# Radiogalaxies in the Sloan Digital Sky Survey: spectral index-environment
correlations

Carlos G. Bornancini1,2, Ana Laura O’Mill1,2, Sebastián Gurovich1,2 and Diego
García Lambas1,2
1Instituto de Astronomía Teórica y Experimental, IATE, Observatorio
Astronómico, Universidad Nacional de Córdoba,
Laprida 854, X5000BGR, Córdoba, Argentina.
2Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Avenida
Rivadavia 1917, C1033AAJ, Buenos Aires, Argentina.

###### Abstract

We analyze optical and radio properties of radiogalaxies detected in the Sloan
Digital Sky Survey (SDSS). The sample of radio sources are selected from the
catalogue of Kimball & Ivezić (2008) with flux densities at 325, 1400 and 4850
MHz, using WENSS, NVSS and GB6 radio surveys and from flux measurements at 74
MHz taken from VLA Low-frequency Sky Survey (Cohen et al., 2006). We study
radiogalaxy spectral properties using radio colour-colour diagrams and find
that our sample follows a single power law from 74 to 4850 MHz. The spectral
index vs. spectroscopic redshift relation ($\alpha-z$) is not significant for
our sample of radio sources. We analyze a subsample of radio sources
associated with clusters of galaxies identified from the maxBCG catalogue and
find that about 40% of radio sources with ultra steep spectra (USS,
$\alpha<-1$, where $S_{\nu}\propto\nu^{\alpha}$) are associated with galaxy
clusters or groups of galaxies. We construct a Hubble diagram of USS radio
sources in the optical $r$ band up to $z\sim 0$.8 and compare our results with
those for normal galaxies selected from different optical surveys and find
that USS radio sources are around as luminous as the central galaxies in the
maxBCG cluster sample and typically more than 4 magnitudes brighter than
normal galaxies at $z\sim 0$.3.

We study correlations between spectral index, richness and luminosity of
clusters associated with radio sources. We find that USS at low redshift are
rare, most of them reside in regions of unusually high ambient density, such
of those found in rich cluster of galaxies. Our results also suggest that
clusters of galaxies associated with steeper than the average spectra have
higher richness counts and are populated by luminous galaxies in comparison
with those environments associated to radio sources with flatter than the
average spectra. A plausible explanation for our results is that radio
emission is more pressure confined in higher gas density environments such as
those found in rich clusters of galaxies and as a consequence radio lobes in
rich galaxy clusters will expand adiabatically and lose energy via synchrotron
and inverse Compton losses, resulting in a steeper radio spectra.

###### keywords:

surveys – radio continuum: general – radio continuum: galaxies – galaxies:
high-redshift

††pubyear: 2010

##  1 Introduction

Radio sources are frequently associated with massive systems at low and high
redshifts. In the Local Universe these objects are usually identified with
evolved red ellipticals and with luminous cD galaxies located at the centres
of clusters of galaxies (West, 1994). Radio sources at high redshifts ($z\sim
4$) are identified with massive forming systems, i.e galaxies with diffuse UV
morphologies and consistent with small substructures around a dominant bright
galaxy (Miley et al., 2006).

Several works show that some distant radio sources are embedded in highly
spatially extended ionized gas nebulae of 100-200 kpc (Venemans et al., 2002;
Villar-Martín et al., 2007). These gas structures are observed in massive
ellipticals or cD galaxies at the center of nearby clusters of galaxies. This
evidence suggests that distant radio sources represent the progenitors of the
most massive galaxies observed in the Local Universe and therefore important
for the study of structure formation, such as clusters or groups of galaxies.

A high fraction of radio sources associated with clusters of galaxies have
steep radio spectra as measured by the slope between two fixed ranges of
frequencies, i.e the spectral index $\alpha$ (USS, $\alpha<-1$, where
$S_{\nu}\propto\nu^{\alpha}$, Roettgering et al. (1997); Chambers et al.
(1996); Jarvis et al. (2001)). Such a correlations between spectral index and
redshift ($\alpha-z$ relation), has been used with success to search for
distant galaxies (De Breuck et al., 2000; Jarvis et al., 2004; Cruz et al.,
2006; Broderick et al., 2007).

There are at least three main explanations given in the literature for this
phenomenon: The first is a radio k-correction. The spectral energy
distribution (SED) of radio sources is usually concave, i.e the spectral index
increases with frequency. The observed spectral index determined from two
fixed observed frequencies will therefore sample a steeper part of the radio
spectrum for sources at higher redshifts. The second is related with the
interaction between photons of the cosmic microwave background radiation (CMB)
and the relativistic electron population observed in the plasma gas of radio
sources. The energy density of the CMB increases as $(1+z)^{4}$ and hence
Inverse Compton scattering (IC) of the CMB becomes increasingly important for
sources at high redshifts (Krolik & Chen, 1991). The third is related to an
intrinsic correlation between radio luminosity and rest-frame spectral index
(Blundell & Rawlings, 1999a; Chambers et al., 1990) that due to a Malmquist
like bias in flux density limited surveys translates into a correlation
between spectral index and redshift. An alternative explanation is related
with an ambient density effect. The presence of USS radio sources residing
closest to cluster centres may be due to a manifestation of pressure-confined
radio lobes which slow adiabatic expansion of the plasma. Radio lobes will be
pressure-confined and lose energy primarily via synchrotron and IC losses
(Klamer et al., 2006).

Studies of radio sources at low and moderate redshifts ($z<0.5$) show
different environments.

Hill & Lilly (1991) find that only 50% of powerful radio sources at $z\sim
0.5$ are located in rich galaxy clusters, even though similar sources avoid
such environments at low redshifts. However, Geach et al. (2007) analyzed
radio sources in the Subaru/XMM-Newton Deep Field and found that low-power
radio galaxies at $z\sim 0.5$ reside in moderately rich groups - intermediate
environments between poor groups and rich clusters.

Prestage & Peacock (1988) investigate the local galaxy density around powerful
radio sources using the angular cross-correlation technique and find that
compact radio sources appear to lie in regions of low galaxy density.
Moreover, that complex Fanaroff-Riley class I sources are typically found in
regions of significantly enhanced galaxy density.

Allington-Smith et al. (1993) study the evolution of galaxies in radio-
selected groups at $z<0.5$ with the same range of radio power and find that
strong radio galaxies are located in a wide range of environments but not as
wide as for groups in general. At low redshifts ($z<0.1$) radio-selected
groups have the same richness and blue fraction as do optically-selected
groups. At high redshifts ($z\sim 0.4$) all groups have the same proportion of
blue galaxies.

Studying the prevalence of radio loud AGN activity in nearby groups and galaxy
clusters, selected from the SDSS catalog, Best et al. (2007) find that
brightest group and cluster galaxies are more likely to host a radio loud AGN
than other galaxies of the same stellar mass.

In this work we analyze optical and radio properties of radio sources with
steep radio spectra, and we determine the main characteristics of clusters of
galaxies associated with radio sources.

The structure of this paper is organized as follows: Section 2 describes the
optical and radio samples analyzed. We analyze radio spectral properties of
our sample in Section 3. Section 4 compares the optical and the radio
luminosities of sources associated with steep spectrum and central galaxy
clusters. In section 5, we study the Hubble diagram in the optical $r$ band
for USS sources. We study in Section 6 spectral index and richness properties
of galaxies associated with clusters of galaxies and finally, in Section 7, we
discuss our main results.

Throughout this work we assume a standard $\Lambda$CDM model Universe with
cosmological parameters, $\Omega_{M}$=0.3, $\Omega_{\Lambda}$=0.7 and a Hubble
constant of $H_{0}=$100 h km s-1Mpc-1.

##  2 Radio and optical Galaxy samples

The sample of radio sources was selected from the catalogue of Kimball &
Ivezić (2008). This catalogue presents information in radio and optical bands
taken from several surveys, including Faint Images of the Radio Sky survey
(FIRST, 1400 MHz), NRAO VLA Sky Survey (NVSS, 1400 MHz), Westerbork Northern
Sky Survey (WENSS, 325 MHz), Green Bank survey (GB6, 4850 MHz ), and the Sloan
Digital Sky Survey (SDSS) optical survey. The flux density limits for each
radio catalogue are 1, 2.5, 18 and 18 mJy for the FIRST, NVSS, GB and WENSS
surveys, respectively.

The SDSS catalogue contains flux densities of detected objects measured nearly
simultaneously in u, g, r, i, and z optical bands (Fukugita et al. 1996) with
a limiting magnitude of $r<22.2$ in an area of $\sim 10^{4}$ square degrees in
the North Galactic cap and a small region of 225 square degrees in the South
Galactic cap.

The sample of optical galaxies in the fields of radio sources were selected
using the Catalog Archive Server Jobs System (CASJOBS) interface of SDSS,
which allows one to obtain catalogues with parameters from the SDSS survey
(DR6). 111http://casjobs.sdss.org/CasJobs/.

The matching radius to correlate the radio (FIRST) and optical (SDSS) surveys
was 2$\arcsec$. We chose this matching radius in order to avoid contamination
by line of sight matches of physical unrelated objects, since Kimball & Ivezić
(2008) previously found an efficiency (fraction of matches which are
physically real) of 95% and completeness (fraction of real matches that were
found) of 98% with this matching radius. In this work we used the following
catalogue subsets: Sample D (detected by FIRST, NVSS and WENSS survey, with
63,660 sources), sample E (detected by FIRST, NVSS, WENSS, GB6 and the SDSS
survey, 4732 sources) and sample G (detected by FIRST, NVSS, WENSS and the
SDSS spectroscopic survey, 2885 sources). For all these samples Kimball &
Ivezić (2008) estimated matching efficiencies of $>80$% and completeness
limits of $>90$%, using an appropriate matching radius.

A more detailed description of the radio sample and the criteria used to merge
catalogues can be found in Kimball & Ivezić (2008).

