i have questions about docker-compose
I searched for the healthcheck/postgres:alpine and I found the following repository with the Dockerfile:

https://github.com/docker-library/healthcheck/blob/master/postgres/Dockerfile.alpine

Assuming this is the correct repo for your docker image, the dockerfile specifies:

FROM postgres

COPY docker-healthcheck /usr/local/bin/

HEALTHCHECK CMD ["docker-healthcheck"]


So it extends the postgres docker image which is documented here:

https://hub.docker.com/_/postgres

Specifically for the password they mention the following:


  POSTGRES_PASSWORD This environment variable is recommended for you to
  use the PostgreSQL image. This environment variable sets the superuser
  password for PostgreSQL. The default superuser is defined by the
  POSTGRES_USER environment variable.
  
  Note 1: The PostgreSQL image sets up trust authentication locally so
  you may notice a password is not required when connecting from
  localhost (inside the same container). However, a password will be
  required if connecting from a different host/container...


Read the whole documentation at the image homepage.