OLED - dobles

AIMS

PROCEDIMIENTOS

ANALYSIS

TECHNIQUES

PREDICTIONS

OBSERVERS

REPORT

RESULTS

DOCUMENTS

LINKS

CAMPAINGS

NEWSLETTER

Double stars

The aim of the OLED project is to study double star astrometry using lunar occultations. This is a very accurate technique, comparable in spatial resolution to some interferometric techniques, and therefore ideal to access binary stars with angular separations in the range 0.010"-0.1". We expect to be able to measure double stars that are not accessible to standard visual or speckle interferometric techniques available to the amateur. Also, the collaboration between groups of observers allow for the determination of two-dimensional positions, rather than the standard one-dimensional (projected) solutions normally obtained from single observations.

Lunar occultations of stars have historically played an important role as a method for measuring a uniform time scale (the so-called Ephemeris Time), impossible to materialize using traditional methods based on the (irregular) rotation of the Earth. Nowadays, the development of atomic clocks, based on quantum transitions of certain atoms, allows for the construction of a highly uniform scale independent of the Earth's rotation. This is one of the reasons why lunar occultations have lost interest within the professional astronomical community.

However, over the years, lunar occultations have undergone other vicissitudes unrelated to the measurement of a uniform time, some positive, some negative. These phenomena greatly contributed to the knowledge of the lunar limb, and consequently the topography, of the lunar surface. Additionally, they helped to assess the accuracy of lunar ephemerides and stellar ephemerides (i.e., the precision of star catalogues regarding position and proper motions).

Nevertheless, recent advances in celestial mechanics, the improvement of stellar astrometry (for example, Gaia), and lunar topographic surveys carried out by various probes orbiting the Moon, have once again relegated lunar occultations to a corner of history: few professional or amateur astronomers are involved in lunar occultations.

Light curves of occultations of double stars. On the left, an emersion (observation made by Rosendo Jorba, AAM), and on the right, an immersion (observation made by Enrique Velasco, AAM), both taken with commercial digital astronomical cameras. In both cases, the existence of an intermediate step is observed, at a level of 0.14 (left) and 0.11 (right; in this case, the drop in the curve just before the occultation was due to adverse atmospheric phenomena). The durations were 5571 milliseconds (ms) on the left and 680 ms on the right, resulting in separations of 3.06" and 0.37", respectively. These distances correspond to the separation between the components of the double star, projected onto the apparent motion direction of the Moon and with respect to the local limb in each occultation. The step levels, at 0.14 and 0.11 above the unit, correspond to drops of -2.5 x log 0.14 = 2.1 and -2.5 x log 0.11 = 2.4 magnitudes, respectively.

And yet, there is still some hope for lunar occultations! In this project, we propose revitalizing the field by focusing on occultations of double stars. Why double stars?

As the Moon moves across the sky, it completes one orbit in 27.3 days (sidereal period), which averages about 13.2 degrees per day, or 0.55 arcseconds per second of time. Imagine the Moon occulting a double star: first, we see one of the components disappear, followed by the other. The light curve of the pair will show a step, corresponding to the time interval between the two occultations. The figure above shows two examples where the presence of steps was detected, revealing the existence of a double star.

The duration of this interval is directly related to the apparent separation between the components and their position angle (as defined in the field of double stars), but other parameters are involved in this relationship: the point on the lunar limb where the occultation occurs and the velocity (magnitude and direction) of the lunar motion. These latter two parameters are generally known, so an observer must reconstruct two parameters (relative distance and position angle between the components of the double star) from a single measurement: the duration of the interval in the light curve. This is mathematically impossible.

This is where the collaborative aspect of the project comes into play:

If at least two observers located in different and sufficiently separated stations observe and measure the event, we will be able to extract values for the parameters of the double star.

The more observers participate, the more accurate the estimation will be, as the statistical aspect comes into play, allowing for optimization and considerable error reduction.

How far apart should the observers be? We need the occultation contact points for different observers to ideally distribute along the entire "front" limb of the Moon (i.e., the limb that hides stars) if it's an immersion, or the "rear" limb (from which stars emerge) if it's an emersion, in an arc of almost 180°. Speaking in terms of latitude, and assuming the Moon is on the common meridian of observers with the same geographic longitude, the difference in latitude associated with the maximum 180° arc depends on lunar parallax and is close to 28° under optimal conditions. Translated to distance on Earth, that means about 3000 km: covering the entire arc becomes a pan-European project, also involving North Africa! But it doesn't have to go that far: a separation of 100 km in latitude implies a difference in arc along the limb of about 6°, enough for the reduction procedure to provide reasonable accuracy. However, the greater the distance and the more observers, the better.

The lunar occultation technique can be extremely sensitive and even allow the measurement of parameters of double stars cataloged as spectroscopic. Returning to the average motion of the Moon (about 0.5" per second of time), a measurement of a few tens of milliseconds of time for the duration of the interval (which is perfectly achievable with any amateur-level imaging equipment) implies a separation of a few tens or even units of milliseconds of arc. It's advisable to have access to the UTC scale with an accuracy of 0.1 seconds or better, as this will allow us to correctly position the Moon, and measuring the duration of the step accurately; this is easy to do in principle.