Laser Frequency Combs for Precision Radial Velocity Measurements in Astrophysics

David F. Phillips

A collaboration between astronomers (CfA), physicists (CfA) and electrical engineers (MIT)

~15 scientists

“Astro-Comb”

•!Precision spectroscopy essential for advances in astrophysics

•!Currently limited by spectrograph wavelength calibration

•!Laser frequency combs can solve calibration problem

•!Rapid progress in last 3 years:! concept => lab demo => operation at observatories

•!Coming soon: discovery & characterization of Earth-like planets

•!10-20 years: direct measurement of cosmological dynamics

Diddams et al., Nature 445, 627 (2007).Murphy et al., MNRAS 380, 839 (2007).

Existing calibratorTh:Ar lamp

~1 m/s stability

Unique Opportunity

Over the next decade, we will:

•!Discover the first Earth-like planets around other stars

•!Search these planets forchemical signatures of life

•!Image planets directly Is the Earth special, or just another planet?

=> Complete Copernican revolution?

Origins of Life in the Universe

http://origins.harvard.edu/

Extrasolar Planets

Habitable zone

Hot Jupiters

Super-Earths

Jupiter mass planets close to their stars

(D. Sasselov, Nature 451, 29 2008)

> 400 exoplanets found to date• Primarily hot Jupiters• “Super Earths” now being found• Soon, earth-like planets Super Earths

Transit Method

HD 189733BHot jupiter63 light-years awayMass = 1.13 MJ

Radius = 1.14 RJ

T=1000 KP = 2.2 days

primary eclipse

secondary eclipse

Spitzer space telescope at 8 µm

Kepler satellite has hundreds of exoplanet candidate systems.

Need confirmation!

Heather Knutson & Dave Charbonneau (2007)

http://www.kepler.arc.nasa.gov/

arXiv:1001.0268v2 [astro-ph.EP]

Radial Velocity Method

•!Heavier planet causes larger Doppler shift in star light

•!Gives planet mass and orbital period & radius, not size

•!Doppler-shift from Earth-mass planet is VERY SMALL

Unseenexoplanet

Pre-comb sensitivity

Δλ ΔRV

10–7 Å 1 cm/s

10–6 Å 10 cm/s

10–5 Å 1 m/s

0.01 Å 1 km/s

Earth-mass planetaround Sun-like star

“Hot Jupiter”

Doppler shift:Δλ/λ = ΔRV/c

v = 1 km/sv = 1 GHzλ = 2 10-3 nmx = 1 pixel = 20 µm

KRV = 28.4�

P

1 year

�−1/3 �MP sin i

MJ

� �M�

M⊙

�−2/3

m/s

Stellar velocity due to planetary pull

100,000 absorption linesfew GHz linewidths

Stellar Spectrum

SpectrographSmall frequency shifts => Use echelle spectrograph! => broad spectral coverage & high-resolution

corrector

collimator

slit

2DCCD array

From telescope

cross disperser(low-dispersion)

echelle grating(high dispersion)

Slit is often a multimode fiber, allowing the spectrograph to reside in an environmentally controlled room, away from the telescope

v = 1 km/sv = 1 GHzλ = 2 10-3 nmx = 1 pixel = 20 µm

http://www.eso.org/sci/facilities/lasilla/instruments/harps/index.html

SpectrographSmall frequency shifts => Use echelle spectrograph! => broad spectral coverage & high-resolution

corrector

collimator

slit

2DCCD array

From telescope

cross disperser(low-dispersion)

echelle grating(high dispersion)

State-of-the-art astrophysical spectroscopy is broadband, photon-starved => spectrograph resolution R = λ/Δλ ~ 100,000 => minimum resolution element Δν > 5 GHz

Slit is often a multimode fiber, allowing the spectrograph to reside in an environmentally controlled room, away from the telescope

v = 1 km/sv = 1 GHzλ = 2 10-3 nmx = 1 pixel = 20 µm

http://www.eso.org/sci/facilities/lasilla/instruments/harps/index.html

Octave-Spanning CombOctave-spanning comb => atomic clock accuracy & stability for all comb lines

~300 nm

RF beat frequencies =>lock ωr & ωCE

to atomic clock

• 105 comb lines• narrow lines (<kHz) • coherent• equally-spaced• intense (10 µW/line)

ωr ~ 1 GHz

nH = 2nL

τpulse < 4 fs

We use Ti:Sapphire laser

Cr:Forsterite lasers and fiber lasers also used.

Broadband gain, Kerr effect => octave spanningKerr-lens mode-locking => stabilize pulsing Cavity sets Trep ~1 GHz

Double-chirped mirror pairs => compensate broadband dispersionhttp://nobelprize.org/nobel_prizes/physics/laureates/2005/index.html

Astro-Comb

PID lock box

λ/2

Photo-detector

Fabry-Perot cavity

PZT

Octave-spanning 1-GHzlaser frequency comb

Diode laser

Astro-comb beam

EOM

Synthesizer

Photo-detector

SynthesizerPhase lock box

Filter out most comb lines with a stabilized Fabry-Perot Cavity to yield line-spacing up to ~40 GHz

Li, et al., Nature 452, 610-612 (2008).

