Chun-Shing Jason Pun
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street,
Cambridge, MA 02138
as
.
The best-fit observed diameter, 
, at day 2932 (1995 March 3)
for the F675W (broadband R) image is found to be 
mas, and
the power index, 
, to be 
.
The debris size varies with wavelength and is larger in the UV
than in the optical with 
.
The expansion of the debris is consistent with a linear
expansion with time.
The angular rate of expansion at the optical wavelengths
at the distance of the LMC (50 kpc), 2300--3000
,
corresponds reasonably well with the observed widths of the emission lines
(
2500 km s
).
With the post-COSTAR images, we are also able to study the symmetry of the
supernova debris. We found the debris to be elliptical at all
broadband optical wavelengths from U through I.
The major-to-minor axis ratio is found to be 
on day 2932
in the R band, with the major axis corresponding to a position angle of
20.7^o 
3.7^o.
The results are consistent with the picture in which the
long axis of the supernova debris is perpendicular to the plane of the
circumstellar ring which, for any viewing angle, appears along the minor
axis of the ring in the sky.
Keywords: Supernovae,debris
The Supernova INtensive Study (SINS) is a long term project
studying supernovae with the Hubble Space Telescope.
Supernova 1987A, the brightest supernova in the last 400 years, has been
studied extensively---imaging and spectroscopic data of the
supernova debris and the circumstellar rings totaling 50 hours of HST
exposure time have been obtained (Panagia et al. 1991,1996,
Plait et al. 1995, Chugai, Chevalier, & Kirshner 1996,
Pun et al. 1996, Scuderi et al. 1996, Wang et al. 1996).
The SINS collaboration has obtained imaging data on SN 1987A before COSTAR
(four epochs each with FOC and WF/PC from 1992 April to 1993 October)
and after (two epochs with WFPC2 at 1994 September and 1995 March).
Additional FOC and WFPC2 data for SN 1987A from the archive
are included in this study (Jakobsen et al. 1991,1993,1994,
Burrows et al. 1995).
With the debris of the shredded star resolved in the images, we are able to
measure the expansion and shape of the supernova debris (figure 1).
The supernova, now fully 5 million times fainter than at outburst
(V = 19.7 at day 2932), is located in a densely populated region of the
LMC and has close neighbors.
Extensive efforts were necessary for the correct subtraction of flux from
nearby stars in the images (Star 3, 
16, at 1.6 and Star 2,
V = 15.0, at 2.9), especially for the pre-COSTAR data with extended
point spread functions.
Figure: WFPC2 image of SN 1987A and its neighborhood, taken with
the F814W (I) filter on 1994 September 24 (day 2770) with exposure time of
600 sec.
The expansion of the SN 1987A debris can be determined by measuring its size
at different epochs.
The angular diameter has been measured by speckle interferometry technique
from day 38 to day 665 (Karovska et al. 1991, Nulsen et al. 1990).
Assuming a uniform disk brightness profile, the H
debris diameter
was found to be 
mas on day 665.
With the resolution of HST (FOC 
22 mas/pixel; PC in WF/PC and
PC1 in WFPC2 
45 mas/pixel), the SN 1987A debris was resolved
in the first HST observation obtained on day 1278 with FOC
(
mas with the F275W filter).
The expanding supernova debris continues to be resolved in the subsequent
epochs of HST observations.
We can therefore measure its angular size by fitting the observed HST image
by convolving the point spread function with a surface brightness function,
, in form of
(Jakobsen et al. 1993,1994) where 
is the angular radius.
The FWHM of the profile 
is 2
, which we defined
as the observed diameter of the supernova debris.
The 
goodness of the fit was calculated under the assumption that
the noise of the data is dominated by the photon statistics.
We minimize 
to obtain values of the best fit parameters
, and 
.
For the pre-COSTAR data, the best-fit profiles have 
,
where 
is the number of degrees of freedom. However, for the post-COSTAR
WFPC2 data where we obtained high S/N, the best-fit profiles have
--8, suggesting that the debris has
a more complicated structure than the profile that was assumed in 
.
