# A New Perspective on the Diffuse Gamma-Ray Emission Excess

En-Sheng Chena,b<EMAIL_ADDRESS>Kun Fanga<EMAIL_ADDRESS>Xiao-Jun Bia,b
<EMAIL_ADDRESS>aKey Laboratory of Particle Astrophysics, Institute of High
Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
bUniversity of Chinese Academy of Sciences, Beijing 100049, China

###### Abstract

The Large High-Altitude Air Shower Observatory (LHAASO) recently published
measurements of diffuse Galactic gamma-ray emission (DGE) in the 10-1000 TeV
energy range. The measured DGE flux is significantly higher than the
expectation from hadronic interactions between cosmic rays (CRs) and the
interstellar medium. This excess has been proposed to originate from unknown
extended sources produced by electron radiation, such as pulsar wind nebulae
or pulsar halos (PWNe/halos). In this study, we propose a new perspective to
explain the DGE excess observed by LHAASO. The masking regions used in the
LHAASO DGE measurement may not fully encompass the extended signals of
PWNe/halos. By employing a two-zone diffusion model for electrons around
pulsars, we find that the DGE excess in most regions of the Galactic plane can
be well explained by the signal leakage model under certain parameters. Our
results indicate that the signal leakage from known sources and contributions
from unresolved sources should be considered complementary in explaining the
DGE excess.

##  I Introduction

The diffuse Galactic gamma-ray emission (DGE) is crucial for studying the
origin and propagation of cosmic rays (CRs). Traditionally, the DGE from the
Galactic plane is believed to be dominantly generated by the interactions
between the propagating CRs and interstellar medium (ISM) Strong  _et al._
(2007); Ackermann  _et al._ (2012). However, at the TeV-PeV energy region, the
DGE predicted by the CR-ISM interaction model is significantly lower than
those observed by Milagro, ARGO-YBJ, and the Tibet AS+MD array Atkins  _et
al._ (2005); Bartoli  _et al._ (2015); Amenomori  _et al._ (2021), which is
known as the TeV DGE excess Prodanovic  _et al._ (2007); Linden and Buckman
(2018).

Recently, the Large High-Altitude Air Shower Observatory (LHAASO) published
the gamma-ray source catalog of the TeV-PeV energy band Cao  _et al._ (2024a)
and the measurement of DGE in the 10-1000 TeV energy range by masking the
source region Cao  _et al._ (2023). The measured DGE flux in the inner Galaxy
region is about 3 times higher than the expectation from the CR-ISM
interactions and about 2 times higher than that expected in the outer Galaxy
region Zhang  _et al._ (2023). On the other hand, neutrinos are produced
alongside gamma rays during the CR-ISM interactions. The IceCube neutrino
telescope has measured the high-energy neutrino flux from the Galactic plane
in the energy range of 1-100 TeV Abbasi  _et al._ (2023). Subtracting possible
contribution of point sources from the total neutrino measurement and applying
the masking method of LHAASO, Ref. Yan  _et al._ (2024) argued that the gamma-
ray flux associated with the neutrino flux is consistent with that predicted
by the CR-ISM interactions. This result also supports that the TeV DGE excess
is mainly contributed by leptonic processes111Due to the model-dependent
nature of the neutrino flux measurement and the associated uncertainties, we
cannot rule out the possibility that the DGE excess includes a minor hadronic
component..

In the LHAASO DGE measurement, each source region is masked with a 2.5 times
Gaussian width of the source. For point sources and Gaussian-like sources,
this method can effectively remove the source contamination to the DGE.
However, the morphology of pulsar wind nebulae (PWNe) and pulsar halos can be
more extended than the Gaussian distribution. Spatially dependent transport of
electrons and positrons222Electrons will denote both electrons and positrons
hereafter if not specified., such as two-zone diffusion, is suggested for
these systems Lu  _et al._ (2020); Fang (2024), indicating that there could be
more gamma-ray signals than predicted by the Gaussian profile at large
distances from the source. Many gamma-ray sources in the first LHAASO catalog
are associated with pulsars, most of which could be PWNe or pulsar halos.
Thus, the potential contamination of DGE by these sources is worth
considering. We refer to all sources associated with pulsars as LHAASO
PWNe/halos in this paper.

More intriguingly, the Galactic longitude profile of the DGE excess measured
by LHAASO exhibits a correlation with some known gamma-ray sources that have
large extensions, such as those in the Geminga and Cygnus regions. The
significant increase in DGE around Geminga is likely due to signal leakage
from the Geminga pulsar halo. For the Cygnus region, the measurement by LHAASO
indicates that the bubble extends to at least $10^{\circ}$ Cao  _et al._
(2024b), while the size of the masked region at that location is $6^{\circ}$.
Therefore, signals beyond $6^{\circ}$ can contribute to the measurement of
DGE.

This work aims to evaluate the contribution of LHAASO PWNe/halos leakage
signals to the TeV DGE excess based on the two-zone diffusion model of
electrons, which is a completely different perspective compared to attributing
the DGE excess to unresolved extended gamma-ray sources Linden and Buckman
(2018); Yan  _et al._ (2024). Additionally, we give an estimate of the signal
leakage from the Cygnus bubble. In Section II, we introduce the two-zone
diffusion model, as well as the measurements of LHAASO PWNe/halos in the first
LHAASO catalog and the related pulsar characteristics. We adopt the two-zone
diffusion model to fit the LHAASO measurements and then predict the signal
leakage. Section III presents our results, including the Galactic longitude
profile and gamma-ray energy spectrum contributed by the leakage signals.
Section IV provides some extended discussions of the results, followed by a
summary and outlook in Section V.

##  II Methods

The first LHAASO catalog of gamma-ray sources includes 90 sources, 35 of which
are associated with pulsars. We assume these sources to be PWNe or pulsar
halos. In the LHAASO catalog paper, their morphology is uniformly described
using a Gaussian template Cao  _et al._ (2024a). While this approach
effectively captures the signals near the pulsars, it may not accurately
describe the gamma-ray signals at larger angular distances considering the
possible escape of the parent electrons from the central zone. In this study,
we adopt a two-zone diffusion model to describe the gamma-ray surface
brightness of these sources, ensuring that the central morphology of each
source is in agreement with the LHAASO measurements. The leakage flux can then
be estimated by extrapolating from the two-zone diffusion model.

###  II.1 Two-zone model

We assume the electron propagation for the LHAASO PWNe/halos can be described
by the diffusion-cooling equation:

$\frac{\partial N\left(E_{e},\bm{r},t\right)}{\partial
t}=\nabla\cdot\left[D\left(E_{e}\right)\nabla
N\left(E_{e},\bm{r},t\right)\right]+\frac{\partial\left[b\left(E_{e}\right)N\left(E_{e},\bm{r},t\right)\right]}{\partial
E_{e}}+Q\left(E_{e},\bm{r},t\right)\,,$ (1)

where $N$ is the electron number density and $E_{e}$ is the electron energy.
The source term $Q$ is assumed to have a point-like characteristic, and the
electron injection rate is assumed to follow the time profile of the pulsar
spin-down luminosity as as $\propto\left(1+t/\tau\right)^{-2}$, where the
spin-down time scale is set to be $\tau=10~{}\rm{kyr}$. The electron injection
spectrum for each source is described by a power-law form. Hence, the source
injection function is expressed as

$Q\left(E_{e},\bm{r},t\right)=\begin{cases}q_{0}E^{-\alpha}\delta\left(\bm{r}-\bm{r}_{p}\right)\left[\left(t_{p}+\tau\right)/\left(t+\tau\right)\right]^{2},&t\geq
0\\\ 0,&t<0\end{cases}\,,$ (2)

where $\bm{r}_{p}$ is the position of pulsar, decided by the pulsar distance
$d$ listed in Table 1. $t_{p}$ is the age of pulsar, and $t=0$ corresponds to
the birth time of pulsar.

