The inner nebula and central binary of the symbiotic star HM Sge

13 Pages·0.36 MB·English

by  S. P. S. Eyres

The inner nebula and central binary of the symbiotic star HM Sge
S. P. S. Eyres and M. F. Bode
Astrophysics Research Institute, Liverpool John Moores University, Twelve Quays House, Egerton Wharf,
Birkenhead, CH41 1LD, UK
[email protected], [email protected]
1
0
0 A. R. Taylor
2
The Department of Physics and Astronomy, The University of Calgary, 2500 University Dr. N.W.,
n
Calgary, Alberta, T2N 1N4, Canada
a
J [email protected]

6 and
1

2 M. M. Crocker, R. J. Davis
v
University of Manchester, Jodrell Bank Observatory, Macclesfield, Cheshire, SK11 9DL, UK
9
8 [email protected], [email protected]
1
1
0
1
0
ABSTRACT
/
h
We present contemporaneous HST WFPC2 and VLA observations of the symbiotic nova
p
- HM Sge. We identify a number of discreet features at spatial scales smaller than ∼ 0.1 arcsec
o embedded in the extended nebula, with radio and optical emission well correlated in the inner
r
t 1arcsec. Forthefirsttimewemeasurethepositionsofthebinarycomponentsofasymbioticstar
s directly. We estimate the projected angular binary separation to be 40±9 milli–arcsec, with the
a
: binary axis at position angle 130◦±10◦. The latter is consistent with previous estimates made
v
byindirectmethods. The binaryseparationis consistentwith a previousestimate of50auifthe
i
X distance is 1250±280 pc. Temperature and density diagnostics show two distinct regions in the
r surrounding nebula, with a cool wedge to the south–west. An extinction map indicates the true
a
interstellar extinction to be no more than E(B–V) = 0.35. This is consistent with a minimum
distance of ∼700 pc, but this would be reduced if there is a circumstellar contribution to the
minimum in the extinction map. The extinction map also suggests a patchy dust distribution.
We suggestthat a southern concentration of dust and the south–westwedge are associatedwith
the coolcomponentwind. Alternatively, the southerndust concentrationis the causeofthe cool
wedge, as it shields part of the nebula from the hot component radiation field.
Subject headings: binaries: symbiotic – stars: individual (HM Sge) – circumstellar matter – radio con-
tinuum: stars
1. Introduction withanionizedcomponentoftheCCwind. Anin-
frared sub–classification has been made, dividing
Symbioticstarsareanextremecaseofinteract-
the class into D(usty)–types, and S(tellar)–types,
ingbinaries,withseparationsofafewtoafew10s
based on the dominant contribution to the IR.
ofau. Theycompriseacoolcomponent(CC),typ-
Early modeling of the radio emission has shown
icallyaredgiantorMira–typevariable,andahot
that D–types typically have separations of 10 or
component(HC),usuallyawhitedwarfassociated
moretimesthatofS–types. Someoftheseobjects
1
show very slow optical outbursts, similar to those Kwok, Bignell & Purton (1984) found a diffuse
of novae, but lasting decades (see e.g. Kenyon halo ∼0.5 arcsec in diameter, surrounding a cen-
1986 and Miko lajewska 1997 for further discus- tral nebula ∼0.15 arcsec in size. More recently,
sion.) Eyres et al. (1995) demonstrated that the struc-
HM Sge is a D–type symbiotic star which un- ture seen in the radio could be correlated with
derwent such an optical outburst in 1975. Since HST images at the same spatial resolution, sug-
then, there has been evidence of dust obscuration gesting that at least the HC was centrally lo-
events, as in 1985 (Munari & Whitelock 1989) cated in the inner nebula. Richards et al. (1999)
when A ≃ 13.5 (Whitelock 1988; Munari & tracedthedevelopmentoftheradiostructureover
V
Whitelock1989),andin1979–1980whenA ≃12 5years,andrelatedittothebinarymotion. They
V
(Thronson & Harvey 1981). The different values derived a period of 80 years and a binary separa-
of A have led to a suggestion of clumping in the tion of 50 au1. Non–thermal emission associated
V
dust (e.g. Thronson & Harvey 1981), which was with an E–W outflow has also been found (Eyres
alsosuggestedbyRichardsetal.(1999)toexplain etal.1995),andRichardsetal.(1999)showedthat
the nebula structural changes seen in the radio. this is rareinsymbiotic starsdue to the relatively
Various distance estimates to HM Sge are sum- short timescale on which the emission dissipates.
