2 DIVA DISPIS

2.1 The concept of a DISPI

The DIVA satellite is not only unique in its applications and abilities but also in the way it records spectra. DIVA will use a grating system yielding a dispersion of $\simeq$200 nm/mm on the focal plane with a total efficiency of about 60%. For astrometric and other reasons, the resulting (spectral) orders of the grating are not separated. Thus "classical" spectrophotometry will not be obtained. Instead, the detector will record a pixel related intensity function for each star, in which all orders (and thus wavelengths) overlap. Such a one-dimensional position-coded intensity distribution is called DISPI ( DISPersed Intensity). Figure 1 shows the position-coded wavelength of the grating's orders. One can see that the resolution of the second and third orders increases by factors of two and three relative to the first order one, respectively. In the cross-dispersion direction, there are physical pixels while in the direction of dispersion there will be on-chip binning, resulting in "effective pixels". One such effective pixel corresponds to about 11.6 nm in the first order.

The maximum transmission of the first order is at about 750 nm (see Fig. 2), while that of the second and third orders are at about 380 and 250 nm respectively (see also Scholz 1998; Scholz 2000).

2.2 Dealing with DISPIs

Given the nature of the DISPIs, a classical spectrophotometric analysis - like line and continuum fitting - to derive astrophysical parameters is cumbersome. We will show that by training Artificial Neural Networks (ANNs) on simulated DISPIs, we can readily access this information without any further pre-processing of the signal. Using DISPIs from calibration stars, i.e. stars with known physical and apparent properties, we would initially build up a standard set of DISPI data. The automated classification technique as developed will then use this library. The calibration could be iteratively improved using DISPIs and their parametrization results obtained during the mission. Note that in these simulations, we did not use absolute fluxes as they will be available from the mission (see below). In this work, only the shape of a DISPI and its line features were used for tests to determine basic stellar parameters.

Figure 2: Transmission curves for the first, second and third grating orders, plus the quantum efficiency. The order's curves have been scaled down by a factor of 0.6 to better represent data from the real grating.

Typical DISPIs can be seen in Figs. 3 and 4 for a cool and a hot star, respectively. One can see that the first, second and third orders contribute different amounts to the total light in a DISPI for different temperatures. The first order's transmission maximum is at about 700 nm while the second and third orders contribute mostly at shorter wavelengths. Thus, for the cooler star, the second order contributes less to the DISPI in the case of the bluer, hotter star. The third order's contribution becomes negligible for low temperatures. Note that the "continuum" of a DISPI is mainly defined by the first and partly by the second order. For a hot star, spectral line features are essentially only visible in the second and third orders due to their two- and threefold higher resolution. Only for strong molecular bands in very cool stars are features resolved in the first order.

 

 

Table 1: The signal-to-noise ratio (S/N) for single measured DISPIs with different temperatures and visual magnitudes as measured from the 10 central pixels around effective pixel position 60 in the direction of dispersion. The innermost 13 TDI-rows of the two-dimensional SC image were summed up to build the DISPI (see Sect. 4). The stated temperature is the central value for each sample (sample names are given in parentheses, see Table 2). The S/N for temperatures in the range of 6000 K $\leq$ $T_{\rm eff}$ $\leq$ 10 000 K is almost the same for a given magnitude.

V[mag]	S/N
$T_{\rm eff}$ = 3000 K (L1)
8	122
9	77
10	47
11	28
12	16
$T_{\rm eff}$ = 5000 K (L2)
8	91
9	56
10	34
11	20
12	11
$T_{\rm eff}$ = 9000 K (L3, M1, M2)
8	82
9	50
10	30
11	17
12	9
$T_{\rm eff}$ = 15 000 K (H1)
8	95
9	59
10	36
11	21
12	12
$T_{\rm eff}$ = 30 000 K (H2)
8	118
9	74
10	46
11	28
12	16

The signal-to-noise ratio of a single DISPI as measured from the 10 central pixels around effective pixel position 60 is shown for different visual magnitudes and temperatures in Table 1.

Figure 3: Input spectrum (top) and simulated DIVA DISPI (bottom) for a star with $T_{\rm eff}$ = 4500 K, $\log g$ = 4 and solar metallicity (no noise added). Top: the model spectrum sampled in steps of 4 nm, which matches roughly the resolution of the third order of the DIVA dispersed image, shows spectral structure of which the TiO band is marked. Bottom: DIVA DISPI showing total counts (in arbitrary units) detected along the effective pixels in the extracted DIVA dispersed information. The TiO feature of the input spectrum (top) can be recognized in the contributions to the first and second orders.

Figure 4: Input spectrum (top) and simulated DIVA DISPI (bottom) for a star with $T_{\rm eff}$ = 9500 K, $\log g$ = 4, solar metallicity (without noise, as in Fig. 3). Here the H$_{\alpha }$, H$_{\beta }$ and H$_{\gamma }$ features are marked in the model spectrum as well as in the resulting DISPI. For such a star, the third order starts to contribute to the signal.