ggalaxies
Article
Jsolated Stars of Low Metallicity
Efrat Sabach
Department of Physics, Technion—Israel Institute of Technology, Haifa 32000, Israel;[email protected]: 15 July 2018; Accepted: 9 August 2018; Published: 15 August 2018
Abstract:
We study the effects of a reduced mass-loss rate on the evolution of low metallicity Jsolatedstars, following our earlier classification for angular momentum (J) isolated stars. By using thestellar evolution code
MESA we study the evolution with different mass-loss rate efficiencies forstars with low metallicities of Z = Z = Z = Keywords: late stage stellar evolution; planetary nebulae; binarity; stellar evolution
1. Introduction
Jsolated stars are stars that do not gain much angular momentum along their post main sequenceevolution from a companion, either stellar or substellar, thus resulting with a lower mass-loss ratecompared to non-Jsolated stars [1]. As previously stated in Sabach and Soker [1,2], the fittingformulae of the mass-loss rates for red giant branch (RGB) and asymptotic giant branch (AGB) singlestars are set empirically by contaminated samples of stars that are classified as “single stars” butunderwent an interaction with a companion early on, increasing the mass-loss rate to the observedrates. The mass-loss rate on the giant branches has extensive effects on stellar evolution and on theresulting planetary nebula (PN) in low and intermediate mass stars. The reduced mass-loss rate ofJsolated stars results in a larger AGB radii compared to the RGB and compared to the “traditional”evolution with the high mass-loss rate efficiency of non-Jsolated stars. The higher AGB radii reachedfor Jsolated stars can lead to possible late interaction with a low mass companion. If such a Jsolated starinteracts late in its evolution with a companion, thus no longer qualifying as a Jsolated star afterwards,strong interaction might cause angular momentum gain, spin up, and increase in the mass-loss rate.The role of low mass companions (brown dwarfs or planets) in shaping PNe has been longdiscussed over the past few decades and it has been suggested that most PNe result from binaryinteraction (e.g., [3–15]). As we have shown in Sabach & Soker [1] for solar type Jsolated stars (bothin mass and in metallicity), such an interaction can occur during the AGB phase of evolution, wherethe companion is likely to be engulfed by the star. The engulfed companion will deposit angularmomentum to the primary’s envelope, increasing the mass-loss rate and by that later accelerating thepost-AGB evolution. This late interaction can shape an elliptical bright PN. In addition, we furtherfound under the Jsolated framework that as the sun is a Jsolated star it will most likely engulf the earthduring the AGB rather than during the RGB.We have also shown that such Jsolated stars have implications related to the puzzle of the brightend cut-off in the PN luminosity function (PNLF) of old stellar populations ([1,2]; for studies on thePNLF see, e.g., [16–22]). It was observed that both young and old populations have a steep bright end
Galaxies , a r X i v : . [ a s t r o - ph . S R ] A ug alaxies , , 89 2 of 7 cut-off in the PNLF in [OIII] emission lines at M ∗ (cid:39) − L ≥ L (cid:12) in order to ionizethe observed bright nebulae to the desired level. Our previous results indicate that also for low massstars the post-AGB luminosities of Jsolated stars are bright enough to account for the bright end cut-offin the PNLF of old stellar populations.In Sabach & Soker [2] we focused on the implications of a reduced mass-loss rate on stellarevolution of solar-type stars and the shaping of elliptical PNe by a companion. In Sabach & Soker [1]we set the term Jsolated stars and studied the possible solution for the puzzling finding of bright PNe inold stellar populations, where the stellar mass is up to 1.2 M (cid:12) . Yet, we have only focused on Jsolatedstars of solar metallicity, Z =
