Late Thermal Pulse Research Articles

RELICS OF ANCIENT POST-AGB STARS IN A PRIMITIVE METEORITE

Graphite is one of the many presolar circumstellar condensate species found in primitive meteorites. While the isotopic compositions of low-density graphite grains indicate an origin in core-collapse supernovae, some high-density grains have extreme isotopic anomalies in C, Ca and Ti, which cannot be explained by envelope predictions of asymptotic giant branch (AGB) stars or theoretical supernova models. The Ca and Ti isotopic anomalies, however, match the predictions of He-shell abundances in AGB stars. In this study, we show that the C, Ca, and Ti isotopic anomalies are consistent with nucleosynthesis predictions of the H-ingestion phase during a very late thermal pulse (VLTP) event in post-AGB stars. The low $^{12}$C/$^{13}$C isotopic ratios in these grains are a result of abundant $^{12}$C efficiently capturing the protons that are being ingested during the VLTP. Very high neutron densities of $\sim 10^{15}$ cm$^{-3}$, typical of the $i$-process, are achieved during this phase in post-AGB stars. The large $^{42,43,44}$Ca excesses in some graphite grains are indicative of neutron capture nucleosynthesis during VLTP. The comparison of VLTP nucleosynthesis calculations to the graphite data also indicate that apparent anomalies in the Ti isotopic ratios are due to large contributions from $^{46,48}$Ca, which cannot be resolved from the isobars $^{46,48}$Ti during the measurements. We conclude that presolar graphite grains with moderate to extreme Ca and Ti isotopic anomalies originate in post-AGB stars that suffer a very late thermal pulse.

Observations and three-dimensional ionization structure of the planetary nebula SuWt 2★

The planetary nebula SuWt 2 (PN G311.0+02.4) is an unusual object with a prominent, inclined central emission ellipse and faint bipolar extensions. It has two A-type stars in a proven binary system at the centre. However, the radiation from these two central stars is too soft to ionize the surrounding material leading to a so far fruitless search for the responsible ionizing source. Such a source is clearly required and has already been inferred to exist via an observed temporal variation of the centre-of-mass velocity of the A-type stars. Moreover, the ejected nebula is nitrogen rich which raises question about the mass-loss process from a likely intermediate-mass progenitor. We use optical integral-field spectroscopy to study the emission lines of the inner nebula ring. This has enabled us to perform an empirical analysis of the optical collisionally excited lines, together with a fully three-dimensional photoionization modelling. Our empirical results are used to constrain the photoionization models, which determine the evolutionary stage of the responsible ionizing source and its likely progenitor. The time-scale for the evolutionary track of a hydrogen-rich model atmosphere is inconsistent with the dynamical age obtained for the ring. This suggests that the central star has undergone a very late thermal pulse. We conclude that the ionizing star could be hydrogen deficient and compatible with what is known as a PG 1159-type star. The evolutionary tracks for the very late thermal pulse models imply a central star mass of ∼0.64 M⊙, which originated from an ∼3 M⊙ progenitor. The evolutionary time-scales suggest that the central star left the asymptotic giant branch about 25 000 yr ago, which is consistent with the nebula's age.

