TN 0074: Proposal for Extrasolar Planet Transit Searches Using the Mark IV Camera

Mike Gutzwiller
Feb 26, 2001

This technical note details the necessary parameters and conditions that need to be met if the TASS Mark IV camera is to be used to search for extrasolar planets.

Introduction

In the last few years many extrasolar planets have been discovered, primarily using the radial velocity technique. A catalog of these planets revealed many surprises.  Primary among these are the “Hot Jupiters,” planets with Jovian masses but with a semi major axis less than Mercury’s.  The planet circling HD 209458 has been seen to transit its star by the STARE project.  The transit in this case was predicted in advance using an ephemeris derived from the radial velocity data.  The STARE project uses a single camera with properties very like the Mark IV, e.g. the main objective is 10 cm and the CCD is a 2k x 2k device.

An interesting project for the Mark IV camera would be to discover new extrasolar planets by observing their transits across the stellar disk.  For this paper I'm using the data published at the exoplanets.org site as of 9 Jan 2001.

Definitions

For our purposes a hot Jupiter is considered to be any Jovian mass planet with a semi-major axis of less than 0.1 au.  Based on the catalog the typical hot Jupiter has the following properties (median values for the 15 hot Jupiters).

Hot Jupiter Characteristics

The following characteristics are the basis of further calculations.

Mark IV Parameters

Tom designed the Mark IV as a good tool for generating a survey of stars and not a general-purpose instrument. The properties of the Mark IV include:

• The RA axis can track stars only within one hour from either side of the meridian.
• The Dec axis can track stars between the pole and the southern horizon.
• The RA axis is accurate enough to track to less than a pixel a minute.
• The Dec axis is accurate enough to reposition to within 0.5 degrees.
• The Mark IV controls two cameras simultaneously; typically with one V filter and one I filter.
• An image takes about 1/2 minute to read out.

Photometric Parameters

Only one transiting hot Jupiter has been studied photometricly, i.e. the planet circling HD209458.  The graph below shows the photometric data gathered during the transit.

At the minimum the relative flux was lowered by 1.6% or about 0.017 magnitudes.  The ingress and egress each took about 15 minutes.

Initial Observations

One of the first items to note is the length of time the Mark IV can track a star (2 hours) is less than the length of a transit (2.7 hours), so the Mark IV will not be able to see both the ingress and egress of the transit.  Since the Mark IV can not move to an arbitrary RA it can not usually slew to targets of opportunity based on ephemeris values like the STARE project did.

For a particular transiting hot Jupiter the Mark IV would have a about a 5% chance of seeing either the ingress or egress over a 2 hour period.  Putting all the numbers together I estimate that any one star observed over a 2 hour period would have a 0.010% chance of a transition (ingress or egress).

In other words on average one star out of 500 would have an transiting hot jupiter and one star in 10,000 would transition during a typical two hour observation.

The light reduction is small for these planets.  To see the transition reliably we will need to achieve a relative photometric accuracy of 0.005 magnitudes to get a 3 sigma separation.

A Program for Finding Hot Jupiters

Two Phase Approach

To make the most of the Mark IV, I propose a two phase approach, a discovery phase and a followup phase.  In the discovery phase several sites will be monitoring different fields looking for transitions.  Candidates found in the discovery phase would be monitored in the followup phase.  The followup phase would be best served by general purpose telescopes which could track candidates for longer periods of time to find subsequent transitions.

Discovery Phase

To maximize the propability of detecting a hot Jupiter we would not point the Mark IV at a single field and follow it for two hours.  Instead we would take an exposure of a field, move to an adjacent field in RA, take an exposure, move to the next etc. and eventually return to the first field and repeat the process for a two hour period.  We would then rewind the Mark IV in RA and begin the process for another set of fields.  This allows us to effectively track more than one field during the two hour window.  Different sites would track different sets of fields.  This gives us a better chance of finding transitions and would contribute to generating an overall survey.

There are limits to the number of fields we can track effectively though.  In order to see a transition we would require a minimum number of exposures on either side of the transition itself.  This gives us an efficiency based on the number of exposures and the minimum number of exposures on either side of the transition, i.e. efficiency = (# exposures - 2*min)/# exposures.  The table below shows how to determine the most effective number of fields and exposure time.  All the numbers are for a single site.

Exposure Time (seconds)	Number of Fields	Effective Cycle time (seconds)	Exposures in two hours	Efficiency	Effective Number of Fields	Stars within Photometric Tolerance	Effective Total Number of Stars Monitored	% chance of seen a transition per night (8 hours)	# of transitions per year (100 nights)
60	1	90	80	0.90	0.90	200	180	7.2%	7
60	2	90	40	0.80	1.60	200	320	12.8%	13
60	3	100	24	0.67	2.00	200	400	16.0%	16
60	4	105	17	0.53	2.12	200	424	16.9%	17
90	1	120	60	0.87	0.87	238	206	8.2%	8
90	2	120	30	0.73	1.47	238	349	14.0%	14
90	3	130	18	0.56	1.67	238	396	15.9%	16
90	4	135	13	0.38	1.54	238	366	14.6%	15
120	1	150	48	0.83	0.83	283	236	9.4%	9
120	2	150	24	0.67	1.33	283	377	15.1%	15
120	3	160	15	0.47	1.40	283	396	15.8%	16
120	4	165	10	0.20	0.80	283	226	9.1%	9

The cycle time is based on a 30 second movement between adjacent fields in RA.  The cycle time increases if the number of fields is greater than two since rewind to the first position takes longer.

The efficiency is based on having a minimum of four exposures on either side of the transition.

The number of stars within photometric tolerance is based on the results I've been obtaining with the sample CD set Tom sent out a couple of months ago and a sqrt progression for exposure time.

The best program for discovery seems to center on three fields.  The exposure time doesn't matter too much in this example but if the number of minimum exposures on either side of the transition increases then shorter exposure times or fewer fields are favored but not dramatically.

Taking everything into account I recommend a program of 90 minute exposures with three fields.  This would generate about 16 transitions per year per site.

Followup Phase

Once a transition was discovered a followup phase would look for additional tranistions for the candidate.  This would probably be best accomplished with something other than the Mark IV.  Several individuals or institutions with more traditional systems could follow a candidate for 8 hours a night for several nights until more tranists were seen and the system characterized.  This might be an excellent program for a small college or university with an Astronomy department and the appropriate equipment.

Conclusion

I think a program of looking for transiting hot Jupiters using the Mark IV is a viable with a predicted 16 transitions seen per site per year.  Side benefits would include a lot of well measured, short period variable stars.