We present a closed-form, self-consistent spectroscopic framework in which extinction correction is treated as an integral part of the inference rather than as a separate preprocessing step. From emission-line measurements alone, the method simultaneously solves for the electron density (ne), electron temperature (Te), extinction index (c(H beta)), and total-to-selective extinction ratio (RV) within an adopted parametric family of extinction curves. The solution is obtained by minimizing the variance among c(H beta) surfaces in the logne - logTe plane constructed from multiple line-ratio pairs, with RV treated as a free parameter, allowing the extinction law to be constrained directly from the data rather than fixed a priori. A simple rank condition, requiring n >= k + 4 lines for k ionic species, ensures the identifiability of unique solutions, while diagnostics based on the c(H beta)-variance surface provide inexpensive quality control metrics. Noise-free tests recover input parameters exactly at grid points and to interpolation-limited accuracy off grid, validating the analytic formulation and its numerical implementation. When measurement uncertainty is introduced, a clear hierarchy of robustness emerges: plasma parameters remain accurate to less than or similar to 10% over wide ranges of line measurement precision, whereas extinction parameters require subpercent accuracy. For Balmer-line diagnostics, this implies a practical uncertainty threshold of similar to 0.1%-0.2% per line for stable four-parameter recovery, while (ne, Te) alone remain informative at the 1%-2% level. This behavior follows from the geometric conditioning of the objective function surface, where noise flattens constrained directions. The framework clarifies how diagnostic geometry and diversity govern the solution stability in extinction-aware plasma diagnostics, from nebulae to integrated galaxy spectra.

The hydrogen recombination lines H30 alpha, H40 alpha, H42 alpha, H50 beta, and H57 gamma and the underlying bremsstrahlung continuum emission were detected with ALMA in the bipolar nebula Mz3. The source was not spatially resolved, but the velocity profile of the H30 alpha line shows clear indication of maser amplification, confirming previous reports of laser amplification in the far-infrared H recombination lines observed with Herschel Space Observatory. Comparison between the flux densities of the H50 beta, H40 alpha, and H42 alpha lines show overcooling, or darkness amplification by stimulated absorption (dasar effect) at the LSR velocity of about -25 km s-1, which constrains the density of the absorbing region to about 103 cm-3. The H30 alpha line, on the other hand, presents maser lines at LSR velocities of -69 and -98 km s-1, which indicates ionized gas with densities close to 107 cm-3. Although the source of emission was not resolved, it was possible to find the central position of the images for each velocity interval, which resulted in a well defined position-velocity distribution.

As mass-losing asymptotic giant branch (AGB) stars evolve to planetary nebulae (PNe), the mass outflow geometries transform from nearly spherical to extreme aspherical. The physical mechanisms governing this transformation are widely believed to be linked to binarity and the associated production of disks and fast jets during transitional (post-AGB) evolutionary stages. We are carrying out a systematic ALMA survey (Pre-planetAry Nebulae high-angular-resOlution suRvey with ALMA or PANORAMA) of a representative sample of bipolar and multipolar post-AGB objects. We have obtained high angular-resolution (0".1-0".4) observations of the CO(3–2) and/or 6–5 emission in order to probe the spatio-kinematic structure of the collimated outflows and the central disk/torii. The results are remarkable, generally showing the presence of bipolar or multipolar high-velocity outflows, dense toroidal waists, and in one case, a geometrically-thin circular ring around the central bipolar nebula. A high degree of point-symmetry characterizes the morphology of the mass ejecta. In this contribution, we present these and other highlights from our survey. We aim to use 2D/3D radiative transfer modeling in order to derive accurate outflow momenta, masses and mass-loss rates for our sample, and build hydrodynamical models that can explain the observed spatio-kinematic structures. These results will then be used to distinguish between different classes of PN-shaping binary interaction models.

H4-1 is a planetary nebula (PN) located in the Galactic halo, and is notably carbon-rich and one of the most metal-deficient PNe in the Milky Way. To unveil its progenitor evolution through the accurate measurement of the gas mass, we conducted a comprehensive investigation of H4-1, using the newly obtained Seimei/KOOLS-IFU spectra and multiwavelength spectro-photometry data. The emission line images generated from the KOOLS-IFU datacube successfully resolve the ellipsoidal nebula and the equatorial flattened disk that are frequently seen in bipolar PNe evolved from massive progenitors. By a fully data-driven method, we directly derived the seven elemental abundances, the gas-to-dust mass ratio, and the gas and dust masses based on our own distance scale. By comparing the observed quantities with both the photoionization model and the binary nucleosynthesis model, we conclude that the progenitors of an initial mass of 1.87 Msun and 0.82 Msun are second generation stars formed ~4 Gyrs after the Big Bang, and underwent mass-transfers, binary merger, and ultimately evolved into a PN showing unique chemical abundances. Our binary model successfully reproduces the observed abundances and also explains evolutionary time scale of H4-1.

