The Transit Light Source Effect: False Spectral Features
and Incorrect Densities for M-dwarf Transiting Planets
Item Type Article
Authors Rackham, Benjamin V.; Apai, Dániel; Giampapa, Mark S.
Citation The Transit Light Source Effect: False Spectral Features and
Incorrect Densities for M-dwarf Transiting Planets 2018, 853
(2):122 The Astrophysical Journal
DOI 10.3847/1538-4357/aaa08c
Publisher IOP PUBLISHING LTD
Journal The Astrophysical Journal
Rights © 2018. The American Astronomical Society. All rights reserved.
Download date 10/08/2022 07:17:08
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Version Final published version
Link to Item http://hdl.handle.net/10150/627040
The Transit Light Source Effect: False Spectral Features and Incorrect Densities for
M-dwarf Transiting Planets
Benjamin V. Rackham
1,4,5
, Dániel Apai
1,2,5
, and Mark S. Giampapa
3
1
Department of Astronomy/Steward Observatory, The University of Arizona, 933 N. Cherry Avenue, Tucson, AZ 85721, USA; brackham@as.arizona.edu
2
Department of Planetary Sciences, The University of Arizona, 1629 E. University Boulevard Tucson, AZ 85721, USA
3
National Solar Observatory, 950 N. Cherry Avenue, Tucson, AZ 85719, USA
Received 2017 October 4; revised 2017 December 5; accepted 2017 December 6; published 2018 January 30
Abstract
Transmission spectra are differential measurements that utilize stellar illumination to probe transiting exoplanet
atmospheres. Any spectral difference between the illuminating light source and the disk-integrated stellar spectrum
due to starspots and faculae will be imprinted in the observed transmission spectrum. However,few constraints
exist for the extent of photospheric heterogeneities in M dwarfs. Here we model spot and faculae covering fractions
consistent with observed photometric variabilities for M dwarfs and the associated 0.3–5.5μm stellar
contamination spectra. We find that large ranges of spot and faculae covering fractions are consistent with
observations and corrections assuming a linear relation between variability amplitude, and covering fractions
generally underestimate the stellar contamination. Using realistic estimates for spot and faculae covering fractions,
we find that stellar contamination can be more than 10×larger than the transit depth changes expected for
atmospheric features in rocky exoplanets. We also find that stellar spectral contamination can lead to systematic
errors in radius and therefore the derived density of small planets. In the case of the TRAPPIST-1 system, we show
that TRAPPIST-1ʼs rotational variability is consistent with spot covering fractions
f 8
%
spot
7
18
=
-
+
and faculae
covering fractions
f 54
%
fac
46
16
=
-
+
. The associated stellar contamination signals alter the transit depths of the
TRAPPIST-1 planets at wavelengths of interest for planetary atmospheric species by roughly 1–15× the strength
of planetary features, significantly complicating JWST follow-up observations of this system. Similarly, we find
that stellar contamination can lead to underestimates of the bulk densities of the TRAPPIST-1 planets of
8%
20
7
r
D
=-
-
+
()
, thus leading to overestimates of their volatile contents.
Key words: methods: numerical – planets and satellites: atmospheres – planets and satellites: fundamental
parameters – stars: activity – starspots – techniques: spectroscopic
1. Introduction
Transmission spectroscopy, the multiwavelength study of
transits that reveals the apparent size of the exoplanet as a
function of wavelength (e.g., Seager & Sasselov 2000;
Brown 2001), provides the best opportunity to study the
atmospheres of small and cool exoplanets in the coming
decades. During a transit, exoplanets appear larger at some
wavelengths due to absorption or scattering of starlight by their
atmospheres. The scale of the signal depends inversely on the
square of the stellar radius (Miller-Ricci et al. 2009), prompting
a focus on studying exoplanets around M-dwarf stars.
