"Susan" walked into my office, shoulders slumped, clothes disheveled and hair unkempt. Eyes sunken, even the most mundane decision regarding where to sit challenged her on this day.
She stumbled into a chair and, without removing her coat, proceeded to tell me how she had reached a new low in her depression. She wasn't eating. She hadn't left her bed except to tend to the obligatory restroom break to relieve her discomfort, but even the importance of that she debated. She looked up, her despair emanating from her sad, drawn eyes.
She looked up seeking approval.
"Offer her Reiki," the voice in my head whispered.
"I will not!" I replied to my internal consultant.
After all, I had just received my Reiki Level 2 training the previous weekend. What if I didn't do it right?
Even though my training as a Reiki practitioner had fully prepared me to offer the ancient energy, my ego refused to get out of the way, and I continued to ignore the increasingly irritating internal prodding.
"I read about something called Reiki. Do you know anything about it?" Susan asked.
I almost fell out of my chair as my client continued her inquisition regarding energy psychology. My internal voice squealed with delight.
Susan's eyes, now the size of saucers, took in my brief explanation about the energy therapy and, following an informed verbal consent, I began to prepare her to receive the treatment. I had her relax and close her eyes while sitting in her chair. I told her I would offer her the subtle energy from across the room, keeping the intention for her greater good and healing. I asked her to imagine a lighted stone pathway spanning the space between my heart and hers on which a bright, golden flow of rich, healing light flowed, filling any spaces in her body that wanted to receive the energy.
I prepared myself, holding the intention of healing and compassion for my client, and then, reciting the ancient symbols silently, I offered her Reiki. We sat in this quiet, contemplative space for 10 of the remaining 15 minutes of the session. I wanted to have time to debrief my client and assess her degree of despair and possible need for hospitalization.
I could feel my heart leap with joy, and I began to assess Susan's emotional pain and safety. She stated that she felt as if an enormous psychic weight had been lifted off her chest and she could finally breathe. She indicated that she actually felt hungry … famished … and was going to go home and eat for the first time in days.
Although I did not feel that hospitalization was warranted for Susan, I was still apprehensive about waiting until our regularly scheduled appointment to see her again, so I scheduled her to come in the following week. Imagine my delight and surprise when Susan arrived to her appointment the following week with makeup on and hair coiffed and a list of goals that she wanted to tackle in her life. That became the first of many integrated psychotherapy sessions in which I employed Reiki.
Reiki (pronounced RAY-kee) is from the Japanese words Rei, which translates to mean universal or being everywhere, and Ki, which translates to mean life energy. Reiki is believed to be spiritually guided life energy. It was developed by Mikao Usui in 1922. However, it has been practiced for thousands of years.
The National Center for Complementary and Alternative Medicine (NCCAM) categorizes Reiki as an energy therapy. Reiki practitioners place their hands on or just above their clients to offer healing energy that is believed to transmit through the attuned practitioner to the client. Practitioners believe this energy to be of the purest and highest frequency of energy or "life force," allowing the client's body to enter a relaxed state. This relaxed state helps the body to activate its natural healing properties. Because the practitioner is channeling the energy through the body, the belief is that it does not deplete the provider and, in fact, provides healing to the healer.
Initially, Usui employed Reiki with the poor in Kyoto, Japan. He then began training others to offer this energy, including a former naval officer, Chujiru Hayashi. Following the death of Usui, Hayashi opened a clinic in Tokyo and trained a Reiki patient named Madame Takata. It is Takata who is believed to be responsible for bringing Reiki to Europe and America.
Currently, there are an estimated 50,000 Reiki masters (of which I am one) and 1 million Reiki practitioners worldwide. These providers are from a variety of clinical and nonclinical fields and include physicians, nurses, respiratory therapists, physical therapists, massage therapists and psychotherapists.
Reiki is easy to learn. It does not require that one meditate, nor does it require years of study. A practitioner is able to offer Reiki following attunement by a Reiki master-teacher.
There are three levels of learning in Reiki. The first level is learning to offer Reiki to oneself. The second level introduces three symbols considered to be sacred and promote a connection to the energy. Completion of Level 2 affords the title of Reiki practitioner and indicates that one is equipped to offer Reiki and distance Reiki to clients. A practitioner can be attuned in advanced Reiki to a higher frequency of energy.
The master level of learning involves additional symbols and another attunement or ignition to the energy. A person is not considered a master-teacher until she or he has taught a class. Organizations such as the International Association of Reiki Professionals and the International Center for Reiki Training promote quality and standardized approaches to Reiki training.
According to Eastern medicine, life energy or ki flows through the body. When this energy is compromised in some capacity, it hinders well-being. The goal of Reiki is to allow the body to be at its optimal condition for life energy to flow freely, thereby affording the opportunity for natural healing properties to occur in the body. The natural healing mechanism is promoted by helping the client to obtain a relaxed state through the laying on of hands or distance treatment and channeling the energy to the client.
Records of Reiki's use are growing as Western medicine seeks ways to provide care in a holistic manner. Reiki is currently being offered not only for management of physical pain but emotional pain as well. According to a survey conducted by Health Forum, a subsidiary of the American Hospital Association, 42 percent of the responding hospitals in the United States and 70 percent of the responding hospitals in Canada offer complementary and alternative treatments including Reiki and healing touch. Reiki is used in the treatment of anxiety, depression, trauma, stress and memory loss, as well as in palliative and oncological care.
Reiki is offered in hospitals, clinics and hospice settings. For example, the Integrative Medicine Department of Memorial Sloan Kettering Hospital offers and teaches Reiki to patients and caregivers. In a 2010 study conducted by Yale University and published in the Journal of the American College of Cardiology, researchers Rachel Friedman, Matthew Burg, Pamela Miles, Forrester Lee and Rachel Lampert found that 20 minutes of Reiki significantly improved mood and variable heart rate following a heart attack. This was above and beyond control for other variables.
More and more mental health professionals are seeking ways to empower clients with tools to manage their emotional and physical discomfort. Anxiety and emotional discomfort may provide information regarding behavioral and life changes that would be more healthful. Reiki allows clients to ground and be fully present in their bodies, listening to what the body, mind and soul are disclosing and manifesting as symptoms of anxiety and depression.
Reiki provides a tool that integrates grounding exercises with talk therapy. For example, I like to use a Reiki tool that allows clients to imagine whatever they want to rid themselves of as a shape with color, weight and texture. Once they have completely created their image, I ask them if they really want to release themselves from this (anxiety, resentment, depression, anger, etc.). They affirm this out loud. I then ask if they are willing to make the necessary changes to release their manifestation. Again, they affirm this out loud.
These preparations for the actual Reiki healing resonate with cognitive behavior therapy and expressive therapies. Clients employ their senses in creating an image that captures their sensory experience of their perceived angst. They are then asked to affirm their desire for change and their desire to make the changes necessary to affect change. Following this setup, I prepare myself and energetically help clients excise the imagined object from their being. This is one of my favorite tools because it has led to great success with clients who just seem stuck and need additional clearing.
Reiki is also a tool that clients can learn for their own personal use in self-care. The tenets of counseling promote the empowerment and self-sufficiency of the client. Reiki promotes a practice of clients becoming more self-aware to their physiological and energetic needs and provides a means to address care and healing.
A variety of universities, hospitals and organizations are conducting research to assess the efficacy of Reiki and touch therapies. The Center for Reiki Research (TCRR) uses a Touchstone Process of peer-reviewed consultation and analysis of current research projects.
In a controlled experiment reviewed by TCRR, Ann Baldwin and colleagues were able to demonstrate that Reiki offered at a distance decreased the stress response in rats. This was indicated by a reduction in heart rate and a significant increase in the physiological indicators of relaxation state. Animal studies reduce the placebo bias previously suggested by critics.
Ancient modalities appear to have wisdom to offer Western medicine. As mental health providers continue to seek ways to help clients with pain reduction and self-care, Reiki and touch therapies will be further explored. As a Karuna Reiki master practitioner, I have countless anecdotal experiences that speak to the effectiveness of Reiki. However, as a scholar-practitioner, I recognize the need for continued rigor in research as we discern the efficacy and standard of practice in the integration of Reiki and counseling practices.
Cheryl Fisher is a licensed clinical professional counselor and a Karuna Reiki master in private practice in Annapolis, Maryland. In addition to her practice, she is a visiting full-time faculty in the pastoral counseling program for Loyola University Maryland. Contact her at Cyfisherphd@gmail.com.
Chances are that an online review of a product or service has significantly influenced your decision to purchase something (or not purchase something) recently. In fact, one research study reports that 84 percent of Americans say online reviews influence such decisions (see www.saurageresearch.com/online-consumer-reviews-drive-sales/). Furthermore, 63 percent of customers say they are more likely to make purchases from a site that has user reviews (see mycommerce.com/blog/item/309-use-customer-reviews-to-drive-sales). Many marketing and research firms point to even negative reviews as a positive marketing opportunity. They suggest that the presence of negative reviews makes the reviews as a whole seem more realistic and believable. This opportunity can be especially beneficial if the business responds to negative reviews in a courteous and helpful manner.
No data exists on how reviews influence consumers' choice of a counselor, so we don't know exactly how these findings translate to our field. What we do know is that such findings are pretty consistent across the board for other businesses. In addition, the presence of a business on sites such as Yelp, Google Places and others, along with corresponding reviews, has been shown to be beneficial in terms of search engine optimization. This can result in a business appearing more prominently in searches. If we stop there, it would seem to be a no-brainer for counselors to participate in review sites and post testimonials on their own websites.
It is interesting to note that the second sentence was added in the 2014 revision of the ethics code. The summary is that counselors can use unsolicited testimonials as long as they have discussed the implications with the client and received his or her permission.
This would seem to create a very narrow window of opportunity. First, a client has to offer a testimonial, completely unprompted, and then still agree to its public use after the counselor explains how this use might affect the client's privacy. Here begins an interesting dance between advocating for client autonomy and ensuring that no harm is done. Following are just some of the questions that might come up when exploring this situation.
Is there any potential for harm, regardless of how minor, in asking the client if the testimonial can be placed online or in marketing materials?
What is your responsibility for informed consent in this situation?
Does the client understand the implications and potential ramifications of placing the testimonial online, even if the client's name isn't attached?
If the testimonial is from one member of a couple or family you have worked with, how do the other family members feel about this? Should they not also be included in the informed consent?
Do you or your business stand to truly gain anything from anonymous or anonymized testimonials? (I'm pretty certain that testimonials with real names attached to them carry much greater weight, although I wasn't able to find conclusive data. For example, Amazon even goes so far as specially marking reviews from people who definitely purchased the product).
How might the existence of testimonials affect other current and potential clients? Although we know reviews can be influential for many individuals, might the presence of these reviews also raise privacy concerns?
Does any review or testimonial from one person truly represent how well you can establish rapport and an effective counseling relationship with another person, especially without revealing personal and confidential data?
It is especially important to explore these questions before making your decision because the primary motivation for using testimonials is to benefit your business. Meanwhile, there is likely little identified benefit to the client.
I'll leave the exploration of ethics to the individual reader and instead focus on additional information and considerations, should the counselor decide to proceed with testimonials or need to address an online review.
Lest counselors insist that they don't utilize social media ("I don't have a website, Facebook, Twitter or other accounts"), it should be noted that the presence of a business on social review sites isn't always voluntary. With a site such as Yelp, any user wanting to write a review can add a business. Keely Kolmes has an excellent example of a social media policy available on her site at drkkolmes.com/social-media-policy/.
Because we're branching into reviews, let's examine the two basic differences between testimonials and reviews.
1) Location: Testimonials typically will be presented by the business on its marketing materials (brochures, websites and so on). The business chooses which testimonials to use. Reviews, on the other hand, can be found on any number of websites that specifically offer reviews, on other social media sites such as Google Places, on blogs or even on someone's Facebook wall.
2) Objectivity: Reviews are supposed to be objective opinions offered by customers. Reviews may be positive, negative or neutral. Testimonials tend to be hand-chosen, positive comments, often solicited for a specific purpose. Testimonials are a sales tool meant to highlight the benefits of the business, product or service.
As it relates to the ACA Code of Ethics, there is essentially no difference between reviews and testimonials. They offer an equal likelihood of compromising confidentiality/privacy or causing harm. This calls into question whether a counseling practice should be listed on sites such as Yelp at all. Because such sites exist solely for the purpose of people reviewing businesses, couldn't listing your business there equate to soliciting reviews?
Regardless of your take on this question, we've already established that a business can end up listed on such sites involuntarily. So, given this gray area, how can counselors address reviews?
One way that I've seen counselors approach this issue is by seeking testimonials or reviews from other professionals. Nothing prevents us from soliciting such statements from colleagues and other professionals who are familiar with our work, in part because there are no privacy concerns to be addressed.
Although there is some question about whether this is as effective as a review from someone who directly participated in counseling with you, it is likely to have some positive effect. When taking this approach, counselors should still clearly state what the relationship is between them and the person offering the testimonial. In particular, it should be abundantly evident that the reviewer is not a current or past client. Both for effectiveness and to avoid an ethical dilemma, it should also be clear from the description and testimonial why this other professional is able to speak to the counselor's qualifications and abilities.
Roy Huggins, a licensed professional counselor and my co-host on Therapy Tech With Rob and Roy, has a great example of such a statement for his Yelp account, which he modified from Kolmes' template. You can find a link to it and additional thoughts about the topic at http://bit.ly/1Fm6dbd.
As each counselor considers how to approach this situation, note that a Nielsen poll recently determined that "recommendations from personal acquaintances [were] cited as the most trusted form of advertisement by U.S. Internet consumers (76%). Forty-nine percent said they trusted consumer opinions posted online." So, although the Internet and social media continue to grow in importance in the marketing realm, they still lag behind the effectiveness of solid word-of-mouth advertising.
I know I have clients who openly and gladly tell their friends, family members and acquaintances that they are working with me or have worked with me in the past. They are not concerned about keeping that information private or confidential, and I'm confident they would gladly offer a testimonial. So I don't want to give the impression that this is an open-and-shut case against testimonials and reviews. I do think it is important, however, for counselors to think through all of the ramifications before going down that road.
Rob Reinhardt, a licensed professional counselor supervisor, is a private practice and business consultant who helps counselors create and maintain efficient, successful private practices. Before becoming a professional counselor, he worked as a software developer and director of information technology. Contact him at rob@tameyourpractice.com.
Coming on the heels of its successful annual conference and expo in March in Orlando, Florida, the American Counseling Association is turning its attention to another conference in a tropical locale. This one, however, will be across an ocean.
Samuel T. Gladding will be among the small contingent of ACA leaders traveling to Singapore next month for ACA-APCC 2015. Gladding, a past president of ACA and a well-known counselor educator, will deliver the conference keynote address, but he says he's equally eager to learn from the conference's attendees.
ACA-APCC 2015 will be ACA's first conference in Singapore. The two-day event will be held at the Suntec Conference Centre in Suntec City. In addition to Gladding and Smith, ACA CEO Richard Yep, ACA President-elect Thelma Duffey and ACA Chief Professional Officer David Kaplan will attend on behalf of ACA.
Po is founder and past president of the Association of Psychotherapists and Counsellors in Singapore; Lee is the association's current vice president.