However, to determine the errors on the size of the debris
and the power index, 
, a good fit with 
is
assumed with a reduced 
.
The average value of the fitted power index, 
, is 4.2 for all images
from different epochs and different filters while the range of 
is
between 3 and 6.
The apparent debris size varies with wavelength and is found to be
50% larger in the UV.
An example of the result of the 
fitting is shown in figure 2.
Figure: The 3
confidence contours for the power index parameter,
, and the debris radius, 
, for R band data (F702W for
WF/PC and F675W for WFPC2). The best-fit values are marked by crosses.
Fransson & Chevalier (1989) show how the density distribution
of the supernova atmosphere can be obtained from the shape of the emission
line profiles.
Using the FOS spectra of SN 1987A (Wang et al. 1996) obtained
by the SINS collaboration on day 1825 and day 2190, we have calculated
the density profile of the debris using the shape of the H
emission.
The calculated profile can be fitted with a 
profile with
power index 
, which is consistent with the results
obtained from 
fitting of the observed debris shape with the surface
brightness function 
(see table 2).
The increased signal from the post-COSTAR observations allowed better
precisions in measuring the fitting parameters 
and 
.
The debris is expanding and its expansion is consistent with a
linear expansion with time.
By assuming a distance to the LMC (50 kpc),
we can determine the expansion velocity, v
, of the debris
from the slope of the angular radius (
) vs time graph
(figure 3).
The best-fit linear expansion velocity of various wavelengths bands
are listed in table 1.
The constant expansion velocity over seven years implied by the small intercepts
in table 1 suggests that the emission comes from a fixed
range in velocity in the expanding debris.
It seems likely that this is the velocity range of the radioactive power
sources of the emission and it provides a clue to the initial velocity
range of the iron-peak radionuclides in the explosion.
At the distance of the LMC, the rate of expansion in all the broad-band
and narrow emission optical wavelengths is 
2500 km s
, which
corresponds well with the widths of the emission lines.
The observed expansion velocity increases with decreasing wavelength from
the optical to UV, where v
3500 km s
.
This result is also consistent with the FOS spectral data where the
widths for the UV emission lines are larger than for optical lines
(Wang et al. 1996).
Li & McCray (1996) have shown that the UV radiation is scattered by
thousands of metal lines in the UV and converted by fluorescence into
optical and IR emissions.
The opacity explains the large apparent size and large
expansion velocity observed in ultraviolet.
Figure: The size of the supernova debris with time in R band
(F702W for WF/PC and F675W for WFPC2). The best-fit linear expansion
is also shown
Table 1: Expansion velocity, v
, of the SN 1987A debris.
The distance to the LMC is assumed to be 50 kpc.
Early polarimetric observations of SN 1987A (before day 300) have revealed
a polarization of 
0.5% in the optical continuum,
suggesting a shape asymmetry of 10--20% (Jeffery 1991).
The polarization position angle was determined to be 
,
suggesting a major axis direction of either 
or
.
Speckle images taken from day 95 to day 411 also suggest
that the SN 1987A debris was aspherical (Papaliolios et al. 1989).
The major-to-minor axis ratio was found to be 
for H
emission at day 410 and the position angle of the major axis determined
as 
.
Therefore, the speckle interferometry results are consistent with earlier
polarimetry measurements.
With the post-COSTAR optics, we can measure the asymmetry of
the SN 1987A debris directly.
This measurement was impossible for the pre-COSTAR data because
of the overlapping of Star 3 with the debris and the poor resolution of
the debris at the earlier epochs in the images.
Even with WFPC2 images, the debris at 
200 mas diameter
is only about 4 to 5 pixels in width.
This makes it difficult to determine the ellipticity of the debris by fitting
it to a elliptical brightness profile.
Instead, we studied the non-sphericity of the debris by evaluating its
width along different axes.
As shown in figure 4, by integrating the observed flux along each
vertical axis (y), we have a distribution of integrated flux 
versus the horizontal axis (x).