A rapidly growing number of exciting M-dwarf exoplanet
systems hosting super-Earth and Earth-mass planets have been
discovered to date, including GJ 1132b (Berta-Thompson
et al. 2015), LHS 1140b (Dittmann et al. 2017), and the
TRAPPIST-1 system (Gillon et al. 2016, 2017; Luger
et al. 2017), an ultracool dwarf only 12 pc away hosting a
system of seven transiting Earth-sized planets. The low
densities of the TRAPPIST-1 planets may indicate high volatile
contents, and as many as three of them may have surface
temperatures temperate enough for long-lived liquid water to
exist (Gillon et al. 2017). Frequent flaring (Vida et al. 2017)
and strong XUV radiation from the host star (Wheatley
et al. 2017), however, can lead to significant water loss for
these planets (Bolmont et al. 2017), and 3D climate modeling
suggests that TRAPPIST-1e provides the best opportunity for
present-day surface water and an Earth-like temperature in the
system (Wolf 2017). While M-dwarf exoplanets provide an
excellent opportunity to study small and cool exoplanets
(Barstow & Irwin 2016
), they also represent a significant
challenge. Spots with covering fractions as low as 1% on M
dwarfs introduce radial velocity jitter that can mask the
presence of habitable-zone Earth-sized exoplanets ( Andersen
& Korhonen 2015). Variability monitoring suggests that 1%–
3% of M dwarfs have spot covering fractions of 10% or more
(Goulding et al. 2012). In addition to radial velocity jitter,
unocculted spots also introduce errors in wavelength-dependent
planetary radii recovered from transit observations (e.g., Pont
et al. 2008). Given the dependence of density calculations on
measurements of exoplanet radii (
R
3
r
µ
-
), any errors in
radius determination are amplified by a factor of 3 in the
estimate of the exoplanet bulk density and can lead to
significant consequences for the development of accurate
exoplanet models.
Unocculted spots are one manifestation of a generic issue
with transit observations that we term the “transit light source
effect” (Figure 1): any transmission spectroscopic measurement
relies on measuring the difference between the incident and
transmitted light to identify the absorbers present in the media
studied (e.g., Seager & Sasselov 2000). The level of accuracy
with which the incident spectrum is known will directly
determine the level of accuracy with which the transmitted light
The Astrophysical Journal, 853:122 (18pp), 2018 February 1 https://doi.org/10.3847/1538-4357/aaa08c
© 2018. The American Astronomical Society. All rights reserved.
4
National Science Foundation Graduate Research Fellow.
5
Earths in Other Solar Systems Team, NASA Nexus for Exoplanet System
Science.
1
is understood. In the transiting exoplanet case, the incident light
is measured by observing the disk-integrated stellar spectrum
before the transit (e.g., Brown 2001), the assumption being that
the disk-integrated spectrum is identical to the light incident on
the planetary atmosphere. However, this is only an approx-
imation: the planet is not occulting the entire stellar disk but
only a small region within the transit chord at a given time.
Thus, the light source for the transmission measurement is a
small time-varying annulus within the stellar disk defined by
the planet’s projection, the spectrum of which may differ
significantly from the disk-averaged spectrum. Such differ-
ences are expected due to the fact that stellar atmospheres are
rarely perfectly homogeneous, as illustrated by spatially
resolved observations of the Sun (e.g., Llama & Shkolnik
2015, 2016). Cool stellar spots (umbra and penumbra), hot
faculae, and even latitudinal temperature gradients will result in
a spectral mismatch, even if some of these will not be evident
in broadband photometric light curves.
The Sun displays a clear latitudinal dependence of active
regions that gives rise to the so-called butterfly diagram
(Maunder 1922; Babcock 1961; Mandal et al. 2017). Transiting
exoplanets have been proposed to be tools to probe the
latitudinal and temporal distributions of active regions in other
stars (Dittmann et al. 2009; Llama et al. 2012). High-resolution
transit observations can be used to spatially resolve the
emergent stellar spectrum along the transit path of the planet
(Cauley et al. 2017; Dravins et al. 2017a, 2017b). Morris et al.
(2017) recently utilized the highly misaligned exoplanet HAT-
P-11b to probe the starspot radii and latitudinal distribution of
its K4 dwarf host star and found that, much like the Sun, spots
on HAT-P-11 emerge preferentially at two low latitudes. In
general, however, orbital planes of transiting exoplanets tend to
be more aligned with stellar rotation axes than that of HAT-P-
11b, displaying obliquities of
20
(Winn et al. 2017).To
complicate matters further, unlike the Sun and HAT-P-11, M
dwarfs may exhibit spots at all latitudes (Barnes et al. 2001).
Thus, stellar latitudes sampled by transit chords may not
provide a representative picture of photospheric active regions.
