BIBECHANA 18 (2) (2021) 130-137

130

A study of dust structure nearby white dwarf WD1334-678
Ishwor Nath Joshi, Ajay Kumar Jha*, Binil Aryal
Central Department of Physics, Tribhuvan University, Kirtipur
*Email: ajay.jha@cdp.tu.edu.np

Article Information:
Received: December 31, 2020
Accepted: May 26, 2021

Keywords:
White dwarf
Interstellar medium
AKARI
Flux density
Dust color temperature

ABSTRACT
A low flux density region nearby white dwarf WD1334-678 in the 140 µm
AKARI survey maps has been systematically searched and found a far-infrared
cavity centerd at R.A. (J2000) = 13h38m14.4s, Dec.(J2000) = −68◦40’42”, in
which minimum flux is 19.5 MJy/sr at 90 µm wavelength. The physical
properties (Size, dust color temperature, dust mass) and thermodynamic property
(Planck function distribution) of the cavity using 140 µm and 90 µm AKARI
survey data has been presented. The size of the cavity is found to be 0.17◦× 0.12◦ .
The dust color temperature is found in the range 17.70 ± 0.01 K to 18.81 ± 0.01 K.
The Plank function distribution along major and minor diameters shows a very
good agreement with sinusoidal fitting. The period of oscillation of dust particles
along major and minor diameters are 3.2 Wm-2Sr-1Hz-1arcmin-1and 1.6 Wm-2Sr-
1Hz-1arcmin-1, respectively.

DOI: https://doi.org/10.3126/bibechana.v18i2.37439
This work is licensed under the Creative Commons CC BY-NC License. https://creativecommons.org/licenses/by-nc/4.0/

1. Introduction

The low and intermediate-mass (M < 10 Mo) stars
formed by nuclear burning, appears as a red giant
in the region of Hertzsprung-Russell diagram, is
called Asymptotic Giant Branch (AGB) stars [1].
When an Asymptotic Giant Branch star exhausts
the supply of hydrogen in its core, the core shrink
and its temperature increases, causing the outer
layers of the star to expand and cool. The star's
luminosity increases, and it becomes a red giant,
following a track leading into the upper right hand
corner of the HR diagram (Blandford& Rees, 1974).
The AGB phase is divided into two parts, the early
AGB (E-AGB) and the thermally pulsing AGB

(TP-AGB). During the E-AGB phase the principal
source of energy is helium fusion in a shell around
a core consisting mostly of carbon and oxygen.
During this phase the star swells up to giant
proportions to become a red giant again. The star
may become as large as one astronomical unit.
After the helium shell runs out of fuel, the TP-AGB
starts. Now the star derives its energy from fusion
of hydrogen in a thin shell, inside of which lies in
the now inactive helium shell. However, on periods
of 10,000 to 100,000 years the helium shell
switches on again, and the hydrogen shells switches
of a process known as a helium shell ash [2].

Towards the end of their lifetime, almost all (95-
98%) stars lose a substantial fraction of their mass

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131

on the Asymptotic Giant Branch (AGB) in form of
massive winds, which compels them into the
Planetary Nebula (PN) phase. The central star of
PN is the white dwarf. The massive stellar wind
emitted from the AGB star interacts with the
ambient interstellar medium. Thus the structure
(gas or the dust) around the white dwarf preserve
the history as a fossil record of the early and late
AGB phase of the star. It is important to understand
the shaping process of interstellar clouds as well as
the nature of the emission from AGB to PN phase.
The white dwarf is suspected to reside within giant
dust structures which may represent fossil records
of its progenitor's transition from spherically
symmetric to bipolar or unipolar mass loss. It can
be suspected that the white dwarf is not the only
one where fossil records of ancient mass loss in its
neighborhood as well as signs of the resulting
shaping can be traced. Besides being ideal
laboratories for the study of various astrophysical
processes prevailing in highly excited dilute
nebulae, PNe and their ancestors are key objects for
the understanding of the evolution of stars. In this
connection, the transformation from spherically
symmetric AGB winds to non-spherical PNe
represents one of the most enduring problems of
stellar astrophysics [3]. The study regarding
evolved planetary system around white dwarfs has
produced a separate insight into the end state of
planetary system and provided that the
measurements of proportion of the extra-solar
planets [4].