Our sample of tracer galaxies for this work are drawn from the catalogue of
galaxies with photometric redshifts of the DR6 catalogue (Oyaizu et al.,
2008). These photometric redshifts were calculated using a Artificial Neural
Network technique and the Nearest Neighbor Error (NNE) method to estimate
photo-z errors for 77 million objects classified as galaxies in DR6 with
$r<22$. In order to study and analyze the properties of clusters of galaxies
associated with radio sources, we correlate the radio sources detected from
the FIRST, NVSS and WENSS catalogues with clusters of galaxies selected from
the maxBCG survey (Koester et al., 2007a) using a matching radius of
$10\arcsec$. The maxBCG catalogue includes 13,823 clusters selected from the
SDSS photometric data, using two well-known features of rich clusters of
galaxies: the red-sequence observed as a ridge line in the colour-magnitude
diagram (the E/S0 ridgeline) and the presence of a bright dominant central
galaxy (BCG). The catalogue includes the position, cluster photometric
redshifts, BCG spectroscopic redshifts, $r$ e $i$ total galaxy luminosities
and luminosities of the central galaxies, the cluster richness, $N_{\rm gal}$
calculated as the number of galaxies projected within 1 $h^{-1}$ Mpc, brighter
than $0.4L_{*}$ and with colours matching the E/S0 ridgeline, the cluster
richness within $R_{200}$ from the cluster center, defined as the mean density
of 200 times the mean density of the Universe (see for instance Koester et al.
(2007b)).

Figure 1: Spectral index, $\alpha_{325}^{1400}$, vs. spectroscopic redshift
from the SDSS catalogue for radio sources detected in FIRST (1.4 GHz), NVSS
(1.4 GHz), WENSS (325 MHz) and the SDSS spectroscopic catalogue with a
matching radius of 2$\arcsec$. The contours represent the 50, 70, 80 and 90%
of total objects.

##  3 Radio Properties

###  3.1 $\alpha-z$ relation

In Figure 1 we plot spectral index $\alpha_{325}^{1400}$ vs. spectroscopic
redshift for radio sources identified in the SDSS catalogue. The data were
obtained from the catalogue subset G taken from Kimball & Ivezić (2008). The
contours represent the 50, 70, 80 and 90% of total objects. We do not find a
tendency of $\alpha$ with redshift, showing that the most distant ($z>0$.5)
radio galaxies in our sample do not show steep spectra due to a k-correction
effect applied to a concave radio SED.

###  3.2 Analysis of the SED in radio frequencies

Figure 2: Radio Colour-colour diagram distributions for sources in the VLSS
(74 MHz), WENSS (325 MHz) and NVSS (1.4 GHz) samples (grey circles). Filled
circles represent measurements obtained for radio sources associated with
maxBCG clusters. The dashed line indicates the relation for radio sources
whose spectra follow a single power law from 74 to 1400 MHz.Histograms
represent the corresponding distribution of spectral index. Figure 3: Radio
Colour-colour diagram distributions for sources in the WENSS (325 MHz), NVSS
(1.4 GHz) and GB6 (4.85 GHz) samples (grey circles). Filled circles represent
measurements obtained for radio sources associated with maxBCG clusters. The
dashed lines correspond to a single power law spectra from 325 to 4850
MHz.Histograms represent the corresponding distribution of spectral index.

In order to study radiogalaxy properties we analyze radio colour-colour
diagrams. In Figure 2 we show the radio two-colour diagram which compares the
spectral index at 74-352 MHz and 352-1400 MHz. We use the CATS database of the
Special Astronomy Observatory (Verkhodanov et al., 1997) in order to obtain
flux measurements at 74 MHz taken from the VLA Low-frequency Sky Survey (VLSS)
(Cohen et al., 2006), using a matching radius of 60$\arcsec$ for the FIRST and
NVSS samples. Grey circles represent sources detected in the FIRST, NVSS and
WENSS catalogues (listed as Sample D in Kimball & Ivezić (2008)). Filled
circles represent data for radio sources associated with clusters of galaxies
identified in the maxBCG catalogue. The dashed line indicates the relation for
radio sources whose spectra follow a single power law from 74 to 1400 MHz.
Again, we do not find a clear tendency that most of radio sources show some
flattening towards low frequencies. In Figure 3 we show a similar analysis for
radio sources with radio emission in 325, 1400 and 4850 MHz, listed as Sample
E in Kimball & Ivezić (2008) (grey circles). Filled circles represent data
obtained for radio sources identified with clusters of galaxies detected in
the maxBCG catalogue. The equal number of points on either side of this line
indicate no significant spectral curvature.

##  4 Optical and radio luminosities

In order to study radio source luminosity properties at optical and radio
frequencies as well as other possible correlations, we calculated the rest-
frame radio luminosity at 1.4 GHz:

$\centering
L_{1.4}=4\pi~{}{D^{2}_{L}(z)}S_{1.4}~{}(1+z)^{-(1+\alpha)},\@add@centering$
(1)

where $D_{L}(z)$ is the luminosity distance in the adopted $\Lambda$–CDM
cosmology, $S_{1.4}$ is the observed flux density at 1.4 GHz and
$(1+z)^{-(1+\alpha)}$ is the standard k-correction term used in radio
frequencies.

In Figure 4 we show the luminosity distribution of radio sources associated
with maxBCG clusters (shaded histogram) and USS ($\alpha_{325}^{1400}<-1$)
radio sources with spectroscopic redshifts (solid line histogram). The dashed
line histogram shows the distribution for radio sources without a maxBCG
cluster association. We note the good agreement between these three
distributions, indicating that most of the radio sources associated with
central clusters of galaxies and USS sources are radio-loud
($L_{1.4GHz}>10^{23}$ W Hz-1). Several works show a correlation between
spectral index and radio luminosity (or radio power) ($e.g.,$ Blundell et al.,
1999b; Gopal-Krishna, 1988; Laing & Peacock, 1980). As can be seen, we do not
find any trend in radio luminosity and spectral index for these subsamples of
radio sources. It should be noted that the results shown in this figure are
not likely to be biased by possible luminosity selection effects in steep
spectral index sources.

To obtain absolute magnitudes in the $r$ band we use the de-reddened model
magnitudes and k-correct using the V4.1 public code of Blanton & Roweis
(2007). Figure 5 shows the distribution of absolute $r$ band magnitude for USS
radio sources (solid line histogram) and for central cluster objects in the
maxBCG catalogue (shaded line histogram). The dashed line histogram shows the
distribution obtained for radio sources associated with maxBCG clusters. As
can be seen there is only a small difference between the two samples, where
USS radio sources are marginally brighter than the central galaxies associated
with maxBCG clusters.

Figure 4: Radio luminosity distribution in 1.4 GHz. Shaded histogram
represents the luminosity distribution for maxBCG clusters detected in the
FIRST, NVSS and WENSS survey. Dashed line histogram shows the distribution for
radio sources without a maxBCG cluster association. Solid line histogram
represents the distribution for USS sources. Dashed line shows the criterion
for radio–loud radio sources ($L_{1.4GHz}>10^{23}$ W Hz-1) Figure 5: Absolute
magnitude distribution in $r$ band. Shaded histogram represents the
distribution for central galaxies in the maxBCG cluster catalogue. Solid and
dashed line histograms shows the corresponding distribution for USS sources
and for radio sources associated with clusters of galaxies identified in the
maxBCG catalogue, respectively.

##  5 Hubble diagram in the $\rm r$ band

In the last three decades the Hubble diagram in the $K-$ band ($K-z$ diagram)
has been used to detect and study distant radio galaxies. One of the first
works using the Hubble diagram was publish by Lilly & Longair  (1984) using a
sample of radio sources detected in the 3CR catalogue. The first radiogalaxy
identified at $z>3$ in fact was selected at radio frequencies as a faint
source in the $K-$band (Lilly, 1988). This technique was used in combination
with spectral index cuts and rejecting radio sources with large angular sizes
($<30\arcsec$) (De Breuck et al., 2000, 2002; Cohen et al., 2004; Cruz et al.,
2006).

In this work we perform a similar analysis in the optical $r$ band. Figure 6
shows the Hubble diagram using the $r$ band (petrosian magnitudes) vs.
spectroscopic redshift. Filled circles represent measurements obtained for USS
objects, big circles represent radio sources associated to maxBCG clusters.
Light grey circles correspond to galaxies detected in the SDSS catalogue
within the NOAO Deep Wide–Field Survey area, with photometric redshifts taken
from (Oyaizu et al., 2008). Dark grey points represent measurements of
galaxies detected in the VIMOS VLT deep survey (VVDS-DEEP) (Le Fevre et al.
2005), with spectroscopic redshift and magnitudes converted to the SDSS system
222http://www.sdss.org/dr4/algorithms/sdssUBVRITransform.html. Crosses
represent spectroscopic measurements for galaxies identified in the Hubble
Deep Field North region obtained in the ACS-GOODS survey (Cowie et al. 2004).
The solid line represent the best fit obtained for the USS source sample,
$r=(4.46\pm 0.21)\times$log10(z)$+(20.28\pm 0.16)$. As can be seen, USS radio
sources are typically more than 4 magnitudes brighter than normal galaxies at
$z\sim 0$.3. In Figure 7 we plot a similar Hubble diagram for radio sources
with spectroscopic redshift quoted in sample G from Kimball & Ivezić (2008)
(grey points). Open red triangles represent measurements obtained for maxBCG
clusters with radio emission and USS radio sources are displayed with open
squares. The solid line represents the best fit obtained for the USS source
sample. USS radio sources follow a similar distribution in comparison with
that obtained in the maxBCG cluster sample in the redshift range $0.1<z<0.3$.
We find that USS sources are typically as luminous as the central galaxies in
the maxBCG cluster sample. In the next Section, we analyze the nature of USS
sources detected at low redshifts ($z<0.1$).