Extinction correction is the quintessence of astronomy. To achieve precision astrophysics in plasma diagnostics as in the theme of the present Proceedings, one must perform extinction correction properly before executing any line diagnostics of line-emitting objects including planetary nebulae. By making use of the inseparable relationship between extinction correction and plasma diagnostics, we establish a novel method to determine the physical conditions of a line-emitting target and the extinction characteristics along the line of sight toward the target simultaneously and self-consistently. This approach is made possible by the exact analytical expressions for the extinction parameters in terms of the emission properties of the target and by statistical optimization of the extinction parameters to find the robust physical conditions of the target.

As AGB stars evolve to planetary nebulae (PNe), the geometry of the ejected mass transforms from nearly spherical to extremely aspherical. The mechanisms governing this transformation are plausibly linked to binarity and the associated production of disks and jets during the transitional (post-AGB) evolutionary stage. We are carrying out an ALMA survey of a representative sample of bipolar/multipolar post-AGB objects to obtain high angular-resolution (0″.11) observations of the CO(3–2) and 6–5 emission and study the collimated outflows and central disks. We present highlights from our ongoing survey – e.g., the presence of bipolar or multipolar high-velocity outflows, dense toroidal waists, and in one case, a circular ring around the central bipolar nebula. We will use radiative transfer modeling to derive accurate outflow momenta, masses, and mass-loss rates for our sample, thereby constraining different classes of binary PN-shaping models.

Planetary nebulae (PNe), the ejected envelopes of red giant stars, provide us with a history of the last, mass-losing phases of 90 percent of stars initially more massive than the Sun. Here, we analyse James Webb Space Telescope (JWST) Early Release Observation (ERO) images of the PN NGC3132. A structured, extended H2 halo surrounding an ionised central bubble is imprinted with spiral structures, likely shaped by a low-mass companion orbiting the central star at 40-60 AU. The images also reveal a mid-IR excess at the central star interpreted as a dusty disk, indicative of an interaction with another, closer companion. Including the previously known, A-type visual companion, the progenitor of the NGC3132 PN must have been at least a stellar quartet. The JWST images allow us to generate a model of the illumination, ionisation and hydrodynamics of the molecular halo, demonstrating the power of JWST to investigate complex stellar outflows. Further, new measurements of the A-type visual companion allow us to derive the value for the mass of the progenitor of a central star to date with excellent precision: 2.86+/-0.06 Mo. These results serve as path finders for future JWST observations of PNe providing unique insight into fundamental astrophysical processes including colliding winds, and binary star interactions, with implications for supernovae and gravitational wave systems.

To understand the physical conditions of various gaseous systems, plasma diagnostics must be performed properly. To that end, it is equally important to have extinction correction performed properly, even before performing plasma diagnostics. This means that the physical conditions of the target sources—the very quantities to be derived via plasma diagnostics—must be known even before performing extinction correction, because the degree of extinction is determined by comparing the observed spectra of the target sources with their theoretically predicted counterparts. One way to resolve this conundrum is to perform both extinction correction and plasma diagnostics together by iteratively seeking a converged solution. In fact, if these analyses are performed self-consistently, a converged solution can be found based solely on well-calibrated line intensities, given the adopted extinction law and the RV value. However, it is still rare to find these analyses performed numerically rigorously without unnecessary analytical approximations from start to finish. In this contribution for the APN 8e conference, we would like to review this convoluted problem and sort out critical issues based on the results of our recent experiments. It appears that the convoluted theoretical and observational progresses exacerbated by the highly numerical nature of these analyses necessitated a number of analytical simplifications to make the problem analytically tractable in the pre-computer era and that such analytical simplifications still remain rampant in the literature today, even after ample computational resources became readily available. Hence, the community is encouraged to do away with this old habit of sidestepping numerical calculations that was a necessary evil in the past. This is especially true in the context of spatially-resolved 2-D spectroscopy, which obviously conflicts with the uniformity assumption often blindly inherited from 1-D spectroscopy.

