SDSS-IV/MaNGA: SPECTROPHOTOMETRIC CALIBRATION TECHNIQUE

TLDR: In this article, a technique for spectral surface photometry using multiple small fiber-bundles targeting standard stars simultaneously with galaxy observations was developed, which achieved an accuracy of better than 5% for more than 89% of MaNGA's wavelength range.

Abstract: Mapping Nearby Galaxies at Apache Point Observatory (MaNGA), one of three core programs in the Sloan Digital Sky Survey-IV, is an integral-field spectroscopic survey of roughly 10,000 nearby galaxies. It employs dithered observations using 17 hexagonal bundles of 2'' fibers to obtain resolved spectroscopy over a wide wavelength range of 3600–10300 A. To map the internal variations within each galaxy, we need to perform accurate spectral surface photometry, which is to calibrate the specific intensity at every spatial location sampled by each individual aperture element of the integral field unit. The calibration must correct only for the flux loss due to atmospheric throughput and the instrument response, but not for losses due to the finite geometry of the fiber aperture. This requires the use of standard star measurements to strictly separate these two flux loss factors (throughput versus geometry), a difficult challenge with standard single-fiber spectroscopy techniques due to various practical limitations. Therefore, we developed a technique for spectral surface photometry using multiple small fiber-bundles targeting standard stars simultaneously with galaxy observations. We discuss the principles of our approach and how they compare to previous efforts, and we demonstrate the precision and accuracy achieved. MaNGA's relative calibration between the wavelengths of Hα and Hβ has an rms of 1.7%, while that between [N ii] λ6583 and [O ii] λ3727 has an rms of 4.7%. Using extinction-corrected star formation rates and gas-phase metallicities as an illustration, this level of precision guarantees that flux calibration errors will be sub-dominant when estimating these quantities. The absolute calibration is better than 5% for more than 89% of MaNGA's wavelength range.

Figures

Figure 1. The convolution kernel used in modeling the effect of a focus offset on the PSF.

Figure 5. Top: the throughput ratio distribution as a function of wavelength between two completely independent measurements of the throughput curves, constructed by dividing throughput measured in Spectrograph 1 for Exposure 1 and Spectrograph 2 for Exposure 2 for 627 consecutive exposure pairs with different dither positions but similar transparency. The thick line indicates the median ratio among these exposure pairs, which reflects the intrinsic throughput difference between the two spectrographs. The thin lines indicate the 2.5-, 15.85-, 84.15-, and 97.5-percentiles of the distribution at each wavelength, corresponding to the enclosed fractions of 1σ and 2σ limits of a Gaussian distribution. The curves below (above) 6000 Å are for the blue (red) camera. Bottom: the estimated fractional error of the flux calibration for an individual exposure in a spectrograph. This is derived by taking the standard deviation of the 627 throughput ratio curves, divided by the mean ratio,

Figure 4. The measured system throughput for one of the exposures (Exposure number: 177380) taken on MJD 56741 at an airmass of 1.0175. The throughput includes the transparency of the atmosphere, the efficiency of the whole telescope, an average fiber, spectrograph, and the detector. The solid and dashed curves show the throughput for Spectrograph 1 and 2, respectively, with the blue (left) and red (right) colors indicating the two cameras in each spectrograph.

Figure 8. The 1d image profiles of the output beams as presented in Figure 7. The two panels show the results of a 2 m long fiber with a 300 μm core (left) and a 25 m long fiber with a 400 μm core (right). The shorter fiber provides insufficient scrambling.

Figure 7. Result of light scrambling inside a 2 m long fiber with a 300 μm core. The top row shows the six different input beam location relative to the fiber. The middle row shows the output beams. The bottom row shows the normalized difference of output images relative to the centered image. It shows the scrambling of light inside the 2 m long fiber is insufficient to always feed a smaller fiber with the same fraction of light, as the position of the star changes within the bundle due to dithered observations or DAR. Even if we couple an 7-fiber mini-bundle at the output end, the variation would still be at the several percent level. Additionally, DAR will make the fraction of light recovered by the 2″ fibers a function of wavelength.

