Question

In an eclipsing binary system, star \(A\) is brighter, larger, and cooler than its companion, star \(B\). What can be said about the depths of the minima when each of the stars is eclipsed?

Short answer

The primary minimum is deeper than the secondary minimum.

Step-by-step solution

Understanding the Eclipsing Binary System

An eclipsing binary system consists of two stars orbiting each other, where one star periodically passes in front of the other, causing a change in the observed brightness. The primary minimum occurs when the brighter star, star A, is eclipsed by the dimmer star, star B. The secondary minimum occurs when the dimmer star B is eclipsed by the brighter star A.

Analyzing Primary Minimum

The primary minimum happens when the dimmer star B moves in front of the brighter star A, causing a significant drop in the system's observed brightness. Since star A is brighter than star B, eclipsing star A will lead to a deeper minimum.

Analyzing Secondary Minimum

The secondary minimum occurs when star A eclipses star B. Because star B is fainter, its eclipse by star A results in a smaller drop in brightness. Therefore, the secondary minimum will be less deep compared to the primary minimum.

Conclusion on Minima Depths

In an eclipsing binary system where star A is brighter and larger than star B, the primary minimum (when star B eclipses star A) will be deeper than the secondary minimum (when star A eclipses star B).

Key concepts

Understanding the Primary Minimum

In an eclipsing binary system, the concept of the primary minimum is essential in understanding the brightness changes observed from Earth. This phenomenon occurs when the dimmer star, star B, passes directly in front of the brighter star, star A.
Due to this alignment, a significant reduction in the observed brightness of the system is noticed.
Since star A is naturally brighter and larger, when it gets eclipsed by star B, a larger portion of the total light from the binary system is blocked. This blocking results in a noticeable drop in brightness, hence the term 'primary minimum'. This minimum is more profound because star A, being the dominant source of light, contributes to most of the system's luminosity.
The primary minimum is a key indicator in binary systems for assessing the relative characteristics of the stars involved:

• It tells us that the drop in light is mainly due to the brighter star being obscured.
• It signifies the moment when the system's brightness is at its lowest due to the larger star being hidden.

Exploring the Secondary Minimum

Now, let's look at the secondary minimum in an eclipsing binary system.
This event takes place when the brighter star A eclipses the dimmer star B. Unlike the primary minimum, the secondary minimum is less noticeable.
This is because the dimmer star B contributes significantly less to the total light output of the binary system. When star A is directly blocking star B, the decrease in brightness is minimal since the majority of the light emission seen from the system comes from star A itself.
Thus, the term 'secondary minimum' accurately represents this slight dip in brightness:

• The secondary minimum shows only a minor drop due to the less luminous star B being hidden behind star A.
• This marks a smaller decline in the overall brightness compared to the primary minimum.

Examining the Minima Depths

The depth of the minima in an eclipsing binary system is a crucial factor that helps astronomers evaluate the properties of the stars.
Minima depths describe how deep each minimum drop in brightness is relative to the base brightness level. In the case of our stars, A and B:
The primary minimum's depth is more significant than that of the secondary minimum. This is due to star A, the brighter star, being eclipsed and thus leading to a substantial reduction in observed brightness.
On the other hand, the secondary minimum has a shallower depth because it involves star B, the dimmer star, being eclipsed.
Important points about minima depths include:

• The primary minimum's greater depth indicates the brightness contribution of the larger, brighter star is essential to the system's luminosity.
• The smaller drop observed during the secondary minimum reflects the lesser contribution of the dimmer star to the system's overall light.

By understanding these depths, we gain insights into the respective influence of each star on the perceived brightness within an eclipsing binary system.