Figure 6: Hubble diagram in the $r$ band vs. spectroscopic redshift taken from
the SDSS catalogue. Filled circles represent measurements obtained for USS
objects. USS radio sources identified with maxBCG clusters are displayed as
big circles. Light grey circles correspond to galaxies detected in the SDSS
catalogue in the NOAO Deep Wide–Field Survey area with photometric redshifts
taken from (Oyaizu et al., 2008). Dark grey points represent measurements of
galaxies detected in the VIMOS VLT deep survey (VVDS-DEEP) (Le Fevre et al.
2005) with spectroscopic redshift and magnitudes converted to the SDSS system.
Crosses represent spectroscopic measurements for galaxies identified in the
Hubble Deep Field North region obtained in the ACS-GOODS survey (Cowie et al.
2004). The solid line represent the best fit line obtained for the USS source
sample Figure 7: Hubble diagram in the $r$ band vs. redshift. Radio sources
with spectroscopic redshift measurements (grey points). Open red triangles
represent measurements obtained for maxBCG clusters with radio emission. USS
radio sources are displayed with open squares.

##  6 Ultra steep spectrum sources

In order to study the nature of radio sources with ultra steep spectra at low
redshifts, we select a set of galaxies detected by NVSS, FIRST, WENSS, and
SDSS with spectroscopic redshifts (catalogue subset G in Kimball & Ivezić
(2008)). We use the NED database 333http://nedwww.ipac.caltech.edu/ the NASA-
IPAC Extragalactic Database. to search for known objects present in the
literature and find that 40% of USS sources are associated with clusters or
groups of galaxies identified in the maxBCG (Koester et al., 2007a), Abell
(Abell et al., 1989), Zwicky (Zwicky & Kowal, 1968) catalogues and Northern
Sky optical Cluster Survey (NSCS, Lopes et al. (2004)) catalogues. Table 1
lists the sample of USS sources identified with galaxies with optical spectra
in the SDSS catalogue. The columns are the following: ID taken from Kimball &
Ivezić (2008), position, spectroscopic redshift, spectral index obtained
between 352MHz and 1.4 GHz, 1.4 GHz radio luminosity, $r$ band absolute
magnitude, and ID taken from literature. In Figure 14 we show a sample of
colour images of radio sources with $\alpha_{325}^{1400}<-1$. At low redshift
($z<0.1$) we find that most USS sources are associated with nearby bright
spiral galaxies or interacting systems, with a possible AGN. This may be due
to the low limiting flux density used ($S_{1400}=2.5$ mJy, from the NVSS
survey) since we note that De Breuck et al. (2000) found that they can select
against low redshift spiral galaxies among USS sources by selecting sources
with $S_{1400}>$ 10 mJy.

Some radio sources that are associated to bright red galaxies are located in
similar density environments as those found in clusters or groups of galaxies,
but do not have a cluster association in the literature. In the next Section
we analyze the galaxy density associated with these systems.

##  7 Spectral index and richness

In order to study the nature of radio sources associated to clusters of
galaxies we analyze possible correlations between spectral index, the richness
associated with each cluster and the luminosity properties of galaxies in
these environments. The spectral index ($\alpha_{325}^{1400}$) distribution
for radio sources detected in FIRST, NVSS and WENSS catalogues (listed as
Sample D) not associated with a maxBCG cluster can be seen in Figure 8 (shaded
histogram). The solid line histogram represents the corresponding spectral
index distribution for radio sources associated with maxBCG clusters. The mean
value distribution for clusters is $\overline{\alpha}_{325}^{1400}=-0.65$. We
find a tendency that most radio sources associated with maxBCG clusters have
steep radio spectra in comparison with field radio sources at similar
redshifts. This result is in agreement with Baldwin & Scott (1973) and Slingo
(1974), who also find that nearby radio sources with steep spectra reside in
rich clusters of galaxies.

Figure 8: Spectral index $\alpha_{325}^{1400}$ distribution for radio sources
without a maxBCG match (shaded histogram) and with a maxBCG cluster match
(solid lines).

In Figure 9 we plot the absolute $r$ band magnitude of central maxBCG cluster
galaxies vs. richness ($N_{\rm gal}$ ) for each cluster associated to radio
sources with steeper than average, $\alpha_{325}^{1400}<-0.65$ (filled grey
circles) and with flatter than average spectra, $\alpha_{325}^{1400}>-0.65$
(open circles), respectively. The contours represent the 90% of total objects
(grey line) for steep sources, solid line for flat sources and dashed lines
for maxBCG clusters without radio emission. We find that clusters of galaxies
associated with steep spectrum sources have brighter central galaxies and have
a high galaxy richness in comparison with clusters associated with flatter
than the average radio sources.

Figure 9: Absolute magnitude in the $r$ band of central maxBCG cluster
galaxies as a function of galaxy richness ($N_{gal}$ ). Grey circles represent
measurements for clusters associated with radio sources with
$\alpha_{325}^{1400}<-0.65$ and black circles represent clusters identified
with sources with $\alpha_{325}^{1400}>-0.65$. The contours represent the 90%
of total objects (grey line for steep sources, solid line for flat sources and
in dashed lines for maxBCG clusters without radio emission). Figure 10: Abell
richness vs. maxBCG richness $N_{gal}$ from (Koester et al., 2007a). Dashed
lines shows the corresponding Abell richness group. Solid line represents the
best fit obtained for these parameters.

In order to provide a suitable calibration to help the reader judge how Abell
richness counts relate to the $N_{\rm gal}$ values, we show in Figure 10 this
correlation using the revised northern Abell Catalog (Abell et al., 1989). As
it can be appreciated in this figure, although with a large scatter, there is
a positive correlation between these richness estimates. Abell richness class
$R=0$ clusters have commonly $N_{\rm gal}$ $\sim$ 20, while objects with
richness class 2 correspond to $N_{\rm gal}$$>$ 30.

In Figure 11 we present the distribution of richness ($N_{\rm gal}$ ) for
clusters of galaxies taken from the maxBCG catalogue calculated from the red-
sequence of the colour–magnitude diagram. We plot in solid line the richness
distribution of radio sources with $\alpha_{325}^{1400}<-0.65$. The shaded
histogram represents the distribution for radio sources with
$\alpha_{325}^{1400}>-0.65$ and the dashed line histogram the richness
distribution for maxBCG clusters without radio emission. We find a tendency
that radio sources with steeper than the average spectra are found
preferentially in higher galaxy richness environments than are radio sources
with flatter than the average spectra.

For reference, we have also indicated in this figure the mean values of
$N_{\rm gal}$ corresponding Abell richness class 0, 1, 2 and 3.

Figure 11: Galaxy richness distribution for maxBCG clusters in the WENSS–NVSS
catalogues. The solid line histogram represents the richness associated to
radio sources with $\alpha_{325}^{1400}<-0.65$ and the shaded histogram
corresponds to sources with $\alpha_{325}^{1400}>-0.65$. The dashed line
histogram shows the distribution for maxBCG clusters without radio emission.
The corresponding Abell richness class are marked at the top of the figure.
Figure 12: Total luminosity distribution for galaxies associated with maxBCG
clusters detected in the WENSS–NVSS catalogues. Solid line histogram
corresponds to radio sources with $\alpha_{325}^{1400}<-0.65$ and the shaded
histogram represents the corresponding distribution for sources with
$\alpha_{325}^{1400}>-0.65$. The dashed line histogram shows the distribution
obtained for maxBCG clusters without radio emission.

In order to compare the $N_{\rm gal}$ richness to other cluster parameters, we
note the relation $N_{\rm gal}$ and $R_{200}$ ($R_{200}$ $\sim$
$N_{gals}^{0.6}$) (See figure 7, Hansen et al., 2005)

In Figure 12 we plot the total $r$ band luminosity of galaxies for clusters of
galaxies associated with radio sources with $\alpha_{325}^{1400}<-0.65$ (solid
line histogram) and those with ($\alpha_{325}^{1400}>-0.65$) as a shaded
histogram. The dashed line histogram represents the distribution obtained for
maxBCG clusters without radio emission. We find that radio sources with
steeper than average spectra in central clusters of galaxies are populated by
luminous galaxies in comparison with radio sources with flatter than average
spectra. In contrast clusters of galaxies without radio emission have a lower
distribution of total galaxy luminosity.

In a similar way, we analyze the density of galaxies associated with different
types of radio sources. In Figure 13 left panel, we show the projected galaxy
density using the 5th nearest neighbour in the plane of sky ($\Sigma_{5}$,
O’Mill et al. (2008)) as a function of spectral index for maxBCG clusters with
$0.2<z<0.3$. The dashed line shows the USS criterion. Galaxies were selected
with a range of radial velocity difference ($\Delta$V), adopting a fixed
$\Delta$V=1000 km s-1 (for $z<0.3$) and a varying $\Delta$V=1000-3000 km s-1.

Figure 13: Left panel: Logarithm of the 5th nearest neighbour local galaxy
density estimator ($\Sigma_{5}$) as a function of the spectral index for
maxBCG clusters. Dashed vertical line show the selection criterion for USS
sources. Right panel: Projected density of galaxies within $<1~{}h^{-1}$ Mpc
vs. spectral index $\alpha_{325}^{1400}$ for cluster of galaxies in the maxBCG
catalogue (filled circled). The projected density was calculated as a number
of galaxies with photometric redshifts in the range $\Delta$z=0.01 from the
BCG in the cluster in the redshift range $0.2<z<0.3$. Stars represent values
obtained for the USS sample without a maxBCG cluster association.

In Figure 13 right panel, we plot the projected density of galaxies within 1
$h^{-1}$ Mpc and with photometric redshifts in the range $\Delta$z=0.01 from
the central cluster galaxies (N1) as a function of the spectral index for
clusters in the redshift range $0.2<z<0.3$ (filled circles). Stars represent
the same values obtained for USS radio sources without a know cluster
association, from the literature. As can be seen in both plots, we found that
these USS sources inhabit environments with galaxy densities similar to those
clusters selected from the maxBCG catalogue.

