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Extended TullyFisher relations
using HI stacking
Scott Meyer, Martin Meyer, Danail
Obreschkow, Lister Staveley-Smith
Summary
Intro
• 
• 
• 
TFR
Where traditional methods fail
HI Stacking
Calibrations and simulated data
• 
• 
Analytical galaxies
Simulated galaxies (from the S3-SAX model)
Real data test case (HIPASS and HICAT)
• 
• 
HIPASS direct detections
Extension work to 6df / SKA and precursors
Extended Tully-Fisher relations using HI stacking - Scott Meyer
2
2
Tully-Fisher relation (TFR)
The Astrophysical Journal, 777:140 (10pp), 2013 November 10
What is the TFR?
The TFR is an empirical
relation between absolute
magnitude and intrinsic HI
emission line width (as a
tracer of rotation velocity)
that spiral galaxies follow.
What’s happening
here?
This particular plot
demonstrates a novel way
of getting TFR parameters
without having galaxy
inclinations (See
Obreschkow & Meyer 2013
for more info)
Figure 4. Absolute K-band (left) and B-band (right) magnitudes, plotted against v (red big dots, i >
Obreschkow & red
Meyer, pJ, show
2013, Vol 7obtained
77, pg by1applying
40 the MLE using in
TFRs with
1-σ scatter. The
dashed A
lines
the TFRs
to the red big dots. In turn, the blue solid lines are obtained without inclination data, by applying the
Extended
relations
using
HIfits
stacking
- Scott
Meyer
3 blue small d
inclinations,
i.e., ρ(i)Tully-Fisher
= sin i. In other
words,
these
are based
purely
on the scattered
(A color version of this figure is available in the online journal.)
Current limitations
Optical vs Radio rotation measures
The TFR can be Wavelength inves<gated in op<cal or radio. Op<cal Radio Op<cal probes deep, but does not necessarily retrieve the full velocity profile. Radio probes much more of the velocity profile but is limited to z < 0.1. Observed Quan2ty Max Redshi8 Radius Probed Hα Z ~ 1-­‐1.5 low HΙ z < 0.1 High NGC 6946 – leZ: Op<cal, right: Radio Extended Tully-Fisher relations using HI stacking - Scott Meyer
4
4
HI stacking
998
S. Fabello et al.
What?
◦
−1
◦
−1
and velocity, a value of flux density is recorded. For each target in sample A, we extract a spectrum at a given position of the sky, over the velocity range of
the data cube which contains the source. Two examples of extracted spectra are shown on the right, illustrating an H I detection (green, bottom) and an H I
non-detection (red, top).
How?
Downloaded from http://mnras.oxfordjournals.org/ at University of Western
This technique
seeks to creates
an HI emission
spectrum with
increased improved
signal-to-noise by
combining several
HI spectra (usually
in an attempt to get
a detection from a
collection of nonFigure 4. A schematic representation of the fully processed ALFALFA 3D data cube. The data cubes are 2.4 × 2.4 in size and about 5500 km s detections).
in velocity
Fabello et. resolution
al. 2011 range (25 MHz in frequency). The raw spectral resolution is ∼5.5 km
s ; the angular
is ∼4 arcmin. For each pixel, which is a point in RA, Dec.
Rest-frame HI spectra from40 galaxies
are
created
using
optical
redshift (or
each source;
strong continuum
sources
can
× 40 arcmin around
affect
our spectraare
by creating
standing
waves.
available).
These
then
co-added.
Signal increases
The signal fromradio
each target redshifts
is integrated over a if
region
of the data
cube centred onproportional
its 3D position. Because noise
with number
the
to increases
N (the
of galaxies included) while noise increases
square root of the integration area, integrating over too large a
3.1.2 Rms evaluation
as
√N.
region lowers the
quality
of the spectrum without increasing the
2
3.1.1 Spectrum extraction
4
For each spectrum we need to measure the rms noise, which will
Movie at https://vimeo.com/69062721
signal. Our GASS targets are always smaller then the ALFA beam
(the mean R90 for sample A is 10 arcsec), so we simply integrate
over a sky region of 4×4 arcmin2 . In Fig. 4, we illustrate how we
extract spectra at two different positions in the sky inside the same
data cube. The coloured regions indicate where the spectra would
be evaluated.
later be used as a weighting factor when we stack spectra. The rms
has to be evaluated in regions of the spectrum where there is no
Tully-Fisher
relations
using
HI stacking - Scott Meyer
emission fromExtended
the target galaxy,
and we also
have to avoid
spectral
regions where there are any spurious signals (e.g. residual RFI that
we failed to flag or H I emission from companion galaxies). In order
5
5
Simulated galaxies 1
Analytically solvable galaxy profiles
A single galaxy was modeled as a disk with constant linear velocity
(not constant rotation). This galaxy was projected to various different
inclinations and convolved with Gaussians of varying σ/Vmax values to
simulate different random gas velocities (dispersion). Random
projections of this galaxy were stacked to investigate the relation
between the FWHM of the stack, and the FWHM of the deprojected
galaxy.