Kiss et al [5] and koenyves et al [6] investigated
462 far-infrared loops and studied their size,
temperature luminosity. Wienberger and
Armsdorfer discovered very large (90) jet like
structures in the FIR (Far Infrared) suggest in the
interaction of the wind of the Asymptotic Giant
Branch (AGB) stars with ambient ISM matter [7].
Aryal et al [8] found two giant (2.1 pc, 0.9pc)
bipolar dust emission structures centered on
NGC1514. This is one of the very few known cases
where the history of all main mass-loss phases of
the intermediate initial mass star is preserved. Jha

& Aryal [9] performed the study of dust color
distribution of two new cavity-like structures (sizes
∼ 2.7pc × 0.8pc and ∼ 1.8pc × 1pc) using IRAS
and AKARI maps near Pulsars. They found the
difference in the average temperature in IRAS and
AKARI maps to be 3.2 ± 0.9K and 4.1 ± 1.2K. A
larger value of dust color temperature was found in
a longer wavelength AKARI map than in the IRAS
map which is not normally possible. So, we are
interested to study the physical properties of far
infrared cavity nearby the white dwarf WD1334-
678 in 90 and 140 μm AKARI which will give the
clear hint of shaping mechanism of ISM.

2. Methods

We found a far-infrared cavity at 90 and 140 μm
AKARI nearby white dwarf WD1334-678. We
downloaded the FITS (Flexible Transport Image
System) image of a cavity structure at 90 and 140
μm. We had processed it by using the software
Aladin v2.5. Contours were drawn to separate the
minimum flux region within the structure. The
corresponding flux at 90 and 140 μm at each pixel
were measured in the region of interest. Possible
sources for the background flux were studied using
the SIMBAD database (https://simbad.u-
strasbg.fr/simbad/). We adopt the following
methods for calculations of flux densities, dust
color temperature, Planck’s function a dust mass
and size of cavity in the selected region nearby the
white dwarf.
Dust color temperature

We adopt the method developed by Schnee et al
[10] to determine the dust color temperature of dust.
The flux density of emission at a wavelength ⋋ i is
given by

�� =
2ℎ�

⋋�
3 �

ℎ�
⋋����−1

���⋋�
−�Ω� (1)

where h is Planck's constant, k is Boltzmann's
constant, c is the speed of light, Nd is the column
density of dust grains, � is a constant which relates
the Flux with the optical depth of the dust, � is the

https://simbad.u-strasbg.fr/simbad/
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Ishwor Nath Joshi et al./ BIBECHANA 18 (2) (2021) 130-137

132

spectral emissivity index and Ω� is the solid angle
subtended at ⋋ i by the detector.

We assumes Td<< 1 and Ω140 = Ω90 and also
⋋ 140=

ℎ�
��140

and ⋋ 90 =
ℎ�

��90
, the ratio R of the Flux

densities at 90 and 140 µm is given as

� = �(90��)
�(140��)

= ( 90
140

)-(3+β) [�
�140
�� − 1

�
�90
�� − 1

] Ω90
Ω140

(2)

But �140 = 103 and �90 = 160 from equation (2)
becomes

� =0.64-(3+β)�
103
�� − 1

�
160
�� − 1

(3)

Following Dupac et al. [11], we use the equation,

� = 1
(�+ ���)

(4)

to describe the observed inverse relationship
between �� and �. Here, � and � are free
parameters found that the temperature dependence
of the emissivity index fits very well with the
hyperbolic approximating function. The value of �
depends on dust grain properties as composition,
size, and compactness. For reference, � = 0, 1 and
2 for pure blackbody, the amorphous layer-lattice
matter and the metals and crystalline dielectrics
respectively [12]. We used � = 2 for dust as
suggested by Jha & Aryal (2017) [13]. For a
smaller value of �� , 1 can be dropped from both
numerator and denominator of equation and it takes
the form

� = 0.64−(3+β) . �
103
��

�
160
��

(5)

Taking the natural logarithm on both sides of
equation (5) we get,

ln(R) = ln 0.64 -(3+β)[103
��

− 160
��
] = ln 0.64 -(3+β)[−57

��
]

(6)
We find the expression for the temperature as,

�� =
−57

ln [�×0.64 3+� ]

where � = �(90��)
�(140��)

(7)

F(90 µm) & F(140 µm) are the flux densities at 90
µm and 140 µm, respectively. In this way, we can
use equation (7) for the determination of the dust
grain temperature [14].