Figure 3. The PSF-covering fractions of the reference fiber in six mini-bundles as a function of wavelength are shown for three dithered exposures in a set. The top row shows a low airmass observation and the bottom row shows a high airmass observation. Each color indicates a unique mini-bundle with consistent color-coding between the two rows. The PSF-covering fraction for the same star can differ signficantly between different airmasses.

Full text

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SDSS-IV/MaNGA: SPECTROPHOTOMETRIC CALIBRATION TECHNIQUE
Renbin Yan
1
, Christy Tremonti
2
, Matthew A. Bershady
2
, David R. Law
3
, David J. Schlegel
4
, Kevin Bundy
5
,
Niv Drory
6
, Nicholas MacDonald
7
, Dmitry Bizyaev
8,9
, Guillermo A. Blanc
10,11,12,21
, Michael R. Blanton
13
,
Brian Cherinka
14
, Arthur Eigenbrot
2
, James E. Gunn
15
, Paul Harding
16
, David W. Hogg
13
, José R. Sánchez-Gallego
1
,
Sebastian F. Sánchez
17
, David A. Wake
2,18
, Anne-Marie Weijmans
19
, Ting Xiao
20
, and Kai Zhang
1
1
Department of Physics and Astronomy, University of Kentucky, 505 Rose St., Lexington, KY 40506-0057, USA; yanrenbin@uky.edu
2
Department of Astronomy, University of Winsconsin-Madison, 475 N. Charter Street, Madison, WI 53706-1582, USA
3
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
4
Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720-8160, USA
5
Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
6
McDonald Observatory, Department of Astronomy, University of Texas at Austin, 1 University Station, Austin, TX 78712-0259, USA
7
Department of Astronomy, Box 351580, University of Washington, Seattle, WA 98195, USA
8
Apache Point Observatory, P.O. Box 59, sunspot, NM 88349, USA
9
Sternberg Astronomical Institute, Moscow State University, Universitetskij pr. 13, Moscow, Russia
10
Departamento de Astronomía, Universidad de Chile, Camino el Observatorio 1515, Las Condes, Santiago, Chile
11
Centro de Astrofísica y Tecnologǵas Afines (CATA), Camino del Observatorio 1515, Las Condes, Santiago, Chile
12
Observatories of the Carnegie Institution for Science, 813 Santa Barbara St, Pasadena, CA, 91101, USA
13
Center for Cosmology and Particle Physics, Department of Physics, New York University, 4 Washington Place, New York, NY 10003, USA
14
Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, Ontario M5S 3H4, Canada
15
Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
16
Department of Astronomy, Case Western Reserve University, Cleveland, OH 44106, USA
17
Instituto de Astronomia, Universidad Nacional Autonoma de Mexico, A.P. 70-264, 04510 Mexico D.F., Mexico
18
Department of Physical Sciences, The Open University, Milton Keynes, MK7 6AA, UK
19
School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
20
Shanghai Astronomical Observatory, Nandan Road 80, Shanghai 200030, China
Received 2015 August 17; accepted 2015 November 3; published 2015 December 21
ABSTRACT
Mapping Nearby Galaxies at Apache Point Observatory (MaNGA), one of three core programs in the Sloan Digital
Sky Survey-IV, is an integral-field spectroscopic survey of roughly 10,000 nearby galaxies. It employs dithered
observations using 17 hexagonal bundles of 2″ fibers to obtain resolved spectroscopy over a wide wavelength
range of 3600–10300 Å. To map the internal variations within each galaxy, we need to perform accurate spectral
surface photometry, which is to calibrate the specific intensity at every spatial location sampled by each individual
aperture element of the integral field unit. The calibration must correct only for the flux loss due to atmospheric
throughput and the instrument response, but not for losses due to the finite geometry of the fiber aperture. This
requires the use of standard star measurements to strictly separate these two flux loss factors (throughput versus
geometry), a difficult challenge with standard single-fiber spectroscopy techniques due to various practical
limitations. Therefore, we developed a technique for spectral surface photometry using multiple small fiber-
bundles targeting standard stars simultaneously with galaxy observations. We discuss the principles of our
approach and how they compare to previous efforts, and we demonstrate the precision and accuracy achieved.
MaNGAʼs relative calibration between the wavelengths of Hα and Hβ has an rms of 1.7%, while that between
[N
II] λ 6583 and [O II] λ3727 has an rms of 4.7%. Using extinction-corrected star formation rates and gas-phase
metallicities as an illustration, this level of precision guarantees that flux calibration errors will be sub-dominant
when estimating these quantities. The absolute calibration is better than 5% for more than 89% of MaNGAʼs
wavelength range.
Key words: atmospheric effects – methods: observational – surveys – techniques: imaging spectroscopy
1. INTRODUCTION
Spectrophotometry refers to the calibration of the observed
flux density as a function of wavelength to the intrinsic flux
density of the target. This calibration is critically important for
deriving accurate quantities for many physical properties from
spectroscopic measurements of galaxies, including emission
line measures of star formation rates (SFRs) and gas-phase
metallicities and stellar population parameters from spectral
fitting. The success of Sloan Digital Sky Survey (York
et al. 2000) would not be possible without its accurate
spectrophotometric calibration. In SDSS-I, -II and -III, multiple
standard stars were observed simultaneously with the science
targets, and the achieved calibration accuracy is on the order of
5% (Adelman-McCarthy et al. 2008; Dawson et al. 2013).
The Mapping Nearby Galaxies at Apache Point Observatory
(MaNGA) project (Bundy et al. 2015) is an integral field
spectroscopic (IFS) survey of nearby galaxies using the 2.5 m
Sloan Foundation Telescope (Gunn et al. 2006) and the BOSS
spectrographs (Smee et al. 2013). It is one of three surveys that
comprise Sloan Digital Sky Survey-IV (SDSS-IV), which
started in 2014 July. With 17 hexagonal fiber bundles (Drory
et al. 2015), deployed across each 3° diameter pointing,
MaNGA will obtain spatially resolved spectroscopy for
roughly 10,000 nearby galaxies by 2020. The fiber bundles
are made with 2″ fi
bers and have sizes ranging from 12″ to
32″ diameter in the long axis. The spatial fill factor is 56%. The
The Astronomical Journal, 151:8 (18pp), 2016 January doi:10.3847/0004-6256/151/1/8
© 2016. The American Astronomical Society. All rights reserved.
21
Visiting Astronomer.
1