2. Results
We continue the study of Jsolated stars in old stellar populations by studying the evolution of lowand intermediate mass stars with reduced mass-loss rates and with low metallicities of Z = Z = Z = Z = MESA , version 10398 [24]). We comparethe evolution of stars with low metallicity to the evolution of stars with solar metallicity, Z = M (cid:12) and 1.2 M (cid:12) . We here consider stars with an initial mass as low as 0.9 M (cid:12) for our study of Jsolated stars and the implications to the resulting PNe.We focus on the effects of a reduced mass loss rate efficiency, as expressed by the empiricalmass-loss formula for red giant stars of Reimers [26]˙ M = η × × − LM − R . (1)We repeat the procedure described in Sabach & Soker [1] and follow the evolution with severalmass-loss rate efficiency parameters, from η = η = M J planet companion, is given by a m = R (cid:16) τ ev × yr (cid:17) (cid:16) L L (cid:12) (cid:17) (cid:16) R R (cid:12) (cid:17) − (cid:16) M env M (cid:17) (cid:16) M env M (cid:12) (cid:17) − (cid:16) M M (cid:17) , (2)where L , R and M are the luminosity, radius, and mass of the giant (RGB or AGB star), respectively, M env is the giant’s envelope mass, and τ ev is the evolution time on the upper RGB or AGB. In otherwords, for a 10 M J companion to be engulfed by the star the condition on the ratio between the giant’sradius and the orbital separation is R / a > M (cid:12) star and a 1.2 M (cid:12) star, since these masses bound the relevant mass range of PN progenitors of old stellar populations.In Figure 1 we present the final (cid:39) × yr of the AGB and focus on 2 metallicities, Z = Z = η = η = η = t = M env = − M (cid:12) . We present (top to bottom)the mass, the mass loss rate, the radius and the luminosity. Since tidal interaction brings the planetinto the envelope, and this interaction is highly sensitive to the ratio of R ( t ) / a ( t ) , We examine this alaxies , , 89 3 of 7 quantity in details. We define the value of L pAGB, max by the maximum value of the luminosity duringthe last AGB pulse (around t = R / a as expressed in Equation (2), both on the RGB and on the AGB, and the maximum valueof the post-AGB luminosity. Figure 1.
The evolution during the final (cid:39) × yr of the asymptotic giant branch (AGB) of starsof initial mass 0.9 M (cid:12) ( left plot ) and 1.2 M (cid:12) ( right plot ). The graphs are shifted so that at t = M (cid:12) . We present the evolution for 2 metallicities: Z = Z = η = η = η = alaxies , , 89 4 of 7 η M f [ M ⊙ ] M i = 0 . M ⊙ M i = 0 . M ⊙ M i = 0 . M ⊙ Z = 0 . Z = 0 . Z = 0 . η ( R / a ) m a x ( R/a ) RGB , max ( R/a ) AGB , max ( R/a ) RGB , max ( R/a ) AGB , max ( R/a ) RGB , max ( R/a ) AGB , max η L p A G B , m a x [ L ⊙ ] η M f [ M ⊙ ] M i = 1 . M ⊙ M i = 1 . M ⊙ M i = 1 . M ⊙ Z = 0 . Z = 0 . Z = 0 . η ( R / a ) m a x ( R/a ) RGB , max ( R/a ) AGB , max ( R/a ) RGB , max ( R/a ) AGB , max ( R/a ) RGB , max ( R/a ) AGB , max η L p A G B , m a x [ L ⊙ ] Figure 2.
The summary of the evolution of a 0.9 M (cid:12) star ( left plot ) and a 1.2 M (cid:12) star ( right plot ).For each star we studied the evolution from zero age main sequence until the formation of a white dwarf,for several mass-loss rate efficiency parameters, from η = η = Z = Z = ( R / a ) max , for both the red giant branch (RGB; blue) and the asymptotic giant branch (AGB; red).The companion mass is 10 M J and the initial orbital separation taken is 3 AU . The green horizontal lineindicates the capture condition above which planet engulfment can take place (Equation (2)). The lowerpanels present the maximum value of the luminosity on the post-AGB, L pAGB, max .