Correcting transmission spectra for photospheric heteroge-
neities within the transit chord, such as spots (e.g., Pont
et al. 2013; Llama & Shkolnik 2015) and faculae (Oshagh
et al. 2014), is possible, provided they are large enough to
produce an observable change in the light curve during the
transit. Modulations in the shape of the transit light curve can
be used to constrain the temperature (Sing et al. 2011) and size
(Béky et al. 2014) of the occulted photospheric feature, which
determine its contribution to the transmission spectrum, or
more simply, time points including the crossing event may be
excluded from the transit fit (e.g., Pont et al. 2008; Carter
et al. 2011; Narita et al. 2013).
Unocculted heterogeneities, however, represent a more
pathological manifestation of the transit light source effect
because they do not produce temporal changes in the observed
light curve. Previous attempts to correct for unocculted
photospheric features have largely relied on photometric
monitoring of the exoplanet host star to ascertain the extent
of photospheric heterogeneities present (Pont et al. 2008, 2013;
Berta et al. 2011; Désert et al. 2011; Sing et al. 2011; Knutson
et al. 2012; Narita et al. 2013; Nascimbeni et al. 2015; Zellem
et al. 2015). This approach is limited in two respects: (1)
rotational variability monitoring traces only the nonaxisym-
metric component of the stellar heterogeneity (Jackson &
Jeffries 2012), i.e., any persistent, underlying level of
heterogeneity will not be detectable with variability monitor-
ing; and (2)
the source of the variability is commonly assumed
to be a single giant spot, the size of which scales linearly with
the variability amplitude, an assumption that provides only a
lower limit on the extent of active regions.
Zellem et al. (2017) presented a novel method to remove
relative changes in the stellar contribution to individual transits
utilizing the out-of-transit data flanking each transit observa-
tion. The strength of this approach lies in that it does not
require additional measurements to provide a relative correc-
tion for differences in spot and faculae covering fractions
between observations. However, as with other variability-based
techniques, this approach cannot correct for any persistent level
Figure 1. Schematic of the transit light source effect. During a transit, exoplanet atmospheres are illuminated by the portion of a stellar photosphere immediately
behind the exoplanet from the point of view of the observed. Changes in transit depth must be measured relative to the spectrum of this light source. However, the light
source is generally assumed to be the disk-integrated spectrum of the star. Any differences between the assumed and actual light sources will lead to apparent
variations in transit depth.
2
The Astrophysical Journal, 853:122 (18pp), 2018 February 1 Rackham, Apai, & Giampapa
of spots or faculae that may be present in all observations and
can strongly alter transmission spectra (McCullough
et al. 2014; Rackham et al. 2017).
Useful constraints on spot and faculae covering fractions are
hindered by observational and theoretical limits on our
knowledge of stellar photospheres. On the Sun, the disk
passage of sunspots can produce relative declines in the solar
total irradiance in the range of ∼0.1%–0.3% (e.g., Kopp
et al. 2005). By contrast, field mid-to-late M dwarfs
(
MM0.35<
☉
) with detectable rotation periods display
rotational modulations with semi-amplitudes of 0.5%–1.0%
(Newton et al. 2016), corresponding to peak-to-trough
variability full amplitudes of 1%–2%. Thus, variability
amplitudes in M dwarfs are roughly an order of magnitude
larger than those in the Sun.
Despite the clear importance of constraining spot and faculae
covering fractions for exoplanet host stars, a systematic attempt
to connect observed variabilities to covering fractions and thus
stellar contamination signals is absent in the literature on
transmission spectroscopy.
In this work, we employ a forward-modeling approach to
explore the range of spot covering fractions consistent with
observed photometric variabilities for field M-dwarf stars and
their associated effects on visual and near-infrared
(0.3–5.5 μm) planetary transmission spectra. In Section 2,we
detail our model for placing constraints on spot and faculae
covering fractions and their associated stellar contamination
spectra. Section 3 provides the modeling results. We place our
results in the context of observational attempts to constrain
stellar heterogeneity and examine their impact on transmission
spectra and density estimates of M-dwarf exoplanets in
Section 4, including a focused discussion of the TRAPPIST-
1 system. Finally, we summarize our conclusions in Section 5.