Figure: The contour map of the SN 1987A image taken by WFPC2 F555W (V)
filter on March 1995 (left panel).
The debris flux is integrated along the broken lines (PA = 0^o)
to give 
, which is displayed in the middle panel.
The equivalent width 
is also shown.
The equivalent width function 
for the debris and
the PSF are shown in the right panel, along with the best fit function
as described in Section 3.
The equivalent width, 
, is defined as
where 
is the maximum value of the distribution 
.
By rotating the image through 360^o, 
can then
be expressed as a function of position angle 
.
If the observed image is circularly symmetric, then
is constant.
If it is elliptical, then 
.
For each image, the equivalent width functions are computed for the
supernova debris, 
, and for the point spread function,
. We then attempt to fit 
with
a circular symmetric component (a constant), an elliptical component
(a sine function), and a contribution that takes into account the
diffraction spikes of the point spread function for each observation.
The final expression has the form
where 
is the angular average of the 
function.
Best fit parameters are obtained for 
, a, b, and 
.
The measured ellipticity of the debris, 
, is defined to be
Monte Carlo simulations are then performed with different input profiles
for each debris image, using the
size parameters 
, 
, and 
as determined in Section 2,
together with the intrinsic ellipticity of the debris, 
,
and the position angle of the elongation axis, 
.
The simulations are important in two aspects.
First, one can establish relations between the measured values of
(
, 
) of each frame and the intrinsic ellipticity
parameters (
, 
) of the debris.
Second, while whole process is too complex for a simple error estimate,
one can assess the uncertainties of the measured quantities with
the Monte Carlo results.
The SN 1987A debris is aspherical at all optical wavelengths with
ellipticity 
0.2--0.3, except for the F439W (B) data
which shows a higher asymmetry at both epochs, and for the F547M data
taken by Burrows et al. (1995).
There is only one measurement for emission line data with F502N,
where 
.
The ellipticity is not measured for the F656N (H
) and
F658N (N II) images where a significant amount of flux from the northern outer
loops overlaps with the supernova debris (Panagia et al. 1996).
However, flux from the outer loops is negligible for the determination of
and 
for the broadband data.
No meaningful measurements can be made in the UV because of the low signals
levels in the F255W images.
The size and ellipticity of the SN 1987A debris determined from the WFPC2
images are summarized in table 2.
Table 2: Size and Ellipticity of the SN 1987A debris with WFPC2.
The elongation axis of the debris lies within the range of
PA = 10--20^o for all the images at different epochs and
wavebands. Our present result of the position angle of the major axis of
ellipticity is consistent with the early polarimetric and speckle
measurements.
With the SINS data, Plait et al. (1995) studied the circumstellar
ring around SN 1987A and determined the minor axis of the ring in the sky
is located at PA = 179^o 
3^o.
The result is consistent with the model which the supernova debris is
elongated along the axis perpendicular to the plane of the circumstellar ring.
This model is consistent with the linear polarization calculations of
Steinmetz & Höflich (1992) where a spherically symmetric shock wave
propagates through a rotating progenitor.
Another conceivable scenario is that the asymmetry axis of the supernova
debris lies in the plane of the circumstellar ring and this axis is
accidentally aligned with the projection we see as the minor axis of
the ring in the sky.
However, this picture would only be true for one particular projection angle,
while the picture with the debris elongated out of the plane of the ring
would always appear to have the long axis of the debris along the
apparent minor axis of a circular ring.
Therefore, we regard this geometry as much more likely.
Continuing observations with the Hubble Space Telescope in the future with
certainly provide more information on the asymmetry of the supernova debris.
I am grateful to my collaborators of the SINS group for making the observation program a success. I would also like to thank R. P. Kirshner, P. Challis, P. Garnavich, D. Jeffery, and P. Höflich for many insightful discussions. This work was supported in part by NASA through grant number GO-2563.01-87A from the Space Telescope Science Institute, which is operated by the AURA, Inc., under NASA contract NAS5-26555.
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