Comparing heliospheric absorption with model predictions

4.2 Comparing heliospheric absorption with model predictions

In this article, we are more interested in the astrospheric Ly $α$ absorption than the heliospheric absorption, since we are concerned with using the astrospheric detections to measure the properties of solar-like stellar winds. However, hydrodynamic models of the astrospheres are required to do this (see Section 4.3). In order to believe the results of these models, it is crucial to demonstrate that they are properly extrapolated from heliospheric models that can reproduce observed heliospheric absorption. Thus, the heliospheric absorption and efforts to reproduce it using models are reviewed in this section.

Figure 7:

Comparison between the Ly $α$ spectra of $α$ Cen B (green histogram) and Proxima Cen (red histogram) from Wood et al. (2001

). The inferred ISM absorption is shown as a green dashed line. The Alpha/Proxima Cen data agree well on the red side of the H I absorption, but on the blue side the Proxima Cen data do not show the excess Ly $α$ absorption seen toward $α$ Cen (i.e. the astrospheric absorption).

Gayley et al. (1997 ) were the first to clearly demonstrate that heliospheric models are capable of reproducing the observed excess Ly $α$ absorption, at least on the red side of the line (see Section 4.1). However, the exact amount of absorption predicted depends on exactly what properties are assumed for the surrounding LISM. Since many of these LISM properties are not precisely known (see Section 2.2), there is the hope that the heliospheric absorption can be used as a diagnostic for the LISM properties, such that the heliospheric absorption is only reproduced when the correct LISM parameters are assumed. In practice, this has proven to be very difficult.

One problem has been finding enough detections of heliospheric Ly $α$ absorption to provide proper constraints for the models, although the situation has been gradually improving. The first heliospheric absorption detection was for the $α$ Cen line of sight described in detail in Section 4.1. The second detection was for the downwind line of sight towards Sirius (Izmodenov et al., 1999b ), though the analysis of Hébrard et al. (1999 ) suggests that this detection is not very secure. The upwind line of sight towards 36 Oph (Wood et al., 2000a ) provided the third detection, and there is a marginal detection for the crosswind line of sight towards HZ 43 (Kruk et al., 2002 ). An HST archival Ly $α$ survey by Wood et al. (2005b ) resulted in four more detections (70 Oph, $ξ$ Boo, 61 Vir, and HD 165185). Most recently, a detailed analysis of all reconstructed stellar Ly $α$ lines based on HST data has found evidence for very broad, weak heliospheric absorption for three lines of sight ( $χ1$ Ori, HD 28205, HD 28568) observed within $20∘$ of the downwind direction (Wood et al., 2007b ). This brings the grand total of absorption detections to 11. In addition, Lemoine et al. (2002 ) and Vidal-Madjar and Ferlet (2002 ) have claimed to find evidence for weak heliospheric absorption towards the similar Capella and G191-B2B lines of sight, but these claims rely on subtle statistical arguments rather than clearly visible excess absorption.

The heliospheric absorption detections can be supplemented with other lines of sight observed by HST that at least provide useful upper limits for the amount of heliospheric absorption. Figure 8 shows the Ly $α$ absorption profiles observed for three

Figure 8:

Comparison of the H I absorption predicted by a four-fluid heliospheric model (dashed lines) and the observations, where the model heliospheric absorption is shown after having been added to the ISM absorption (dotted lines). Reasonably good agreement is observed, although there is a slight underprediction of absorption towards 36 Oph and Sirius, and a slight overprediction towards $ε$ Eri (Wood et al., 2000b

of the lines of sight with detected heliospheric absorption (36 Oph, $α$ Cen, and Sirius) and three additional lines of sight with nondetections (31 Com, $β$ Cas, and $ε$ Eri). The figure zooms in on the red sides of the profiles where the heliospheric absorption should be located. The $θ$ angles in the figure indicate the angle of the line of sight with respect to the upwind direction of the interstellar flow. The six sight lines sample diverse orientiation angles, ranging from the nearly upwind direction towards 36 Oph ( $∘ θ = 12$ ) to the nearly downwind line of sight to $ε$ Eri ( $∘ θ = 148$ ). The dotted lines show the ISM absorption alone, constrained by forcing consistency with D I (see Section 4.1) – only 36 Oph, $α$ Cen, and Sirius show excesses that reveal the presence of heliospheric absorption. A successful heliospheric model should accurately reproduce the amount of heliospheric absorption detected towards these three stars, while predicting no detectable absorption towards the other three.

