.4906 1656.822 3.415 10.93 43.51477 821.473 21.032 1.41 30.54248 1805.937 20.986 2.10 146.5695 512.461 19.193 1.44 47.96863 1535.633 16.891 2.54 93.25903 94.558 23.258 1.77



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Use in Estimation of Reddening and Cosmic Microwave Background Radiation Foregrounds; ApJ, 500:525-553, 1998 June 20

• Badiali, M., et al, 2007; Age and Morphology of the Main Sequence from HIPPARCOS HR Diagram Data; Istituto di Astrofisica Spaziale, C.P. 67, 00044 Frascati, Italy; Osservatorio Astronomico di Roma, 00044 Monteporzio, Italy

• Harris, Dahn, Canzian, Guetter, et al, 2007; Trigonometric Parallaxes of Central Stars of Planetary Nebulae; The Astronomical Journal, 133:631 – 638, 2007 February

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• O’Dell, C.R.; 1963, U. Cal., Berkeley; Notes from Observatories, On the Association of NGC 2437 and NGC 2438; Publications of the ASP, Vol. 75, No. 445, p.370-372

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