Fajr and Isha Times During Persistant Twilight

What is persistent twilight?
As the sun sets below the horizon, the sky goes a deep red colour. This colouring is because the sun's rays can still reach the sky above it. After a while, the sun will descend further, by a certain angle, below the horizon until none of its rays will be able to reach the sky. It is at this point we get complete darkness.
In northern parts of the world, the sun does not descend by an angle sufficiently below the horizon for the sky to go completely dark. The sun's rays will continue to reach and illuminate the sky for the whole night. It is this phenomenon that is termed persistent twilight. This can be seen in this online video: (Please click here for video redirect)
How does this effect prayer times?
The time for Isha salah begins when the sky has gone dark due to the sun descending the horizon by a certain angle. As we can see from the definition above, Isha time can not technically begin as visible twilight still remains in the sky.
Are there any other prayer times that are effected?
Yes, the starting time of Fajr. This is because Fajr time begins when, in the darkness of night, a white line rises parallel to the horizon. When persistent twilight occurs and the sky does not go dark, the white line will never appear as the horizon is already illuminated.
So there is no Fajr time either?
There is no visible start time, but there is a finish time. That is, when the sun itself begins to become visible on the horizon.
So when do we pray Isha and Fajr?
Scholars have studied this case in depth and have provided many options based on a Prophetic Hadith on this specific issue. The three that are most commonly used are:
1. The One Seventh Rule: Isha time starts after one seventh of the night has passed. Fajr time starts with the last seventh of the night.
2. Estimation: In a county where there is no persistent twilight, the the times of Isha and Fajr as a percentage of the length of the night are found. These percentages are then used in areas of persistent twilight.
3. Alternately for Isha: Combining it with Maghrib.
For details, please refer to resolutions passed by the international Fiqh Councils.
What is the value of the sun's depreciation angle at which one starts to adopt one of the above methods?
Different values are given by different sources. They range from 14 to 18 degrees. An attempt to resolve this is being made in an Online Open Project: Variant Fajr and Isha Times. The project is currently open and can be found at the following site: thesunangle.blogspot.com