two BOSS spectrographs, each with a blue and a red camera,
provide a wavelength coverage from 3600 to 10300 Å at a
resolution of R∼2000.
Different from other previous and current SDSS surveys that
target each source with only one fiber, MaNGA will cover and
map individual galaxies. This important difference reshapes the
goal of spectrophotometry in the IFS context. For MaNGA, we
wish to calibrate spectral surface photometry as we explain
below.
In spectroscopic studies of external galaxies, stars have
always been used as calibrators for spectrophotometry.
However, stars are effectively point sources, while external
galaxies often appear as extended sources and in the MaNGA
sample cannot be approximated as point sources. Because of
this difference between the calibrator and the object of study,
the detailed approach of spectrophotometry varies depending
on the particulars of the instrument and observation setup, and
the desired goal of the calibration.
When the spectroscopic aperture is much larger than the size
of the point-spread function (PSF) at all relevant wavelengths,
flux calibration using a star can be a trivial exercise. When the
aperture is smaller or comparable to the size of the PSF, some
fraction of the light from a point source will fall outside the
aperture and be lost, with the amount of loss depending on the
location of the source within the aperture. Usually, instrument
apertures are more closely matched to the PSF for the sake of
maximizing the obtained signal-to-noise ratio (S/N) and
optimizing spectral resolution. However, apertures placed on
an extended source will not see the same amount of flux loss as
for point sources for the simple reason that as some light is
shifted out of the aperture other light may be shifted in. The
exact amount of light either lost or gained in this manner as the
effective location of the aperture changes will be a complicated
function of the 2D surface brightness profile of the target. In
such cases, there are at least three different spectrophotometry
goals as applied to galaxy targets.
[A.] Calibrate to the slit- or fiber-aperture flux density (f
λ
) of
a PSF-convolved spatial profile, or in other words, the specific
intensity (a.k.a.surface brightness) integrated within the
measurement aperture of a PSF-convolved spatial profile. Here
the PSF includes the combined effects of atmospheric seeing,
the PSF of the telescope and instrument, and chromatic
aberration in the whole system. The goal is to correct for the
atmospheric attenuation of the flux density and the instrument
response, but not to deconvolve the PSF or correct for
geometric shifts due to differential atmospheric refrac-
tion (DAR).
[B.] Calibrate to the total flux density incident on the
atmosphere if the galaxy were a point source. This is in practice
straightforward because the same flux correction vector is
applied to both stars and galaxies. But it assumes the target
galaxies experience the same DAR and aperture flux losses as
the stars do, which is usually not true.
[C.] Calibrate to the total flux density derived from imaging
photometry assuming that the relative shape of the spectral
energy distribution is uniform within the galaxy. The
uniformity assumption is appropriate only for certain science
cases.
We consider the first of the above options the most
fundamental goal for spectrophotometry. It truly reflects what
is being measured. It makes no assumption about the property
of the extended source to be observed. The only correction
required is the system throughput, without any flux correction
due to geometric factors. However, this goal is difficult to
achieve given practical limitations, especially for single-fiber
spectroscopy, as we will detail below. For slit spectroscopy,
one approach is to place a slit much wider than the PSF on
standard stars to obtain the needed correction, with the caveat
that the resulting spectral resolution will be different.
Given the difficulty of actually achieving Goal A, many
observational projects have chosen to fall back to Goal B or C.
For single-fiber spectroscopy of galaxies, especially distant
ones where galaxies are marginally resolved, these can be
sufficient for the purpose of deriving redshifts and measuring
approximately global spectral properties.
However, in the IFS context, the ultimate goal is to study the
internal variations within a galaxy. Therefore, Goal A is the
only sensible choice for spatially mapping the specific intensity
as a function of wavelength. There are a number of practical