2. Methods
2.1. Synthetic Stellar Spectra
We employed the PHOENIX (Husser et al. 2013) and
DRIFT-PHOENIX (Witte et al. 2011) stellar spectral model
grids to generate spectra for the immaculate photospheres,
spots, and faculae of main-sequence M dwarfs with spectral
types from M0V to M9V. Both model grids are based on the
stellar atmosphere code PHOENIX (Hauschildt & Baron 1999),
with the DRIFT-PHOENIX model grids including additional
physics describing the formation and condensation of mineral
dust clouds (Woitke & Helling 2003, 2004; Helling &
Woitke 2006; Helling et al. 2008a, 2008b; Witte et al. 2009)
that is applicable to late-M dwarfs and brown dwarfs. We
considered models with solar metallicity ([Fe/H]=0.0) and
no α-element enrichment
([α/Fe]=0.0). We linearly inter-
polated between spectra in the grids to produce 0.3 – 5.5μm
model spectra for the surface gravities and temperatures we
required. The implicit assumption with this approach is that the
emergent spectrum from distinct components of a stellar
photosphere, such as the immaculate photosphere, spots, and
faculae, can be approximated by models of disk-integrated
stellar spectra of different temperatures. This approximation is
commonly used in transit spectroscopy studies to constrain the
contribution of unocculted photospheric heterogeneities to
exoplanet transmission spectra (Pont et al. 2008, 2013; Sing
et al. 2011, 2016; Huitson et al. 2013; Jordán et al. 2013; Fraine
et al. 2014; Rackham et al. 2017). However, this simplification
neglects the dependence of the spectra of photospheric
heterogeneities on magnetic field strength and limb distance,
both of which modulate the emergent spectra of magnetic
surface features (Norris et al. 2017). Nonetheless, we adopt the
simplifying assumption of parameterizing component spectra
by temperature and note that future efforts may benefit from the
increased realism of 3D magnetohydrodynamics models.
Table 1 lists our adopted stellar parameters. For each spectral
type, we calculated the surface gravity g from the stellar masses
and radii summarized by Kaltenegger & Traub (2009) and
adopted the stellar effective temperature from that same work
as the photosphere temperature T
phot
. Following Afram &
Berdyugina (2015), we adopted the relation
T 0.86
spot
=´
T
pho
t
, in which T
spot
is the spot temperature. We adopted
the scaling relation
TT 100
fac phot
=+
K (Gondoin 2008) for
the facula temperature. Although there are uncertainties in the
scaling relations of starspots and faculae, we do not expect our
general results to be sensitive to the adopted relations. The
temperature ranges of the spectral grids allowed us to simulate
photosphere, spot, and facula spectra for spectral types M0V–
M5V with the PHOENIX model grid and M5V–M9V with the
DRIFT-PHOENIX model grid.
2.2. Spot Covering Fraction and Variability Amplitude
Relation
We explored the range of spot covering fractions consistent
with an observed 1% I-band variability full amplitude for each
spectral type. We modeled the stellar photosphere using a
rectangular grid with a resolution of 180×360 pixels. We
initialized the model with an immaculate photosphere, setting
the value of each resolution element to the flux of the
photosphere spectrum integrated over the Bessel I-band
response.
6
Likewise, when adding spots or faculae to the
model, we utilized the integrated I-band fluxes of their
respective spectra.
We considered four cases of stellar heterogeneities by
varying two parameters: spot size and the presence or absence
of faculae. In terms of spot size, we examined cases with
smaller and larger spots, which we deem the “solar-like spots”
and “giant spots” cases. In the solar-like spots case, each spot
had a radius of
R
2
spot
=
, covering 400ppm of the projected
Table 1
Adopted Stellar Parameters
Sp. Type T
phot
(K) T
spot
(K) T
fac
(K) log g (cgs)
M0V 3800 3268 3900 4.7
M1V 3600 3096 3700 4.7
M2V 3400 2924 3500 4.8
M3V 3250 2795 3350 4.9
M4V 3100 2666 3200 5.3
M5V 2800 2408 2900 5.4
M6V 2600 2236 2700 5.6
M7V 2500 2150 2600 5.6
M8V 2400 2064 2500 5.7
M9V 2300 1978 2400 5.6
Note.The photosphere temperature T
phot
, spot temperature T
spot
, facula
temperature T
fac
, and surface gravity
g
log
we adopt for each M-dwarf spectral
type are listed.
