4 Candidate planetary nebulae

The H$\alpha$+[N  II] and [O  III] continuum-subtracted images (Fig. 1, left panels) show a number of emission-line objects. Some of them are clearly extended H  II regions, which were previously studied by Moles et al. (1990), Strobel et al. (1991), Hunter et al. (1993), Hunter & Hoffman (1999), and Roye & Hunter (2000). We note that these regions form an approximate ring, with another H$\alpha$ nebulosity in the centre of the ring, perhaps close to the nucleus.

Figure 1: INT+WFC images of Sextans B. The size of each frame is 5".1$\times$4".0, i.e. a small fraction of the whole field of view of the WFC. North is at the top, East to the left. In the continuum subtracted images, candidate PNe are indicated by the arrows and marked with the identification number as given in Table 1.

Candidate PNe in Sextans B were selected using the following criteria (Magrini et al. 2000, 2001):

i) they should appear both in the [O  III] and H$\alpha$+[N  II] images but not in the continuum frame;

ii) they should have a stellar point spread function: at the distance of Sextans B. PNe are normally 0.1-1 pc in diameter, corresponding to 15-150 mas at the distance of Sextans B.

Five objects in Sextans B fulfill the criteria above; these new candidate PNe are listed in Table 1 and marked in Fig. 1. Only [O  III] and H$\alpha$+[N  II] fluxes are quoted in Table 1: they were not detected in He  II and [S  II]. The upper limit to these latter fluxes is estimated to be 10^-16 erg cm^-2 s^-1. The [O  III] fluxes were converted into equivalent V-band magnitudes following Jacoby (1989):

 

Table 1: PN candidates in Sextans B. Positions and reddening corrected H$\alpha$+[N  II] and [O  III] emission-line fluxes (in units of 10^-16 erg cm^-2 s^-1) are given, and luminosity in solar units.

Identification	RA (2000.0) Dec		$F_{\rm [OIII]}$	$F_{\rm H\alpha}$	m $_{\rm [O~III]}$	L
SexB PN1	9 59 53.06	5 18 52.1	16.0	7.0	23.24	2000
SexB PN2	9 59 56.50	5 19 29.5	11.2	8.1	23.64	2300
SexB PN3	9 59 56.64	5 19 52.6	19.2	13.0	23.05	3600
SexB PN4	10 00 00.19	5 20 37.2	12.8	6.6	23.49	1800
SexB PN5	10 00 10.48	5 20 31.9	38.4	20.0	22.30	5600

$$m_{\rm [O~{III}]}=-2.5\log F_{\rm [O~{III}]} -13.74. \nonumber$$ (1)

The luminosity was obtained from the relation $L \approx 150 \times L({\rm {H}}\beta)$(Zijlstra & Pottasch 1989), which is correct when the nebula is optically thick. This assumes that the [N II] lines make a negligible contribution to the H$\alpha$ line, which is likely correct at this low metallicity. The luminosities are close to but below the value of $7000~ L_\odot$, as expected for progenitor masses ${<}2~ M_\odot$.

This is the first identification of PNe in Sextans B: previous surveys did not find any suitable candidate (Jacoby & Lesser 1981). The five candidate PNe are distributed over an area of $1\farcm5\times4\farcm5$, corresponding to a linear, projected size of 0.6 kpc$\times$1.7 kpc. Three of them are found in regions densely populated by stars, whilst the other two (SexB PN1 and SexB PN5) are located in the outskirts of Sextans B, at projected distances from the galaxy centre of 0.8 and 1.1 kpc. All the candidate PNe have [O  III]/(H$\alpha$+[N  II]) flux ratios between 1.4 and 2.3. These are typical values for Galactic PNe (cf. Magrini et al. 2000), although the oxygen abundance of Sextans B is only 0.16 times solar (Moles et al. 1990).

4.1 Completeness limits

The detection of the five PNe raises the question: how many more remain to be discovered? Some PNe could have been missed in the most crowded region of Sextans B. We have estimated this number by adding "artificial stars'' within the range of luminosities expected for PNe (Jacoby 1989) in both the [O  III] and the off-band, y, frames using the IRAF task ADDSTAR. These artificial stars were recovered following the same procedures used to detect PNe. A 3$\sigma$ detection limit was adopted in the off-band frame. The recovery rate is significantly lower in the continuum-subtracted frames because of the larger noise produced in the scaling and subtraction of two images. This effect is dominant in recovering emission-line objects at faint magnitudes.

The incompleteness is a combination of the probability of missing an object in the emission-line image and the probability of wrongly identifying a star in the continuum frame. Incompleteness is defined as a recovery rate of artificial stars less then 50% (e.g. Minniti & Zijlstra 1997). This was computed in different regions of Sextans B, and for a range of assumed magnitudes. We find that incompleteness occurs for emission-line objects fainter than $m_{\rm [O~{III}]}=24.5$, located within 1'.5 from the centre of the galaxy.

