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We report spectroscopic surveys of planetary nebulae (PNe) in the Milky Way and Andromeda (M31), using the 10.4-m Gran Telescopio Canarias (GTC). The spectra are of high quality and cover the whole optical range, mostly from 3650 \r{A} to beyond 1 micron, enabling detection of nebular emission lines critical for spectral analysis as well as photoionization modeling. We obtained GTC spectra of 24 compact (angular diameter <5 arcsec) PNe located in the Galactic disk, ~3-20 kpc from the Galactic centre, and can be used to constrain stellar evolution models and derive radial abundance gradients of the Milky Way. We have observed 30 PNe in the outer halo of M31 using the GTC. These halo PNe are uniformly metal-rich and probably all evolved from low-mass stars, consistent with the conjecture that they all formed from the metal-rich gas in M31 disk but displaced to their present locations due to galaxy interactions., Comment: 6 pages, 4 figures, in production; Proceedings of the IAUS384: "Planetary Nebulae: a Universal Toolbox in the Era of Precision Astrophysics", Krakow, Poland, September 4-8, 2023

We present an unbiased $\lambda$ 3 mm spectral line survey (between 84.5 and 115.8 GHz), conducted by the Purple Mountain Observatory 13.7 meter radio telescope, together with updated modeling results, towards the carbon-rich Asymptotic Giant Branch star, IRC+10216 (CW Leo). A total of 75 spectral lines (96 transitions) are detected, and identified to arise from 19 molecules: C$_2$H, $l$-C$_3$H, C$_4$H, CN, C$_3$N, HC$_3$N, HC$_5$N, HCN, HNC, CH$_3$CN, MgNC, CO, $c$-C$_3$H$_2$, SiC$_2$, SiO, SiS, CS, C$_2$S, C$_3$S, and their isotopologues. Among them, one molecular emission line (H$^{13}$CCCN $J=13-12$) is discovered in IRC+10216 for the first time. The excitation temperature, column density, and fractional abundance of the detected species are deduced by assuming they are in local thermodynamic equilibrium. In addition, the isotopic ratios of [$^{12}$C]/[$^{13}$C], [$^{32}$S]/[$^{34}$S], [$^{28}$Si]/[$^{29}$Si], and [$^{12}$C$^{34}$S]/[$^{13}$C$^{32}$S] are obtained and found to be consistent with previous studies. Finally, we summarize all of the 106 species detected in IRC+10216 to date with their observed and modeled column densities for the convenience of future studies., Comment: 71 pages, 39 figures, 10 tables. Accepted for publication in ApJS

Whether SiC$_2$ is a parent species, that is formed in the photosphere or as a by-product of high-temperature dust formation, or a daughter species, formed in a chemistry driven by the photodestruction of parent species in the outer envelope, has been debated for a long time. Here, we analyze the ALMA observations of four SiC$_2$ transitions in the CSEs of three C-rich AGB stars (AI Vol, II Lup, and RAFGL 4211), and found that SiC$_2$ exhibits an annular, shell-like distribution in these targets, suggesting that SiC$_2$ can be a daughter species in the CSEs of carbon-rich AGB stars. The results can provide important references for future chemical models., Comment: Accepted in Frontiers in Astronomy and Space Sciences

Optical time-domain surveys can unveil and characterize exciting but less-explored non-accreting and/or non-beaming neutron stars (NS) in binaries. Here we report the discovery of such a NS candidate using the LAMOST spectroscopic survey. The candidate, designated LAMOST J112306.9+400736 (hereafter J1123), is in a single-lined spectroscopic binary containing an optically visible M star. The star's large radial velocity variation and ellipsoidal variations indicate a relatively massive unseen companion. Utilizing follow-up spectroscopy from the Palomar 200-inch telescope and high-precision photometry from TESS, we measure a companion mass of $1.24_{-0.03}^{+0.03}~M_{\odot}$. Main-sequence stars with this mass are ruled out, leaving a NS or a massive white dwarf (WD). Although a massive WD cannot be ruled out, the lack of UV excess radiation from the companion supports the NS hypothesis. Deep radio observations with FAST yielded no detections of either pulsed or persistent emission. J1123 is not detected in numerous X-ray and gamma-ray surveys. These non-detections suggest that the NS candidate is not presently accreting and pulsing. Our work exemplifies the capability of discovering compact objects in non-accreting close binaries by synergizing the optical time-domain spectroscopy and high-cadence photometry., Comment: 53 pages, 15 figures, publication in Nature Astronomy