ACA members have been involved in cross-cultural experiences, such as teaching or working abroad, for decades, Smith notes. He says the Singapore conference came together this year because the ACA leadership decided the time was right to organize an international conference.
The theme of ACA-APCC 2015 is "Being an Effective and Resilient Counselor." Gladding says his keynote will focus on the qualities of competent and effective counselors, and how these qualities stretch across cultures. "What do we share in our perspectives about what a counselor should be, and what can we learn from one another that transcends cultures and helps clients?" he asks.
Gladding has previously spent time as a Fulbright specialist in China and has spoken at conferences, led workshops and worked closely with universities in Singapore, Malaysia and the Philippines. He notes that professional counseling is practiced and taught at the university level in more than 40 countries worldwide.
Visit the website at aca-apcc2015.org for more information.
I was raised with my mother telling me that the three things you were not supposed to discuss in polite company were religion, politics and money. Historically, counselors have also been hesitant to talk about religion or religious issues. This hesitancy is grounded in the profession's belief in the separation of church and state and the idea that counselors should never impose their values on a client. Additionally, there is seldom training on how to ethically navigate these areas as practitioners. Consequently, when issues in counseling turn to religion or spirituality, many of us quickly suggest that clients should discuss such things with their pastors, rabbis, priests, imams or other religious leaders. But the old thinking that a client's religious or spiritual issues must somehow be kept separate from the rest of counseling has changed, thanks in part to the 2014 ACA Code of Ethics and the ASERVIC Competencies for Addressing Spiritual and Religious Issues in Counseling.
The ACA Code of Ethics requires counselors to practice within the boundaries of their competence, and counselors must be able to ethically and appropriately respond to spiritual needs presented by their clients. The Association for Spiritual, Ethical and Religious Values in Counseling's (ASERVIC's) spiritual competencies, revised and approved in 2009, have been endorsed by the American Counseling Association. The competencies complement and are consistent with the ACA Code of Ethics. Spiritual and religious beliefs are considered a part of the multicultural approach to counseling. In addition, they are relevant constructs of holistic philosophies that guide the counseling profession.
1) The professional counselor can describe the similarities and differences between spirituality and religion, including the basic beliefs of various spiritual systems, major world religions, agnosticism and atheism.
2) The professional counselor recognizes that the client's beliefs (or absence of beliefs) about spirituality and/or religion are central to his or her worldview and can influence psychosocial functioning.
3) The professional counselor actively explores his or her own attitudes, beliefs and values about spirituality and/or religion.
4) The professional counselor continuously evaluates the influence of his or her own spiritual and/or religious beliefs and values on the client and the counseling process.
5) The professional counselor can identify the limits of his or her understanding of the client's spiritual and/or religious perspective and is acquainted with religious and spiritual resources, including leaders, who can be avenues for consultation and to whom the counselor can refer.
6) The professional counselor can describe and apply various models of spiritual and/or religious development and their relationship to human development.
7) The professional counselor responds to client communications about spirituality and/or religion with acceptance and sensitivity.
8) The professional counselor uses spiritual and/or religious concepts that are consistent with the client's spiritual and/or religious perspectives and that are acceptable to the client.
9) The professional counselor can recognize spiritual and/or religious themes in client communication and is able to address these with the client when they are therapeutically relevant.
10) During the intake and assessment processes, the professional counselor strives to understand a client's spiritual and/or religious perspective by gathering information from the client and/or other sources.
12) The professional counselor sets goals with the client that are consistent with the client's spiritual and/or religious perspectives.
13) The professional counselor is able to a) modify therapeutic techniques to include a client's spiritual and/or religious perspectives and b) utilize spiritual and/or religious practices as techniques when appropriate and acceptable to a client's viewpoint.
14) The professional counselor can therapeutically apply theory and current research supporting the inclusion of a client's spiritual and/or religious perspectives and practices.
In 2009, Jennifer R. Curry published an article in the Journal of Creativity in Mental Health regarding the use of spiritual timelines with clients in counseling. She and Stephanie Dailey developed a lesson plan to expand the use of spiritual timelines to address counselor competency and to explore our own values, beliefs and attitudes about spirituality and religion. Their spiritual timeline activity assists clinicians and counselor educators in this exploration.
The activity involves an experiential component of developing a drawing and an accompanying narrative to highlight critical events, defining moments, developmental crises and other experiences that have contributed to spiritual development or challenged spiritual assumptions and beliefs. The goal is for professional counselors to become effective at addressing client spirituality issues by first becoming aware of their own.
When addressing spirituality in the classroom, I asked master's-level counseling students to engage in the spiritual timeline activity. In addition, at the 2014 ACA Conference in Honolulu, I facilitated the activity for attendees at a professional presentation. I found that the spiritual timeline narratives were deeply personal for both the students and professional counselors and informed much of their own framework of working with clients. The following examples of three narratives and drawings demonstrate how this spiritual timeline activity contributes to awareness, competency and working more effectively with clients.
The timeline in Drawing 1 (above) belongs to Dorinda. Initially, she didn't believe this activity would apply to her at all because she did not identify as religious. She has since expanded her view and now sees herself as a deeply spiritual person and clinician. The numbers in her narrative correspond with the figures in her spiritual timeline.
1) When I was a kid, we lived on the West Coast. My family did not go to church. My brother and I would sometimes attend church with friends if we spent the night at their house.
2) I remember talking with my mom about what religion we were. My dad was not raised in any religion, and my mom described herself as a "recovering Catholic." My mom said that we were best described as humanists and believed in the good in other people.
3) We moved to a Southern state when I was in middle school. The move was a big culture shock. Religion was never a big issue where we used to live, but in this community, it seemed like people categorized others by what church they attended.
4) I went to church a few times with a girl of the same age who was my neighbor. They attended a megachurch, and I did not like the service. There was a lack of community, and we didn't talk with anyone else; just went for the service and left right away.
5) My whole family was relieved when we moved back to the West Coast when I was a freshman in high school. When we were visiting the area to look at houses, we went to a café for breakfast on Sunday morning. Everyone was very casual and looked like they had just rolled out of bed and came down for coffee. We felt much more at home here where people were "real." In the Southern state, we had known women who had never let their husbands see them without makeup.
6) I rode horses and spent a lot of time at the barn working and riding. My favorite times were early in the morning when I was alone with the horses as the sun was rising. It was so peaceful, quiet … almost spiritual.
7) When I was a teenager and young adult, I spent a lot of time outdoors and in nature. I enjoyed going for hikes alone or with friends. When I was upset, I would always go out in nature and usually to the beach.
8) My husband and I moved to Wales and then England after graduating from college. I was really depressed during this time and realized how important friends, family and a sense of belonging are to my well-being.
9) While living in England, I started working at a woodland organization teaching children. This was the first step in a slow process of moving toward a career in counseling.
10) We moved to Boise, Idaho, seven years ago, sight unseen. This was a big leap for us, and we ended up loving the city and found a great community of friends.
11) For two and a half years, I worked as an instructor in wilderness therapy. Some of my most peaceful and spiritual moments have been spent alone contemplating my life in the desert.
12) When my husband and I got married, neither of us had any close ties to religious traditions. Instead, we spent a lot of time researching different wedding ceremonies and ended up creating our own. We asked a friend to officiate, and she helped us come up with a beautiful ceremony that was much more spiritual than either of us would have created on our own but was so perfectly us.
13) Being in grad school for my master's in counseling has been a spiritual journey on its own. I have spent a lot of time re-examining my own values and beliefs and creating a stronger core in myself.
14) The next step for me is thinking about having kids. I have been thinking a lot about how I was raised and how I might want to parent and raise my own kids in the future.
After engaging in this activity, Dorinda initially focused on using the spiritual timeline as an intervention when working with clients. As her counselor identity developed, she would bring questions about client spirituality into sessions to broaden the client's perspective of how unique spirituality can be for each individual. She started observing how clients' beliefs about spirituality contributed to the underlying themes in counseling sessions and how those beliefs and themes were interwoven into clients' counseling journeys.
Dorinda now also believes that this timeline activity has facilitated an awareness of spirituality in her own life, including what aspects of spirituality are important and continue to develop in her, and how those aspects affect her work as a professional counselor.
Drawing 2 (above) is a spiritual timeline by Madeline. Before engaging in the timeline activity, Madeline saw spirituality and religion as the same thing. She now separates the two and feels very comfortable broaching the topic of religion and spirituality with clients. The reference for each picture is labeled in parentheses with an accompanying age and brief description. Madeline was raised with a strong religious and spiritual belief system that has changed as a result of significant events in her life.
(Water, 4) — One of my first memories is a religious one. I was getting baptized in our church. I remember being scared of how long I would be underwater and remember knowing my parents were proud of me.
(Two Choices, Black or White, 4-12) — Growing up, there was always a right and a wrong for everything, per the Bible, and no gray. It made life simple and easy to understand.
(Church with lots of people, 13-18) — My social life in my teenage years was focused around church. I was a youth leader and very passionate about my faith.
(Equal Monster & Scale, 18-19) — In college, something bad happened to me despite the fact that I was doing everything "right." I questioned how God could love the person who did that to me equally as much as He loved me. I did not want to participate in a religion where this was the case.
(Anger, 19-20) — I went through a period of being angry with God and at myself for believing in Him.
(Books & Questions, 20-24) — I decided I did not want to blindly believe in something again and began to research all of the religions in order to find one that made sense to me.
(Heart & Eye, 24-27) — I began to try and live my life using my mind and my heart, trying to balance the two.
(People affect one another, 27-30) — I realized that everyone affects one another through different types of energy. We are connected.
(My heart and energy affecting others, 30-32) — The realization that I can effect positive outcomes in others through using my heart and energy. This became my truth.
(Energy and love is in nature as well, 33 to present) — My truth extended to feeing the energy and love that is in nature and feeling connected to it.
Since completing her spiritual timeline, Madeline has found herself more comfortable discussing her own spirituality as well as embracing the topic with clients. For her, the spiritual timeline was a verbal and visual way for her to process and solidify her own personal journey and conclusions regarding her spirituality. Madeline has expressed more confidence and acceptance within herself and believes this leads her to feel at ease in discussing religious and spiritual issues with her clients.
Susan (see timeline above) was raised in a home with strong religious and spiritual beliefs that she continues to maintain. Susan feels very comfortable working with spiritual and religious issues with clients from varying backgrounds and belief systems. She said that knowing her own values and beliefs has helped her work with clients. She also recognizes that this is not the same for everyone.
Girl: This is me as a child. I am happy.
House: This represents the foundation for my spiritual development. Home is where I learned about myself and my role in the world. My spiritual beginnings/awareness began in my childhood home as my parents taught me important values. This is where I was first taught about families, forgiveness and service. I was also taught about prayer and a Heavenly Father who loved me, was aware of me and had a plan for me.
Heart: This is connected to my home — notice the plus sign. I feel love is the foundation for all my spiritual growth. As a child, I was shown love in my home and taught to love others. Love is what underlies so much of my spiritual beliefs.
Sun: This represents "The Son" or Jesus Christ for me. It is a central part of my spirituality. My belief in a Savior is what drives me to be a good person. My belief of love and family are connected to my belief in Christ.
Coconut Tree: This represents my college days. I was about 18-19, and I felt like I needed to find out for myself about the religion I was taught growing up. I felt like I couldn't continue to say it was all true unless I knew for myself. This time in my life I did a lot of Scripture study and prayer. I came to know for myself that what I had been taught — that is, the faith of my fathers — was true for me also.
The couple: This represents my marriage.
Baby: This represents our first child. My spirituality increased as I became a mother. To hold a new baby and recognize the awesome responsibility I now had as a mom. The miracle of it all. The connection of love and family.
Home with heart: This represents my efforts at making our home a place of love. A place where spirituality can grow. A place where my children can learn how to pray and receive their own answers. A place where my family can learn the important values I learned as a child.
Church: This represents a place of continued learning and opportunities to serve others. My church is very important to me and has been my whole life. It is a place to expand on what I already know. It is a place to continue to feel and recognize love and truth. It is also a place to be with others who share similar beliefs.
Moving/graduate school: This has been a few challenging years for me. I went through several months of depression after moving to a new state. My children were starting to leave home. Baby No. 1 got married. I felt like things were changing for me. My decision to go to graduate school was made after much thought and prayer. I felt like Heavenly Father was guiding me toward this. I felt an answer to my prayers that this is part of some plan for me. At times throughout graduate school, I have felt that other students viewed spirituality as stifling or oppressive. Sometimes I have had to examine my own beliefs. I have come to recognize my beliefs and my spirituality as a great benefit/advantage over someone without beliefs.
Sun (Son)/my dad dying/hearts/question marks: This represents a difficult time but a powerful time spiritually for me. In my second year of graduate school, my dad was dying. I knew he was going to die. I recognized the truth in my heart when I prayed. I didn't want to lose this man who taught me all about love and family. A man who served selflessly and taught me by his example. A man who was central to my spiritual growth. His death was one of the most spiritual things I have ever witnessed or felt. My beliefs of love and family and a Heavenly Father were actually strengthened during this time. His dying also brought up questions about the afterlife. I knew what I believed, but now it was being put to the test. His death has continued to expand my growth spiritually.
What's next: I know that my spiritual growth will continue. I welcome what may come. I am who I am because of my spirituality. It is fair to say that my spirituality is stronger as difficulties come.
Through the spiritual timeline activity, Susan became more aware of her own spiritual journey. She found that she had often failed to recognize the changes and growth in her life, especially when she was in the midst of a challenge. This activity helped her gain that awareness.
Looking back on her timeline, Susan was able to recognize how some of the most challenging things in her life promoted the greatest amount of spiritual growth for her. Susan says that now she recognizes how spiritual and religious values are different for each person. She does not feel afraid of incorporating client spiritual and religious beliefs into sessions.
The three emergent or professional counselors who have shared their timelines are from different backgrounds and have different beliefs regarding spirituality and religion. Dorinda was raised with humanistic values and beliefs and initially did not think this exercise on religion and spirituality applied to her. Madeline came from a family with strong ties to religion. However, she has moved away from those ties to develop her own set of values and beliefs around spiritual and religious issues. Susan maintains the religious and spiritual beliefs from her family of origin and continues to grow and develop within those beliefs. It has been valuable for each of these counselors to understand their own beliefs. As a result, all three feel comfortable and competent when addressing issues in counseling with a client from any religious or spiritual background.
It is important to understand how a client's worldview and psychosocial functioning are influenced by his or her beliefs or absence of beliefs surrounding spirituality and religion. As ethical and competent professional counselors, we are required to explore our own attitudes, beliefs and values about spirituality and religion and continually evaluate how these things influence our work with clients and the counseling process.
Lynn Bohecker is a postdoctoral fellow at the Idaho State University Center for Health Research and will be a senior lecturer for Messiah College in the fall. She received a 2014 ASERVIC research grant to conduct research on the use of spiritual timelines in counselor education. Contact her at bohelynn@isu.edu.