Multi-element isotopic analyses of presolar graphite grains from Orgueil

We report C, N, O, Si, Al–Mg, K, Ca, and Ti isotopic analyses of presolar graphite grains from the Orgueil CI chondrite. NanoSIMS isotopic measurements were made on 345 grains from seven density fractions, with grain sizes >1μm: low-density grains from OR1b, OR1c, and OR1d; and high-density grains from OR1f, OR1g, OR1h, and OR1i. In all fractions, except OR1b and OR1h, we found presolar graphite as demonstrated by the large range of 12C/13C ratios (4–2480) measured in individual grains. Some isotopic properties are dependent on density: low-density grains contain 18O, 15N, and 28Si excesses, while the majority of high-density grains contain normal N and O, and are generally enriched in 29Si and 30Si. The 15N, 18O, and 28Si excesses and very high derived isotopic ratios for the extinct radionuclides 26Al, 41Ca, and 44Ti in low-density grains indicate an origin from supernovae. In order to explain the isotopic ratios measured in these grains, we present mixing scenarios between different layers of supernovae and discuss the limitations of various theoretical models. Silicon-30 and 12C excesses in high-density grains and lower values for short-lived radionuclides (26Al and 41Ca) indicate an origin in asymptotic giant branch stars with low metallicities. Some supernova grains, with 44Ca excesses, are also present amongst the high-density grains. Grains with low 12C/13C ratios (without evidence for 44Ti) and large excesses in 42,43Ca and 46,47,49,50Ti probably originate from post-asymptotic giant branch stars, that have suffered a very late thermal pulse, and can achieve low 12C/13C ratios and large neutron capture signatures in Ca and Ti isotopes.We conclude that most low-density graphite grains originate from supernovae while high-density graphite grains have multiple stellar sources: low-metallicity and born-again asymptotic giant branch stars, Type II supernovae, and possibly, J-type stars.

Can R Coronae Borealis stars form from the merger of two helium white dwarfs?

Abstract Due to orbital decay by gravitational wave radiation, some close binary helium white dwarfs are expected to merge within a Hubble time. The immediate merger products are believed to be He-rich subdwarf O (sdO) stars, essentially helium main-sequence stars. We present new evolution calculations for these post-merger stars beyond the core He-burning phase. The most massive He-rich sdO stars develop a strong He-burning shell and evolve to become He-rich giants. We include nucleosynthesis calculations following the merger of 0.4 M⊙ He white dwarf pairs with metallicities Z= 0.0001, 0.004, 0.008 and 0.02. The surface chemistries of the resulting giants are in partial agreement with the observed abundances of R Coronae Borealis (R CrB) and extreme He stars. Such stars might represent a third, albeit rare, evolution channel for the latter, in addition to the CO+He white dwarf merger and the very late thermal pulse channels proposed previously. We confirm a recent suggestion that Li seen in R CrB stars could form naturally during the hot phase of a merger in the presence of 3He from the donor white dwarf.

REBIRTH OF X-RAY EMISSION FROM THE BORN-AGAIN PLANETARY NEBULA A30

The planetary nebula A30 is believed to have undergone a very late thermal pulse resulting in the ejection of knots of hydrogen-poor material. Using multi-epoch Hubble Space Telescope images, we have detected the angular expansion of these knots and derived an age of 850+280 – 150 yr. To investigate the spectral and spatial properties of the soft X-ray emission detected by ROSAT, we have obtained Chandra and XMM-Newton deep observations of A30. The X-ray emission from A30 can be separated into two components: a point source at the central star and diffuse emission associated with the hydrogen-poor knots and the cloverleaf structure inside the nebular shell. To help us assess the role of the current stellar wind in powering this X-ray emission, we have determined the stellar parameters and wind properties of the central star of A30 using a non-LTE model fit to its optical and UV spectra. The spatial distribution and spectral properties of the diffuse X-ray emission are highly suggestive that it is generated by the post-born-again and present fast stellar winds interacting with the hydrogen-poor ejecta of the born-again event. This emission can be attributed to shock-heated plasma, as the hydrogen-poor knots are ablated by the stellar winds, under which circumstances the efficient mass loading of the present fast stellar wind raises its density and damps its velocity to produce the observed diffuse soft X-rays. Charge transfer reactions between the ions of the stellar winds and material of the born-again ejecta have also been considered as a possible mechanism for the production of diffuse X-ray emission, and upper limits on the expected X-ray production by this mechanism have been derived. The origin of the X-ray emission from the central star of A30 is puzzling: shocks in the present fast stellar wind and photospheric emission can be ruled out, while the development of a new, compact hot bubble confining the fast stellar wind seems implausible.

