How commonauth service work with SSO in WSO2 Identity Server

Considering two SAML service providers configured under the same tenant, they are by default in single sing on, so after I login in Service provider A I can use the same browser to access Service provider B without inserting my credentials again. This blog explains in details how this happened with commonauth service during the second login

What happens here is:

On the first login to service provider A, it stores a cookie with a name "commonAuthId"
When the first request comes; DefaultRequestCoordinator.handle() [1] method invokes DefaultAuthenticationRequestHandler.handle() method, see [2]
within the DefaultAuthenticationRequestHandler.handle() it invokes concludeFlow() private method [3], that sets the 'commonAuthId' cookie via setAuthCookie() method [4]

private void setAuthCookie(HttpServletRequest request, HttpServletResponse response, AuthenticationContext context,
                               String sessionKey, String tenantDomain) throws FrameworkException {
        Integer authCookieAge = null;

        if (context.isRememberMe()) {
            authCookieAge = IdPManagementUtil.getRememberMeTimeout(tenantDomain);
        }

        FrameworkUtils.storeAuthCookie(request, response, sessionKey, authCookieAge);
    }

FrameworkUtils.storeAuthCookie() method

public static void storeAuthCookie(HttpServletRequest req, HttpServletResponse resp, String id, Integer age) {

        Cookie authCookie = new Cookie(FrameworkConstants.COMMONAUTH_COOKIE, id);
        authCookie.setSecure(true);
        authCookie.setHttpOnly(true);
        authCookie.setPath("/");

        if (age != null) {
            authCookie.setMaxAge(age.intValue() * 60);
        }

        resp.addCookie(authCookie);
    }

[1] https://github.com/wso2/carbon-identity/blob/v5.0.7/components/authentication-framework/org.wso2.carbon.identity.application.authentication.framework/src/main/java/org/wso2/carbon/identity/application/authentication/framework/handler/request/impl/DefaultRequestCoordinator.java#L80

[2] https://github.com/wso2/carbon-identity/blob/v5.0.7/components/authentication-framework/org.wso2.carbon.identity.application.authentication.framework/src/main/java/org/wso2/carbon/identity/application/authentication/framework/handler/request/impl/DefaultRequestCoordinator.java#L135

[3] https://github.com/wso2/carbon-identity/blob/v5.0.7/components/authentication-framework/org.wso2.carbon.identity.application.authentication.framework/src/main/java/org/wso2/carbon/identity/application/authentication/framework/handler/request/impl/DefaultAuthenticationRequestHandler.java#L120

[4] https://github.com/wso2/carbon-identity/blob/v5.0.7/components/authentication-framework/org.wso2.carbon.identity.application.authentication.framework/src/main/java/org/wso2/carbon/identity/application/authentication/framework/handler/request/impl/DefaultAuthenticationRequestHandler.java#L284

Then, when we access the service provider B, it checks whether the "commonAuthId" is available in cookie list, if yes, then it gets the authentication details from SessionContext and by pass the authentication step.
see [5] findPreviousAuthenticatedSession() method

[5]https://github.com/wso2/carbon-identity/blob/v5.0.7/components/authentication-framework/org.wso2.carbon.identity.application.authentication.framework/src/main/java/org/wso2/carbon/identity/application/authentication/framework/handler/request/impl/DefaultRequestCoordinator.java