Measuring stellar mass loss rates

4.3 Measuring stellar mass loss rates

Update

The $α$ Cen line of sight provided the first detection of astrospheric Ly $α$ absorption (Linsky and Wood, 1996

), but the use of models by Gayley et al. (1997

) was necessary to clearly demonstrate that heliospheric absorption could not explain the blue-side excess as well as the stronger red-side excess (see Figure 6

). By that time, there were already two other lines of sight, $ε$ Ind and $λ$ And, with excess Ly $α$ absorption found only on the blue side of the absorption line, which clearly could not be heliospheric in origin (Wood et al., 1996

). This excess absorption was immediately interpreted as being solely astrospheric. Thus, a case could be made for either $α$ Cen AB or $ε$ Ind/ $λ$ And being the first stars with detected solar-like coronal winds.

There are now a total of 13 published detections of astrospheric absorption. These detections are listed in Table 1, in addition to Proxima Cen since the nondetection for Proxima Cen is used to derive an upper limit for its mass loss rate (see below).

Table 1:

Published Astrospheric Detections and Mass Loss Measurements


Star	Spectral	$d$	Surf. Area	Log $Lx$	$VISM$	$θ$	$M˙$	Reference
	Type	(pc)	( $A⊙$ )		( $km s−1$ )	(deg)	( $M˙⊙$ )

$α$ Cen	G2 V+K0 V	1.3	2.22	27.70	25	79	2	1,2,3
Prox Cen	M5.5 V	1.3	0.023	27.22	25	79	$< 0.2$	3
$ε$ Eri	K1 V	3.2	0.61	28.32	27	76	30	4,10
61 Cyg A	K5 V	3.5	0.46	27.45	86	46	0.5	5,10
$ε$ Ind	K5 V	3.6	0.56	27.39	68	64	0.5	6,7,8
EV Lac	M3.5 V	5.1	0.123	28.99	45	84	1	11,12
70 Oph	K0 V+K5 V	5.1	1.32	28.49	37	120	100	11,12
36 Oph	K1 V+K1 V	6.0	0.88	28.34	40	134	15	9,10
$ξ$ Boo	G8 V+K4 V	6.7	1.00	28.90	32	131	5	11,12
61 Vir $a$	G5 V	8.5	1.00	26.87	51	98	0.3	11,12
$δ$ Eri	K0 IV	9.0	6.66	27.05	37	41	4	11,12
HD 128987	G6 V	24	0.71	28.60	8	79	?	11,12
$λ$ And $a$	G8 IV-III+M V	26	55	30.53	53	89	5	6,7,8
DK UMa $a$	G4 III-IV	32	19.4	30.36	43	32	0.15	11,12

$a$ Uncertain detection.

References: (1) Linsky and Wood (1996 ). (2) Gayley et al. (1997 ). (3) Wood et al. (2001 ). (4) Dring et al. (1997 ). (5) Wood and Linsky (1998 ). (6) Wood et al. (1996 ). (7) Müller et al. (2001a ). (8) Müller et al. (2001b ). (9) Wood et al. (2000a ). (10) Wood et al. (2002 ). (11) Wood et al. (2005b ). (12) Wood et al. (2005a ).

Some of these stars are binaries where the individual components are clearly close enough that both stars will reside within the same astrosphere, meaning that the observed astrospheric absorption is indicative of the combined mass loss of both stars. For these binaries ( $α$ Cen, 36 Oph, and $λ$ And), the spectral types of both stars are listed in Table 1 and the listed stellar surface areas are the combined areas of both stars. In contrast, 61 Cyg A’s companion is far enough away that 61 Cyg A should have an astrosphere all to itself, so it is listed alone in Table 1.

Three detections are flagged as uncertain in Table 1 for various reasons that will not be discussed here (see Wood et al., 2002 , 2005b ). Results regarding these three lines of sight should be considered with caution. There was originally another uncertain astrospheric detection, 40 Eri A (Wood and Linsky, 1998 ; Wood et al., 2002 ), which has now been dropped entirely from the list of astrospheric detections. Since astrospheric hydrogen scatters stellar Ly $α$ photons, solar-like stars should in principle be surrounded by faint nebulae of astrospheric Ly $α$ emission. There was an unsuccessful attempt to detect this emission surrounding 40 Eri A, and the lack of success was used to argue that the tentative detection of astrospheric absorption for 40 Eri A could not be correct (Wood et al., 2003a ).