marized by Ivison et al. (1991). Those authors’ Here, we discuss our observations of the neb-
ownestimateof1300pcwasbasedonareddening ulaassociatedwiththisstarusingWFPC2onthe
estimate of E(B–V) = 0.53. Kenyon, Fernandez– Hubble Space Telescope (HST). We also present
Castro & Stencel (1988) used far–infrared IRAS contemporaneous radio images of the inner neb-
colors to derive the extinction and a distance of ulamadewiththeVeryLargeArray(VLA).These
1800 pc. These estimates clearly depend on the observationsallowustodeterminethephysicalpa-
effects of variable circumstellar extinction. Re- rameters in the nebula, and to attempt to relate
cently the Mira–type cool component has been theconditionswiththe binaryinteractionandthe
clearly seen in spectro–polarimetry(Schmid et al. outburst history of the system.
2000), indicating that dust obscuration has sub-
sided somewhat. The spectra of Schmid et al. 2. Observations
(2000)are dominated by the line emission, with a
risingcontinuumbeyond∼8000˚A.Theyalsosug- The HST observations were made on 1999 Oc-
tober 22, as part of a GO program 8330 on sym-
gestedthatthebinaryaxishadapositionangleof
123◦ in 1998. This contradicts tentative conclu- biotic stars, as shown in Table 1. Three orbits
were allocated to HM Sge, and observations were
sions by Richards et al. (1999) placing the Mira–
made in seven filters, including F218W, F437N,
type due north of the hot component (i.e. posi-
tion angle ∼0◦). Many of the observations of the F469N, F487N, F502N, F547M and F656N. The
exposuretimesanddominantlinesforimagespre-
outburst and subsequent development of HM Sge
sented here are given in Table 1. Further details
are described in Nussbaumer & Vogel (1990) and
of these filters are available from Biretta et al.
Mu¨rset & Nussbaumer (1994).
(1996). The calibrated data were retrieved from
Corradi et al. (1999) have conducted ground–
the HST archive. Each exposure was executed in
based imaging of the extended nebula of HM Sge.
two sub–exposures to allow cosmic ray subtrac-
They find a number of filaments and discrete fea-
tion. The F656N image presented here was also
turesembeddedinanebulaextendingto∼13arc-
dithered to allow recovery of the full spatial reso-
sec. This emission is extremely faint, and if the
lution (Biretta et al. 1996). In addition, the stel-
nebulaisduetoactivityinthecentralbinary,sug-
lar positions (section 3.3) were determined from
gests a much longer history to such activity than
dithered images taken through the F218W and
observed since 1975.
F547M filters. The pixel size was 0.0455 arcsec
HM Sge was detected in the radio shortly af-
ter the optical outburst (Feldman 1977). Radio 1The references in Richards et al. (1999) to a binary sep-
surveys showed HM Sge to be one of the bright- aration of 25 au are made in error – the binary orbital
est radio emitters in the class (Seaquist, Taylor& semi–major axis is 25 au, giving the binary separation as
50au.
Button 1984; Seaquist, Krogulec & Taylor 1993).
2
Table 1: Observation log.
Filter Exposure λ¯ ∆λ¯ Peak λ Scientific features
times (s) (˚A) (˚A) (˚A) and wavelengths (˚A)
F218W† 40 2136 355.9 2091 Interstellar absorption
F218W 100 2136 355.9 2091 Interstellar absorption
F437N 800 4369 25.2 4368 [O III] λ4363
F469N 100 4695 24.9 4699 He II λ4686
F487N 200 4865 25.8 4863 Hβ λ4861
F502N 100 5012 26.8 5009 [O III] λλ4959, 5007
F547M† 2 5454 486.6 5362 Stro¨mgren y
F547M 20 5454 486.6 5362 Stro¨mgren y
F656N† 100 6562 22.0 6561 Hα λ6563
†ditheredimages
for the undithered images and 0.02275 arcsec for at larger scales from the ground by Corradi et al.