##  8 Conclusions

We study optical and radio properties of radiogalaxies detected in the Sloan
Digital Sky Survey (SDSS) with flux densities of 74, 325, 1400 and 4850 MHz,
using the VLSS, WENSS, NVSS and GB6 radio catalogues. We search for a possible
empirical correlation between the spectral index and redshift, however we find
no significant trend. We analyze the functional form of the SED using colour-
colour diagrams at radio frequencies. We do not find a clear tendency of radio
sources to show flattening towards low frequencies, as expected assuming
concave curvature in the radio SED. It is well known that a narrow relation
exists between $K-$band and redshift as observed in Hubble diagrams (De Breuck
et al., 2002; Willott et al., 2003; Jarvis et al., 2001; Eales & Rawlings,
1993). In this work we construct a Hubble diagram of USS radio sources in the
optical $r$ band to $z\sim 0$.8. Despite any k-correction and possible
extinction effects, our $r$ band Hubble diagram (Figure 6) also clearly shows
a tight correlation. We find that USS radio sources are as bright as central
galaxies in the maxBCG cluster sample and are typically more than 4 magnitudes
brighter than normal galaxies at $z\sim 0$.3. We note that this result is not
entirely new, for example De Breuck et al. (2002) also find that at redshifts
$<\sim 1$ radio-loud galaxies define the luminous envelope using near infrared
$K-$band magnitudes.

Regarding the possible dependence of radio luminosity on environment, we
notice that the radio luminosity distribution of USS, radio sources in
general, and radio sources in clusters are remarkably similar (Figure 4),
indicating that USS prefer higher denstity environments, independent of radio
luminosity.These results are consistent with those by Hill & Lilly (fig. 8,
1991) who find no significant correlation in cluster richness $N_{0.5}$ and
the rest-frame 2.0 GHz radio power for a sample of radio sources with
$z<0.$5\. Similar results were obtained by Allington-Smith et al. (1993) who
find no trend of richness with radio luminosity at 408 MHz for a sample of
radiosources with $z<0.$5.

We also analyze the richness and spectral index properties of clusters of
galaxies associated with radio sources and find that 40% of USS sources
identified in the SDSS spectroscopic catalogue are associated with cluster or
groups of galaxies identified in the literature, such as in the maxBCG, Abell,
or Zwicky catalogues. We analyze the local density of galaxies around the
sample of USS sources without a know cluster association from the literature,
using the $\Sigma_{5}$ and N1 estimators and find that these USS sources have
similar galaxy densities to clusters selected from the maxBCG catalogue.

We also find that USS sources at low redshift are rare objects (99 from a
total sample of 2885 radio sources detected in the SDSS spectroscopic
catalogue). However a majority reside in regions of unusually high ambient
density, such as those regions found in rich cluster of galaxies.

Our results complement those found by De Breuck et al. (2000). These authors
define a sample of 669 USS sources selected from the WENSS, TEXAS, MRC, NVSS
and PMN radio surveys. They conclude that the majority of relative nearby
($z<\sim 0.4$) USS objects are located in galaxy clusters. They find that at
least 85% of the X-ray objects associates with USS sources are galaxy clusters
or known groups from the literature.

At lower redshifts, we find that radio sources with
$\alpha_{325}^{1400}<-0.65$, are preferentially located in galaxy cluster
environments. This result contrast with Prestage & Peacock (fig. 7, 1988)
where it is found no dependence of the spatial cross–correlation amplitude on
spectral index. We note although that this statistical analysis concerns more
the large-scale, rather than the local environment of our study.

We also find that clusters hosting radio sources with spectra steeper than the
average have a higher galaxy richness and are populated by brighter galaxies
in comparison to clusters associated to radio sources with
$\alpha_{325}^{1400}>-0.65$. A natural explanation for these correlations is
that radio emission in rich cluster of galaxies is pressure-confined in a high
gas density environment. Radio lobes in galaxy cluster environment will expand
adiabatically and lose energy via synchrotron and inverse Compton losses,
resulting in a steeper radio spectra (Klamer et al., 2006).

Figure 14: Cutout colour images of a subsample of galaxies associated with
Ultra Steep radio sources in the SDSS catalogue. The open cross indicates the
radio position taken from the FIRST survey. The ID and redshift (increasing
from left to right) are indicated above each plot. Information for the
complete sample is listed in Table 1.

Table 1. Sample of USS radio sources in the SDSS catalogue with spectroscopic
redshifts.

ID |  R.A${}^{radio}_{J2000}$ |  DEC${}^{radio}_{J2000}$ | z | $\alpha_{352}^{1400}$ |  Log($L_{1.4}$) | $M_{r}$ | ID from literature
---|---|---|---|---|---|---|---
| ${}^{h}\;\;{}^{m}\;\;\;\;{}^{s}\;\;\,$ |  °  ′  ″ |  |  |  W Hz-1 |  | Designation
608550 | 07 25 57.08 |  $+$41 23 05.13 | 0.1113 |  $-$1.40 | 23.76 |  $-$22.18 | MaxBCG J111.48808+41.38519
664059 | 07 51 31.86 |  $+$43 49 29.49 | 0.4249 |  $-$1.00 | 24.22 |  $-$22.63 | …
668611 | 07 53 32.47 |  $+$38 57 52.71 | 0.1484 |  $-$1.04 | 23.37 |  $-$21.71 | …
672034 | 07 54 57.66 |  $+$38 15 22.71 | 0.3030 |  $-$1.10 | 23.73 |  $-$20.00 | …
683214 | 07 59 49.48 |  $+$35 32 33.82 | 0.4823 |  $-$1.04 | 25.19 |  $-$22.54 | …
709796 | 08 10 54.66 |  $+$49 11 03.90 | 0.1147 |  $-$1.24 | 23.28 |  $-$22.27 | MaxBCG J122.72750+49.18436
717149 | 08 13 50.80 |  $+$39 32 32.11 | 0.2045 |  $-$1.03 | 23.90 |  $-$21.79 | MaxBCG J123.46125+39.54183
734111 | 08 20 32.39 |  $+$30 34 48.65 | 0.3628 |  $-$1.04 | 25.98 |  $-$21.97 | …
735423 | 08 21 03.64 |  $+$52 44 35.82 | 0.4441 |  $-$1.38 | 25.08 |  $-$22.79 | …
748224 | 08 26 00.38 |  $+$40 58 51.75 | 0.0576 |  $-$1.11 | 22.78 |  $-$22.79 | SDSS-C4-DR3 3247
780016 | 08 38 23.27 |  $+$29 45 21.67 | 0.1068 |  $-$1.06 | 22.68 |  $-$22.00 | SHK 182 GGroup
794634 | 08 43 59.18 |  $+$51 05 25.55 | 0.1264 |  $-$1.12 | 24.37 |  $-$22.63 | …
801800 | 08 46 37.85 |  $+$51 27 16.56 | 0.1800 |  $-$1.27 | 23.88 |  $-$21.71 | MaxBCG J131.65796+51.45436
814626 | 08 51 17.29 |  $+$37 04 29.00 | 0.2207 |  $-$1.00 | 24.11 |  $-$20.32 | …
837935 | 08 59 57.32 |  $+$56 47 12.15 | 0.1833 |  $-$1.06 | 23.71 |  $-$22.11 | …
838957 | 09 00 20.28 |  $+$52 29 39.73 | 0.0302 |  $-$1.02 | 22.01 |  $-$24.49 | CGCG 264-047
842071 | 09 01 30.10 |  $+$55 39 16.42 | 0.1155 |  $-$1.80 | 23.81 |  $-$22.75 | MaxBCG J135.37558+55.65463
846087 | 09 03 00.14 |  $+$35 27 04.82 | 0.3488 |  $-$1.01 | 25.53 |  $-$21.09 | …
848084 | 09 03 44.85 |  $+$41 38 19.31 | 0.2189 |  $-$1.01 | 24.42 |  $-$21.42 | MaxBCG J135.93682+41.63908
932725 | 09 34 42.25 |  $+$35 14 16.48 | 0.4618 |  $-$1.15 | 24.31 |  $-$22.62 | …
940538 | 09 37 37.11 |  $+$37 05 35.37 | 0.4492 |  $-$1.01 | 25.24 |  $-$22.53 | …
955678 | 09 43 09.29 |  $+$29 50 18.31 | 0.2969 |  $-$1.05 | 24.42 |  $-$18.71 | …
981931 | 09 52 49.14 |  $+$51 53 04.99 | 0.2151 |  $-$1.77 | 24.08 |  $-$22.49 | ZwCl 0949.6+5207
989139 | 09 55 29.87 |  $+$60 23 17.47 | 0.1989 |  $-$1.55 | 23.82 |  $-$22.03 | MaxBCG J148.87452+60.38814
1002970 | 10 00 31.01 |  $+$44 08 42.94 | 0.1533 |  $-$1.44 | 23.16 |  $-$21.32 | RBS 0819
1027752 | 10 09 28.28 |  $+$46 17 37.17 | 0.3858 |  $-$1.04 | 24.29 |  $-$19.86 |
1051000 | 10 17 58.13 |  $+$37 10 54.02 | 0.0442 |  $-$1.16 | 22.04 |  $-$22.34 | CGCG 183-009
1075981 | 10 27 09.98 |  $+$39 08 06.04 | 0.3378 |  $-$1.02 | 24.93 |  $-$23.20 | …
1080596 | 10 28 54.68 |  $+$48 09 38.20 | 0.4851 |  $-$1.45 | 24.99 |  $-$22.19 | …
1109542 | 10 39 32.11 |  $+$46 12 05.54 | 0.1864 |  $-$1.21 | 24.85 |  $-$21.92 | …
1128337 | 10 46 25.51 |  $+$59 37 37.59 | 0.2282 |  $-$1.07 | 23.56 |  $-$22.91 | MaxBCG J161.60635+59.62690
1138526 | 10 50 10.03 |  $+$32 22 05.09 | 0.1150 |  $-$1.33 | 23.01 |  $-$21.94 | NSCS J105005+322256 /CLtr
1160615 | 10 58 19.46 |  $+$41 03 40.76 | 0.1299 |  $-$1.07 | 23.41 |  $-$22.44 | MaxBCG J164.58100+41.06140
1177112 | 11 04 33.11 |  $+$46 42 25.96 | 0.1410 |  $-$1.82 | 23.45 |  $-$21.08 | …
1179743 | 11 05 30.73 |  $+$31 14 36.74 | 0.4381 |  $-$1.43 | 24.12 |  $-$21.34 | …
1216462 | 11 18 45.25 |  $+$52 16 00.95 | 0.4309 |  $-$1.24 | 24.60 |  $-$22.18 | …
1228632 | 11 23 22.90 |  $+$47 55 14.34 | 0.1262 |  $-$1.03 | 22.91 |  $-$21.08 | …
1233822 | 11 25 16.31 |  $+$42 29 10.97 | 0.1882 |  $-$1.02 | 24.12 |  $-$23.00 | ABELL 1253
1239404 | 11 27 18.46 |  $+$53 02 21.12 | 0.3236 |  $-$1.04 | 24.49 |  $-$23.56 | …
1244341 | 11 29 01.60 |  $+$32 45 50.65 | 0.5759 |  $-$1.10 | 25.02 |  $-$22.24 | …
1250737 | 11 31 20.94 |  $+$33 34 46.95 | 0.2219 |  $-$1.61 | 23.72 |  $-$22.26 | MaxBCG J172.83707+33.57975
1260844 | 11 34 57.39 |  $+$53 46 24.20 | 0.1695 |  $-$1.05 | 23.24 |  $-$21.52 | …
1262111 | 11 35 26.68 |  $+$31 53 33.14 | 0.2310 |  $-$1.05 | 24.71 |  $-$22.67 | MACS J1135.4+3153
1268493 | 11 37 50.23 |  $+$46 36 33.65 | 0.3151 |  $-$1.03 | 24.72 |  $-$23.08 | …
1286560 | 11 44 27.21 |  $+$37 08 32.42 | 0.1148 |  $-$1.56 | 23.55 |  $-$21.11 | …
1294316 | 11 47 12.35 |  $+$38 19 26.32 | 0.5977 |  $-$1.01 | 25.34 |  $-$22.11 | …
1304138 | 11 50 49.21 |  $+$62 19 49.04 | 0.3453 |  $-$1.69 | 24.37 |  $-$23.04 | …
1307368 | 11 51 58.63 |  $+$31 40 32.05 | 0.5079 |  $-$1.04 | 25.69 |  $-$23.39 | …
1307436 | 11 52 00.09 |  $+$33 13 42.49 | 0.3573 |  $-$1.48 | 23.97 |  $-$23.15 | …

