Recently, SBS 1150+599A has been recognized as a planetary nebula in the Galactic halo by Tovmassian et al. (2001) and renamed PNG 135.9+55.9. The spectra then available for this object were quite unusual for a planetary nebula, presenting only the Balmer lines of hydrogen, He II $\lambda\lambda$ 4686, 5411, and very weak [O III] $\lambda$ 5007 ( $\sim$ $4 \%$ of HH $\beta$ ). A photoionization model analysis showed that such a spectrum implies a strongly density bounded and extremely oxygen-poor nebula ionized by a very hot star. The oxygen abundance was estimated to be less than 1/50 of the solar value, and probably between 1/100 and 1/500 of solar assuming canonical properties for the central star, making of PNG 135.9+55.9 by far the most oxygen-poor planetary nebula known, with an oxygen abundance similar to the lowest measured to date in stars (Boesgaard et al. 1999; Howard et al. 1997).

In this paper, we report detailed follow-up observations, aimed at providing more stringent constraints on the nature of this exceptional object. Section 2 presents the new spectroscopic data, while Sect. 3 deals with narrow-band imaging. In Sect. 4, we present an updated photoionization model analysis, taking full advantage of the constraints provided by our new observational data. This leads to a limit on the oxygen abundance which is now independent of any assumption about the evolutionary status of the central star. In Sect. 5, we estimate the abundances of the other elements. Section 6 presents a brief concluding discussion.

**Table 1:** Log of the spectroscopic observations.
	SPM1	SPM2	CFHT	WHT	SPM3^a	SPM4
date	22 Jan. 2001	23-24 Jan. 2001	3-4 Mar. 2001	11 May 2001	5 Mar. 2002	8 Apr. 2002
CCD	Thomson	Thomson	EEV	Tektronix	SITe	SITe
format	$2048\times 2048$	$2048\times 2048$	$2048\times 4500$	$1024\times 1024$	$1024\times 1024$	$1024\times 1024$
pixel size^b	$14~\mu$ m, $0\hbox{$.\!\!^{\prime\prime}$ }61$	$14~\mu$ m, $0\hbox{$.\!\!^{\prime\prime}$ }61$	$13.5~\mu$ m, $0\hbox{$.\!\!^{\prime\prime}$ }283$	$24~\mu$ m, $0\hbox{$.\!\!^{\prime\prime}$ }36$	$24~\mu$ m, $1\hbox{$.\!\!^{\prime\prime}$ }05$	$24~\mu$ m, $1\hbox{$.\!\!^{\prime\prime}$ }05$
gain (e^-/ADU)	0.5	0.5	1.8	1.4	1.3	1.3
read noise (e^-)	4.8	4.8	3.1	4.6	8	8
spectrograph	B&C	B&C	MOS	ISIS	B&C	B&C
grating^c	300/4550 Å	600/4550 Å	B400/5186 Å	R158R/6500 Å	300/4550 Å	400/5150 Å
slit width	3 $.\!\!^{\prime\prime}$ 8	3 $.\!\!^{\prime\prime}$ 8	5 $^{\prime\prime}$	1 $^{\prime\prime}$	2 $.\!\!^{\prime\prime}$ 3	2 $.\!\!^{\prime\prime}$ 3
spectral resolution^d	12.7 Å	5.6 Å	23.0 Å	7.8 Å	8.1 Å	5.8 Å
wavelength interval	3700-6700 Å	4745-7200 Å	3400-8000 Å	6820-9740 Å	3600-7100 Å	3660-6760 Å
arc lamp	HeAr	HeAr	HgNeAr	CuNe+CuAr	HeAr	HeAr
standard stars	HD 93521	G191B2B	Feige 66	Hz44	BD+33 $^\circ$ 2642	HD 93521
	BD+33 $^\circ$ 2642	HD 93521				BD+33 $^\circ$ 2642
total exp. time	4500 s	7800 s	7200 s	3600 s	5400 s	12600 s
number of spectra	3	4	4	3	3	7

^a These observations were obtained through clouds.
^b Both the physical pixel size and the angle subtended on the sky are given.
^c The gratings are described by their ruling (lines/mm) and effective blaze wavelength. For the grism used at CFHT, the ruling and zero deviation wavelength are given. All of the observations were obtained in first order.
^d This is the spectral resolution measured at H $\alpha$ , defined as the FWHM of the H $\alpha$ line, except for the WHT spectrum, where this is the FWHM of P9 $\lambda$ 9229.

1 Introduction