the dithered ones. (1999). The inner parts ofthe nebula showsthree
TheVLAobservationsweremadeon1999Septem- structures: a ridge to the north (N), a peak at
ber 26 at 8.56 GHz and 23 GHz. Comparison the center (C) anda more irregularfeature to the
with the primary calibrator 1331+305 (3C286) south (S), which may be the brightest part of a
gave the flux of secondary calibrator 1935+205 loop of emission. In the case of the F656N image
as 0.385±0.001 Jy at 8.56 GHz and 0.41±0.01 Jy Fig.2(a), dominatedby Hα, the centralstar posi-
at 23 GHz. The complex gain solutions for this tionhas been fitted andthe pointspreadfunction
calibrator were applied to HM Sge. MERLIN ob- (PSF) subtracted,using aPSF modeledusing the
servationsby Richardset al.(1999)showthat the TinyTIMsoftware(Krist1995). Thisimageshows
structures in the inner nebula move by ∼4 milli– that features C,N andS are distinct in hydrogen,
arcsec per year and the flux density remained and they are also present in the weaker Hβ emis-
roughly constant at 22 GHz between 1994 and sionintheF487NimageFig.1(c). ThefeaturesC,
1996. Thus the VLA and HST images can be NandSarepresentintheF218WimageFig.2(d),
directly compared. but the latter two features are extremely weak.
3.2. VLA images
3. Results
The VLA images are presented in Figs. 3(a) &
3.1. HST WFPC2 images
(b). At 23 GHz there is a northern ridge running
The HST WFPC2 images are shown in Figs. 1 E–W, a central, almost circular peak, and a more
and2. Someextendedemissionis apparentoutto irregularsouthernfeature. Thesefeaturescoincide
2arcsec,butthebrightestpartsarewithin0.5arc- withfeaturesN,CandSinFig.1(a),andweadopt
sec of the central star, which is readily identified thesamelabelsfortheradiostructure. Fromcom-
from the diffraction spikes in Fig. 1(c). Feature 1 parison of Fig. 3(a) and e.g. Fig. 1(a) we suggest
visible in Fig. 1(a) is almost a ring of emission at that at least one of the binary components is co-
the south–west edge of the inner nebula. There incidentwith radiofeature C.We discussthis fur-
are three compact knots to the east of the central therinsection3.3. The8.56GHzimage[Fig.3(b)]
emission (features 2, 3 & 4), and a fourth one to has significantly lower resolution, but is sensitive
the south–west (feature 5), which are most obvi- to more extended emission. Two features are ap-
ousintheF502Nfilter[Fig.1(a)]. Weakfilaments parent: acentralN–Selongatedstructure,encom-
are also present to the north (feature 6 & 7), and passing features N, C and S, and an extension to
maybeassociatedwithnorthernprominencesseen the S–W coincident with feature 1.
3
N N
C C
3 3
(a) (b)
7
2 6 2
1 S1 S
C C
SE 2 SE
C 0 C 0
AR 3 AR
4
-1 -1
1
-2 -2
F502N [O III] 5 F437N [O III]
-3 -3
3 2 1 0 -1 -2 -3 3 2 1 0 -1 -2 -3
ARC SEC ARC SEC
3 3
(c) (d)
6405
2 2
5307.5
1 1
C SEC 0 C SEC 0 4300
R R
A A
3202.5
-1 -1
2105
-2 -2
F487N Hβ R
OIII 170.5
-3 -3
3 2 1 0 -1 -2 -3 3 2 1 0 -1 -2 -3
ARC SEC ARC SEC
Fig. 1.— HST images of HM Sge, dereddenned for E(B–V) = 0.35, in the WFPC2 filters (a) F502N;
greyscale range 9.1×10−15 to 1.3×10−12 (main panel) and 1.3×10−12 to 2.9×10−11 (inset); (b) F437N;
greyscale range 4.7×10−15 to 2.3×10−13 (main panel) and 2.3×10−13 to 10−11 (inset); and (c) F487N;
greyscale range 3.8×10−15 to 9.6×10−13 (main panel) and 9.6×10−13 to 2.5×10−11 (inset). Units are
erg s−1 cm−2 ˚A−1 arcsec−2. In each case the inset is at the same scale as used in the radio images in
Figs. 3(a) and (b). Image (d) is the ratio of images (a) and (b) with greyscale range 2 to 50, and a single
contour at R = 15. Uncertainties in R are of order 10%.