Table 1.

ID |  R.A${}^{radio}_{J2000}$ |  DEC${}^{radio}_{J2000}$ | z | $\alpha_{352}^{1400}$ |  Log($L_{1.4}$) | $M_{r}$ | ID from literature
---|---|---|---|---|---|---|---
| ${}^{h}\;\;{}^{m}\;\;\;\;{}^{s}\;\;\,$ |  °  ′  ″ |  |  |  W Hz-1 |  | Designation
1309157 | 11 52 36.33 |  $+$37 32 43.86 | 0.2294 |  $-$1.19 | 24.22 |  $-$20.23 | MaxBCG J178.15191+37.54548
1319027 | 11 56 05.51 |  $+$34 33 05.33 | 0.2536 |  $-$1.10 | 25.05 |  $-$21.83 | [EAD2007] 200 Arcs
1326519 | 11 58 48.07 |  $+$57 17 19.11 | 0.2598 |  $-$1.04 | 25.12 |  $-$24.49 | …
1348701 | 12 06 47.88 |  $+$51 57 10.95 | 0.3446 |  $-$1.28 | 24.66 |  $-$21.51 | …
1351855 | 12 08 00.78 |  $+$43 39 19.12 | 0.2657 |  $-$1.00 | 24.77 |  $-$22.57 | MaxBCG J182.00318+43.65537
1353531 | 12 08 37.16 |  $+$61 21 06.52 | 0.2748 |  $-$1.48 | 23.96 |  $-$22.17 | …
1354974 | 12 09 08.84 |  $+$44 00 11.30 | 0.0376 |  $-$1.12 | 22.12 |  $-$22.98 | NGC4135, (G. group)
1362044 | 12 11 46.22 |  $+$32 38 38.16 | 0.6115 |  $-$1.07 | 24.94 |  $-$22.25 | …
1406400 | 12 28 02.17 |  $+$34 40 40.12 | 0.2775 |  $-$1.40 | 23.81 |  $-$22.53 | MaxBCG J187.00902+34.67753
1439302 | 12 40 04.88 |  $+$37 44 15.46 | 0.1879 |  $-$1.15 | 23.75 |  $-$21.53 | NSC J124001+374544
1468909 | 12 51 07.51 |  $+$56 25 44.98 | 0.2008 |  $-$1.22 | 23.42 |  $-$21.73 | …
1505383 | 13 04 31.36 |  $+$51 43 42.64 | 0.2757 |  $-$1.56 | 24.43 |  $-$22.28 | MaxBCG J196.15441+51.71551
1510127 | 13 06 12.17 |  $+$51 44 06.94 | 0.2773 |  $-$1.16 | 24.55 |  $-$22.54 | MaxBCG J196.55069+51.73530
1532575 | 13 14 18.32 |  $+$41 24 30.18 | 0.1987 |  $-$1.05 | 23.25 |  $-$20.90 | MaxBCG J198.57609+41.40825
1547051 | 13 19 38.92 |  $+$61 39 11.68 | 0.1333 |  $-$1.21 | 23.49 |  $-$22.47 | …
1559285 | 13 24 12.38 |  $+$31 17 24.33 | 0.4268 |  $-$1.19 | 24.63 |  $-$22.47 | …
1604023 | 13 40 32.89 |  $+$40 17 38.79 | 0.1719 |  $-$1.17 | 23.32 |  $-$22.35 | RX J1340.5+4017 GGroup
1607910 | 13 41 59.68 |  $+$42 21 32.32 | 0.4261 |  $-$1.22 | 24.07 |  $-$22.75 | …
1627288 | 13 49 03.74 |  $+$30 52 27.51 | 0.0814 |  $-$1.13 | 22.53 |  $-$19.43 | …
1628350 | 13 49 27.88 |  $+$46 20 15.29 | 0.4212 |  $-$1.14 | 24.17 |  $-$14.98 | …
1673236 | 14 06 03.34 |  $+$52 09 51.98 | 0.4823 |  $-$1.01 | 24.75 |  $-$23.38 | …
1707796 | 14 18 37.62 |  $+$37 46 22.63 | 0.1349 |  $-$1.34 | 23.37 |  $-$21.87 | ABELL 1896
1714152 | 14 20 56.84 |  $+$53 13 07.25 | 0.7430 |  $-$1.05 | 25.29 |  $-$23.57 | …
1714768 | 14 21 10.18 |  $+$42 09 12.97 | 0.3529 |  $-$1.12 | 24.03 |  $-$20.99 | NSCS J142115+420743
1735168 | 14 28 41.23 |  $+$43 41 34.03 | 0.2136 |  $-$1.04 | 23.70 |  $-$22.42 | NSCS J142842+434009
1735918 | 14 28 57.67 |  $+$54 36 27.65 | 0.3819 |  $-$1.50 | 24.39 |  $-$21.60 |
1744373 | 14 32 04.05 |  $+$46 37 43.79 | 0.0927 |  $-$1.03 | 22.65 |  $-$19.72 | NSC J143143+463738
1755382 | 14 36 02.53 |  $+$33 07 53.79 | 0.0939 |  $-$1.02 | 22.80 |  $-$20.51 | …
1756038 | 14 36 19.44 |  $+$48 32 10.68 | 0.1912 |  $-$1.07 | 24.03 |  $-$21.62 | …
1759889 | 14 37 42.41 |  $+$39 27 45.12 | 0.2455 |  $-$1.36 | 24.35 |  $-$21.94 | MaxBCG J219.42655+39.46313
1768885 | 14 40 57.03 |  $+$46 36 46.91 | 0.8395 |  $-$1.12 | 25.35 |  $-$19.00 | …
1775379 | 14 43 17.07 |  $+$46 43 48.40 | 0.2424 |  $-$1.34 | 23.68 |  $-$21.83 | …
1793973 | 14 50 03.51 |  $+$31 30 15.02 | 0.2746 |  $-$1.10 | 24.25 |  $-$21.95 | MaxBCG J222.55394+31.49750
1795282 | 14 50 31.54 |  $+$32 53 03.73 | 0.1775 |  $-$1.38 | 23.45 |  $-$21.67 | …
1830754 | 15 03 23.78 |  $+$46 06 16.28 | 0.4269 |  $-$1.06 | 24.19 |  $-$22.74 | …
1836180 | 15 05 23.43 |  $+$47 06 25.59 | 0.2615 |  $-$1.63 | 23.90 |  $-$22.52 | ABELL 2024
1837171 | 15 05 46.23 |  $+$54 54 01.56 | 0.2824 |  $-$1.24 | 24.49 |  $-$22.69 | …
1838173 | 15 06 08.41 |  $+$60 02 16.86 | 0.5196 |  $-$1.03 | 24.72 |  $-$24.11 | …
1862173 | 15 15 05.54 |  $+$43 09 01.38 | 0.0177 |  $-$1.14 | 21.11 |  $-$23.69 | CGCG 221-045
1929427 | 15 39 50.77 |  $+$30 43 03.90 | 0.0971 |  $-$1.18 | 23.10 |  $-$22.36 | MaxBCG J234.96158+30.71777
1932815 | 15 41 05.46 |  $+$32 04 50.85 | 0.0529 |  $-$1.06 | 22.51 |  $-$20.79 | …
1934628 | 15 41 46.53 |  $+$45 56 14.29 | 0.2024 |  $-$1.08 | 24.31 |  $-$21.37 | …
1958800 | 15 50 51.44 |  $+$42 02 30.47 | 0.0334 |  $-$1.09 | 21.91 |  $-$20.61 | …
1963482 | 15 52 41.11 |  $+$37 24 34.16 | 0.3710 |  $-$1.92 | 24.23 |  $-$23.69 | …
1967858 | 15 54 23.54 |  $+$48 41 07.36 | 0.2271 |  $-$1.04 | 23.93 |  $-$22.32 | MaxBCG J238.59817+48.68496
2001242 | 16 07 25.43 |  $+$47 50 24.15 | 0.3282 |  $-$1.02 | 24.76 |  $-$22.54 | ABELL 2157
2064005 | 16 33 10.92 |  $+$36 07 35.15 | 0.1648 |  $-$1.02 | 23.93 |  $-$21.42 | MaxBCG J248.29532+36.12611
2088195 | 16 43 26.82 |  $+$39 30 39.92 | 0.4119 |  $-$1.05 | 24.72 |  $-$22.15 | …
2122675 | 16 59 01.01 |  $+$32 29 38.93 | 0.0627 |  $-$1.26 | 23.82 |  $-$21.61 | ABELL 2241
2134416 | 17 04 26.40 |  $+$39 10 12.25 | 0.1283 |  $-$1.01 | 23.23 |  $-$21.34 | NSC J170432+390956

