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Astron. Astrophys. 361, 1112-1120 (2000)

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4. Physical conditions

4.1. Electron temperature (Te)

In absence of diagnostic line intensity ratios (e.g. 4363/5007 Å of [OIII] and 5755/6584 Å of [NII]), the electron temperature of the ionized gas was derived by comparing the H[FORMULA] and [OIII] emission line profiles; the basic assumption is that, for a given Te, the thermal motion in H is four times larger that in O (the former element being sixteen times lighter that the second).

CAVEAT :This method can be rightly applied to PNe only if the H+ and O[FORMULA] layers do coincide (as in NGC 1501, which is an optically thin, high excitation PN). In many cases, the presence of large stratification effects invalidates the results, since H+ and O[FORMULA] are emitted in separated layers expanding in different ways (due to the presence of a gradient in the velocity field). Similarly, the H+ and N+ line profile comparison fails in medium and high excitation PNe.

The full width at half maximum (W) of an emission line is the convolution of different components:

[EQUATION]

where the last (too frequently neglected) term takes into account the existence of a radial gradient in the expansion velocity field.

A further broadening factor concerns H[FORMULA]: its seven fine structure components can be modeled as the sum of two equal Gaussians separated by 0.14 Å (Dyson & Meaburn, 1971, and Dopita, 1972).

Since in NGC 1501 the H+ and O[FORMULA] layers do coincide, we have:

[EQUATION]

A mean value of [FORMULA] is derived by analysing both the blue-shifted and red-shifted H[FORMULA] and [OIII] profiles in the central region of the lines; the spread in Te, only partially due to instrumental + measurement uncertainties, testifies the existence of electron temperature variations within the ionized gas, although no clear correlation was found with position and/or flux.

The only previous Te determination in this nebula is reported by Stanghellini et al. (1994), who obtained Te=10700 K from the 4363/5007 Å [OIII] intensity ratio. Moreover, some statistical works on a large sample of PNe (e.g. Cahn et al., 1992, and Phillips, 1998) adopt Te=15100 K, based on the strength of the HeII [FORMULA]4686 Å line and Kaler's, 1986, calibration.

Having obtained Te, the value of ([FORMULA]) can be inferred from relation (1); since in NGC 1501 the expansion velocity gradient is small (see Table 2), it can be neglected, allowing us to quantify turbulent motions in the ionized gas. We obtain for [FORMULA] a mean value of 18 [FORMULA] from both the H[FORMULA] and [OIII] profiles, but small scale fluctuations (up to [FORMULA]) are present.

A comparison with previous data reported in the literature for PNe gives poor results, because of our "caveat", of the scarce bibliography and of the different reduction methods. We recall the analysis performed by Gesicki et al. (1998) on seven PNe, indicating that the highest turbulent motions (15 km s-1) occur in M 3-15, a nebula powered by a WC 4-6 star. Although this result is weakened by the evidence that M 3-15 is ionization bounded (at least in some directions), we agree with the statement of these authors: "It is possible that nebulae with [WC] central stars have less regular velocity fields than the other PNe... The assumed very high turbulence may only be an approximation to a more complicated situation with strong velocity variations in radial direction".

4.2. Electron density (Ne)

Also Ne diagnostic line ratios (e.g. 6717/ 6731 Å of [SII], 3726/3729 Å of [OII], 4711/4740 Å of [ArIV] and 5517/5537 Å of [ClIII]) are absent in our echellograms of NGC 1501. In order to derive the electron density, we will proceed in three steps:

  • a) determination of the relative Ne radial trend in the "zero-velocity pixel column" (as defined by Sabbadin et al., 2000);

  • b) transformation to absolute Ne values by means of a suitable calibrator;

  • c) extension of the absolute Ne determination to the whole nebula's slice covered by the slit.

Points a) and b) will be discussed here and point c) in the next section, dedicated to tomography.

Let's consider a long-slit, spatially resolved, high resolution spectrum of a typical planetary nebula expanding at [FORMULA]. Following Sabbadin et al. (2000), the zero-velocity pixel column of an emission line represents the slice of nebula centred in the plane of the sky crossing the exciting star and having a depth along the line of sight [FORMULA], where r is the nebular radius and [FORMULA] is the pixel spectral resolution. As an example, in the velocity maps shown in Fig. 3, the observed H[FORMULA] zero-velocity column at each position angle is represented by a vertical strip centred at [FORMULA] (systemic radial velocity of NGC 1501) and [FORMULA] wide.