OIII OIII
4
N
C
3 3
(a) (b)
2 2
1 S1
C C
E E
S S
C 0 C 0
R R
A A
-1 -1
-2 F656N Hα -2 F547M
-3 -3
3 2 1 0 -1 -2 -3 3 2 1 0 -1 -2 -3
ARC SEC ARC SEC
3 3
(c) (d)
2 2
1 1
ARC SEC 0 ARC SEC 0
-1 -1
-2 -2
F469N He II F218W
-3 -3
3 2 1 0 -1 -2 -3 3 2 1 0 -1 -2 -3
ARC SEC ARC SEC
Fig. 2.— HST images of HM Sge, dereddenned for E(B–V) = 0.35, in the WFPC2 filters (a) F656N
star subtracted; greyscale range 1.47×10−15 to 2.93×10−14 (main panel) and 2.93×10−14 to 2.14×10−12
[inset, same scale as Figs. 3(a) and (b)]; (b) F547M; greyscale range 1.58×10−16 to 4.74×10−13; (c) F469N;
greyscalerange2.09×10−16 to1.47×10−11; and(d) F218W;greyscalerange2×10−13 to2×10−12. Units are
erg s−1 cm−2 ˚A−1 arcsec−2. Ineachcase the insetis atthe same scaleas used in the radio imagesin Fig.3.
5
16 44 41.0 41.0
N
40.5 40.5
N (J2000) 40.0 C 40.0
O
TI
A
N
LI
EC 39.5 S 39.5
D
39.0 39.0
(a) (b)
38.5 38.5
19 41 57.16 57.14 57.12 57.10 57.08 57.06 57.04 57.02 57.00 19 41 57.16 57.14 57.12 57.10 57.08 57.06 57.04 57.02 57.00
RIGHT ASCENSION (J2000) RIGHT ASCENSION (J2000)
0.4 0.6 0.8 1.0
16 44 40.2 (c) (d)
40.1
40.0
N (J2000) 39.9
O 39.8
ATI
N
CLI 39.7
DE
39.6
39.5
39.4
39.3
19 41 57.11 57.10 57.09 57.08 57.07 57.06 57.05
RIGHT ASCENSION (J2000)
Fig. 3.— Radio images of HM Sge at (a) 23 GHz with the VLA; contours are −3, 3, 6, 12, 18, 24 and 36 ×
262 µJy beam−1, greyscale range is 0.262 to 12.05 mJy beam−1. In each case the beam size is illustrated in
thebottomlefthandcorner;and(b)8.56GHzwiththeVLA;contoursare−3,3,6,12,24,48,96and192×
80 µJy beam−1, greyscale range is 0.08 to 18.96 mJy beam−1. (c) Extinction map (greyscale) derived from
Figs. 1(c) and 3(a), with VLA image at 23 GHz overlaid as contours. Propagated uncertainty in E(B–V)
is ∼0.07. (d) Electron temperature versus density; solid lines are the loci for values of R as indicated.
OIII
Dashed lines are for ν = 8.56 GHz, T = 140 K [lowest contour in Fig. 3(b)] and different values of l (i)
b
0.00063 pc, (ii) 0.005 pc, (iii) 0.025 pc. Dotted lines are for ν = 8.56 GHz, T = 2260 K [fifth contour in
b
Fig. 3(b)] and different values of l (iv) 0.00063 pc, (v) 0.005 pc, (vi) 0.025 pc. The dot–dashed line (vii) is
for ν = 23 GHz, T = 6760 K [the peak of feature C in Fig. 3(a)]. See text for discussion.
b
6
3.3. Stellar positions gest that the peak position in the F218W image
is that of the HC while the peak position in the
A simple estimate of the relative contributions
F547M image is that of the CC. Thus, the line
oftheHCandCCinHMSgeatagivenwavelength
connecting the two stars on the sky, the “binary
can be made assuming blackbodies with THC =
eff axis”, is at a position angle of 130◦±10◦. The
200 000 K (Mu¨rset, Wolff & Jordan 1997), TCC
eff schematic in Fig. 4 illustrates the relationshipbe-
= 3 000 K, and taking approximate radii of 0.01
tween the binary components and the features
and 100 R respectively. This shows that the HC
⊙ apparent in the inner nebula.
dominates the CC by a factor ∼ 80 at 220 nm
To test further these measurements, we also
[F218W, Fig 2(d)] and the CC dominates the HC
looked at other observations of symbiotic stars
byafactor∼ 18000at550nm[F547M,Fig2(b)].
made under our GO programme. In the case
Note that UV spectra show negligible line contri-
of CH Cyg (paper in preparation), the star was
butiontotheF218Wfilter(seee.g.Kenyon1986).