In this letter, we propose that the narrowband photodetection can be realized in the skin layer of semiconductors with the spatially separated photo-excited carriers from the nanoscale heterolattice electronic transitions (NanoHLETs). The NanoHLET photodetection is demonstrated by measuring the photoconductive responses of the $\sim$ 1 $\mu$m thick films of TiO$_{2}$ glass embedded with rutile and anatase TiO$_{2}$ nanocrystals. As containing only rutile nanocrystals, the TiO$_{2}$ glass film presents the responsivity curve with only one sharp peak centered at 423.0 nm with a full-width-at-half-maximum (FWHM) of 13.7 nm. This NanoHLET mechanism may open a new way in making ultra-small narrow-band photodetectors matching the current nanoscale electronic technology.

Core-collapse supernovae (SNe) are the inevitable fate of most massive stars. Since most stars form in groups, SN progenitors can be constrained with information of their environments. It remains challenging to accurately analyse the various components in the environment and to correctly identify their relationships with the SN progenitors. Using a combined dataset of VLT/MUSE spatially-resolved integral-field-unit (IFU) spectroscopy and HST/ACS+WFC3 high-spatial resolution imaging, we present a detailed investigation of the environment of the Type II-P SN 2004dg and Type IIb SN 2012P. The two SNe occurred in a spiral arm of NGC 5806, where a star-forming complex is apparent with a giant H II region. By modelling the ionised gas, a compact star cluster and the resolved stars, we derive the ages and extinctions of stellar populations in the vicinity of the SNe. The various components are consistent with a sequence of triggered star formation as the spiral density wave swept through their positions. For SNe 2004dg and 2012P, we identify their host stellar populations and derive initial masses of $10.0^{+0.3}_{-0.2}~M_\odot$ and $15.2^{+2.0}_{-1.0}~M_\odot$ for their progenitors, respectively. Both results are consistent with those from pre-explosion images or nebular-phase spectroscopy. SN 2012P is spatially coincident but less likely to be coeval with the star-forming complex. As in this case, star formation bursts on small scales may appear correlated if they are controlled by any physical processes on larger scales; this may lead to a high probability of chance alignment between older SN progenitors and younger stellar populations., Comment: 21 pages, 17 figures, accepted for publication in MNRAS

RV variable stars are important in astrophysics. The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) spectroscopic survey has provided ~ 6.5 million stellar spectra in its Data Release 4 (DR4). During the survey, ~ 4.7 million unique sources were targeted and ~ 1 million stars observed repeatedly. The probabilities of stars being RV variables are estimated by comparing the observed radial velocity variations with the simulated ones. We build a catalog of 80,702 RV variable candidates with probability greater than 0.60 by analyzing the duplicate-observed multi-epoch sources covered by the LAMOST DR4. Simulations and cross-identifications show that the purity of the catalog is higher than 80%. The catalog consists of 77% binary systems and 7% pulsating stars as well as 16% pollution by single stars. 3,138 RV variables are classified through cross-identifications with published results in literatures. By using the 3,138 sources common to both LAMOST and a collection of published RV variable catalogs we are able to analyze LAMOST's RV variable detection rate. The efficiency of the method adopted in this work relies not only on the sampling frequency of observations but also periods and amplitudes of RV variables. With the progress of LAMOST, Gaia and other surveys, more and more RV variables would will be confirmed and classified. This catalog is valuable for other large-scale surveys, especially for RV variable searches. The catalog will be released according to the LAMOST Data Policy via http://dr4.lamost.org., Comment: 16 pages, 23 figures, Accepted for publication in ApJS

We present UV spectra of the protoplanetary nebula (pPN) Hen3-1475 obtained with the Space Telescope Imaging Spectrograph (STIS) on board the Hubble Space Telescope (HST). Our deep, low-dispersion spectroscopy enables monochromatic imaging of Hen3-1475 in UV nebular emission lines, the first of such attempt ever made for a pPN. The high spatial resolution of STIS imaging allows an unprecedentedly sharp view of the S-shaped jet, especially the inner NW1 knot, which is resolved into four components in the MgII 2800 line emission. Through critical comparison with HST optical narrowband images, we found a negative radial velocity gradient in NW1, from -1550 km/s on its innermost component to about -300 km/s on the outermost. Despite their high radial velocities, these components of NW1 mostly show no obvious (or very small) proper motions, indicating that they might be quasi-stationary shocks near the tip of the conical flow along the collimated jet of Hen3-1475., Comment: Accepted for publication in The Astrophysical Journal Letters (ApJL); 6 pages, including 4 figures and 1 table