The astrospheric absorption detections represent an indirect detection of solar-like winds from the observed stars, and the amount of absorption observed has diagnostic power. Frisch (1993 ) envisioned using astrospheres as probes for the interstellar medium, but so far work has focused on the use of the astrospheric absorption for estimating stellar mass loss rates. The higher the stellar mass loss rate, the larger the astrosphere will be, and the more Ly $α$ absorption it will produce. However, extracting quantitative mass loss measurements from the data requires the assistance of astrospheric models analogous to the heliospheric models discussed in Section 2.3.

The first step in modeling an astrosphere is to determine what the interstellar wind is like in the rest frame of the star. The proper motions and radial velocities of the nearby stars in Table 1 are known very accurately, as are their distances (see Perryman et al., 1997 ). The ISM flow vector is generally assumed to be the same as the LIC flow vector seen by the Sun (Lallement et al., 1995 ). Although multiple ISM velocity components are often seen towards even very nearby stars, the components are never separated by more than $−1 5– 10km s$ , meaning that the LIC vector should be a reasonable approximation for these other clouds. An example is the nearby “G” cloud. Since $α$ Cen, 70 Oph, and 36 Oph are known to lie within this cloud rather than the LIC, the “G” cloud vector from Lallement and Bertin (1992 ) is used instead of the LIC vector, but this does not change things very much. In any case, Table 1 lists the ISM wind velocity seen by each star ( $VISM$ ). The $θ$ value in Table 1 indicates the angle between our line of sight to the star and the upwind direction of the ISM flow seen by the star.

Figure 9:

Distribution of H I density predicted by hydrodynamic models of the Alpha/Proxima Cen astrospheres, assuming stellar mass loss rates of (from top to bottom) $0.2M˙⊙$ , $0.5M˙⊙$ , $1.0M˙⊙$ , and $2.0M˙⊙$ (Wood et al., 2001

). The distance scale is in AU. Streamlines show the H I flow pattern.

Astrospheric models are extrapolated from a heliospheric model that fits the observed heliospheric Ly $α$ absorption. The principle heliospheric model used in the past for this purpose is the four-fluid model described in Section 4.2, which is the source of the predicted heliospheric absorption in Figure 8 . In order to convert this to an astrospheric model, the model is recomputed using the same wind and ISM input parameters, except for the ISM wind speed which is changed to the $VISM$ value appropriate for the star (see Table 1). The stellar wind proton density is varied to experiment with mass loss rates different from that of the Sun. Figure 9 shows four models of the $α$ Cen astrosphere computed assuming different mass loss rates in the range of $M˙ = 0.2 –2M˙⊙$ (Wood et al., 2001 ). The model astrospheres naturally become larger as the mass loss is increased. The figure shows the H I density distribution, but the models also provide temperature distributions and flow patterns. From these models astrospheric absorption can be computed for the $∘ θ = 79$ line of sight to the star, for comparison with the data. Figure 10 shows this comparison for $α$ Cen, along with similar comparisons for five other stars in Table 1 (Wood et al., 2002 ). The model with $M˙ = 2M˙⊙$ agrees best with the data, so this is the estimated mass loss rate of $α$ Cen. Figure 11 shows similar data-model comparisons for six additional stars from Table 1 (Wood et al., 2005a ).

Figure 10:

Closeups of the blue side of the H I Ly $α$ absorption lines for six stars with detected astrospheric absorption, plotted on a heliocentric velocity scale. Narrow D I ISM absorption is visible in all the spectra just blueward of the saturated H I absorption. Green dashed lines indicate the interstellar absorption alone, and blue lines in each panel show the additional astrospheric absorption predicted by hydrodynamic models of the astrospheres assuming various mass loss rates (Wood et al., 2002

Figure 11:

A figure analogous to Figure 10

, but for six other lines of sight (Wood et al., 2005a

Figure 12:

Maps of H I density from hydrodynamic models of stellar astrospheres (Wood et al., 2002

). The models shown are the ones that lead to the best fits to the data in Figure 10

. The distance scale is in AU. The star is at coordinate (0,0) and the ISM wind is from the right. The dashed lines indicate the Sun–star line of sight.