Planck’s function

The power emitted by a body as radiation of
different frequencies per unit surface area of the
body, per unit solid angle per unit frequency is
termed as spectral radiance of that body. According
to Planck, the spectral radiance of a body at
frequency � and temperature (T) is given by [15],

� �, � = 2ℎ�3

�2
[ 1

�
ℎ�
���−1

] (8)

This equation is called the expression for Planck's
function
where,
�� = Boltzmann's constant
� = Speed of light
� = Frequency at which the emission is observed
ℎ = Planck's constant
and
� = Dust color temperature of each pixel
By using the formula given by equation (8), we can
calculate the Planck's function of each pixels of the
cavity. We finally plot graphs of Planck's function
versus distance along the major and minor axes to
study the distribution of Planck's function along the
extension and compression of the cavity. The value
of Planck’s function depends on the wavelength
(frequency) and temperature [16]. The mass of the
dust within the region of interest can be calculated
by the method of Hildebrand (1983) [17].

3. Results and Discussion
Structure: Contour map

For the systematic search on AKARI maps, the
white dwarf WD1334-678 is located at R.A. (J2000)
= 13h38m14.4s, Dec. (J2000) = −68◦40’42”. The size
of the cavity found nearby the White Dwarf is
0.17◦× 0.12◦. Using the ALADIN v2.5 suitable
contours are made at level 1 and 50 that enclose the
minimum flux density of the isolated cavity. The



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133

contour map of cavity the contour level 1 to 50 at
140µm as shown in figure 1 (a).

Fig. 1: (a) Showing contour levels in FITS image
of far-infrared cavity nearby WD1334-678 at 140
µm. Two contours at 140 µm image for the best
selection of contour with major axis CD and minor
axis AB and (b) JPEG image of WD1334-678 at
140 µm [18].

Distribution of flux density and contour map at
140 µm

The values of AKARI flux densities at 90 µm and
140 µm have measured using ALADIN2.5 software.
Figure2 (a) shows graph between flux at 90 µm and

140 µm. A best fit straight line is drawn on the data.
The slope of the line is 0.035. Using equation (7)
and values of the slope of best fit line, we
calculated the dust color temperature. Inside the
cavity, the dust color temperature found to be
varied from 17.70 ± 0.01 K to 18.81 ± 0.01 K. For
the minimum and maximum fluxes, no good
correlation is seen whereas for the intermediate flux
values, there is good correlation.

Fig 2 (b) shows the AKARI 140 µm far infrared
image of the core region of the cavity located
nearby white dwarf WD1334-678 having size
0.17◦×0.12◦ at R.A. (J2000) = 13h38m 14.4s, Dec.
(J2000) = −68◦40’42”. We got different contours
levels by plotting the flux densities at 140 µm. The
contour levels are at fluxes 46.14, 49.02, 51.90, and
53.82MJy/sr respectively. From Fig. 2 (b), we can
see that the gap between two counter levels at
northern-east region is very small, while the gaps
between counter levels become broaden at
southern-west region. There may be external
sources in northern-east region so that that the
counter levels at northern region are compressed.
This indicates that mass loading takes place in the
middle part of the cavity.

Contour maps of dust color temperature and
dust mass distribution

Fig.3a and 3b represent the dust color temperature
and dust mass contour maps. From Fig. 3a, in
southern-east, low temperature can be seen, while
higher mass can be seen in this region (Fig. 3b).
Similarly, along north-east temperature is high,
while the mass is low. It is seen that the lower the
temperature higher the mass in the contour maps
which is expected trend. In the core region, higher
mass distribution can be seen (Fig. 3b) but in that
region, temperature is not low. This shows that
there might be an external cause. Dust mass
contour map and dust color temperature contour
map gives the information of the distribution of the
dust mass and dust color temperature within the
region of interest respectively.



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134

Gaussian nature of dust color temperature and
dust mass

Fig.4a and 4b represent the Gaussian temperature
and the Gaussian mass distributions respectively.
The value of standard deviation is found to be (σ) =
0.21 and mean value is (��) = 18.15 K. Since the
standard deviation is small, we can expect that the
data values tend to be close to the mean value of
the temperature i.e. small variation of data values
from mean can be expected. From fig.4a, it is clear
that the data are skewed right. This implies that the
temperature distribution is not quite symmetric.
The Gaussian distribution curve is left skewed in
Fig. 4b. This suggests that the mass distribution has
lack of perfect symmetry.
The average value of the dust color temperature in
the core region of the cavity is found to be 18.15 K,
equal to the Gaussian center (Fig.4a) with an offset
of 1.10 K (< 2 K), suggests that the cavity is
dynamically stable [19]. Generally, the Gaussian
distribution is found to be in the good agreement
with both Td and Md distributions (Figs. 4a, b).
However, Gaussian width and skewness are found
to be different in these plots, suggesting an external
effect, probably from any wind blowing objects.