DRAMATIC INFRARED VARIABILITY OF WISE J1810-3305: CATCHING EARLY-TIME DUST EJECTION DURING THE THERMAL PULSE OF AN ASYMPTOTIC GIANT BRANCH STAR?

We present the discovery of a source with broadband infrared photometric characteristics similar to Sakurai's Object. WISE J180956.27-330500.2 (hereafter, J1810-3305) shows very red WISE colors, but a very blue 2MASS [K] vs. WISE [W1 (3.4 micron)] color. It was not visible during the IRAS era, but now has a 12 micron flux well above the IRAS point source catalog detection limit. There are also indications of variability in historical optical photographic plates, as well as in multi-epoch AKARI mid-infrared measurements. The broadband infrared spectral energy distribution, post-IRAS brightening and multiwavelength variability are all characteristics also shared by Sakurai's Object - a post asymptotic giant branch (post-AGB) star which underwent a late thermal pulse and recently ejected massive envelopes of dust that are currently expanding and cooling. Optical progenitor colors suggest that J1810-3305 may have been of late spectral class. Its dramatic infrared brightening, and the detection of a late-type optical counterpart are consistent with a scenario in which we have caught an extremely massive dust ejection event (in 1998 or shortly before) during the thermal pulse of an AGB star, thus providing a unique opportunity to observe stellar evolution in this phase. J1810-3305 is the only source in the entire WISE preliminary data release with similar infrared SED and variability, emphasizing the rarity of such sources. Confirmation of its nature is of great importance.

NSV 11749, AN ELDER SIBLING OF THE BORN-AGAIN STARS V605 Aql AND V4334 Sgr?

We argue that NSV 11749, an eruption observed in the early twentieth century, was a rare event known as "very late thermal pulse" (VLTP). To support our argument we compare the lightcurve of NSV 11749 with those of the two bonafide VLTP objects known to date, V4334 Sgr and V605 Aql, and with those predicted by state of the art stellar evolution models. Next, we explore the IPHAS and 2MASS catalogues for possible counterparts of the eruption. Our analysis shows that the VLTP scenario outperforms all other proposed scenarios as an explanation of NSV 11749. We identify an IPHAS/2MASS source at the eruption location of NSV 11749. The derived colors suggest that the object is not enshrouded in a thick dust shell as V605 Aql and V4334 Sgr. Also the absence of an apparent planetary nebula (PN) at the eruption location suggests differences with known VLTP objects which might be linked to the intensity of the eruption and the mass of the object. Further exploration of this source and scenario seems desirable. If NSV 11749 was a born again star, it would be the third event of its kind to have been observed and will strongly help us to increase our understanding on the later stages of stellar evolution and violent reactive convective burning.

A 3D photoionization model of the extreme planetary nebula NGC 6302

We present a 3D photoionization model of the PN NGC 6302, one of the most complex objects of its kind. Our Mocassin model is composed of an extremely dense circumstellar disk and a large pair of diffuse bipolar lobes, a combination necessary to reproduce the observed spectrum. The masses of these components gives a total nebular mass of 4.7Mo. Discrepancies between our model fit and the observations are attributed to complex density inhomogeneities in the nebula. The potential to resolve such discrepancies with more complex models is confirmed by a range of models introducing small-scale structures. Compared to solar abundances He is enhanced by 50%, C is slightly subsolar, O is solar, and N is enhanced by a factor of 6. These imply a significant 3rd dredge-up coupled with hot-bottom burning CN-cycle conversion of dredged-up C to N. The central star is partly obscured by the edge-on circumstellar disk and its properties are not well constrained. Emission from a number of high-ionization `coronal' lines provides constraints on the form of the high-energy ionizing flux. Using a solar abundance stellar atmosphere we are unable to fit all of the observed line fluxes, but a substantially better fit was obtained using a 220,000K H-deficient stellar atmosphere with L*=14,300 Lo. The H-deficient nature of the central star suggests it has undergone a late thermal pulse, and fits to evolutionary tracks imply a central star mass of 0.73-0.82Mo. Timescales for these tracks suggest the object left the top of the AGB ~2100 years ago, in agreement with studies of the recent mass-loss event that formed the bipolar lobes. Based on the modelled nebular and central star masses we estimate the initial mass of the central star to be 5.5Mo, in agreement with that derived from evolutionary tracks. (Abstract truncated)