known to be in eclipse during the observation, so
A number of lines contribute to the F547M filter
that only one star could possibly be seen. The
(see e.g. Schmid et al. 2000, their Fig. 2). The
shift in that case was ∼ 10 mas, comparable to
CC is clearly badly modeled by this estimate, as
the estimatefromthe ditheringuncertainties,and
itdoesnotaccountfortheabsorptionbandschar-
hence consistent with the star being in eclipse.
acteristic of Mira–types. In addition, a simple es-
timate of the luminosity of the HC Mu¨rset et al. The peak positions in the other filters are not
(1991) and the contribution at λ ∼2200˚A shows necessarily coincident with the stars as they are
that the central pixel will be entirely dominated dominated by nebular lines. These positions are
by stellar emission, rather than nebular emission. illustratedinFig.4. By definitionthese filters are
These estimates show that if the two stars were sensitive to more extended emission. This means
displaced by more than a few pixels on the sky, thatfitting a gaussianis invalid, asthe nebulosity
the peak of the emission should clearly move be- may be asymmetrical but strongly emitting near
tween the F218W image and the F547M image. the stars. Thus a lack of coincidence between the
That this is not the case means that both stars peaks of the narrow filters and the peaks of the
must be within feature C. F218W and F547M filters is to be expected. The
HαandHβ imageshavepeaksveryclosetothatof
AsthePSFofthestarineachimageextendsto
the F547M image. The He II image, which traces
a large angular distance from the peak, we have
the highestionisationregions,hasapeakbetween
attempted to fit a Gaussian component to the
thetwostarsandslightlysouthofthebinaryaxis,
peak positions in the F218W and F547M images.
consistent with the model of Nussbaumer & Vo-
The best resolution was available in our dithered
gel(1990). Finally,theF437NandF502Nimages,
images, where the pixel size is 0.02275 arcsec.
dominated by [O III] lines which are sensitive to
The position of the peak relative to 19 41 57
temperatures and densities, have peaks which dif-
+16 44 39 in the F218W image [Fig. 2(d)]
fer from those of all the other images and from
is α = 0.08067±0.00004, δ = 0.6195±0.0005
one another. The results for these latter three
while in the F547M image [Fig. 2(b)] it is α =
filters are most readily explained in the context
0.08258±0.000005 δ = 0.5920±0.00002. The er-
of the suggested wind interaction which might be
rorsquotedaretheformaluncertaintiesofthefits.
expectedtohavethestrongesteffectsbetweenthe
Whendithering,themeasuredshifts(fromthepo-
two stars.
sitions of bright stars in each frame) can be up to
0.2 undithered pixels or ∼ 9 milli–arcsec (mas)
3.4. Nebular diagnostics
different from the requested value of 5.5 pixels.
This is probably the best estimate we have of the A number of diagnostics of the physical condi-
true uncertainty of the measured peak shift from tionsinthenebulacanbederivedfromtheimages
F218W to F547M. Thus, the peaks in the two fil- presentedhere. TheratioR oftheF502Nim-
OIII
ters are displaced from each other by 40±9 mas age(including both[O III] λλ4959& 5007)to the
at a position angle of 130◦±10◦ measured north F437N image (including [O III] λ4363) depends
through east. The position angle agrees well with on both electron temperature T and density n
e e
that suggested by Schmid et al. (2000). We sug-
7
N
(i)
HC
θ
(iii)
CC (ii)
(iv) C
S
1
Fig. 4.— Schematic illustrating the relationship between the binary components and the features of the
inner nebula (not to scale.) North is up. The position angle of the binary axis is θ=130◦±10◦. The inner
nebula features (N, C, S and 1) are marked. The hot component (HC) and the cool component (CC) are
markedat the positions of the peak in the F218W and F547Mimage respectively. Other peak positions are
(i) F437N, (ii) F469N (iii) F487N & F656N and (iv) F502N, marked as crosses.