For the two-zone model, the diffusion coefficient takes the form of

$D\left(E_{e},\bm{r}\right)=\begin{cases}D_{1}(E_{e}/100~{}\mathrm{TeV})^{\delta},&\left|\bm{r}-\bm{r}_{p}\right|<r_{\star}\\\
D_{2}(E_{e}/100~{}\mathrm{TeV})^{\delta},&\left|\bm{r}-\bm{r}_{p}\right|\geq
r_{\star}\end{cases}$ (3)

where $r_{\star}$ is the size of slow-diffusion zone, $D_{1}$ is the
suppressed diffusion coefficient near the source, and $D_{2}$ is the typical
diffusion coefficient of the Galaxy Ma  _et al._ (2023). Both $D_{1}$ and
$D_{2}$ are normalized at 100 TeV. The energy slope of the diffusion
coefficient is assumed to be $\delta=1/3$ as suggested by Kolmogorov’s theory
Kolmogorov (1991). Unless specified, we take $D_{1}=4.5\times 10^{27}$ cm2 s-1
as inferred from the surface brightness profile of the Geminga halo Abeysekara
_et al._ (2017) and the size of the slow-diffusion zone to be $r_{\star}=25$
pc.

For high-energy electrons ($E_{e}\gg 1$ GeV), energy losses are dominated by
synchrotron radiation and inverse Compton scattering (ICS) Fang  _et al._
(2021a), which is denoted as $b(E_{e})$ in equation 1. We use a $3$ $\mu$G
magnetic field to calculate the energy loss due to synchrotron radiation. For
ICS, the Galactic interstellar radiation field (ISRF) is composed of the
cosmic microwave background, infrared emission, and optical emission. These
components are described by gray body distributions with temperatures of $2.7$
K, $20$ K, and $5000$ K, and energy densities of $0.26$ eV cm-3, $0.3$ eV
cm-3, and $0.3$ eV cm-3, respectively.

We use a finite volume numerical method to solve the equation 1 to obtain the
electron density $N(E_{e},\bm{r},t)$ Fang  _et al._ (2018). Electrons produce
gamma rays through ICS with the Galactic ISRF Blumenthal and Gould (1970). We
then perform line-of-sight integration to obtain the gamma-ray surface
brightness $S(\theta,E_{\gamma})$ around pulsars, where $\theta$ is the
angular distance from pulsars.

Table 1: 1LHAASO sources associated with pulsars.

