Borders of Arnor the Northern Kingdom

Arnor the Northern Kingdom:

I will start here with the kingdom of the north, the lands from which I hail. Many of its borders are straight forward from the words of Tolkien, the kingdom of the north would cover just about all the lands of Eriador. The direct exceptions to the rule of all would be the lands that lay beyond the river of the Lhûn or the Westernized Lune and the lands east of the river Greyflood or Gwathló and the river Bruinen also known as the Loudwater. These lands contained Rivendell along with the regions of Eragion also known as Hollin and the lands of Enedwaith, forming most of the eastern borders of Arnor. The last remaining bit of the eastern border of Arnor is finished with the misty mountains in the north east. As for the last of the south eastern borders they run into the elven realm of Lindon, this realm had extended around the Gulf of Lune and the Grey Havens. Along with Emyn Beraid the Tower Hills held in part by Arnor forming the border, the the towers were likely in the hands of Arnor during this time as many elves had already left and in the first time of Arnor Elstirion the tallest and westernmost tower held one of the palantíri of Arnor. Lastly the Blue Mountains also helped to define the western most border of south western Arnor. The southern border of the north kingdom is by far the easiest border to define as it is defined by the sea, a very clear cut border by any means as there is no land of Middle Earth past this point.

Now the last border of Arnor is the hardest to define and the one that took me the longest of this kingdom. In the north eastern half beyond the kingdom it is well known that the lands of Angmar are defined there between the Grey Mountains and the Mountains of Angmar in the lands of the Ettenmoors. In contrast to this the north western half of Arnor is not as clear so to this here is why I have not continued them up to the lake like some other maps have. The start of my conclusion has to do with the Lossoth or the Snowmen of Forochel, they being the remnants of the ancient people of Forodwaith. These people outside of the influences of the Númenóreans had lived mainly on the cape that had enclosed the bay, though it is noted that at least during the times of winter with the bay frozen they could camp and dwell in the areas of the southern rim. This does point to them having some control of the regions north west of Arnor, south of the bay as you can see in this drawing done by Christopher Tolkien with the bay labeled. 

This alone does decently well to the notion of the border falling on the line defined on my map, however in looking into the text there is mention of Arvedui the last King of Arthedain, the kingdom making up the north western kingdom of Arnor after it split into three, fleeing north to escape the destruction of Arthedain in which he flees to the Lossoth people and they help him escape on a elven ship, though warn him of his coming doom. Nonetheless the important part is he leaves his kingdom north to this bay, this indicates that the bay itself had no direct border with the lands of Arthedain and thus none with the lands of Arnor and leading to the completion of the northern border of Arnor.