difficulties, however, which we discuss in detail in this paper.
For MaNGA, we have developed and tested a method to
achieve this goal. The approach we present here is broadly
applicable to other IFS studies of extended sources.
This paper is organized in the following way. In Section 2,
we first discuss the causes of flux loss and error, how
spectrophotometry was done in previous generations of SDSS,
and the different spectrophotometry needs for integral field
spectroscopy. In Section 3
, we discuss how we set the
requirements for spectrophotometry given the MaNGA science
requirements. We then describe our calibration method and the
implementation in Section 4, present the resulting spectro-
photometry accuracy achieved in Section 5 and summarize in
Section 6.
2. WHAT TO CORRECT: SOURCES OF FLUX ERRORS
2.1. Sources of Flux Loss and Flux Error
To evaluate whether a spectrophotometric calibration
method will achieve the above Goal A, we first have to
understand the various reasons why observed spectra differ
from the intrinsic spectra of the targets. We put these flux
losses and erorrs into two categories.
2.1.1. Throughput Loss
The first is flux loss due to imperfect throughput of the
system, including atmospheric transparency, reflectance and
transmission of all optical elements in the telescope and
instrument (including fibers), and CCD quantum efficiency. All
these throughput losses are a function of wavelength.
2.1.2. Aperture-induced Flux Error
The second kind of flux error is due to aperture mis-
centering which can also lead to wavelength-dependent flux
errors. We refer to this as flux error rather than flux loss
because for extended sources unaccounted flux can be both
added or lost. The list of causes of this kind of flux error differs
for point sources and extended sources. Common to both are
mechanical alignment errors from manufacturing, guiding
errors at the guiding wavelength, and DAR. In detail, the
exact source of these errors and their significance depend on
the performance of the observing system hardware and the
observing strategy. Below, for the specific case of SDSS, we go
through each source in detail.
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1. Fiber Positioning: In SDSS, fibers are positioned on
science targets by being plugged into custom-drilled
aluminum plates that are mounted at the telescopeʼs focal
plane. The holes on the plug plates have positional errors
from drilling. The fibers are held within their indiviual
metal housings (so called ferrules), which are plugged
into the holes. The fiber is not always perfectly centered
within the ferrule due to limited precision in manufactur-
ing. The plate hole needs to be slightly larger than the
ferrule in order for it to be pluggable, and as a result the
ferrule will not be perfectly centered within the hole
either. The fiber centration error within the ferrule, the
hole-ferrule clearance, and the positional error from
drilling can stack up to 0
36 rms positional error on the
target (see Drory et al. 2015 for the detailed error stack
up), as compared to the 2″ diameter fibers used in SDSS-
III and IV. The dominant component is the drilling error.
A large part of the drilling offset can be measured post-
drilling, and in principle could be taken into account in
the spectrophotometric calibration. In practice, this was
not done in previous generations of SDSS as it was not
deemed scientifically essential.
2. Monochromatic Atmospheric Field Distortions: The
monochromatic component of the atmospheric refraction
(AR) distorts the field in a non-circularly symmetric way
when the telescope is not pointed at zenith. When a plate
is drilled, the offsets due to AR at the guide wavelength
are taken into account according to the hour angle and
altitude at which the plate is planned to be observed.
However, observations can last several hours during
which the magnitude and direction of the AR will change
causing a misalignment between the fiber and the target.
Given the Sloan Telescopeʼs wide 3° diameter field of
view, the misalignment can be signficant. By tuning the
distance between the primary and the secondary mirror,
the scale of the field can be adjusted to partially
compensate. However, the quadrupole distortion cannot
be corrected (for more details, see Section 4.2 of Law
et al. 2015). This means some fibers, depending on their
positions on the plate, will be offset from the target even
if guiding is perfect. The global guiding error for SDSS is