text:
Carl Stephen Sandri (born 11 July 1983) is an Italian-Australian cricket coach and former player. He represented Italy from 2012 to 2017 and also played a single season with the Sydney Thunder. He is an all-rounder who bats right-handed and bowls off-spin. He coached Papua New Guinea from 2021 to 2022.

Playing career
Sandri played for the Victoria Second XI in the 2005/06 Australian season. Sandri later moved to England, where he played a single match in county cricket for the Worcestershire Second XI against the Yorkshire Second XI in 2008, but unable to force his way into the Worcestershire first eleven. While in England, he also played in the Central Lancashire League in 2008 for Radcliffe, and in the Lancashire League for Lowerhouse in 2009.

By 2012, he had qualified to play for Italy by way of his Italian heritage.   He was selected as part of Italy's fourteen man squad for the 2012 World Twenty20 Qualifier in the United Arab Emirates in March 2012. He made his Twenty20 debut during the tournament against Oman.  He made eight further appearances during the tournament, the last of which came against Kenya.

In his nine matches, he took 13 wickets with the ball at a bowling average of 19.23, with best figures of 4/9. He ended the tournament as Italy's joint leading wicket-taker alongside Damian Crowley. With the bat, he scored 122 runs at an average of 20.33, with a high score of 49 not out. Italy finished the tournament in tenth place and therefore missed out on qualification for the 2012 World Twenty in Sri Lanka.

In April 2013, he was selected in Italy's fourteen man squad for the World Cricket League Division Three in Bermuda. In the same year he also played for Sydney Thunder

In September 2017, he took the most wickets for Italy in the 2017 ICC World Cricket League Division Five tournament, with a total of thirteen dismissals in five matches.

Coaching career
In March 2021, Sandri was appointed as coach of the Papua New Guinea national cricket team, replacing fellow Australian Joe Dawes. He resigned in August 2022, having coached the team to its maiden World Cup appearance at the 2021 ICC T20 World Cup in the Middle East.