8
according to the equation 5.9. Itisclearthatthemainsourceofuncertainty
in this analysis is the value adopted for l. A rea-
ROIII =≃ 7jλ.7439j5eλ9x4+p3[j63λ3.52090×7104Te−1] (1) swohnearbelebeetswtiemenattehewloaurlgdesbteantdotphleacsemaitlleasttsaonmgue--
1+4.5×10−4(neTe0.5) lar size seen on the sky. When estimated in this
(see Osterbrock 1989). Examination of ground– fashion, it also depends linearly on the distance,
based optical spectra indicate that these two which is not well known. However,we should still
WFPC2 filters are dominated by the three lines be able to draw qualitative conclusions about the
whichcontributetotheratio,andthenebularcon- relativetemperaturesanddensitiesofthedifferent
tinuum is very weak (see e.g. Schmid et al. 2000, regionsdespitethisdistanceuncertainty. Mostim-
theirFig.2). Thus,Figs.1(a)and(b)canbeused portantly,it is apparentfromFig.3(d) thatalong
to derive the ratio map Fig. 1(d) which traces Te contoursofconstantTb,Fig.1(d)primarilytraces
and ne, and in principle depends on both of these variationsinTe. Atthesametime,variationsinTb
quantities. This diagnostic has been applied ef- trace variations in ne. We must be careful not to
fectively to HM Sge by Schmid & Schild (1990), use this analysis to draw conclusions about those
using spatially–unresolved spectra for the entire regions of the nebula where no radio emission is
nebula. detected. An interferometer such as the VLA will
resolve–out smooth extended structure, meaning
TheWFPC2ChargeTransferEfficiency(CTE)
thatthetrueextendedradiobrightnesswillgener-
effect on the WFPC2 chips (Whitmore & Heyer
allybegreaterthanthatpresentintheradiomap.
1998;Whitmore 1998)has a bearing on this anal-
We note that the value of R from Schmid &
ysis. For aperture photometry, this causes stars OIII
Schild (1990) is effectively an average, dominated
atthe topofthe chip(rownumber800)toappear
by the brightest nebular feature. We have plot-
systematically fainter than those at the bottom
ted a locus in Fig 3(d) for the peak emission in
(row number 0). The effect is also stronger for
the 23 GHz image (the peak of feature C) as the
brighter stars. The consequences of this effect for
mostrelevantoneforcomparisonwiththeSchmid
extended emission is not well understood. In our
& Schild (1990) locus. Given the variable nature
case the observed emission falls on the same re-
ofthe innernebula(Richardsetal.1999),the val-
gionofthechipforallobservations,andbrightness
ueswhichmightbe derivedforthatcentralregion
variations are not severe across the nebula. This
are similar to those derived by Schmid & Schild
means that we can draw firm qualitative conclu-
(1990), which were effectively a weighted average
sions from Fig. 1(d).
for the entire nebula.
Radio brightness, expressed as a brightness
temperature T , is given by The F469N image [Fig. 2(c)] is dominated by
b
He II λ4686 emission. This is a discriminator of
T =T (1−e−τν) K, (2) strongly ionized regions (see Osterbrock 1989). It
b e
canbeseenfromtheimagethatfeaturesC,Nand
where the optical depth at frequency ν is SarevisibleinHeII.Thissuggeststhatthesefea-
tures are strongly ionized, and is consistent with
τ ≃8.24×10−2T−1.35ν−2.1n2l (3)
ν e e thesefeaturesbeingwelldefinedintheF437Nand
F502N images [Figs. 1(a) & (b)], as [O III] shows
assumingn isconstant,wherelisthepathlength
e
roughly the same ionization structure. In addi-
through the nebula (again see Osterbrock 1989).
tion, the He II emission does not extend far be-
Thus, the radio brightness temperature also de-
yond a radius of ∼1 arcsec, suggesting that the
pends on both T and n . Relationships (1), (2)
e e
intermediate scale nebulosity is more weakly ion-
and (3) provide loci in a T –n plot, which inter-
e e
izedthanthe smallestscalefeatures. This ismore
sect at the conditions appropriate to the various
difficult to reconcile with the extended structure
features. Comparing Figs. 1(d) and 3(b), we can
seen particularly in Fig. 1(a). However, as noted
determinetheconditionsasafunctionofposition.
abovethe [OIII]lines seeninthese filtersaresen-
LocifortypicalvaluesofR ,T andl areil-
OIII b sitive to temperature and density, so we may well
lustratedinFig.3(d). Alsoshownhereisthelocus
be seeing the effects of density inhomogeneities in
for the Schmid & Schild (1990) value of R =
OIII
9
the nebula. Suchinhomogeneitiesareinturncon- tion. As the brightest radio emission most likely
sistentwiththeveryclumpynatureofmuchofthe comes from the regions of greatest optical depth,
emission at sub–arcsec scales. this effectworksinthe opposite sense to the CTE
effect. Finally, E(B–V) depends on electron tem-
3.5. Extinction mapping perature. IfT =40000K,insteadofthe10000K
e
assumed above,E(B–V) woulddecrease by ∼ 0.2.