Ablation and Wind Mass-Loading in the Born-Again Planetary Nebula A 30

AbstractWe present XMM-Newton and Chandra observations of the born-again planetary nebula A 30. These X-ray observations reveal a bright unresolved source at the position of the central star whose X-ray luminosity exceeds by far the model expectations for photospheric emission and for shocks within the stellar wind. We suggest that a “born-again hot bubble” may be responsible for this X-ray emission. Diffuse X-ray emission associated with the petal-like features and one of the H-poor knots seen in the optical is also found. The weakened emission of carbon lines in the spectrum of the diffuse emission can be interpreted as the dilution of stellar wind by mass-loading or as the detection of material ejected during a very late thermal pulse.

(F)UV spectroscopy of the hybrid PG1159-type central stars of the planetary nebulae NGC 7094 and Abell43

Hydrogen-deficient post-AGB stars have experienced a late helium-shell flash that mixes the hydrogen-rich envelope and the helium-rich intershell (between hydrogen- and helium-burning shell). The amount of hydrogen remaining in the stellar envelope depends on the particular moment when this late thermal pulse occurs. Previous spectral analyses of hydrogen-deficient post-AGB stars, namely PG 1159-035 and the central stars of the planetary nebulae (CSPN) K 1-16, NGC 7094, and Abell 78, surprisingly revealed strong iron deficiencies of up to 1 dex. A possible explanation may be neutron captures due to an efficient s-process on the AGB that transformed iron into heavier elements. An increased abundance of these would be a strong indication for this scenario. Since reliable atomic data for highly ionized species heavier than iron is only available for cobalt and nickel, we can presently determine only the nickel abundance. We performed a detailed spectral analysis by means of NLTE model-atmosphere techniques based on high-resolution UV observations of the two PG 1159-type CSPN of NGC 7094 and Abell 43 which are spectroscopic twins, i.e., they exhibit very similar spectra. We confirmed a strong iron-deficiency of at least one dex in both stars. The search for nickel lines in their UV spectra was entirely negative. We find that both stars are even nickel deficient by about one dex.

Very late thermal pulses influenced by accretion in planetary nebulae

We consider the possibility that a mass of ∼ 10 - 5 - 10 - 3 M ⊙ flows back from the dense shell of planetary nebulae and is accreted by the central star during the planetary nebula phase. This backflowing mass is expected to have a significant specific angular momentum even in (rare) spherical planetary nebulae, such that a transient accretion disk might be formed. This mass might influence the occurrence and properties of a very late thermal pulse (VLTP), and might even trigger it. For example, the rapidly rotating outer layer, and the disk if still exist, might lead to axisymmetrical mass ejection by the VLTP. Unstable burning of accreted hydrogen might result in a mild flash of the hydrogen shell, also accompanied by axisymmetrical ejection.