References

External links
Carl Sandri at ESPNcricinfo
Carl Sandri at CricketArchive

1983 births
Living people
Cricketers from Melbourne
Italian people of Australian descent
Italian cricketers
Sydney Thunder cricketers
Australian expatriates in Papua New Guinea
Coaches of the Papua New Guinea national cricket team

redpajama_set_name: RedPajamaWikipedia


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What happens to the permissions of a file if you move the file to a folder within the same volume?
/Microsoft / 98-365 / What happens to the permissions of a file if you move the file to a folder within the same volume?
A. The file will have the permissions as before.
B. The file will acquire the permissions of the target folder.
C. The file will acquire the permissions of the source folder.
D. The file will have no permissions.
What happens to a file's permissions if you copy it from one volume to another?
What permissions are directly assigned to a file or folder?
What do you do with a folder that you do not have permissions to and you need to access immediately?
What is required to create a volume mount point?


text:
Islam and Politics ( 9 March 2018, NewAgeIslam.Com)
In The Tragedy of Afghanistan, A Sliver Of Hope
By Shahzaib Khan<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />
An average of 66 civilians die in the Afghan conflict each week. The country has not seen peace now for almost half a century. The Taliban now control more territory than at any other point in time after the US invasion in 2001. The US currently has around 10,000 troops on the ground in Afghanistan. And even when the US had 100,000 troops on the ground, the Taliban stood unvanquished.
While airing the possibility of negotiations with a group like the Taliban may sound morally unappealing, it is with these facts in mind, that Afghan President Ashraf Ghani has made a generous, mostly unconditional offer to the Afghan Taliban for direct peace talks.
Ghani's offer is indeed generous, with the latter offering political recognition to the Taliban along with citizenships for the group's members, amnesty for the group's imprisoned fighters and protection for the fighters' families.
In a conflict as protracted as Afghanistan, a singularly fragile ray of hope for peace can stir up global interest. Ghani's offer has done that. With the Americans having already recognised the impossibility of a military solution to the Afghan war, the Trump administration's bellicose "new" approach of taking the fight to the Taliban, is in fact an attempt to fight the Taliban to the negotiating table. Also, part of this new approach is Trump's increased pressure on Pakistan to play a role in bringing the Taliban to the negotiating table.
But this is not the first time an Afghan government has reached out to the Taliban to end the conflict. The infamously ineffective former president, Hamid Karzai, in 2010 and 2011 had conducted grand jirgas, or peace talks between the various stakeholders in Afghanistan. Karzai offered much of what is being offered by Ghani, amnesties, citizenships, power sharing, the likes. Interestingly, though, the Taliban were quick to reject the offer, responding in kind instead with a renewed campaign against the government.
Ghani's offer seems to be more of the same. By extending the olive branch, Ghani has illustrated to the world, and more importantly the Afghan nation his earnest intent to end the bloodshed. If this offer is spurned, Ghani would have increased legitimacy in seeking a military solution against the Taliban. Having more territory now than ever before, the Taliban may just decide to wait out the tiring American war machine, and run over Kabul once the Americans depart.
If historical trends are to be respected, as they should be, Ghani's offer of peace seems to be destined to be doomed, just as Karzai's offer was.
In what is most similar to the rarest celestial alignment, considering the infinite complexity of the Afghan conflict, the interests of the numerous central actors, while far from merging seamlessly, seem to be possibly reconciling.
Ghani's call for peace has been welcomed, or at least subject to tacit acceptance by the major actors. The Americans with their renewed campaign against the Taliban have maintained a strategic silence on the peace offering with repeated affirmations by their top Generals of a political solution to the conflict. The Trump administration would understandably not want to be seen as too excited at the prospect of peace with the Taliban as a legitimate political actor, considering Trump's decision of taking the fight to the Taliban, to finally "win" the war. But the silence of the administration in this respect speaks for itself. The Taliban also have had a similar yet distinctive response. The Taliban leadership has refrained from overtly jumping on the offer, given its reluctance to publicly recognise the Afghan government; however, they have maintained their own form of silence, a momentary lull in violence, indicating perhaps a reluctant willingness. Pakistan, as the other major influencer in the conflict, has vociferously welcomed the offer, joining Afghanistan in becoming the leading proponent of the peace proposal. The reactions are a swift departure from Karzai's peace offering where the proposal was shot down within days by the Taliban and had failed to excite the Americans and the Pakistanis.
So Why Is Everyone Reacting The Way They Are?
First and foremost, Ghani's offer for peace is a genuine attempt at curbing the incredible blood-letting in the streets of Kabul and around Afghanistan. After a spate of attacks, which claimed hundreds of lives in the capital, Ghani, as he attended a conference where representatives of numerous countries had gathered to brainstorm a solution to the conflict, chose bravely, generously and wisely to extend an olive branch to the Taliban. Brave because it is hard to make a peace offering as the leader of the country, to a militant group that has just wreaked havoc in the capital. As he made this peace offer Ghani risked irking his Western partners, and a local population that may have supported the government in its fight against the Taliban. But more than being generous and brave, the offer was wise. Ghani recognises the increased bloodletting by the Taliban as a symptom not of a willingness to fight, but as a symptom of willingness to negotiate with greater strength.
With the Trump administration choosing to bomb the Taliban to the talks table, the Taliban had decided to bomb back, just to strengthen their position. In the same line, Washington, while willing to extend the firepower to squeeze the Taliban, has emphasised on the Afghan government its responsibility to lead a political solution with the Taliban.
The Trump administration is eager to impress the US electorate with quick, headlining successes that define Trump's first term to ensure a possible second term. What would be better than what will definitely be portrayed as a negotiated victory in Afghanistan allowing US soldiers to return home? The other option for the US is stark, considering in a strictly military arena a guerrilla group like the Taliban win by not losing, while the American war machine definitely loses unless it wins absolutely.
The Taliban, on the other hand, have the possibility of an American departure and power sharing with the Afghan government. While the latter is a compromise for the Taliban, the former is definitely a driving priority. Entering this situation is a Pakistan, wary of militancy and continuous conflict which has spilled into its own territory. The Pakistan of today is significantly different from the Pakistan that was cold to Karzai's offer in 2011.
As long as it has a friendly regime in Kabul, a Pakistan worn out by terrorism, and now importantly looking to protect and grow the hundreds of billions of dollars in investment coming in through Beijing, will be more than willing, as it has been, to broker a peaceful power-sharing arrangement between the Taliban and the Afghan government. While there are many other actors in this complex conflict, the aforementioned four are definitely enough in their capability to ensure peace.
Peace in Afghanistan is by no means imminent; the situation is unprecedentedly complex and gets worse every passing day. One is inclined to exercise cautious pragmatism by reluctantly, acknowledging the unfortunate near impossibility of peace in Afghanistan. But given this rare alignment of interests, there is a sliver of hope, and one can cautiously claim, that the impossibility of peace in Afghanistan is perhaps at its most vulnerable today.
Source: tribune.com.pk/story/1653855/6-tragedy-afghanistan-sliver-hope/
URL: http://www.newageislam.com/islam-and-politics/shahzaib-khan/in-the-tragedy-of-afghanistan,-a-sliver-of-hope/d/114541

redpajama_set_name: RedPajamaCommonCrawl


Opportunities for funded research serve as a major incentive for scholarly productivity among college and university faculty members. Yet, considering the number of activities which compete for faculty members' time, grant-related activities are frequently neglected. The present study sought to determine some of the barriers that impede faculty members' involvement in grant activities. Data were collected via structured interviews with selected college of education faculty members at the University of New Orleans during the 1988-1989 academic year.
Three major impediments to funded research activities were identified—lack of procedural information about funding sources, and lack of a clearly-defined system of rewards for those who obtain external funding. Other impediments were also identified. Based upon these findings, a number of recommendations are offered for improving faculty involvement for grant-related activities.
Daniel, L. G., Gallaher, I. (1990). Impediments to Faculty Involvement in Grant Related Activities: A Case Study. SRA: Journal of the Society of Research Administrators, 22(2), 5-13.


Click on the links below to hear the tracks on Soundcloud. We haven't recorded them all yet, so check back for updates! Some are polished studio recordings, others are field recordings made at groups and live events.
We also have other music recorded from the project – click here to listen to Sheena & Darrin's tracks!


In the midst of a still-lagging economy, where expensive benefits are disappearing, some employers are getting creative with a growing trend in benefits.
A Paid Time Off (PTO) policy, where employees accrue and withdraw vacation and sick time from a "bank," continues to be the norm - but a few outlying companies are trying a creative alternative.
WorldatWork.org began studying employee benefits [PDF] in 2002, and recently discovered a new trend: one percent of U.S. companies are now offering unlimited paid vacation time to salaried employees. That's right - no more PTO, no more tracking accrued/used time, and no more administrating it. Instead, employees are expected to get their work done, while managing their own work and time off schedules - as business and team needs dictate.
This flexible, more self-scheduled workforce model works well for many internet-based companies, such as Netflix, which has had an open-ended vacation policy in their corporate offices since 2004.
Their "freedom and responsibility culture" doesn't count the number of hours at the office or how hard one is perceived to be working, but instead focuses on rewarding individual performance. This benefit doesn't apply to their distribution centers.
The innovative and policy-averse culture at Netflix keeps the company nimble, non-bureaucratic and reactive to the marketplace, while it continues to grow.
HubSpot, a Cambridge, MA inbound marketing software company, has also done away with a formalized PTO program. CEO Brian Halligan notes on Hubspot's blog that he always thought it strange that employees would need to hand in a PTO form whenever they took a day off, yet no "credit" forms were submitted for the late nights or weekends they worked. "We trust that the folks will use 'common sense' with regards to taking an appropriate amount of time off," Halligan wrote.
From an employee's perspective, it puts control back into their hands. Not only can staff control their own schedules, they can take ownership for their job and feel empowered to make an impact on the company's bottom line - all based on their own decisions, creativity, teamwork and planning.
As an employer, unlimited vacation means that you can offer a generous yet budget-friendly benefit to employees that frees up HR from administering PTO bank accruals/withdrawals and the cost of unused PTO payouts.
Are your employees ready to embrace unlimited vacation? There's no such thing as a perfect work culture, but when a company trusts its employees, the end result is giving your most important assets what they want - control and the means to succeed.


As a British nerd growing up in the '80s, my education in fantasy went from Harryhausen movies aired during the school holidays, to Fighting Fantasy gamebooks, to Games Workshop wargames and miniatures. The grimdark worlds of Warhammer remain milestones in my imaginative development and one of the great - and distinctively British - contributions to the fantasy genre.
I was recommended to the publishing team by fellow writer George Mann in 2015, and was soon commissioned to write a short Space Wolves vs. Dark Eldar tale, which became Stormseeker. The story had to centre around aerial combat, which was tricky to write as the excitement of ship-to-ship battles is tough to convey on the page - since the action has to be described from the point of view of someone essentially sat in a chair and staring out of a window!
All these prose stories are written to tight deadlines and require detailed knowledge of the source-lore before you can even pitch an idea. Fortunately, I get plenty of support from Black Library's brilliant editorial team, including Nick Kyme, Hannah Hughes and Lindsey Priestley.
My stories have been well received so far with plenty more tales in development. My latest project is an audio drama (my first step into that medium). I'll post more information as and when these are officially announced.
Superstitious Iron Priest Anvarr Rustmane takes to the air in defence of his Space Wolf brothers, but has he met his match in a pair of vicious Dark Eldar pirates?
Stormseeker is available as an ebook from the Black Library webstore, from iTunes, and from Amazon UK and Amazon US.
It's the Purity Cup final, and the purest team in the league, the Bright Crusaders, are losing to a pack of low-down, cheating rats? Can the team convince their self-sabotaging star player Gerhardt the Penitent that winning is more important than fair play?
Pride and Penitence is available as an ebook from the Black Library webstore, from iTunes, from Amazon UK and Amazon US.
This story is also due to be collected in Death on the Pitch: A Blood Bowl Anthology (due for publication December 2018), available for pre-order on Amazon UK and Amazon US.
Venturing into an ancient ruined city alongside the grim Sisters of Battle, Imperial Missionary Marcus Amouris discovers that the Emperor works in mysterious ways… as do other, darker powers.
Whispers is available as an ebook from the Black Library webstore, from iTunes, from Amazon UK and Amazon US.
"Hugely entertaining... Characterful, beautifully paced..."


