CONOCIMIENTOS PREVIOS:

HD 169142 was the first selected for modelling. It is an A5Ve star with an Ljr/L , ratio of 0.24 (Sylvester et al. 1997), and was the first Vega-like star discovered to show unidentified- IR (UIR) bands in its mid-IR spectrum (Sylvester, Barlow & Skinner 1994). The models here were run using pure am orphous carbon grains, although it was later realised th a t HD 169142 does show a very weak silicate emission feature in its 20/xm spectrum (Sylvester et al. 1996). Models were run using six single grain radii, ranging from 0.01/^m to 1mm, and a composite grain size m ade up of 15 individual sizes (Table 6.3). This particular composite size was selected so th a t a comparison with the work of Sylvester et al. (1997) could be made.

The near-IR excess indicates the presence of very hot grains ('^1500 K) and so initial models were run with inner radii small enough for the grains to reach th a t tem perature. For each of the grain radii used, no fit could be found for optical depths >1.0 (Table 7.3). For grain sizes of 0.5,um and larger, no fit at all could be found for the near-IR excess. An optical depth of 1.0 at V for the 0.01/zm grain and composite grain gave significantly too much flux to fit the observed excess (Fig 7.5) and so, for these grain sizes, optically thin m aterial must be present if they are responsible for the near-IR excess seen. The optically thin modelling of Sylvester et al. (1997) used very small grains (5Â) close to the star (0.67 AU) to get a good agreement with the observed near-IR flux. F urther experim entation with the CoUison & Fix code found th a t a satisfactory fit to the near-IR excess could be obtained by using O.lyum grains at a distance of 0.4 AU, a very similar distance to th a t of Sylvester et al. (1997). Sylvester et al. derived a mass of 1.2xlO"^M@ from their near-IR opticaUy thin model (where M@ is the mass of the E arth). The 0.1/xm grain model used here impUed a mass of 2.81xlO""*M@, i.e. more than Sylvester et al., but a greater mass is expected for an opticaUy thick model. This fit (Figure 7.6) did not, however, produce a simultaneous fit to the mid-IR excess. No combination of param eters was able to produce such a fit, and so the two excesses were modeUed separately.

00

0 5

Table 7.3: Results of SED modelling for HD 169142 with 100% amorphous carbon grains.

radius NIR FIR

a 'f'm in ^ m a x ^ m i n ^ m a x ^ B Mass ’^ m in '^m a x f'm in f'm a x T B Mass

(x r* ) ( x r , n i n ) (AU) (AU) (M@) (x r* ) ( X T-rain) (AU) (AU) (M e)

0.01/im N O F I T F O R r > 1.0 17000 1000 138 137500 1.0 2.0 2.84x10-4 composite N O F I T F O R T > 1.0 12000 1000 97 97000 1.5 2.0 2.68x10-4 0.5/xm N O F I T 14000 1000 113 113000 3.0 2.0 5.58x10-4 l/im N O F I T 7000 1000 57 56600 3.0 2.0 6.20x10-4 10;im N O F I T 1000 1000 8 8100 3.0 1.9 1.16x10-4 100/im N O F I T 1000 1000 8 8100 3.0 2.0 7.28x10-4 1mm N O F I T 1000 1000 8 8100 3.0 2.0 7.35x10-3

a) O.Olyum g r a in s 1 10 100 1000 W a v e le n g th (/im ) BTTTTTTl n I I I o m p o s i t e 10 100 W a v ele n g th Gum) 1000

Figure 7.5: Near-IR models for HD 169142 using a) 0.01/im grains and b) composite grains. The optical depth is 1.0 in both cases, producing too much flux at the short wavelengths.

For the mid- and far-IR excess, each grain size was able to produce a reasonable fit to the observed data exluding the near-IR points (Figure 7.7). The 0.01/im grains gave a very good fit to all data points (Figure 7.7), although a very large inner radius was required to do so (138 AU). In addition, a large outer radius (1000r,rim) was also necessary to fit the longest wavelength points. For scale, 138 AU is almost 3^ times the Sun-Pluto distance, and 1000 times this would place the outer edge of the disk halfway between the Sun and Proxima Centauri, just past the outer edge of the Oort Cloud.