Faint recombination lines in Galactic PNe with a [WC] nucleus

Aims. We present spatially resolved high-resolution spectrophotometric data for the planetary nebulae PB 8, NGC 2867, and PB 6. We have analyzed two knots in NGC 2867 and PB 6 and one in PB 8. The three nebulae are ionized by [WC] type nuclei: early [WO] for PB 6 and NGC 2867 and [WC 5-6] in the case of PB 8. Our aim is to study the behavior of the abundance discrepancy problem (ADF) in this type of planetary nebula. Methods. We measured a large number of optical recombination (ORL) and collisionally excited lines (CEL), from different ionization stages (many more than in any previous work), thus, we were able to derive physical conditions from many different diagnostic procedures. We determined ionic abundances from the available collisionally excited and recombination lines. Based on both sets of ionic abundances, we derived total chemical abundances in the nebulae using suitable ionization correction factors. Results. From CELs, we have found abundances typical of Galactic disk planetary nebulae. Moderate ADF(O ++ ) were found for PB 8 (2.57) and NGC 2867 (1.63). For NGC 2867, abundances from ORLs are higher but still consistent with Galactic disk planetary nebulae. On the contrary, PB 8 presents a very high O/H ratio from ORLs. A high C/O was obtained from ORLs for NGC 2867; this ratio is similar to C/O obtained from CELs and with the chemical composition of the wind of the central star, indicating that there was no further C-enrichment in the star, relative to O, after the nebular material ejection. On the contrary, we found C/O < 1 in PB 8. Interestingly, we obtain (C/O) ORLs /(C/O) CELs < 1 in PB 8 and NGC 2867; this added to the similarity between the heliocentric velocities measured in [O III] and O II lines for our three objects argue against the presence of H-deficient metal-rich knots coming from a late thermal pulse event.

Sakurai's Object: characterizing the near-infrared CO ejecta between 2003 and 2007

We present observations of Sakurai's Object obtained at 1–5 μm between 2003 and 2007. By fitting a radiative transfer model to an echelle spectrum of CO fundamental absorption features around 4.7 μm, we determine the excitation conditions in the line-forming region. We find 12C/13C = 3.5+2.0−1.5, consistent with CO originating in ejecta processed by the very late thermal pulse, rather than in the pre-existing planetary nebula. We demonstrate the existence of 2.2 × 10−6≤MCO≤ 2.7 × 10−6 M⊙ of CO ejecta outside the dust, forming a high-velocity wind of 500 ± 80 km s−1. We find evidence for significant weakening of the CO band and cooling of the dust around the central star between 2003 and 2005. The gas and dust temperatures are implausibly high for stellar radiation to be the sole contributor.

The hydrogen-deficient knot of the ‘born-again’ planetary nebula Abell 58 (V605 Aql)

We have analysed deep optical spectra of the 'born-again' planetary nebula Abell 58 and its hydrogen-deficient knot, surrounding V605 Aql, which underwent a nova-like eruption in 1919. Our analysis shows that the extinction towards the central knot is much higher than previously thought, with c(Hβ) = 2.0. The outer nebula is less reddened, with c(Hβ) = 1.04. We find that the outer nebula has a Ne/O ratio higher than the average PN value. The electron temperature we derive for the central knot varies widely depending on the diagnostic used. The [O iii] nebular-to-auroral transition ratio gives a temperature of 20 800 K, while the ratio of the [N ii] nebular and auroral lines gives Te= 15 200 K. The helium line ratios λ5876/ λ4471 and λ6678/λ4471 imply temperatures of 350 and 550 K, respectively. Weakly temperature-sensitive O ii recombination line ratios imply similarly low electron temperatures. Abundances derived from recombination lines are vastly higher than those found from collisionally excited lines, with the abundance discrepancy factor (ADF) for O2+reaching 89 - the second highest known value after that found for the hydrogen-deficient knots in Abell 30. The observed temperature diagnostics and abundances support the idea that, like Abell 30, the knot of Abell 58 contains some very cold ionized material. Although the central star is carbon-rich (C/O > 1), the knot is found to be oxygen-rich, a situation not predicted by the single-star 'born-again' theory of its formation. We compare the known properties of Abell 58 to those of Abell 30, Sakurai's Object and several novae and nova remnants. We argue that the abundances in the ejecta observed in A 30 and A 58 have more in common with neon novae than with Sakurai's Object, which is believed to have undergone a final helium flash. In particular, the C/O ratio of less than unity and the presence of substantial quantities of neon in the ejecta of both Abell 30 and Abell 58 are not predicted by very late thermal pulse models. Journal compilation © 2007 RAS.

