Photometric Study of Transition Objects Which Lie Between the Asymptotic Giant Branch ( AGB ) and Planetary Nebulae ( PNe )

Post-Asymptotic Giant Branch (post-AGB) stars are generally believed to be on their way to the planetary nebula stage. However, there has been a question about the evolutionary path for the low-mass ones. We investigate the evolution of 31 very likely and possible post-AGB candidates selected from the Torun catalogue of Galactic post-AGB sources. The sources in the sample belong to the IRAS selected sources (IRASsel), High Galactic latitude supergiants (hglsg), High Galactic latitude B-type supergiants (hglB) and Bright stars with infrared (IR) excess (IRexc) classifications in the catalogue and are found to lie between AGB and planetary nebulae (PNe). Out of the 31 selected sources, 26 were studied. We compared the IRAS color-color plots of these sources with that of van der Veen & Habing and Szczerba and found that the 26 sources are possibly post-AGB stars. Their temperature and dynamical time plots showed that 11 objects in our sample have their shells completely detached. One object was found to be on the evolutionary track of Mcore = 0.55MΘ and may likely evolve to a white dwarf, by-passing the PN stage.


Introduction
The evolution of the late type stars from Asymptotic Giant Branch (AGB) to Planetary Nebula (PN) has been studied by Van der Veen and Habing (1988) using the [12]- [25] versus [25]- [60] color-color diagram.Their color-color diagram was divided into regions, each corresponding to different stellar evolutionary stage.Regions I through IIIb (see Figure 5b in Van der Veen & Habing 1988) contain the stars evolving from O-rich Miras to OH/IR stars.Region IV mainly consists of transition objects, and region V consists of planetary nebulae.From their study of transitional objects from AGB to PN, using a sample of 42 IRAS sources, Veen et al. (1989) classified the sources into five categories based on the Spectral Energy Distribution (SED) shape from optical to far-infrared wavelength.The authors concluded that the SED category did not indicate the stellar evolutionary stage and could not show an evolutionary path in the near-infrared and the IRAS color-color diagrams.Thus the analysis of the SED of post-AGB stars needs a combination of the optical and near-infrared photometry, in addition to the IRAS data.In order to understand the nature of the SED in the shorter wavelength, optical and near-infrared photometry has been performed for some of the post-AGB stars.For instance, Manchado et al. (1989), García-Larío et al. (1990, 1997) carried out JHK photometric survey of several IRAS sources with colors like Planetary Nebulae (PNe).Also, Hrivnak et al. (1989) studied the SEDs of eight post-AGB candidates based on BVRIJHK photometry.They showed that multi-color photometry, in combination with spectral types of the IRAS sources, enables one to estimate the parameters of the stars and their circumstellar dust envelopes.Fuji et al. (2002) showed that the SED of post-AGB stars is double peaked.One peak is at far-infrared wavelengths due to the cold dust-shell (100-200 K) and the other peak is at shorter wave-lengths (optical or near-infrared) from the obscured central star.
The Torun Catalogue of Galactic post-AGB and related objects (Szczerba, 2007, hereafter TC objects) has offered a new opportunity for studying the AGB -PN evolution in infrared color−color diagrams.Hence, the main purpose of this work is to ascertain if these transition objects can be classified as post-AGB stars and to verify if the evolutionary track and color-color distribution of these selected objects are consistent with those obtained in previous studies (e.g.Van der Veen & Habing, 1988;Fuji et al., 2002;Szczerba et al., 2007), using the IRAS color-color diagram.Though the analysis of the SED of post-AGB stars requires a combination of the optical and near-infrared photometry in addition to the IRAS data, in this work we analyzed the evolution of post-AGB stars using 2MASS data.
The selected samples contain very likely post-AGB objects and possible post-AGB objects from the IRASsel, hglsg, hflB and IRexc classifications in the TC to study how these objects are distributed in the IRAS color-color diagrams.We also determined the temperature and dynamical ages of the selected sources in order to understand their evolutionary track.The scheme of this paper is divided as follows: in Sect. 2 we present an overview of the database used in this work; in Sect. 3 color-color diagrams are discussed; Sect. 4 contains a discussion about the stellar temperature and dynamic time relationship; and in Sect. 5 we present our conclusions.