At every position along the slit, the intensity in the zero-velocity column is proportional to [FORMULA]; in the case of complete ionization and Te=constant, I[FORMULA] (we implicitly assume the constancy of the local filling factor, [FORMULA], within the slice of nebula identified by the zero-velocity pixel column; [FORMULA] is the fraction of the local nebular volume which is actually filled by matter with density Ne; the local nebular volume is given by: (pixel area)[FORMULA], where [FORMULA]).

In short: the zero-velocity pixel column, isolating a slice of nebula unaffected by the expansion velocity field, establishes a direct link between the intensity profile and the ionic and electron density distributions, thus allowing us the detailed analysis of the radial gas structure (and ionization) in the expanding nebula.

The H[FORMULA] zero-velocity column distributions, corrected for contamination by the adjacent spectral columns and for seeing and guiding uncertainties (for details, see Sabbadin et al., 2000), are shown in Fig. 4; they are normalized to the strongest intensity (i.e. the peak in the N-E sector of P.A.=55o).

[FIGURE] Fig. 4. Relative (left ordinate scale) and absolute (right ordinate scale) radial density trends obtained from the H[FORMULA] zero-velocity pixel columns. Note the steep outwards profile and the broad inwards tail present at all the four position angles (less evident in P.A.=55o).

The radial density profile of NGC 1501 results quite complex; the main features, common at all the four position angles, are the following:

  • the outermost parts correspond to the faint, roundish halo detected in our R image (representing the vestiges of the photospheric material ejected in the AGB phase);

  • the density peaks are located in the external nebular regions (close to the edge of the bright disk visible in Fig. 1 and Fig. 2); their distribution confirms that the main component of NGC 1501 is a shell of moderate thickness;

  • the density peaks show steep outwards profiles;

  • inwards tails of different shapes are present at all the four position angles; their extent seems anti-correlated to the height of the density peak: small at P.A.=55o, intermediate at P.A.=10o, broad at P.A.=145o (note the detached structure in the N-W sector) and at P.A.=100o (note the jagged profile).

Very similar radial density trends are obtained by analysing the [OIII] zero-velocity pixel columns.

In order to scale to absolute values the relative electron density profiles shown in Fig. 4, we will utilize the direct intensity-[FORMULA] (cm-3) relation given by the H[FORMULA] zero-velocity pixel column of NGC 40 (observed in the same nights and with the same instrumental setup used for NGC 1501).

We recall that the [SII] red doublet is quite strong in the low excitation PN NGC 40 (Aller & Epps, 1976, and Clegg et al., 1983), thus an accurate determination of Ne can be obtained from the diagnostic ratio 6717/6731 Å (Sabbadin et al., 2000).

From the general expression:

[EQUATION]

we obtain the following relation between the surface brightnesses of the zero-velocity pixel columns of NGC 1501 and NGC 40:

[EQUATION]

where the suffixes (1) and (2) refer to NGC 1501 and to NGC 40, respectively, I is the H[FORMULA] intensity in a pixel of the zero-velocity column (corrected for interstellar extinction), [FORMULA] is the apparent nebular radius, D is the distance and [FORMULA] is the local filling factor (as previously defined). For both nebulae we assumed [FORMULA]).

The calibration through relation (4) gives for NGC 1501 the absolute radial density profiles shown in Fig. 4, right ordinate scale. The following parameters (some taken from the literature) were adopted:

NGC 40: c(H[FORMULA])=0.60, Te=8000 K, [FORMULA]=25 km s-1, [FORMULA]=20", D=1.1 Kpc.

NGC 1501: c(H[FORMULA])=1.05, Te=11500 K, [FORMULA]=40 km s-1, [FORMULA]=28", D=1.3 Kpc.

Moreover, we assumed [FORMULA]; in general, this appears to be a reasonable condition; some particular cases will be discussed later-on.

The estimated inaccuracy in the Ne scaling factor is [FORMULA]20%, mainly due to our poor knowledge of the PNe distances; fortunately, in relation (4) the electron density has a low dependance on the distance.

We wish to point out that the foregoing method [i.e. the use of a PN (NGC 40) as a density calibrator for an other PN (NGC 1501)] represents a procedural escamotage : we were forced to adopt it since the night sky during the observational run was stable only at intervals. A more elegant analysis, based on the "absolute" surface brightness [i.e. formula (3)] will be presented and discussed in a future paper dedicated to the double envelope PN NGC 2022.

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© European Southern Observatory (ESO) 2000

Online publication: October 10, 2000
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