Dispersed Fixed-Delay
Interferometry and its
Application in SDSS-III
MARVELS
Brian Lee,
for the MARVELS collaboration,
Aug. 31, 2011
Lots of early
SDSS-III
MARVELS
collaborators(list still growing!)
Principal investigator: Jian Ge (UF)
Survey scientist:
Scott Gaudi (OSU)
Science Team Chair:
Keivan Stassun (VU)
Instrument scientist:
Xiaoke Wan (UF)
SWG coordinator :
Data coordinator:
Eric Agol (UW)
Brian Lee (UF)
Basic physics of Dispersed
Fixed-Delay Interferometry
(DFDI)
Mirror 1
B1
Input light
B2
Mirror 2
Beamsplitter
Physical path difference: B2-B1
MARVELS basic physics
(DFDI Refs.: Erskine &
Ge (2000), Ge et al. 2001,
Erskine 2003, Ge 2002,
Mosser et al. 2003,
Mahadevan et al. 2008, van
Eyken et al. 2010)
Mirror 1
B1
Input light
B2
Mirror 2
Beamsplitter
Physical path difference:
B2-B1 = N*lambda
-> constructive interference
MARVELS basic physics
(DFDI Refs.: Erskine &
Ge (2000), Ge et al. 2001,
Erskine 2003, Ge 2002,
Mosser et al. 2003,
Mahadevan et al. 2008, van
Eyken et al. 2010)
Mirror 1
B1
Input light
B2
Mirror 2
Beamsplitter
(0.5*lambda
of added delay)
Physical path difference:
B2-B1 = N*lambda + 0.5*lambda
-> destructive interference
MARVELS basic physics
(DFDI Refs.: Erskine &
Ge (2000), Ge et al. 2001,
Erskine 2003, Ge 2002,
Mosser et al. 2003,
Mahadevan et al. 2008, van
Eyken et al. 2010)
Mirror 1
Y
B1
Input light
B2
Mirror 2
Beamsplitter
Tilt mirror 2
over, so path
length is a
function of
height Y
Y
->Intensity is
now a function
of height Y =
fringes
MARVELS basic physics
Mirror 1
Y
B1
Input light
B2
Mirror 2
Now consider
slightly longer
wavelength of
input light
Beamsplitter
Y
New
Old
lambda lambda
MARVELS basic physics
Mirror 1
Y
B1
Input light
B2
Mirror 2
Beamsplitter
So multiple
wavelengths
look like this:
Y
lambda
MARVELS basic physics
Zooming out in lambda, you’d see more strongly
the dependence of periodicity of interference on
wavelength. We call that the “interferometer fan”:
MARVELS basic physics
Orders
m are
evenly
spaced
in y…
m=4
m=3
m=2
m=1
MARVELS basic physics
(The MARVELS instrument can only collect a small cutout from the fan, with
m~13000 and 5000A~<lambda~<5700A. We typically refer to the small cutout
as, “comb.”)
this way to m=13000…
m=4
m=3
m=2
m=1
MARVELS basic physics
Mirror 1
Y
B1
Input light
B2
Mirror 2
Beamsplitter
Spectrograph
(Have to add a low-resolution
spectrograph so the fringes
aren't all on top of each other)
Y
MARVELS basic physics
lambda
Mirror 1
Y
B1
Input light
B2
Mirror 2
Beamsplitter
Spectrograph
Gradient in tilt of fringes across
lambda is present, but fairly
small.
Y
MARVELS basic physics
lambda
This was for a continuum light
source...
Y
MARVELS basic physics
lambda
Now multiply in a stellar source
with absorption lines instead.
Y
MARVELS basic physics
lambda
Now multiply in a stellar source
with absorption lines instead.
Note intersections.
Y
MARVELS basic physics
lambda
Small x shift (e.g., from RV) of
stellar lines gives larger y shift
in intersections (amplification
higher if slope is steeper)!
Y shift
Y
X shift
MARVELS basic physics
lambda
Actual intensities follow a
sinusoidal model, in theory.