The 0.5/im and 1/im grains lose a little flux at the 12/im point (Figure 7.7), but presumably this would be remedied by the addition of the near-IR excess contribution. The 10/zm grain model was the only model to require a modification of its radial density param eter, B. A value for B of 1.9 as opposed to 2.0 provided just enough additional grains in the outer regions to fit the mm-wave points. As the grains get larger, the inner radius required to obtain the correctly positioned mid-IR peak decreased somewhat. The very largest grains ( 10/^m, 100/im and 1mm) required only a lOOOr. inner radius (8AU, a little less that the Sun-Saturn distance) to fit the mid-IR peak well, but still required an outer radius of lQGOr,„,n to fit the mm points (this time corresponding to ~8000AU, somewhere between the outer edge of the Kuiper belt and the inner edge of the Oort cloud). The optical depth required to produce enough flux remained constant for each model at r= 3 .0 , with the exception of the two smallest grain models (0.01/zm grains and the composite grains) where much smaller optical depths were needed (r= 1 .0 and 1.5

s

Figure 7.6: Near-IR model for HD 169142 which successfully reproduces the observed fluxes. The grain radius is O.l/im.

respectively).

Although the modelling failed to reproduce the entire observed spectral energy distribu­ tion of HD 169142, the results of the single grain size models do provide useful insights into the possible nature of the system. We know, from the calculated extinctions (Table 7.2) and from the spherical envelope modelling in Section 7.2, th at spherical geometries are an extremely unlikely scenario for the case of the HD 169142 system. In a disk geometry, it has been shown that a population of small grains (<0.1/xm) must reside in the cicumsteUar disk in order to reproduce the observed near-IR excess (Figure 7.6). In addition, these small grains must be located very close to the parent star (0.5 AU) to achieve the high (~1500K) temperatures associated with excesses at these short wavelengths (2-5^m ). It is unbkely th at such small grains are solely responsible for the excesses seen simultaneously at mid- and far-IR wavelengths (10-100;:/m). The modelling here has shown th a t such small grains would have to be located at very large distances from the star (Table 7.3). However, whilst this fact does not rule-out the possibility of small grains residing in the outer regions of the disk (our own Oort Cloud is believed to extend to 100,000 AU), a more appealing scenario would be one where larger grains, which require smaller disk radii, make up a significant proportion of the outer disk. The presence of larger grains would imply th at the action of grain agglomeration was taking place, making the whole HD 169142 system a more interesting one to study.

From Figure 7.7, it is clear that many of the grain sizes modelled produce good fits

10 0 . 0 1 / i m g r a i n s 19 10' 100 1000 1 10 s 10 0 . 5 / i m g r a i n s ' - ■ LP i I mi l l W a v e l e n g t h ( / i m ) 10 100 W a v e l e n g t h ( / i m ) 1000 10 10 13 10 1000 10 100 1 W a v e l e n g t h ( / i m ) 1 0 / i m g r a i n s 1 10 100 1000 W a v e l e n g t h ( / i m ) 10 r ■13 >10 X 10" 1 m m g r a i n s 10 10 100 1000 1 10 1000 1 100 W a v e l e n g t h ( / i m ) W a v e l e n g t h ( / i m )

Figure 7.7: Models for HD 169142 which successfully reproduce the observed mid- and far-IR fluxes.

-12 - 1 3 E 10 1 1 - 1 7 c o m p o s i t e g r a in s - 1 8 - 1 9 10 100 1 1000 W a v e le n g th (/im ) Figure 7.7; continued

to the observed data. This implies th a t any one of those grain sizes, or a combination of some, or aU of them, could be responsible for the mid-IR excess seen. By studying the SED’s alone, it is virtually impossible to distinguish between grain sizes, which is not helpful when trying to constrain input param eters for these models. One solution is to produce surface intesity maps to distinguish between them. Figure 7.8 shows such maps at 450^m and 1.3mm for three of the grain sizes modelled (0.01//m, composite and 1mm grains). Clearly the profile of each one are of similar shape, but the im portant feature to note is the angular sizes they produce on the sky. The angular sizes show a large difference between the small grains and the large (1mm) grains. If sufficient angular resolution was available to image these sources, it would be one way of determining the dominant grain size in these systems.