Plasma diagnostics are the bases of investigation into the physical and chemical properties of line-emitting gaseous systems. To perform plasma diagnostics properly, it is essential to correct the input spectrum for extinction properly. This is simply because determining the degree of extinction is dependent on the physical properties of the line-emitting gas. Hence, both extinction correction and plasma diagnostics have to be performed simultaneously and self-consistently. By comparing the results of analyses performed for a sample of nine bright planetary nebulae in M 31 with and without the proper extinction correction and plasma diagnostics, we demonstrate how initial assumptions for the physical conditions of the line-emitting gas in extinction correction would compromise the results of the entire analyses. While the electron density/temperature are relatively immune to the imposed inconsistent assumptions, the compromised extinction would cause systematic offsets in the extinction-corrected line strengths, which consequently would impose adverse effects on the resulting ionic and elemental abundances, and other inferences made from the incorrect results. We find that this M 31 PN sample simply represents those around the high-mass end of the mass range for low-mass planetary nebula progenitor stars as expected from the existing theoretical models. It appears that the suspicion raised in the previous study - these PNe being anomalously nitrogen overabundant - is simply caused by the apparent underestimate in extinction that originates from the imposed inconsistent assumptions in extinction correction. In a larger context, the results of plasma diagnostics in the literature without seeking simultaneous self-consistency with extinction correction have to be handled cautiously. Ideally, such previous results should be re-evaluated by seeking simultaneous self-consistency.

Six images of IRC+10216 taken by the Hubble Space Telescope at three epochs in 2001, 2011, and 2016 are compared in the rest frame of the central carbon star. An accurate astrometry has been achieved with the help of Gaia Data Release 2. The positions of the carbon star in the individual epochs are determined using its known proper motion, defining the rest frame of the star. In 2016, a local brightness peak with compact and red nature is detected at the stellar position. A comparison of the color maps between 2016 and 2011 epochs reveals that the reddest spot moved along with the star, suggesting a possibility of it being the dusty material surrounding the carbon star. The relatively red, ambient region is distributed in an Ω shape and corresponds well to the dusty disk previously suggested based on near-infrared polarization observations. In a larger scale, differential proper motion of multiple ring-like patterns in the rest frame of the star is used to derive the average expansion velocity of transverse wind components, resulting in ∼12.5 km s−1(d/123 pc), where d is the distance to IRC+10216. Three-dimensional geometry is implied from its comparison with the line-of-sight wind velocity determined from half widths of submillimeter emission line profiles of abundant molecules. Uneven temporal variations in brightness for different searchlight beams and anisotropic distribution of the extended halo are revisited in the context of the stellar light illumination through a porous envelope with postulated longer-term variations for a period of ≲10 yr.

In this work, we propose a proper plasma analysis practice (PPAP), an updated procedure of plasma diagnostics in the era of spatially resolved spectroscopy. In particular, we emphasize the importance of performing both of the extinction correction and the direct method of plasma diagnostics simultaneously as an integrated process. This approach is motivated by the reciprocal dependence between critical parameters in these analyses, which can be resolved by iteratively seeking a converged solution. The use of PPAP allows us to eliminate unnecessary assumptions that prevent us from obtaining an exact solution at each element of the spectral imaging data. Using a suite of Hubble Space Telescope/WFC3 narrowband images of the planetary nebula, NGC 6720, we validate PPAP by (1) simultaneously and self-consistently deriving the extinction, c(Hβ), and electron density/temperature distribution, (n e([S ii]), T e([N ii])), maps that are consistent with each other, and (2) obtaining identical metal abundance distribution maps, (n(N+)/n(H+), n(S+)/n(H+)), from multiple emission line maps at different wavelengths/transition energies. We also determine that the derived c(Hβ) consists both of the interstellar medium and circumsource components and that the ionized gas-to-dust mass ratio in the main ring is at least 437 and as high as about 1600. We find that, unless we deliberately seek self-consistency, uncertainties at tens of % can easily arise in outcomes, making it impossible to discern actual spatial variations that occurs at the same level, defeating the purpose of conducting spatially resolved spectroscopic observations.

Recent abrupt changes of CW Leonis may indicate that we are witnessing the moment that the central carbon star is evolving off the Asymptotic Giant Branch (AGB) and entering into the pre-planetary nebula (PPN) phase. The recent appearance of a red compact peak at the predicted stellar position is possibly an unveiling event of the star, and the radial beams emerging from the stellar position resemble the feature of the PPN Egg Nebula. The increase of light curve over two decades is also extraordinary, and it is possibly related to the phase transition. Decadal-period variations are further found in the residuals of light curves, in the relative brightness of radial beams, and in the extended halo brightness distribution. Further monitoring of the recent dramatic and decadal-scale changes of this most well-known carbon star CW Leonis at the tip of AGB is still highly essential, and will help us gain a more concrete understanding on the conditions for transition between the late stellar evolutionary phases.