Figure 13:

Maps of H I density from hydrodynamic models of stellar astrospheres (Wood et al., 2005a

), analogous to Figure 12

. The models shown are the ones that lead to the best fits to the data in Figure 11

Table 1 lists all mass loss rates measured in this manner, and Figures 12 and 13 show the astrospheric models that lead to the best fits to the data. The astrospheres vary greatly in size, both due to different mass loss rates and to different ISM wind speeds. It is worth noting that the largest of these astrospheres ( $ε$ Eri, 70 Oph) would be comparable in size to the full Moon in the night sky, if we could see them.

Given the model dependence and other difficulties described in Section 4.2, one might wonder if mass loss rates derived using the astrospheric models are at all reliable. However, the crucial point is that the heliospheric model from which the astrospheric models are extrapolated successfully reproduces the heliospheric absorption. For the astrospheric modeling purposes described here, this is more important than whether the input parameters of that model are actually correct. In essence, the observed heliospheric absorption is calibrating the models before they are being applied to modeling astrospheres, and in this way the mass loss measurement technique is actually semi-empirical. Nevertheless, the mass loss rates measured using the astrospheric Ly $α$ absorption technique should not be considered to be terribly precise. Uncertainties in the mass loss rates are probably of order a factor of 2 (Wood et al., 2002 ).

Other assumptions are implicitly made in this mass loss measurement procedure. One is that the LISM does not vary greatly from one star to the next. However, for these very nearby stars LISM variations should be modest, and as discussed in Section 4.2 modest variations probably do not greatly affect the predicted astrospheric absorption. Another assumption is that the stellar wind speeds of the stars in Table 1 are similar to that of the Sun. An argument in favor of this assumption is that stellar wind velocities are generally not very different from the surface escape speeds based on past experience, regardless of the type of wind or star one is considering (see Section 2.1). This includes the Sun, which has a surface escape speed of $619 km s−1$ , very similar to observed solar wind velocities. All the main sequence stars in Table 1 have similar escape speeds, so one might expect them to have similar wind velocities. However, the magneto-centrifugal wind acceleration models of Holzwarth and Jardine (2007 ) suggest that rapidly rotating stars might have wind speeds much faster than their surface escape speeds. Thus, the appropriateness of the constant wind speed assumption is still a matter for debate. The one star in Table 1 that has an escape velocity significantly different from that of the Sun is $λ$ And. The G8 IV-III primary that surely dominates the wind from this binary is not a main sequence star, and it has a surface escape speed about 3 times lower than that of the Sun. Perhaps in the future the mass loss rate listed in Table 1 should be remeasured assuming a lower wind velocity.

In addition to the mass loss measurements for stars with detected astrospheric absorption, Table 1 also lists an upper limit derived from a nondetection for Proxima Cen. Upper limits cannot be computed for most stars with nondetections, because a likely interpretation for most nondetections is that the star is surrounded by hot, fully ionized ISM material, rather than partially neutral gas like that which surrounds the Sun. The Local Bubble in which the Sun is located is mostly filled with this hot material (see Section 2.2). The Sun just happens to be located within one of the cooler, partially neutral clouds that lie within the Bubble. For Proxima Cen, the hot ISM explanation for the astrospheric nondetection can be discarded, because Proxima Cen’s distant companion $α$ Cen has detected astrospheric absorption, proving that Proxima Cen is not located within the hot ISM. Thus, for Proxima Cen a meaningful upper limit to the stellar mass loss rate can be derived.

No mass loss measurement is reported for HD 128987 in Table 1, since no astrospheric model seems to be able to reproduce the apparent astrospheric absorption, bringing into question the astrospheric interpretation of the absorption for this star (Wood et al., 2005a ). The fundamental problem is the very low LISM wind speed seen by this star ( $VISM = 8km s−1$ ; see Table 1). This low speed is not sufficient to result in much deceleration and heating of neutral H within the astrosphere, thereby yielding little predicted absorption. Thus, the apparent astrospheric detection for HD 128987 remains a mystery at this time.