Astro-Comb

PID lock box

λ/2

Photo-detector

Fabry-Perot cavity

PZT

Octave-spanning 1-GHzlaser frequency comb

Diode laser

Astro-comb beam

EOM

Synthesizer

Photo-detector

SynthesizerPhase lock box

wavelength

inte

nsity

Astro-Comb

PID lock box

λ/2

Photo-detector

Fabry-Perot cavity

PZT

Octave-spanning 1-GHzlaser frequency comb

Diode laser

Astro-comb beam

EOM

Synthesizer

Photo-detector

SynthesizerPhase lock box

€

FSR = m × frep

wavelength

inte

nsity

Astro-combAstro-comb tested using a 1.5 m telescope with high-resolution echelle spectrograph (TRES)

Astro-combAstro-comb tested using a 1.5 m telescope with high-resolution echelle spectrograph (TRES)

Astro-combAstro-comb tested using a 1.5 m telescope with high-resolution echelle spectrograph (TRES)

TRES spectrographR~40,000

Astro-combAstro-comb tested using a 1.5 m telescope with high-resolution echelle spectrograph (TRES)

TRES spectrographR~40,000

Calibration Spectrum

Th:Ar calibrator

Astro-comb spectrum

Red astro-comb and Th:Ar spectrumTRES spectrograph on 1.5 m Tillinghast reflector at Mt. Hopkins2 dimensional spectrum on spectrograph CCD

echelle grating(high dispersion)

cross disperser(low-dispersion)

lens

2D CCD

100 µm fiber

Red Astro-Comb

• 100 nm bandwidth.• 32 GHz spacing.• 10 GHz FWHM on spectrograph.• 100 nW per line.• 25000-40000 counts in 5 minutes through

integrating sphere.

Red Astro-Comb SNRδν = A

FWHM

S/N ×√

n

A ≈ 0.7FWHM ≈ 10 GHz(S/N)300 s ≈ 200(S/N)max ≈ 300n ≈ 6 pixels∆ν ≈ 15 MHz or 15 m/s for one peak250 peaks/order: ∆ν ≈ 1 MHz in one order

Fit Model

CCDModel as flatTails from charge diffusion don't appear to help

Comb∆ν = 1 GHz S • δI/IS = side mode suppression ∆ν = 3 MHz • δI/I Negligible at the 1 m/s level

Fiber100 µm fiberModeled as flat top in 2DHalf circle in 1DAdd skew

OpticsModeled as Hermite-GaussiansUp to 16 terms

One order of comb lines superimposed Residuals of fit

near shot noise floor

Calibration

! !

!"#$%&"'$()*+$',*-.#./0(1.*2'"'$()"&3

455*67/*/,$8'/9*:$;./9116*/,$8'/*$)*',.*/1.0'&(<&"1,

•Calculate wavelength calibration order by order.•Compare calibration to reference frame.•Calculate deviation of all orders from mean drift.

! !

!"#$%&"'$()*+$',*-.#./0(1.*2'"'$()"&3

Blue Astro-Comb

• 1 GHz Ti:Sapphire source laser• BBO doubling crystal• 50 nm bandwidth

• Fabry-Perot Cavity:• Bragg Mirror Stack• Bandwidth limited by air

Dispersion to ~15 nm• Improved flux to spectrograph• Phase scrambling

A. Benedick, Optics Express, 18, 19175-19184 (2010).

Blue Astro-CombOne order of comb lines superimposed

Residuals of fit

Much closer to shot noise!420 nm with less fringing.Fiber shaking active.

50 cm/s resolution

faster data rate

Green Astro-Comb

PID lock box

λ/2

Photo-detector

Fabry-Perot cavity

PZT

Octave-spanning 1-GHzlaser frequency comb

Diode laser

Astro-comb beam

EOM

Photo-detector

SynthesizerPhase lock box

Synthesizer

Photonic Crystal Fiber (PCF)High nonlinear coefficientZero-dispersion wavelength ~700 nmFour-wave mixingNear Gaussian mode profile

FP CavityComplementary-Chirped Mirror Pair

Green Astro-Comb• 45 GHz green astro-comb• Various Ti:Sapphire settings• Astro-comb lines not resolved on OSA• Lab demo. Next, test at telescope

• 240 GHz green astro-comb• demo for low-resolution OSA• Side suppression minimal

What’s Next?

Harvard, Smithsonian, Geneva Observatory

• Observe Earth candidates found by Kepler • Use Doppler-shift method to distinguish

new Earths from exotics

William Herschel telescope,Canary Islands, 4.2 meter mirror

HARPS clone fornorthern hemisphere

Astro-combcalibrator =>ΔRV < 10 cm/s