3. Discussion
We studied the evolution of Jsolated stars with low metallicities ( Z = Z = η = η = Z = M f , implies a more luminous central starfor the ionization of the PN. It can be seen for all metallicities that as the mass-loss rate efficiencyparameter η decreases the value of M f increases. There are very small differences between thevalues of M f for different metallicities (yet with the same initial mass and the same value of η ).Overall, by comparing M f , η = and M f , η = there is an increase of 5–8%. On the one hand thisincrease in M f might be too small for dynamical effects, but on the other hand it has a large effect alaxies , , 89 5 of 7 on the luminosity, as we shall discuss below, since the luminosity is very sensitive to the centralstar mass.2. The ratio of the maximum stellar radius and the orbital separation, ( R / a ) max , clearly increasesboth with the decrease in η and with increasing Z . Moreover, when examining Equation (2)for a planet companion of 10 M J and at an initial orbital separation of 3 AU we reach the finalconclusions as in Sabach & Soker [2]: For the RGB phase it is only marginal for the planet tobe engulfed in all cases, hence the probability for an early interaction is at most very small.In addition, for the traditional evolution with a high mass-loss rate efficiency parameter of η = ( R / a ) AGB, max is too small for planet engulfment for the low mass of 0.9 M (cid:12) ,and is marginal for the larger mass of 1.2 M (cid:12) . However, when reducing the mass-loss rateefficiency to η ≤ η ≤ ( R / a ) max not only increases with an increasing value of Z , but the increase is also “stronger” as η reducesand the metallicity increases.4. Our results have implications on the bright end cut-off of the PNLF in old stellar populations,where luminosities of (cid:39) L (cid:12) and higher are needed for the central star to ionize the brightnebula. To examine this possibility of such a bright central star we focus on the post-AGBluminosities reached in our simulations. We find that the post-AGB luminosity also increases withthe decrease of the mass-loss rate, reaching the high (cid:39) L (cid:12) luminosities needed to explain thebrightest PNe in old stellar populations. Interestingly it seems that as the value of η decreases thevalues for different metallicities grow closer together. We point out that the value of L pAGB, max has a wide range since it is an approximate value taken at the final AGB phase (the maximumvalue of the luminosity around t = Z = Z = η ≤ M i = 0.9–1.2 M (cid:12) , reach higher radii on the AGB compared to theRGB and also higher AGB radii compared to non-Jsolated stars, both for solar metallicity and lowmetallicities. The post-AGB luminosities of Jsolated stars also reach higher values for all metallicitiesstudied. For the higher masses of 1.2 M (cid:12) we find that the luminosities reached with a mass-lossrate efficiency parameter of η = (cid:39) L (cid:12) and might account for the PNLF in old stellarpopulations. For the lower mass stars of 0.9 M (cid:12) we find that planet engulfment can take place onthe AGB for a low mass loss rate efficiency parameter, but only for a very low efficiency parameter of η = L (cid:12) .Together with a late interaction with a low mass companion such Jsolated stars could account forthe shaping of elliptical PNe and possibly also the bright PNe in old stellar populations [1,2]. Once suchan interaction takes place the star is no longer considered a Jsolated star. Recently, Giles et al. [29] foundthe longest period transiting planet candidate from radial velocity measurements, EPIC248847494b.The relevant system parameters are a planet of mass 1 − M J at 4.5 ± AU from a 0.9 ± M (cid:12) star. It will be interesting to examine the future of the system within our Jsolated framework.We point out that new stellar evolution simulations find higher post-AGB luminosities comparedto old calculations (e.g., [30–32]). Gesicki et al. [22] present new evolutionary tracks of low-mass starsand study the bright end cut-off of the PNLF. They use a different stellar evolution code and find alaxies , , 89 6 of 7 for populations up to an age of 7 Gyr that the PNLF peak can be obtained by lower-mass stars thanpreviously thought. The full answer to the puzzle of the PNLF might be a combination of our resultsof a low mass-loss rate of Jsolated stars and such new stellar evolution calculations. Funding:
This research was funded from the Israel Science Foundation and a grant from the Asher Space ResearchInstitute at the Technion.
Acknowledgments:
I thank Noam Soker and the referees for useful comments that helped improve the paper.
Conflicts of Interest:
The author declares no conflicts of interest.
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