text:
\section{Introduction}

The kinematics of stars perpendicular to the Galactic plane
traditionally had (and still has) great importance, for instance as a
probe of the vertical force and mass density in the Solar neighborhood
(e.g.,
\citealt{KuijkenGil91,Creze98,Siebert03,Bienayme14,Read2014}). In
dynamical modeling, the natural zeroth order approximation is to
assume a null mean vertical motion everywhere in the Galaxy (as it
should be in a steady-state axisymmetric stellar system, see
\citealt{BT2008}). However, thanks to the spatial extension and
accuracy of recent surveys, it has been discovered that significant
non-zero mean vertical motions do exist in the extended Solar
neighborhood (\citealt{Widrow2012,Williams2013,Carlin2013}).  These
consist in patterns looking like ``rarefaction-compression'' waves or
``breathing modes" of the disc. Whilst originally associated solely
with excitations by external sources such as a passing satellite
galaxy or a small dark matter substructure crossing the Galactic disc
(\citealt{Widrow2012}, \citealt{Gomez2013,YannyGardner2013,Feldmann}),
it was then shown that if the density perturbation has even parity
with respect to the Galactic plane (i.e., is plane-symmetric), and the
vertical velocity field has odd parity (i.e., a breathing mode). Then
{\it internal} non-axisymmetric perturbations, such as spiral arms,
could be sufficient to cause this (\citealt{Faure2014}, hereafter
F14). This was shown analytically by solving the linearized Euler
equations in a cold fluid toy model, and confirmed through
test-particle simulations for quasi-static spiral arms. Subsequently,
the same effect was found in self-consistent simulations
\citep{Debattista2014}. Such an effect from internal non-axisymmetries
is of course not mutually incompatible with external perturbers
playing a role in shaping the velocity field \citep[e.g.][in which
  satellite interactions cause both bending and breathing modes
  depending on the velocity of the satellite]{Widrow2014}, and such
perturbers are themselves exciting non-axisymmetric modes such as
spiral waves \citep{Widrow2015}.

There is a long history of theoretical studies of the dynamical
effects of disc non-axisymmetries in two dimensions in the Galactic
plane, dating back to the seminal works of, e.g., \cite{LinShu} and
\cite{Toomre} on spiral arms. From the observational point of view,
striking kinematic features related to the bar and spiral arms were
for instance found in the Solar neighbourhood in the form of moving
groups, i.e. local velocity-space substructures made of stars of very
different ages and chemical compositions
\citep{Dehnen,Chereul,Famaey,Antoja}. At a less fine-grained level, it
is obvious that such local velocity-space substructures will affect
the {\it mean} motions too. And indeed, it has long been well
established that a non-zero mean radial motion is a natural response
to disc instabilities such as spiral arms (e.g., \citealt{LinShu}, see
also \citealt{BT2008}), independently of the exact nature of the
perturber (quasi-static or transient). The same is true for the
effects of the Galactic bar across the whole Galactic disc (see, e.g.,
\citealt{Kuijken1991}).

Such non-zero mean radial motions have recently been detected in the
extended Solar neigbourhood with the RAVE survey \citep{Siebert2011},
and shown to be consistent with the effect of spiral arms in the form
of Lin-Shu density waves \citep{Siebert2012}. Velocity fluctuations
have also been detected on larger scales with the APOGEE survey, and
attributed to the effects of the Galactic bar
\citep{Bovy2015}. \citet[][hereafter M14]{Monari2014}, found that the
bar can also explain the RAVE radial velocity gradient of
\cite{Siebert2011}, but did not find hints of the observed vertical
bulk motions \citep{Williams2013}. On the contrary, the spiral arm
model of F14 has been shown to generate a ``breathing mode''
qualitatively similar to what is observed for vertical
motions. Generally speaking, theoretical studies of the dynamical
response to disc non-axisymmetries in 3D are much less developed than
in 2D (see however \citealt{Patsis}; \citealt{Cox}).

In this paper, our aim is to provide a general analytical framework
linking the vertical bulk motions generated by disc non-axisymmetries
to the horizontal bulk motions. This analytic treatment goes beyond
the analytic toy-model of F14 for a pressureless three-dimensional fluid, which
was only suitable for an extremely cold stellar population, and which
required a few unrealistic assumptions (for instance that the vertical
force of the axisymmetric potential was negligible w.r.t. to the
maximum vertical force of the perturber). Our reasoning hereafter is
based on a linearization of the zeroth order moment of the
collisionless Boltzmann equation, i.e., the continuity equation for
stellar systems. As an improvement over the analytic treatment in F14,
the present calculation is valid for the whole range of velocity
dispersions compatible with the epicyclic approximation, and it is
valid close to the plane for all non-axisymmetric perturbations of the
potential described by small-amplitude Fourier modes. In particular,
we show that even the Galactic bar is expected to induce vertical bulk
motions in the Galactic disk. We use this particular case to compare
our analytic results with a numerical study.

The paper is organized as follows. In \Sec{sect:dynamics} we linearize
the continuity equation, deriving a theoretical prediction for the
vertical bulk motion. More specifically, we relate it to the
horizontal motions in the case where the potential perturbation is a
Fourier mode of small amplitude. In \Sec{sect:sim} we present the
outcome of a numerical test-particle simulation with a realistic model
of the Galactic disc under the influence of the gravity of the Milky
Way and the bar, and compare it with the analytical results. In
\Sec{sect:concl} we conclude.

\section{Vertical effects of perturbations}\label{sect:dynamics}

\subsection{The linearized continuity equation}

Using the cylindrical coordinates $\pare{R,\phi,z}$ and velocities
$\pare{v_R,v_\phi,v_z}=\pare{\dot{R},R\dot{\phi},\dot{z}}$, and
integrating the collisionless Boltzmann equation over velocity space,
one gets the following form of the continuity equation for stellar
systems:
\begin{equation}\label{eq:continuity}
  \ddp{\rho}{t}+\frac{1}{R}
  \ddp{\pare{R\rho u_R}}{R}+
  \frac{1}{R}\ddp{\pare{\rho u_\phi}}{\phi}+
  \ddp{\pare{\rho u_z}}{z}=0,
\end{equation}
where $\rho$ is the density of the system in configuration space, and
$u_i\equiv\av{v_i}$ are the average $v_i$ velocities, all estimated at
$\pare{R,\phi,z}$ and at the time $t$.

For an axisymmetric stationary system, symmetric with respect to
the plane $z=0$, all observables depend on $\pare{R,z}$ only, and one has
\begin{equation}
  \rho=\rho_0,\quad u_R=0,\quad u_\phi=u_{\phi,0},\quad u_z=0.
\end{equation}

Let us now consider the case where the system is perturbed by a small
non-axisymmetric perturbation in the potential, i.e.,
\begin{equation}\label{pottot}
  \Phi\pare{R,\phi,z,t}=\Phi_0\pare{R,z}+\epsilon\Phi_1\pare{R,\phi,z,t},
\end{equation}
where $\Phi_0$ is the unperturbed axisymmetric potential, $\epsilon
\ll 1$, and $\Phi_1$ has the same order of magnitude as $\Phi_0$.

Considering a small response to this small perturbation, we can write:
\begin{equation}\label{eq:pert}
  u_R=\epsilon u_{R,1},\quad u_\phi=u_{\phi,0}+\epsilon
  u_{\phi,1},\quad u_z=\epsilon u_{z,1},\quad \rho=\rho_0+\epsilon \rho_1.
\end{equation}
Plugging \Eq{eq:pert} into \Eq{eq:continuity} and dropping the terms
that are $\mathrm{O}\pare{\epsilon^2}$, we obtain the well-known linearized
continuity equation:
\begin{equation}\label{eq:continuity_2}
  \ddp{\rho_1}{t}+\frac{1}{R}
  \ddp{\pare{R\rho_0 u_{R,1}}}{R}+
  \frac{\rho_0}{R}\ddp{u_{\phi,1}}{\phi}+
  \frac{u_{\phi,0}}{R}\ddp{\rho_1}{\phi}=
  -\ddp{\pare{\rho_0 u_{z,1}}}{z}.
\end{equation}
From this equation, it is immediately apparent that, for a given
background axisymmetric model, one will be able to relate the vertical
bulk motion $u_{z,1}$ to the horizontal responses $u_{R,1}$ and $u_{\phi,1}$ and
the density wake of the perturbation $\rho_1$.

\subsection{Solution for an exponential disc}

Disc non-axisymmetries respect the plane symmetry, hence on the
galactic plane $u_{z,1}(z=0)=0$. This would not be true in the case where
a bending mode, due to satellite interactions for example, is
present \citep{Xu, Widrow2015}. This will be the subject of further
work.

From $u_{z,1}(z=0)=0$, the solution of \Eq{eq:continuity_2} reads
\begin{equation}\label{eq:rhouz1}
  \rho_0\pare{R,z}u_{z,1}\pare{R,\phi,z,t}=-\int_0^{z}{\cal F}\pare{R,\phi,\xi,t}\de\xi,
\end{equation}
where
\begin{equation}\label{eq:fA}
  {\cal F}\pare{R,\phi,z,t}\equiv\ddp{\rho_1}{t}+
  \frac{1}{R}\ddp{\pare{R\rho_0 u_{R,1}}}{R}+
  \frac{\rho_0}{R}\ddp{u_{\phi,1}}{\phi}+
  \frac{u_{\phi,0}}{R}\ddp{\rho_1}{\phi}.
\end{equation}
We now assume that the unperturbed stellar system that we consider is an
axisymmetric exponential disc, i.e.,
\begin{equation}
  \rho_0\pare{R,z}=\rho_0\pare{0,0}\exp\pare{-\frac{R}{h_{\mathrm{R}}}-\frac{|z|}{h_z}}
\end{equation}
where $h_{\mathrm{R}}$ and $h_z$ are the scale length and height respectively. We
also assume that $\rho_1$ and $\rho_0$ have the same exponential
vertical dependence, i.e., $\tilde{\rho}\equiv \rho_1/\rho_0$ is constant
with $z$.
With these assumptions \Eq{eq:rhouz1} becomes
\begin{equation}\label{eq:rhouz2}
  u_{z,1}\pare{R,\phi,z,t}=-\frac{\int_0^{z}\mathrm{e}^{-|\xi|/h_z}{\cal G}\pare{R,\phi,\xi,t}\de\xi}{\mathrm{e}^{-|z|/h_z}},
\end{equation}
where
\begin{equation}\label{eq:G}
  {\cal G}\pare{R,\phi,z,t}\equiv\ddp{\tilde{\rho}}{t}+
  \frac{u_{\phi,0}}{R}\ddp{\tilde{\rho}}{\phi}
  +\frac{u_{R,1}}{R}-\frac{u_{R,1}}{h_{\mathrm{R}}}+\ddp{u_{R,1}}{R}+\frac{1}{R}\ddp{u_{\phi,1}}{\phi}.
\end{equation}