Description of the Database
The TC (http://www.ncac.torun.pl/postagb)objects were compiled with the purpose of including objects discovered with the ongoing AKARI infrared sky survey, which has a much greater sensitivity than IRAS.This catalogue is organized into 3 sub-catalogues: very likely post-AGB objects, possible post-AGB objects and disqualified post-AGB objects.The category of very likely post-AGB objects is made up of several classes and gives the available optical and infrared photometry, infrared spectroscopy and spectral types, and links to finding charts and bibliography.The coolest post-AGB objects included in the catalogue have spectral types not later than K, while the hottest have effective temperatures below 25,000 K.The catalogue considered as disqualified post-AGB objects those that have central stars classified as M-or as cool AGB carbon stars.Also luminosity class V objects as well as objects that have been classified as PNe (especially those appearing in the Strasbourg-ESO Catalogue of Galactic Planetary Nebulae (Szczerba et al., 2007) were considered as disqualified.Two sources IRAS 00509+6623 and IRAS 06518-1041 were taken from IRAS point source catalogue.The nature and spectral class of the two sources have not been identified in the observation done by Suarez et al. (2006), though IRAS 06518-1041 was identified as a PN.
The objects used in this study were selected from the classes of very likely post-AGB and possible post-AGB objects.They include: i. IRAS selected (IRASsel) sources; selected on the basis of their IRAS colors which were found to be between those of AGB stars and Planetary Nebulae (Szcerba et al., 2007); ii. High Galactic latitude supergiants (hglsg); selected on the assumption that they are low-mass stars in their final stages of evolution and their spectral types are found to be K, G, F and A (Szcerba et al., 2007); iii. High Galactic latitude B-Type supergiants (hglB); selected on the basis of their location at high Galactic latitudes (|b| > 15 o ) (Szcerba et al., 2007).
The list of the objects together with their photometric data and IRAS fluxes are given in Table 1.Figures 1 and 2 show J -H versus H -K and J -K versus K -[25] diagrams for the selected objects.The IRAS flux at 25µm was converted to magnitude using [25] = -2.5log(F25/6.73)(e.g.Szczerba, 2007).

Stellar Temperature and Dynamical Time of the Sample Objects
To determine the dynamical time, we applied the Stefan-Boltzmann law for stellar luminosity; where L is the Luminosity, R is the stellar radius, T is the stellar temperature and σ (= 5.67×10 -8 Wm 2 K -4 ) is the Boltzmann constant.We used this relation to determine the stellar radius.Following Fuji et al. (2002), we assumed that the central star is a blackbody source with a temperature T star and luminosity L = 8000 L Θ .To estimate stellar temperature of the objects we used the (B-V)-Temperature relation from literature (e.g.Flower, 1995).Thus, the dynamical time t dyn is derived from the relation (Fuji et al., 2002). ( where V exp the expansion velocity is assumed to be 15 kms -1 and R in is the inner radius of the dust shell.The values of R in were determined from the relation, This relation is derived from (Fuji et al., 2002) T dust (r) = (4) T dust is the dust temperature at the inner boundary of the dust shell and r = R in .The value 4.062×10 3 is the determined mean value of 1 2 / .
Table 2 shows the calculated values of the stellar temperature, inner radius and dynamical time of the dust shells of the selected objects.In Figure 4, one star exist in the main group, despite its relatively low stellar temperature, the dynamical age of the dust shell is large.It is on the evolutionary track of M core = 0.546M Θ , suggesting low mass for its parent star.This may indicate that this star might evolve directly to white dwarf by-passing the PNe stage as predicted by Renzizni (1981).Scarcity of PNe in globular clusters supports this hypothesis.
In general, the agreement between the observational results and the theoretical evolutionary tracks is satisfactory.However, the observations appear to fit with a somewhat lower core mass indicating a somewhat lower luminosity than assumed luminosity L = 8000L Θ used in our calculation.

Conclusion
We have studied 31 transition objects (very likely post-AGB and possible post-AGB objects) selected from Torun Catalogue of Galactic post-AGB and related objects.The selected objects belong to the IRASsel source, hglsg, hglB and IRexc classifications in the catalogue.Their IRAS color-color distribution and flux density at the 12, 25, and 60µm wavelength were determined.We obtained estimates of the inner radii of the circumstellar shell, stellar temperature and the dynamical ages of the objects.
The IRAS color-color distribution of our objects showed that most of the objects were found within the IRAS color box defined by [12]-[25] > 0.75 and [25]-[60] < 1.15 as defined by van der Veen and Habing (1988) and Szczerba (2007).The only exceptions are IRAS07018-5013, IRAS07506-0345, IRAS07577-2806 and IRAS18313-1738.Apart from IRAS18313-1738, which happens to belong to the category of very likely post-AGB objects, the other three objects belong to the possible post-AGB objects.We also found that eleven objects have their shells completely detached from the central stars.Comparing with the theoretical evolutionary tracks of the post-AGB stars (Schonberner, 1983), one object can be classified as a slowly evolving post-AGB star which may evolve into white dwarf without experiencing the PNe phase.Thus we can conclude that the 26 sources studied are post-AGB stars.Their temperature and dynamical time plots showed that 11 sources have their shells completely detached.One object was found to be on the evolutionary track of M core = 0.55M ʘ and may likely evolve to a white dwarf, by-passing the PN stage. Figu

Table 1 .
IRAS fluxes, and Photometric data of the selected objects

Table 2 .
Stellar temperature, inner radius and dynamical time of the dust envelope of the selected objects