DDD, CQRS - Identity service and user avatar (image) handling

I'm designing an Identity Service using DDD and CQRS pattern. So far I have one aggregate User that has all the logic for changing user's state (creating, resetting password, confirming email, etc.). In my understanding, user's avatar is also part of his identity and should be handled in the context.

I've decided that such small pictures can be saved directly to the database, but I'm not sure how to design it inside the domain (or whether it should belong to the domain at all).

Avatar could in fact be modelled as an Entity and referenced in User aggregate by its ID, like that:

public class Avatar: Entity<AvatarId>
{
    AvatarId Id { get; } // Strongly typed ID
    byte[] Picture { get; private set; }
    AvatarExtension Extension { get; private set; } // Enumeration: JPG, PNG, GIF, etc.

    public void ChangePicture(byte[] newPicture, AvatarExtension newExtension)
    {
        // Ommited parameters validation for brevity
        Picture = newPicture;
        Extension = newExtension;
    }
}

public class User: IAggregateRoot, Entity<UserId>
{
    ...
    AvatarId AvatarId { get; } //Avatar referenced by ID

    public void SetAvatar(AvatarId avatarId)
    {
        AvatarId = avatarId;
    }
}

I'm afraid it leaks some infrastructure concerns, Avatar seems more like a table definition in EF Core (code-first). In addition, Avatar would require to has its own repository, because it has to be handled separately (added to DdContext etc. before creating User), but this is not an aggregate root and my gut feeling is that it shouldn't be. Maybe referencing Avatar directly as an object in User and keeping it as one-to-one relationship would be a good idea?