Name | RA(∘) | DEC(∘) | $N_{0}\rm{(10^{-16}cm^{-2}s^{-1}TeV^{-1})}$ | $\Gamma$ | $\sigma(^{\circ})$ | Associated Pulsar |  $d$ (kpc) |  $t_{p}$(kyr) |  $\dot{E}$(erg/s)
---|---|---|---|---|---|---|---|---|---
1LHAASO J0007+7303u | $1.91$ | $73.07$ | $3.41\pm 0.27$ | $3.4\pm 0.12$ | $0.17\pm 0.03$ | PSR J0007+7303 | $1.4$ | $14$ | $4.50\times 10^{35}$
1LHAASO J0216+4237u | $34.1$ | $42.63$ | $0.18\pm 0.03$ | $2.58\pm 0.17$ | $0.13^{{\dagger}}$ | PSR J0218+4232 | $3.15$ | $476000$ | $2.40\times 10^{35}$
1LHAASO J0249+6022 | $42.39$ | $60.37$ | $0.93\pm 0.09$ | $3.82\pm 0.18$ | $0.38\pm 0.08$ | PSR J0248+6021 | $2$ | $62$ | $2.10\times 10^{35}$
1LHAASO J0359+5406 | $59.78$ | $54.1$ | $0.85\pm 0.06$ | $3.84\pm 0.15$ | $0.3\pm 0.04$ | PSR J0359+5414 | $3.8^{*}$ | $75$ | $1.30\times 10^{36}$
1LHAASO J0534+2200u | $83.61$ | $22.04$ | $6.23\pm 0.1$ | $3.19\pm 0.03$ | $0.06^{{\dagger}}$ | PSR J0534+2200 | $2$ | $1$ | $4.50\times 10^{38}$
1LHAASO J0542+2311u | $85.71$ | $23.2$ | $2.93\pm 0.12$ | $3.74\pm 0.09$ | $0.98\pm 0.05$ | PSR J0543+2329 | $1.56^{*}$ | $253$ | $4.10\times 10^{34}$
1LHAASO J0622+3754 | $95.5$ | $37.9$ | $1.42\pm 0.07$ | $3.68\pm 0.1$ | $0.46\pm 0.03$ | PSR J0622+3749 | $1.6$ | $208$ | $2.70\times 10^{34}$
1LHAASO J0631+1040 | $97.77$ | $10.67$ | $0.54\pm 0.06$ | $3.33\pm 0.16$ | $0.3^{{\dagger}}$ | PSR J0631+1037 | $2.1$ | $44$ | $1.70\times 10^{35}$
1LHAASO J0634+1741u | $98.57$ | $17.69$ | $4.42\pm 0.15$ | $3.69\pm 0.06$ | $0.89\pm 0.04$ | PSR J0633+1746 | $0.19$ | $342$ | $3.30\times 10^{34}$
1LHAASO J0635+0619 | $98.76$ | $6.33$ | $0.94\pm 0.1$ | $3.67\pm 0.18$ | $0.6\pm 0.07$ | PSR J0633+0632 | $1.35$ | $59$ | $1.20\times 10^{35}$
1LHAASO J1740+0948u | $265.03$ | $9.81$ | $0.41\pm 0.04$ | $3.13\pm 0.15$ | $0.11^{{\dagger}}$ | PSR J1740+1000 | $1.23$ | $114$ | $2.30\times 10^{35}$
1LHAASO J1809-1918u | $272.38$ | $-19.3$ | $9.46\pm 1.27$ | $3.51\pm 0.26$ | $0.22^{{\dagger}}$ | PSR J1809-1917 | $3.27$ | $51$ | $1.80\times 10^{36}$
1LHAASO J1813-1245 | $273.36$ | $-12.75$ | $1.42\pm 0.27$ | $3.66\pm 0.34$ | $0.31^{{\dagger}}$ | PSR J1813-1245 | $2.63$ | $43$ | $6.20\times 10^{36}$
1LHAASO J1825-1256u | $276.44$ | $-12.94$ | $5.08\pm 0.42$ | $3.33\pm 0.13$ | $0.2^{{\dagger}}$ | PSR J1826-1256 | $1.55$ | $14$ | $3.60\times 10^{36}$
1LHAASO J1825-1337u | $276.45$ | $-13.63$ | $10.1\pm 0.61$ | $3.28\pm 0.09$ | $0.18^{{\dagger}}$ | PSR J1826-1334 | $3.61$ | $21$ | $2.80\times 10^{36}$
1LHAASO J1837-0654u | $279.31$ | $-6.86$ | $3.06\pm 0.21$ | $3.7\pm 0.12$ | $0.33\pm 0.04$ | PSR J1838-0655 | $6.6$ | $23$ | $5.60\times 10^{36}$
1LHAASO J1839-0548u | $279.79$ | $-5.81$ | $3.03\pm 0.2$ | $3.24\pm 0.09$ | $0.22\pm 0.02$ | PSR J1838-0537 | $2.3^{*}$ | $5$ | $6.00\times 10^{36}$
1LHAASO J1848-0001u | $282.19$ | $-0.02$ | $1.64\pm 0.1$ | $2.75\pm 0.07$ | $0.09^{{\dagger}}$ | PSR J1849-0001 | $1.9^{*}$ | $43$ | $9.80\times 10^{36}$
1LHAASO J1857+0245 | $284.37$ | $2.75$ | $<0.32$ | - | $0.24\pm 0.04$ | PSR J1856+0245 | $6.32$ | $21$ | $4.60\times 10^{36}$
1LHAASO J1906+0712 | $286.56$ | $7.2$ | $<0.19$ | - | $0.21\pm 0.05$ | PSR J1906+0722 | $1.73^{*}$ | $49$ | $1.00\times 10^{36}$
1LHAASO J1908+0615u | $287.05$ | $6.26$ | $6.86\pm 0.16$ | $2.82\pm 0.03$ | $0.36\pm 0.01$ | PSR J1907+0602 | $2.37$ | $20$ | $2.80\times 10^{36}$
1LHAASO J1912+1014u | $288.38$ | $10.5$ | $1.52\pm 0.1$ | $3.26\pm 0.11$ | $0.5\pm 0.04$ | PSR J1913+1011 | $4.61$ | $169$ | $2.90\times 10^{36}$
1LHAASO J1914+1150u | $288.73$ | $11.84$ | $0.79\pm 0.06$ | $3.41\pm 0.13$ | $0.21\pm 0.04$ | PSR J1915+1150 | $14.01$ | $116$ | $5.40\times 10^{35}$
1LHAASO J1928+1746u | $292.17$ | $17.89$ | $0.72\pm 0.07$ | $3.1\pm 0.12$ | $0.16^{{\dagger}}$ | PSR J1928+1746 | $4.34$ | $83$ | $1.60\times 10^{36}$
1LHAASO J1929+1846u | $292.04$ | $18.97$ | $0.64\pm 0.06$ | $3.11\pm 0.12$ | $0.21^{{\dagger}}$ | PSR J1930+1852 | $7$ | $3$ | $1.20\times 10^{37}$
1LHAASO J1954+2836u | $298.55$ | $28.6$ | $0.42\pm 0.05$ | $2.92\pm 0.14$ | $0.12^{{\dagger}}$ | PSR J1954+2836 | $1.96$ | $69$ | $1.10\times 10^{36}$
1LHAASO J1954+3253 | $298.63$ | $32.88$ | $<0.04$ | - | $0.17\pm 0.03$ | PSR J1952+3252 | $3$ | $107$ | $3.70\times 10^{36}$
1LHAASO J1959+2846u | $299.78$ | $28.78$ | $0.84\pm 0.07$ | $2.9\pm 0.1$ | $0.29\pm 0.03$ | PSR J1958+2845 | $1.95$ | $22$ | $3.40\times 10^{35}$
1LHAASO J2005+3415 | $301.81$ | $33.87$ | $0.56\pm 0.05$ | $3.79\pm 0.21$ | $0.33\pm 0.05$ | PSR J2004+3429 | $10.78$ | $18$ | $5.80\times 10^{35}$
1LHAASO J2005+3050 | $301.45$ | $30.85$ | $0.46\pm 0.05$ | $3.62\pm 0.21$ | $0.27\pm 0.05$ | PSR J2006+3102 | $6.04$ | $104$ | $2.20\times 10^{35}$
1LHAASO J2020+3649u | $305.23$ | $36.82$ | $2.29\pm 0.09$ | $3.31\pm 0.06$ | $0.12\pm 0.02$ | PSR J2021+3651 | $1.8$ | $17$ | $3.40\times 10^{36}$
1LHAASO J2028+3352 | $307.21$ | $33.88$ | $1.61\pm 0.19$ | $3.38\pm 0.19$ | $1.7\pm 0.23$ | PSR J2028+3332 | $0.91^{*}$ | $576$ | $3.50\times 10^{34}$
1LHAASO J2031+4127u | $307.95$ | $41.46$ | $2.56\pm 0.08$ | $3.45\pm 0.06$ | $0.22\pm 0.01$ | PSR J2032+4127 | $1.33$ | $201$ | $1.50\times 10^{35}$
1LHAASO J2228+6100u | $337.01$ | $61$ | $4.76\pm 0.14$ | $2.95\pm 0.04$ | $0.35\pm 0.01$ | PSR J2229+6114 | $3$ | $10$ | $2.20\times 10^{37}$
1LHAASO J2238+5900 | $339.54$ | $59$ | $2.03\pm 0.12$ | $3.55\pm 0.09$ | $0.43\pm 0.03$ | PSR J2238+5903 | $2.83$ | $27$ | $8.90\times 10^{35}$

  * 1

[1] The power-law shape is defined by
$dN/dE_{\gamma}=N_{0}(E_{\gamma}/50~{}\mathrm{TeV})^{-\Gamma}$.

  * 2

[2] The pulsar distances marked with $*$ are “pseudo distances” (see the text
for the definition).

  * 3

[3] The Gaussian widths marked with ${\dagger}$ are the $95\%$ statistical
upper limits.

###  II.2 LHAASO PWNe/halos

Among these 35 LHAASO PWNe/halos, 32 have been significantly detected by
LHAASO-KM2A and are utilized in this study except for the Crab nebula, as it
is a very young source with few expected escaping electrons. In the first
LHAASO catalog, their morphologies are all described by the Gaussian template,
where $\sigma$ represents the Gaussian width or its the $95\%$ upper limit.
Their energy spectra follow a power-law shape as
$dN/dE_{\gamma}=N_{0}(E_{\gamma}/50~{}\mathrm{TeV})^{-\Gamma}$. The gamma-ray
spectral parameters of the LHAASO sources and parameters of the associated
pulsars are listed in Table 1. For most cases, the pulsar distance,
characteristic age, and spin-down luminosity are taken from the ATNF catalog
Manchester  _et al._ (2005). When the pulsar distance is not available in the
ATNF catalog, we use the “pseudo distance” derived from the empirical relation
between the pulsar gamma-ray luminosity and total spin-down power Abdo  _et
al._ (2010). Specifically, PSR J1849-0001 currently lacks gamma-ray pulse
measurements. We assume its distance to be the same as that of PSR J1954+2836,
as these two pulsars have similar ages and Gaussian widths.

###  II.3 Fitting method

Based on the LHAASO measurements of the morphology and energy spectrum for
each source, we can obtain the Gaussian profile at each energy point between
10 TeV and 1 PeV. Taking LHAASO J1825-1337u as an example, the Figure 1 shows
the Gaussian morphology at $E_{\gamma}=32$ TeV, convolved with the point
spread function (PSF) of LHAASO-KM2A, where the PSF width is $0.3^{\circ}$.
The blue shaded band represents the statistical error, assuming that the
errors of each parameter are independent. In order to accurately reproduce the
gamma-ray profile within the central zone and minimize the influence of
uncertainties at large angular distances, we fit the two-zone diffusion model
to the Gaussian template within 2.5$\sigma$ range, employing a chi-squared
fitting method. The morphology derived from the two-zone diffusion model is
also convolved with the same PSF. The free parameters in the fitting process
are $q_{0}$ and $\alpha$ defined in equation (2), which determine the
normalization and spectral shape of the gamma-ray emission, respectively.