The born-again (very late thermal pulse) scenario revisited: the mass of the remnants and implications for V4334 Sgr

We present 1D numerical simulations of the very late thermal pulse (VLTP) scenario for a wide range of remnant masses. We show that by taking into account the different possible remnant masses, the observed evolution of V4334 Sgr (a.k.a. Sakurai's object) can be reproduced within the standard 1D mixing length theory (MLT) stellar evolutionary models without the inclusion of any ad hoc reduced mixing efficiency. Our simulations hint at a consistent picture with present observations of V4334 Sgr. From energetics, and within the standard MLT approach, we show that low-mass remnants (M ≤ 0.6 M⊙ ) are expected to behave markedly differently from higher mass remnants (M ≥ 0.6 M⊙ ) in the sense that the latter remnants are not expected to expand significantly as a result of the violent H-buming that takes place during the VLTP. We also assess the discrepancy in the born-again times obtained by different authors by comparing the energy that can be liberated by H-burning during the VLTP event.

The onset of photoionization in Sakurai's Object (V4334 Sagittarii)

We investigate the reheating of the very late thermal pulse (VLTP) object V4334 Sgr (Sakurai’s Object) using radio observations from the Very Large Array, and optical spectra obtained with the Very Large Telescope. We find a sudden rise of the radio flux at 5 and 8 GHz – from ≤90 µJy and 80 ± 30 µJy in February 2005 to 320 µJy and 280 µJy in June 2006. Optical line emission is also evolving, but the emission lines are fading. The optical line emission and early radio flux are attributed to a fast shock (and not photoionization as was reported earlier) which occurred around 1998. The fading is due to post-shock cooling and recombination. The recent rapid increase in radio flux is evidence for the onset of photoionization of carbon starting around 2005. The current results indicate an increase in the stellar temperature to 12 kK in 2006. The mass ejected in the VLTP eruption is Mej ≥ 10 −4 M� , but could be as high as 10 −2 M� , depending mainly on the distance and the clumping factor of the outflow. We derive a distance between 1.8 and 5 kpc. A high mass loss could expose the helium layer and yield abundances compatible with those of [WC] and PG1159 stars.

The enigma of the oldest ‘nova’: the central star and nebula of CK Vul

CK Vul is classified as, amongst others, the slowest known nova, a hibernating nova or a very late thermal pulse object. Following its eruption in ad 1670, the star remained visible for 2 yr. A 15-arcsec nebula was discovered in the 1980s, but the star itself has not been detected since the eruption. We here present radio images which reveal a 0.1-arcsec radio source with a flux of 1.5 mJy at 5 GHz. Deep Hα images show a bipolar nebula with a longest extension of 70 arcsec, with the previously known compact nebula at its waist. The emission-line ratios show that the gas is shock-ionized, at velocities >100 km s−1. Dust emission yields an envelope mass of ∼5 × 10−2 M⊙. Echelle spectra indicate outflow velocities up to 360 km s−1. From a comparison of images obtained in 1991 and 2004 we find evidence for expansion of the nebula, consistent with an origin in the 1670 explosion; the measured expansion is centred on the radio source. No optical or infrared counterpart is found at the position of the radio source. The radio emission is interpreted as thermal free–free emission from gas with Te∼ 104 K. The radio source may be due to a remnant circumbinary disc, similar to those seen in some binary post-AGB stars. We discuss possible classifications of this unique outburst, including that of a sub-Chandrasekhar mass supernova, a nova eruption on a cool, low-mass white dwarf or a thermal pulse induced by accretion from a circumbinary disc.