expected to be much smaller than all these effects.
For example, at a zenith distance of 18° (airmass of
1.05), the compression of the 3° field in the altitude
direction is 2
4. Compensating with the scale change, the
residual offset due to the AR for a target on the plate
could be somewhere between 0″ and 0
6 at the guiding
wavelength. The global guiding error is on the order
of 0
05.
3. Differential Atmospheric Refraction: The third contribu-
tor to the aperture centering error is the differential
atmosphere refraction. This means the images of the
targets at blue wavelengths are offset from those at red
wavelengths. At an airmass of 1.05, the separation
between the monochromatic images at 3600 and
10300 Å is 0
54. At airmass 1.25, it is 1 27. For a
point source, this means the flux loss due to a finite fixed
aperture is different for different wavelengths (e.g., a
point source centered in a fiber at one wavelength may
fall near the edge of that fiber at another wavelength). For
an extended source, this means the fiber is seeing
different parts of the source at different wavelengths.
The spectrum one eventually extracts from an individual
fiber contains mixed information from different parts of
the galaxy. In slit spectroscopy, one could align the slit
with the parallactic angle to capture all the flux. For
single-fiber spectroscopy on extended sources with
internal variations, we will not be able to correct for
DAR to get a spectrum for the same physical aperture at
all wavelengths, because we cannot correct for flux that
we do not observe and is a priori unknown. This is why
we excluded DAR corrections in Goal A above, and why
Goal A is the most sensible spectrophotometry goal for
extended sources.
In SDSS-I to SDSS-III, the approach of Goal B was
adopted for spectrophotometry. Due to the different flux
loss experienced by point sources and extended sources,
there could be significant wavelength-dependent sys-
tematics in the flux calibration for each galaxy, especially
when DAR is large. For many science topics this may not
matter, but avoiding such systematics becomes critical in
the context of IFS.
4. Seeing and Chromatic Aberrations: For point sources,
aperture losses arise from two additional factors, both of
which lead to wavelength-dependent PSF variation. The
first is the wavelength-dependent seeing profile. The
second is the chromatic aberration of the system. For
example, for the Sloan Telescope, the plate is designed to
follow the focal plane shape at 5300 Å. The focal planes
for other wavelengths are different. The resulting PSF
shape as a function of wavelength as seen by fibers at
different plate locations can be distorted.
The treatment of these effects for extended sources
depends on the spectrophotometry goals. For example,
for Goal A, these two factors should be included in the
intrinsic source properties for which there should be no
corrections. What one observes with fiber spectroscopy is
the aperture flux of the surface brightness distribution
convolved with the wavelength-dependent PSF. One
cannot reliably deconvolve the PSF without knowing the
intrinsic intensity distribution within each galaxy. If, on
the other hand, one adopts Goal B for practical reasons,
then galaxies are assumed to experience the same flux
loss due to these two factors as stars do, even though this
assumption is in general incorrect.
The first three factors above are all related to alignment.
Their combined effects are different for stars and galaxies. For
stars, a certain fraction of flux is lost as a function of
wavelength and the needed correction factor is usually a slow
function of wavelength. There are no high-frequency changes
to the spectral shape. For galaxies, the impact is more
complicated because alignment errors combined with DAR
mean that different parts of the galaxy are sampled at different
wavelengths.
Given the sources of flux errors above, it is clear that IFS
requires calibration of spectral surface photometry (i.e., Goal
A), which necessitates corrections only for the throughput loss
of the system but not any aperture-induced flux error. However,
because we use stars as calibrators, they do experience
aperture-induced flux error as well. Thus, to separate these
two sources of flux errors for calibration stars, we have to know
exactly how the stars are positioned relative to the spectro-
scopic aperture and the shape of the PSF.
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The Astronomical Journal, 151:8 (18pp), 2016 January Yan et al.