\subsection{Taylor expansion close to the plane}
We now indicate only the dependence on $z$ of the functions to
simplify the notation, and Taylor expand ${\cal G}$ in powers of $z$
up to second order close to the plane, i.e., from \Eq{eq:rhouz2},
\begin{equation}\label{eq:rhouz3}
  u_{z,1}\pare{z}\approx-\frac{\int_0^{z}\mathrm{e}^{-|\xi|/h_z}
  \paresq{{\cal G}\pare{0}+\frac{1}{2}\ddp{^2{\cal G}}{z^2}(0)\xi^2}\de\xi}{\mathrm{e}^{-|z|/h_z}}.
\end{equation}
Therefore, from \Eq{eq:pert} and \Eq{eq:rhouz3},
\begin{align}\label{eq:uz}
  u_z(z) &=\epsilon~\mathrm{sgn}(z)h_z\biggl[
    {\cal G}(0)\pare{1-\mathrm{e}^{|z|/h_z}} \nonumber \displaybreak[0] \\
    &+\ddp{^2{\cal G}}{z^2}(0)
    \pare{\frac{z^2}{2}+h_z|z|+h_z^2-\mathrm{e}^{|z|/h_z}h_z^2}\biggr],
\end{align}
and, averaging $u_z$ over $z>0$, weighted by $\rho$, we obtain
\begin{align}\label{eq:uzint}
  &\Delta \av{u_z} \pare{z}\equiv 2\frac{\int_0^z\rho\pare{\xi} u_z\pare{\xi}~\de
    \xi} {\int_0^z \rho\pare{\xi} ~\de \xi}= \nonumber \displaybreak[0] \\
  &=2\epsilon\Biggl\{\paresq{{\cal G}(0)(h_z-z)+\ddp{^2{\cal G}}{z^2}(0)h_z^2\pare{3h_z-z}} \nonumber \displaybreak[0] \\
  &-z\paresq{{\cal G}(0)+
        \ddp{^2{\cal G}}{z^2}(0)\frac{h_z}{2}\pare{6h_z+z}}/\pare{\mathrm{e}^{z/h_z}-1}\Biggr\},
\end{align}
the difference between the mean vertical velocities of stars within
$z$, above and below the Galactic plane, since $u_z(z)=-u_z(-z)$. A
value $\Delta \av{u_z}>0$ ($\Delta \av{u_z}<0$) implies that the stars of both Galactic
hemispheres tend to move away from (towards) the Galactic plane, while
for $\Delta \av{u_z}=0$ we have $u_z=0$, like in an axisymmetric Galaxy.

Note that, whilst being $C^0$ continuous, the function $u_z(z)$ given
by \Eq{eq:uz} is not continuously differentiable ($C^1$) at
$z=0$. This is a consequence of the fact that the vertical density
distribution $\exp\pare{-|z|/h_z}$ is itself not $C^1$ at $z=0$. This
technical issue disappears for a $\mathrm{sech}^2(z/h_z)$ density
distribution, which is $C^1$ at $z=0$. In \App{app:sech} we compute
the formulae corresponding to \Eqs{eq:uz}{eq:uzint} in the $\mathrm{sech}^2$
case, and show that the results are quantitatively similar for the
same value of $h_z$ close to the plane.

\subsection{Computing the horizontal bulk motions}

At this point, we will need to estimate ${\cal G}(0)$ and
$\lddp{^2{\cal G}(0)}{z^2}$. To do so, we consider the potential
perturbation $\Phi_1$, the density response $\tilde{\rho}$, and the
horizontal mean velocities as Fourier $m$-modes propagating in the disc, i.e.,
\begin{equation}\label{eq:phi1fourier}
  \Phi_1\pare{R,\phi,z,t}=\operatorname{Re}\parec{\Phi^\mathrm{a}(R,z)\exp\paresq{\mathrm{i} m\pare{\phi-\Omega_{\mathrm{b}} t}}}.
\end{equation}
\begin{equation}\label{eq:rho}
  \tilde{\rho}\pare{R,\phi,t}=\operatorname{Re}\parec{\tilde{\rho}^\mathrm{a}(R)\exp\paresq{\mathrm{i} m\pare{\phi-\Omega_{\mathrm{b}} t}}},
\end{equation}
\begin{equation}\label{eq:uro}
  u_{R,1}\pare{R,\phi,z,t}=\operatorname{Re}\parec{u_R^\mathrm{a}(R,z)\exp\paresq{\mathrm{i} m\pare{\phi-\Omega_{\mathrm{b}} t}}},
\end{equation}
\begin{equation}\label{eq:uphi}
  u_{\phi,1}\pare{R,\phi,z,t}=\operatorname{Re}\parec{u_\phi^\mathrm{a}(R,z)\exp\paresq{\mathrm{i} m\pare{\phi-\Omega_{\mathrm{b}} t}}},
\end{equation}
where we have reintroduced the $R$, $\phi$, and $t$ explicit
dependencies. Dividing \Eq{eq:continuity_2} by $\rho_0$ and integrating
over $z$ we obtain the 2D continuity equation,
i.e.,
\begin{equation}\label{eq:2Dcont}
  \ddp{\tilde{\rho}}{t}+
  \frac{U_{\phi,0}}{R}\ddp{\tilde{\rho}}{\phi}+
  \frac{U_{R,1}}{R}-\frac{U_{R,1}}{h_R}+\ddp{U_{R,1}}{R}+\frac{1}{R}\ddp{U_{\phi,1}}{\phi}=0,
\end{equation}
where
\begin{equation}
  U_i\equiv \frac{\int_{-\infty}^\infty\rho\pare{z} u_i\pare{z}~\de
    \xi}{\int_{-\infty}^\infty\rho\pare{z}~\de z},
\end{equation}
and $u_i$ is one of the $u_{R,1}$, $u_{\phi,1}$, $u_{\phi,0}$, $u_R^\mathrm{a}$, and
$u_\phi^\mathrm{a}$, functions defined above. Using the condition \Eq{eq:2Dcont}
we can derive $\tilde{\rho}^\mathrm{a}$ as
\begin{equation}\label{eq:rhoa}
  \tilde{\rho}^\mathrm{a}(R)=\frac{mU_\phi^\mathrm{a}/R+\mathrm{i}\pare{U_R^\mathrm{a}/h_R-U_R^\mathrm{a}/R-\lddp{U_R^\mathrm{a}}{R}}}
       {m\pare{\Omega_{\mathrm{b}}-U_{\phi,0}/R}}.
\end{equation}

The perturbative regime cannot give accurate estimates of $\rhou_R^\mathrm{a}$,
$\rhou_\phi^\mathrm{a}$, and $\rhou_{\phi,0}$ far from the $z=0$ plane. However,
typically these functions must decrease quite fast as a function of
$z$ and tend to $0$ as $z$ goes to infinity. Therefore, we can
approximate
\begin{equation}\label{eq:av}
  U_i\pare{R,\phi,t}\approx\frac{\int_{-\zeta}^\zeta\rho(R,\xi)u_i\pare{R,\phi,\xi,t}~\de\xi}
  {\int_{-\zeta}^\zeta\rho(R,\xi)~\de\xi},
\end{equation}
where $\zeta$ is the height from the plane up to which we are
computing the average and at which the integral in the perturbative
regime is converging to a constant value\footnote{In the rest of the
  paper we adopt $\zeta=1~\mathrm{kpc}$, as it is sufficient for the
  convergence of the $\rho u_i$ functions in the barred case of
  \Sec{sect:sim}.}.

We then obtain the value of $u_R^\mathrm{a}$ and $u_\phi^\mathrm{a}$ close the $z=0$ plane by
linearizing Jeans equations, in the same way than
\cite{Kuijken1991} in the 2D case. Under the assumptions that the
velocity dispersions $\sigma_{R}^2$ and $\sigma_\phi^2$ are related by
the epicyclic approximation (\citealt{BT2008}), that the radial scale
length of $\Phi_1$ is larger than
$\max\paresq{|u_{R,1}|,\sigma_R}/\kappa$, and that the mixed terms in the
velocity dispersion $\sigma_{R,z}$ and $\sigma_{\phi,z}$ are
negligible, one obtains the two following equations for $u_R^\mathrm{a}$ and $u_\phi^\mathrm{a}$:
\begin{subequations}
  \begin{equation}\label{eq:uRa}
    u_R^\mathrm{a}\pare{R,z}=\frac{\mathrm{i}}{\tilde{\Delta}}
    \paresq{m\pare{\Omega_{\mathrm{b}}-\tilde{\Omega}}\ddp{\Phi^\mathrm{a}}{R}-\frac{2m\tilde{\Omega}}{R}\Phi^\mathrm{a}},
  \end{equation}
  \begin{equation}\label{eq:uphia}
    u_\phi^\mathrm{a}\pare{R,z}=-\frac{1}{\tilde{\Delta}}
    \paresq{2\tilde{B}\ddp{\Phi^\mathrm{a}}{R}+\frac{m\pare{m\Omega_{\mathrm{b}}-m\tilde{\Omega}}}{R}\Phi^\mathrm{a}},
  \end{equation}
\end{subequations}
where
\begin{subequations}\label{eq:quant}
  \begin{equation}
    \tilde{\Omega}(R,z)=\frac{u_{\phi,0}(R,z)}{R},
  \end{equation}
  \begin{equation}
    \tilde{\kappa}(R,z)^2=R\ddp{\tilde{\Omega}^2}{R}(R,z)+4\tilde{\Omega}^2(R,z),
  \end{equation}
  \begin{equation}
    \tilde{\Delta}(R,z)=\tilde{\kappa}^2(R,z)-m^2\paresq{\Omega_{\mathrm{b}}-\tilde{\Omega}(R,z)}^2,
  \end{equation}
  \begin{equation}
    \tilde{B}(R,z)=-\tilde{\Omega}(R,z)-\frac{1}{2}R\ddp{\tilde{\Omega}}{R}(R,z).
  \end{equation}
\end{subequations}
Notice how the quantities \Eq{eq:quant} would yield the well known
$\Omega$, $\kappa$, $\Delta$, $B$ functions (\citealt{BT2008}) on the
$z=0$ plane for a zero-asymmetric-drift cold fluid.

The assumption that the radial scale length of $\Phi_1$ is larger than
$\max\paresq{|u_{R,1}|,\sigma_R}/\kappa$ is in general not valid for
spiral arms, except for very cold populations. Nevertheless, our
framework for relating the vertical and horizontal motions remains
very general. In the case of spirals we should use the generalized
equations for $u_R^\mathrm{a}$ and $u_\phi^\mathrm{a}$ from \cite{LinShu}, including
reduction factors depending on the velocity dispersion of the
background stellar population \citep{BT2008}. Hereafter, we will
concentrate on the case of the bar, where the above assumption on the
radial variation of $\Phi_1$ remains valid even for a realistic
background stellar velocity dispersion.

\subsection{Relating the vertical and horizontal bulk motions}

To get the vertical bulk motions, we need ${\cal G}(0)$ and
$\lddp{{\cal G}(0)}{z^2}$ in order to evaluate $\Delta \av{u_z}(z)$ in
\Eq{eq:uzint}. To do so, we need $\tilde{\rho}^\mathrm{a}$ and its derivatives.  Hence,
we further simplify the integrals in \Eq{eq:av} by expanding, up to
the second order, the functions $u_i$ in \Eq{eq:uRa} and
\Eq{eq:uphia}. These are even function with the respect of $z$, so
\begin{equation}
  u_i(R,z)\approx u_i(R,0)+\frac{1}{2}\ddp{^2u_i}{z^2}(R,0)z^2.
\end{equation}
For the specific function $u_{\phi,0}$ coming from the background
axisymmetric model, in \App{app:uphiz} we estimate
\begin{equation}
  \ddp{^2u_{\phi,0}}{z^2}(R,0)\approx \frac{R}{u_{\phi,0}(R,0)}\dd{\nu^2}{R}(R),
\end{equation}
where $\nu(R)\equiv \sqrt{\lddp{^2\Phi_0(R,0)}{z^2}}$ is the vertical
epicyclic frequency.