The Spitzer Infrared Spectrometer view of V4334 Sgr (Sakurai's Object)

We present an observation of the very late thermal pulse object V4334 Sgr (Sakurai's Object) with the Infrared Spectrometer (IRS) on the Spitzer Space Telescope. The emission from 5–38 μm is dominated by the still-cooling dust shell. A number of features are seen in absorption against the dust shell, which we attribute to HCN and polyyne molecules. We use these features to determine the 12C/13C ratio for the absorbing gas to be ∼3.2+3.2−1.6; this implies that, despite the H-content of the molecules, the hydrocarbon-bearing gas must have originated in material produced in the very late thermal pulse. We see no evidence of emission lines, despite the recently-reported optical and radio observations that suggest the effective temperature of the stellar remnant is rising.

Stellar archaeology: the evolving spectrum of FG Sagittae

Over an interval of 120 years, the extraordinary object FG Sge has been transformed from a hot post-AGB star to a very luminous cool supergiant. Theoretically, this evolution has been associated with the reignition of a helium-shell during the post-AGB stage. A series of studies of the chemical composition of the photosphere have suggested that this evolution has been associated with a dramatic increase of approximately 3 dex in the abundances of s-process elements between about 1960 and 1995. The problem with this apparent change is that it occurred at a time when the surface convection zone, which is governed by the star's effective temperature, could not have developed sufficiently to dredge processed material from the stellar interior to the surface. We have reviewed the chemical evolution of FG Sge by means of modelling the time-varying spectrum under a range of assumptions. By comparing these models with published observational data, a self-consistent picture has emerged. In particular we find that surface hydrogen has been depleted during the interval in question. In contrast, the s-process abundances have generally maintained a steady enhancement of around dex, although some modest changes may have occurred since 1950. This implies that FG Sge has not just completed dredging up freshly-produced s-process isotopes. However, there remains a contradiction between the observed hydrogen-depletion, the age of the associated planetary nebula, and current evolutionary models for a pre-white dwarf suffering a late thermal pulse.

The mass of helium in white dwarf stars and the formation and evolution of hydrogen-deficient post-AGB stars

We use two sets of ‘cradle-to-grave’ evolutionary calculations to investigate how the mass of the helium buffer layer between the CO core and the hydrogen-burning shell in thermally pulsing asymptotic giant branch (AGB) stars depends on the initial stellar mass and heavy element abundance. Cool star mass loss is included by augmenting the Reimers’ formula with fits to mass-loss rates observed for Galactic Mira variables, obscured Large Magellanic Cloud (LMC) AGB variables and Galactic OH/IR sources. Resulting white dwarf masses are in good agreement with the semi-empirical final mass‐initial mass relation. We derive lower and upper limits on the mass of helium in white dwarfs as functions of their mass and initial heavy element abundance. We find that stars that experience a very late thermal pulse (VLTP) have final helium masses that are about 25 per cent below the lower limit for stars that do not experience a VLTP. We have derived a modified form of Iben’s criterion for a star to experience a post-AGB helium shell flash, and subcriteria for discriminating between the occurrence of late and VLTPs. We find that a post-AGB flash does not necessarily result in formation of a nonDA white dwarf. Furthermore, we find that the relative amount of time spent burning helium or hydrogen depends on how the mass-loss rate varies with stellar surface parameters. These two considerations complicate the relationship between the probability that a star experiences a post-AGB flash and the relative formation rates of DA and non-DA white dwarfs. However, our calculations do lead to a non-DA/DA ratio that is consistent with the observed ratio. We find that our predicted abundances for PG1159 stars agree within the error bars with the observed abundances, without the need of convective overshoot. We also find that nitrogen is produced during VLTPs but not in the other evolutionary paths to hydrogen-deficient objects. Hence, we propose this as the reason why nitrogen is observed in some PG1159 stars but not all. Our VLTP models also produce surface abundances close to those of the low-gravity hybrid PG1159 stars. An inconsistency between asteroseismological and our evolutionary model determinations of helium layer mass remains.