6
http://www.aip.de/en/research/facilities/stella/instruments/data/
johnson-ubvri-filter-curves
3
The Astrophysical Journal, 853:122 (18pp), 2018 February 1 Rackham, Apai, & Giampapa
hemisphere and representing a large spot group on the Sun
(Mandal et al. 2017). In the giant spots case, each spot had a
radius of
R
7
spot
=
, covering 5000ppm of the projected
hemisphere and corresponding roughly to the largest spots
detectable on active Mdwarfs through molecular spectro-
polarimetry (Berdyugina 2011). For cases with faculae, we
included faculae at a facula-to-spot area ratio of 10:1, following
observations of the active Sun (Shapiro et al. 2014). Thus, the
stellar heterogeneity cases we considered were the following:
solar-like spots, giant spots, solar-like spots with faculae, and
giant spots with faculae.
For each spectral type and stellar heterogeneity case, we
examined the dependence of the variability on the spot
covering fraction through an iterative process. In each iteration,
we added a spot to the model photosphere at a randomly
selected set of coordinates,
7
recorded the spot covering
fraction, and generated a phase curve. In cases including
faculae, we added half of the facular area at positions adjacent
to the spot and half in a roughly circular area at another
randomly selected set of coordinates. We allowed spots to
overwrite faculae but not vice versa in successive iterations to
ensure the spot covering fraction increased monotonically. We
generated a phase curve by applying a double cosine weighting
kernel to one hemisphere of the rectangular grid (180 × 180
pixels), summing the flux, and repeating the process for all 360
x-coordinates (“latitudes”) in the model (Figure 2). We reco-
rded the variability full amplitude A as the difference between
the minimum and maximum normalized flux in the phase curve
at each iteration. This approach assumes that the stellar rotation
axis is aligned well with the plane of the sky. As the presence
of transits ensures that the planetary orbital plane is nearly
edge-on, and obliquities between the stellar rotation axis and
planetary orbital plane are generally
20
(Winn et al. 2017),
this assumption is good for most transiting exoplanet systems.
Following this procedure, we iteratively added spots to the
immaculate photosphere until reaching 50% spot coverage.
We repeated this procedure 100 times for a given set of
stellar parameters and heterogeneity case to examine the central
tendency and dispersion in modeling results. In each trial, we
recorded the minimum spot covering fraction that produced a
variability full amplitude of 1% (A=0.01). Using the results
of the 100 trials, we calculated the mean spot covering fraction
f
spot,mean
corresponding to A=0.01 and its standard deviation.
We defined the spot covering fractions
1s
below and above the
mean as
f
spot,min
and
f
spot,max
, respectively.
As spots were allowed to overwrite faculae in our model but
not vice versa, the facula-to-spot area ratio drifted from its
original 10:1 value as spots were added to the model. Thus, a
distribution of faculae covering fractions existed for each spot
covering fraction of interest. Accordingly, to quantify the
central tendency and dispersion in results for models including
faculae, we calculated the mean and standard deviation of
faculae covering fractions in the 100 trials for each spot
covering fraction of interest. We defined
f
fac,mean
as the mean
faculae covering fraction corresponding to
f
spot,mean
,
f
fac,min
as
the mean faculae covering fraction corresponding to
f
spot,min
minus one standard deviation of that distribution, and
f
fac,max
as
the mean faculae covering fraction corresponding to
f
spot,max
plus one standard deviation of that distribution.
2.3. Model for Stellar Contamination Spectra
Using the spot and faculae covering fractions determined
through our variability modeling, we modeled the effect of
stellar heterogeneity on observations of visual and near-infrared
(0.3–5.5 μm) exoplanet transmission spectra. We utilized the
composite photosphere and atmospheric transmission model
described in Rackham et al. (2017) and the spectra described in
Section 2.1. Recasting Equation (11) of Rackham et al. (2017)
Figure 2. Example of a model stellar photosphere and variability amplitude determination. The left panel shows one hemisphere of an example model photosphere
with giant spots and facular regions after applying a double cosine weighting kernel. The right panel displays the phase curve produced by summing the hemispheric
flux over one complete rotation of the model. The vertical dashed line illustrates the variability full amplitude A,defined as the difference between the maximum and
minimum normalized flux, which is ∼4% in this case.
7
We assumed no latitudinal dependence for the spot distribution. This
assumption is good for active M-dwarf stars (Barnes et al. 2001; Barnes &
Collier Cameron 2001) but may not hold for earlier spectral types (Morris
et al. 2017). We will examine the additional complication of latitudinal
dependence of photospheric features in a future paper.
4
The Astrophysical Journal, 853:122 (18pp), 2018 February 1 Rackham, Apai, & Giampapa