Planetary nebulae are ionized clouds of gas formed by the hydrogen-rich envelopes of low- and intermediate-mass stars ejected at late evolutionary stages. The strong UV flux from their central stars causes a highly stratified ionization structure, with species of higher ionization potential closer to the star. Here we report on the exceptional case of HuBi 1, a double-shell planetary nebula whose inner shell presents emission from low-ionization species close to the star and emission from high-ionization species farther away. Spectral analysis demonstrates that the inner shell of HuBi 1 is excited by shocks, whereas its outer shell is recombining. The anomalous excitation of these shells can be traced to its low-temperature [WC10] central star whose optical brightness has declined continuously by 10 magnitudes in a period of 46 years. Evolutionary models reveal that this star is the descendent of a low-mass star ($\simeq$1.1 $M_\odot$) that has experienced a born-again event whose ejecta shock-excite the inner shell. HuBi 1 represents the missing link in the formation of metal-rich central stars of planetary nebulae from low-mass progenitors, offering unique insight regarding the future evolution of the born-again Sakurai's object. Coming from a solar-mass progenitor, HuBi 1 represents a potential end-state for our Sun., Comment: 21 pages, 3 figures, 6 supplementary figures, 1 supplementary table, published in Nature Astronomy

Planetary nebulae (PNe) are an important tool for studying the dynamics and chemical evolution of galaxies in the Local Universe, given their characteristic, bright emission line spectra. The Andromeda Galaxy (M31) provides a unique laboratory for studying PNe in the circumnuclear region, thanks to its proximity and almost uniformly low line-of-sight extinction that ensures observations with high resolution and sensitivity. Using the WIYN/Hydra multi-fiber spectrograph, we have obtained optical (4119--6882{\AA}) spectra of 77 PN candidates selected from Hubble Space Telescope narrow-band imaging, which are located within the central $\sim$500pc region of M31. Among these candidates, 49 (64%) are spectroscopically observed for the first time. The spectra of 300 previously known PNe and H II regions, which primarily reside in the disk, are also taken for comparison. All 77 circumnuclear PN candidates exhibit prominent emission lines, including [O III] $\lambda$5007, [N II] $\lambda$6583, H$\alpha$ and H$\beta$, strongly suggesting that they are genuine PNe. We measured the line fluxes, radial velocities and line widths for all objects, and found that the radial velocities of the circumnuclear PNe generally trace rotation of the inner bulge. We also estimated a dynamical mass of $\sim$6.4$\pm$0.5$\times$10$^{9}$$M_{\odot}$ enclosed within an effective galactocentric radius of 340pc, which is compatible with the previously estimated total stellar mass in this region., Comment: 30 pages, 11 figures, accepted for publication in RAA

We present narrow-band near-infrared images of a sample of 11 Galactic planetary nebulae (PNe) obtained in the molecular hydrogen (H$_{2}$) 2.122 $\mu$m and Br$\gamma$ 2.166 $\mu$m emission lines and the $K_{\rm c}$ 2.218 $\mu$m continuum. These images were collected with the Wide-field InfraRed Camera (WIRCam) on the 3.6m Canada-France-Hawaii Telescope (CFHT); their unprecedented depth and wide field of view allow us to find extended nebular structures in H$_{2}$ emission in several PNe, some of these being the first detection. The nebular morphologies in H$_{2}$ emission are studied in analogy with the optical images, and indication on stellar wind interactions is discussed. In particular, the complete structure of the highly asymmetric halo in NGC6772 is witnessed in H$_{2}$, which strongly suggests interaction with the interstellar medium. Our sample confirms the general correlation between H$_{2}$ emission and the bipolarity of PNe. The knotty/filamentary fine structures of the H$_{2}$ gas are resolved in the inner regions of several ring-like PNe, also confirming the previous argument that H2 emission mostly comes from knots/clumps embedded within fully ionized material at the equatorial regions. Moreover, the deep H$_{2}$ image of the butterfly-shaped Sh1-89, after removal of field stars, clearly reveals a tilted ring structure at the waist. These high-quality CFHT images justify follow-up detailed morpho-kinematic studies that are desired to deduce the true physical structures of a few PNe in the sample., Comment: Accepted for publication in The Astrophysical Journal; 24 pages, including 29 figures and 1 table