##  9 Acknowledgments

We are grateful to the anonymous referee for his/her careful reading of the
manuscript and a number of comments, which improved the paper. This work was
partially supported by the Consejo Nacional de Investigaciones Científicas y
Técnicas (CONICET),the Secretaría de Ciencia y Técnica de la Universidad
Nacional de Córdoba . The authors made use of the database CATS (Verkhodanov
et al. 1997) of the Special Astrophysical Observatory and the NASA/IPAC
extragalactic database (NED) which is operated by the Jet Propulsion
Laboratory, Caltech, under contract with the National Aeronautics and Space
Administration. This publication makes use of data products from the Sloan
Digital Sky Survey (SDSS). Funding for the SDSS and SDSS-VI has been provided
by the Alfred P. Sloan Foundation, the Participating Institutions, the
National Science Foundation, the U.S. Department of Energy, the National
Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max
Planck Society, and the Higher Education Funding Council for England. The SDSS
Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical
Research Consortium for the Participating Institutions. The Participating
Institutions are the American Museum of Natural History, Astrophysical
Institute Potsdam, University of Basel, University of Cambridge, Case Western
Reserve University, University of Chicago, Drexel University, Fermilab, the
Institute for Advanced Study, the Japan Participation Group, Johns Hopkins
University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute
for Particle Astrophysics and Cosmology, the Korean Scientist Group, the
Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-
Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for
Astrophysics (MPA), New Mexico State University, Ohio State University,
University of Pittsburgh, University of Portsmouth, Princeton University, the
United States Naval Observatory, and the University of Washington.

## References

  * Allington-Smith et al. (1993) Allington-Smith, J. R., Ellis, R., Zirbel, E. L., & Oemler, A. J. 1993, ApJ, 404, 521
  * Abell et al. (1989) Abell, G. O., Corwin, H. G., Jr., & Olowin, R. P. 1989, ApJS, 70, 1
  * Baldwin & Scott (1973) Baldwin, J. E., & Scott, P. F. 1973, MNRAS, 165, 259
  * Best et al. (2007) Best, P. N., von der Linden, A., Kauffmann, G., Heckman, T. M., & Kaiser, C. R. 2007, MNRAS, 379, 894
  * Blanton & Roweis (2007) Blanton, M. R., & Roweis, S. 2007, AJ, 133, 734
  * Blundell & Rawlings (1999a) Blundell, K. M., & Rawlings, S. 1999, Nature, 399, 330
  * Blundell et al. (1999b) Blundell, K. M., Rawlings, S., & Willott, C. J. 1999, AJ, 117, 677
  * Broderick et al. (2007) Broderick, J. W., Bryant, J. J., Hunstead, R. W., Sadler, E. M., & Murphy, T. 2007, MNRAS, 381, 341
  * Chambers et al. (1990) Chambers, K. C., Miley, G. K., & van Breugel, W. J. M. 1990, ApJ, 363, 21
  * Chambers et al. (1996) Chambers, K. C., Miley, G. K., van Breugel, W. J. M., & Huang, J.-S. 1996, ApJS, 106, 215
  * Cohen et al. (2004) Cohen, A. S., Röttgering, H. J. A., Jarvis, M. J., Kassim, N. E., & Lazio, T. J. W. 2004, ApJS, 150, 417
  * Cohen et al. (2006) Cohen, A. S., Lane, W. M., Kassim, N. E., Lazio, T. J. W., Cotton, W. D., Perley, R. A., Condon, J. J., & Erickson, W. C. 2006, Astronomische Nachrichten, 327, 262
  * Cowie et al. (2004) Cowie, L. L., Barger, A. J., Hu, E. M., Capak, P., & Songaila, A. 2004, AJ, 127, 3137
  * Cruz et al. (2006) Cruz, M. J., et al. 2006, MNRAS, 373, 1531
  * De Breuck et al. (2000) De Breuck, C., van Breugel, W., Röttgering, H. J. A., & Miley, G. 2000, A&AS, 143, 303
  * De Breuck et al. (2002) De Breuck, C., van Breugel, W., Stanford, S. A., Röttgering, H., Miley, G., & Stern, D. 2002, AJ, 123, 637
  * Eales & Rawlings (1993) Eales, S. A., & Rawlings, S. 1993, ApJ, 411, 67
  * Fukugita et al. (1996) Fukugita, M., Ichikawa, T., Gunn, J. E., Doi, M., Shimasaku, K., & Schneider, D. P. 1996, AJ, 111, 1748
  * Geach et al. (2007) Geach, J. E., Simpson, C., Rawlings, S., Read, A. M., & Watson, M. 2007, MNRAS, 381, 1369
  * Gopal-Krishna (1988) Gopal-Krishna 1988, A&A, 192, 37
  * Hansen et al. (2005) Hansen, S. M., McKay, T. A., Wechsler, R. H., Annis, J., Sheldon, E. S., & Kimball, A. 2005, ApJ, 633, 122
  * Hill & Lilly (1991) Hill, G. J., & Lilly, S. J. 1991, ApJ, 367, 1
  * Intema et al. (2006) Intema, H. T., Venemans, B. P., Kurk, J. D., Ouchi, M., Kodama, T., Röttgering, H. J. A., Miley, G. K., & Overzier, R. A. 2006, A&A, 456, 433
  * Jarvis et al. (2001) Jarvis, M. J., Rawlings, S., Eales, S., Blundell, K. M., Bunker, A. J., Croft, S., McLure, R. J., & Willott, C. J. 2001, MNRAS, 326, 1585
  * Jarvis et al. (2004) Jarvis, M. J., Cruz, M. J., Cohen, A. S., Röttgering, H. J. A., & Kassim, N. E. 2004, MNRAS, 355, 20
  * Kajisawa et al. (2006) Kajisawa, M., Kodama, T., Tanaka, I., Yamada, T., & Bower, R. 2006, MNRAS, 371, 577
  * Kimball & Ivezić (2008) Kimball, A. E., & Ivezić, 2008, AJ, 136, 684
  * Klamer et al. (2006) Klamer, I. J., Ekers, R. D., Bryant, J. J., Hunstead, R. W., Sadler, E. M., & De Breuck, C. 2006, MNRAS, 371, 852
  * Koester et al. (2007a) Koester, B. P., et al. 2007a, ApJ, 660, 239
  * Koester et al. (2007b) Koester, B. P., et al. 2007b, ApJ, 660, 221
  * Krolik & Chen (1991) Krolik, J. H., & Chen, W. 1991, AJ, 102, 1659
  * Kurk et al. (2004a) Kurk, J. D., Pentericci, L., Röttgering, H. J. A., & Miley, G. K. 2004a, A&A, 428, 793
  * Kurk et al. (2004b) Kurk, J. D., Pentericci, L., Overzier, R. A., Röttgering, H. J. A., & Miley, G. K. 2004b, A&A, 428, 817
  * Laing & Peacock (1980) Laing, R. A., & Peacock, J. A. 1980, MNRAS, 190, 903
  * Le Fèvre et al. (2005) Le Fèvre, O., et al. 2005, A&A, 439, 845
  * Lilly & Longair (1984) Lilly S.J., Longair M.S., 1984, MNRAS, 211, 833
  * Lilly (1988) Lilly, S. J. 1988, ApJ, 333, 161
  * Lopes et al. (2004) Lopes, P. A. A., de Carvalho, R. R., Gal, R. R., Djorgovski, S. G., Odewahn, S. C., Mahabal, A. A., & Brunner, R. J. 2004, AJ, 128, 1017
  * Miley et al. (2004) Miley, G. K., et al. 2004, Nature, 427, 47
  * Miley et al. (2006) Miley, G. K., et al. 2006, ApJ, 650, L29
  * O’Mill et al. (2008) O’Mill, A. L., Padilla, N., & Lambas, D. G. 2008, MNRAS, 389, 1763
  * Overzier et al. (2006) Overzier, R. A., et al. 2006, ApJ, 637, 58
  * Oyaizu et al. (2008) Oyaizu, H., Lima, M., Cunha, C. E., Lin, H., Frieman, J., & Sheldon, E. S. 2008, ApJ, 674, 768
  * Prestage & Peacock (1988) Prestage, R. M., & Peacock, J. A. 1988, MNRAS, 230, 131
  * Roettgering et al. (1997) Roettgering, H. J. A., van Ojik, R., Miley, G. K., Chambers, K. C., van Breugel, W. J. M., & de Koff, S. 1997, A&A, 326, 505
  * Slingo (1974) Slingo, A. 1974, MNRAS, 168, 307
  * Venemans et al. (2002) Venemans, B. P., et al. 2002, ApJ, 569, L11
  * Venemans et al. (2007) Venemans, B. P., et al. 2007, A&A, 461, 823
  * Verkhodanov et al. (1997) Verkhodanov, O. V., Trushkin, S. A., & Chernenkov, V. N. 1997, Baltic Astronomy, 6, 275
  * Villar-Martín et al. (2007) Villar-Martín, M., Sánchez, S. F., Humphrey, A., Dijkstra, M., di Serego Alighieri, S., De Breuck, C., & González Delgado, R. 2007, MNRAS, 378, 416
  * West (1994) West, M. J. 1994, MNRAS, 268, 79
  * Willott et al. (2003) Willott, C. J., Rawlings, S., Jarvis, M. J., & Blundell, K. M. 2003, MNRAS, 339, 173
  * Zwicky & Kowal (1968) Zwicky, F., & Kowal, C. T. 1968, ”Catalogue of Galaxies and of Clusters of Galaxies”, 1968, Volume VI Pasadena: California Institute of Technology, CGCG6,