Figure 8 shows a model that agrees reasonably well with the data, despite a slight overprediction of absorption towards $ε$ Eri and slight underpredictions for 36 Oph and Sirius (Wood et al., 2000b ). This model assumes $T = 8000 K$ , $−3 n (H I) = 0.14 cm$ , and $+ −3 n(H ) = 0.10cm$ for the ambient LISM, parameters well within the range of values inferred by other means (see Section 2.2). However, not all heliospheric models that assume these parameters find agreement with the data.

This brings us to the second problem with trying to infer ambient LISM parameters from the heliospheric Ly $α$ data: Results currently seem to be very model dependent. It is mentioned in Section 2.3 just how difficult it is to properly consider neutrals in heliospheric models due to charge exchange processes driving the neutral H out of thermal equilibrium. The model used in Figure 8 is a “four-fluid” model of the type developed by Zank et al. (1996 ), where one fluid represents the protons, and three distinct fluids are used to represent the neutral hydrogen, one fluid for each distinct region where charge exchange occurs (inside the TS, between the TS and HP, and between the HP and BS). However, there are other approaches, such as the hybrid kinetic code of Müller et al. (2000 ) and the Monte Carlo kinetic code of Baranov and Malama (1993 , 1995 ). The heliospheric absorption predicted by these kinetic models is not identical to that predicted by the four-fluid models (Wood et al., 2000b ; Izmodenov et al., 2002 ). Currently the kinetic models seem to have more difficulty reproducing the observed heliospheric absorption than the four-fluid models, especially in downwind directions where they tend to predict too much absorption. However, the kinetic models should in principle yield more accurate velocity distributions for the neutral H than codes with multi-fluid approximations. A complex multi-component treatment of the protons in the heliosphere seems to improve the kinetic models’ ability to fit the data (Malama et al., 2006 ; Wood et al., 2007b ). Clearly more work is required to attain some sort of convergence in the models before LISM parameters can be unambiguously derived from the data.

However, a third difficulty with using the heliospheric absorption to infer ambient LISM properties is that the absorption may not be as sensitive to these properties as one might wish. Izmodenov et al. (2002 ) experiment with different LISM proton and neutral hydrogen densities and find surprisingly little change in the predicted Ly $α$ absorption, at least in upwind and sidewind directions. This may be bad news for the diagnostic power of the heliospheric absorption, but it is actually good news for the astrospheric analyses that are described in Section 4.3. In using astrospheric models to help extract stellar mass loss rates from the astrospheric absorption, one has to assume that the LISM does not vary much from one location to another. The results of Izmodenov et al. (2002 ) suggest that the models are not very sensitive to the modest variations in LISM properties that one might expect to be present in the solar neighborhood.

Finally, there are some aspects of heliospheric physics that are only beginning to be considered in the models. The models mentioned previously do not consider either the heliospheric magnetic field carried outwards by the solar wind (see Nerney et al., 1991 ), or the poorly known interstellar magnetic field. Not only is a proper MHD treatment of the heliosphere difficult, but the problem is inherently three dimensional, whereas the models mentioned previously assume a 2D axisymmetric geometry. Using a 2D approach, Florinski et al. (2004 ) find that a strong ISM field oriented parallel to the LISM flow does not yield significantly different predictions for heliospheric Ly $α$ absorption than models without magnetic fields. However, 3D models are required to include the heliospheric field, and 3D models are also required to consider ISM field orientations other than parallel to the flow vector.

Initial 3D models developed to model these effects (see Linde et al., 1998 ) did not include neutrals in a self-consistent manner. Dealing with both neutrals and magnetic fields properly in a 3D model is a very formidable problem. Nevertheless, the 3D models without neutrals do suggest that MHD effects could in principle lead to changes in the heliospheric structure that could affect the Ly $α$ absorption. Examples include the unstable jet sheet and north-south asymmetries predicted by Opher et al. (2003 , 2004 , 2006 ). In addition, Ratkiewicz et al. (1998 ) find that if the LISM magnetic field is skewed with respect to the ISM flow, the effective nose of the heliosphere could be significantly shifted from the upwind direction. Even in the absence of magnetic fields, latitudinal variations in solar wind properties could also cause asymmetries in the heliosphere (Pauls and Zank, 1997 ). It is possible that all these asymmetries suggested by 3D models could be detectable in Ly $α$ absorption. However, neutrals must be included properly in the models to make clearer predictions. Only very recently has this been done (Izmodenov et al., 2005 ; Pogorelov et al., 2006 ). Wood et al. (2007a ) have made the first comparison between such models and the Ly $α$ data, finding that the absorption predicted by the models is modestly affected by the assumed LISM field strength and orientation, allowing some constraints on these quantities to be inferred from the data. However, with the absorption being modestly dependent on so many uncertain LISM properties, including particle densities, it is probably unreasonable to expect analysis of the absorption by itself to yield a single set of acceptable LISM parameters.