Extended Tully-Fisher relations using HI stacking - Scott Meyer
6
6
Simulated galaxies 2
Correction factor
In order to reproduce the TFR,
our measured stack widths must
relate in some predictable way
to the deprojected widths of the
input galaxies.
stack
W50
= width of stacked
profile
ref
•  W50 = width of single
analytical spectra,
deprojected and
dedispersed
•  Blue = high dispersion
(random gas velocities)
•  Red = low dispersion
• 
Extended Tully-Fisher relations using HI stacking - Scott Meyer
7
7
Simulated galaxies 3
Galaxies with differential rotation
Galaxies were given an exponential
⇣ rotation curve
⌘ of the form:
V (r) = Vmax 1
e
r/rflat
Since galaxies no longer have constant velocity profiles, we prescribe a HI
surface density of the form:
M
⌃HI (r) =
1
0.9
Constant rotation, edge-on
Constant rotation, stack
Differential rotation, edge-on
Differential rotation, stack
σ/Vmax = 1/10
σ/V
σ/V
0.7
0.6
max
= 1/5
σ/Vmax = 1/10
1.1
part
ref
Fθ = W50
/W50
Normalised flux density
0.8
1.15
HI
r/rHI
e
2
2⇡rHI
max
= 1/20
1.05
0.5
0.4
0.3
1
0.95
0.2
0.1
0
0.9
-1
-0.5
0
0.5
Normalised velocity v = V/ Vmax
1
0
10
20
30
40
50
60
70
80
90
Minimal inclination of stack imin [deg]
Extended Tully-Fisher relations using HI stacking - Scott Meyer
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8
Simulated galaxies 4
Low number statistic corrections
Because galaxies enter the stack without being corrected for
inclination, having a sample too small introduces an offset and
stack
scatter into W50
.
Extended Tully-Fisher relations using HI stacking - Scott Meyer
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9
Simulated galaxies 5
1902
Vol. 703
S3-SAX simulation
HI and H2 semianalytical model made
by post-processing the
Millennium simulation.
1896
AND CO OBSERVING CONES
n Commuay Design
ium Simuline access
he German
OBRESCHKOW ET AL.
OBRESCHKOW ET AL.
Vol. 703
1901
Obreschkow 2009 ATALOG
- and COve parameFrom these
Ψ(V ) can
on
obs
peak /2,
obs
peak /2,
(A1)
ation (A1)
Figure 9. Simulated sky field covering 3 × 1 arcmin2 . The three panels correspond to three different redshift slices, with an identical comoving depth of 240 Mpc.
The coloring is identical to Figure 4, but the flux scales are 10 times smaller at z = 3 and 100 times smaller at z = 6.
APPENDIX D
The sensitivity of a survey may be high enough that galaxies
Figure 8. Comparison of a simulated normalized emission line Ψ(V ) (solid
areofdetected
theofgalaxy
the cone
simulation
is
2 . regions
Figure 4. Illustration
of the galaxies
the redshift
range z = 1.0–1.1 in a small field
1 arcminin
The full of
field
view ofMF,
the where
observing
is 60,000
ANALYTIC
FITSinFOR
dN/dz-FUNCTIONS
Extended
Tully-Fisher
relations using
HI
stacking
-CO(1–0)
Scott
Meyer
10
10fortimes
line) with the emission line Ψapprox (V ) (dashed line), recovered from thelarger
fivethan this example.
emission
each color
sensitivity
The gradual coloring represents integrated line fluxes per unit incomplete.
solid angle forInH fact,
i (left)for
andeach
(right).line
Theand
different
tones
CO
obs
obs
obs
obs
belowof which
sources
limit,
there
a critical
redshift
zc , curves
represent the
brightness
ICO(5−4) /I
. The
around
H i is
sources
represent
iso-density
CO at the
50 percentile
, c2 , and
c3white
for contours
Table
1 liststemperature
the valuesintensity
of the ratio
parameters
c1CO(1−0)
parameters Ψobs
0 , Ψmax , wpeak , w50 , and w20 .