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Sdss-iv/manga: spectrophotometric calibration technique" ?

To map the internal variations within each galaxy, the authors need to perform accurate spectral surface photometry, which is to calibrate the specific intensity at every spatial location sampled by each individual aperture element of the integral field unit. The authors discuss the principles of their approach and how they compare to previous efforts, and they demonstrate the precision and accuracy achieved. 

Q2. How many nearby galaxies will MaNGA achieve by 2020?

With 17 hexagonal fiber bundles (Drory et al. 2015), deployed across each 3° diameter pointing, MaNGA will obtain spatially resolved spectroscopy for roughly 10,000 nearby galaxies by 2020. 

Q3. Why do the authors not include PSF size as one variable in the MCMC?

The reason the authors do not include PSF size as one variable in the MCMC is that the computation of the PSF is a slow process as it involves two convolution procedures. 

Q4. Why are instrument apertures more closely matched to the PSF?

instrument apertures are more closely matched to the PSF for the sake of maximizing the obtained signal-to-noise ratio (S/N) and optimizing spectral resolution. 

Q5. What are the important factors in the calculation of the indicators that involve widely separated lines?

Dust extinction corrections are also needed in computing some of the indicators that involve widely separated lines, such as [N II]/[O II]. 

Q6. What is the fit to the flux ratios among the seven central fibers?

Fitting the minimum Chi Square as a function of PSF size by a quadratic function, the authors find the PSF size that yields the best fit to the flux ratios among fibers, along with the position of the star and DAR. 

Q7. What is the step required before all exposures can be coadded?

This step is required before all exposures can be coadded and involves only low-order polynomial scaling as a function of wavelength. 

Q8. How many percentiles of the error distribution are there?

Given that the distribution of the spectrographs’ throughput ratio is fairly close to a Gaussian distribution, these numbers correspond to roughly 68.3- percentile of the error distribution. 

Q9. What is the rband flux of a 61-fiber bundle?

Yan et al.example, for a 61-fiber bundle, there will be 61 synthetic rband flux from MaNGA spectra and 61 r-band aperture photometry measurements from the image. 

Q10. What is the calibration accuracy for the g-band?

The resulting absolute calibration accuracy is better than 4% in all bands (upper panels in Figure 6) and the relative calibration between bands is better than 3% (lower panels). 

Q11. What is the way to correct for the error caused by the drilling error?

If the drilling error, guiding error, and DAR can all be approximated by low order functions of wavelength and/or plate position, this step should correct for those errors.