Athirddiagnosticcomesfromthefactthatthe
Fig. 3(d) demonstrates that T can vary consid-
dereddenned Hβ flux, F(Hβ), canbe derivedfrom e
erably over the nebula. However, for the larger
the radio flux S via the equation
ν
values of T in the inner regions relationships (2)
b
S =2.51×108T0.53ν−0.1F(Hβ) Jy, (4) and (3) lead to loci at higher electron densities,
ν e
while the curves derived from equation (1) con-
whereF(Hβ)isinergcm−2s−1. Thisassumesthe
verge towards lower T , and extend over a nar-
e
radiofluxisduetoopticallythinthermalemission.
rower range of temperatures. Thus in the inner
Thus, with a measured Hβ flux we can derive the
regionsshown in Fig. 3(c) the variations in T are
e
reddening E(B–V).In the past this has been used
relatively small. As the hotter regions are closest
toderivethe interstellarreddeningusingthe total
to the white dwarf, it seems likely that the inter-
radio and Hβ fluxes. However, in dusty environ-
mediatevaluesofE(B–V)=0.7maybesomewhat
ments such as that seen in HM Sge, there may be
reduced by the expected higher T in that region.
e
acontributiontothereddeningfromcircumstellar
Bearinginmindtheseconsiderations,weareconfi-
matter. Such variations in circumstellar redden-
dentthatwecandrawqualitativeconclusionsfrom
ing have been suggested to explain the different
Fig. 3(c).
estimates of E(B–V) and A towards HM Sge in
V
the past (e.g. Munari & Whitelock 1989). In our
4. Discussion
case, the images of both Hβ emission [Fig. 1(c)]
and radio emission [e.g. Fig. 3(a)] allow us to de- 4.1. Dust distribution and interstellar ex-
rive an extinction map, as is shown in Fig. 3(c) tinction
forT =10000K.WenotethatIvison,Hughes&
e
TheextinctionmapinFig.3(c)canbetakento
Bode(1992)presentaspatially–unresolvedradio–
trace the circumstellar variation in the dust dis-
infraredspectrumforHMSge,indicatingthatthe
tribution, assuming the interstellar extinction is
turn–over from optically thick to thin radio emis-
reasonably uniform over the relatively small an-
sion occurs at 8.5 GHz. However, it is clear from
gular size of the inner nebula. In this case, the
their Fig. 1 that the turn–over is gradual, con-
best estimate of the true interstellar extinction
sistentwithpartiallyopticallythinemissionupto
∼30GHz. Inaddition,theinnernebulaofHMSge comes from the minimum values in the extinction
map. Three distinct regions are apparent: (i) to
is variable in both brightness and structure (e.g.
the south E(B–V) ≃ 1, coincident with feature S;
Richardsetal.1999),makingthespectrumofIvi-
(ii) to the northaroundfeature N, E(B–V)≃ 0.6,
son, Hughes & Bode (1992) out of date. This
consistentwith previousreddeningestimates; and
means that it remains difficult to assess the op-
(iii) a low–ratio band running from east to west
tical depth conditions within the inner nebula as
across the position of feature C. Note that the
a function of position.
peak itself does not give a reliable E(B–V) esti-
TheconsequencesoftheCTEeffectforFig.3(c)
mate,as the emissioninthe opticalis notentirely
are to provide an overestimate of the extinction,
nebular. This band is also weakly contaminated
withthelargestoverestimatesbeingatthebright-
by the diffraction spikes, which have a position
est parts of Fig. 1(c). This extinction map is
angle of ∼ 80◦. The eastern part of this low–
also affected by our assumptions about the ra-
ratio band has E(B–V) = 0.35, the lowest value
dio emission. Equation4 relies onthe assumption
on the map, and presumably the best estimate of
that the radio emission is optically thin thermal.
the true interstellar extinction. As high E(B–V)
While the brightness temperatures are consistent
correlates with a greater quantity of dust, we can
with thermal emission, the optical depth is not
see that the dust is concentrated at feature S. In
well constrained. However, where emission is op-
addition, there is a deficit of dust closer to fea-
tically thick, we would underestimate the extinc-
10