of
the
incomplete
part
of
the
simulated
galaxy
MF
will
be
level of the
full
CO
density
scale
and
vise
versa.
the analytic dN/dz fit of Equation (15). The parameters are
(A color version of this figure is available in the online journal.)
detected at a sufficiently high rate that the number of real
given for both peak-flux-density-limited and integrated-flux-
Simulated galaxies 6
S3-SAX Tully-Fisher
relation
103.6
-25
-24
-22
101.8
-21
-23
102.4
101.2
100.6
-19
K band absolute magnitude
103
-20
1.2 Million galaxies
stack
•  Blue diamonds = W50
•  White diamonds =
stack
W50
before
correction
•  Black circles =
averages from
individual galaxies
• 
stack,c
W50
2
stack
W50 2
Wref
50 2
100
40
50 60
80 100
200
Vrot [km s 1]
Extended Tully-Fisher relations using HI stacking - Scott Meyer
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11
Simulated galaxies 7
Simulated HIPASS
(b)
Vctotal
Vchalo
Vcdisk
500 h-1Mpc
(a)
-24
2
-22
Obreschkow et al.
stack
50
stack,c
W50
Wind
50 2
-20
The Astrophysical Journal, 766:137 (11pp), 2013 April 1
K band absolute magnitude
-26
5 independent regions of the S3-SAX box were selected and
HIPASS was reproduced. TFR reproduced extremely well
using HI stacking technique.
W
2
HI
-18
Vcbulge
5
0
10
15
radius [kpc]
500
40
h-1
Mp
c
(c)
-1Mpc
500 h
50 60
80
100
200
300
1
[km s ]
Obreschkow 2009 Figure 3. The five colors represent our five virtual HIPASS volumes fitted inside
the cubic box of the Millennium simulation. The box obeys periodic boundary
conditions, such that the truncated volumes (blue and purple) are in fact simply
connected. The five HIPASS volumes do not overlap and can hence be used to
estimate the magnitude of cosmic variance.
Extended Tully-Fisher relations using HI stacking - Scott Meyer
of turbulent/thermal dispersion. The linewidth W50 at the 50%level of the peak flux density is then measured from the
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12
Real data (HIPASS & HICAT)
HIPASS
Galaxy selection was kept to a minimum: Galaxies to be
stacked were only cut based on angle from CMB equator. Red
galaxies were cut based on angle from CMB equator as well
as a 45 degree cut.
-18
-24
-22
-20
K band absolute magnitude
-26
Wstack
2
50
stack,c
W50
2
HIPASS i > 45 deg
-18
-20
-22
Wstack
2
50
stack,c
W50
2
HIPASS i > 45 deg
-16
B band absolute magnitude
stack
•  Blue = W50
•  Red =
HIPASS
galaxies
stack
•  White = W50
without
corrections
20
30
50
70
100
[km s 1]
200
300
20
30
50
70
100
200
300
[km s 1]
Extended Tully-Fisher relations using HI stacking - Scott Meyer
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13
Extension work
Non-detections
Work is on-going in the HIPASS region by stacking 6df
galaxies (non-detections in radio).
SKA
With significantly deeper data sets such as DINGO,
WALLABY and LADUMA, stacking can be used to squeeze
more science out of these instruments.
Other uses for stacking
So far stacking has only been used to recover total HI flux
(and now average rotation velocities), how far can we take
this technique?
Optical and Radio survey overlap
This work relies heavily on overlapping optical (or IR) and
radio surveys.
Extended Tully-Fisher relations using HI stacking - Scott Meyer
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14
Summary
Calibrations and simulated data
• 
• 
Analytical galaxies
Simulated galaxies (from the S3-SAX model)
Real data test case (HIPASS and HICAT)
• 
HIPASS direct detections
Extension work
• 
• 
• 
Non-detections
SKA
Other stacking work
Extended Tully-Fisher relations using HI stacking - Scott Meyer
15
15
Extra plots
HIPASS simula<on Millennium Extended Tully-Fisher relations using HI stacking - Scott Meyer
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16
Extra plots
103.6
stack,c
Millennium data WITH ellip<cal galaxies -24
103
-22
101.2
-20
101.8
-21
-23
102.4
100.6
-19
W50ref = deprojected but WITH dispersion K band absolute magnitude
-25
W50
2
stack,c,e
W50
2
100
40
50 60
80 100
200
1
Vrot [km s ]
Extended Tully-Fisher relations using HI stacking - Scott Meyer
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17