11institutetext:  Department of Astrophysics/IMAPP, Radboud University,
P.O.Box 9010, 6500 GL Nijmegen, The Netherlands
11email<EMAIL_ADDRESS>22institutetext: South African Astronomical
Observatory, PO Box 9, Observatory, 7935, Cape Town, South Africa
33institutetext: Department of Astronomy, University of Cape Town, Private Bag
X3, Rondebosch, 7701, South Africa

# Satellite shadows through stellar occultations

Paul J. Groot 112233

(Received month day, year; accepted month day, year)

###### Abstract

Aims.  The impact of mega-constellations of satellites in low-Earth orbit
during nighttime optical observations is assessed.

Methods. Orbital geometry is used to calculate the impact of stellar
occultations by satellites on the photometry of individual stars as well as
the effect on the photometric calibration of wide-field observations.

Results. Starlink-type satellites will have occultation disks several
arcseconds across. Together with occultation crossing times of 0.1–100 msec,
this will lead to photometric ‘jitter’ on the flux determination of stars. The
level of impact for a given star depends on the ratio of the integration time
of the frame over the occultation crossing time. In current-day CCD-based
synoptic surveys, this impact is negligible ($<<1\%$), but with future CMOS-
based wide-field surveys obtaining data at frequencies $>$1Hz, the impact will
grow towards complete dropouts. At integration times similar to the
occultation crossing time, the orbit of a satellite can be traced using the
occultation method. At even shorter integration times, the shape of the
occulting satellite can be deduced.

Conclusions. Stellar occultations by passing satellites, enabled by high-speed
CMOS technology, will be a new method for studying orbiting satellites. Large-
scale monitoring programs will be needed to independently determine and update
the orbits of satellites.

###### Key Words.:

Methods: observational – space vehicles – surveys – occultations

##  1 Introduction

As mega-constellations of man-made satellites are being launched, their impact
on astronomy needs to be assessed. The aspect of pollution in the optical and
radio bands has been greatly emphasised (e.g. Witze 2019; Gallozzi et al.
2020). In the optical, this pollution is mostly restricted to the twilight
hours of the night when the satellites still catch sunlight while night has
already descended on the ground-based telescopes (see e.g. Bassa et al. 2022;
Mróz et al. 2022; Tregloan-Reed et al. 2021; Mallama 2021; Tyson et al. 2020;
Hainaut & Williams 2020; McDowell 2020). However, the effect of satellite
constellations on optical ground-based observations is not limited to the
twilight hours. During the night, satellites will cause occultations of stars
located along their path. As both the occulter (the satellite) and the
occulted object (the star) are above the Earth’s atmosphere, the occultation
will be complete as the angular diameter of the satellite ($\theta_{s}$) will
be much larger than that of the background star ($\theta_{\star}$).

In Sect. 2 we revisit the basic geometries involved. In Sect. 3 we overview
various current and upcoming satellite constellations. In Sect. 4 we apply the
analysis to a number of satellite types, and in Sect. 5 we revisit the
question on how feasible it is to discover and characterise satellites through
optical observations of stellar occultations.

##  2 Geometry

Throughout this exercise we make two simplifying assumptions. First, we assume
a satellite has a circular shape as seen from any observatory on Earth,
characterised by a satellite radius, $R_{s}$, over which area the satellite is
completely opaque. Secondly, we assume the path of the satellite to be on a
great circle passing through the zenith.

The assumed geometry is that of a satellite circling the Earth (with radius,
$R_{\oplus}$, taken as 6378 km) at an orbital altitude $h$. With an Earth
mass, $M_{\oplus}$, taken as 5.976$\times$1024 kg, the orbital period, $P$,
follows from Kepler’s laws as

$P=\sqrt{\frac{4\pi^{2}a_{s}^{3}}{GM_{\oplus}}}=2\pi\sqrt{\frac{a_{s}^{3}}{GM_{\oplus}}},$
(1)

with $a_{s}$ = $R_{\oplus}+h$, the radius of the satellite’s orbit from the
centre of the Earth, and $G$ Newton’s gravitational constant.

The tangential velocity of a satellite passing overhead, ignoring the Earth’s
rotation, is given by

$v_{s}=\frac{2\pi a_{s}}{P}=\sqrt{\frac{GM_{\oplus}}{a_{s}}}.$ (2)

The satellite will produce an occultation disk ($\theta_{s}$) with an angular
diameter of

$\theta_{s}={\rm atan}{(\frac{2R_{s}}{h})}\simeq\frac{2R_{s}}{h},$ (3)

where the approximation is justified for the small angles involved. The
angular diameter of a satellite is, in all practical cases, much larger than
the angular diameter ($\theta_{\star}$) of a background star
($\theta_{\star}<<10\,$ mas). The occultation will therefore be complete, and
the duration is set by the rate of motion of the satellite. To first order,
the crossing time, $\tau_{s}$, is the time it takes the satellite to move its
own size as it passes through the zenith, that is,

$\tau_{s}=\frac{2R_{s}}{v_{s}},$ (4)

where $v_{s}$ is the orbital velocity of the satellite. It is the crossing
time, $\tau_{s}$, that needs to be compared to the typical integration time in
synoptic surveys to assess the impact of a stellar occultation by a satellite.

The size of the satellite’s shadow on Earth is equal to the size of the
satellite, as stars can be taken to be infinitely far away. Hence, if the
aperture, $D$, of the telescope is larger than the size of the satellite
($D>2R_{s}$), the occultation will not be total and the ingress and egress
duration of the occultation will be flattened. This sets an upper limit to the
size of the telescope used if one aims to detect a total occultation.

##  3 Shadows by satellite constellations

Most satellites can be grouped into a small number of orbits: low-Earth orbit
(LEO), at altitudes $h$=350-500 km; the global positioning system (GPS)
medium-Earth orbit (MEO) belt at $h\sim$20 000 km; and geostationary (GEO)
satellites at $h$=36 000 km. The sizes of satellites vary strongly, from
CubeSats with $R_{s}\sim 0.5$m, to Starlink-type satellites with $R_{s}\sim
5$m, to larger, but rarer, satellites such as the KeyHole Hubble-type
satellites with $R_{s}\sim 15$m and the Orion/Mentor radio dishes ($R_{s}\sim
100$m) in GEO orbits.

In Table 1 we list the relevant occultation disks and crossing times for the
categories listed above. Figure 1 shows the crossing times as a function of
orbital altitude and size of the satellite. Figure 1 shows that, for feasible
satellite sizes, the crossing times are generally $\mathrel{\hbox{\hbox
to0.0pt{\lower 2.36806pt\hbox{$\sim$}\hss} \kern-3.00003pt\raise
1.72218pt\hbox{$<$}}}$100 msec. Although this appears low, we highlight the
impact of this in Sect. 4.

Table 1: Overview of orbital altitudes ($h$), sizes ($R_{s}$), angular diameters ($\theta_{s}$), speeds ($\omega_{s}$), and crossing times ($\tau_{s}$) of satellite categories  Orbit/Class | $h$ | $R_{s}$ | $\theta_{s}$ | $v_{s}$ | $\tau_{s}$
---|---|---|---|---|---
| [km] | [m] | [″] | [km/s] | [msec]
LEO ‘CubeSat’ | 400 | 0.5 | 0.5 | 7.67 | 0.13
LEO ‘Starlink’ | 400 | 5 | 5.2 | 7.67 | 1.30
LEO ‘KeyHole’ | 400 | 15 | 15.5 | 7.67 | 3.91
GPS ‘Galileo’ | 20 000 | 2 | 0.04 | 3.89 | 1.02
GEO ‘Orion’ | 36 000 | 100 | 1.14 | 3.06 | 65.2
Figure 1: Shadow crossing time as a function of orbital altitude of a
satellite around Earth, for various satellite sizes. Indicated are
representative classes of satellites in LEO, MEO, and GEO orbits.

##  4 Impact on ground-based astronomy

Mega-constellations of satellites are of major concern to ground-based
astronomy. With more than 40 000 satellites planned to be launched over the
next few years, ground-based astronomy will face the situation that there will
be one to several satellites at any moment per square degree of sky (see e.g.
Bassa et al. 2022). Major synoptic surveys with instantaneous fields-of-view,
$\Omega$ $>$ 1 square degree, will have multiple to tens of satellites
crossing each image (Mróz et al., 2022). The effect on nighttime ground-based
photometry will be that occulted stars will be completely blocked out for a
crossing time, $\tau_{s}$. The effect on the resulting photometry depends on
the ratio of the crossing time over the integration time, $t_{\rm int}$, of an
exposure: $f=t_{\rm int}/\tau_{s}$. The impact depends on whether this ratio,
$f$, is larger or smaller than unity.