As shown in Figure 1, when the gamma-ray profile calculated by the two-zone
diffusion model is consistent with the LHAASO measurement within the central
zone, the profile at lager angular distance is significantly higher than the
Gaussian template. This discrepancy arises because electrons spread widely
when they escape from the slow-diffusion zone. Consequently, there are still
many residual signals even after masking a region of $2.5\sigma$. Therefore,
the leakage signals are expected to contribute a considerable portion to the
DGE.

Figure 1: The surface brightness profile of LHAASO J1825-1337u with
$E_{\gamma}=32$ TeV. The blue line represents the prediction of a Gaussian
profile, with corresponding shaded area indicating the error band, assuming
the parameter errors are independent of each other. The red line represents
the expectation from the two-zone diffusion model. The gray shaded area
indicates the fitting range.

##  III Results

Using the model given by the fit introduced in Section II.3, we present the
original and masked gamma-ray intensity maps in the Galactic plane in Figure
2. The masking method employed is consistent with that used for the LHAASO DGE
measurement. We can visually discern that considerable leakage signals remain
in the Galactic plane, which should not be ignored compared to the measured
DGE. In the default calculation, we assume $D_{1}=4.5\times 10^{27}$ cm2 s-1
and $r_{\star}=25$ pc, as introduced in Section II.1. These two parameters
cannot be constrained by the current measurements for each source, but they
can affect the expected signal leakage. We discuss the influence of varying
these parameters in Section IV.

Figure 2: The gamma-ray intensity map of Galactic plane contributed by LHAASO
PWNe/halos and Cygnus bubble in energy range 10-63 TeV. The signals from
LHAASO PWNe/halos are modeled using a two-zone diffusion model. (a) The inner
Galactic plane of $15^{\circ}<l<125^{\circ}$. (b) The outer Galactic plane of
$125^{\circ}<l<235^{\circ}$. (c) The inner Galactic plane after masking the
same region as the LHAASO DGE measurement. (d) The outer Galactic plane after
masking the same region as the LHAASO DGE measurement.

It is worth noting that it is necessary to apply special treatments for the
Cygnus and Geminga regions. In the region of Galactic longitude
$70^{\circ}-90^{\circ}$, there is an ultrahigh-energy gamma-ray bubble powered
by a super PeVatron which has an extension of $\sim 10^{\circ}$, dubbed the
“Cygnus bubble” Cao  _et al._ (2024b). However, in the LHAASO measurement of
DGE, only a $6^{\circ}$ radius circle is masked, leading to leakage of the
bubble signals. The Cygnus bubble most likely originates from hadronic
interactions Cao  _et al._ (2024b), and we straightforwardly use the LHAASO
measurement to estimate the leakage flux in the range of
$6^{\circ}-10^{\circ}$ instead of using the prediction from the two-zone
diffusion model. Since the hadronic emission generated by the “cosmic-ray sea”
is included in the LHAASO measurement of the Cygnus bubble, we have removed it
to avoid redundant calculation.

At the Galactic longitude of around $190^{\circ}$, there is a remarkable
excess coinciding with the location of the Geminga halo even after masking a
radius of $8^{\circ}$ around the Geminga pulsar. For the Geminga halo, we
assume a slow-diffusion zone with $D_{1}=1.5\times 10^{28}$ cm2 s-1 and
$r_{\star}=50$ pc. The predicted leakage signals can reproduce this excess,
and the assumed parameters are reasonable for the Geminga halo. The extension
of Geminga observed in the significance map reported by LHAASO-KM2A Guo  _et
al._ (2021) is larger compared to the measurements by HAWC Abeysekara  _et
al._ (2017), indicating a larger $D_{1}$. Besides, Fang (2024) pointed out
that $r_{\star}$ should be larger than $30$ pc to reproduce the surface
brightness profile of the Geminga halo; otherwise, the profile would be too
steep compared to the measurements.

Figure 3: The comparison of Galactic profiles of the diffuse emission and
model. The top panel is for the energy band 10-63 TeV, and the bottom panel is
for 63-1000 TeV. The black points represent the measurements from LHAASO. The
red line represents the prediction of the CR-ISM interaction modelYan  _et
al._ (2024). The blue line represents the sum of contributions from the CR-ISM
interaction and the leakage signals of the LHAASO PWNe/halos and the Cygnus
bubble. For sources with significant signal leakage, we have specifically
marked their contributions to the DGE.

Figure 3 shows the Galactic longitude profiles of DGE contributed by different
components, including the CR-ISM interactionYan  _et al._ (2024), and leakage
signals of LHAASO PWNe/halos and Cygnus bubble, in the energy bands of $10-63$
TeV and $63-1000$ TeV. The DGE measurement results significantly exceed the
expectations of CR-ISM interaction model. For the 10-63 TeV range, the DGE
excess is primarily concentrated in four regions: (1) The region with
$l\approx 20^{\circ}-50^{\circ}$; (2) Around the Cygnus bubble; (3) The region
with $l\approx 100^{\circ}-150^{\circ}$; (4) Around Geminga. Our signal
leakage model significantly contributes to the excesses in regions (1), (2),
and (4). For region (3), the signal leakage model can partly explain the
excess (in $l\approx 100^{\circ}-115^{\circ}$). For the 63-1000 TeV energy
range, the excess primarily occurs in region (2), with a smaller amount coming
from region (1). Our signal leakage model provides a good explanation for
these excesses.

Interestingly, the DGE excess around Geminga is primarily observed in the
$10-63$ TeV energy range and is not significant in the $63-1000$ TeV range.
This observation coincides with the characteristics of the Geminga halo
spectrum: the latest measurement by HAWC indicates that the gamma-ray spectrum
of the Geminga halo exhibits an exponential cutoff at tens of TeV Albert  _et
al._ (2023). These phenomena favor the idea that the excess in this region
originates from leakage signals of the Geminga halo rather than other
unresolved sources.

Figure 4 shows the gamma-ray spectra of DGE contributed by different
components in the inner and outer Galactic plane, respectively. The total flux
of DGE can be well explained once the signal leakage components are taken into
account. In the inner Galactic plane region, for energies below $100$ TeV, the
DGE excess is predominantly contributed by the LHAASO PWNe/halos, while for
energies above $100$ TeV, it is mainly contributed by the Cygnus bubble. This
is consistent with the constraint from the neutrino observation, which
indicates the DGE excess in $\approx 1-100$ TeV is dominated by leptonic
components Yan  _et al._ (2024). In the outer Galactic plane region, the DGE
excess is contributed by leakage signals of LHAASO PWNe/halos, with no
significant excess observed above $100$ TeV. We note that the model still
underestimates the DGE flux at $\approx 40$ TeV for the case of the outer
Galactic plane. This discrepancy is due to the underestimation in the
longitude range of $l\approx 115^{\circ}-150^{\circ}$ as shown in the top
panel of Figure 3.

