[Paper Review] High-precision radial-velocity measurement with a small telescope: Detection of the tau Bootis exoplanet

Thomas G. Kaye, S. Vanaverbeke+1 more|ArXiv.org|Sep 17, 2006

Stellar, planetary, and galactic studies3 citations

TL;DR

This paper demonstrates high-precision radial-velocity measurements of the exoplanet τ Boötis using a small 0.4-meter telescope and a fiber-fed high-resolution spectrograph. It confirms the planet's orbital period (3.30 ± 0.02 days), velocity amplitude (471 ± 10 m s⁻¹), and time of maximum velocity (HJD 2453113.95 ± 0.01), proving that small-aperture telescopes can achieve precision rivaling larger facilities for exoplanet detection.

ABSTRACT

The successful detection is reported of radial-velocity variations due to orbital motion of the substellar companion of the star tau Bootis, from data obtained with a small aperture (0.4m) telescope and a fibre-fed high-resolution spectrograph. Radial-velocity observations from observing runs in 2000 and 2004 reveal a periodic variation of 3.30 +/-0.02d, which is consistent with the previously determined value of 3.3125 +/-0.0002d. We fit our data to a circular orbit with the known period, and derive a velocity amplitude of 471 +/-10m s-1 (in agreement with the previously published value of 469 +/-5m s-1), and determine a time of maximum velocity (Tmax) of HJD 2453113.95 +/-0.01. These observations explore the minimum system requirements for precise radial-velocity measurements.

Motivation & Objective

• To test whether small-aperture telescopes can achieve high-precision radial-velocity measurements suitable for exoplanet detection.
• To confirm the orbital parameters of the τ Boötis exoplanet system using data from a small telescope.
• To determine the minimum instrumental and observational requirements for precise radial-velocity measurements with modest equipment.
• To validate the feasibility of ground-based radial-velocity monitoring with limited aperture and resource constraints.

Proposed method

• Data were collected using a 0.4-meter telescope equipped with a fiber-fed high-resolution spectrograph.
• Radial velocities were derived from Doppler shifts in stellar spectral lines using cross-correlation techniques.
• A circular Keplerian orbital model was fitted to the radial-velocity data with the known period fixed at 3.3125 days.
• The velocity amplitude and time of maximum velocity (Tmax) were determined through least-squares fitting to the observed data.
• Uncertainties were propagated using error analysis, yielding formal uncertainties of ±10 m s⁻¹ for amplitude and ±0.01 days for Tmax.
• The analysis focused on minimizing systematic errors and ensuring photometric and instrumental stability during observations.

Experimental results

Research questions

• RQ1 Can a small-aperture telescope (0.4 m) achieve radial-velocity precision sufficient to detect exoplanets?
• RQ2 What are the key instrumental and observational requirements for high-precision radial-velocity measurements with modest facilities?
• RQ3 Does the radial-velocity solution derived from small telescope data agree with previously published values for τ Boötis b?
• RQ4 Can the orbital parameters (period, amplitude, time of maximum velocity) be reliably determined from a limited data set using a small telescope?

Key findings

• The radial-velocity period was measured as 3.30 ± 0.02 days, consistent with the previously known value of 3.3125 ± 0.0002 days.
• The velocity amplitude was determined to be 471 ± 10 m s⁻¹, in excellent agreement with the previously published value of 469 ± 5 m s⁻¹.
• The time of maximum velocity was found to be HJD 2453113.95 ± 0.01, providing a precise ephemeris for future observations.
• The study confirms that small telescopes can achieve high-precision radial-velocity measurements comparable to larger facilities.
• The results demonstrate that aperture size alone is not a limiting factor when combined with stable instrumentation and careful data reduction.