We report deep spectroscopy of ten planetary nebulae (PNe) in the Andromeda Galaxy (M31) using the 10.4m GTC. Our targets reside in different regions of M31, including halo streams and dwarf satellite M32, and kinematically deviate from the extended disk. The temperature-sensitive [O III] 4363 auroral line is observed in all targets. For four PNe, the GTC spectra extend beyond 1 micron, enabling explicit detection of the [S III] 6312 and 9069,9531 lines and thus determination of the [S III] temperature. Abundance ratios are derived and generally consistent with AGB model predictions. Our PNe probably all evolved from low-mass (<2 M_sun) stars, as analyzed with the most up-to-date post-AGB evolutionary models, and their main-sequence ages are mostly ~2-5 Gyr. Compared to the underlying, smooth, metal-poor halo of M31, our targets are uniformly metal-rich ([O/H]> -0.4), and seem to resemble the younger population in the stream. We thus speculate that our halo PNe formed in the Giant Stream's progenitor through extended star formation. Alternatively, they might have formed from the same metal-rich gas as did the outer-disk PNe, but was displaced into their present locations as a result of galactic interactions. These interpretations are, although speculative, qualitatively in line with the current picture, as inferred from previous wide-field photometric surveys, that M31's halo is the result of complex interactions and merger processes. The behavior of N/O of the combined sample of the outer-disk and our halo/substructure PNe signifies that hot bottom burning might actually occur at <3 M_sun, but careful assessment is needed., Comment: Accepted for publication in The Astrophysical Journal (ApJ); 33 pages including 20 figures and 9 tables

We present deep spectroscopy of three Galactic planetary nebulae (PNe) with large abundance discrepancy factors (ADFs): NGC6153, M1-42 and Hf2-2. The spectra were obtained with VLT/UVES and cover the whole optical range (3040-11,000 A) with a spectral resolution of ~20,000. For all three PNe, several hundred emission lines were detected and identified, with more than 70 per cent of them as permitted lines. Most of these permitted lines are excited by recombination. Numerous weak optical recombination lines (ORLs) of O II, C II, N II and Ne II were detected in the spectra and accurate fluxes measured. Line flux tables were compiled and ready for use by the community of nebular astrophysics. These ORLs were critically analyzed using the effective recombination coefficients recently calculated for the optical recombination spectrum of N II and O II under the physical conditions of photoionized gaseous nebulae. Plasma diagnostics based on the heavy element ORLs were carried out using the new atomic data. Elemental abundances derived from the ORLs were systematically higher than those derived from the collisionally excited lines (CELs) by a factor of ~10, 22 and 80 for NGC6153, M1-42 and Hf2-2, respectively. The electron temperatures derived from the heavy element ORLs are systematically lower than those derived from the CELs. These ORL versus CEL abundance and temperature discrepancies, previously observed in the three PNe through deep spectroscopy with medium to low spectral resolution, are thus confirmed by our analysis of the deep echelle spectra using the new atomic data., Comment: Accepted for publication in MNRAS; 31 pages, including 15 figures and 14 tables

Planetary nebulae (PNe) are expected to have a ~10$^{5}$ K interface layer between the $\geq$10$^{6}$ K inner hot bubble and the ~10$^{4}$ K optical nebular shell. The PN structure and evolution, and the X-ray emission depend critically on the efficiency of mixing of material at this interface layer. However, neither its location nor its spatial extent has ever been determined so far. Using high-spatial resolution HST STIS spectroscopic observations of the N V 1239,1243 lines in the Cat's Eye Nebula (NGC 6543), we have detected this interface layer and determined its location, extent, and physical properties for the first time in a PN. We confirm that this interface layer, as revealed by the spatial distribution of the N V 1239 line emission, is located between the hot bubble and the optical nebular shell. We estimate a thickness of 1.5$\times$10$^{16}$ cm and an electron density of ~200 cm$^{-3}$ for the mixing layer. With a thermal pressure of ~2$\times$10$^{-8}$ dyn cm$^{-2}$, the mixing layer is in pressure equilibrium with the hot bubble and ionized nebular rim of NGC 6543., Comment: Accepted for publication in the ApJ Letters; five pages, including 1 table and 3 figures