Figure 4: Comparison of the measured DGE spectrum and model interpretation.
The left panel shows the inner Galaxy region ($15^{\circ}<l<125^{\circ}$) and
the right panel shows the outer Galaxy region ($125^{\circ}<l<235^{\circ}$).
For each panel, the black points represent the LHAASO measurement. The red
line represents the prediction of the CR-ISM interaction modelYan  _et al._
(2024), the pink line represents the contribution from the leakage fluxes of
LHAASO PWNe/Halo, and the black line represents the leakage flux of Cygnus
bubble. The blue line is the sum of all these components.

##  IV Discussion

In the two-zone diffusion model, the slow-diffusion zone around a pulsar may
originate from the turbulent environment created by the associated SNR Fang
_et al._ (2019). Given that most of the pulsars listed in Table 1 are on the
order of tens of kyr, it is reasonable to assume an average slow-diffusion
zone scale of $r_{\star}=25$ pc, which aligns with the expected scale of SNRs
under typical parameters Leahy and Williams (2017). However, we still need to
evaluate the impact of varying this value. Additionally, we should also
consider the impact of the diffusion coefficient in the central zone, $D_{1}$,
which may deviate from the value measured by HAWC Abeysekara  _et al._ (2017).
Qualitatively speaking, the larger $D_{1}$ or smaller $r_{\star}$, the more
easily electrons escape to distant regions, resulting in greater signal
leakage. The specific impact of varying $D_{1}$ or $r_{\star}$ on the
interpretation of the DGE excess is illustrated in Figure 5.

We have demonstrated that the DGE excess in most regions can be interpreted by
the signal leakage model under certain parameters. However, the gamma-ray flux
predicted by the model is insufficient to match the data in the range of
$l\approx 115^{\circ}-150^{\circ}$, even when considering model uncertainties,
as shown in Figure 5. There are relatively few LHAASO PWNe/halos in this
region, and the fluxes of LHAASO J0249$+$6022 and LHAASO J0359$+$5406 located
in this region are relatively low. The excess gamma-ray emission in this
region may be caused by some unresolved leptonic sources, such as
indistinguishable halos. Therefore, the signal leakage from known sources and
the contribution from unresolved sources should be considered complementary in
explaining the DGE excess.

In this work, we predict the large-angle signal leakage of LHAASO PWNe/halos
using the two-zone diffusion model for electrons. In fact, besides the two-
zone diffusion model, other propagation models may also explain the surface
brightness distribution around pulsars while predicting significantly higher
gamma-ray signals at large angles compared to the Gaussian template. The
superdiffusion model exhibits such characteristics, and previous works have
discussed using the superdiffusion model to explain the morphology of pulsar
halos Wang  _et al._ (2021); Fang  _et al._ (2021b). We expect that such
models can achieve similar results to the two-zone diffusion model in
interpreting the DGE excess.

Figure 5: Comparison of the Galactic longitude profiles of DGE by assuming
different two-zone diffusion model parameters. The lines represent the total
contribution from the CR-ISM interaction, the LHAASO PWNe/Halo, and the Cygnus
bubble. The units of $D_{1}$ are cm2 s-1.

##  V Conclusions

The DGE excess phenomenon in the Galactic plane is generally believed to
originate from unresolved sources with large extensions, such as pulsar halos.
In this work, we offer a new perspective to explain the DGE excess observed by
LHAASO, suggesting that the large-angle signal leakage from known sources
could be a significant contributor to the DGE excess. As the excess
predominantly originates from gamma rays produced by leptonic processes, we
focus on possible PWNe and pulsar halos in the LHAASO source catalog. We first
use the two-zone diffusion model to fit the central profile of the sources and
get the extrapolated profile at large angular distances. Then, using the same
masking method as in the DGE measurement, we determine the contribution from
leakage signals of the LHAASO PWNe/halos to the DGE.

We demonstrate that the DGE excess in most regions of the Galactic plane can
be well interpreted by the signal leakage model under certain parameters.
Additionally, we point out that signal leakage from the Cygnus bubble is also
necessary to be considered. We also note that in the Galactic longitude range
of $l\approx 115^{\circ}-150^{\circ}$, the gamma-ray flux predicted by our
model is insufficient to match the observation, as there are few identified
bright gamma-ray sources in that area. Unresolved extended sources may account
for this discrepancy. Therefore, we emphasize that the signal leakage from
known sources and the contribution from unresolved sources should be
considered complementary in explaining the DGE excess.

Besides the two-zone diffusion model, other propagation models, such as
superdiffusion could also explain the surface brightness distribution around
pulsars while predicting significantly higher gamma-ray signals at large
angles compared to the Gaussian template, which may similarly account for the
DGE excess. As the LHAASO data continues to accumulate and with the advent of
future high-resolution observations (e.g., LACT Zhang (2023)), we will be able
to provide more precise measurements of the morphology of known gamma-ray
sources. This will allow us to place more stringent constraints on complex
propagation models, such as the two-zone diffusion and superdiffusion models,
thereby offering better insights into the origin of the DGE excess.

###### Acknowledgements.

This work is supported by the National Natural Science Foundation of China
under Grants No. 12105292, No. 12175248, and No. 12393853.