Non-variable OH/IR stars are thought to have just left the asymptotic giant branch (AGB) phase. In this conventional picture, they must still show strong circumstellar extinction caused by the dust ejected during the AGB phase, and the extinction is expected to decrease over time because of the dispersal of the circumstellar dust after the cessation of the stellar mass loss. The reduction of the extinction makes the stars become apparently brighter and bluer with time especially in the near-infrared (NIR) range. We look for such long-term brightening of non-variable OH/IR stars by using 2MASS, UKIDSS, and OAOWFC survey data. As a result, we get multi-epoch NIR data taken over a 20-year period (1997-2017) for 6 of 16 non-variable OH/IR stars, and all six objects are found to be brightening. The K-band brightening rate of five objects ranges from 0.010 to 0.130 mag yr$^{-1}$, which is reasonably explained with the conventional picture. However, one OH/IR star, OH31.0-0.2, shows a rapid brightening, which cannot be explained only by the dispersal of the dust shell. Multi-color (J-, H-, and K-band) data are obtained for three objects, OH25.1-0.3, OH53.6-0.2, and OH77.9+0.2. Surprisingly, none of them appears to have become bluer, and OH53.6-0.2 is found to have been reddened with a rate of 0.013 mag yr$^{-1}$ in (J-K). Our findings suggest other mechanisms such as rapid changes in stellar properties (temperature or luminosity) or a generation of a new batch of dust grains.

This workshop is the second of the WORKPLANS series, which we started in 2016. The main goal of WORKPLANS is to build up a network of planetary nebulae (PNe) experts to address the main open questions in the field of PNe research. The specific aims of the WORKPLANS workshop series are (i) to discuss and prioritize the most important topics to be investigated by the PN community in the following years; (ii) to establish a network of excellent researchers with complementary expertise; (iii) to formulate ambitious observing proposals for the most advanced telescopes and instrumentation presently available (ALMA, SOFIA, VLT, GTC, HST, etc.), addressing those topics; and (iv) to develop strategies for major proposals to future observatories (JWST, ELT, SPICA, Athena, etc.). To achieve these goals, WORKPLANS II brought together experts in all key sub-areas of the PNe research field, namely: analysis and interpretation of PNe observational data; theoretical modeling of gas and dust emission; evolution from Asymptotic Giant Branch stars (PNe progenitors) to PNe; and the instrumentation and technical characteristics of the relevant observatories.

Planetary nebulae (PNe) are often recognized as the hallmark of compact H ii regions in the Universe. However, there exist dusty neutral regions extending beyond the central ionized region. We demonstrate that such dusty neutral regions (also known as photo-dissociation regions, or PDRs) around the central ionized region are significant parts of PNe in terms of energetics and mass. We do so by using our latest dusty photoionization model of NGC 6781 (of 13 parameters) based on one of the most comprehensive panchromatic data sets ever assembled for a PN encompassing from X-ray to radio (of 136 constraining data, including 19 flux densities, 78 line fluxes, and 37 band fluxes). We find that NGC 6781, evolved out of a 2.25–3.0 M ⊙ star located 460 pc away from us, possesses a massive concentration of neutral gas (molecular hydrogen) just beyond the central ionized region and that the amount of ionized gas in NGC 6781 is only 22% of the observationally accounted amount of matter in the circumstellar environment, which itself does not even account for the amount of mass presumably ejected by the central star during the last thermal pulse event according to the latest evolutionary models. This means that the observed nebula in this PN is only the tip of the iceberg.

The AKARI infrared astronomical satellite produced all-sky survey (AFASS) maps in the far-infrared at roughly arcminute spatial resolution, enabling us to investigate the whole sky in the far-infrared for objects having surface brightnesses greater than a few to a couple of dozen MJy sr(-1). While the AFASS maps are absolutely calibrated against large-scale diffuse emission, it was uncertain whether or not an additional flux correction for point sources was necessary. Here, we verify that calibration for point-source photometry in the AFASS maps is proper. With the aperture correction method based on the empirical point spread function templates derived directly from the AFASS maps, fluxes in the AKARI bright source catalogue (BSC) are reproduced. The AKARI BSC fluxes are also satisfactorily recovered with the 1 sigma aperture, which is the empirical equivalent of an infinite aperture. These results confirm that in the AFASS maps far-infrared photometry can be properly performed by using the aperture correction method for point sources and by summing all pixel values within an appropriately defined aperture of the intended target (i.e., the aperture photometry method) for extended sources.