Counting all stars brighter than this completeness limit, we find that the total luminosity of these stars in the inner regions is about 40% of the total. This agrees (roughly) with 3 of the 5 PNe found in this region. As completeness is better than 50% in this area, we conclude that at most five PNe brighter than $m_{\rm [OIII]}=24.5$may have been missed there.

Figure 2: The number of PNe of galaxies in or near the Local Group, versus the V-band luminosity in solar units. The dotted line shows the expected numbers based on a total number of PNe in the MW of 23 000. The dashed line is fitted to the known population in the LMC. Filled squares indicate LG gaseous galaxies, triangles indicate spheroidal galaxies and open circles show the NGC 3109 group.

4.2 Total PNe population size

The number of candidate PNe that we found in Sextans B is consistent with the expected population size for this galaxy, which can be estimated from stellar population models. For a simple (i.e. coeval and chemically homogeneous) stellar population, the number of stars n_j in any post-main-sequence phase j (Renzini & Buzzoni 1986) is given by

$$n_{j}=\dot{\xi} L_{\rm {T}} t_j, \nonumber$$ (2)

where $\dot{\xi}$ is the specific evolutionary flux (number of stars per unit luminosity leaving the main sequence each year), $L_{\rm T}$ the total luminosity of the galaxy, and t_j the duration of the evolutionary phase j ($\le$20 000 yrs for the PN phase). Adopting a bolometric luminosity of Sextans B of $\sim$10⁸ $L_\odot$ (van den Bergh 2000), and a specific evolutionary flux between $5\times10^{-12}$ and $2\times10^{-11}$ yr^-1  $L_\odot^{-1}$(cf. Renzini & Buzzoni 1986; Mendez et al. 1993), the corresponding population size of PNe in Sextans B is between 5 and 20 objects. This appears to be in good agreement with the number of PNe discovered. However, the [O III] luminosity of a PN rapidly declines once the nebulae becomes optically thin, and the phase during which a PN is bright enough to be discovered here is much shorter, typically 5000 yr (assuming an expansion velocity of 20  ${\rm {km~s}}^{-1}$ and a radius of 0.1 pc). Thus, the number of PNe may be a little higher than expected.

Figure 2 shows the number of known PNe for all nearby galaxies, using data in van den Bergh (2000), with three exception: M 33 now has 131 known PNe (Magrini et al. 2001), whilst for the Sagittarius dwarf spheroidal 3 PNe are now known (Walsh, priv. comm.), and for WLM both published PNe have been shown to be normal stars (Minniti & Zijlstra 1997). For the Milky Way (MW), about 1100 PNe are now known, but the total number has been estimated to be as high as 23 000 (Zijlstra & Pottasch 1991). Figure 2 plots the number of PNe versus the V-band luminosity of the galaxy, in solar units. Equation (1) suggests that this relation should be strictly linear, for a uniform star formation history. The dashed line gives the expected total number of PNe scaling from 23 000 in the MW. The dotted line is fitted to the known number in the LMC, where surveys have been most complete. It is clear that only the bright tip of the PN luminosity function can be detected. Figure 2 also shows that for galaxies with M_V > -12.5, one would not expect to detect the PN population.

Given its distance, the PN census in Sextans B may be expected to be less deep than that in the LMC. However, the two fall on the same line. This could be explained if Sextans B has a large proportion of intermediate-age stars, with a significant fraction of this star formation over the past 5 Gyr or so, compared to the LMC: a younger population has a higher death rate and will produce more PNe. The star formation in the Universe has declined rapidly from its peak around $z \approx 1.5$ (Lilly et al. 1995; Madau et al. 1998); however, Sextans B may be an example of a galaxy with a more delayed star formation history. The distribution in Fig. 2, once completeness has been reached, can be used to measure the star formation history for intermediate-age stars.

The small population size prevents us from building a meaningful Planetary Nebulae Luminosity Function (PNLF) for Sextans B, a property that is generally used as an extragalactic distance indicator (Jacoby 1989). In fact, the absolute magnitude of the bright cutoff of the PNLF depends on the size of the PN population. For a small population as in Sextans B, the bright PNe defining the "universal'' cutoff of the PNLF ( $m_{\rm [O~{III}]}^\star=-4.48$, Jacoby 1989) are not observed owing to the poor sampling. The simulations of Mendez et al. (1993) show, that even for a population size of 500 PNe, typical of the LMC and much larger than in Sextans B, no PNe with absolute magnitude lower than -4.0 are expected. Therefore, the absolute magnitude of the brightest PN in Sextans B, equal to -3.59 mag, is qualitatively consistent with its small population size, and can only provide an upper limit of $\sim$2 Mpc for the distance of the galaxy.

Figure 2 and the completeness analysis above suggest that the PN census in Sextans B is now fairly complete. In many other galaxies (especially IC 10), significant PN populations remain to be found.