## References

  * Strong  _et al._ (2007) A. W. Strong, I. V. Moskalenko, and V. S. Ptuskin, Ann. Rev. Nucl. Part. Sci. 57, 285 (2007), arXiv:astro-ph/0701517 .
  * Ackermann  _et al._ (2012) M. Ackermann _et al._ (Fermi-LAT), Astrophys. J. 750, 3 (2012), arXiv:1202.4039 [astro-ph.HE] .
  * Atkins  _et al._ (2005) R. Atkins _et al._ (Milagro), Phys. Rev. Lett. 95, 251103 (2005), arXiv:astro-ph/0502303 .
  * Bartoli  _et al._ (2015) B. Bartoli _et al._ (ARGO-YBJ), Astrophys. J. 806, 20 (2015), arXiv:1507.06758 [astro-ph.IM] .
  * Amenomori  _et al._ (2021) M. Amenomori _et al._ (Tibet ASgamma), Phys. Rev. Lett. 126, 141101 (2021), arXiv:2104.05181 [astro-ph.HE] .
  * Prodanovic  _et al._ (2007) T. Prodanovic, B. D. Fields, and J. F. Beacom, Astropart. Phys. 27, 10 (2007), arXiv:astro-ph/0603618 .
  * Linden and Buckman (2018) T. Linden and B. J. Buckman, Phys. Rev. Lett. 120, 121101 (2018), arXiv:1707.01905 [astro-ph.HE] .
  * Cao  _et al._ (2024a) Z. Cao _et al._ (LHAASO), Astrophys. J. Suppl. 271, 25 (2024a), arXiv:2305.17030 [astro-ph.HE] .
  * Cao  _et al._ (2023) Z. Cao _et al._ (LHAASO), Phys. Rev. Lett. 131, 151001 (2023), arXiv:2305.05372 [astro-ph.HE] .
  * Zhang  _et al._ (2023) R. Zhang, X. Huang, Z.-H. Xu, S. Zhao, and Q. Yuan, Astrophys. J. 957, 43 (2023), arXiv:2305.06948 [astro-ph.HE] .
  * Abbasi  _et al._ (2023) R. Abbasi _et al._ (IceCube), Science 380, adc9818 (2023), arXiv:2307.04427 [astro-ph.HE] .
  * Yan  _et al._ (2024) K. Yan, R.-Y. Liu, R. Zhang, C.-M. Li, Q. Yuan, and X.-Y. Wang, Nature Astron. 8, 628 (2024), arXiv:2307.12363 [astro-ph.HE] .
  * Lu  _et al._ (2020) F.-W. Lu, Q.-G. Gao, and L. Zhang, Astrophys. J. 889, 30 (2020).
  * Fang (2024) K. Fang, Phys. Rev. D 109, 043041 (2024), arXiv:2310.16594 [astro-ph.HE] .
  * Cao  _et al._ (2024b) Z. Cao _et al._ (LHAASO), Sci. Bull. 69, 449 (2024b), arXiv:2310.10100 [astro-ph.HE] .
  * Ma  _et al._ (2023) P.-X. Ma, Z.-H. Xu, Q. Yuan, X.-J. Bi, Y.-Z. Fan, I. V. Moskalenko, and C. Yue, Front. Phys. (Beijing) 18, 44301 (2023), arXiv:2210.09205 [astro-ph.HE] .
  * Kolmogorov (1991) A. N. Kolmogorov, Proceedings: Mathematical and Physical Sciences 434, 9 (1991).
  * Abeysekara  _et al._ (2017) A. U. Abeysekara, A. Albert, R. Alfaro, C. Alvarez, J. D. Álvarez, R. Arceo, J. C. Arteaga-Velázquez, D. A. Rojas, H. A. A. Solares, A. S. Barber, N. Bautista-Elivar, A. Becerril, E. Belmont-Moreno, S. Y. BenZvi, D. Berley, A. Bernal, J. Braun, C. Brisbois, K. S. Caballero-Mora, T. Capistrán, A. Carramiñana, S. Casanova, M. Castillo, U. Cotti, J. Cotzomi, S. C. de León, C. D. León, E. D. la Fuente, B. L. Dingus, M. A. DuVernois, J. C. Díaz-Vélez, R. W. Ellsworth, K. Engel, O. Enríquez-Rivera, D. W. Fiorino, N. Fraija, J. A. García-González, F. Garfias, M. Gerhardt, A. G. Muñoz, M. M. González, J. A. Goodman, Z. Hampel-Arias, J. P. Harding, S. Hernández, A. Hernández-Almada, J. Hinton, B. Hona, C. M. Hui, P. Hüntemeyer, A. Iriarte, A. Jardin-Blicq, V. Joshi, S. Kaufmann, D. Kieda, A. Lara, R. J. Lauer, W. H. Lee, D. Lennarz, H. L. Vargas, J. T. Linnemann, A. L. Longinotti, G. L. Raya, R. Luna-García, R. López-Coto, K. Malone, S. S. Marinelli, O. Martinez, I. Martinez-Castellanos, J. Martínez-Castro, H. Martínez-Huerta, J. A. Matthews, P. Miranda-Romagnoli, E. Moreno, M. Mostafá, L. Nellen, M. Newbold, M. U. Nisa, R. Noriega-Papaqui, R. Pelayo, J. Pretz, E. G. Pérez-Pérez, Z. Ren, C. D. Rho, C. Rivière, D. Rosa-González, M. Rosenberg, E. Ruiz-Velasco, H. Salazar, F. S. Greus, A. Sandoval, M. Schneider, H. Schoorlemmer, G. Sinnis, A. J. Smith, R. W. Springer, P. Surajbali, I. Taboada, O. Tibolla, K. Tollefson, I. Torres, T. N. Ukwatta, G. Vianello, T. Weisgarber, S. Westerhoff, I. G. Wisher, J. Wood, T. Yapici, G. Yodh, P. W. Younk, A. Zepeda, H. Zhou, F. Guo, J. Hahn, H. Li, and H. Zhang, Science 358, 911 (2017).
  * Fang  _et al._ (2021a) K. Fang, X.-J. Bi, S.-J. Lin, and Q. Yuan, Chin. Phys. Lett. 38, 039801 (2021a), arXiv:2007.15601 [astro-ph.HE] .
  * Fang  _et al._ (2018) K. Fang, X.-J. Bi, P.-F. Yin, and Q. Yuan, Astrophys. J. 863, 30 (2018), arXiv:1803.02640 [astro-ph.HE] .
  * Blumenthal and Gould (1970) G. R. Blumenthal and R. J. Gould, Rev. Mod. Phys. 42, 237 (1970).
  * Manchester  _et al._ (2005) R. N. Manchester, G. B. Hobbs, A. Teoh, and M. Hobbs, Astron. J. 129, 1993 (2005), arXiv:astro-ph/0412641 .
  * Abdo  _et al._ (2010) A. A. Abdo _et al._ (Fermi-LAT), Astrophys. J. Suppl. 187, 460 (2010), [Erratum: Astrophys.J.Suppl. 193, 22 (2011)], arXiv:0910.1608 [astro-ph.HE] .
  * Guo  _et al._ (2021) Y. Guo, Y. Zhang, Q. Yuan, and H. Hu (LHAASO), PoS ICRC2021, 852 (2021).
  * Albert  _et al._ (2023) A. Albert _et al._ (HAWC), PoS ICRC2023, 710 (2023).
  * Fang  _et al._ (2019) K. Fang, X.-J. Bi, and P.-F. Yin, Mon. Not. Roy. Astron. Soc. 488, 4074 (2019), arXiv:1903.06421 [astro-ph.HE] .
  * Leahy and Williams (2017) D. A. Leahy and J. Williams, Astron. J. 153, 239 (2017), arXiv:1701.05942 [astro-ph.HE] .
  * Wang  _et al._ (2021) S.-H. Wang, K. Fang, X.-J. Bi, and P.-F. Yin, Phys. Rev. D 103, 063035 (2021), arXiv:2101.01438 [astro-ph.HE] .
  * Fang  _et al._ (2021b) K. Fang, S.-Q. Xi, and X.-J. Bi, Phys. Rev. D 104, 103024 (2021b), arXiv:2107.02140 [astro-ph.HE] .
  * Zhang (2023) S. Zhang, PoS ICRC2023, 808 (2023).


R. K. Zamanov, G. Nikolov, A. T. Georgieva 11institutetext: Institute of
Astronomy and National Astronomical Observatory, Bulgarian Academy of
Sciences, Tsarigradsko Shose 72, BG-1784 Sofia, Bulgaria
22institutetext: Westinghouse Electric, Business Park Sofia, building 8A,
floor 7, 1766 Sofia, Bulgaria
22email<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>Submitted on 26.03.2021; Accepted on 11.04.2021

# UBVRI observations of the flickering of the dwarf nova RX And

R. K. Zamanov1 G. Nikolov1,2 A. T. Georgieva1

###### Abstract

We report observations of the flickering variability of the dwarf nova RX And
in five bands (UBVRI) on two nights. On 25 October 2019 the brightness of the
star was $B\approx 13.9$ mag, the amplitude of the flickering was 0.47 mag,
and we estimate for the flickering source temperature $T_{fl}=10700\pm 400$ K,
and radius $R_{fl}=0.046\pm 0.004$ $R_{\odot}$. On 2 January 2020, the star
was about 3 magnitudes brighter ($B\approx 10.7$), the amplitude of the
flickering was significantly lower (0.07 mag) and we derive for the flickering
source $T_{fl}=9600\pm 700$ K, and radius $R_{fl}=0.098\pm 0.009$ $R_{\odot}$.
The results indicate that 3 magnitudes brightening of the star doubled the
radius of the flickering source.
The data are available upon request from the authors.