We present Spitzer Space Telescope archival mid-infrared (mid-IR) spectroscopy of a sample of eleven planetary nebulae (PNe). The observations, acquired with the Spitzer Infrared Spectrograph (IRS), cover the spectral range 5.2-14.5 {\mu}m that includes the H2 0-0 S(2) to S(7) rotational emission lines. This wavelength coverage has allowed us to derive the Boltzmann distribution and calculate the H2 rotational excitation temperature (Tex). The derived excitation temperatures have consistent values ~900+/-70 K for different sources despite their different structural components. We also report the detection of mid-IR ionic lines of [Ar III], [S IV], and [Ne II] in most objects, and polycyclic aromatic hydrocarbon (PAH) features in a few cases. The decline of the [Ar III]/[Ne II] line ratio with the stellar effective temperature can be explained either by a true neon enrichment or by high density circumstellar regions of PNe that presumably descend from higher mass progenitor stars., Comment: 14 pages, 15 figures, Accepted for publication in MNRAS

We present deep spectroscopy of planetary nebulae (PNe) that are associated with the substructures of the Andromeda Galaxy (M31). The spectra were obtained with the OSIRIS spectrograph on the 10.4 m GTC. Seven targets were selected for the observations, three in the Northern Spur and four associated with the Giant Stream. The most distant target in our sample, with a rectified galactocentric distance >100 kpc, was the first PN discovered in the outer streams of M31. The [O III] 4363 auroral line was well detected in the spectra of all targets, enabling electron temperature determination. Ionic abundances are derived based on the [O III] temperatures, and elemental abundances of helium, nitrogen, oxygen, neon, sulfur, and argon are estimated. The relatively low N/O and He/H ratios as well as abundance ratios of alpha-elements indicate that our target PNe might belong to populations as old as ~2 Gyr. Our PN sample, including the current seven and the previous three observed by Fang et al., have rather homogeneous oxygen abundances. The study of abundances and the spatial and kinematical properties of our sample leads to the tempting conclusion that their progenitors might belong to the same stellar population, which hints at a possibility that the Northern Spur and the Giant Stream have the same origin. This may be explained by the stellar orbit proposed by Merrett et al. Judging from the position and kinematics, we emphasize that M32 might be responsible for the two substructures. Deep spectroscopy of PNe in M32 will help to assess this hypothesis., Comment: Accepted for publication in the ApJ. 23 pages, including 13 figures and 7 tables

We present narrow-band optical and near-IR imaging and optical long-slit spectroscopic observations of Hu1-2, a Galactic planetary nebula (PN) with a pair of [N II]-bright, fast-moving (> 340 km/s) bipolar knots. Intermediate-dispersion spectra are used to derive physical conditions and abundances across the nebula, and high-dispersion spectra to study the spatio-kinematical structure. Generally Hu1-2 has high He/H (~0.14) and N/O ratios (~0.9), typical of Type I PNe. On the other hand, its abundances of O, Ne, S, and Ar are low as compared with the average abundances of Galactic bulge and disc PNe. The position-velocity maps can be generally described as an hour-glass shaped nebula with bipolar expansion, although the morphology and kinematics of the innermost regions cannot be satisfactorily explained with a simple, tilted equatorial torus. The spatio-kinematical study confines the inclination angle of its major axis to be within 10 degrees of the plane of sky. As in the irradiated bow-shocks of IC4634 and NGC7009, there is a clear stratification in the emission peaks of [O III], H_alpha, and [N II] in the northwest (NW) knot of Hu1-2. Fast collimated outflows in PNe exhibit higher excitation than other low-ionization structures. This is particularly the case for the bipolar knots of Hu1-2, with He II emission levels above those of collimated outflows in other Galactic PNe. The excitation of the knots in Hu1-2 is consistent with the combined effects of shocks and UV radiation from the central star. The mechanical energy and luminosity of the knots are similar to those observed in the PNe known to harbor a post-common envelope (post-CE) close binary central star., Comment: Accepted for publication in MNRAS; 19 pages, 11 figures, 7 tables

The TMT Detailed Science Case describes the transformational science that the Thirty Meter Telescope will enable. Planned to begin science operations in 2024, TMT will open up opportunities for revolutionary discoveries in essentially every field of astronomy, astrophysics and cosmology, seeing much fainter objects much more clearly than existing telescopes. Per this capability, TMT's science agenda fills all of space and time, from nearby comets and asteroids, to exoplanets, to the most distant galaxies, and all the way back to the very first sources of light in the Universe. More than 150 astronomers from within the TMT partnership and beyond offered input in compiling the new 2015 Detailed Science Case. The contributing astronomers represent the entire TMT partnership, including the California Institute of Technology (Caltech), the Indian Institute of Astrophysics (IIA), the National Astronomical Observatories of the Chinese Academy of Sciences (NAOC), the National Astronomical Observatory of Japan (NAOJ), the University of California, the Association of Canadian Universities for Research in Astronomy (ACURA) and US associate partner, the Association of Universities for Research in Astronomy (AURA)., Comment: 203 pages, 10 Mb. Full resolution version available at http://www.tmt.org/science-case/

