Why the period of early morning (brahma muhurta or amrut wela) important for meditation? And what is that period (approx. from hhmm AM to hhmm AM)? (I know the twilight period for sandhya vandanam. But here I am talking about amrut wela). Would like to have scriptural references, not just opinions please.
Your enquiry is about Brahma Muhurta or Amrit Vela. The scriptural ref. can be found in one of the ancient text called Ashtanga Hridaya , which is an Ayurvedic text The author is called Vagbhata .The approximate best time to wake up or Brahma Muhurta is mentioned there. Pratahkalotthana (Wakeup Time).
ब्राहमे मुहुर्त उत्थिष्ठेत स्वस्थो रक्षार्थमायुष:
in order to protect his life , healthy person should get up from the Bed in Brahma Muhurta.
Arundatta in his "Sarvangasundari" commentary on Asthanga Hrdaya it is clearly stated as
रात्रेश्चतुर्दाशो मुहूर्तो ब्रहमो मुहूर्त: |
That means brhama muhurta is the 14 th muhurta kala of the night. One muhurta is equivalent to 48 minutes.
Whole night consisit of 15 muhurtas = 15*48 =720 minutes.
Brahma muhurta is te time , which is after completion of 13 muhurtas in the night time i.e.
Hence one has to getup from the bed early in the morning 96 minutes before sunrise i.e. about 4:24 a.m. It is sutaible time to study and obtain knowledge. It is also the time when all the three doshas are in equilibrium state.
Here more about Ashtanga Hridaya-
There is also mentioning of Daybreak or Brahma Muhurta in Srimad Bhagavata Purana. Swami Prabhupada in his commentary of the below shloka is explaining significance of Brahma Muhurta. It's said that this time is recommended very suitable for conducting Spiritual activities , at this time they will have great effect than any other part of the day or night.
ते तु तज्जगृहू रूपं त्यक्तं यत्परमेष्ठिना ।
मिथुनीभूय गायन्तस्तमेवोषसि कर्मभिः ॥SB 3.20.46||
te tu taj jagṛhū rūpaḿ tyaktaḿ yat parameṣṭhinā
mithunī-bhūya gāyantas tam evoṣasi karmabhiḥ
The Kimpurusas and Kinnaras took possession of that shadowy form left by Brahma. That is why they and their spouses sing his praises by recounting his exploits at every daybreak.
Purport -The time early in the morning, one and a half hours before sunrise, is called brahma-muhurta. During this brahma-muhurta, spiritual activities are recommended. Spiritual activities performed early in the morning have a greater effect than in any other part of the day.
Ganganatha Jha, in his translation of Medhatithi's commentary on the Manusmriti quotes the following from a Dharmashastra digest:
Vīramitrodaya (Āhnika, p. 13), which explains ‘Brāhma muhūrta’ as ‘the last quarter of the night’, and adds that the time is so called because it is the time for the awakening of Brāhmī, i.e., Bhāratī, the goddess of speech; and that the term ‘muhūrta’ is to be taken as standing for time in general, and not in the restricted technical sense of a period of 48 minutes; and this on the ground that 48 minutes would not suffice for all those acts that are prescribed for being done after rising and before sunrise. It goes on to add that according to other Nibandhas, the last but one Muhūrta (48 minutes) of the night is called ‘Brāhma’, because it is sacred to Brahman. The conclusion that it arrives at is that those who have to perform all the acts of Vedic study and the rest should rise in the beginning of the last quarter of the night, i.e., at 3 a.m. while others in the third Muhūrta of that quarter, i.e., after 4-36 a.m.
See source link for more quotations of the same author.
As to its significance and duties, see the various Puranas such as the Brahma-purana 113.17-18:
One shall get up in the Brāhma Muhūrta and think about virtue and wealth. After getting up, one shall perform the Ācamana rite. After taking both and making himself pure one shall worship the Sandhyās. The early Sandhyā (i.e. dawn) he shall worship even when the stars are seen. He shall worship the late Sandhyā (i.e. dusk) even when the sun is visible. He shall perform Sandhyā prayers duly. Unless in extreme case of emergency he shall not forsake it.
As well as the Garuda-Purana chapter 229:
Rising at the Brahma Muhurta (about half an hour before the dawn) a house-holder shall attend to the calls of nature, and then having carefully washed himself, at the close of the night, shall think of his own good both in this world and the next. Then he shall bathe and attend to the rite of his Sandhya meditation. He shall perform the rite of his morning Sandhya after having washed his face and cleansed his teeth.
Also, the Rudra-samhita of the Shiva-purana:
16-18. One shall get up early in the morning during the Brāhma Muhūrta (about an hour before dawn). He shall remember the preceptor and Śiva. O sage, he shall then remember the holy centres and meditate on Hari. Thereafter he shall remember me, the deities and the sages. Then he shall recite a prayer in the name of Śiva duly. Then he shall get up and evacuate his bowels in southern quarter.
In his comments on the above verse, the translator J. L. Shastri, says the following about Brahma-muhurta:
It is the period between the fourth and the second ghaṭikas before sunrise. “rātriśca paścime yāme muhūrto brāhmya ucyate”