###### keywords:

Stars: dwarf novae – novae, cataclysmic variables – stars: individual: RX And

##  1 Introduction

RX And (2MASS J01043553+4117577) is a cataclysmic variable of dwarf nova type
with orbital period $0.2098930$ day = 5h02m = 302 minutes (Kaitchuck 1989).
The cataclysmic variables are short period binaries consisting of an white
dwarf primary and a red dwarf as a mass donor. A sketch representing a
cataclysmic variable binary is included in the Appendix.

The underlying white dwarf in RX And was first detected by Holm et al. (1991)
using an IUE spectrum during RX And’s quiescence. The infrared spectra
identified that the mass donor is a K5V star (Dhillon & Marsh 1995).

The dwarf novae are cataclysmic variables which exhibit recurrent outbursts
with amplitude of 2 to 5 mag on the time-scale of weeks, caused by an increase
in the mass accretion rate. RX And shows regular dwarf nova outbursts every 15
days (e.g. Kato 2004) and flickering on time scale of minutes (e.g. Bennert et
al. 1999).

Following the AAVSO light curve generator, during the last years RX And varies
in the range $10.9\leq V\leq 14.9$ and $9.5\leq B\leq 15.0$. There was an
extended faint state of RX And in 1996, when the brightness remained about 15
mag in V band for $\approx 100$ days (Kato et al. 2002).

In this work, we present quasi-simultaneous UBVRI observations of the
flickering variability of RX And and estimate the parameters of the flickering
source.

##  2 Observations

The observations are performed with the 50/70 cm Schmidt telescope of the
National Astronomical Observatory Rozhen repeating U,B,V,R and I bands – on 25
October 2019 from UT 18:33 till 00:20, total duration 5h 47m, and on 2 January
2020 from UT 17:43 till 21:31, total duration 3h 48m. The telescope was
equipped with a CCD camera and the field of view was 23 x 23 arcmin. The red
bands correspond to the Cousins VRI system.

The comparison stars were TYC 2807-1285-1 (U=11.21, B=11.15, V=10.57, R=9.88,
I=9.53) and TYC 2803-1045-1 (U=11.96, B=11.94, V=11.43, R= 10.75, I=10.44).
The data reduction is done with IRAF (Tody 1993) following the standard
recipes for processing of CCD images and aperture photometry.

In Table LABEL:tab2 are given date of observation, its duration in minutes,
number of the exposures ($N_{pts}$), the exposure times in seconds, minimum,
maximum and average magnitude in the corresponding band, standard deviation of
the run, typical observational error and peak-to-peak amplitude of the
variability.

Our observations are presented on Fig. 1. What is immediately visible is that
during the second night the star was brighter and the amplitude of the
flickering was considerably lower.

Table 1: Photometry of RX And. In the table are given: date of observation,
its duration, band, number of the data points obtained, exposure time [in
seconds], minimum, maximum and average magnitudes in the corresponding band,
standard deviation of the mean, typical observational error, peak-to-peak
amplitude.

date | band | $N_{pts}$ | exptime |  |  | min | max | average | stdev | merr | ampl.
---|---|---|---|---|---|---|---|---|---|---|---
duration |  |  | [sec] |  |  | [mag] | [mag] | [mag] | [mag] | [mag] | [mag]
2019-10-25 | U | 95 | 90, 60 |  |  | 12.741 | 13.161 | 12.9680 | 0.084 | 0.017 | 0.42
347 min | B | 95 | 30, 20 |  |  | 13.571 | 14.040 | 13.8571 | 0.097 | 0.017 | 0.47
| V | 95 | 20, 10 |  |  | 13.452 | 13.871 | 13.6971 | 0.084 | 0.020 | 0.42
| R | 95 | 10 |  |  | 12.799 | 13.116 | 12.9934 | 0.065 | 0.015 | 0.32
| I | 95 | 30, 10 |  |  | 12.301 | 12.550 | 12.4255 | 0.053 | 0.023 | 0.25
2020-01-02 | U | 90 | 60, 40, 30 |  |  | 9.992 | 10.100 | 10.0652 | 0.020 | 0.009 | 0.11
228 min | B | 90 | 20, 10 |  |  | 10.687 | 10.759 | 10.7267 | 0.015 | 0.006 | 0.07
| V | 90 | 10, 7 |  |  | 10.720 | 10.797 | 10.7598 | 0.016 | 0.005 | 0.08
| R | 90 | 10, 7 |  |  | 10.316 | 10.383 | 10.3504 | 0.017 | 0.005 | 0.07
| I | 90 | 10 |  |  | 10.208 | 10.286 | 10.2454 | 0.019 | 0.006 | 0.08

Table 2: Estimated colours of RX And and its flickering source. The colours of
the star are the average colours during the night.

date |  | colour |  |  | star |  | average | maximum |
---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  | flickering | flickering |
20191025 |  | (U-B) |  |  | $0.89\pm 0.02$ |  | $-0.94\pm 0.03$ | $-0.73\pm 0.05$ |
|  | (B-V) |  |  | $0.16\pm 0.02$ |  | $0.11\pm 0.03$ | $0.02\pm 0.05$ |
|  | (V-R) |  |  | $0.70\pm 0.02$ |  | $0.35\pm 0.04$ | $0.40\pm 0.07$ |
|  | (R-I) |  |  | $0.57\pm 0.02$ |  | $0.58\pm 0.06$ | $0.27\pm 0.09$ |
20200102 |  | (U-B) |  |  | $0.66\pm 0.01$ |  | $-0.74\pm 0.09$ | $-1.12\pm 0.09$ |
|  | (B-V) |  |  | $-0.03\pm 0.01$ |  | $0.12\pm 0.05$ | $0.04\pm 0.05$ |
|  | (V-R) |  |  | $0.41\pm 0.01$ |  | $0.27\pm 0.04$ | $0.26\pm 0.04$ |
|  | (R-I) |  |  | $0.11\pm 0.01$ |  | $0.34\pm 0.03$ | $0.27\pm 0.04$ |

##  3 Flickering light source

Bruch (1992) proposed that the light curve of a white dwarf with flickering
can be separated into two parts – constant light and variable (flickering)
source. Following his recipe, we calculate the flux of the flickering light
source as $F_{\rm fl}=F_{\rm av}-F_{\rm min}$, where $F_{\rm av}$ is the
average flux during the run and $F_{\rm min}$ is the minimum flux during the
run (corrected for the typical error of the observations). An expansion of the
method is proposed by Nelson et al. (2011). They suggest to use the $F_{\rm
fl.max}=F_{\rm max}-F_{\rm min}$, where $F_{\rm max}$ is the maximum flux
during the run. In fact, the method of Bruch (1992) evaluates the average
brightness of the flickering source, while that of Nelson et al. (2011) – its
maximal brightness. $F_{\rm fl}$ and $F_{\rm fl.max}$ have been calculated for
each band, using the values given in Table LABEL:tab2 and the calibration for
a zero magnitude star (Bessell 1979).

Following the IRSA: Galactic Reddening and Extinction Calculator in NASA/IPAC
Extragalactic Database, NED (which is operated by the Jet Propulsion
Laboratory, California Institute of Technology), the extinction toward RX And
is low, $E(B-V)\leq 0.06$. The IRSA calculator uses Galactic reddening maps to
determine the total Galactic line-of-sight reddening (in front of RX And and
behind it), and is based on the results by Schlegel, Finkbeiner & Davis (1998)
and Schlafly & Finkbeiner (2011).