Y
Continuum level
Line depth
Y
Inten.
MARVELS basic physics
lambda
Y
Continuum level
Line depth
Okay, now what messes this
up?
Inten.
MARVELS basic physics
Y
lambda
Slanted spectral lines…
…tilted trace apertures…
…illumination profile of the slit…
…higher order distortions (probably time-variable)…
…PSF (not necessarily constant across CCD)…
…a touch of scattered light…
…integrated onto the CCD
(still assuming infinite SNR).
Can you still track the intersections?
The final image: Sample full 4kx4k real data frame
(ThAr lamp calib.) (60 objects give 120 spectra)
Pipeline flow: attempting to
remove the optical effects
Pipeline flow- current preprocessing order (not
necessarily the ideal one!)
0. Starting point
(assume bias,
dark, flat already
done)
2. Try to measure
(using calib. lamp)
& undo slant
4. Try to measure (using
calib. lamp) & undo
vertical distortions
5. Apply a horizontal spatial
freq. filter to subtract
continuum fringes (since
unaffected by star RV)
1. Try to measure
(using calib. lamp)
& undo trace
3. Try to measure &
divide out slit
illumination profile
(using current image
itself)
6. Trim the image down and
fit a sinusoidal model to the
intensity at each wavelength
Pipeline flow- intermediate data product “whirl” and
RV extraction
Phases (radians):
[ 1.3, 1.4,
6.28, 2.0]
Sine amplitude/DC offset: [0.02, 0.05, 0.00001, 0.034]
Normalized fluxes:
[0.98, 0.56, 0.9999, 0.71]
7. Record sine fit parameters (and errors) and fluxes at each
wavelength into a multi-extension FITS file (“whirl”)
8. For each star or calibration source to have differential radial
velocity measured, choose template epoch
8a. For each other epoch, do chi-squared minimization to find
best fitting velocity (x and y axes treated as separate velocity
parameters; final answer used is the y-velocity only)
9. For star exposures only, subtract off barycentric velocity
10. For star exposures only, subtract off apparent lamp
velocity derived from adjacent lamp exposures from the final
star velocity.
11. Write RV’s to disk as a FITS table.
Zoom of raw MARVELS data (Tungsten lamp behind Iodine cell):
Above fringing spectrum, fully preprocessed:
MARVELS survey stats: what
data are available?
Vital stats
• Site: SDSS 2.5-m Telescope (3 deg. FOV)
• Multi-object feed: 60 fibres
• Spectrograph R~10000, wavelength 500570nm
• Interferometer operating order m~13000
• Throughput of telescope plus instrument: 2-3%
• Magnitudes surveyed: 7.6<V<12
• Stellar types F9 through K
• Up to 30% giant stars per field; similarly large
% of subgiants
Data: Yrs. 1-2
Data: Year 3
74,040 RV points
20,880 RV points
1234 Observations
348 Observations
43 Fields > 18 Epochs
6 Fields > 18 Epochs
2,580 Total Stars
2,460 Total Stars
Min Epochs: 18
Min Epochs: 1
Max Epochs: 42
Max Epochs: 29
(Median: 28)
(Median: 5)
Data collection will end
in year 4 with
completion of a dozen
spring Year 3 fields
MARVELS KEPLER overlap fields
Field
RA
DEC
Epochs
K15
296.12
43.53
21
K4
295.69
49.90
20
K10
294.12
46.01
21
K8
281.91
43.44
26
K21
291.58
38.15
18
TRES-2
285.90
49.20
23
K7
285.05
45.20
20
KEPLER 282.52
4
47.46
23
K5
291.93
48.45
21
K20
294.71
39.63
23
K14
299.64
44.87
24
38
Bonus SEGUE spectra
600 spectra per Kepler field ->
R=2000, wavelength 380-920nm
Current RV performance
Current 1 month stellar RV
rms scatter (rerun
v001.17)- (seems okay)
-300 stars (5 plates) from Oct. 2009
-Noise floor @ 10 m/s
-One-month timescales are basically
okay, with rms approximately at the level
of the instrument requirements
-Green squares = median phot. limits of
mag. bins
-Magenta squares = median total rms of
mag. bins
Current multi-month (<17
mo.) stellar RV rms scatter
(rerun v001.17)
-1680 stars (28 plates) from yrs. 1-2
-rms scatter ~2x the phot. limit at faint
magnitudes
-Bright-end noise floor@ 50 m/s- much
larger than the one-month floor
-Noise due to slowly-varying month-tomonth offsets (see next slide for specific
example)
5 M_Jup det. thresh
-Green squares = median phot. limits of
mag. bins
1 M_Jup det. thresh
-Magenta squares = median 1-month total
rms of mag. bins
-Blue squares = median multi-month total
rms of mag. bins
Orange=giants
Red=<1.5% visib.