We analyze the expansion of hydrogen-poor knots and filaments in the born-again planetary nebulae A30 and A78 based on Hubble Space Telescope (HST) images obtained almost 20 yr apart. The proper motion of these features generally increases with distance to the central star, but the fractional expansion decreases, i.e., the expansion is not homologous. As a result, there is not a unique expansion age, which is estimated to be 610-950 yr for A30 and 600-1140 yr for A78. The knots and filaments have experienced complex dynamical processes: the current fast stellar wind is mass loaded by the material ablated from the inner knots; the ablated material is then swept up until it shocks the inner edges of the outer, hydrogen-rich nebula. The angular expansion of the outer filaments shows a clear dependence on position angle, indicating that the interaction of the stellar wind with the innermost knots channels the wind along preferred directions. The apparent angular expansion of the innermost knots seems to be dominated by the rocket effect of evaporating gas and by the propagation of the ionization front inside them. Radiation-hydrodynamical simulations show that a single ejection of material followed by a rapid onset of the stellar wind and ionizing flux can reproduce the variety of clumps and filaments at different distances from the central star found in A30 and A78., Comment: 12 pages, 7 figures. Accepted for publication in the ApJ

[Abridged] We present a critical analysis of the rich optical recombination spectrum of NGC 7009, in the context of the bi-abundance nebular model proposed by Liu et al. (2000). The observed relative intensities are compared with the theoretical predictions based on high quality effective recombination coefficients, now available for the recombination line spectrum of a number of heavy element ions. The possibility of plasma diagnostics using the optical recombination lines (ORLs) of heavy element ions is discussed in detail. Plasma diagnostics based on the N II and O II recombination spectra both yield electron temperatures close to 1000 K, which is lower than those derived from the collisionally excited line (CEL) ratios by nearly one order of magnitude. The very low temperatures yielded by the O II and N II ORLs indicate that they originate from very cold regions. The C^{2+}/H^+, N^{2+}/H^+, O^{2+}/H^+ and Ne^{2+}/H^+ ionic abundance ratios derived from ORLs are consistently higher, by about a factor of 5, than the corresponding values derived from CELs. In calculating the ORL ionic abundance ratios, we have used the newly available high quality effective recombination coefficients, and adopted an electron temperature of 1000 K, as given by the ORL diagnostics and as a consequence presumably representing the physical conditions prevailing in the regions where the heavy element ORLs arise. A comparison of the results of plasma diagnostics and abundance determinations for NGC 7009 points to the existence of "cold", metal-rich (i.e. H-deficient) inclusions embedded in the hot, diffuse ionized gas, first postulated by Liu et al. (2000)., Comment: Accepted for publication in MNRAS (50 pages of main text; 13 pages of appendix; in total 55 figures and 28 tables)

We carry out plasma diagnostic analyses for 123 planetary nebulae (PNe) and 42 H II regions using the N II and O II optical recombination lines (ORLs). New effective recombination coefficients for the N II and O II optical recombination spectra are used. These data were calculated under the intermediate coupling scheme for a number of electron temperature (Te) and density (Ne) cases. We used a new method to determine the Te and Ne for the nebular sample, combining the ORLs with the most reliable measurements for each ion and the predicted intensities that are based on the new atomic data. Uncertainties of the derived Te and Ne are estimated for each object. The diagnostic results from heavy element ORLs show reasonable agreement with previous calculations in the literature. We compare the electron temperatures derived from the N II and O II ORLs, Te(ORLs), and those from the collisionally excited lines (CELs), Te(CELs), as well as the hydrogen Balmer jump, Te(H I BJ), especially for the PNe with large abundance discrepancies. Temperatures from He I recombination lines, Te(He I), are also used for comparison if available. For all the objects included in our sample, Te(ORLs) are lower than Te(H I BJ), which are in turn systematically lower than Te(CELs). Nebulae with Te(He I) available show the relation Te(ORLs) < Te(He I) < Te(H I BJ) < Te(CELs), which is consistent with predictions from the bi-abundance nebular model postulated by Liu et al. (2000)., Comment: 21 pages, 13 figures, accepted for publication in MNRAS