Distribution of Planck’s function along the ex-
tension and compression of the cavity

Fig. 5a and 5b represent the variation of Planck’s
function along major and minor diameter of the
cavity respectively. The solid curve stand for the
sinusoidal plot, Fig. (5 a,b) clearly shows that the
Planck’s function first decreases along with
distance for the major diameter. It goes down to a
certain minimum value 1.42× 10−16 and then
increases with the distance. The fluctuation of
Planck’s function with distance frequently implies
the instability inside the cavity which is responsible
for the violation of the thermodynamic equilibrium.
This might tell us the presence of effect of wind
blower inside the cavity.

But in case of minor diameter, the Planck’s
function increases slightly and then decreases with

the distance. Here the materials are in the local
thermodynamic equilibrium along the compression
(minor diameter) of the cavity. So, this variation
seems to make our cavity is isolated and stable.

Fig. 2: (a) Flux density at 90 µm versus 140 µm
plot. The solid line represents the best fitted line.
The best fitted line and the regression coefficient
are given. The R2value and the distribution of data
suggests that there is no correlation between 90 and
140 µm fluxes in the far-infrared cavity. This
suggests that this cavity might not be formed
naturally and (b) AKARI 140 µm far infrared
images of the core region of White Dwarf cavity
WD1334-678 centered at R.A. (J2000) =
13h38m14.4s, Dec. (J2000) = −68◦40’42”. The color
bars are given for flux density in MJy/Sr..

The Planck’s function of dusts found to obey
sinusoidal variation along extension given by



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135

B (ν,T) = 1.656×10-16 + 1.697×10-17 ·sin[ � (�−3.289)
3.227

]

(10)
Similarly, for minor diameter Planck’s function
distribution is shown in Fig. 5b.
Along the compression (minor diameter), best fit
sinusoidal curve obey the equation (11)
B (ν,T) = (1.592×10-16) + (1.374×10-17)·sin[� (�−0.861)

1.691
]

(11)
From figures 5a and 5b, it can be concluded that
dust particles are oscillating sinusodially along
extension and compression with periods 3.2 Wm-

2Sr-1Hz-1arcmin-1 and 1.6 Wm-2Sr-1Hz-1arcmin-1,
respectively.

Fig. 3: The contour map of dust Color temperature
(a) and dust mass (b). The contour levels are shown.

Fig. 4: The distribution of dust color temperature (a)
and dust mass (b). The solid curve represents
Gaussian fits. The Gaussian parameters are given.
The error bar represents ±1σ of the deviation.



Ishwor Nath Joshi et al./ BIBECHANA 18 (2) (2021) 130-137

136

Fig. 5: Variation of Planck’s function with distance
along the major (a) and minor (b) diameter of the
cavity. The solid lines represent sinusoidal fit. The
error bar is the standard error of the deviation.

4. Conclusion

We systematically searched a far infrared cavity
nearby White Dwarf WD1334-678 in AKARI
maps centered at R.A. (J2000) = 13h38m14.4s, Dec.
(J2000) =−68◦40’42”. We studied physical (size,
dust color temperature, dust mass) and dynamic
(Planck function distribution) properties of the
cavity. We conclude our results as follows:
(a) The size of the far infrared cavity is found to be
0.17◦× 0.12◦. The minimum flux density at 140µm
is found to be 46 MJy/sr. The dust color
temperature is found to lie in the range17.70 ± 0.01
K to 18.81 ± 0.01 K.
(b) The average mass of the dust in the cavity is
found to be 1.1×1025 kg. It indicates that the region

is mass deficiency region, suggest the external
cause (White Dwarf). The White Dwarf (WD1334-
678) might have blown and swept away the
material from the region of cavity.
(c) The Planck function distribution along the
major and minor diameter of the cavity showed
non-uniform distribution, suggesting that the dust
in the cavity are not in the thermodynamically
equilibrium.
(d) Planck function distribution show sinusoidal
nature. This indicates that the dust in the cavity
might be oscillating in order to gain stability. The
period of oscillation along extension (major
diameter) and compression (minor diameter) are
found to be 3.2 Wm-2Sr-1Hz-1arcmin-1 and 1.6 Wm-

2Sr-1Hz-1arcmin-1, respectively.

Acknowledgement

We acknowledge Sky View Virtual Observatory,
AKARI Survey, SIMBAD database, ORIGIN5.0,
ORIGIN8.0 and GIRL catalog. One of the author
(INJ) acknowledges Central Department of Physics,
Tribhuvan University, Kirtipur, Nepal for all kind
of support for his research work.

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