We thus now have a fully analytical expression for $\Delta \av{u_z}(z)$ in
\Eq{eq:uzint}, which we can apply to the case of the Galactic bar
hereafter. Indeed, according to the above calculations, non-zero
vertical motions should be induced by {\it any} non-axisymmetric
perturbations described by small-amplitude Fourier modes, even though
M14 had not found them in a bar simulation. This means that they are
probably quite small, but they should be present: here, we can
explicitly estimate them analytically, and then check for their
presence in a numerical simulation similar to that of M14. Note
however that the present analytical perturbative approach breaks down
close to the corotation and Lindblad resonances where our analytical
expression for $\Delta \av{u_z}$ diverges. Note also that we consider here only
the response to the potential perturbation, and do not relate back the
density response to the potential perturbation.

\section{Application to the Galactic bar}\label{sect:sim}

\subsection{Galactic potential and disc stellar population}\label{sect:pot}
We take for the background axisymmetric potential $\Phi_0$ the Milky
Way Model~I by \cite{BT2008}.  It consists of a spheroidal dark halo
and bulge, and three disc components: thin, thick, and ISM disc. The
disc densities decrease exponentially with Galactocentric radius and
height from the Galactic plane. The position of the Sun in this model
is $(R_0,z_0)=(8~\mathrm{kpc},0)$. In this axisymmetric potential, we consider
a background stellar population described by an exponential disc of
scale length $h_{\mathrm{R}}=2~\mathrm{kpc}$ and scale height $h_z=0.3~\mathrm{kpc}$, with radial and vertical velocity
dispersions varying as $\sigma_R =
\sigma_{R,0}\exp\paresq{-\pare{R-R_0}/R_{\mathrm{s}}}$, $\sigma_z =
\sigma_{z,0}\exp\paresq{-\pare{R-R_0}/R_{\mathrm{s}}}$, where
$(\sigma_{R,0},\sigma_{z,0})=(35,15)~\mathrm{km}~\mathrm{s}^{-1}$, and $R_{\mathrm{s}}=5h_{\mathrm{R}}$. The mean
tangential velocity has an asymmetric drift described by Stromgren's
formula (\citealt{BT2008}) adapted to our case, i.e.,
\begin{equation}
  u_{\phi,0}(R,0)=v_{\mathrm{c}}-\frac{\sigma_R^2}{2v_{\mathrm{c}}}
  \pare{\frac{\kappa^2}{4\Omega^2}-1+\frac{7}{5}\frac{R}{h_{\mathrm{R}}}}.
\end{equation}

\subsection{Bar potential}
We describe the perturbation due to the bar by a 3D extension of the
quadrupole bar used by \cite{Weinberg1994} and \cite{Dehnen2000},
i.e. $\Phi_1$ as described in \Eq{eq:phi1fourier} with $m=2$ and the
angle $\phi$ measured from the long axis of the bar, with
\begin{equation}\label{phia}
  \Phi^\mathrm{a}(R,z) = \frac{V_0^2}{3} \left( \frac{R_0}{R_{\mathrm{b}}} \right)^3 \frac{R^2}{r^2} {\cal U}(r)
\end{equation}
and
\begin{equation}
  {\cal U}(r) = \left\{
  \begin{array}{l l}
    -(r/R_{\mathrm{b}})^{-3} & \quad \text{for } r \geq R_{\mathrm{b}},\\
    (r/R_{\mathrm{b}})^{3}-2 & \quad \text{for } r < R_{\mathrm{b}},
  \end{array} \right.
\end{equation}
where $R_0$ is the Galactocentric radius of the Sun, $V_0=v_{\mathrm{c}}(R_0)$
the local circular velocity, $R_b$ the bar length, and $r^2=R^2+z^2$.

The amplitude $\epsilon$ in \Eq{pottot} then represents the ratio
between the bar and axisymmetric background radial forces at
$\pare{R,\phi,z}=\pare{R_0,0,0}$.

Here we choose $\epsilon=0.01$ (\citealt{Dehnen2000}),
$\Omega_{\mathrm{b}}=52.23~\mathrm{km}~\mathrm{s}^{-1}~\mathrm{kpc}^{-1}$, $\Omega_{\mathrm{b}}/\Omega(R_0)=1.89$,
(\citealt{Antoja2014}), and $R_{\mathrm{b}}=3.5~\mathrm{kpc}$ (\citealt{Dwek1995}).

\subsection{Analytical results}

With all these inputs, we can then immediately compute $\Delta \av{u_z}$ from
\Eq{eq:uzint}, and in \Fig{fig:diffvz_th} we plot the predicted
difference between the mean vertical velocities within 300~pc above
and below the Galactic plane, i.e. $\Delta \av{u_z}(R,\phi,z=0.3~\mathrm{kpc},t=0)$.
\begin{figure}
  \centering
  \includegraphics[width=\columnwidth]{diffvz_th_up.pdf}
  \caption{Difference between the average vertical motion of stars in
    the northern and southern hemisphere of the Milky Way $\Delta \av{u_z}$
    in our analytical model for $z=0.3~\mathrm{kpc}$, as a function of the $x$
    and $y$ positions in the plane. The dashed line corresponds to the
    long axis of the bar, and the dashed circles to the position of the
    corotation and OLR.}
  \label{fig:diffvz_th}
\end{figure}
The dashed line represents the orientation of the long axis of the
bar, and the dashed circles the position of the corotation and outer
Lindblad resonance (OLR), i.e., $R$ where $\Omega(R)=\Omega_{\mathrm{b}}$,
and $\paresq{\Omega(R)-\Omega_{\mathrm{b}}}+\kappa(R)/2=0$.

We are interested in studying the response of the background
axisymmetric thin disc to the bar potential, hence we focus on the
outside of the bar region ($R>R_{\mathrm{b}}$). We also limit ourselves to
$R<10~\mathrm{kpc}$ in this plot, since that is the interesting region where
there are still non-negligible effects. In this plot the Galaxy and
the bar rotate counter-clockwise.

\Fig{fig:diffvz_th} shows that the mean vertical motions induced by
the Milky Way bar are small, of the order of a few tenth of $~\mathrm{km}~\mathrm{s}^{-1}$,
and up to about $0.5~\mathrm{km}~\mathrm{s}^{-1}$. More importantly, it shows how these
motions depend on the angle from the long axis of the bar and the
distance from the center of the Galaxy. The angular dependence of
$\Delta \av{u_z}$ is that of an $m=2$ mode propagating in the disk while
keeping the same configuration w.r.t. the bar as the bar rotates.

As noted earlier, close to the corotation and OLR, $\Delta \av{u_z}$
diverges, because the linear theory presents poles there, as is
evident in \Eq{eq:rhoa}, and \Eqs{eq:uRa}{eq:uphia}. Higher order
expansions (and changing variables so that the new variables only vary
slowly there) would be required near these resonances, where we leave
our predictions as blank. Notice how the correspondence in the figure
to the resonances is not exact. This is due to the fact that, since we
consider a stellar disk rather than a cold fluid, in the analytical
model we use $u_{\phi,0}$ which differs from $v_{\mathrm{c}}$ for the asymmetric
drift and the dependence from $z$, and shift the position of the
resonances in the model. At the OLR there is a
phase shift of $\mathrm{\pi}/2$ in $\Delta \av{u_z}$: along a given fixed azimuth
$\phi$, the value of $\Delta \av{u_z}$ inside and outside the OLR has
always opposite signs.

At a given radius, the function $\Delta \av{u_z}$ also changes sign between the
regions ahead of the bar ($\phi>0$) and behind the bar
($\phi<0$). This is due to the fact that $u_z$ is an odd function in
$\phi$, as it is the sum of odd functions, as we can find out by
looking at Eqs.~(\ref{eq:G}), (\ref{eq:uzint}),
(\ref{eq:rho}-\ref{eq:uphi}), (\ref{eq:rhoa}), (\ref{eq:uRa}), and
(\ref{eq:uphia}). In particular, the compression ($\Delta \av{u_z}<0$) is ahead
of the bar between the corotation and the OLR, while it is behind the
bar outside the OLR, due to the change of sign of $\tilde{\Delta}$ in
\Eq{eq:quant}.

We note that the pattern in $\Delta \av{u_z}$ is actually qualitatively following
the $u_{R,1}$ pattern, because they are both odd functions in $\phi$, as
can be seen from \Eq{eq:uro} and \Eq{eq:uRa} for $u_{R,1}$. This is in
stark contrast with what happens in the case of spiral arms, for which
F14 showed a clear phase shift between the vertical and radial bulk
motions. The reason for this difference is that $\Phi^\mathrm{a}(R,z)$ is a pure
real function in the case of the bar, but depends on ${\rm exp}(i \, m
{\rm ln}(R)/{\rm tan} p)$ in the case of spirals\footnote{Where $p$ is
  the pitch angle}, inducing a phase shift in \Eq{eq:uro} and
\Eq{eq:uRa} for spirals.

\begin{figure}
  \centering
  \includegraphics[width=\columnwidth]{uR.pdf}
  \includegraphics[width=\columnwidth]{uphi.pdf}
  \caption{As in \Fig{fig:diffvz_th} for the horizontal motions $u_R$
    (top panel) and $u_\phi-u_{\phi,0}$ (bottom panel) in our analytical
    models for $z=0$.}
  \label{fig:hori-ana}
\end{figure}
For visual comparison with the $\Delta \av{u_z}$ pattern of \Fig{fig:diffvz_th},
we plot the analytical $u_R$ and $\epsilon u_{\phi,1}$ patterns for the
bar model in \Fig{fig:hori-ana}. In particular, we see that between
the corotation and OLR and for $\phi<0$ there is a net outward motion
of stars ($u_R>0$) with vertical expansion, while for $\phi>0$ the
radial motion is inward ($u_R<0$) and there is a vertical
compression. The same behaviour has been seen in Fig.~12 of
\citet{Widrow2014}, where a satellite-induced bar has been shown to
create the same qualitative pattern. Outside the OLR, the pattern is
reversed, both in $u_R$ and $\Delta \av{u_z}$.

A heuristic explanation of this phenomenon is that the net radial
flows are related to the shape of the orbits induced by the bar inside
and outside the resonances (see \citealt{BT2008}). Outside the OLR,
the orbits in the bar frame are aligned with the bar and retrograde,
while they are perpendicular to the bar and retrograde between the
corotation and OLR: this naturally explains the shape of the radial
flow. Stars are then also adapting to the vertical restoring force,
stronger in the inner parts than the outer parts of the Galaxy: when
the flow is inward, the force is stronger and the vertical motion
corresponds to a compression, and when the flow is outward it
corresponds to an expansion-rarefaction. We note that the situation is
different in the case of spirals because of the restoring force from
the spiral potential itself.