###  4.1 Long integration times: $f>1$

Most current ground-based synoptic surveys use integration times $t_{\rm
int}>1$s. The effect of a satellite shadow passing through the field-of-view
is therefore that of an occulting trail that blocks part of the integrated
light of stars located along its path with a width $\theta_{s}$. The
fractional decrease in the light of any given star is equal to $1/f$, assuming
the occultation to be complete for the crossing time, $\tau_{s}$, which also
depends on the ratio $2R_{s}/D$.

For a Starlink-type satellite, the ratio $f$ is $\sim$12 000 for a Vera Rubin
Observatory exposure time of 15s (LSST Science Collaboration et al., 2017),
$\sim$23 000 for Zwicky Transient Facility integration times of 30s (Bellm et
al., 2019), and $\sim$46 000 for BlackGEM exposure times of 60s (Bloemen et
al., 2016). As the absolute photometric precision in ground-based astronomy
rarely exceeds the 1% level, such drops in the light curve may not be
noticeable as of yet.

The area affected, $f_{\Omega}$, by a worst-case crossing (corner to corner)
is about $f_{\Omega}\sim$ 0.2% (= $\sqrt{2}\times\theta_{s}/(3600*A)$) for a
wide-field imager with an $A\times A$ square degrees field-of-view. In some
parts of the Galactic plane and bulge, the ground-based, discernible stellar
densities reach $>$ 500 000 per square degree down to $g\sim$ 20 mag (Drew et
al., 2014; Groot et al., 2009), and therefore hundreds of stars will lie in
the path of occultation.

A secondary effect is introduced by the absolute photometric calibration of a
single frame. Generally, this is achieved by measuring the flux of a number of
calibrator stars across the field-of-view and taking the ratio of the measured
flux with the tabulated brightness of these stars. This is currently done
using Gaia Data Release 2 or 3 (DR2 or DR3) photometry for the calibrator
stars. As a satellite shadow crosses the field-of-view during an integration,
the measured brightness of the calibrator stars that lie on the path of the
satellite will be lower than expected, and therefore the photometric
calibration of the whole frame will be affected, artificially ‘brightening’
the whole frame: as the calibrators are fainter than expected, this will
result in an artificial increase in the apparent brightness of all other stars
in the frame. In current-day surveys this will not be a major problem as the
calibrator dimming will be equal to the ratio of the number of affected
(calibrator) stars over the total number of (calibrator) stars in the image.
For a 1°$\times$ 1° field-of-view and a single Starlink-type satellite, the
occulted area is, at worst, 0.2% of the total area (7.2 square arcminutes),
and therefore, assuming a uniform stellar density, also only 0.2% of stars are
affected, at a level of 1/$f$ per star, so the total impact on the photometric
calibration is negligible.

We note that the total crossing time, $t_{\rm cross}$, of a Starlink-type
satellite over a 1-degree field-of-view is equal to $t_{\rm cross}$ =
${A}/{\theta_{s}\tau_{s}}$ = 0.9s. To demonstrate these satellite shadows, the
best current-day option would be to observe GEO satellites that will cause a
trail of 1 arcminute for a 60s exposure.

###  4.2 Short integration times: $f\mathrel{\hbox{\hbox to0.0pt{\lower
2.36806pt\hbox{$\sim$}\hss} \kern-3.00003pt\raise 1.72218pt\hbox{$<$}}}1$

CMOS-camera technology is rapidly advancing. CMOS cameras with frame sizes
exceeding 6 000 x 6 000 pixels and quantum efficiencies $>$90% are available.
The expectation is therefore that within a few years CMOS technology will
completely replace current-day CCD technology in ground-based astronomy (e.g.
Niino et al. 2022; Zhang et al. 2020). With this comes the possibility to take
much shorter exposures thanks to the parallel read-out technology in CMOS
cameras. Integration times shorter than 1s become feasible. As can be seen in
Table 1 and Fig. 1, the 1% influence on any given star in absolute photometry
becomes relevant for integration times shorter than 0.1s for Starlink-type
satellites, and shorter than 6s for an Orion-type satellite.

Full-frame read-out speeds on large-format CMOS cameras are currently in the
24Hz range. Therefore, ‘SuperHertz’ wide-field cameras will appear, coupled to
large-aperture telescopes (e.g. Sako et al. 2018; Niino et al. 2022).

At 24Hz the integration times come in the range of the crossing times given in
Table 1. With 2$\times$2 binning, speeds up to 100Hz can be achieved, and a
10% dimming effect can be expected for Starlink-type satellites. With further
binning or windowing crossing times can be resolved in time, and the path of a
satellite can be followed by a series of ‘dropouts’ of stars along the orbit.
This will allow for orbit determinations of satellites larger than a few
metres, depending on their orbital altitudes.

Additionally, the assumption of a circular, fully opaque occultation patch can
be relaxed. Set against a sufficiently dense stellar field, the shape of each
satellite can be deduced from the complex light curve that will be produced as
the satellite path is followed across the sky. With Gaia (Early) DR3
astrometric precision ($\sigma$) on the location of each star at a level of 1
mas (Lindegren et al., 2021), the ratio $\sigma/\theta_{s}<<f$, and therefore
it will be the integration time, $t_{\rm int}$, that is the limiting factor on
the level of detail that will be retrievable. Conceptually, the level of
detail will be of the order of $fR_{s}$.

For satellites in known orbits CMOS cameras can be sub-arrayed to allow for
read-out speeds of $\sim$1000 Hz, leading to smaller $f$. A detailed modelling
is outside the scope of this study, but can easily be conceptualised. This
method will allow for the determination of the position and shape of a
satellite at accuracies $<$1 m when $f$ reaches 0.1 or less.

The effect noted in Sect. 4.1 on the photometric calibration of the full frame
will disappear when $f<1$. Although the effect on each individual star will
become stronger as $f$ approaches unity, the length of a trail through each
exposure will become shorter and shorter, and $f_{\Omega}$ will approach zero.

##  5 Outlook and discussion

Mega-constellations in LEO will have a significant impact on ground-based
astronomy, in particular for wide-field synoptic surveys. During twilight
hours the reflected sunlight will cause bright streaks in the images. We have
shown that during hours of darkness, satellites will cause a shadow path by
blocking out the light of background stars through occultations.

For current-day longer-duration exposures ($t_{\rm int}>$ 1 s), the effect is
modest and restricted to downwards photometric jitter on individual stars.
However, with CMOS technology advancing quickly, integration times similar to
the satellite’s crossing time over any given star come within reach. This will
lead to strong dropouts on an individual star’s light curve. It also opens up
the possibility to use the occultation trail to detect and track the satellite
in its orbit across the sky. This effect is completely independent from the
albedo or ‘stealth’ capabilities of the satellite, and also extends beyond
just the optical wavelength regime.

With integration times shorter than the occultation crossing time, and set
against sufficiently crowded stellar fields (e.g. the Galactic plane and
bulge, or the Magellanic Clouds), the shape of satellites will be deducible,
opening up a completely new way to characterise satellites in orbit.

###### Acknowledgements.

PJG is partially supported by NRF SARChI grant 111692. The author thanks Frank
Verbunt for an insightful discussion, and David Palmer for pointing out a
conceptual mistake in a previous version and making useful suggestions for
simplifications.

## References

  * Bassa et al. (2022) Bassa, C. G., Hainaut, O. R., & Galadí-Enríquez, D. 2022, A&A, 657, A75
  * Bellm et al. (2019) Bellm, E. C., Kulkarni, S. R., Barlow, T., et al. 2019, PASP, 131, 068003
  * Bloemen et al. (2016) Bloemen, S., Groot, P., Woudt, P., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9906, Ground-based and Airborne Telescopes VI, ed. H. J. Hall, R. Gilmozzi, & H. K. Marshall, 990664
  * Drew et al. (2014) Drew, J. E., Gonzalez-Solares, E., Greimel, R., et al. 2014, MNRAS, 440, 2036
  * Gallozzi et al. (2020) Gallozzi, S., Paris, D., Scardia, M., & Dubois, D. 2020, arXiv e-prints, arXiv:2003.05472
  * Groot et al. (2009) Groot, P. J., Verbeek, K., Greimel, R., et al. 2009, MNRAS, 399, 323
  * Hainaut & Williams (2020) Hainaut, O. R. & Williams, A. P. 2020, A&A, 636, A121
  * Lindegren et al. (2021) Lindegren, L., Klioner, S. A., Hernández, J., et al. 2021, A&A, 649, A2
  * LSST Science Collaboration et al. (2017) LSST Science Collaboration, Marshall, P., Anguita, T., et al. 2017, arXiv e-prints, arXiv:1708.04058
  * Mallama (2021) Mallama, A. 2021, arXiv e-prints, arXiv:2101.00374
  * McDowell (2020) McDowell, J. C. 2020, ApJ, 892, L36
  * Mróz et al. (2022) Mróz, P., Otarola, A., Prince, T. A., et al. 2022, ApJ, 924, L30
  * Niino et al. (2022) Niino, Y., Doi, M., Sako, S., et al. 2022, ApJ, 931, 109
  * Sako et al. (2018) Sako, S., Ohsawa, R., Takahashi, H., et al. 2018, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 10702, Ground-based and Airborne Instrumentation for Astronomy VII, ed. C. J. Evans, L. Simard, & H. Takami, 107020J
  * Tregloan-Reed et al. (2021) Tregloan-Reed, J., Otarola, A., Unda-Sanzana, E., et al. 2021, A&A, 647, A54
  * Tyson et al. (2020) Tyson, J. A., Ivezić, Ž., Bradshaw, A., et al. 2020, AJ, 160, 226
  * Witze (2019) Witze, A. 2019, Nature, 575, 268
  * Zhang et al. (2020) Zhang, Y.-h., Zhang, H.-f., Qu, W.-q., et al. 2020, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 11454, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, 1145407