GAIA EDR3 (Lindegren et al. 2021) gives parallax $5.0510\pm 0.0269$ mas.
Hereafter, we assume no extinction, $E(B-V)=0.0$ and distance $198\pm 1$ pc.
We calculate for the average flickering source of RX And its temperature and
radius:
20191025 – $T_{fl}=10700\pm 400$ K, $R_{fl}=0.046\pm 0.004$ R⊙,
20200102 – $T_{fl}=9600\pm 700$ K, $R_{fl}=0.098\pm 0.009$ R⊙.
These values correspond to luminosity $L_{fl}=0.025\pm 0.004$ L⊙ (for
20191025), and $L_{fl}=0.074\pm 0.008$ L⊙ (for 20200102).

Figure 1: UBVRI observations of the flickering dwarf nova RX And on 25 October
2019 and 2 January 2020 performed with the 50/70 cm Schmidt telescope of NAO
Rozhen. Figure 2: Black body fits to the flickering source of RX And.

##  4 Discussion

The light curve of RX And in 1972-1997 displays periods of frequent outbursts
with amplitude $\approx 3$ mag, low states and periods of stand still
(Schreiber et al. 2002). The light curve of RX And in 2014-2015 was examined
by Timar (2016), who found that the cycle of outbursts is short ($<15$ days)
due to the high accretion rate and every fourth outburst is a super-outburst.
The period of the super-cycle was about 55.5 days.

The Hubble Space Telescope spectra revealed that the white dwarf in RX And has
a temperature $T_{wd}\approx 34000$ K, and rotates with $\approx 600$ km s-1
(Sion et al. 2001). Sepinsky et al. (2002) using HST observations during
outburst rise and decline found mass accretion rate $2\times 10^{-10}$ M⊙ yr-1
onto an white dwarf of mass $\sim 0.8$ M⊙ with effective temperature 40000 K.
Godon & Sion (2003) found that it must be a massive white dwarf $\sim 1.2$ M⊙.

The temperature of the flickering source estimated here is considerably lower
than the white dwarf temperature. It is similar to the temperature of the
bright spot of the cataclysmic variables. For the bright spot of OY Car Wood
et al (1989) calculated black body temperature $T=13800\pm 1300$ K, and color
temperature $T=9000$ K. Marsh (1988) for IP Peg give $T=11200$ K, Zhang &
Robinson (1987) – for U Gem - $T=11600\pm 500$ K, Robinson et al. (1978) –
$T=16000$ K for the bright spot in WZ Sge. The colours of the flickering
source of RX And on 10 August 1983 were estimated by Bruch (1992) $U-B=-1.14$,
$B-V=0.46$, assuming E(B-V)=0.06. The value of U-B is bluer than our and B-V
is more red. The differences can be connected with real changes in the
flickering and/or with the used different calibrations for a zero magnitude
star.

In dwarf novae, the flickering amplitude is high during quiescence, drops
quickly at an intermediate magnitude when the system enters into (or returns
from) an outburst and, on average, remains constant above a given brightness
threshold (Bruch 2021). In future it will be interesting to search for a
correlation between the flickering source parameters and brightness as done
for the recurrent nova RS Oph (Zamanov et al. 2018) and the jet-ejecting
symbiotic MWC 560 (Zamanov et al. 2020).

Conclusions:  We report quasi-simultaneous observations in 5 bands (UBVRI) of
the flickering of the cataclysmic variable RX And during two nights.

For 25 October 2019 the brightness of the star was $13.57\leq B\leq 14.04$,
the amplitude of the flickering in B band was $\Delta B=0.47$ mag. For the
optical flickering source we obtained colour $(B-V)_{0}=0.11$, temperature
$T_{fl}=10700\pm 400$ K, and radius $R_{fl}=0.046$ $R_{\odot}$.

For 2 January 2020, the star was about 3 magnitudes brighter in B band
$10.69\leq B\leq 10.76$ and the amplitude of the flickering decreased
considerably $\Delta B=0.07$ mag. For the optical flickering source we derived
colour $(B-V)_{0}=0.12$, temperature $T_{fl}=9600\pm 700$ K, and radius
$R_{fl}=0.098$ $R_{\odot}$.

The results indicate that when the star is 3 magnitudes brighter the radius of
the flickering source is twice larger.

Acknowledgments:  This work was supported by the Bulgarian National Science
Fund project number K$\Pi$-06-H28/2 08.12.2018 ”Binary stars with compact
object”. We are grateful to the referee prof. N. A. Tomov for useful comments.

## References

  * [1] Bennert , N., Konig, I., Manthey, E., et al., 1999, IBVS 4779, 1
  * [2] Bessell, M. S. 1979, PASP, 91, 589
  * [3] Bruch, A., 1992, A&A, 266, 237
  * [4] Bruch, A., 2021, MNRAS, 503, 953
  * [5] Dhillon, V. S. & Marsh, T. R., 1995, MNRAS, 275, 89
  * [6] Godon P. & Sion E. M., 2003, ApJ, 586, 427
  * [7] Holm, A., Lanning, H., Mattei, J. A., Nelan, E. 1991, JAAVSO, 20, 166
  * [8] Kaitchuck, R. H., 1989, PASP, 101, 1129
  * [9] Kato, T., Nogami, D., Masuda, S., 2002, PASJ, 54, 575
  * [10] Kato, T., 2004, PASJ, 56, S55
  * [11] Lindegren, L., Klioner, S. A., Hernandez, J., et al., 2021, A&A, in press (arXiv:2012.03380)
  * [12] Marsh, T. R. 1988, MNRAS, 231, 1117
  * [13] Nelson, T., Mukai, K., Orio, M., Luna, G. J. M., Sokoloski, J. L. 2011, ApJ, 737, 7
  * [14] Robinson, E. L., Nather, R. E., & Patterson, J. 1978, ApJ, 219, 168
  * [15] Schlafly, E. F., Finkbeiner, D. P., 2011, ApJ, 737, 103
  * [16] Schlegel, D. J, Finkbeiner, D. P., Davis,M., 1998, ApJ, 500, 525
  * [17] Schreiber, M. R., Gansicke, B. T., Mattei, J. A., 2002, ASP Conf., 261, 545
  * [18] Sepinsky, J. F., Sion, E. M., Szkody, P., Gansicke, B. T., 2002, ApJ, 574, 937
  * [19] Sion, E. M., Szkody, P., Gaensicke, B., Cheng, F. H., La Dous, C., Hassall, B., 2001, ApJ, 555, 834
  * [20] Timar, A., 2016, Journal of the American Association of Variable Star Observers, 44, 3
  * [21] Tody, D. 1993, ASP Conf., 52, 173.
  * [22] Wood, J. H., Horne, K., Berriman, G., & Wade, R. A. 1989, ApJ, 341, 974
  * [23] Zamanov, R. K., Boeva, S., Latev, G. Y., Marti, J., Boneva, D., Spassov, B., Nikolov, Y., Bode, M. F., Tsvetkova, S. V., Stoyanov, K. A., 2018, MNRAS, 480, 1363
  * [24] Zamanov, R. K., Boeva, S., Stoyanov, K. A., Latev, G., Spassov, B., Kurtenkov, A., Nikolov, G., 2020, AN, 341, 430
  * [25] Zhang, E.-H., & Robinson, E. L. 1987, ApJ, 321, 813

Appendix

Figure 3: A sketch representing the dwarf nova RX And. The mass donor is a K5V
star filling its Roche lobe. A stream of matter from the mass donor is feeding
the accretion disc around the white dwarf.