Our analytical predictions for the vertical bulk motions induced by
the bar can now be compared to a simulation akin to M14 in the next
subsection.

\subsection{Numerical results}
\subsubsection{Initial conditions and integration time}
A simple and yet very effective way to study numerically the response
of a stellar disc to an external perturbation is through test-particle
simulations. These consist of the numerical integration of the
equations of motion of massless particles (representing the stars in
the disc), accelerated by a gravitational field (representing the
potential of the galaxy) which is uninfluenced by the particles
themselves.

We generate $5\times 10^7$ initial positions and velocities for our
simulations, as discrete realizations of the Shu-Schwarzschild
phase-space distribution function
(\citealt{Shu1969,BienaymeSechaud1997,BT2008}) described in
Section~2.2 of F14, with the same parameters adopted in our analytical
calculations.  The surface density of the initial conditions obtained
in this way is approximately distributed in space as an exponential
disc of scale length $h_{\mathrm{R}}=2~\mathrm{kpc}$. The radial and vertical velocity
dispersion on the disc plane vary approximately as
$\sigma_R\approx\sigma_{R,0}\exp\paresq{-\pare{R-R_0}/R_{\mathrm{s}}}$,
$\sigma_z\approx\sigma_{z,0}\exp\paresq{-\pare{R-R_0}/R_{\mathrm{s}}}$, where
$(\sigma_{R,0},\sigma_{z,0})=(35,15)~\mathrm{km}~\mathrm{s}^{-1}$, and $R_{\mathrm{s}}=5h_{\mathrm{R}}$
(\citealt{BienaymeSechaud1997}, F14).

We then integrate forward our initial conditions for a total time
$T=9~\mathrm{Gyr}$, from $t_\mathrm{i}=-3~\mathrm{Gyr}$ to $t_\mathrm{e}=6~\mathrm{Gyr}$. For $t<0$ the bar is
absent and the axisymmetric gravitational field is only given by
Model~I of \cite{BT2008}. This period of time allows the initial
conditions to become well mixed in the background
potential\footnote{The Shu-Schwarzschild distribution function is
  built on approximate integrals of motion for an axisymmetric galaxy:
  in particular, the vertical energy is a good approximate integral
  only very close to the plane. Because of Jeans' theorem
  (\citealt{BT2008}), the worse the approximation of the integrals,
  the faster the distribution function will evolve in time.}. After
the initial $3~\mathrm{Gyr}$, we obtain a stable particle configuration, with
velocity dispersions at $(R,z)=(R_0,0)$:
$(\sigma_R,\sigma_\phi,\sigma_z)\approx(37,27,13)~\mathrm{km}~\mathrm{s}^{-1}$. The vertical
restoring force determines the $z$ density profile, which, at $R=R_0$
is nicely described by an exponential or $\mathrm{sech}^2$ profile (see
\App{app:sech}), both with scale height $h_z\approx0.3~\mathrm{kpc}$ close to
the plane.

The bar is introduced smoothly in the simulation at $t=0$ with the
potential defined in \Eq{pottot}, \Eq{eq:phi1fourier} and \Eq{phia},
its amplitude reaching $\epsilon=0.01$ only at $t=3~\mathrm{Gyr}$. For $0\leq
t<3~\mathrm{Gyr}$ the amplitude grows with time by a factor
(\citealt{Dehnen2000})
\begin{equation}
  \eta(t)=\left(\frac{3}{16}\xi^5-
  \frac{5}{8}\xi^3+\frac{15}{16}\xi+\frac{1}{2}\right),\quad
  \xi\equiv2\frac{t}{3~\mathrm{Gyr}}-1.
\end{equation}
The amplitude then stays constant at $\epsilon=0.01$ for another
$3~\mathrm{Gyr}$. The response becomes almost stable in the rotating frame of
the bar\footnote{Some transient effects are still present in the
  kinematics at the end of the simulation, resulting in minor
  asymmetries in the maps of the mean motions. To reach complete
  stability one should integrate for many more dynamical times, which
  would be unphysical (see, e.g., \citealt{Muhlbauer2003}).}, and the end
of the simulation can be used to compare with our analytical
predictions.

\subsubsection{Comparison with the analytical model}
\begin{figure}
  \centering
  \includegraphics[width=\columnwidth]{diffvz_new.pdf}
  \includegraphics[width=\columnwidth]{diffvz_all.pdf}
  \caption{Difference between the average vertical motion of the
    northern and southern hemisphere of the simulated Milky Way
    $\Delta \av{v_z}$, as a function of the $x$ and $y$ positions. The dashed
    line corresponds to the long axis of the bar, and the dashed
    circles to the position of the corotation and OLR. Top panel:
    particles at $|z|<0.3~\mathrm{kpc}$ only, to be directly compared with the
    analytical model. Bottom panel: all particles.}
  \label{fig:diffvz}
\end{figure}
In \Fig{fig:diffvz} we present the mean vertical kinematics as a function
of the cartesian $(x,y)$ position in the Galaxy, at the end of the
simulation. We plot the difference $\Delta \av{v_z}\equiv\av{v_z}_\mathrm{p} - \av{v_z}_\mathrm{n}$, where
$\av{v_z}_\mathrm{p}$ ($\av{v_z}_\mathrm{n}$) is the average $v_z$ of particles found at $z>0$
($z<0$) at the end of the simulation. We present it both for particles
at $|z|<0.3~\mathrm{kpc}$ (top panel) and at every $z$ (bottom panel). The
averages are computed inside bins of $0.25~\mathrm{kpc} \times  0.25~\mathrm{kpc}$, also
applying a Gaussian smoothing on a scale $1~\mathrm{kpc}$.

\Fig{fig:diffvz} shows a very good agreement with \Fig{fig:diffvz_th},
with clear trends in the vertical kinematics, depending on the angle
from the long axis of the bar $\phi$ and on the distance from the
resonances in the same way as on \Fig{fig:diffvz_th}. The quantity
$\Delta \av{v_z}$ appears always to be periodic with $\phi$, fluctuating twice
for $\phi \in \paresq{0,2\mathrm{\pi}}$, so that
$\Delta \av{v_z}\pare{\phi}\approx\Delta \av{v_z}\pare{\phi+\mathrm{\pi}}$ and
$\Delta \av{v_z}\pare{\phi}\approx-\Delta \av{v_z}\pare{\phi+\mathrm{\pi}/2}$. Notice how the phase
of the periodic oscillations changes inside and outside the OLR: the
maxima of $\Delta \av{v_z}$ are at $\phi \sim \mathrm{\pi}/4\pm \mathrm{\pi}/2$ inside the
resonance and at $\phi \sim-\mathrm{\pi}/4\pm \mathrm{\pi}/2$ outside, as predicted by
our analytical model.

The agreement between the analytical and numerical model is not only
qualitative, but also quantitative.
\begin{figure}
  \centering
  \includegraphics[width=\columnwidth]{comp_up.pdf}
  \caption{Predictions of the analytical model for
    $\Delta \av{u_z}(R,\phi,z)=\Delta \av{u_z}(5~\mathrm{kpc},\phi,0.3~\mathrm{kpc})$ (blue line) and
    $\Delta \av{u_z}(R,\phi,z)=\Delta \av{u_z}(8.5~\mathrm{kpc},\phi,0.3~\mathrm{kpc})$ (red line), where
    $\phi$ is measured from the long axis of the bar. The $90\%$
    confidence bands are obtained fitting $\Delta \av{v_z}$ for particles in the
    simulation with $|R-5~\mathrm{kpc}|<0.2~\mathrm{kpc}$ (blue band) and
    $|R-8.5~\mathrm{kpc}|<0.2~\mathrm{kpc}$ (red band) with the model $a\sin(2\phi+b)$.}
  \label{fig:comp}
\end{figure}
In \Fig{fig:comp} we show the predictions of the analytical model for
$\Delta \av{u_z}(R,\phi,z)=\Delta \av{u_z}(5~\mathrm{kpc},\phi,0.3~\mathrm{kpc})$ (blue line) and
$\Delta \av{u_z}(R,\phi,z)=\Delta \av{u_z}(8.5~\mathrm{kpc},\phi,0.3~\mathrm{kpc})$ (red line), where $\phi$
is measured from the long axis of the bar. In the same plot we show
the $90\%$ confidence bands obtained fitting the model
$a\sin(2\phi+b)$ to $\Delta \av{v_z}$ for particles in the simulation with
$|R-5~\mathrm{kpc}|<0.2~\mathrm{kpc}$ (blue band), and $|R-8.5~\mathrm{kpc}|<0.2~\mathrm{kpc}$ (red
band). The concordance between analytical model and simulations shows
how our assumptions in the analytical model are convincing. Notice how
a small phase shift is present between the analytical predictions and
the simulation. This is due to the fact that the kinematics in the
simulation did not reach a complete stability w.r.t.
the bar disturbance, as previously mentioned.

\section{Discussion and conclusions}\label{sect:concl}
In this paper we demonstrated analytically how the mean vertical
motions of stars in disc galaxies are affected by small,
non-axisymmetric perturbations of the potential in the form of Fourier
modes (e.g., bar or spiral arms). This was previously shown
numerically for spiral arms in F14, and supported by an analytical
toy-model for a pressureless fluid. The present analytical treatment
goes beyond this toy-model, and is valid for the response of realistic
disc populations to any non-axisymmetric perturbation described by
small amplitude Fourier modes.

Our general analytical solution shows that, depending on the distance
from the Lindblad resonances and azimuth in the frame of the
perturber, the mean vertical motion points towards or away from the
galactic plane, with a bulk velocity depending on the position
projected in the galactic plane and on the distance from the galactic
plane.

Although M14 did not find hints of significant vertical bulk motions
in a Galactic bar simulation, our present analytical treatment
indicates that non-zero vertical motions should be induced by the bar
too. We thus explicitly estimate them analytically, and then check for
their presence in a numerical simulation similar to that of M14. These
vertical mean motions induced by the Galactic bar are indeed modest in
magnitude, especially if compared with those observed recently in the
Solar neighborhood
(\citealt{Widrow2012},\citealt{Williams2013,Carlin2013}), but
they are well existing, as we have shown here for the very first
time. And the results of our test-particle simulation are well in line
with our analytical prediction away from the main resonances. However,
it is clear that perturbations exerting vertical forces that change
more rapidly than that of the bar with the distance from the galactic
plane (e.g., the spiral arms) do create much more significant mean
vertical velocities.

Our analytical treatment being valid close to the plane for {\it all}
the non-axisymmetric perturbations of the disc that can be described
by small-amplitude Fourier modes, it will be extremely useful for
interpreting the outcome of simulations including any such
perturbation, and to estimate how much of the observed breathing modes
can be explained by such non-axisymmetries alone. Further work should
study how the coupling of multiple internal perturbers (bar+ multiple
spirals) and external perturbers (satellite interactions themselves
exciting spiral waves, but also bending modes) is affecting the
present analytical results.

\section*{acknowledgements}
We thank the anonymous referee for useful comments. We are grateful to
James Binney for pointing out a mistake in the original version of the
manuscript. This work has been supported by a postdoctoral grant from
the {\it Centre National d'Etudes Spatiales} (CNES) for GM.

\bibliographystyle{mn2e}

redpajama_set_name: RedPajamaArXiv