Specific example of multi-month systematic noise
(400 days)
-Planet-bearing RV reference star HD 68988
-RV offsets and varying background slopes between months
Current Science Projects
Project 119 (3): MARVELS-1c (b)
Project 3: TYC 1240-945-1 (PUBLISHED)
Lee et al. 2011: MARVELS-1b discovery
msini ~ 28 Jupiter Masses, Period ~ 5.89 days.
Project 119: follow-up to Project 3
A second Coherent RV signal is present in the data
Project 119: The Plot Thickens (a bit)
AO image of system (courtesy Justin Crepp). Initial photometry by Ji Wang shows that
the secondary is ~3.5 mags fainter in Kp and the tertiary is ~4 mags fainter
49
Project 119: Summary
•Intriguing inner signal on Brown Dwarf
•If inner signal is a planet, this would be the first example of
a combined short-period BD / Planet system
•This is a very dynamically interesting system- not many
stable scenarios
• 3:1 period ratio (possibly a resonance?)
• Further N-body simulations could be helpful
• Temporary “Working group” to try and understand
this system
50
Project 87: Defringed MARVELS
spectra
Project 87: Defringed MARVELS
spectra
MARVELS resolution →
•
Problems for EWs.
1.1
•
•
•
Spectral indices →
[Fe/H], log g, Teff and
[α/Fe] (?).
Catalogue along with 3D vels. from MARVELS
RVs and Tycho proper
motions
Galactic chemical and
dynamical evolution in
solar neighborhood?
Statistical studies of stars
with and without
companions?
1.0
0.9
Normalized Flux
•
0.8
0.7
0.6
Fe I
 = 4.37 eV
(Y I)
0.5
Fe I
 = 3.57 eV
 = 3.65 eV
R ~ 48,000
R ~ 12,000
0.4
Ganymede
0.3
5461
5462
5463
5464
5465
5466
 (Å)
5467
5468
5469
5470
5471
Project 31: Statistics of binaries in MARVELS
Sample binary RV
Project 31: Statistics of binaries in MARVELS
Example
binary
completeness
prediction for
just one
month of data
collection (~4
epochs) @ 100
m/s err. (slice @
0.6 solar mass
primary)
Project 31: Statistics of binaries
MARVELS preliminary binary star orbit fits:
eccentricity-period relation (high eccentricity fits less
reliable to fit)
MARVELS prelim.
Project 31: Statistics of binaries
Raghavan 2010
Project 24: Statistics of brown dwarfs in
MARVELS
Project 24: Statistics of brown dwarfs in
MARVELS
The desert
Grether and
Lineweaver
(2006)
Project 24: Filling in the Desert
Project 24: BD Temperatures
Project 24: Family Portrait
Summary
• MARVELS current RV syst. noise floor 50 m/s,
but is ample to find brown dwarfs and binaries
• Broad, shallow survey strategy especially
suited for finding rare objects
• Follow-up RV and AO studies often show extra
complexity of objects
• Spectra can be used without the fringes for
traditional analyses. Available for solar
neighbourhood and Kepler.